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0705.0053 | 1 | We show that the mutual fund theorems of Merton (1971) extend to the problem of optimal investment to minimize the probability of lifetime ruin. We obtain four such theorems by considering a financial market both with and without a riskless asset and by considering both constant and random consumption. | We show that the mutual fund theorems of Merton (1971) extend to the problem of optimal investment to minimize the probability of lifetime ruin. We obtain two such theorems by considering a financial market both with and without a riskless asset for random consumption. The striking result is that we obtain two-fund theorems despite the additional source of randomness from consumption. | [
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0705.1606 | 1 | The self-propelled motion of microscopic bodies immersed in a fluid medium is studied using molecular dynamics simulation. The advantage of the atomistic approach is that the detailed level of description allows complete freedom in specifying the swimmer design and its coupling with the surrounding fluid. A series of two-dimensional swimming bodies employing a variety of propulsion mechanisms -- motivated by biological and microrobotic designs -- is investigated, including the use of moving limbs, changing body shapes and fluid jets. The efficiencies of the mechanisms and the nature of the induced, time-dependent flow fields are found to differ widely among swimmers . | The self-propelled motion of microscopic bodies immersed in a fluid medium is studied using molecular dynamics simulation. The advantage of the atomistic approach is that the detailed level of description allows complete freedom in specifying the swimmer design and its coupling with the surrounding fluid. A series of two-dimensional swimming bodies employing a variety of propulsion mechanisms -- motivated by biological and microrobotic designs -- is investigated, including the use of moving limbs, changing body shapes and fluid jets. The swimming efficiency and the nature of the induced, time-dependent flow fields are found to differ widely among body designs and propulsion mechanisms . | [
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0705.1949 | 1 | We employ perturbation analysis technique to study trading strategies for multi-asset portfolio and obtain optimal trading methods for wealth maximization under arbitrary utility functions . | We employ perturbation analysis technique to study multi-asset portfolio optimisation with transaction cost. We allow for correlations in risky assets and obtain optimal trading methods for general utility functions. Our analytical results are supported by numerical simulations in the context of the Long Term Growth Model . | [
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0706.0482 | 1 | We perform a stability analysis for the utility maximization problem in a general semimartingale model where both liquid and illiquid assets (random endowments) are present. Small misspecifications of preferences (as modeled via expected utility), as well as views of the world or the market model (as modeled via subjective probabilities) are considered. Simple sufficient conditions are given for the problem to be well-posed, in the sense that optimal wealths and marginal utility-based prices are continuous functionals of the inputs . | We perform a stability analysis for the utility maximization problem in a general semimartingale model where both liquid and illiquid assets (random endowments) are present. Small misspecifications of preferences (as modeled via expected utility), as well as views of the world or the market model (as modeled via subjective probabilities) are considered. Simple sufficient conditions are given for the problem to be well-posed, in the sense the optimal wealth and the marginal utility-based prices are continuous functionals of preferences and probabilistic views . | [
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0706.2383 | 1 | The utilization of multiple post translational modifications (PTMs) in regulating a biological response is ubiquitous in cell signaling. If each PTM contributes an additional, equivalent binding site, then one consequence of an increase in the number of PTMs may be to increase the probability that, upon disassociation, a ligand immediately rebinds to its receptor. How such effects may influence cell signaling systems has been less studied. Here, a self-consistent integral equation formalism for ligand rebinding in conjunction with Monte Carlo simulations are employed to further investigate the effects of multiple, equivalent binding sites on shaping biological responses. Multiple regimes that characterize qualitatively different physics due to the differential prevalence of rebinding effects and their relation to systems-level properties are predicted and studied. Calculations suggest that when ligand rebinding contributes significantly to the dose response, a purely allovalent model can influence the binding curves nonlinearly but other mechanistic ingredients are required to achieve high degrees of biochemical cooperativity. It is our hope that these calculations motivate experiments that can further unravel the many functional consequences of multi-site phosphorylation. | the paper is withdrawn for the moment | [
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0706.2383 | 2 | the paper is withdrawn for the moment | The utilization of multiple phosphorylation sites in regulating a biological response is ubiquitous in cell signaling. If each site contributes an additional, equivalent binding site, then one consequence of an increase in the number of phosphorylations may be to increase the probability that, upon disassociation, a ligand immediately rebinds to its receptor. How such effects may influence cell signaling systems has been less studied. Here, a self-consistent integral equation formalism for ligand rebinding in conjunction with Monte Carlo simulations are employed to further investigate the effects of multiple, equivalent binding sites on shaping biological responses. Multiple regimes that characterize qualitatively different physics due to the differential prevalence of rebinding effects and their relation to systems-level properties are predicted and studied. Calculations suggest that when ligand rebinding contributes significantly to the dose response, a purely allovalent model can influence the binding curves nonlinearly but other mechanistic ingredients are required to achieve high degrees of biochemical cooperativity. It is our hope that these calculations motivate experiments that can further unravel the many functional consequences of multi-site phosphorylation. | [
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0706.2383 | 3 | The utilization of multiple phosphorylation sites in regulating a biological response is ubiquitous in cell signaling. If each site contributes an additional, equivalent binding site, then one consequence of an increase in the number of phosphorylations may be to increase the probability that, upon disassociation, a ligand immediately rebinds to its receptor. How such effects may influence cell signaling systems has been less studied. Here, a self-consistent integral equation formalism for ligand rebinding in conjunction with Monte Carlo simulations are employed to further investigate the effects of multiple, equivalent binding sites on shaping biological responses. Multiple regimes that characterize qualitatively different physics due to the differential prevalence of rebinding effects and their relation to systems-level properties are predictedand studied . Calculations suggest that when ligand rebinding contributes significantly to the dose response, a purely allovalent model can influence the binding curves nonlinearly but other mechanistic ingredients are required to achieve high degrees of biochemical cooperativity. It is our hope that these calculations motivate experiments that can further unravel the many functional consequences of multi-site phosphorylation . | The utilization of multiple phosphorylation sites in regulating a biological response is ubiquitous in cell signaling. If each site contributes an additional, equivalent binding site, then one consequence of an increase in the number of phosphorylations may be to increase the probability that, upon disassociation, a ligand immediately rebinds to its receptor. How such effects may influence cell signaling systems has been less studied. Here, a self-consistent integral equation formalism for ligand rebinding , in conjunction with Monte Carlo simulations , is employed to further investigate the effects of multiple, equivalent binding sites on shaping biological responses. Multiple regimes that characterize qualitatively different physics due to the differential prevalence of rebinding effects are predicted . Calculations suggest that when ligand rebinding contributes significantly to the dose response, a purely allovalent model can influence the binding curves nonlinearly . The model also predicts that ligand rebinding in itself appears insufficient to generative a highly cooperative biological response . | [
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0707.0026 | 1 | A probabilistic structure on sequential dynamical systems is introduced here, the new model will be called Probabilistic Sequential Network, PSN. The morphisms of Probabilistic Sequential Networks are defined using two algebraic conditions , whose imply that the distribution of probabilities in the systems are close . It is proved here that two homomorphic Probabilistic Sequential Networks have the same equilibrium or steady state probabilities . Additionally, the proof of the set of PSN with its morphisms form the category PSN, having the category of sequential dynamical systems SDS, as a full subcategory is given. Several examples of morphisms, subsystems and simulations are given. | A probabilistic structure on sequential dynamical systems is introduced here, the new model will be called Probabilistic Sequential Network, PSN. The morphisms of Probabilistic Sequential Networks are defined using two algebraic conditions . It is proved here that two homomorphic Probabilistic Sequential Networks have the same equilibrium or steady state probabilities if the morphism is either an epimorphism or a monomorphism . Additionally, the proof of the set of PSN with its morphisms form the category PSN, having the category of sequential dynamical systems SDS, as a full subcategory is given. Several examples of morphisms, subsystems and simulations are given. | [
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0707.2076 | 1 | We propose a biologically motivated quantity, twinness, to evaluate local similarity between nodes in a network. The twinness of a pair of nodes is the number of connected, labelled subgraphs of size n in which the two nodes possess identical neighbours. The graph animal algorithm is used to estimate twinness for each pair of nodes (for subgraph sizes n=4 to n=12) in four different protein interaction networks (PINs). These include an Escherichia coli PIN and three Saccharomyces cerevisiae PINs - each obtained using state-of-the-art high throughput methods. In almost all cases, the average twinness of node pairs is vastly higher than expected from a null model obtained by switching links. For all n, we observe a difference in the ratio of type A twins (which are unlinked pairs) to type B twins (which are linked pairs) distinguishing the prokaryote E. Coli from the eukaryote S. Cerevisiae . Interaction similarity is expected due to gene duplication, and whole genome duplication paralogues in S. Cerevisiae have been reported to co-cluster into the same complexes. Indeed, we find that these paralogues are over-represented as twins compared to pairs chosen at random. These results indicate that twinness can detect ancestral relationships from currently available PIN data. | We propose a biologically motivated quantity, twinness, to evaluate local similarity between nodes in a network. The twinness of a pair of nodes is the number of connected, labeled subgraphs of size n in which the two nodes possess identical neighbours. The graph animal algorithm is used to estimate twinness for each pair of nodes (for subgraph sizes n=4 to n=12) in four different protein interaction networks (PINs). These include an Escherichia coli PIN and three Saccharomyces cerevisiae PINs -- each obtained using state-of-the-art high throughput methods. In almost all cases, the average twinness of node pairs is vastly higher than expected from a null model obtained by switching links. For all n, we observe a difference in the ratio of type A twins (which are unlinked pairs) to type B twins (which are linked pairs) distinguishing the prokaryote E. coli from the eukaryote S. cerevisiae . Interaction similarity is expected due to gene duplication, and whole genome duplication paralogues in S. cerevisiae have been reported to co-cluster into the same complexes. Indeed, we find that these paralogous proteins are over-represented as twins compared to pairs chosen at random. These results indicate that twinness can detect ancestral relationships from currently available PIN data. | [
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0707.3621 | 1 | We calculate analytically the critical connectivity K_c of Random Threshold Networks (RTN) for homogeneous and inhomogeneous thresholds, and confirm the results by numerical simulations. We find a super-linear increase of K_c with the (average) absolute threshold |h|, which approaches K_c(|h|) \sim |h|^{\alpha with \alpha \approx } 2 for large |h|, and show that this asymptotic scaling is universal for RTN with Poissonian distributed connectivity and threshold distributions with a variance that grows slower than |h|^{\alpha . Interestingly, we find that inhomogeneous distribution of thresholds leads to increased propagation of perturbations for sparsely connected networks, while for densely connected networks damage is reduced . Further, damage propagation in RTN with in-degree distributions that exhibit a scale-free tail k_{in^{\gamma} is studied; we find that a decrease of \gamma can lead to a transition from supercritical (chaotic) to subcritical (ordered) dynamics} . Last, local correlations between node thresholds and in-degree are introduced. Here, numerical simulations show that even weak (anti-)correlations can lead to a transition from ordered to chaotic dynamics, and vice versa. Interestingly, in this case the annealed approximation fails to predict the dynamical behavior for sparse connectivities , suggesting that even weak topological correlations can strongly limit its applicability for finite N . | We calculate analytically the critical connectivity K_c of Random Threshold Networks (RTN) for homogeneous and inhomogeneous thresholds, and confirm the results by numerical simulations. We find a super-linear increase of K_c with the (average) absolute threshold |h|, which approaches K_c(|h|) \sim with \alpha \approx } h^2/( 2 \ln{|h| for large |h|, and show that this asymptotic scaling is universal for RTN with Poissonian distributed connectivity and threshold distributions with a variance that grows slower than h^2 . Interestingly, we find that inhomogeneous distribution of thresholds leads to increased propagation of perturbations for sparsely connected networks, while for densely connected networks damage is reduced ^{\gamma} is studied; we find that a decrease of \gamma can lead to a transition from supercritical (chaotic) to subcritical (ordered) dynamics} ; the cross-over point yields a novel, characteristic connectivity K_d, that has no counterpart in Boolean networks . Last, local correlations between node thresholds and in-degree are introduced. Here, numerical simulations show that even weak (anti-)correlations can lead to a transition from ordered to chaotic dynamics, and vice versa. It is shown that the naive mean-field assumption typical for the annealed approximation leads to false predictions in this case, since correlations between thresholds and out-degree that emerge as a side-effect strongly modify damage propagation behavior . | [
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0708.0046 | 1 | The Markowitz mean-variance optimizing framework has served as the basis for modern portfolio theory for more than 50 years. However, efforts to translate this theoretical foundation into a viable portfolio construction algorithm have been plagued by technical difficulties stemming from the instability of the original optimization problemwith respect to the available data. In this paper we address these issues of estimation error by regularizing the Markowitz objective function through the addition of an \ell_1 penalty . This penalty stabilizes the optimization problem, encourages sparse portfolios, and facilitates treatment of transaction costs in a transparent way . We implement this methodology using the Fama and French 48 industry portfolios as our securities . Using only a modest amount of training data, we construct portfolios whose out-of-sample performance, as measured by Sharpe ratio, is consistently and significantly better than that of the na\"{i . In addition to their excellent performance, these portfolios have only a small number of active positions, a highly desirable attribute for real life applications. We conclude by discussing a collection of portfolio construction problems which can be naturally translated into optimizations involving \ell_1 penalties and which can thus be tackled by algorithms similar to those discussed here . | We consider the problem of portfolio selection within the classical Markowitz mean-variance optimizing framework , which has served as the basis for modern portfolio theory for more than 50 years. To stabilize the problem, we propose to add to the Markowitz objective function a penalty which is proportional to the sum of the absolute values of the portfolio weights ( \ell_1 penalty ) . This penalty stabilizes the optimization problem, automatically encourages sparse portfolios, and facilitates an effective treatment of transaction costs . We implement our methodology using as our securities two sets of portfolios constructed by Fama and French: the 48 industry portfolios and 100 portfolios formed on size and book-to-market . In addition to their excellent performance, these portfolios have only a small number of active positions, a desirable feature for small investors, for whom the fixed overhead portion of the transaction cost is not negligible . | [
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0708.0370 | 1 | Biochemical reaction systems with a low to moderate number of molecules are typically modeled as discrete jump Markov processes. These systems are oftentimes simulated using the Gillespie Algorithm or the Next Reaction Method , which are exact simulation methods . In this paper we make explicit use of the fact that the initiation times of each reaction are given by the firing times of an independent, unit Poisson process with integrated propensity function. We use this representation to develop a modified version of the Next Reaction Method . We then demonstrate how this modified Next Reaction Method is the appropriate method to use to simulate systems in which the rate constants are functions of time (that is, systems that are time dependent Markov Processes). Finally, we extend our modified Next Reaction Method to systems with delays and compare its efficiency with those of the recent algorithms designed for systems with delays. | Chemical reaction systems with a low to moderate number of molecules are typically modeled as discrete jump Markov processes. These systems are oftentimes simulated with methods that produce statistically exact sample paths such as the Gillespie Algorithm or the Next Reaction Method . In this paper we make explicit use of the fact that the initiation times of the reactions can be represented as the firing times of independent, unit rate Poisson processes with internal times given by integrated propensity functions. Using this representation we derive a modified Next Reaction Method and, in a way that achieves efficiency over existing approaches for exact simulation, extend it to systems with time dependent propensities as well as to systems with delays. | [
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0708.0377 | 1 | By explicitly representing well-stirred chemical reaction systems with independent, unit Poisson processes we develop a new adaptive tau-leaping procedure. The procedure developed is novel in that we enforce any leap condition via a post-leap check as opposed to performing a pre-leap tau selection. Further, we perform the post-leap check in such a way that the statistics of the sample paths generated will not be skewed by the rejection of a leap. By performing a post-leap check to ensure accuracy, the method developed in this paper is guaranteed to never produce negative population values . The efficiency of the method developed here is demonstrated on a model of a decaying dimer . | By explicitly representing the reaction times of discrete chemical systems as the firing times of independent, unit rate Poisson processes we develop a new adaptive tau-leaping procedure. The procedure developed is novel in that accuracy is guaranteed by performing post-leap checks. Because the representation we use separates the randomness of the model from the state of the system, we are able to perform the post-leap checks in such a way that the statistics of the sample paths generated will not be skewed by the rejections of leaps. Further, since any leap condition is ensured with a probability of one, the simulation method naturally avoids negative population values . | [
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0708.0377 | 2 | By explicitly representing the reaction times of discrete chemical systems as the firing times of independent, unit rate Poisson processes we develop a new adaptive tau-leaping procedure. The procedure developed is novel in that accuracy is guaranteed by performing post-leap checks. Because the representation we use separates the randomness of the model from the state of the system, we are able to perform the post-leap checks in such a way that the statistics of the sample paths generated will not be skewed by the rejections of leaps. Further, since any leap condition is ensured with a probability of one, the simulation method naturally avoids negative population values . | By explicitly representing the reaction times of discrete chemical systems as the firing times of independent, unit rate Poisson processes , we develop a new adaptive tau-leaping procedure. The procedure developed is novel in that accuracy is guaranteed by performing postleap checks. Because the representation we use separates the randomness of the model from the state of the system, we are able to perform the postleap checks in such a way that the statistics of the sample paths generated will not be biased by the rejections of leaps. Further, since any leap condition is ensured with a probability of one, the simulation method naturally avoids negative population values | [
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0708.0544 | 1 | Continuous time random walks are a well suited tool for the description of market behaviour at the smallest scale: the tick-to-tick evolution. We will apply this kind of market model to the valuation of perpetual American options: derivatives with no maturity that can be exercised at any time. Our approach leads to option prices that fulfil the financial formulas when canonical assumptions on the dynamics governing the process are made, but it is still suitable for considering more exotic market conditions. | Continuous-time random walks are a well suited tool for the description of market behaviour at the smallest scale: the tick-to-tick evolution. We will apply this kind of market model to the valuation of perpetual American options: derivatives with no maturity that can be exercised at any time. Our approach leads to option prices that fulfil financial formulas when canonical assumptions on the dynamics governing the process are made, but it is still suitable for more exotic market conditions. | [
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0708.0703 | 1 | Neurons in brains are subject to various kinds of noises. Beside of the synaptic noise, the stochastic opening and closing of ion channels represents an intrinsic source of noise that affects the signal processing properties of the neuron. Here we investigated the response of a stochastic Hodgkin-Huxley neuron model to transient input pulses. We found that the response (firing or no firing), as well as the response time, is dependent on the state of the neuron at the moment when input pulse is applied. The state-dependent properties of the response is studied with phase plane analysis method. Using a simple pulse detectionscenario, we demonstrated channel noise enable the neuron to detect subthreshold signals. A simple neuronal network which can marvelously enhance the pulses detecting ability was also proposed. The phenomena of intrinsic stochastic resonance is found both in single neuron level and network level. In single neuron level, the detection ability of the neuron was optimized versus the ion channel patch size(i. e., channel noise intensity). Whereas in network level, the detection ability of the network was optimized versus the number of neurons involved in . | Neurons are subject to various kinds of noise. In addition to synaptic noise, the stochastic opening and closing of ion channels represents an intrinsic source of noise that affects the signal processing properties of the neuron. In this paper, we studied the response of a stochastic Hodgkin-Huxley neuron to transient input subthreshold pulses. It was found that the average response time decreases but variance increases as the amplitude of channel noise increases. In the case of single pulse detection, we show that channel noise enables one neuron to detect the subthreshold signals and an optimal membrane area (or channel noise intensity) exists for a single neuron to achieve optimal performance. However, the detection ability of a single neuron is limited by large errors. Here, we test a simple neuronal network that can enhance the pulse detecting abilities of neurons and find dozens of neurons can perfectly detect subthreshold pulses. The phenomenon of intrinsic stochastic resonance is also found both at the level of single neurons and at the level of networks. At the network level, the detection ability of networks can be optimized for the number of neurons comprising the network . | [
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0708.2244 | 1 | Random Threshold Networks (RTN) are widely used in modeling biological systems, such as neural and gene regulatory networks. RTNs with binary elements and random topology have been found to display a phase transition to an ordered phase at low connectivities Physica A 310, 245 (2002)%DIFDELCMD < ]%%% . Here we show that this phase transition is the result of a seemingly minor detail in the update rule, which acts like a biasing external field for a paramagnetic system. For unbiased update rules, there is no phase transition for RTNs of nonzero connectivity. We also show that RTNs with constant number of inputs, K, which have been claimed to be ordered for K=1 Phys. Lett. A 129, 157 (1988)%DIFDELCMD < ]%%% , are actually critical . | %DIFDELCMD < ]%%% %DIFDELCMD < ]%%% This paper has been withdrawn . | [
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0708.2707 | 1 | Cooperation plays a key role in the evolution of complex systems. However, the level of cooperation extensively varies with the topology of agent networks in the widely used models of repeated games. Here we show that cooperation remains rather stable by applying long-term learning + innovative strategy adoption rules on a variety of random, regular, small-word, scale-free and modular networks in repeated, multi-agent games. Furthermore, we found that while long-term learning promotes cooperation, innovation makes the level of cooperation less dependent on the actual network topology. Our results demonstrate that long-term learning and innovation , when acting together, extend the range of network topologies enabling the development of cooperation at a wider range of costs and temptations. Learning and innovation help to preserve cooperation during network URLanization , and may be key mechanisms promoting the evolution of URLanizing, complex systems. | Cooperation plays a key role in the evolution of complex systems. However, the level of cooperation extensively varies with the topology of agent networks in the widely used models of repeated games. Here we show that cooperation remains rather stable by applying the reinforcement learning strategy adoption rule, Q-learning on a variety of random, regular, small-word, scale-free and modular network models in repeated, multi-agent Prisoners Dilemma and Hawk-Dove games. Furthermore, we found that using the above model systems other long-term learning strategy adoption rules also promote cooperation, while introducing a low level of noise (as a model of innovation) to the strategy adoption rules makes the level of cooperation less dependent on the actual network topology. Our results demonstrate that long-term learning and random elements in the strategy adoption rules , when acting together, extend the range of network topologies enabling the development of cooperation at a wider range of costs and temptations. These results suggest that a balanced duo of learning and innovation may help to preserve cooperation during the URLanization of real-world networks , and may play a prominent role in the evolution of URLanizing, complex systems. | [
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0708.2953 | 1 | The numbers of each sort of molecule present in an equilibrium chemical reaction mixture are Poisson distributed . We ask when the same is true of the steady state of a nonequilibrium reaction network and obtain a nearly complete answer. In particular, we show that networks with certain topological features must have a Poisson distribution, whatever the reaction rates. Such driven systems also obey an analog of the fluctuation-dissipation theorem and can equilibrate when in contact with each other . Our results may be relevant to biological systems and to the larger question of how equilibrium ideas might extend to nonequilibrium systems. | In an equilibrium chemical reaction mixture , the number of molecules present obeys a Poisson distribution . We ask when the same is true of the steady state of a nonequilibrium reaction network and obtain an essentially complete answer. In particular, we show that networks with certain topological features must have a Poisson distribution, whatever the reaction rates. Such driven systems also obey an analog of the fluctuation-dissipation theorem . Our results may be relevant to biological systems and to the larger question of how equilibrium concepts might apply to nonequilibrium systems. | [
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0709.0561 | 1 | Using our recent contribution, the " partitioned leaping algorithm" [L. A. Harris and P. Clancy, J. Chem. Phys. 125, 144107 (2006)], we investigate the effects of stochasticity in two model biochemical reaction networks. By considering situations both where "leaping" proves beneficial and where it does not, we gain valuable insight that can aid in and advance the use of leaping methods in computational biology. In particular, we identify reaction subnetworks with small populations and large rate constants as a major bottleneck for leaping. We also demonstrate the use of "model reduction" in conjunction with leaping to circumvent this problem and expose a current need in this area: a model-reduction hierarchy analogous to that on which the leaping methods are based D. T. Gillespie, J. Chem. Phys. 113, 297 (2000); 115, 1716 (2001)%DIFDELCMD < ]%%% . In situations where leaping is seen to perform well, we emphasize the significant advantages to using these methods over more traditional simulation approaches. We show how leaping allows for statistical investigations beyond the reach of "exact-stochastic" methods and demonstrate how one can uncover, via such investigations, subtle stochastic effects that would be ignored in deterministic treatments. We then show, using examples taken from the literature, that conditions identified here as lending well to leaping do, in fact, arise in natural biological systems. This leads us to discuss and demonstrate how the statistical information garnered from a leaping study can be used to infer mechanistic details of a biological process and motivate experiments . Overall, we demonstrate to biologists the great potential that leaping methods hold for real-world biological research while highlighting to algorithmists areas still in need of improvement . | " Leaping" methods show great promise for significantly accelerating stochastic simulations of complex biochemical reaction networks. However, few practical applications of leaping have appeared in the literature to date. Here, we address this issue using the " partitioned leaping algorithm" (PLA) [L. A. Harris and P. Clancy, J. Chem. Phys. 125, 144107 (2006)], a recently-introduced multiscale leaping approach. We use the PLA to investigate stochastic effects in two model biochemical reaction networks. %DIFDELCMD < ]%%% The networks that we consider are simple enough so as to be accessible to our intuition but sufficiently complex so as to test the limits of the leaping approach. We demonstrate how the PLA allows us to quantify subtle effects of stochasticity that would be difficult to ascertain otherwise as well as not-so-subtle behaviors that would strain commonly-used "exact" stochastic methods. We also illustrate prime bottlenecks that can hinder the approach and discuss possible strategies for overcoming them . Overall, our aim is to aid and motivate future applications of leaping by providing stark illustrations of the benefits of the method while also elucidating the obstacles that one can expect to encounter . | [
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0709.0561 | 2 | "Leaping" methods show great promise for significantly accelerating stochastic simulations of complex biochemical reaction networks. However, few practical applications of leaping have appeared in the literature to date. Here, we address this issue using the "partitioned leaping algorithm" (PLA) [L.A. Harris and P. Clancy, J. Chem. Phys. 125, 144107 (2006)], a recently-introduced multiscale leaping approach. We use the PLA to investigate stochastic effects in two model biochemical reaction networks. The networks that we consider are simple enough so as to be accessible to our intuition but sufficiently complex so as to test the limits of the leaping approach . We demonstrate how the PLA allows us to quantify subtle effects of stochasticity that would be difficult to ascertain otherwise as well as not-so-subtle behaviors that would strain commonly-used "exact" stochastic methods. We also illustrate prime bottlenecks that can hinder the approach and discuss possible strategies for overcoming them. Overall, our aim is to aid and motivate future applications of leaping by providing stark illustrations of the benefits of the method while also elucidating the obstacles that one can expect to encounter . | "Leaping" methods show great promise for significantly accelerating stochastic simulations of complex biochemical reaction networks. However, few practical applications of leaping have appeared in the literature to date. Here, we address this issue using the "partitioned leaping algorithm" (PLA) [L.A. Harris and P. Clancy, J. Chem. Phys. 125, 144107 (2006)], a recently-introduced multiscale leaping approach. We use the PLA to investigate stochastic effects in two model biochemical reaction networks. The networks that we consider are simple enough so as to be accessible to our intuition but sufficiently complex so as to be generally representative of real biological systems . We demonstrate how the PLA allows us to quantify subtle effects of stochasticity in these systems that would be difficult to ascertain otherwise as well as not-so-subtle behaviors that would strain commonly-used "exact" stochastic methods. We also illustrate bottlenecks that can hinder the approach and exemplify and discuss possible strategies for overcoming them. Overall, our aim is to aid and motivate future applications of leaping by providing stark illustrations of the benefits of the method while at the same time elucidating obstacles that are often encountered in practice . | [
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0709.3291 | 1 | The major objective of this paper is to introduce a novel method for the functional annotation of genes. Our method is based on a graph theoretical measure we call joint betweenness, which is an extension of the well known betweenness centrality measure, involving pairs of genes. We apply our method to the transcriptional regulatory network of yeast to, first, provide a large scale proof of concept of our method and, second, make predictions about the biological function of previously unknown genes . | This paper has been withdrawn . | [
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0709.3606 | 1 | We find that discrete noise of inhibiting (signal) molecules can greatly delay the extinction of a regulated component in a prototypical biochemical regulatory network. We calculate analytically the probability distribution of the metastable state of the regulated component and show that deterministic reaction rate equations may fail in predicting the average number of regulated molecules even when this number is large, and the time is short compared to the mean extinction time. | We find that discrete noise of inhibiting (signal) molecules can greatly delay the extinction of plasmids in a plasmid replication system: a prototypical biochemical regulatory network. We calculate the probability distribution of the metastable state of the plasmids and show on this example that the reaction rate equations may fail in predicting the average number of regulated molecules even when this number is large, and the time is much shorter than the mean extinction time. | [
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0709.3675 | 1 | Microtubules (MTs), nano-tubes which act as struts in the scaffolding of eucaryotic cells, also serve as tracks for intracellular molecular motor transport in eucaryotic cells. In many biological processes, the length distribution of the MTs is controlled by a class of motor proteins called depolymerases (DPs). A DP diffuses or walks along a MT to reach one of the tips of the MT andthen begins depolymerizing the MT itself . We develop a quantitative model that captures both these processes within a single theoretical framework. We show that the action of both diffusing and walking DPs leads to a length-dependent depolymerization of the MT; however, their effects on the length distribution are different. Under experimental conditions, the diffusing DP produces a non-monotonic distribution of lengths as opposed to a nearly exponential distribution in the case of the walking DP. The former also shows a minimum in the r.m.s fluctuation to mean ratio of the length against the DP concentration, while the latter does not. Our findings imply that a diffusing DP, like MCAK, might be used by the cell for precise length control during cell division, while a walking DP, like Kip3p, would be more useful for fast depolymerization . | In many intracellular processes, the length distribution of microtubules is controlled by a class of motor proteins , called depolymerases. Experiments have shown that, following binding to the surface of a microtubule, depolymerases are transported to the microtubule tip(s) by diffusion or directed walk and, then, depolymerize the microtubule from the tip(s) after accumulating there . We develop a quantitative model to study the depolymerizing action of such a generic motor protein, and its possible effects on the length distribution of microtubules. We show that, when the motor protein concentration in solution exceeds a critical value, a steady state is reached where the distribution is non-monotonic provided the motor processivity is sufficiently small. Our findings suggest that such motor proteins have a central role in ensuring precise control of MT lengths . | [
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0709.3675 | 2 | In many intracellular processes, the length distribution of microtubules is controlled by a class of motor proteins, called depolymerases . Experiments have shown that, following binding to the surface of a microtubule, depolymerases are transported to the microtubule tip(s) by diffusion or directed walk and, then, depolymerize the microtubule from the tip(s) after accumulating there. We develop a quantitative model to study the depolymerizing action of such a generic motor protein, and its possible effects on the length distribution of microtubules. We show that, when the motor protein concentration in solution exceeds a critical value, a steady state is reached where the distribution is non-monotonic provided the motor processivity is sufficiently small . Our findings suggest that such motor proteins have a central role in ensuring precise control of MT lengths . | In many intracellular processes, the length distribution of microtubules is controlled by depolymerizing motor proteins . Experiments have shown that, following non-specific binding to the surface of a microtubule, depolymerizers are transported to the microtubule tip(s) by diffusion or directed walk and, then, depolymerize the microtubule from the tip(s) after accumulating there. We develop a quantitative model to study the depolymerizing action of such a generic motor protein, and its possible effects on the length distribution of microtubules. We show that, when the motor protein concentration in solution exceeds a critical value, a steady state is reached where the length distribution is, in general, non-monotonic with a single peak. However, for highly processive motors and large motor densities, this distribution effectively becomes an exponential decay . Our findings suggest that such motor proteins may be selectively used by the cell to ensure precise control of MT lengths . The model is also used to analyze experimental observations of motor-induced depolymerization . | [
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0710.0892 | 1 | We develop a network-based algorithm to predict and verify indirect regulatory interactions in a large-scale genetic regulatory network. Indirect regulations are important as they constitute the majority of experimental data. Our approach is based on the network topology and can be easily incorporated using a matrix formalism. The essence of the method is to extend the transitivity of indirect regulations ( i.e. A regulates B and B regulates C implies A regulates C) to longer cascades and effectively take care of the signs of the regulations. This algorithm is tailored for large and heavily interconnected networks, which are of growing importance due to the accruement of data from high-throughput experiments. We apply the algorithm to the regulatory networks of Homo sapiens, Saccharomyces cerevisiae, Arabidopsis thaliana and Drosophila melanogaster , resulting in novel predictions with calibrated reliability . | We develop a matrix-based approach to predict and verify indirect interactions in gene and protein regulatory networks. It is based on the approximate transitivity of indirect regulations ( e.g. A regulates B and B regulates C often implies that A regulates C) and optimally takes into account the length of a cascade and signs of intermediate interactions. Our method is at its most powerful when applied to large and densely interconnected networks. It successfully predicts both the yet unknown indirect regulations, as well as the sign (activation or repression) of already known ones. The reliability of sign predictions was calibrated using the gold-standard sets of positive and negative interactions. We fine-tuned the parameters of our algorithm by maximizing the area under the Receiver Operating Characteristic (ROC) curve. We then applied the optimized algorithm to large literature-derived networks of all direct and indirect regulatory interactions in several URLanisms ( Homo sapiens, Saccharomyces cerevisiae, Arabidopsis thaliana and Drosophila melanogaster ) . | [
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0710.3959 | 1 | The t copula is often used in risk management as it allows for modelling tail dependence between risks and it is simple to simulate and calibrate. However the use of a standard t copula is often criticized due to its restriction of having a single parameter for the degrees of freedom (dof) that may limit its capability to model the tail dependence structure in a multivariate case. To overcome this problem, grouped t copula was proposed recently where risks are grouped a priori in such a way that each group has a standard t copula with its specific dof parameter. In this paper we propose the use of a new t copula, generalizing grouped t copula to have each group consisting of one risk only, so that a priori grouping is not required. The characteristics of this copula in the bivariate case are described . We explain simulation and calibration procedures and provide examples . | The t copula is often used in risk management as it allows for modelling tail dependence between risks and it is simple to simulate and calibrate. However , the use of a standard t copula is often criticized due to its restriction of having a single parameter for the degrees of freedom (dof) that may limit its capability to model the tail dependence structure in a multivariate case. To overcome this problem, grouped t copula was proposed recently , where risks are grouped a priori in such a way that each group has a standard t copula with its specific dof parameter. In this paper we propose the use of a grouped t copula , where each group consists of one risk factor only, so that a priori grouping is not required. The copula characteristics in the bivariate case are studied . We explain simulation and calibration procedures , including a simulation study on finite sample properties of the maximum likelihood estimators and Kendall's tau approximation. This new copula can be significantly different from the standard t copula in terms of risk measures such as tail dependence, value at risk and expected shortfall. Keywords: grouped t copula, tail dependence, risk management . | [
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0710.4127 | 1 | Stimulated by the long term goal of identifying gene targets for corn crop improvement, we perturbed a simple plant cell system by the addition of abscisic acid, a well-characterized plant hormone, and measured the gene expression with transcriptional microarrays for 150 minutes, every 10 minutes after treatment. Parameters of biochemistry-based models were inferred for 25 downstream (regulated) genes of interest using a thoroughly studied approximation of the posterior distribution, accounting for model uncertainty through Bayesian model averaging. The four causal gene interactions thereby identified as probable under a first-order difference model present testable hypotheses for future experimentation that could conceivably build knowledge of the complex biological system. The small scale of this result compared to many of the reconstructed networks reported in recent literature reflects a cautious approach to systems biology, but without a priori skepticism. The number of putative genes represented on the microarrays used is on the order of the size of the genome; a modification of the methodology for cases in which the number of measured genes is a small fraction of the genome size is also provided. For purposes of inferring biological networks, the main advantage of microarray technology over low-throughput methods may be that the representation of a large enough portion of the genome enables computation of an informative upper bound of how much confidence one may reasonably place in causal relationships between genes on the basis of observed data. | Motivation: Measurements of gene expression over time enable the reconstruction of transcriptional networks. However, Bayesian networks and many other current reconstruction methods rely on assumptions that conflict with the differential equations that describe transcriptional kinetics. Practical approximations of kinetic models would enable inferring causal relationships between genes from expression data of microarray, tag-based and conventional platforms, but conclusions are sensitive to the assumptions made. Results: The representation of a sufficiently large portion of genome enables computation of an upper bound on how much confidence one may place in influences between genes on the basis of expression data. Information about which genes encode transcription factors is not necessary but may be incorporated if available. The methodology is generalized to cover cases in which expression measurements are missing for many of the genes that might control the transcription of the genes of interest. The assumption that the gene expression level is roughly proportional to the rate of translation led to better empirical performance than did either the assumption that the gene expression level is roughly proportional to the protein level or the Bayesian model average of both assumptions. Availability: URL points to R code implementing the methods (R Development Core Team 2004). Supplementary information: URL | [
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0711.0916 | 1 | We present a theoretical investigation of the folding of small proteins assisted by chaperones. We describe the proteins in the framework of an effective potential model which contains the Ramachandran angles as degrees of freedom {\it . The cage of chaperonins is modeled by an external confining potential which is also able to take into account hydrophobic and hydrophilic effects inside the cavity. Using the Wang-Landau algorithm Phys. Rev. Lett.%DIFDELCMD < {\bf %%% 86 , 2050 (2001) we determine the density of states g(E ) and analyze in detail the thermodynamical properties of the confined proteins for different sizes of the cage . We show how the confinement through the chaperon dramatically reduces the phase space available for the protein leading to a much faster folding process. Slightly hydrophobic cages seem to make the native structure more stable . However, not any confining potential helps folding . If the inner walls of the cage are strongly hydrophobic, a denaturation process is induced, in which the proteins partially unfold and stick to the walls . | We present a theoretical study of the folding of small proteins inside confining potentials. Proteins are described in the framework of an effective potential model which contains the Ramachandran angles as degrees of freedom and does not need any{\it a priori information about the native state. Hydrogen bonds, dipole-dipole- and hydrophobic interactions are taken explicitly into account. An interesting feature displayed by this potential is the presence of some intermediates between the unfolded and native states. We consider different types of confining potentials in order to study the structural properties of proteins folding inside cages with repulsive or attractive walls . Using the Wang-Landau algorithm %DIFDELCMD < {\bf %%% we determine the density of states (DOS ) and analyze in detail the thermodynamical properties of the confined proteins for different sizes of the cages . We show that confinement dramatically reduces the phase space available to the protein and that the presence of intermediate states can be controlled by varying the properties of the confining potential. Cages with strongly attractive walls lead to the disappearance of the intermediate states and to a two-state folding into a less stable configuration. However, cages with slightly attractive walls make the native structure more stable than in the case of pure repulsive potentials, and the folding process occurs through intermediate configurations. In order to test the metastable states we analyze the free energy landscapes as a function of the configurational energy and of the end-to-end distance as an order parameter . | [
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0711.2624 | 1 | In this paper we will develop an original approach, based in the use of renewal equations, for obtaining pricing expressions for financial instruments whose underlying asset can be solely described through a simple continuous-time random walk (CTRW). This enhances the potential use of CTRW techniques in finance. We solve these equations for different contract specifications in a particular but exemplifying case. We recover the celebrated results for the Wiener process under certain limits. | In this paper we will develop an original approach, based in the use of renewal equations, for obtaining pricing expressions for financial instruments whose underlying asset can be solely described through a simple continuous-time random walk (CTRW). This enhances the potential use of CTRW techniques in finance. We solve these equations for typical contract specifications, in a particular but exemplifying case. We also show how a formal general solution can be found for more exotic derivatives, and we compare prices for alternative models of the underlying. Finally, we recover the celebrated results for the Wiener process under certain limits. | [
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0711.2624 | 2 | In this paper we will develop an original approach, based in the use of renewal equations, for obtaining pricing expressions for financial instruments whose underlying asset can be solely described through a simple continuous-time random walk (CTRW) . This enhances the potential use of CTRW techniques in finance. We solve these equations for typical contract specifications, in a particular but exemplifying case. We also show how a formal general solution can be found for more exotic derivatives, and we compare prices for alternative models of the underlying. Finally, we recover the celebrated results for the Wiener process under certain limits. | In this paper we will develop a methodology for obtaining pricing expressions for financial instruments whose underlying asset can be described through a simple continuous-time random walk (CTRW) market model. Our approach is very natural to the issue because it is based in the use of renewal equations, and therefore it enhances the potential use of CTRW techniques in finance. We solve these equations for typical contract specifications, in a particular but exemplifying case. We also show how a formal general solution can be found for more exotic derivatives, and we compare prices for alternative models of the underlying. Finally, we recover the celebrated results for the Wiener process under certain limits. | [
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0711.2799 | 1 | Boolean networks have been the object of much attention, especially since S. Kauffman proposed them in the 1960's as models for gene regulatory networks. These systems are characterized by being defined on a Boolean state space and by simultaneous updating at discrete time steps. Of particular importance for biological applications are networks in which the indegree for each variable is bounded by a fixed constant, as was stressed by Kauffman in his original papers. An important question is which conditions on the network topology can rule out exponentially long periodic orbits in the system. In this paper, we consider systems with positive feedback interconnections among all variables , which in a continuous setting guarantees a very stable dynamics. We present a construction that shows that for an arbitrary constant 0<c<2 and sufficiently large n there exist n-dimensional Boolean networks with this property in which both the indegree and outdegree of each for each variable is bounded by two and which nevertheless contain periodic orbits of length at least c^n. In Part II of this paper we will prove an inverse result showing that any system with such a dynamic behavior must in a sense be similar to the example described. | Boolean networks have been the object of much attention, especially since S. Kauffman proposed them in the 1960's as models for gene regulatory networks. These systems are characterized by being defined on a Boolean state space and by simultaneous updating at discrete time steps. Of particular importance for biological applications are networks in which the indegree for each variable is bounded by a fixed constant, as was stressed by Kauffman in his original papers. An important question is which conditions on the network topology can rule out exponentially long periodic orbits in the system. In this paper, we consider systems with positive feedback interconnections among all variables (known as cooperative systems) , which in a continuous setting guarantees a very stable dynamics. We show that for an arbitrary constant 0<c<2 and sufficiently large n there exist n-dimensional cooperative Boolean networks in which both the indegree and outdegree of each variable is bounded by two , and which nevertheless contain periodic orbits of length at least c^n. In Part II of this paper we will prove an inverse result showing that any system with such a dynamic behavior must in a sense be similar to the example described. | [
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0711.3812 | 1 | Experiments in recent years have vividly demonstrated that gene expression can Hobe highly stochastic. How protein concentration fluctuations affect the growth rate of a population of cells, is, however, a wide open question. We present a mathematical model that makes it possible to quantify the effect of protein concentration fluctuations on the growth rate of a population of genetically identical cells. The model predicts that the population's growth rate depends on how the growth rate of a single cell varies with protein concentration, the variance of the protein concentration fluctuations, and the correlation time of these fluctuations. Only when the correlation time of the fluctuations is long compared to the cell cycle time, do they affect the population's growth rate. The model also predicts that when the average concentration of a protein is close to the value that maximizes the growth rate, fluctuations in its concentration always reduce the growth rate. However, when the average protein concentration deviates sufficiently from the optimal level, fluctuations can enhance the growth rate of the population, even when the growth rate of a cell depends linearly on the protein concentration. We also apply our model to perform a cost-benefit analysis of gene regulatory control. Our analysis predicts that the optimal expression level of a gene regulatory protein is determined by the trade-off between the cost of synthesizing the regulatory protein and the benefit of minimizing the fluctuations in the expression of its target gene. We discuss possible experiments that could test our predictions. | Experiments in recent years have vividly demonstrated that gene expression can be highly stochastic. How protein concentration fluctuations affect the growth rate of a population of cells, is, however, a wide open question. We present a mathematical model that makes it possible to quantify the effect of protein concentration fluctuations on the growth rate of a population of genetically identical cells. The model predicts that the population's growth rate depends on how the growth rate of a single cell varies with protein concentration, the variance of the protein concentration fluctuations, and the correlation time of these fluctuations. The model also predicts that when the average concentration of a protein is close to the value that maximizes the growth rate, fluctuations in its concentration always reduce the growth rate. However, when the average protein concentration deviates sufficiently from the optimal level, fluctuations can enhance the growth rate of the population, even when the growth rate of a cell depends linearly on the protein concentration. The model also shows that the ensemble or population average of a quantity, such as the average protein expression level or its variance, is in general not equal to its time average as obtained from tracing a single cell and its descendants. We apply our model to perform a cost-benefit analysis of gene regulatory control. Our analysis predicts that the optimal expression level of a gene regulatory protein is determined by the trade-off between the cost of synthesizing the regulatory protein and the benefit of minimizing the fluctuations in the expression of its target gene. We discuss possible experiments that could test our predictions. | [
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0712.2771 | 1 | We investigate the use of Kelly's strategy in the construction of an optimal portfolio of assets. With asset prices undergoing a multiplicative random process , we derive approximate analytical results for the optimal investment fractions under various constraints . We show that , when returns and volatilities of the assets are small and borrowing is forbidden , the Kelly-optimal portfolio lies on Markowitz Efficient Frontier. When short positions are also forbidden, only a small fraction of the available assets is included in the Kelly-optimal portfolio. This phenomenon, that we call condensation, is explored in detail. | We investigate the use of Kelly's strategy in the construction of an optimal portfolio of assets. For lognormally distributed asset returns , we derive approximate analytical results for the optimal investment fractions in various settings . We show that when mean returns and volatilities of the assets are small and there is no risk-free asset , the Kelly-optimal portfolio lies on Markowitz Efficient Frontier. Since in the investigated case the Kelly approach forbids short positions and borrowing, often only a small fraction of the available assets is included in the Kelly-optimal portfolio. This phenomenon, that we call condensation, is explored in detail. | [
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0712.2773 | 1 | Database replication is difficult but indispensable. We report on our experiences building and deploying middleware-based replication systems both as commercial products and research systems. We identify gaps that still separate academic research from industrial practiceand thus thwart potential technology transfer from academia to the field. We structure our analysis along three axes -- performance, availability and management -- and outline unmet database replication challenges at several levels. We hope to both motivate and aid researchers in bridging these gaps between theory and practice . We sift through the last decade of open-source, academic, and commercial database replication systems and combine this material with case studies resulting from developing and deploying real systems at many customer sites . We propose two agendas, one for academic research and one for industrial R&D, which we expect can bridge the gaps within 5-10 years . | The need for high availability and performance in data management systems has been fueling a long running interest in database replication from both academia and industry. However, academic groups often attack replication problems in isolation, overlooking the need for completeness in their solutions, while commercial teams take a holistic approach that often misses opportunities for fundamental innovation. This has created over time a gap between academic research and industrial practice. This paper aims to characterize the gap along three axes : performance, availability , and administration. We build on our own experience developing and deploying replication systems in commercial and academic settings, as well as on a large body of prior related work . We sift through representative examples from the last decade of open-source, academic, and commercial database replication systems and combine this material with case studies from real systems deployed at Fortune 500 customers . We propose two agendas, one for academic research and one for industrial R&D, which we believe can bridge the gap within 5-10 years . This way, we hope to both motivate and help researchers in making the theory and practice of middleware-based database replication more relevant to each other . | [
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0712.3485 | 1 | Using Malliavin calculus techniques, we derive an analytical formula for the price of European options, for any model including local volatility and jump Poisson process. We show that the accuracy of the formula depends on the smoothness of the payoff . Our approach relies on an asymptotic expansion related to small diffusion and small jump frequency . As a consequence, the calibration of such model becomes very fast . | Using Malliavin calculus techniques, we derive an analytical formula for the price of European options, for any model including local volatility and Poisson jump process. We show that the accuracy of the formula depends on the smoothness of the payoff function . Our approach relies on an asymptotic expansion related to small diffusion and small jump frequency /size. Our formula has excellent accuracy (the error on implied Black-Scholes volatilities for call option is smaller than 2 bp for various strikes and maturities). Additionally, model calibration becomes very rapid . | [
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0712.4304 | 1 | Kinesins are biomolecular motors which move on cylindrical nano-tubes called microtubules . A normal microtubule consists of more than one protofilament on which the equispaced motor binding sites form a periodic array. The collective movement of the kinesins on a microtubule is, therefore, analogous to vehicular traffic on multi-lane highways where each protofilament is the analogue of a single lane. We extend a recent model of the traffic of single-headed kinesin KIF1A [{\it Phys. Rev. E {\bf 75}, 041905 (2007)}] by incorporating processes which correspond to shifting of the motor proteins from one protofilament to another. On the basis of analytical treatment of our model, we predict the effects of lane changing on the flux of the KIF1A motors . Our quantitative predictions can be tested, in principle, by carrying out {\it in-vitro} experiments with fluorescently labelled KIF1A molecules. | KIF1A kinesins are single-headed motor proteins which move on cylindrical nano-tubes called microtubules (MT) . A normal MT consists of 13 protofilaments on which the equispaced motor binding sites form a periodic array. The collective movement of the kinesins on a MT is, therefore, analogous to vehicular traffic on multi-lane highways where each protofilament is the analogue of a single lane. Does lane-changing increase or decrease the motor flux per lane? We address this fundamental question here by appropriately extending a recent model [{\it Phys. Rev. E {\bf 75}, 041905 (2007)}] . By carrying out analytical calculations and computer simulations of this extended model, we predict that the flux per lane can increase or decrease with the increasing rate of lane changing , depending on the concentrations of motors and the rate of hydrolysis of ATP, the ``fuel'' molecules. Our predictions can be tested, in principle, by carrying out {\it in-vitro} experiments with fluorescently labelled KIF1A molecules. | [
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0801.0718 | 1 | In \mbox{%DIFAUXCMD Gua the notion of stickiness for stochastic processes was introduced. It was also shown that stickiness implies absense of arbitrage in a market with proportional transaction costs. In this paper, we investigate the notion of stickiness further. In particular, we show that stickiness is invariant under composition with continuous functions. We also prove a time change result on stickiness. As an application we provide sufficient conditions for continuous semimartingales to be sticky (A counter example show that not all semi-martingales are sticky). As a result, our paper provides an extended class of stochastic processes that are consistent with the no arbitrage property in a market with friction . | In 2 the notion of stickiness for stochastic processes was introduced. It was also shown that stickiness implies absense of arbitrage in a market with proportional transaction costs. In this paper, we investigate the notion of stickiness further. In particular, we give examples of processes that are not semimartingales but are sticky . | [
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0801.1480 | 1 | In this paper, we propose a thermodynamic mechanism for the formation of transcriptional foci via the joint agglomeration of DNA-looping proteins and protein-binding domains on DNA: The competition between the gain in protein-DNA binding free energy and the entropy loss due to DNA looping is argued to result in an effective attraction between loops. A mean-field description can be solved analytically via a mapping to a restricted random-graph ensemble . It shows the emergence of protein clusters containing a finite fraction of all looping proteins. If the entropy loss due to a single DNA loop is high enough, this transition is found to be of first order. | In this paper, we propose a thermodynamic mechanism for the formation of transcriptional foci via the joint agglomeration of DNA-looping proteins and protein-binding domains on DNA: The competition between the gain in protein-DNA binding free energy and the entropy loss due to DNA looping is argued to result in an effective attraction between loops. A mean-field approximation can be described analytically via a mapping to a restricted random-graph ensemble having local degree constraints and global constraints on the number of connected components . It shows the emergence of protein clusters containing a finite fraction of all looping proteins. If the entropy loss due to a single DNA loop is high enough, this transition is found to be of first order. | [
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0801.4592 | 1 | It is well-known that power control can affect the wireless network capacity. However, recent works show conflicting results: network capacity may increase or decrease with higher transmission power under different scenarios. In this work, we want to explore this paradoxand provide fundamental understanding on power control . Specifically, we want to explore the following questions: (1)Theoretically, should we increase or decrease transmission power to maximize network capacity? (2) Theoretically, how much network capacity gain can we achieve when using power control? (3) Under realistic situations, how do power control, link scheduling and routing interact with each other? Under which scenarios can we expect a large capacity gain by using higher transmission power? To answer these questions, firstly, we prove that the optimal network capacity is a non-decreasing function of transmission power. Secondly, we prove that the optimal network capacity can be increased unlimitedly by higher transmission power in some network configurations. However, when nodes are distributed uniformly, the gain of optimal network capacity by higher transmission power is upper-bounded by a positive constant. Thirdly, we discuss why network capacity in practice may increase or decrease with higher transmission power under different scenarios using carrier sensing and the minimum hop-count routing. Extensive simulations are carried out to verify our analysis . This work provides a deeper understanding on how power control can affect network capacity. Besides the theoretical contributions, it offers some design intuitions to wireless network researchers . | Recent works show conflicting results: network capacity may increase or decrease with higher transmission power under different scenarios. In this work, we want to understand this paradox . Specifically, we address the following questions: (1)Theoretically, should we increase or decrease transmission power to maximize network capacity? (2) Theoretically, how much network capacity gain can we achieve by power control? (3) Under realistic situations, how do power control, link scheduling and routing interact with each other? Under which scenarios can we expect a large capacity gain by using higher transmission power? To answer these questions, firstly, we prove that the optimal network capacity is a non-decreasing function of transmission power. Secondly, we prove that the optimal network capacity can be increased unlimitedly by higher transmission power in some network configurations. However, when nodes are distributed uniformly, the gain of optimal network capacity by higher transmission power is upper-bounded by a positive constant. Thirdly, we discuss why network capacity in practice may increase or decrease with higher transmission power under different scenarios using carrier sensing and the minimum hop-count routing. Extensive simulations are carried out to verify our analysis . | [
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0802.1288 | 1 | In this work we introduce Heath-Jarrow-Morton (HJM) interest rate models driven by fractional Brownian motions. By using support arguments we prove that the resulting model is arbitrage-free under proportional transaction costs in the same spirit of Guasoni et al (2006 , 2007) . In particular, we obtain a drift condition which is similar in nature to the classical HJM no-arbitrage drift restriction. The second part of this paper deals with consistency problems related to the fractional HJM dynamics. We give a fairly complete characterization of finite-dimensional invariant manifolds for HJM models with fractional Brownian motion by means of Nagumo-type conditions. As an application, we investigate consistency of Nelson-Siegel family with respect to Ho-Lee and Hull-White models. It turns out that similar to the Brownian case such family does not go well with the fractional HJM dynamics with deterministic volatility. In fact, there is no nontrivial fractional interest rate model consistent with the Nelson-Siegel family. | In this work we introduce Heath-Jarrow-Morton (HJM) interest rate models driven by fractional Brownian motions. By using support arguments we prove that the resulting model is arbitrage free under proportional transaction costs in the same spirit of Guasoni Math. Finance 16 (2006 ) 569-582 . In particular, we obtain a drift condition which is similar in nature to the classical HJM no-arbitrage drift restriction. The second part of this paper deals with consistency problems related to the fractional HJM dynamics. We give a fairly complete characterization of finite-dimensional invariant manifolds for HJM models with fractional Brownian motion by means of Nagumo-type conditions. As an application, we investigate consistency of Nelson-Siegel family with respect to Ho-Lee and Hull-White models. It turns out that similar to the Brownian case such a family does not go well with the fractional HJM dynamics with deterministic volatility. In fact, there is no nontrivial fractional interest rate model consistent with the Nelson-Siegel family. | [
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0802.2004 | 1 | We show that a simple model reproduces very closely the evolution of the GDP in constant dollars of many countries during the times of recession and recovery. A theoretical analysis illustrates how an optimal dynamical policy reduces both recession duration and severity, and increases the value of GDP at all times. We propose a criterion to distinguish a posteriori a dynamical policy from a static one . | We show that a simple model reproduces very closely the evolution of the gross domestic product (GDP) in current and constant dollars of many countries during the times of recession and recovery. A theoretical analysis illustrates how an optimal dynamical policy reduces both recession duration and severity, and increases the value of GDP at all times. We propose a criterion to distinguish a posteriori a dynamical policy from a static one . Finally, we predict that Ukraine will recover its current and constant dollar 1990 GDPs in 2009 and Moldova in 2015 in current dollars and 2009 in constant dollars . | [
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0802.2004 | 2 | We show that a simple model reproduces very closely the evolution of the gross domestic product (GDP) in current and constant dollars of many countries during the times of recession and recovery. A theoretical analysis illustrates how an optimal dynamical policy reduces both recession duration and severity, and increases the value of GDP at all times. We propose a criterion to distinguish a posteriori a dynamical policy from a static one. Finally, we predict that Ukraine will recover its current and constant dollar 1990 GDPs in 2009 and Moldova in 2015 in current dollars and 2009 in constant dollars . | We show that a simple and intuitive three-parameter equation fits remarkably well the evolution of the gross domestic product (GDP) in current and constant dollars of many countries during the times of recession and recovery. We then argue that it can be used to detect shocks and discuss its predictive power. Finally, a two-sector theoretical model of recession and recovery illustrates how the severity and length of recession depends on the dynamics of transfer rate between the growing and failing parts of the economy . | [
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0802.2004 | 3 | We show that a simple and intuitive three-parameter equation fits remarkably well the evolution of the gross domestic product (GDP) in current and constant dollars of many countries during the times of recession and recovery. We then argue that it can be used to detect shocks and discuss its predictive power. Finally, a two-sector theoretical model of recession and recovery illustrates how the severity and length of recession depends on the dynamics of transfer rate between the growing and failing parts of the economy. | We show that a simple and intuitive three-parameter equation fits remarkably well the evolution of the gross domestic product (GDP) in current and constant dollars of many countries during times of recession and recovery. We then argue that this equation is the response function of the economy to isolated shocks, hence that it can be used to detect large and small shocks, including those which do not lead to a recession; we also discuss its predictive power. Finally, a two-sector toy model of recession and recovery illustrates how the severity and length of recession depends on the dynamics of transfer rate between the growing and failing parts of the economy. | [
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0802.2172 | 1 | In that paper, we solve dynamically a partial hedging problem for an American contingent claim: assuming superhedging is not feasible, we explain in this context the notion of efficient hedging by introducing a risk minimization criterion: we consider here the problem of minimizing the conditional expected loss for a given convex and non decreasing loss function. To solve this problem, we provide a connection between the dynamic convex risk functional introduced and the solutionof a quadratic RBSDE (Reflected Backward Stochastic Differential Equations): this is achieved by studying the properties of specific non linear expectations . | In that paper, we provide a new characterization of the solutions of specific reflected backward stochastic differential equations (or RBSDEs) whose driver g is convex and has quadratic growth in its second variable: this is done by introducing the extended notion of g-Snell enveloppe. Then, in a second step, we relate this representation to a specific class of dynamic monetary concave functionals already introduced in a discrete time setting. This connection implies that the solution, characterized by means of non linear expectations , has again the time consistency property . | [
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0802.2512 | 1 | Many networks exhibit the small-world property of the neighborhood connectivity being higher than in comparable random networks. However, the standard measure of local neighborhood clustering is typically not defined if a node has one or no neighbor. In such cases, local clustering has traditionally been set to zero and the node was included in the global clustering coefficient. Such a procedure leads to under-estimation of the neighborhood clustering in sparse networks. We propose to include \theta as the proportion of nodes with one or no neighbors to estimate the contribution of these cases to the mean clustering value. Furthermore, we provide a formula for estimating a clustering coefficient that excludes these undefined cases. We find that the definition of the clustering coefficient has a major effect when comparing different networks. For metabolic networks of URLanisms, relations changed for 58\% of the comparisons when a different definition was applied . | Many networks exhibit the small-world property of the neighborhood connectivity being higher than in comparable random networks. However, the standard measure of local neighborhood clustering is typically not defined if a node has one or no neighbor. In such cases, local clustering has traditionally been set to zero and the node was included in the global clustering coefficient. Such a procedure leads to under-estimation of the neighborhood clustering in sparse networks. We propose to include \theta as the proportion of leafs and isolated nodes to estimate the contribution of these cases to the mean clustering value. Furthermore, we provide a formula for estimating a clustering coefficient that excludes these undefined cases. This novel definition leads to values which are up to 140\% higher than the traditional values for the observed networks indicating that neighborhood connectivity is normally underestimated. We find that the definition of the clustering coefficient has a major effect when comparing different networks. For metabolic networks of URLanisms, relations changed for 58\% of the comparisons when a different definition was applied . Values for the clustering coefficient vary with the ratio of isolated and leaf nodes which is critical for comparing networks. We suggest including ratio and definition in publications to enable comparisons across different studies . | [
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0802.2512 | 2 | Many networks exhibit the small-world property of the neighborhood connectivity being higher than in comparable random networks. However, the standard measure of local neighborhood clustering is typically not defined if a node has one or no neighbor . In such cases, local clustering has traditionally been set to zero and the node was included in the global clustering coefficient. Such a procedure leads to under-estimation of the neighborhood clustering in sparse networks. We propose to include \theta as the proportion of leafs and isolated nodes to estimate the contribution of these cases to the mean clustering value. Furthermore, we provide a formula for estimating a clustering coefficient that excludes these undefined cases . This novel definition leads to values which are up to 140\% higher than the traditional values for the observed networks indicating that neighborhood connectivity is normally underestimated. We find that the definition of the clustering coefficient has a major effect when comparing different networks. For metabolic networks of URLanisms, relations changed for 58\% of the comparisons when a different definition was applied. Values for the clustering coefficient vary with the ratio of isolated and leaf nodes which is critical for comparing networks. We suggest including ratio and definition in publications to enable comparisons across different studies . | Many networks exhibit the small-world property of the neighborhood connectivity being higher than in comparable random networks. However, the standard measure of local neighborhood clustering is typically not defined if a node has one or no neighbors . In such cases, local clustering has traditionally been set to zero and this value influenced the global clustering coefficient. Such a procedure leads to underestimation of the neighborhood clustering in sparse networks. We propose to include \theta as the proportion of leafs and isolated nodes to estimate the contribution of these cases and provide a formula for estimating a clustering coefficient excluding these cases from the Watts and Strogatz (1998 Nature 393 440-2) definition of the clustering coefficient. Excluding leafs and isolated nodes leads to values which are up to 140\% higher than the traditional values for the observed networks indicating that neighborhood connectivity is normally underestimated. We find that the definition of the clustering coefficient has a major effect when comparing different networks. For metabolic networks of URLanisms, relations changed for 58\% of the comparisons when a different definition was applied. We also show that the definition influences small-world features and that the classification can change from non-small-world to small-world network. We discuss the use of an alternative measure, disconnectedness D, which is less influenced by leafs and isolated nodes . | [
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0802.3679 | 1 | In Black-Scholes delta-hedging method generalization, a "mirror-diffusion" inverse stochastic process is introduced with condition determined by the underlying price variance and payoff function. The process reduces an expected option value at maturity under equivalent martingale measure back to the current time. The normalized ksi-returns , correspondent to the kernel function in the found general solution and not dependent explicitly on time, were used for verification of the one-parameter model inherent efficiency, i.e. self-calibration using only historical volatility data. The model minimizes implied volatility bias (for 2004-2007 S& P100 index options) and theoretically yields skews correspondent to practical term structure for interest rate derivatives. It allows increasing the number of stock price distribution parameters. | The proposed model modifies option pricing formulas for the basic case of log-normal probability distribution providing correspondence to formulated criteria of efficiency and completeness. The model is self-calibrating by historic volatility data; it maintains the constant expected value at maturity of the hedged instantaneously self-financing portfolio. The payoff variance dependent on random stock price at maturity obtained under an equivalent martingale measure is taken as a condition for introduced "mirror-time" derivative diffusion discount process. Introduced ksi-return distribution , correspondent to the found general solution of backward drift-diffusion equation and normalized by theoretical diffusion coefficient, does not contain so-called "long tails" and unbiased for considered 2004-2007 S& P 100 index data. The model theoretically yields skews correspondent to practical term structure for interest rate derivatives. The method allows increasing the number of asset price probability distribution parameters. | [
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0802.4411 | 1 | We present a positivity preserving numerical scheme for the pathwise solution of nonlinear stochastic differential equations driven by a multi-dimensional Wiener process and governed by non-commutative linear and non-Lipschitz vector fields. This strong order one scheme uses: (i) Strang exponential splitting, an approximation that decomposes the stochastic flow separately into the drift flow, and the pure diffusion flow governed by the diffusion vector fields; (ii) an implicit Euler method to approximate the drift flow; and (iii) an implicit Milstein method to approximate the pure diffusion flow. The separate approximations for the drift and pure diffusion flows preserve positivity. Therefore the Strang exponential splitting approximation does also. We demonstrate the efficacy of our method by applying it to the Heston model and a variance curve model , and compare it against well-established positivity preserving schemes . | For nonlinear stochastic differential systems, we develop strong fully implicit positivity preserving numerical methods in the case that the zero boundary is non-attracting. These methods are implicit in the diffusion vector fields. They thus apply to a restricted class, namely those with sublinear form. This however, still includes most Langevin derived processes typical of volatility models in finance and molecular simulation in physics. When the zero boundary is attracting and attainable, we specialize to a prototypical model, namely the mean-reverting Cox--Ingersoll--Ross process. We thus consider the non-central chi-squared transition density with fractional degrees of freedom. We prove that we can sample from this density by simulating Poisson distributed sums of powers of generalized Gaussian random variables. Further we prove that Marsaglia's polar method extends to the generalized Gaussian distribution, providing an exact and efficient method for generalized Gaussian sampling. We apply our methods to a variance curve model and the Heston model . | [
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0802.4411 | 2 | For nonlinear stochastic differential systems, we develop strong fully implicit positivity preserving numerical methods in the case that the zero boundary is non-attracting. These methods are implicit in the diffusion vector fields. They thus apply to a restricted class, namely those with sublinear form. This however, still includes most Langevin derived processes typical of volatility models in finance and molecular simulation in physics. When the zero boundary is attracting and attainable, we specialize to a prototypical model, namely the mean-reverting Cox--Ingersoll--Ross process. We thus consider the non-central chi-squared transition density with fractional degrees of freedom. We prove that we can sample from this density by simulating Poisson distributed sums of powers of generalized Gaussian random variables. Further we prove that Marsaglia's polar method extends to the generalized Gaussian distribution, providing an exact and efficient method for generalized Gaussian sampling. We apply our methods to a variance curve model and the Heston model . | In the Heston stochastic volatility model, the transition probability of the variance process can be represented by a non-central chi-square density. We focus on the case when the number of degrees of freedom is small and the zero boundary is attracting and attainable, typical in foreign exchange markets. We prove a new representation for this density based on sums of powers of generalized Gaussian random variables. Further we prove Marsaglia's polar method extends to this distribution, providing an exact method for generalized Gaussian sampling. The advantages are that for the mean-reverting square-root process in the Heston model and Cox-Ingersoll-Ross model, we can generate samples from the true transition density simply, efficiently and robustly . | [
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0802.4411 | 3 | In the Heston stochastic volatility model, the transition probability of the variance process can be represented by a non-central chi-square density. We focus on the case when the number of degrees of freedom is small and the zero boundary is attracting and attainable, typical in foreign exchange markets. We prove a new representation for this density based on sums of powers of generalized Gaussian random variables. Further we prove Marsaglia's polar method extends to this distribution, providing an exact method for generalized Gaussian sampling . The advantages are that for the mean-reverting square-root process in the Heston model and Cox-Ingersoll-Ross model, we can generate samples from the true transition density simply, efficiently and robustly . | The transition probability of a Cox-Ingersoll-Ross process can be represented by a non-central chi-square density. First we prove a new representation for the central chi-square density based on sums of powers of generalized Gaussian random variables. Second we prove Marsaglia's polar method extends to this distribution, providing a simple, exact, robust and efficient acceptance-rejection method for generalized Gaussian sampling and thus central chi-square sampling. Third we derive a simple, high-accuracy, robust and efficient direct inversion method for generalized Gaussian sampling based on the Beasley-Springer-Moro method. Indeed the accuracy of the approximation to the inverse cumulative distribution function is to the tenth decimal place. We then apply our methods to non-central chi-square variance sampling in the Heston model . We focus on the case when the number of degrees of freedom is small and the zero boundary is attracting and attainable, typical in foreign exchange markets. Using the additivity property of the chi-square distribution, our methods apply in all parameter regimes . | [
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0803.0483 | 1 | Translocation of a single stranded DNA through genetically engineered \alpha-hemolysin channels with positively charged walls is studied. It is predicted that transport properties of such channels are dramatically different from the neutral wild type \alpha-hemolysin channel. We assume that the wall charges compensate the fraction x of the bare charge q_{b} of the DNA piece residing in the channel. Our prediction are as follows (i) At small concentration of salt the blocked ion current decreases with x. (ii) The effective charge q of DNA piece grows with x and at q_{b x= 1. (iii) The rate of DNA capture by the channel exponentially grows with x. Our theory is also applicable to translocation of a double stranded DNA in narrow solid state nanopores with positively charged walls. | Translocation of a single stranded DNA through genetically engineered \alpha-hemolysin channels with positively charged walls is studied. It is predicted that transport properties of such channels are dramatically different from neutral wild type \alpha-hemolysin channel. We assume that the wall charges compensate the fraction x of the bare charge q_{b} of the DNA piece residing in the channel. Our prediction are as follows (i) At small concentration of salt the blocked ion current decreases with x. (ii) The effective charge q of DNA piece , which is very small at x = 0 (neutral channel) grows with x and at x= 1 reaches q_{b (iii) The rate of DNA capture by the channel exponentially grows with x. Our theory is also applicable to translocation of a double stranded DNA in narrow solid state nanopores with positively charged walls. | [
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0803.1364 | 1 | In the Kelly game (Kelly, 1956 ), a gambler is allowed to invest a part of the wealth in each turn. With a certain probability this investment is doubled, and otherwise it is lost. Motivated by the complexity of real investments, we propose several modifications of this game to investigate the influence of diversification and limited information on investment performance. Analytical and numerical results obtained from these toy games are well related to their real-life counterparts . | Financial markets, with their vast range of different investment opportunities, can be seen as a system of many different simultaneous games with diverse and often unknown levels of risk and reward. We introduce generalizations to the classic Kelly investment game Kelly ( 1956 ) that incorporates these features, and use them to investigate the influence of diversification and limited information on Kelly-optimal portfolios. In particular we present approximate formulas for optimizing diversified portfolios and exact results for optimal investment in unknown games where the only available information is past outcomes . | [
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0803.1558 | 1 | We introduce some new quantitative measures of fluctuations in the process of synthesis of proteins from a single messenger RNA (mRNA) template. We calculate the statistical distributions of these fluctuating quantities and extract the strength of the corresponding translational noise. For these calculations{\bf we use a model that captures both the mechano-chemistry of each individual ribosome as well as their steric interactions in ribosome traffic on the same mRNA track. By comparing our results for a specific gene of the%DIFDELCMD < {\it %%% Escherichia coli bacteria with those for the corresponding homogeneous mRNA template, we demonstrate the effects of the sequence inhomogeneities of real genes on the fluctuations and noise . We also suggest {\it in-vitro} laboratory experimentsfor testing our theoretical predictions . | Proteins are polymerized by cyclic machines called ribosome which use their messenger RNA (mRNA) track also as the corresponding template and the process is called translation. We explore, in depth and detail, the stochastic nature of the translation. We compute various distributions associated with the translation process; one of them, namely dwell time distribution, has been measured in recent single ribosome experiments (Wen et al. Nature{\bf 452 , 598 (2008)). The form of this distribution predicted by our theory is consistent with that extracted from the experimental data. For our quantitative calculations, we use a model that captures both the mechano-chemistry of each individual ribosome as well as their steric interactions %DIFDELCMD < {\it %%% . We also demonstrate the effects of the sequence inhomogeneities of real genes on the fluctuations and noise in translation. In principle, our new predictions can be tested by carrying out {\it in-vitro} experiments . | [
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0803.1890 | 1 | A financial market model where agents can only trade using realistic buy-and-hold strategies is considered. Minimal assumptions are made on the nature of the asset-price process - in particular, the semimartingale property is not assumed. Via a natural assumption of limited opportunities for unlimited resulting wealth from trading, coined the No-Unbounded-Profit-with-Bounded-Risk (NUPBR) condition, we establish that asset-prices have be semimartingales, as well as a weakened version of the Fundamental Theorem of Asset Pricing that involves supermartingale deflators rather than equivalent martingale measures. Further, the utility maximization problem is considered and it is shown that using only buy-and-hold strategies, optimal utilities and wealth processes resulting from continuous trading can be approximated arbitrarily well . | A financial market model where agents trade using realistic combinations of buy-and-hold strategies is considered. Minimal assumptions are made on the asset-price process - in particular, the semimartingale property is not assumed. Via a natural assumption of limited opportunities for unlimited resulting wealth from trading, coined the "No Unbounded Profit with Bounded Risk" condition, we establish that asset-prices have to be semimartingales. In a slightly more specialized case, we extend the previous result in a weakened version of the Fundamental Theorem of Asset Pricing that involves supermartingale deflators rather than Equivalent Martingale Measures . | [
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0803.1890 | 2 | A financial market model where agents trade using realistic combinations of buy-and-hold strategies is considered. Minimal assumptions are made on the asset-price process - in particular, the semimartingale property is not assumed. Via a natural assumption of limited opportunities for unlimited resulting wealth from trading, coined the "No Unbounded Profit with Bounded Risk" condition , we establish that asset-prices have to be semimartingales. In a slightly more specialized case, we extend the previous result in a weakened version of the Fundamental Theorem of Asset Pricing that involves supermartingale deflators rather than Equivalent Martingale Measures. | A financial market model where agents trade using realistic combinations of buy-and-hold strategies is considered. Minimal assumptions are made on the discounted asset-price process - in particular, the semimartingale property is not assumed. Via a natural market viability assumption , namely, absence of arbitrages of the first kind, we establish that discounted asset-prices have to be semimartingales. In a slightly more specialized case, we extend the previous result in a weakened version of the Fundamental Theorem of Asset Pricing that involves strictly positive supermartingale deflators rather than Equivalent Martingale Measures. | [
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0804.0682 | 1 | We address the problem of proteasomal protein translocation . Proteasomes are important for all aspects of the cellular metabolism but the mechanism of protein transport remains unknown. We introduce a new stochastic model of the proteasomal transport. We account for the protein translocation and the topology of the positioning of cleavage centers of a proteasome from first principles. We show by test examples and by a comparison with experimental data that our model allows reconstruction of the translocation rates from mass spectroscopy data on digestion patterns and can be used to investigate the properties of transport in different experimental set-ups. Finally we design an experimental set-up for a synthetic polypeptide with a periodic sequence of amino acids which enables more reliable determination of translocation rates . | We address the problem of proteasomal protein translocation and introduce a new stochastic model of the proteasomal digestion (cleavage) of proteins. In this model we account for the protein translocation and the positioning of cleavage sites of a proteasome from first principles. We show by test examples and by processing experimental data that our model allows reconstruction of the translocation and cleavage rates from mass spectroscopy data on digestion patterns and can be used to investigate the properties of transport in different experimental set-ups. Detailed investigation with this model will enable theoretical quantitative prediction of the proteasomal activity . | [
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0804.1034 | 1 | DNA inversion is an important mechanism by which bacteria and bacteriophage switch reversibly between alternative phenotypic states. In such switches, the orientation of a short DNA element is flipped by a site-specific recombinase enzyme. We propose a simple model for a DNA inversion switch in which recombinase production is dependent on the switch state (orientational control). Our model is inspired by the fim switch in Escherichia coli. We present an exact analytical solution of the chemical master equation for the model switch, as well as stochastic simulations. Orientational control causes the switch to deviate from Poissonian behaviour: the distribution of times in the on state shows a peak and successive flip times are correlated . This model should provide a framework for understanding how DNA inversion switch architecture determines switch flipping statistics, with relevance to the role of such switches in microbial population dynamics . | DNA inversion is an important mechanism by which bacteria and bacteriophage switch reversibly between phenotypic states. In such switches, the orientation of a short DNA element is flipped by a site-specific recombinase enzyme. We propose a simple model for a DNA inversion switch in which recombinase production is dependent on the switch state (orientational control). Our model is inspired by the fim switch in Escherichia coli. We present an exact analytical solution of the chemical master equation for the model switch, as well as stochastic simulations. Orientational control causes the switch to deviate from Poissonian behaviour: the distribution of times in the on state shows a peak and successive flip times are correlated . | [
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0804.1227 | 1 | {\it Transcription} is the process whereby RNA molecules are polymerized by molecular machines, called RNA polymerase (RNAP), using the corresponding DNA as the template. Recent {\it in-vivo} experiments with single cells have established that transcription takes place in ``bursts'' or ``pulses'' . In this letter we present a model that captures not only the mechano-chemistry of individual RNAPs and their steric interactions but also the switching of the gene between the ON and OFF states. This model accounts for the statistical properties of the transcriptional bursts. It also shows how the quantitative features of the distributions of these bursts can be tuned by controlling the appropriate steps of operation of the RNAP machines. | {\it Transcription} is the process whereby RNA molecules are polymerized by molecular machines, called RNA polymerase (RNAP), using the corresponding DNA as the template. Recent {\it in-vivo} experiments with single cells have established that transcription takes place in "bursts" or "pulses" . In this letter we present a model that captures not only the mechano-chemistry of individual RNAPs and their steric interactions but also the switching of the gene between the ON and OFF states. This model accounts for the statistical properties of the transcriptional bursts. It also shows how the quantitative features of the distributions of these bursts can be tuned by controlling the appropriate steps of operation of the RNAP machines. | [
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0804.1720 | 1 | Charge transport modification exhibiting an increase of conductance activated by an external green light in Bacteriorhodopsin is correlated to its conformational change. A theoretical model based on a map of the protein structure into a resistor network is implemented to account for a sequential tunneling mechanism of charge transfer through neighbouring amino-acids . The model is validated by comparison with current-voltage experiments and provides for the potential barriers involved in the charge transfer an average height of 69 meV over an interacting radius of 6 \aa . The predictability of the model is also tested on bovine rhodopsin, the prototype of the G protein coupled receptor (GPCR) family also sensitive to the light, with results exhibiting the opposite behaviour of a decrease of conductance in the presence of light. | When moving from native to light activated bacteriorhodopsin, modification of charge transport consisting of an increase of conductance is correlated to the protein conformational change. A theoretical model based on a map of the protein tertiary structure into a resistor network is implemented to account for a sequential tunneling mechanism of charge transfer through neighbouring amino acids . The model is validated by comparison with current-voltage experiments . The predictability of the model is further tested on bovine rhodopsin, a G-protein coupled receptor (GPCR) also sensitive to light. In this case, results show an opposite behaviour with a decrease of conductance in the presence of light. | [
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0804.2912 | 1 | The numeraire portfolio in a financial market is the unique positive wealth process that makes all other nonnegative wealth processes supermartingales , when deflated by it . The numeraire portfolio depends on market characteristics, which include: (a) the information flow available to acting agents, given by a filtration; (b) the statistical evolution of the asset prices and, more generally, the states of nature, given by a probability measure; and (c) possible restrictions that acting agents might be facing on available investment strategies, modeled by a constraints set. In a financial market with continuous-path asset prices, the stable behavior of the numeraire portfolio is established when each of the aforementioned market parameters is changed in an infinitesimal way. | The numeraire portfolio in a financial market is the unique positive wealth process that makes all other nonnegative wealth processes , when deflated by it , supermartingales . The numeraire portfolio depends on market characteristics, which include: (a) the information flow available to acting agents, given by a filtration; (b) the statistical evolution of the asset prices and, more generally, the states of nature, given by a probability measure; and (c) possible restrictions that acting agents might be facing on available investment strategies, modeled by a constraints set. In a financial market with continuous-path asset prices, we establish the stable behavior of the numeraire portfolio when each of the aforementioned market parameters is changed in an infinitesimal way. | [
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0804.3939 | 1 | Recent works on the emergence of homochirality introduce the concept of recycling, rather than the traditional open-flow system described by Frank. This approach has been criticized by Blackmond et al. They claimed that such systems are thermodynamically impossible, except in the cases where non-microreversible reactions are introduced, like in photochemical reactions, or under the influence of physical actions (e.g. by crystal crushing). This point of view reveals misunderstandings about this model of a recycled system, overlooks the possibility of energy exchanges that could take place in prebiotic systems, and leads the authors to unawarely remove the activation reaction and energy source from their `` non-equilibrium '' models. It is especially important to understand what are the concepts behind the notion of recycled systems, and of activation reactions. These points are fundamental to comprehending how chemical systems -- and especially prebiotic chemical systems -- can be maintained in non-equilibrium steady states, and how free energy can be used and exchanged between systems. The proposed approach aims at the decomposition of the problem, avoiding to embrace the whole system at the same time. | The question of the onset of the homochirality on prebiotic Earth still remains a fundamental question in the quest for the origin of life. Recent works in this field introduce the concept of recycling, rather than the traditional open-flow system described by Frank. This approach has been criticized by Blackmond et al. They claimed that such systems are thermodynamically impossible, except in the cases where non-microreversible reactions are introduced, like in photochemical reactions, or under the influence of physical actions (e.g. by crystal crushing). This point of view reveals misunderstandings about this model of a recycled system, overlooks the possibility of energy exchanges that could take place in prebiotic systems, and leads the authors to unawarely remove the activation reaction and energy source from their " non-equilibrium " models. It is especially important to understand what are the concepts behind the notion of recycled systems, and of activation reactions. These points are fundamental to comprehending how chemical systems -- and especially prebiotic chemical systems -- can be maintained in non-equilibrium steady states, and how free energy can be used and exchanged between systems. The proposed approach aims at the decomposition of the problem, avoiding to embrace the whole system at the same time. | [
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0804.4039 | 1 | In this work we model multicore platforms as chip multiprocessors made up from two different types cores; each type of cores has different computation capabilities. In this simple asymmetric multicore model we study the problem of executing parallel programs that are represented as DAGs or chains of tasks . We assume 2 (essential) speeds in our proposed platform. We relax this assumption and consider many speedsin our energy considerations. This problem has been considered previously in the field of parallel computing and scheduling theory for the general case where multiprocessor platforms have K distinct speeds. Our model is a bridge between the assumptions in these fields and recent advances in multicore processors technology . We provide a refined analysis of a recent scheduling method. Based on this analysis, we specialize the scheduling policy and provide an algorithm of (3 o(1)) expected approximation factor. Note that this improves the previous best factor (6 for two speeds) . | In this work we study the problem of scheduling tasks with dependencies in multiprocessor architectures where processors have different speeds. We present the preemptive algorithm "Save-Energy" that given a schedule of tasks it post processes it to improve the energy efficiency without any deterioration of the makespan. In terms of time efficiency, we show that preemptive scheduling in an asymmetric system can achieve the same or better optimal makespan than in a symmetric system. Motivited by real multiprocessor systems, we investigate architectures that exhibit limited asymmetry: there are two essentially different speeds . Interestingly, this special case has not been studied in the field of parallel computing and scheduling theory ; only the general case was studied where processors have K essentially different speeds. We present the non-preemptive algorithm ``Remnants'' that achieves almost optimal makespan . We provide a refined analysis of a recent scheduling method. Based on this analysis, we specialize the scheduling policy and provide an algorithm of (3 + o(1)) expected approximation factor. Note that this improves the previous best factor (6 for two speeds) . We believe that our work will convince researchers to revisit this well studied scheduling problem for these simple, yet realistic, asymmetric multiprocessor architectures . | [
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0805.0540 | 1 | Stochastic differential equations are commonly used to describe the dynamics of diffusive systems. Since their introduction, they have also been considered natural candidates for the description of the dynamics of financial returns. In this context we analyze the problem of the analytical characterization of the still unknown probability distribution of returns of the exponential Ornstein-Uhlenbeck model with stochastic volatility , where the price is driven by a Geometric Brownian motion, whose diffusion coefficient is expressed as an exponential function of an hidden variable Y governed by an Ornstein-Uhlenbeck process. We derive closed-form expressions for the probability distribution and its characteristic function in two limit cases. In the first one the fluctuations of Y are larger than the volatility normal level, while the second one corresponds to the assumption of a small stationary value for the variance of Y. Theoretical results are tested numerically by intensive use of Monte Carlo simulations. The effectiveness of the analytical predictions is checked via a careful analysis of the parameters involved in the numerical implementation of the Euler-Maruyama scheme . Both analytical and numerical results we obtain can be exploited for useful applications in stock option pricing and risk management . | We analyze the problem of the analytical characterization of the probability distribution of financial returns in the exponential Ornstein-Uhlenbeck model with stochastic volatility . In this model the prices are driven by a Geometric Brownian motion, whose diffusion coefficient is expressed through an exponential function of an hidden variable Y governed by a mean-reverting process. We derive closed-form expressions for the probability distribution and its characteristic function in two limit cases. In the first one the fluctuations of Y are larger than the volatility normal level, while the second one corresponds to the assumption of a small stationary value for the variance of Y. Theoretical results are tested numerically by intensive use of Monte Carlo simulations. The effectiveness of the analytical predictions is checked via a careful analysis of the parameters involved in the numerical implementation of the Euler-Maruyama scheme and is tested on a data set of financial indexes. In particular, we discuss results for the German DAX30 and Dow Jones Euro Stoxx 50, finding a good agreement between the empirical data and the theoretical description . | [
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0805.1293 | 1 | Iterative Logic Arrays (ILAs) are ideal as VLSI sub-systems because of their regular structure and its close resemblance with FPGAs (Field Programmable Gate Arrays). AND-EXOR based circuits are of interest in the design of very low power circuits where energy loss implied by high frequency switching is of much consideration. This paper examines the testability of AND-EXOR based Iterative Logic Arrays (ILAs) . For certain ILAs it is possible to find a test set whose size remains constant irrespective of the size of the ILA, while for others it varies with array size. Former type of ILAs is known as Constant-Testable ( C-Testable ) . It has been shown that AND-EXOR based Logic Arrays are C-Testable and size of test set is equal to number of entries in cell truth table . The test generation problem has been shown to be related to certain properties of cycles in a set of graphs derived from cell truth table. By careful analysis of these cycles an efficient test generation technique that can be easily converted to an ATPG program has been presented for both 1D and 2D ILAs. How this property of ILAs can be used for testing FPGAs has also been discussed.Keywords - C-Testable, Iterative Logic Arrays, Bijective, Test Generation, ATPG | Iterative Logic Arrays (ILAs) are ideal as VLSI sub-systems because of their regular structure and its close resemblance with FPGAs (Field Programmable Gate Arrays). Reversible circuits are of interest in the design of very low power circuits where energy loss implied by high frequency switching is not of much consideration. Reversibility is essential for Quantum Computing. This paper examines the testability of Reversible Iterative Logic Arrays (ILAs) composed of reversible k-CNOT gates . For certain ILAs it is possible to find a test set whose size remains constant irrespective of the size of the ILA, while for others it varies with array size. Former type of ILAs is known as Constant-Testable , i.e. C-Testable . It has been shown that Reversible Logic Arrays are C-Testable and size of test set is equal to number of entries in cells truth table implying that the reversible ILAs are also Optimal-Testable, i.e. O-Testable . Uniform-Testability, i.e. U-Testability has been defined and Reversible Heterogeneous ILAs have been characterized as U-Testable. The test generation problem has been shown to be related to certain properties of cycles in a set of graphs derived from cell truth table. By careful analysis of these cycles an efficient test generation technique that can be easily converted to an ATPG program has been presented for both 1-D and 2D ILAs. The same algorithms can be easily extended for n-Dimensional Reversible ILAs. | [
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0806.1170 | 1 | Based on analogies with statistical physics and complexity theory, we have developed in the last decade an approach that diagnoses bubbles as transient super-exponential regimes. Here, We present an analysis of oil prices in US dollars and in other major currencies that diagnoses unsustainable faster-than-exponential behavior. This provides evidence that the recent oil price run-up has been amplified by speculative behavior of the type found during a bubble-like expansion. | We present an analysis of oil prices in US and in other major currencies that diagnoses unsustainable faster-than-exponential behavior. This supports the hypothesis that the recent oil price run-up has been amplified by speculative behavior of the type found during a bubble-like expansion. We also attempt to unravel the information hidden in the oil supply-demand data reported by two leading agencies, the US Energy Information Administration (EIA) and the International Energy Agency (IEA). We suggest that the found increasing discrepancy between the EIA and IEA figures provides a measure of the estimation errors. Rather than a clear transition to a supply restricted regime, we interpret the discrepancy between the IEA and EIA as a signature of uncertainty, and there is no better fuel than uncertainty to promote speculation! | [
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0806.2763 | 1 | One approach to studying the URLanization of biochemistry is to use statistical graph theory. Even in such a heavily simplified method, which disregards most of the dynamic aspects of biochemistry, one is faced with fundamental questions, such as how the chemical reaction systems should be reduced to a graph so that as much information as possible about the original network is retained. Vertices may represent either chemical substances, or reactions , or both . A common practice in the analysis of metabolic networks is to preprocess the network by deleting so called currency metabolites -- abundant molecular species that react with a large number of metabolites. One of several reasons to do this is that they do not put any constraint on the reactions, and thus do not give much information of the higher order functionality of the system. In this paper we evaluate different network representations of metabolism and describe their structure with respect to both modularity and currency metabolites . We find that a "substance network," where all metabolites participating in a reaction are connected, is a good trade-off between high functional overlap (between network modules and observed functions ) and a reasonable number of currency metabolites. | One approach to studying the URLanization of biochemistry is to use statistical graph theory. Even in such a heavily simplified method, which disregards most of the dynamic aspects of biochemistry, one is faced with fundamental questions, such as how the chemical reaction systems should be reduced to a graph retaining as much functional information as possible from the original reaction system. In such graph representations, should the edges go between substrates and products, or substrates and substrates , or both ? Should vertices represent substances or reactions? Different definitions encode different information about the reaction system. In this paper we evaluate four different graph representations of metabolism , applied to data from URLanisms and databases. The graph representations are evaluated by comparing the overlap between clusters (network modules) and annotated functions, and also by comparing the set of identified currency metabolites with those that other authors have identified using qualitative biological arguments . We find that a "substance network," where all metabolites participating in a reaction are connected, is relatively better than others, evaluated both with respect to the functional overlap between modules and functions and to the number and identity of identified currency metabolites. | [
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0806.4061 | 1 | In this article we study an optimal stopping/optimal control problem which models the decision facing a risk averse agent over when to sell an asset. The market is incomplete so that the asset exposure cannot be hedged. In addition to the decision over when to sell, the agent has to choose a control strategy which corresponds to a feasible wealth process. We formulate this problem as one involving the choice of a stopping time and a martingale. We conjecture the form of the solution and verify that the candidate solution is equal to the value function. The interesting features of the solution are that it is available in a very explicit form, that for some parameter values the optimal strategy is more sophisticated than might originally be expected, and that although the set-up is based on continuous diffusions, the optimal martingale may involve a jump process. One interpretation of the solution is that it is optimal for the risk averse agent to gamble. | In this article we study an optimal stopping/optimal control problem which models the decision facing a risk-averse agent over when to sell an asset. The market is incomplete so that the asset exposure cannot be hedged. In addition to the decision over when to sell, the agent has to choose a control strategy which corresponds to a feasible wealth process. We formulate this problem as one involving the choice of a stopping time and a martingale. We conjecture the form of the solution and verify that the candidate solution is equal to the value function. The interesting features of the solution are that it is available in a very explicit form, that for some parameter values the optimal strategy is more sophisticated than might originally be expected, and that although the setup is based on continuous diffusions, the optimal martingale may involve a jump process. One interpretation of the solution is that it is optimal for the risk-averse agent to gamble. | [
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0806.4125 | 1 | This paper is a survey of recent progress in the theory of ruin for risk processes that earn investment return on invested assets . | This survey treats the problem of ruin in a risk model when assets earn investment income. In addition to a general presentation of the problem, topics covered are a presentation of the relevant integro-differential equations, exact and numerical solutions, asymptotic results, bounds on the ruin probability and also the possibility of minimizing the ruin probability by investment and possibly reinsurance control. The main emphasis is on continuous time models, but discrete time models are also covered. A fairly extensive list of references is provided, particularly of papers published after 1998. For more references to papers published before that, the reader can consult 47 . | [
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0807.0308 | 1 | Active centres and hot spots of proteins have a paramount importance in enzyme action, protein complex formation and drug design. Recently a number of publications successfully applied the analysis of residue networks to predict active centres in proteins. Most real-world networks show a number of properties, such as small-worldness or scale-free degree distribution, which are rather general features of networks from molecules to the society . Based on extensive analogies I propose that the existing findings and methodology enable us to detect active centres in cells, social networks and ecosystems. Members of these active centres are creative elements of the respective networks, which may help them to survive unprecedented, novel challenges, and play a key role in the development, survival and evolvability of complex systems. | Active centres and hot spots of proteins have a paramount importance in enzyme action, protein complex formation and drug design. Recently a number of publications successfully applied the analysis of residue networks to predict active centres in proteins. Most real-world networks show a number of properties, such as small-worldness or scale-free degree distribution, which are rather general features of networks , from molecules to society at large. Using analogy I propose that existing findings and methodology already enable us to detect active centres in cells, and can be expanded to social networks and ecosystems. Members of these active centres are termed here as creative elements of their respective networks, which may help them to survive unprecedented, novel challenges, and play a key role in the development, survival and evolvability of complex systems. | [
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0807.1823 | 1 | We address two issues that puzzled moral and socio-economic thinking since antiquity. The first of the puzzles is the emergence and selection fitness of altruist behavior in a world of self-reproducing individuals (or capital,etc.; memes in general). The second is the sustainability of growth and the survival in a stochastic world where along with large gains individuals incur often very large and even total losses. We show that the solution for each of these puzzles lies within the other one. It is known that in a multiplicative random process even if in the mathematical evaluation of the expected gain the wins overwhelm the losses, one is likely to be faced with extinction.For example if the probability of a total loss event is arbitrarily small but finite, the measure of histories with non-vanishing gains approaches 0 for asymptotic times >. Thus the optimistic theoretical expectation is dominated by event chains whose probability is too small to happen in reality. We find that in those situations, there is a way to insure self survival. The individuals can insure continuous, unlimited growth by sharing their gains/losses after each step of the random process. We compute the minimal necessary sharing group size Ncrit . Usually, in order to make "sharing" a stable profitable strategy, one has to introduce a credible punishment (/reward) mechanism that can be trusted by the individuals. However, such coercion is incompatible with the concept of real altruism. In a group of Ncrit individuals , defection by one individual leads automatically, thus credibly, to the ruin of the entire group (including the defector) . Consequently sharing becomes the only stable survivalstrategy without the need of any additional enforcing mechanism. This implies the survival and thriving of "altruistic genes" for very long evolutionary periods . | Most of real life systems have a random component: the multitude of endogenous and exogenous factors influencing them result in stochastic fluctuations of the parameters influencing their dynamics. While in the physical systems the random component is usually additive (e.g. molecules can absorb or emit spontaneously energy quanta), in biological, social, economic and financial systems the noise is mainly multiplicative. The special properties of multiplicative noise as opposed to the additive noise have been noticed for a long while. Even though apparently and formally the difference between free additive vs. multiplicative random walks consists in just a move from normal to log-normal distributions, in practice the implications are much more far reaching. In the present paper we study in some detail the difference between the emergence of cooperation in additive vs. multiplicative random environments. While in an additive context the emergence and survival of cooperation requires special conditions (especially some level of reward, punishment, reciprocity), we find that in the multiplicative random context the emergence of cooperation is much more natural and effective. In fact given a set of individuals that play independently and repeatedly a game where they can gain by a factor a>1 with probability p or loose by a factor b<1 with probability q=1-p, one can show that for a^p b^q < 1 < pa +q b the cooperation makes the difference between extinction and (thriving) survival. We study quantitatively the various implications of this observation and its applications in various contexts . | [
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0807.1823 | 2 | Most of real life systems have a random component: the multitude of endogenous and exogenous factors influencing them result in stochastic fluctuations of the parameters influencing their dynamics. While in the physical systems the random component is usually additive (e.g. molecules can absorb or emit spontaneously energy quanta), in biological, social, economic and financial systems the noise is mainly multiplicative . The special properties of multiplicative noise as opposed to the additive noise have been noticed for a long while. Even though apparently and formally the difference between free additive vs. multiplicative random walks consists in just a move from normal to log-normal distributions, in practice the implications are much more far reaching. In the present paper we study in some detail the difference between the emergence of cooperation in additive vs. multiplicative random environments. While in an additive context the emergence and survival of cooperation requires special conditions (especially some level of reward, punishment, reciprocity), we find that in the multiplicative random context the emergence of cooperation is much more natural and effective. In fact given a set of individuals that play independently and repeatedly a game where they can gain by a factor a>1 with probability p or loose by a factor b<1 with probability q=1-p, one can show that for a^p b^q < 1 < pa +q b the cooperation makes the difference between extinction and (thriving) survival. We study quantitatively the various implications of this observation and its applications in various contexts. | Most real life systems have a random component: the multitude of endogenous and exogenous factors influencing them result in stochastic fluctuations of the parameters determining their dynamics. These empirical systems are in many cases subject to noise of multiplicative nature . The special properties of multiplicative noise as opposed to additive noise have been noticed for a long while. Even though apparently and formally the difference between free additive vs. multiplicative random walks consists in just a move from normal to log-normal distributions, in practice the implications are much more far reaching. While in an additive context the emergence and survival of cooperation requires special conditions (especially some level of reward, punishment, reciprocity), we find that in the multiplicative random context the emergence of cooperation is much more natural and effective. We study the various implications of this observation and its applications in various contexts. | [
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0808.0321 | 1 | Constraint-based modelling of metabolic networks often gives rise to a linear programming problem. Mathematically, there always exists a dual to any linear programming problem, with dual variables known as shadow prices. Here we analyse the structure of the dual problem and the properties of the shadow prices, for typical constraint-based metabolic models. We apply our results to a representative set of recent genome-scale metabolic reconstructions. The dual problem is found to have an elegant structure. The shadow prices are to be interpreted as yield coefficients Varma and Palsson, J. theor. Biol. v165, 477; 503 (1993)%DIFDELCMD < ]%%% . In combination with reaction fluxes , they can be used to decorate the metabolic model with a yield flux network. The yield flux network shows a kind of gauge invariance with respect to rescaling of the stoichiometric matrix, and is arguably more fundamental than either the reaction fluxes or shadow prices. Complementary slackness implies that the yield flux network also satisfies a conservation law, which can be used to explain why the shadow prices are strongly correlated with measures of molecular complexity such as molecular weight and atom count. For the genome-scale models , the shadow prices have a broad distribution and the overall pattern reflects the URLanisation of the metabolism . | %DIFDELCMD < ]%%% A metabolic model can be represented as bipartite graph comprising linked reaction and metabolite nodes. Here it is shown how a network of conserved fluxes can be assigned to the edges of such a graph by combining the reaction fluxes with a conserved metabolite property such as molecular weight. A similar flux network can be constructed by combining the primal and dual solutions to the linear programming problem that typically arises in constraint-based modelling. Such constructions may help with the visualisation of flux distributions in complex metabolic networks. The analysis also explains the strong correlation observed between metabolite shadow prices (the dual linear programming variables) and conserved metabolite properties. The methods were applied to recent metabolic models for Escherichia coli, Saccharomyces cerevisiae, and Methanosarcina barkeri. Detailed results are reported for E. coli; similar results were found for the URLanisms . | [
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0808.1431 | 1 | The universal scalability law (USL) of computational capacity is a rational function C_p = P(p)/Q(p) with P(p) a linear polynomial and Q(p) a second-degree polynomial in the number of physical processors p, that has long been used for statistical modeling and prediction of computer system performance. We prove that C_p is equivalent to the synchronous throughput bound for a machine-repairman with state-dependent service rate. Simpler rational functions, such as Amdahl's law and Gustafson speedup, are corollaries of this queue-theoretic bound. C_p is both necessary and sufficient for modeling all practical characteristics of computational scalability. | The universal scalability law of computational capacity is a rational function C_p = P(p)/Q(p) with P(p) a linear polynomial and Q(p) a second-degree polynomial in the number of physical processors p, that has been long used for statistical modeling and prediction of computer system performance. We prove that C_p is equivalent to the synchronous throughput bound for a machine-repairman with state-dependent service rate. Simpler rational functions, such as Amdahl's law and Gustafson speedup, are corollaries of this queue-theoretic bound. C_p is further shown to be both necessary and sufficient for modeling all practical characteristics of computational scalability. | [
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0808.3339 | 1 | By analyzing ] financial time series of exceptional events such as bubbles and crashes, we confirm the existence of nonlinear potential forces in the markets. The shape of the potential function changes rather slowly and smoothly, thereby enabling a statistical prediction of market prices for a limited time range in the mathematical sense. This predictability does not ensure profits, but is expected to be applicable for averting catastrophes . | Basic peculiarities of market price fluctuations are known to be well described by a recently developed random walk model in a temporally deforming quadric potential force whose center is given by a moving average of past price traces Physica A 370, pp91-97, 2006]. By analyzing high-frequency financial time series of exceptional events such as bubbles and crashes, we confirm the appearance of nonlinear potential force in the markets. We show statistical significance of its existence by applying the information criterion. This new time series analysis is expected to be applied widely for detecting a non-stationary symptom in random phenomena . | [
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0809.0241 | 1 | In this paper we propose a novel Bayesian methodology for Value-at-Risk computation based on parametric Product Partition Models. Value-at-Risk is a standard tool to measure and control the market risk of an asset or a portfolio, and it is also required for regulatory purposes. Its popularity is partly due to the fact that it is an easily-understood measure of risk. The use of Product Partition Models allows us to remain in a normal setting , and to obtain a closed-form expression for Value-at-Risk computation. We present and compare two different scenarios: a product partition structure on the vector of means and a product partition structure on the vector of variances. We apply our methodology to an Italian stock market data set from Mib30. The numerical results we present clearly show that Product Partition Models can be successfully exploited in order to quantify market risk exposure. Value-at-Risk estimates we obtain are in full agreement with Maximum Likelihood approaches, but our methodology provides richer information about the clustering structure of the data and the presence of outlying points. | In this paper we propose a novel Bayesian methodology for Value-at-Risk computation based on parametric Product Partition Models. Value-at-Risk is a standard tool to measure and control the market risk of an asset or a portfolio, and it is also required for regulatory purposes. Its popularity is partly due to the fact that it is an easily understood measure of risk. The use of Product Partition Models allows us to remain in a Normal setting even in presence of outlying points , and to obtain a closed-form expression for Value-at-Risk computation. We present and compare two different scenarios: a product partition structure on the vector of means and a product partition structure on the vector of variances. We apply our methodology to an Italian stock market data set from Mib30. The numerical results clearly show that Product Partition Models can be successfully exploited in order to quantify market risk exposure. The obtained Value-at-Risk estimates are in full agreement with Maximum Likelihood approaches, but our methodology provides richer information about the clustering structure of the data and the presence of outlying points. | [
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0809.0739 | 1 | We propose a mathematical framework for the study of a family of random fields - called forward performances - which arise as numerical representation of certain rational preference relations in mathematical finance. Their spatial structure corresponds to that of utility functions, while the temporal one reflects a Nisio-type semigroup property, referred to as self-generation. In the setting of semimartingale financial markets, we provide a dual formulation of self-generation in addition to the original one, and show equivalence between the two, thus giving a dual characterization of forward performances. Then, we focus on random fields with a log-affine structure and provide necessary and sufficient conditions for self-generation in that case. Finally, we illustrate our methods in financial markets driven by It\^o-processes, where we obtain an explicit parametrization of all log-affine forward performances. | We propose a mathematical framework for the study of a family of random fields - called forward performances - which arise as numerical representation of certain rational preference relations in mathematical finance. Their spatial structure corresponds to that of utility functions, while the temporal one reflects a Nisio-type semigroup property, referred to as self-generation. In the setting of semimartingale financial markets, we provide a dual formulation of self-generation in addition to the original one, and show equivalence between the two, thus giving a dual characterization of forward performances. Then, we focus on random fields with a exponential structure and provide necessary and sufficient conditions for self-generation in that case. Finally, we illustrate our methods in financial markets driven by It\^o-processes, where we obtain an explicit parametrization of all log-affine forward performances. | [
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0809.0739 | 2 | We propose a mathematical framework for the study of a family of random fields - called forward performances - which arise as numerical representation of certain rational preference relations in mathematical finance. Their spatial structure corresponds to that of utility functions, while the temporal one reflects a Nisio-type semigroup property, referred to as self-generation. In the setting of semimartingale financial markets, we provide a dual formulation of self-generation in addition to the original one, and show equivalence between the two, thus giving a dual characterization of forward performances. Then , we focus on random fields with a exponential structure and provide necessary and sufficient conditions for self-generation in that case. Finally, we illustrate our methods in financial markets driven by It\^o-processes, where we obtain an explicit parametrization of all log-affine forward performances. | We propose a mathematical framework for the study of a family of random fields--called forward performances--which arise as numerical representation of certain rational preference relations in mathematical finance. Their spatial structure corresponds to that of utility functions, while the temporal one reflects a Nisio-type semigroup property, referred to as self-generation. In the setting of semimartingale financial markets, we provide a dual formulation of self-generation in addition to the original one, and show equivalence between the two, thus giving a dual characterization of forward performances. Then we focus on random fields with an exponential structure and provide necessary and sufficient conditions for self-generation in that case. Finally, we illustrate our methods in financial markets driven by It\^o-processes, where we obtain an explicit parametrization of all exponential forward performances. | [
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0809.1516 | 1 | We construct an estimation and de-noising procedure for an input signal perturbed by a continuous-time Gaussian noise, using the local and occupation times of Gaussian processes. The method relies on the almost-sure minimization of a Stein Unbiased Risk Estimator (SURE ) obtained through integration by parts on Gaussian space, and applied to shrinkage estimators which are constructed by soft and hard thresholding . | Using integration by parts on Gaussian space we construct a Stein Unbiased Risk Estimator (SURE) for the drift of Gaussian processes using their local and occupation times . By almost-sure minimization of the SURE risk of shrinkage estimators we derive an estimation and de-noising procedure for an input signal perturbed by a continuous-time Gaussian noise . | [
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0809.1985 | 1 | Affine term structure models have gained a lot of attention in the finance literature, which is due to their analytic tractability and statistical flexibility. The aim of this article is to present both , theoretical foundations and empirical aspects . Starting from the first short rate models , namely the Vasicek and the Cox-Ingersoll-Ross ones, we then give an overview of some properties of affine processes and explain their relation to affine term structure models. Pricing and estimation techniques are eventually mentioned, showing how the analytic tractability of affine models can be exploited for practical purposes. | Affine term structure models have gained significant attention in the finance literature, mainly due to their analytical tractability and statistical flexibility. The aim of this article is to present both theoretical foundations as well as empirical aspects of the affine model class . Starting from the original one-factor short-rate models of Vasicek and Coxet al, we provide an overview of the properties of regular affine processes and explain their relationship to affine term structure models. Methods for securities pricing and for parameter estimation are also discussed, demonstrating how the analytical tractability of affine models can be exploited for practical purposes. | [
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0809.3405 | 1 | We discuss the valuation problem for a broad spectrum of plain vanilla and path-dependent options in a general modeling framework, and specifically for L\'evy driven models. Among the derivatives which we consider are digitals, double digitals, asset-or-nothing options, self-quantos, lookback and one-touch options. Extensions to the multivariate case, i.e. basket options and options on the minimum or maximum of several assets are considered as well. As a link to credit risk we derive a valuation formula for equity default swaps. The key idea of this Fourier, resp. Laplace transform based approach is the clear separation of two ingredients, namely the payoff function and the underlying process . The latter can be the driving process itself, but also the supremum or infimum or another process derived from it. For L\'evy processes the analytically extended characteristic functions of the supremum and the infimum process are derived . | The aim of this article is to provide a systematic analysis of the conditions such that Fourier transform valuation formulas are valid in a general framework; i.e. when the option has an arbitrary payoff function and depends on the path of the asset price process. An interplay between the conditions on the payoff function and the process arises naturally. We also extend these results to the multi-dimensional case, and discuss the calculation of Greeks by Fourier transform methods. As an application, we price options on the minimum of two assets in L\'evy and stochastic volatility models . | [
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0809.4139 | 1 | One of the key socioeconomic phenomena to explain is the distribution of wealth. Bouchaud and Mezard have proposed an interesting model of economy [Bouchaud and Mezard (2000)] based on trade and investments of agents. In the mean-field approximation, the model produces a stationary wealth distribution with a power-law tail. In this paper we examine characteristic time scales of the model and show that for any finite number of agents, the validity of the mean-field result is time-limited and the model in fact has no stationary wealth distribution. Further analysis suggests that for heterogeneous agents, the limitations are even stronger. We conclude with general implications of the presented results. | One of the key socioeconomic phenomena to explain is the distribution of wealth. Bouchaud and M\'ezard have proposed an interesting model of economy [Bouchaud and M\'ezard (2000)] based on trade and investments of agents. In the mean-field approximation, the model produces a stationary wealth distribution with a power-law tail. In this paper we examine characteristic time scales of the model and show that for any finite number of agents, the validity of the mean-field result is time-limited and the model in fact has no stationary wealth distribution. Further analysis suggests that for heterogeneous agents, the limitations are even stronger. We conclude with general implications of the presented results. | [
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0810.2358 | 1 | Certain short polycations, such as TAT and polyarginine, rapidly pass through cell plasma membranes by an unknown mechanism called transduction. These cell-penetrating peptides (CPPs) when fused to biologically active peptides promise to be medically useful . I offer a simple model in which phosphatidylserines (and possibly other anions) transduce CPPs. The model is consistent with the empirical upper limit on the cargo peptide of about 35 amino acids. More importantly, the model fits experimental data on how the transduction of a polyarginine-fluorophore into mouse C2C12 myoblasts depends on the number of arginines in the CPP and on the CPP concentration . | Certain short polycations, such as TAT and polyarginine, rapidly pass through the plasma membranes of mammalian cells by an unknown mechanism called transduction. These cell-penetrating peptides (CPPs) promise to be medically useful when fused to biologically active peptides . I offer a simple model in which phosphatidylserines transduce CPPs. The model is consistent with the empirical upper limit on the cargo peptide of about 50 amino acids. More importantly, it fits experimental data on how the transduction of a polyarginine-fluorophore into mouse C2C12 myoblasts depends on the number of arginines in the CPP and on the CPP concentration . The model makes two testable predictions . | [
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0810.2358 | 2 | Certain short polycations, such as TAT and polyarginine, rapidly pass through the plasma membranes of mammalian cells by an unknown mechanism called transduction . These cell-penetrating peptides (CPPs) promise to be medically useful when fused to biologically active peptides. I offer a simple model in which phosphatidylserines transduce CPPs . The model is consistent with the empirical upper limit on the cargo peptide of about 50 amino acids . More importantly, it fits experimental data on how the transduction of a polyarginine-fluorophore into mouse C2C12 myoblasts depends on the number of arginines in the CPP and on the CPP concentration. The model makes two testable predictions. | Certain short polycations, such as TAT and polyarginine, rapidly pass through the plasma membranes of mammalian cells by an unknown mechanism called transduction as well as by endocytosis and macropinocytosis . These cell-penetrating peptides (CPPs) promise to be medically useful when fused to biologically active peptides. I offer a simple model in which one or more CPPs and the phosphatidylserines of the inner leaflet form a kind of capacitor with a voltage in excess of 180 mV, high enough to create a molecular electropore . The model is consistent with an empirical upper limit on the cargo peptide of 40--60 amino acids and with experimental data on how the transduction of a polyarginine-fluorophore into mouse C2C12 myoblasts depends on the number of arginines in the CPP and on the CPP concentration. The model makes three testable predictions. | [
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0810.3280 | 1 | Sequence comparison and alignment has had an enormous impact on our understanding of evolution, biology, and disease. It is likely that comparison and alignment of biological networks will similarly revolutionize our understanding of biological systems . Existing network alignments are based largely upon information external to the networks, such as sequence, because purely topological alignment of large, noisy networks is a theoretically challenging problem that has yet to be solved . In this paper, we present the first alignments of large networks based solely upon detailed network topology, and demonstrate that both species phylogeny (the ``tree of life'') and detailed biological function of individual proteins can be extracted from topological comparisons of biological networks. Our phylogenetic trees provide a new and independent source of phylogenetic information. Our alignments are large, dense, and contiguous, suggesting functional predictions of hundreds of currently unannotated proteins. Finally, our alignment of the protein-protein interaction network of two very different species--yeast and human--indicate that even distant species share a surprising amount of network topology with each other, suggesting that there may be broad similarities in internal cellular wiring across all life on Earth. | Sequence comparison and alignment has had an enormous impact on our understanding of evolution, biology, and disease. Comparison and alignment of biological networks will likely have a similar impact . Existing network alignments use information external to the networks, such as sequence, because no good algorithm for purely topological alignment has yet been devised . In this paper, we present by far the most complete topological alignments of biological networks to date. We demonstrate that both species phylogeny and detailed biological function of individual proteins can be extracted from a solely topological comparison of networks. Topological alignments provide an independent new source of phylogenetic information. Our alignment of the protein-protein interaction networks of two very different species--yeast and human--indicate that even distant species share a surprising amount of network topology with each other, suggesting broad similarities in internal cellular wiring across all life on Earth. | [
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0810.3280 | 2 | Sequence comparison and alignment has had an enormous impact on our understanding of evolution, biology, and disease. Comparison and alignment of biological networks will likely have a similar impact. Existing network alignments use information external to the networks, such as sequence, because no good algorithm for purely topological alignment has yet been devised. In this paper, we present by far the most complete topological alignments of biological networks to date. We demonstrate that both species phylogeny and detailed biological function of individual proteins can be extracted from a solely topological comparison of networks. Topological alignments provide an independent new source of phylogenetic information. Our alignment of the protein-protein interaction networks of two very different species--yeast and human--indicate that even distant species share a surprising amount of network topology with each other, suggesting broad similarities in internal cellular wiring across all life on Earth. | Sequence comparison and alignment has had an enormous impact on our understanding of evolution, biology, and disease. Comparison and alignment of biological networks will likely have a similar impact. Existing network alignments use information external to the networks, such as sequence, because no good algorithm for purely topological alignment has yet been devised. In this paper, we present a novel algorithm based solely on network topology, that can be used to align any two networks. We apply it to biological networks to produce by far the most complete topological alignments of biological networks to date. We demonstrate that both species phylogeny and detailed biological function of individual proteins can be extracted from our alignments. Topology-based alignments have the potential to provide a completely new, independent source of phylogenetic information. Our alignment of the protein-protein interaction networks of two very different species--yeast and human--indicate that even distant species share a surprising amount of network topology with each other, suggesting broad similarities in internal cellular wiring across all life on Earth. | [
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0810.5146 | 1 | It turns out that a slightly generalised Margrabe formula exhibits symmetry properties leading to semi-static hedges of rather general options in the bivariate Black-Scholes economy . In order to increase the liquidity of the used hedging instruments for currency options, the duality principle can be used to set up the hedges in a foreign market by using only European vanilla options sometimes along with a risk-less bond. Since the semi-static hedges in the Black-Scholes economy are exact, a closed form valuation formula of a certain weighted barrier swap-option can be easily derived. | It turns out that in the bivariate Black-Scholes economy Margrabe type options exhibit symmetry properties leading to semi-static hedges of rather general barrier options. Some of the results are extended to variants obtained by means of Brownian subordination . In order to increase the liquidity of the hedging instruments for certain currency options, the duality principle can be applied to set up hedges in a foreign market by using only European vanilla options sometimes along with a risk-less bond. Since the semi-static hedges in the Black-Scholes economy are exact, closed form valuation formulas for certain barrier options can be easily derived. | [
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0811.1296 | 1 | The problem of inhibiting viral DNA ejection from bacteriophages by Mg^{+2} counterions is studied. Experimentally, it is known that Mg^{+2 has a strong and non-monotonic effect on the amount of DNA ejected. There exists an optimal Mg^{+2 concentration at which the least DNA is ejected from the virus. At lower or higher concentrations, more DNA is ejected from the capsid. We propose that this phenomenon is the result of DNA overcharging by Mg^{+2} multivalent counterions. As Mg^{+2} concentration increases from zero, DNA net charge changes from negative to positive. The optimal inhibition corresponds to the Mg^{+2} concentration where DNA is neutral. At lower/higher concentrations, DNA genome is charged. It prefers to be in solution to lower its electrostatic self-energy, which consequently leads to an increase in DNA ejection. Our theory fits experimental data well. The strength of DNA-DNA short range attraction, mediated by Mg^{+2}, is found to be -0.003 k_BT per nucleotide base. | The problem of inhibiting viral DNA ejection from bacteriophages by multivalent counterions, especially Mg^{+2} counterions , is studied. Experimentally, it is known that MgSO_4 salt has a strong and non-monotonic effect on the amount of DNA ejected. There exists an optimal concentration at which the least DNA is ejected from the virus. At lower or higher concentrations, more DNA is ejected from the capsid. We propose that this phenomenon is the result of DNA overcharging by Mg^{+2} multivalent counterions. As Mg^{+2} concentration increases from zero, DNA net charge changes from negative to positive. The optimal inhibition corresponds to the Mg^{+2} concentration where DNA is neutral. At lower/higher concentrations, DNA genome is charged. It prefers to be in solution to lower its electrostatic self-energy, which consequently leads to an increase in DNA ejection. Our theory fits experimental data well. The strength of DNA-DNA short range attraction, mediated by Mg^{+2}, is found to be -0.003 k_BT per nucleotide base. | [
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0811.1296 | 2 | The problem of inhibiting viral DNA ejection from bacteriophages by multivalent counterions, especially Mg^{+2} counterions, is studied. Experimentally, it is known that MgSO_4 salt has a strong and non-monotonic effect on the amount of DNA ejected. There exists an optimal concentration at which the least DNA is ejected from the virus. At lower or higher concentrations, more DNA is ejected from the capsid. We propose that this phenomenon is the result of DNA overcharging by Mg^{+2} multivalent counterions. As Mg^{+2} concentration increases from zero, DNA net charge changes from negative to positive. The optimal inhibition corresponds to the Mg^{+2} concentration where DNA is neutral. At lower/higher concentrations, DNA genome is charged. It prefers to be in solution to lower its electrostatic self-energy, which consequently leads to an increase in DNA ejection. Our theory fits experimental datawell. The strength of DNA-DNA short range attraction , mediated by Mg^{+2}, is found to be -0.004 k_BT per nucleotide base . | The problem of inhibiting viral DNA ejection from bacteriophages by multivalent counterions, specifically Mg^{+2} counterions, is studied. Experimentally, it is known that MgSO_4 salt has a strong and non-monotonic effect on the amount of DNA ejected. There exists an optimal concentration at which the minimum amount of DNA is ejected from the virus. At lower or higher concentrations, more DNA is ejected from the capsid. We propose that this phenomenon is the result of DNA overcharging by Mg^{+2} multivalent counterions. As Mg^{+2} concentration increases from zero, the net charge of DNA changes from negative to positive. The optimal inhibition corresponds to the Mg^{+2} concentration where DNA is neutral. At lower/higher concentrations, DNA genome is charged. It prefers to be in solution to lower its electrostatic self-energy, which consequently leads to an increase in DNA ejection. By fitting our theory to available experimental data, the strength of DNA-DNA short range attraction energies , mediated by Mg^{+2}, is found to be -0.004 k_BT per nucleotide base . This and other fitted parameters agree well with known values from other experiments and computer simulations. The parameters are also in aggreement qualitatively with values for tri- and tetra-valent counterions . | [
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0811.2209 | 1 | Complex systems are often modeled as Boolean networks in attempts to capture their logical structure and reveal its dynamical consequences. Approximating the dynamics of continuous variables by discrete values and Boolean logic gates may, however, introduce dynamical possibilities that are not accessible to the original system. We show that large random networks of variables coupled through continuous transfer functions often fail to exhibit the complex dynamics of corresponding Boolean models in the disordered (chaotic) regime, even when each individual function appears to be a good candidate for Boolean idealization. A simple criterion identifies continuous systems that exhibit the full dynamical range of their Boolean counterparts. Transfer functions inferred from the literature on transcriptional regulation of genes do not satisfy the criterion . | Complex systems are often modeled as Boolean networks in attempts to capture their logical structure and reveal its dynamical consequences. Approximating the dynamics of continuous variables by discrete values and Boolean logic gates may, however, introduce dynamical possibilities that are not accessible to the original system. We show that large random networks of variables coupled through continuous transfer functions often fail to exhibit the complex dynamics of corresponding Boolean models in the disordered (chaotic) regime, even when each individual function appears to be a good candidate for Boolean idealization. A suitably modified Boolean theory explains the behavior of systems in which information does not propagate faithfully down certain chains of nodes. Model networks incorporating calculated or directly measured transfer functions reported in the literature on transcriptional regulation of genes are described by the modified theory . | [
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0811.3130 | 1 | The creation and annihilation of money and its economic effects are reviewed. Economic values appear "in the mind" of the market participants; e. g., by pretending, maintaining and achieving a particular price for a certain asset. Upon its creation by banks, this kind of " value phantasy " is converted into " real money " often in terms of buyer's debtaccompanied by a simultaneous payment of fiat money to the seller. This money is then multiplied on the money market and is competing against other money supplies for the traded assets, goods and services, where it may cause dilution, inflation and reallocation of resources . | General options for monetary systems, in particular the creation of fiat money, as well as its appropriation in various setups is discussed. We identify private banks as the main source of money through monetization. The asset value is inevitably determined by subjective beliefs and fantasies loosely bound by market constraints. One may imagine such a monetary system as being " suspended in belief. " Inevitably, the interest levied by banks in return for money created via monetizing debt systematically reallocates resources towards the financial institutions, and away from industrial and manual production, farming and labor. Unfortunately, the alternatives appear to be even more troublesome than the present state of affairs. Any system based on interest-free fiat money creation, in order to avoid hyperinflation through excessive borrowing of " free" debt, has either to rely on unjustifiable privileges or chance. And any system based on commodity money such as the gold or silver standard instead of fiat money creation is heavily depending on the quantity of commodities, and also incapable of waging or defending against war through the effective monetization of future loot or loss . | [
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0811.3130 | 2 | General options for monetary systems, in particular the creation of fiat money, as well as its appropriation in various setups is discussed. We identify private banks as the main source of money through monetization . The asset value is inevitably determined by subjective beliefs and fantasies loosely bound by market constraints. One may imagine such a monetary system as being "suspended in belief." Inevitably, the interest levied by banks in return for money created via monetizing debt systematically reallocates resources towards the financial institutions, and away from industrial and manual production, farming and labor. Unfortunately, the alternatives appear to be even more troublesome than the present state of affairs. Any system based on interest-free fiat money creation, in order to avoid hyperinflation through excessive borrowing of "free" debt, has either to rely on unjustifiable privileges or chance. And any system based on commodity money such as the gold or silver standard instead of fiat money creation is heavily depending on the quantity of commodities, and also incapable of waging or defending against war through the effective monetization of future loot or loss. | General options for monetary systems, in particular the creation of fiat money, as well as its appropriation in various setups is discussed. We identify private banks as the main source of money through monetization of assets and future profits . The asset value is determined by subjective beliefs and fantasies loosely bound by market constraints. One may imagine such a monetary system as being "suspended in belief." The interest levied by banks in return for money created via monetizing future profits systematically reallocates resources towards the financial institutions, and away from industrial and manual production, farming and labor. Unfortunately, the alternatives appear to be even more troublesome than the present state of affairs. Any system based on interest-free fiat money creation, in order to avoid hyperinflation through excessive borrowing of "free" debt, has either to rely on unjustifiable privileges or chance. And any system based on commodity instead of fiat money is heavily depending on the quantity of commodities, and also incapable of waging or defending against war through the effective monetization of future loot or loss. | [
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0811.3130 | 3 | General options for monetary systems, in particular the creation of fiat money, as well as its appropriation in various setups is discussed. We identify private banks as the main source of money through monetization of assets and future profits. The asset value is determined by subjective beliefs and fantasies loosely bound by market constraints. One may imagine such a monetary system as being "suspended in belief ." The interest levied by banks in return for money created via monetizing future profits systematically reallocates resources towards the financial institutions, and away from industrial and manual production, farming and labor. Unfortunately, the alternatives appear to be even more troublesome than the present state of affairs. Any system based on interest-free fiat money creation, in order to avoid hyperinflation through excessive borrowing of "free" debt, has either to rely on unjustifiable privileges or chance. And any system based on commodity instead of fiat money is heavily depending on the quantity of commodities, and also incapable of waging or defending against war through the effective monetization of future loot or loss. | General options for monetary systems, in particular the creation of fiat money, as well as its appropriation in various setups are discussed. We identify private banks as the main source of money through monetization of assets and future profits. The asset value is determined by subjective confidence, beliefs and fantasies loosely bound by market constraints. One may imagine such a monetary system as being "suspended in thought ." Interest levied by banks in return for money created via monetizing future profits systematically reallocates resources toward the financial institutions, and away from industrial and manual production, farming and labor. Unfortunately, the alternatives appear to be even more troublesome than the present state of affairs. Any system based on interest-free fiat money creation, in order to avoid hyperinflation through excessive borrowing of "free" debt, has either to rely on unjustifiable privileges or chance. And any system based on commodity instead of fiat money is heavily depending on the quantity of commodities, and also incapable of waging or defending against war through the effective monetization of future loot or loss. | [
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0811.3130 | 4 | General options for monetary systems, in particular the creation of fiat money, as well as its appropriation in various setups are discussed. We identify private banks as the main source of money through monetization of assets and future profits. The asset value is determined by subjective confidence, beliefs and fantasies loosely bound by market constraints. One may imagine such a monetary system as being "suspended in thought . " Interest levied by banks in return for money created via monetizing future profits systematically reallocates resources toward the financial institutions, and away from industrial and manual production, farming and labor. Unfortunately, the alternatives appear to be even more troublesome than the present state of affairs. Any system based on interest-free fiat money creation, in order to avoid hyperinflation through excessive borrowing of "free" debt, has either to rely on unjustifiable privileges or chance. And any system based on commodity instead of fiat money is heavily depending on the quantity of commodities, and also incapable of waging or defending against war through the effective monetization of future loot or loss. | Because of their provable indeterminateness, certain economic values and thus prices are fixed by subjective confidence, beliefs and fantasies loosely bound by market constraints. One may imagine such a monetary system as being "suspended in thought ". Monetization of " (derivative) promises" of any kind, as well as interest levied by banks in return for money created via monetizing future profits systematically reallocates resources toward the financial institutions, and away from industrial and manual production, farming and labor. Unfortunately, the alternatives appear to be even more troublesome than the present state of affairs. Any system based on interest-free fiat money creation, in order to avoid hyperinflation through excessive borrowing of "free" debt, has either to rely on unjustifiable privileges or chance. And any system based on commodity instead of fiat money is heavily depending on the quantity of commodities, and also incapable of waging or defending against war through the effective monetization of future loot or loss. | [
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0811.3130 | 5 | Because of their provable indeterminateness, certain economic values and thus prices are fixed by subjective confidence, beliefs and fantasies loosely bound by market constraints. One may imagine such a monetary system as being " suspended in thought " . Monetization of " (derivative) promises " of any kind, as well as interest levied by banks in return for money created via monetizing future profits systematically reallocates resources toward the financial institutions, and away from industrial and manual production, farming and labor. Unfortunately, the alternatives appear to be even more troublesome than the present state of affairs. Any system based on interest-free fiat money creation , in order to avoid hyperinflation through excessive borrowing of "free" debt, has either to rely on unjustifiable privileges or chance. And any system based on commodity instead of fiat money is heavily depending on the quantity of commodities, and also incapable of waging or defending against war through the effective monetization of future loot or loss . | This review is about the convenience, the benefits, as well as the destructive capacities of money. It deals with various aspects of money creation, with its value, and its appropriation. All sorts of money tend to get corrupted by eventually creating too much of them. In the long run, this renders money worthless and deprives people holding it. This misuse of money creation is inevitable and should come as no surprise. Abusive money creation comes in various forms. In the present fiat money system " suspended in free thought " and sustained merely by our belief in and our conditioning to it, money is conveniently created out of " thin air " by excessive government spending and speculative credit creation. Alas, any too tight money supply could ruin an economy by inviting all sorts of unfriendly takeovers, including wars or competition. Therefore the ambivalence of money as benefactor and destroyer should be accepted as destiny . | [
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0812.0033 | 1 | A financial market model with general semimartingale asset-price processes and where agents can only trade using no-short-sale strategies is considered. We show that wealth processes using continuous trading can be approximated very closely by wealth processes using simple combinations of buy-and-hold trading. This approximation is based on controlling the proportions of wealth invested in the assets. As an application, the utility maximization problem is considered and it is shown that optimal utilities and wealth processes resulting from continuous trading can be approximated arbitrarily well by the use of simple combinations of buy-and-hold strategies. | A financial market model with general semimartingale asset-price processes and where agents can only trade using no-short-sales strategies is considered. We show that wealth processes using continuous trading can be approximated very closely by wealth processes using simple combinations of buy-and-hold trading. This approximation is based on controlling the proportions of wealth invested in the assets. As an application, the utility maximization problem is considered and it is shown that optimal expected utilities and wealth processes resulting from continuous trading can be approximated arbitrarily well by the use of simple combinations of buy-and-hold strategies. | [
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0812.0325 | 1 | The analysis of network topology and dynamics is increasingly used for the description of the structure, function and evolution of complex systems. Here we summarize key aspects of the evolvability and robustness of the hierarchical network-set of macromolecules, URLanisms, and ecosystems. Listing the costs and benefits of cooperation as a necessary behaviour to build this network hierarchy, we outline the major hypothesis of the paper: the emergence of hierarchical complexity needs cooperation leading to the ageing of the constituent networks. Local cooperation in a stable environment may lead to over-optimization developing an always-old network, which ages slowly , and dies in an apoptosis-like process. Global cooperation by exploring a rapidly changing environment may cause an occasional over-perturbation exhausting system-resources, causing rapid degradation, ageing and death of an otherwise forever-young network in a necrosis-like process. Giving a number of examples we explain how local and global cooperation can both evoke and help successful ageing. Finally, we show how various forms of cooperation and consequent ageing emerge as key elements in all major steps of evolution from the formation of protocells to the establishment of the globalized, modern human society . Thus, ageing emerges as a price of complexity, which is going hand-in-hand with cooperation enhancing each other in a successful community . | The network concept is increasingly used for the description of complex systems. Here we summarize key aspects of the evolvability and robustness of the hierarchical network-set of macromolecules, URLanisms, and ecosystems. Listing the costs and benefits of cooperation as a necessary behaviour to build this network hierarchy, we outline the major hypothesis of the paper: the emergence of hierarchical complexity needs cooperation leading to the ageing (i.e. gradual deterioration) of the constituent networks. A stable environment develops cooperation leading to over-optimization , and forming an " always-old " network, which accumulates damage , and dies in an apoptosis-like process. A rapidly changing environment develops competition forming a "forever-young" network, which may suffer an occasional over-perturbation exhausting system-resources, and causing death in a necrosis-like process. Giving a number of examples we demonstrate how cooperation evokes the gradual accumulation of damage typical to ageing. Finally, we show how various forms of cooperation and consequent ageing emerge as key elements in all major steps of evolution from the formation of protocells to the establishment of the globalized, modern human society . | [
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0812.2066 | 1 | Actin networks in certain URLanisms exhibit a complex pattern-forming dynamics that starts with the appearance of static `spots ' of actin on the cell cortex. Spots soon become mobile, and eventually give rise to , and coexist with, traveling waves of actin. Waves confer motility upon the cell by impinging on its periphery. Here we describe a possible physical mechanism for this distinctive set of dynamic transformations . Starting from the observation that excitable reaction-diffusion models of chemical systems can describe both localized spots and traveling waves, we augment one such model with a variable describing the spatial orientation of its chief constituent . We consider this constituent to be a caricature of polymerized actin, and regard its orientation as a measure of local actin fiber alignment. This spatial anisotropy, which is not possessed by conventional chemical species, profoundly affects localized structures to drive a transformation at fixed parameter values from static spots to moving spots to waves. | Actin networks in certain URLanisms exhibit a complex pattern-forming dynamics that starts with the appearance of static spots of actin on the cell cortex. Spots soon become mobile, executing persistent random walks, and eventually give rise to traveling waves of actin. Here we describe a possible physical mechanism for this distinctive set of dynamic transformations , by equipping an excitable reaction-diffusion model with a field describing the spatial orientation of its chief constituent (which we consider to be actin). The interplay of anisotropic actin growth and spatial inhibition drives a transformation at fixed parameter values from static spots to moving spots to waves. | [
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0812.2440 | 1 | We extend the model of liquidity risk of Cetin et al. 5 to allow for price impacts. Starting from simple principles, we show that the impact of a trade on prices is directly proportional to the size of the transaction and the amount of liquidityof the asset. This leads to a new characterization of self-financing trading strategies and a sufficient condition for no arbitrage. We show that, with the use of volatility swaps, contingent claims whose payoffs depend on the value of the asset can be approximately replicated . The replicating costs of such payoffs are obtained from the solutions of BSDEs with | We extend a linear version of the liquidity risk model of Cetin et al. (2004) to allow for price impacts. We show that the impact of a market order on prices depends on the size of the transaction and the level of liquidity. We obtain a simple characterization of self-financing trading strategies and a sufficient condition for no arbitrage. We consider a stochastic volatility model in which the volatility is partly correlated with the liquidity process and show that, with the use of variance swaps, contingent claims whose payoffs depend on the value of the asset can be approximately replicated in this setting . The replicating costs of such payoffs are obtained from the solutions of BSDEs with quadratic growth and analytical properties of these solutions are investigated. | [
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