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Functional macroscopic behavior of weighted random ball model ; We consider a generalization of the weighted random ball model. The model is driven by a random Poisson measure with a product heavy tailed intensity measure. Such a model typically represents the transmission of a network of stations with a fading effect. In a previous article, the authors proved the convergence of the finitedimensional distributions of related generalized random fields under various scalings and in the particular case when the fading function is the indicator function of the unit ball. In this paper, tightness and functional convergence are investigated. Using suitable moment estimates, we prove functional convergences for some parametric classes of configurations under the socalled large ball scaling and intermediate ball scaling. Convergence in the space of distributions is also discussed. |
Developing Experimental Models for NASA Missions with ASSL ; NASA's new age of space exploration augurs great promise for deep space exploration missions whereby spacecraft should be independent, autonomous, and smart. Nowadays NASA increasingly relies on the concepts of autonomic computing, exploiting these to increase the survivability of remote missions, particularly when human tending is not feasible. Autonomic computing has been recognized as a promising approach to the development of selfmanaging spacecraft systems that employ onboard intelligence and rely less on control links. The Autonomic System Specification Language ASSL is a framework for formally specifying and generating autonomic systems. As part of longterm research targeted at the development of models for space exploration missions that rely on principles of autonomic computing, we have employed ASSL to develop formal models and generate functional prototypes for NASA missions. This helps to validate features and perform experiments through simulation. Here, we discuss our work on developing such missions with ASSL. |
On the L2metric of vortex moduli spaces ; We derive general expressions for the Kaehler form of the L2metric in terms of standard 2forms on vortex moduli spaces. In the case of abelian vortices in gauged linear sigmamodels, this allows us to compute explicitly the Kaehler class of the L2metric. As an application we compute the total volume of the moduli space of abelian semilocal vortices. In the strong coupling limit, this then leads to conjectural formulae for the volume of the space of holomorphic maps from a compact Riemann surface to projective space. Finally we show that the localization results of Samols in the abelian Higgs model extend to more general models. These include linear nonabelian vortices and vortices in gauged toric sigmamodels. |
Coexistence and invasibility in a twospecies competition model with habitatpreference ; The outcome of competition among species is influenced by the spatial distribution of species and effects such as demographic stochasticity, immigration fluxes, and the existence of preferred habitats. We introduce an individualbased model describing the competition of two species and incorporating all the above ingredients. We find that the presence of habitat preference generating spatial niches strongly stabilizes the coexistence of the two species. Eliminating habitat preference neutral dynamics the model generates patterns, such as distribution of population sizes, practically identical to those obtained in the presence of habitat preference, provided an higher immigration rate is considered. Notwithstanding the similarity in the population distribution, we show that invasibility properties depend on habitat preference in a nontrivial way. In particular, the neutral model results results more invasible or less invasible depending on whether the comparison is made at equal immigration rate or at equal distribution of population size, respectively. We discuss the relevance of these results for the interpretation of invasibility experiments and the species occupancy of preferred habitats. |
New Model of Inflation with Nonminimal Derivative Coupling of Standard Model Higgs Boson to Gravity ; In this letter we show that there is a unique nonminimal derivative coupling of the Standard Model Higgs boson to gravity such that it propagates no more degrees of freedom than General Relativity sourced by a scalar field, reproduces a successful inflating background within the Standard Model Higgs parameters and, finally, does not suffer from dangerous quantum corrections. |
Selforganized model of cascade spreading ; We study simultaneous price drops of real stocks and show that for high drop thresholds they follow a powerlaw distribution. To reproduce these collective downturns, we propose a minimal selforganized model of cascade spreading based on a probabilistic response of the system elements to stress conditions. This model is solvable using the theory of branching processes and the meanfield approximation. For a wide range of parameters, the system is in a critical state and displays a powerlaw cascadesize distribution similar to the empirically observed one. We further generalize the model to reproduce volatility clustering and other observed properties of real stocks. |
Entropic cosmology a unified model of inflation and latetime acceleration ; Holography is expected as one of the promising descriptions of quantum general relativity. We present a model for a cosmological system involving two holographic screens and find that their equilibrium exactly yields a standard FriedmannRobertsonWalker universe. We discuss its cosmological implications by taking into account higher order quantum corrections and quantum nature of horizon evaporation. We will show that this model could give rise to a holographic inflation at high energy scales and realize a latetime acceleration in a unified approach. We test our model from the SN Ia observations and find it can give a nice fit to the data. |
Limit theorems for a general stochastic rumour model ; We study a general stochastic rumour model in which an ignorant individual has a certain probability of becoming a stifler immediately upon hearing the rumour. We refer to this special kind of stifler as an uninterested individual. Our model also includes distinct rates for meetings between two spreaders in which both become stiflers or only one does, so that particular cases are the classical DaleyKendall and MakiThompson models. We prove a Law of Large Numbers and a Central Limit Theorem for the proportions of those who ultimately remain ignorant and those who have heard the rumour but become uninterested in it. |
Matrix model version of AGT conjecture and generalized Selberg integrals ; Operator product expansion OPE of two operators in twodimensional conformal field theory includes a sum over Virasoro descendants of other operator with universal coefficients, dictated exclusively by properties of the Virasoro algebra and independent of choice of the particular conformal model. In the free field model, these coefficients arise only with a special conservation relation imposed on the three dimensions of the operators involved in OPE. We demonstrate that the coefficients for the three unconstrained dimensions arise in the free field formalism when additional DotsenkoFateev integrals are inserted between the positions of the two original operators in the product. If such coefficients are combined to form an npoint conformal block on Riemann sphere, one reproduces the earlier conjectured betaensemble representation of conformal blocks, thus proving this matrix model version of the celebrated AGT relation. The statement can also be regarded as a relation between the 3jsymbols of the Virasoro algebra and the slightly generalized Selberg integrals IY, associated with arbitrary Young diagrams. The conformal blocks are multilinear combinations of such integrals and the remaining part of the original AGT conjecture relates them to the Nekrasov functions which have exactly the same structure. |
A General Simulation Framework for Supply Chain Modeling State of the Art and Case Study ; Nowadays there is a large availability of discrete event simulation software that can be easily used in different domains from industry to supply chain, from healthcare to business management, from training to complex systems design. Simulation engines of commercial discrete event simulation software use specific rules and logics for simulation time and events management. Difficulties and limitations come up when commercial discrete event simulation software are used for modeling complex real worldsystems i.e. supply chains, industrial plants. The objective of this paper is twofold first a state of the art on commercial discrete event simulation software and an overview on discrete event simulation models development by using general purpose programming languages are presented; then a Supply Chain Order Performance Simulator SCOPS, developed in C for investigating the inventory management problem along the supply chain under different supply chain scenarios is proposed to readers. |
Observational constraint on generalized Chaplygin gas model ; We investigate observational constraints on the generalized Chaplygin gas GCG model as the unification of dark matter and dark energy from the latest observational data the Union SNe Ia data, the observational Hubble data, the SDSS baryon acoustic peak and the fiveyear WMAP shift parameter. It is obtained that the best fit values of the GCG model parameters with their confidence level are As0.730.060.06 1sigma 0.090.09 2sigma, alpha0.090.150.12 1sigma 0.260.19 2sigma. Furthermore in this model, we can see that the evolution of equation of state EOS for dark energy is similar to quiessence, and its current bestfit value is w0de0.96 with the 1sigma confidence level 0.91geq w0degeq1.00. |
Hydrodynamics of inelastic Maxwell models ; An overview of recent results pertaining to the hydrodynamic description both Newtonian and nonNewtonian of granular gases described by the Boltzmann equation for inelastic Maxwell models is presented. The use of this mathematical model allows us to get exact results for different problems. First, the NavierStokes constitutive equations with explicit expressions for the corresponding transport coefficients are derived by applying the ChapmanEnskog method to inelastic gases. Second, the nonNewtonian rheological properties in the uniform shear flow USF are obtained in the steady state as well as in the transient unsteady regime. Next, an exact solution for a special class of Couette flows characterized by a uniform heat flux is worked out. This solution shares the same rheological properties as the USF and, additionally, two generalized transport coefficients associated with the heat flux vector can be identified. Finally, the problem of small spatial perturbations of the USF is analyzed with a ChapmanEnskoglike method and generalized tensorial transport coefficients are obtained. |
Critical interfaces of the AshkinTeller model at the parafermionic point ; We present an extensive study of interfaces defined in the Z4 spin lattice representation of the AshkinTeller AT model. In particular, we numerically compute the fractal dimensions of boundary and bulk interfaces at the FateevZamolodchikov point. This point is a special point on the selfdual critical line of the AT model and it is described in the continuum limit by the Z4 parafermionic theory. Extending on previous analytical and numerical studies 10,12, we point out the existence of three different values of fractal dimensions which characterize different kind of interfaces. We argue that this result may be related to the classification of primary operators of the parafermionic algebra. The scenario emerging from the studies presented here is expected to unveil general aspects of geometrical objects of critical AT model, and thus of c1 critical theories in general. |
GRB spectral parameters within the fireball model ; Fireball model of the GRBs predicts generation of numerous internal shocks, which then efficiently accelerate charged particles and generate magnetic and electric fields. These fields are produced in the form of relatively smallscale stochastic ensembles of waves, thus, the accelerated particles diffuse in space due to interaction with the random waves and so emit so called Diffusive Synchrotron Radiation DSR in contrast to standard synchrotron radiation they would produce in a largescale regular magnetic fields. In this paper we present first results of comprehensive modeling of the GRB spectral parameters within the fireballinternal shock concept. We have found that the nonperturbative DSR emission mechanism in a strong random magnetic field is consistent with observed distributions of the Band parameters and also with crosscorrelations between them; this analysis allowed to restrict GRB physical parameters from the requirement of consistency between the model and observed distributions. |
The SUSY Higgs Mass the Singlet Saves the Day ; We present a generalization of the NexttoMinimal Supersymmetric Standard Model NMSSM, with an explicit muterm and a supersymmetric mass for the singlet superfield, as a route to alleviating the little hierarchy problem of the Minimal Supersymmetric Standard Model MSSM. Though this model does not address the muproblem of the MSSM, we are able to generate masses for the lightest neutral Higgs boson up to 140 GeV with top squarks below the TeV scale, all couplings perturbative to the gauge unification scale, and with no need to fine tune parameters in the scalar potential. This model, which we call the SMSSM, more closely resembles the MSSM phenomenologically than the NMSSM as usually defined. |
Inequality reversal effects of the savings propensity and correlated returns ; In the last decade, a large body of literature has been developed to explain the universal features of inequality in terms of income and wealth. By now, it is established that the distributions of income and wealth in various economies show a number of statistical regularities. There are several models to explain such static features of inequality in an unifying framework and the kinetic exchange models, in particular, provide one such framework. Here we focus on the dynamic features of inequality. In the process of development and growth, inequality in an economy in terms of income and wealth follows a particular pattern of rising in the initial stage followed by an eventual fall. This inverted Ushaped curve is known as the Kuznets Curve. We examine the possibilities of such behavior of an economy in the context of a generalized kinetic exchange model. It is shown that under some specific conditions, our model economy indeed shows inequality reversal. |
Stability of the Einstein Static Universe in open cosmological models ; The stability properties of the Einstein Static solution of General Relativity are altered when corrective terms arising from modification of the underlying gravitational theory appear in the cosmological equations. In this paper the existence and stability of static solutions are considered in the framework of two recently proposed quantum gravity models. The previously known analysis of the Einstein Static solutions in the semiclassical regime of Loop Quantum Cosmology with modifications to the gravitational sector is extended to open cosmological models where a static neutrally stable solution is found. A similar analysis is also performed in the framework of HoravaLifshitz gravity under detailed balance and projectability conditions. In the case of open cosmological models the two solutions found can be either unstable or neutrally stable according with the admitted values of the parameters. |
Smooth double critical state theory for typeII superconductors ; Several aspects of the general theory for the critical states of a vortex lattice and the magnetic flux dynamics in typeII superconductors are examined by a direct variational optimisation method and widespread physical principles. Our method allows to unify a number of conventional models describing the complex vortex configurations in the critical state regime. Special attention is given to the discussion of the relation between the fluxline cutting mechanism and the depinning threshold limitation. This is done by using a smooth double critical state concept which incorporates the socalled isotropic, elliptical, T and CT models as welldefined limits of our general treatment. Starting from different initial configurations for a superconducting slab in a 3D magnetic field, we show that the predictions of the theory range from the collapse to zero of transverse magnetic moments in the isotropic model, to nearly force free configurations in which paramagnetic values can arbitrarily increase with the applied field for magnetically anisotropic current voltage laws. Noteworthily, the differences between the several model predictions are minimal for the low applied field regime. |
Quintessential Phenomena in Higher Dimensional Space Time ; The higher dimensional cosmology provides a natural setting to treat, at a classical level, the cosmological effects of vacuum energy. Here we discuss two situations where starting with an ordinary matter field without any equation of state we end up with a Chaplygin type of gas apparently as a consequence of extra dimensions. In the second case we study the quintessential phenomena in higher dimensional spacetime with the help of a Chaplygin type of matter field. The first case suffers from the disqualification that no dimensional reduction occurs, which is, however, rectified in the second case. Both the models show the sought after feature of occurrence of emphflip in the rate of expansion. It is observed that with the increase of dimensions the occurrence of emphflip is delayed for both the models, more in line with current observational demands. Interestingly we see that depending on some initial conditions our model admits QCDM, LambdaCDM and also Phantom like evolution within a unified framework. Our solutions are general in nature in the sense that when the extra dimensions are switched off the known 4D model is recovered. |
Gestion efficace de series temporelles en P2P Application a l'analyse technique et l'etude des objets mobiles ; In this paper, we propose a simple generic model to manage time series. A time series is composed of a calendar with a typed value for each calendar entry. Although the model could support any kind of XML typed values, in this paper we focus on real numbers, which are the usual application. We define basic vector space operations plus, minus, scale, and also relationallike and application oriented operators to manage time series. We show the interest of this generic model on two applications i a stock investment helper; ii an ecological transport management system. Stock investment requires windowbased operations while trip management requires complex queries. The model has been implemented and tested in PHP, Java, and XQuery. We show benchmark results illustrating that the computing of 5000 series of over 100.000 entries in length common requirements for both applications is difficult on classical centralized PCs. In order to serve a community of users sharing time series, we propose a P2P implementation of time series by dividing them in segments and providing optimized algorithms for operator expression computation. |
A generalized Multipletry Metropolis version of the Reversible Jump algorithm ; The Reversible Jump algorithm is one of the most widely used Markov chain Monte Carlo algorithms for Bayesian estimation and model selection. A generalized multipletry version of this algorithm is proposed. The algorithm is based on drawing several proposals at each step and randomly choosing one of them on the basis of weights selection probabilities that may be arbitrary chosen. Among the possible choices, a method is employed which is based on selection probabilities depending on a quadratic approximation of the posterior distribution. Moreover, the implementation of the proposed algorithm for challenging model selection problems, in which the quadratic approximation is not feasible, is considered. The resulting algorithm leads to a gain in efficiency with respect to the Reversible Jump algorithm, and also in terms of computational effort. The performance of this approach is illustrated for real examples involving a logistic regression model and a latent class model. |
Thermal Dynamics in General Relativity ; We discuss a relativistic model for heat conduction, building on a convective variational approach to multifluid systems where the entropy is treated as a distinct dynamical entity. We demonstrate how this approach leads to a relativistic version of the Cattaneo equation, encoding the finite thermal relaxation time that is required to satisfy causality. We also show that the model naturally includes the nonequilibrium Gibbs relation that is a key ingredient in most approaches to extended thermodynamics. Focussing on the pure heat conduction problem, we compare the variational results to the secondorder model developed by Israel and Stewart. The comparison shows that, despite the very different philosophies behind the two approaches, the two models are equivalent at first order deviations from thermal equilibrium. Finally, we complete the picture by working out the nonrelativistic limit of our results, making contact with recent work in that regime. |
A new tool for the performance analysis of massively parallel computer systems ; We present a new tool, GPA, that can generate key performance measures for very large systems. Based on solving systems of ordinary differential equations ODEs, this method of performance analysis is far more scalable than stochastic simulation. The GPA tool is the first to produce higher moment analysis from differential equation approximation, which is essential, in many cases, to obtain an accurate performance prediction. We identify socalled switch points as the source of error in the ODE approximation. We investigate the switch point behaviour in several large models and observe that as the scale of the model is increased, in general the ODE performance prediction improves in accuracy. In the case of the variance measure, we are able to justify theoretically that in the limit of model scale, the ODE approximation can be expected to tend to the actual variance of the model. |
A new method for calculating the primordial bispectrum in the squeezed limit ; In 2004, Creminelli and Zaldarriaga proposed a consistency relation for the primordial curvature perturbation of all singlefield inflation models; it related the bispectrum in the squeezed limit to the spectral tilt. We have developed a technique, based in part on the Creminelli and Zaldarriaga argument, that can greatly simplify the calculation of the squeezedlimit bispectrum using the inin formalism; we were able to arrive at a generic formula that does not rely on a slowroll approximation. Using our formula, we explicitly tested the consistency relation for powerlaw inflation and for an exactly scaleinvariant model by Starobinsky; for the latter model, Creminelli and Zaldarriaga's argument predicts a vanishing bispectrum whereas our quantum calculation shows a nonzero bispectrum that approaches zero in the longwavelength limit and for inflation with a large number of efolds. |
Scheduling Periodic RealTime Tasks with Heterogeneous Reward Requirements ; We study the problem of scheduling periodic realtime tasks so as to meet their individual minimum reward requirements. A task generates jobs that can be given arbitrary service times before their deadlines. A task then obtains rewards based on the service times received by its jobs. We show that this model is compatible to the imprecise computation models and the increasing reward with increasing service models. In contrast to previous work on these models, which mainly focus on maximize the total reward in the system, we aim to fulfill different reward requirements by different tasks, which offers better fairness and allows finegrained tradeoff between tasks. We first derive a necessary and sufficient condition for a system, along with reward requirements of tasks, to be feasible. We also obtain an offline feasibility optimal scheduling policy. We then studies a sufficient condition for a policy to be feasibility optimal or achieves some approximation bound. This condition can serve as a guideline for designing online scheduling policy and we obtains a greedy policy based on it. We prove that the online policy is feasibility optimal when all tasks have the same periods and also obtain an approximation bound for the policy under general cases. |
Stability Analysis of GIGcK Retrial Queue with Constant Retrial Rate ; We consider a GIGcKtype retrial queueing system with constant retrial rate. The system consists of a primary queue and an orbit queue. The primary queue has c identical servers and can accommodate the maximal number of K jobs. If a newly arriving job finds the full primary queue, it joins the orbit. The original primary jobs arrive to the system according to a renewal process. The jobs have general i.i.d. service times. A job in front of the orbit queue retries to enter the primary queue after an exponentially distributed time independent of the orbit queue length. Telephone exchange systems, Medium Access Protocols and short TCP transfers are just some applications of the proposed queueing system. For this system we establish minimal sufficient stability conditions. Our model is very general. In addition, to the known particular cases e.g., MG11 or MMcc systems, the proposed model covers as particular cases the deterministic service model and the Erlang model with constant retrial rate. The latter particular cases have not been considered in the past. The obtained stability conditions have clear probabilistic interpretation. |
Derivation of a threedimensional phasefieldcrystal model for liquid crystals from density functional theory ; Using a generalized order parameter gradient expansion within density functional theory, we derive a phasefieldcrystal model for liquid crystals composed by apolar particles in three spatial dimensions. Both the translational density and the orientational direction and ordering are included as order parameters. Different terms involving gradients in the order parameters in the resulting free energy functional are compared to the macroscopic GinzburgLandau approach as well as to the hydrodynamic description for liquid crystals. Our approach provides microscopic expressions for all prefactors in terms of the particle interactions. Our phasefieldcrystal model generalizes the conventional phasefieldcrystal model of spherical particles to orientational degrees of freedom and can be used as a starting point to explore phase transitions and interfaces for various liquidcrystalline phases. |
A Generalized QuasiNonlocal AtomistictoContinuum Coupling Method with Finite Range Interaction ; The accurate and efficient computation of the deformation of crystalline solids requires the coupling of atomistic models near lattice defects such as cracks and dislocations with coarsegrained models away from the defects. Quasicontinuum methods utilize a strain energy density derived from the CauchyBorn rule for the coarsegrained model. Several quasicontinuum methods have been proposed to couple the atomistic model with the CauchyBorn strain energy density. The quasinonlocal coupling method is easy to implement and achieves a reasonably accurate coupling for short range interactions. In this paper, we give a new formulation of the quasinonlocal method in one space dimension that allows its extension to arbitrary finite range interactions. We also give an analysis of the stability and accuracy of a linearization of our generalized quasinonlocal method that holds for strains up to lattice instabilities. |
Observational Constraints on Visser's Cosmological Model ; Theories of gravity for which gravitons can be treated as massive particles have presently been studied as realistic modifications of General Relativity, and can be tested with cosmological observations. In this work, we study the ability of a recently proposed theory with massive gravitons, the socalled Visser theory, to explain the measurements of luminosity distance from the Union2 compilation, the most recent TypeIa Supernovae SNe Ia dataset, adopting the current ratio of the total density of nonrelativistic matter to the critical density Omegam as a free parameter. We also combine the SNe Ia data with constraints from Baryon Acoustic Oscillations BAO and CMB measurements. We find that, for the allowed interval of values for Omegam, a model based on Visser's theory can produce an accelerated expansion period without any dark energy component, but the combined analysis SNe Ia BAO CMB shows that the model is disfavored when compared with LambdaCDM model. |
Gauge Mediation with Gauge Messengers in SU5 ; The inclusion of gauge messengers in models of gauge mediation allows for more general predictions that those described by the framework of general gauge mediation. Motivated by this, we explore some models of gauge mediation with gauge messengers in SU5 GUTs. In most previous attempts of building viable models where gauge messengers play a role in determining the soft terms, squark andor slepton masses turned out to be tachyonic. The objective of this paper is to address this problem and propose two possible solutions, one of which has a natural realization in the solution of the doublettriplet problem. Another interesting result is that in these models the association of SUSY breaking with the breaking of the GUT group provides a simple mechanism that can explain why SU5rightarrow SU3times SU2 times U1 is preferred over other symmetry breaking patterns. |
A generalized Monte Carlo loop algorithm for frustrated Ising models ; We introduce a Generalized Loop Move GLM update for Monte Carlo simulations of frustrated Ising models on twodimensional lattices with bondsharing plaquettes. The GLM updates are designed to enhance Monte Carlo sampling efficiency when the system's lowenergy states consist of an extensive number of degenerate or neardegenerate spin configurations, separated by large energy barriers to single spin flips. Through implementation on several frustrated Ising models, we demonstrate the effectiveness of the GLM updates in cases where both degenerate and neardegenerate sets of configurations are favored at low temperatures. The GLM update's potential to be straightforwardly extended to different lattices and spin interactions allow it to be readily adopted on many other frustrated Ising models of physical relevance. |
Continuous matter creation and the acceleration of the universe the growth of density fluctuations ; Cosmologies including continuous matter creation are able to reproduce the main properties of the standard LambdaCDM model, in particular in cases where the particle and entropy production rates are equal. These specific models, characterized by a mass density equal to the critical value, behave like the standard LambdaCDM model at early times whereas their late evolution is similar to the steadystate cosmology. The maximum amplitude of density fluctuations in these models depends on the adopted creation rate, related here to the parameter Omegav and this limitation could be a difficulty for the formation of galaxies and largescale structure in this class of universe. Additional problems are related with predictions either of the random peculiar velocities of galaxies or the present density of massive clusters of galaxies, both being largely overestimated with respect to observational data. |
The end points in the dispersion of Holstein polarons ; We investigate the existence of end points in the dispersion of Holstein polarons in various dimensions, using the Momentum Average approximation which has proved to be very accurate for this model. An end point separates momenta for which the lowestenergy state is a discrete level, i.e., an infinitelylived polaron, from those where the lowestenergy feature is a continuum in which the polaron' is signalled by a resonance with a finite lifetime. While such end points are known to not appear in 1D, we show here that they are generic in 3D if the particleboson coupling is not too strong. The 2D case is critical a pure 2D Holstein model has no end points, like the 1D case. However, any amount of interlayer hopping leads to 3Dlike behavior. As a result, such end points are expected to appear in the spectra of layered, quasi2D systems described by Holstein models. Generalizations to other models are also briefly discussed. |
Bayesian parameter estimation in the second LISA Pathfinder Mock Data Challenge ; A main scientific output of the LISA Pathfinder mission is to provide a noise model that can be extended to the future gravitational wave observatory, LISA. The success of the mission depends thus upon a deep understanding of the instrument, especially the ability to correctly determine the parameters of the underlying noise model. In this work we estimate the parameters of a simplified model of the LISA Technology Package LTP instrument. We describe the LTP by means of a closedloop model that is used to generate the data, both injected signals and noise. Then, parameters are estimated using a Bayesian framework and it is shown that this method reaches the optimal attainable error, the CramerRao bound. We also address an important issue for the mission how to efficiently combine the results of different experiments to obtain a unique set of parameters describing the instrument. |
Fluctuations of the extreme eigenvalues of finite rank deformations of random matrices ; Consider a deterministic selfadjoint matrix Xn with spectral measure converging to a compactly supported probability measure, the largest and smallest eigenvalues converging to the edges of the limiting measure. We perturb this matrix by adding a random finite rank matrix with delocalized eigenvectors and study the extreme eigenvalues of the deformed model. We give necessary conditions on the deterministic matrix Xn so that the eigenvalues converging out of the bulk exhibit Gaussian fluctuations, whereas the eigenvalues sticking to the edges are very close to the eigenvalues of the nonperturbed model and fluctuate in the same scale. We generalize these results to the case when Xn is random and get similar behavior when we deform some classical models such as Wigner or Wishart matrices with rather general entries or the socalled matrix models. |
A Novel Chronic Disease Policy Model ; We develop a simulation tool to support policydecisions about healthcare for chronic diseases in defined populations. Incident diseasecases are generated insilico from an agesex characterised general population using standard epidemiological approaches. A novel diseasetreatment model then simulates continuous life courses for each patient using discrete event simulation. Ideally, the discrete event simulation model would be inferred from complete longitudinal healthcare data via a likelihood or Bayesian approach. Such data is seldom available for relevant populations, therefore an innovative approach to evidence synthesis is required. We propose a novel entropybased approach to fit survival densities. This method provides a fully flexible way to incorporate the available information, which can be derived from arbitrary sources. Discrete event simulation then takes place on the fitted model using a competing hazards framework. The output is then used to help evaluate the potential impacts of policy options for a given population. |
Network coding with modular lattices ; In 1, Kotter and Kschischang presented a new model for error correcting codes in network coding. The alphabet in this model is the subspace lattice of a given vector space, a code is a subset of this lattice and the used metric on this alphabet is the map d U, V longmapsto dimU V dimU bigcap V. In this paper we generalize this model to arbitrary modular lattices, i.e. we consider codes, which are subsets of modular lattices. The used metric in this general case is the map d x, y longmapsto hx bigvee y hx bigwedge y, where h is the height function of the lattice. We apply this model to submodule lattices. Moreover, we show a method to compute the size of spheres in certain modular lattices and present a sphere packing bound, a sphere covering bound, and a singleton bound for codes, which are subsets of modular lattices. 1 R. Kotter, F.R. Kschischang Coding for errors and erasures in random network coding, IEEE Trans. Inf. Theory, Vol. 54, No. 8, 2008 |
Analysis of scalar perturbations in cosmological models with a nonlocal scalar field ; We develop the cosmological perturbations formalism in models with a single nonlocal scalar field originating from the string field theory description of the rolling tachyon dynamics. We construct the equation for the energy density perturbations of the nonlocal scalar field in the presence of the arbitrary potential and formulate the local system of equations for perturbations in the linearized model when both simple and double roots of the characteristic equation are present. We carry out the general analysis related to the curvature and entropy perturbations and consider the most specific example of perturbations when important quantities in the model become complex. |
Shape Quantities for Relational Quadrilateralland ; I investigate useful shape quantities for the classical and quantum mechanics of the relational quadrilateral in 2d. This is relational in the sense that only relative times, relative ratios of separations and relative angles are significant. Relational particle mechanics models such as this paper's have many analogies with the geometrodynamical formulation of general relativity. This renders them suitable as toy models for 1 studying Problem of Time in Quantum Gravity strategies, in particular timeless, semiclassical and histories theory approaches and combinations of these. 2 For consideration of various other quantumcosmological issues, such as structure formationinhomogeneity and notions of uniform states and their significance. The relational quadrilateral is more useful in these respects than previously investigated simpler RPM's due to simultaneously possessing linear constraints, nontrivial subsystems and nontrivial complexprojective mathematics. Such shape have been found to be useful in simpler relational models such as the relational triangle and in 1d. |
Cosmological and SolarSystem Tests of fR Modified Gravity ; We investigate the cosmological and the local tests of the fR theory of modified gravity via the observations of 1 the cosmic expansion and 2 the cosmic structures and via 3 the solarsystem experiments. To fit the possible cosmic expansion histories under consideration, for each of them we reconstruct fR, known as designer fR. We then test the designer fR via the cosmicstructure constraints on the metric perturbation ratio PsiPhi and the effective gravitational coupling Geff and via the solarsystem constraints on the BransDicke theory with the chameleon mechanism. We find that among the designer fR models specified by the CPL effective equation of state weff, only the model closely mimicking general relativity with a cosmological constant LambdaCDM can survive all the tests. Accordingly, these tests rule out the frequently studied weff 1 designer fR models which are distinct in cosmic structures from LambdaCDM. When considering only the cosmological tests, we find that the surviving designer fR models, although exist for a variety of weff, entail finetuning. |
Lightweight Time Modeling in Timed Creol ; Creol is an objectoriented modeling language in which inherently concurrent objects exchange asynchronous method calls. The operational semantics of Creol is written in an actorbased style, formulated in rewriting logic. The operational semantics yields a language interpreter in the Maude system, which can be used to analyze models. Recently, Creol has been applied to the modeling of systems with radio communication, such as sensor systems. With radio communication, messages expire and, if sent simultaneously, they may collide in the air. In order to capture these and other properties of distributed systems, we extended Creol's operational semantics with a notion of time. We exploit the framework of a language interpreter to use a lightweight notion of time, in contrast to that needed for a general purpose specification language. This paper presents a timed extension of Creol, including the semantics and the implementation strategy, and discusses its properties using an extended example. The approach can be generalized to other concurrent object or actorbased systems. |
Emergent relativisticlike Kinematics and Dynamical Mass Generation for a Lifshitztype Yukawa model ; We study the Infra Red IR limit of dispersion relations for scalar and fermion fields in a Lifshitztype Yukawa model, after dressing by quantum fluctuations. Relativisticlike dispersion relations emerge dynamically in the IR regime of the model, after quantum corrections are taken into account. In this regime, dynamical mass generation also takes place, but in such a way that the particle excitations remain massive, even if the bare masses vanish. The group velocities of the corresponding massive particles of course are smaller than the speed of light, in a way consistent with the IR regime where the analysis is performed. We also comment on possible extensions of the model where the fermions are coupled to an Abelian gauge field. |
Yukawa couplings and fermion mass structure in Ftheory GUTs ; The calculation of Yukawa couplings in Ftheory GUTs is developed. The method is applied to the top and bottom Yukawa couplings in an SU5 model of fermion masses based on family symmetries coming from the SU5perp factor in the underlying E8 theory. The remaining Yukawa couplings involving the light quark generations are determined by the Froggatt Nielsen nonrenormalisable terms generated by heavy messenger states. We extend the calculation of Yukawa couplings to include massive states and estimate the full up and down quark mass matrices in the SU5 model. We discuss the new features of the resulting structure compared to what is usually assumed for Abelian family symmetry models and show how the model can give a realistic quark mass matrix structure. We extend the analysis to the neutrino sector masses and mixing where we find that tribimaximal mixing is readily accommodated. Finally we discuss mechanisms for splitting the degeneracy between the charged leptons and the down quarks and the doublet triplet splitting in the Higgs sector. |
Mantis Predicting System Performance through Program Analysis and Modeling ; We present Mantis, a new framework that automatically predicts program performance with high accuracy. Mantis integrates techniques from programming language and machine learning for performance modeling, and is a radical departure from traditional approaches. Mantis extracts program features, which are information about program execution runs, through program instrumentation. It uses machine learning techniques to select features relevant to performance and creates prediction models as a function of the selected features. Through program analysis, it then generates compact code slices that compute these feature values for prediction. Our evaluation shows that Mantis can achieve more than 93 accuracy with less than 10 training data set, which is a significant improvement over models that are oblivious to program features. The system generates code slices that are cheap to compute feature values. |
The roundtable an abstract model of conversation dynamics ; Is it possible to abstract a formal mechanism originating schisms and governing the size evolution of social conversations In this work a constructive solution to such problem is proposed an abstract model of a generic Nparty turntaking conversation. The model develops from simple yet realistic assumptions derived from experimental evidence, abstracts from conversation content and semantics while including topological information, and is driven by stochastic dynamics. We find that a single mechanism namely the dynamics of conversational party's individual fitness, as related to conversation size controls the development of the selforganized schisming phenomenon. Potential generalizations of the model including individual traits and preferences, memory effects and more elaborated conversational topologies may find important applications also in other fields of research, where dynamicallyinteracting and networked agents play a fundamental role. |
Scaling Function, Universality and Analytical Solutions of Generalized OneSpecies Population Dynamics Models ; We consider several onespecies population dynamics model with finite and infinite carrying capacity, time dependent growth and effort rates and solve them analytically. We show that defining suitable scaling functions for a given time, one is able to demonstrate that their ratio with respect to its initial value is universal. This ratio is independent from the initial condition and from the model parameters. Although the effort rate does not break the model universality it produces a transition between the species extinction and survival. A general formula is furnished to obtain the scaling functions. |
Membrane stress tensor in the presence of lipid density and composition inhomogeneities ; We derive the expression of the stress tensor for one and twocomponent lipid membranes with density and composition inhomogeneities. We first express the membrane stress tensor as a function of the freeenergy density by means of the principle of virtual work. We then apply this general result to a monolayer model which is shown to be a local version of the areadifference elasticity ADE model. The resulting stress tensor expression generalizes the one associated with the Helfrich model, and can be specialized to obtain the one associated with the ADE model. Our stress tensor directly gives the force exchanged through a boundary in a monolayer with density and composition inhomogeneities. Besides, it yields the force density, which is also directly obtained in covariant formalism. We apply our results to study the forces induced in a membrane by a local perturbation. |
Model pseudoconvex domains and bumping ; The Levi geometry at weakly pseudoconvex boundary points of domains in Cn, n geq 3, is sufficiently complicated that there are no universal model domains with which to compare a general domain. Good models may be constructed by bumping outward a pseudoconvex, finitetype Omega subset C3 in such a way that i pseudoconvexity is preserved, ii the locally larger domain has a simpler defining function, and iii the lowest possible orders of contact of the bumped domain with bdyOmega, at the site of the bumping, are realised. When Omega subset Cn, ngeq 3, it is, in general, hard to meet the last two requirements. Such wellcontrolled bumping is possible when Omega is hextendiblesemiregular. We examine a family of domains in C3 that is strictly larger than the family of hextendiblesemiregular domains and construct explicit models for these domains by bumping. |
General model selection estimation of a periodic regression with a Gaussian noise ; This paper considers the problem of estimating a periodic function in a continuous time regression model with an additive stationary gaussian noise having unknown correlation function. A general model selection procedure on the basis of arbitrary projective estimates, which does not need the knowledge of the noise correlation function, is proposed. A nonasymptotic upper bound for quadratic risk oracle inequality has been derived under mild conditions on the noise. For the OrnsteinUhlenbeck noise the risk upper bound is shown to be uniform in the nuisance parameter. In the case of gaussian white noise the constructed procedure has some advantages as compared with the procedure based on the least squares estimates LSE. The asymptotic minimaxity of the estimates has been proved. The proposed model selection scheme is extended also to the estimation problem based on the discrete data applicably to the situation when high frequency sampling can not be provided. |
On the PseudoSchrodinger Equation approximation of the TransferIntegral operator for 1dimensional DNA models ; The TransferIntegral TI operator is a powerful method to investigate the statistical physics of 1dimensional models, like those used to describe DNA denaturation. At the cost of a certain number of approximations, the TI equation can be reduced to a PseudoSchrodinger Equation PSE, according to which the DNA sequence is equivalent to a point particle moving in a potential well. In this paper, I check the validity of the standard PSE approximation for two different 1dimensional DNA models, and show that it fails to provide correct results for both of them. I then propose a generalized PSE, which works well for one of the two models. Finally, I discuss the particle description of DNA denaturation that is derived from this generalized PSE. |
Dimension Reduction and Alleviation of Confounding for Spatial Generalized Linear Mixed Models ; Nongaussian spatial data are very common in many disciplines. For instance, count data are common in disease mapping, and binary data are common in ecology. When fitting spatial regressions for such data, one needs to account for dependence to ensure reliable inference for the regression coefficients. The spatial generalized linear mixed model SGLMM offers a very popular and flexible approach to modeling such data, but the SGLMM suffers from three major shortcomings 1 uninterpretability of parameters due to spatial confounding, 2 variance inflation due to spatial confounding, and 3 highdimensional spatial random effects that make fully Bayesian inference for such models computationally challenging. We propose a new parameterization of the SGLMM that alleviates spatial confounding and speeds computation by greatly reducing the dimension of the spatial random effects. We illustrate the application of our approach to simulated binary, count, and Gaussian spatial datasets, and to a large infant mortality dataset. |
Neel to staggered dimer order transition in a generalized honeycomb lattice Heisenberg model ; We study a generalized honeycomb lattice spin12 Heisenberg model with nearestneighbor antiferromagnetic 2spin exchange, and competing 4spin interactions which serve to stabilize a staggered dimer state which breaks lattice rotational symmetry. Using a combination of quantum Monte Carlo numerics, spin wave theory, and bond operator theory, we show that this model undergoes a strong firstorder transition between a Neel state and a staggered dimer state upon increasing the strength of the 4spin interactions. We attribute the strong first order character of this transition to the spinless nature of the core of pointlike Z3 vortices obtained in the staggered dimer state. Unlike in the case of a columnar dimer state, disordering such vortices in the staggered dimer state does not naturally lead to magnetic order, suggesting that, in this model, the dimer and Neel order parameters should be thought of as independent fields as in conventional Landau theory. |
DNA unzipping via stopped birth and death processes with unknown transition probabilities ; In this paper we provide an alternative approach to the works of the physicists S. Cocco and R. Monasson about a model of DNA molecules. The aim is to predict the sequence of bases by mechanical stimulations. The model described by the physicists is a stopped birth and death process with unknown transition probabilities. We consider two models, a discrete in time and a continuous in time, as general as possible. We show that explicit formula can be obtained for the probability to be wrong for a given estimator, and apply it to evaluate the quality of the prediction. Also we add some generalizations comparing to the initial model allowing us to answer some questions asked by the physicists. |
Spin foam models and the WheelerDeWitt equation for the quantum 4simplex ; The asymptotics of some spin foam amplitudes for a quantum 4simplex is known to display rapid oscillations whose frequency is the Regge action. In this note, we reformulate this result through a difference equation, asymptotically satisfied by these models, and whose semiclassical solutions are precisely the sine and the cosine of the Regge action. This equation is then interpreted as coming from the canonical quantization of a simple constraint in Regge calculus. This suggests to lift and generalize this constraint to the phase space of loop quantum gravity parametrized by twisted geometries. The result is a reformulation of the flat model for topological BF theory from the Hamiltonian perspective. The WheelerdeWitt equation in the spin network basis gives difference equations which are exactly recursion relations on the 15jsymbol. Moreover, the semiclassical limit is investigated using coherent states, and produces the expected results. It mimics the classical constraint with quantized areas, and for Regge geometries it reduces to the semiclassical equation which has been introduced in the beginning. |
NonGaussianity Consistency Relation for Multifield Inflation ; While detection of the local form bispectrum of primordial perturbations would rule out all singlefield inflation models, multifield models would still be allowed. We show that multifield models described by the delta N formalism obey an inequality between frm NL and one of the localform it trispectrum amplitudes, taurm NL, such that taurm NLfrac12frac65frm NL2 with a possible logarithmic scale dependence, provided that 2loop terms are small. Detection of a violation of this inequality would rule out most of multifield models, challenging inflation as a mechanism for generating the primoridal perturbations. |
A Minimal Inflation Scenario ; We elaborate on a minimal inflation scenario based entirely on the general properties of supersymmetry breaking in supergravity models. We identify the inflaton as the scalar component of the Goldstino superfield. We write plausible candidates for the effective action describing this chiral superfield. In particular the theory depends apart from parameters of O1 on a single free parameter the scale of supersymmetry breaking. This can be fixed using the amplitude of CMB cosmological perturbations and we therefore obtain the scale of supersymmetry breaking to be 101214 GeV. The model also incorporates explicit Rsymmetry breaking in order to satisfy the slow roll conditions. In our model the etaproblem is solved without extra finetuning. We try to obtain as much information as possible in a model independent way using general symmetry properties of the theory's effective action, this leads to a new proposal on how to exit the inflationary phase and reheat the Universe. |
TopHiggs and Toppion phenomenology in the Top Triangle Moose model ; We discuss the deconstructed version of a topcolorassisted technicolor model wherein the mechanism of top quark mass generation is separated from the rest of electroweak symmetry breaking. The minimal deconstructed version of this scenario is a triangle moose model, where the top quark gets its mass from coupling to a topHiggs field, while the gauge boson masses are generated from a Higgsless sector. The spectrum of the model includes scalar topHiggs and pseudoscalar toppion states. In this paper, we study the properties of these particles, discuss their production mechanisms and decay modes, and suggest how best to search for them at the LHC. |
Geometric Properties of Static EMdL Horizons ; We study nondegenerate and degenerate extremal Killing horizons of arbitrary geometry and topology within the EinsteinMaxwelldilaton model with a Liouville potential the EMdL model in ddimensional d4 static spacetimes. Using Israel's description of a static spacetime, we construct the EMdL equations and the spacetime curvature invariants the Ricci scalar, the square of the Ricci tensor, and the Kretschmann scalar. Assuming that spacetime metric functions and the model fields are real analytic functions in the vicinity of a spacetime horizon, we study behavior of the spacetime metric and the fields near the horizon and derive relations between the spacetime curvature invariants calculated on the horizon and geometric invariants of the horizon surface. The derived relations generalize the similar relations known for horizons of static four and 5dimensional vacuum and 4dimensional electrovacuum spacetimes. Our analysis shows that all the extremal horizon surfaces are Einstein spaces. We present necessary conditions for existence of static extremal horizons within the EMdL model. |
A Kernel Approach to Tractable Bayesian Nonparametrics ; Inference in popular nonparametric Bayesian models typically relies on sampling or other approximations. This paper presents a general methodology for constructing novel tractable nonparametric Bayesian methods by applying the kernel trick to inference in a parametric Bayesian model. For example, Gaussian process regression can be derived this way from Bayesian linear regression. Despite the success of the Gaussian process framework, the kernel trick is rarely explicitly considered in the Bayesian literature. In this paper, we aim to fill this gap and demonstrate the potential of applying the kernel trick to tractable Bayesian parametric models in a wider context than just regression. As an example, we present an intuitive Bayesian kernel machine for density estimation that is obtained by applying the kernel trick to a Gaussian generative model in feature space. |
DeConstructing a Natural and Flavorful Supersymmetric Standard Model ; Using the framework of deconstruction, we construct simple, weaklycoupled supersymmetric models that explain the Standard Model flavor hierarchy and produce a flavorful soft spectrum compatible with precision limits. Electroweak symmetry breaking is fully natural; the muterm is dynamically generated with no B muproblem and the Higgs mass is easily raised above LEP limits without reliance on large radiative corrections. These models possess the distinctive spectrum of superpartners characteristic of effective supersymmetry the third generation superpartners tend to be light, while the rest of the scalars are heavy. |
Nonperturbative aspects of ABJM theory ; Using the matrix model which calculates the exact free energy of ABJM theory on S3 we study nonperturbative effects in the large N expansion of this model, i.e., in the genus expansion of type IIA string theory on AdS4xCP3. We propose a general prescription to extract spacetime instanton actions from general matrix models, in terms of period integrals of the spectral curve, and we use it to determine them explicitly in the ABJM matrix model, as exact functions of the 't Hooft coupling. We confirm numerically that these instantons control the asymptotic growth of the genus expansion. Furthermore, we find that the dominant instanton action at strong coupling determined in this way exactly matches the action of an Euclidean D2brane instanton wrapping RP3. |
Compact vortex in a generalized BornInfeld model ; We study vortexlike solutions in a generalized BornInfeld model. The model is driven by two distinct parameters, one which deals with the BornInfeld term, and the other, which controls the presence of highorder power term in the covariant derivative of the Higgs field. We numerically solve the equations of motion and depict the main vortex features, for several values of the two parameters of the model. The results indicate the presence of compact vortex, when the parameter responsible for the highorder power in the derivative increases to sufficiently large values. |
Lopsided Gauge Mediation ; It has been recently pointed out that the unavoidable tuning among supersymmetric parameters required to raise the Higgs boson mass beyond its experimental limit opens up new avenues for dealing with the so called muBmu problem of gauge mediation. In fact, it allows for accommodating, with no further parameter tuning, large values of Bmu and of the other Higgssector soft masses, as predicted in models where both mu and Bmu are generated at oneloop order. This class of models, called Lopsided Gauge Mediation, offers an interesting alternative to conventional gauge mediation and is characterized by a strikingly different phenomenology, with light higgsinos, very large Higgs pseudoscalar mass, and moderately light sleptons. We discuss general parametric relations involving the finetuning of the model and various observables such as the chargino mass and the value of tanbeta. We build an explicit model and we study the constraints coming from LEP and Tevatron. We show that in spite of new interactions between the Higgs and the messenger superfields, the theory can remain perturbative up to very large scales, thus retaining gauge coupling unification. |
A toy model of wave turbulence ; A novel model of wave turbulence is presented which allows to explain in the same frame various nonlinear wave phenomena intermittency, form and direction of the energy cascades, formation of a zerofrequency band with nonzero energy, etc. as an effect of initial conditions, without any statistical assumptions. Classical KolmogorovZakharov spectra are obtained as a particular case of the more general form of energy spectra. One of the most important phenomenological consequences of the model is the termination of a cascade not due to dissipation but because of the growth of nonlinearity. The model is quite general and can be exploited for the description of an arbitrary wave turbulent system. |
Adding noise to the input of a model trained with a regularized objective ; Regularization is a well studied problem in the context of neural networks. It is usually used to improve the generalization performance when the number of input samples is relatively small or heavily contaminated with noise. The regularization of a parametric model can be achieved in different manners some of which are early stopping Morgan and Bourlard, 1990, weight decay, output smoothing that are used to avoid overfitting during the training of the considered model. From a Bayesian point of view, many regularization techniques correspond to imposing certain prior distributions on model parameters Krogh and Hertz, 1991. Using Bishop's approximation Bishop, 1995 of the objective function when a restricted type of noise is added to the input of a parametric function, we derive the higher order terms of the Taylor expansion and analyze the coefficients of the regularization terms induced by the noisy input. In particular we study the effect of penalizing the Hessian of the mapping function with respect to the input in terms of generalization performance. We also show how we can control independently this coefficient by explicitly penalizing the Jacobian of the mapping function on corrupted inputs. |
Classical and Nonclassical symmetries of the 21dimensional KuramotoSivashinsky equation ; In this paper, we have studied the problem of determining the largest possible set of symmetries for an important example of nonlinear dynamical system the KuramotoSivashinsky KS model in two spatial and one temporal dimensions. By applying the classical symmetry method for the KS model, we have found the classical symmetry operators. Also, the structure of the Lie algebra of symmetries is discussed and the optimal system of subalgebras of the equation is constructed. The Lie invariants associated to the symmetry generators as well as the corresponding similarity reduced equations are also pointed out. By applying the nonclassical symmetry method for the KS model we concluded that the analyzed model do not admit supplementary, nonclassical type, symmetries. Using this procedure, the classical Lie operators only were generated. |
Is backreaction really small within concordance cosmology ; Smoothing over structures in general relativity leads to a renormalisation of the background, and potentially many other effects which are poorly understood. Observables such as the distanceredshift relation when averaged on the sky do not necessarily yield the same smooth model which arises when performing spatial averages. These issues are thought to be of technical interest only in the standard model of cosmology, giving only tiny corrections. However, when we try to calculate observable quantities such as the allsky average of the distanceredshift relation, we find that perturbation theory delivers divergent answers in the UV and corrections to the background of order unity. There are further problems. Secondorder perturbations are the same size as firstorder, and fourthorder at least the same as second, and possibly much larger, owing to the divergences. Much hinges on a coincidental balance of 2 numbers the primordial power, and the ratio between the comoving Hubble scales at matterradiation equality and today. Consequently, it is far from obvious that backreaction is irrelevant even in the concordance model, however natural it intuitively seems. |
Strong coupling expansion for the BoseHubbard and the JaynesCummings lattice model ; A strong coupling expansion, based on the KatoBloch perturbation theory, which has recently been proposed by Eckardt et al. Phys. Rev. B 79, 195131 and Teichmann et al. Phys. Rev. B 79, 224515 is implemented in order to study various aspects of the BoseHubbard and the JaynesCummings lattice model. The approach, which allows to generate numerically all diagrams up to a desired order in the interaction strength is generalized for disordered systems and for the JaynesCummings lattice model. Results for the BoseHubbard and the JaynesCummings lattice model will be presented and compared with results from VCA and DMRG. Our focus will be on the Mott insulator to superfluid transition. |
Closedform EM for Sparse Coding and its Application to Source Separation ; We define and discuss the first sparse coding algorithm based on closedform EM updates and continuous latent variables. The underlying generative model consists of a standard spikeandslab' prior and a Gaussian noise model. Closedform solutions for E and Mstep equations are derived by generalizing probabilistic PCA. The resulting EM algorithm can take all modes of a potentially multimodal posterior into account. The computational cost of the algorithm scales exponentially with the number of hidden dimensions. However, with current computational resources, it is still possible to efficiently learn model parameters for mediumscale problems. Thus the model can be applied to the typical range of source separation tasks. In numerical experiments on artificial data we verify likelihood maximization and show that the derived algorithm recovers the sparse directions of standard sparse coding distributions. On source separation benchmarks comprised of realistic data we show that the algorithm is competitive with other recent methods. |
Generating Similar Graphs From Spherical Features ; We propose a novel model for generating graphs similar to a given example graph. Unlike standard approaches that compute features of graphs in Euclidean space, our approach obtains features on a surface of a hypersphere. We then utilize a von MisesFisher distribution, an exponential family distribution on the surface of a hypersphere, to define a model over possible feature values. While our approach bears similarity to a popular exponential random graph model ERGM, unlike ERGMs, it does not suffer from degeneracy, a situation when a significant probability mass is placed on unrealistic graphs. We propose a parameter estimation approach for our model, and a procedure for drawing samples from the distribution. We evaluate the performance of our approach both on the small domain of all 8node graphs as well as larger realworld social networks. |
BoseEinstein condensation of dark matter solves the corecusp problem ; We analyze the observed properties of dwarf galaxies, which are dark matter dominated astrophysical objects, by assuming that dark matter is in the form of a strongly coupled, dilute Bose Einstein condensate. The basic astrophysical properties of the condensate density profile, rotational velocity, and mass profile, respectively, are derived from a variational principle. To test the validity of the model we compare first the tangential velocity equation of the model with a sample of eight rotation curves of dwarf galaxies. We find a good agreement between the theoretically predicted rotation curves without any baryonic component and the observational data. The mean value of the logarithmic inner slope of the mass density profile of dwarf galaxies is also obtained, and it is shown that the observed value of this parameter is in agreement with the theoretical results. The predictions of the Bose Einstein condensate model are also systematically compared with the predictions of the standard Cold Dark Matter model. The nonsingular density profiles of the BoseEinstein condensed dark matter generally show the presence of an extended core, whose presence is due to the strong interaction between dark matter particles. |
Independent screening for singleindex hazard rate models with ultrahigh dimensional features ; In data sets with many more features than observations, independent screening based on all univariate regression models leads to a computationally convenient variable selection method. Recent efforts have shown that in the case of generalized linear models, independent screening may suffice to capture all relevant features with high probability, even in ultrahigh dimension. It is unclear whether this formal sure screening property is attainable when the response is a rightcensored survival time. We propose a computationally very efficient independent screening method for survival data which can be viewed as the natural survival equivalent of correlation screening. We state conditions under which the method admits the sure screening property within a general class of singleindex hazard rate models with ultrahigh dimensional features. An iterative variant is also described which combines screening with penalized regression in order to handle more complex feature covariance structures. The methods are evaluated through simulation studies and through application to a real gene expression dataset. |
Beyond the Standard cosmological model with CMB ; Measurements of CMB anisotropy and, more recently, polarization have played a very important role in cosmology. Besides precise determination of various parameters of the standard' cosmological model, observations have also established some important basic tenets that underlie models of cosmology and structure formation in the universe acausally' correlated, adiabatic, primordial perturbations in a flat, statistically isotropic universe. These are consistent with the expectation of the paradigm of inflation and the generic prediction of the simplest realization of inflationary scenario in the early universe. Further, gravitational instability is the established mechanism for structure formation from these initial perturbations. Primordial perturbations observed as the CMB anisotropy and polarization is the most compelling evidence for new, possibly fundamental, physics in the early universe. The community is now looking beyond the parameter estimation of the standard' model, for subtle, characteristic signatures of early universe physics. |
Halo clustering and gNLtype primordial nonGaussianity ; A wide range of multifield inflationary models generate nonGaussian initial conditions in which the initial adiabatic fluctuation is of the form zetaG gNL zetaG3. We study halo clustering in these models using two different analytic methods the peakbackground split framework, and brute force calculation in a barrier crossing model, obtaining agreement between the two. We find a simple, theoretically motivated expression for halo bias which agrees with Nbody simulations and can be used to constrain gNL from observations. We discuss practical caveats to constraining gNL using only observable properties of a tracer population, and argue that constraints obtained from populations whose observed bias is 2.5 are generally not robust to uncertainties in modeling the halo occupation distribution of the population. |
The not so squeezed limit of the primordial 3point function ; We prove that, in a generic singlefield model, the consistency relation for the 3point function in the squeezed limit receives corrections that vanish quadratically in the ratio of the momenta, i.e. as kLkS2. This implies that a detection of a bispectrum signal going as 1kL2 in the squeezed limit, that is suppressed only by one power of kL compared with the local shape, would rule out all singlefield models. The absence of this kind of terms in the bispectrum holds also for multifield models, but only if all the fields have a mass much smaller than H. The detection of any scale dependence of the bias, for scales much larger than the size of the haloes, would disprove all singlefield models. We comment on the regime of squeezing that can be probed by realistic surveys. |
Hawking Radiation in Dispersive Media ; Hawking radiation, despite its presence in theoretical physics for over thirty years, remains elusive and undetected. It also suffers, in its original context of gravitational black holes, from conceptual difficulties. Of particular note is the transPlanckian problem, which is concerned with the apparent origin of the radiation in absurdly high frequencies. In order to gain better theoretical understanding and, it is hoped, experimental verification of Hawking radiation, much study is being devoted to systems which model the spacetime geometry of black holes, and which, by analogy, are also thought to emit Hawking radiation. These analogue systems typically exhibit dispersion, which regularizes the wave behaviour at the horizon but does not lend itself well to analytic treatment, thus rendering Hawking's prediction less secure. A general analytic method for dealing with Hawking radiation in dispersive systems has proved difficult to find. This thesis presents new numerical and analytic results for Hawking emission spectra in dispersive systems. It examines two blackhole analogue systems it begins by introducing the wellknown acoustic model, presenting some original results in that context; then, through analogy with the acoustic model, goes on to develop the lesserknown fibreoptical model. |
EdgeBased Compartmental Modeling for Infectious Disease Spread Part III Disease and Population Structure ; We consider the edgebased compartmental models for infectious disease spread introduced in Part I. These models allow us to consider standard SIR diseases spreading in random populations. In this paper we show how to handle deviations of the disease or population from the simplistic assumptions of Part I. We allow the population to have structure due to effects such as demographic detail or multiple types of risk behavior the disease to have more complicated natural history. We introduce these modifications in the static network context, though it is straightforward to incorporate them into dynamic networks. We also consider serosorting, which requires using the dynamic network models. The basic methods we use to derive these generalizations are widely applicable, and so it is straightforward to introduce many other generalizations not considered here. |
WarmIntermediate inflationary universe model in braneworld cosmologies ; Warmintermediate inflationary universe models in the context of braneworld cosmologies, are studied. This study is done in the weak and strong dissipative regimes. We find that, the scalar potentials and dissipation coefficients in terms of the scalar field, evolves as typepowerlaw and powers of logarithms, respectively. General conditions required for these models to be realizable are derived and discussed. We also study the scalar and tensor perturbations for each regime. We use recent astronomical observations to constraint the parameters appearing in the braneworld models. |
Analytical expressions for the deprojected Sersic model II. General expressions in terms of the Fox H function ; The S'ersic model is the de facto standard to describe the surface brightness distribution of hot stellar systems. An important inconvenience of this analytical model is that the corresponding luminosity density and associated properties cannot be expressed using elementary functions or even standard special functions. We present a set of compact and elegant analytical expressions for the luminosity density, cumulative luminosity and potential for the S'ersic model in terms of the Fox H function for general values of the S'ersic index. Furthermore, we present explicit series expansions of these quantities and discuss the asymptotic behaviour. Our analysis completes the work of Mazure Capelato 2002 and Baes Gentile 2011 and demonstrates the power of the underestimated Fox H function as a tool for analytical work. |
NonHermitian multiparticle systems from complex root spaces ; We provide a general construction procedure for antilinearly invariant complex root spaces. The proposed method is generic and may be applied to any Weyl group allowing to take any element of the group as a starting point for the construction. Worked out examples for several specific Weyl groups are presented, focusing especially on those cases for which no solutions were found previously. When applied in the defining relations of models based on root systems this usually leads to nonHermitian models, which are nonetheless physically viable in a selfconsistent sense as they are antilinearly invariant by construction. We discuss new types of Calogero models based on these complex roots. In addition we propose an alternative construction leading to qdeformed roots. We employ the latter type of roots to formulate a new version of affine Toda field theories based on nonsimply laced roots systems. These models exhibit on the classical level a strongweak duality in the coupling constant equivalent to a Lie algebraic duality, which is known for the quantum version of the undeformed case. |
UFO The Universal FeynRules Output ; We present a new model format for automatized matrixelement generators, the so called Universal FeynRules Output UFO. The format is universal in the sense that it features compatibility with more than one single generator and is designed to be flexible, modular and agnostic of any assumption such as the number of particles or the color and Lorentz structures appearing in the interaction vertices. Unlike other model formats where text files need to be parsed, the information on the model is encoded into a Python module that can easily be linked to other computer codes. We then describe an interface for the Mathematica package FeynRules that allows for an automatic output of models in the UFO format. |
Can decaying modes save void models for acceleration ; The unexpected dimness of Type Ia supernovae SNe, apparently due to accelerated expansion driven by some form of dark energy or modified gravity, has led to attempts to explain the observations using only general relativity with baryonic and cold dark matter, but by dropping the standard assumption of homogeneity on Hubble scales. In particular, the SN data can be explained if we live near the centre of a Hubblescale void. However, such void models have been shown to be inconsistent with various observations, assuming the void consists of a pure growing mode. Here it is shown that models with significant decaying mode contribution today can be ruled out on the basis of the expected cosmic microwave background spectral distortion. This essentially closes one of the very few remaining loopholes in attempts to rule out void models, and strengthens the evidence for Hubblescale homogeneity. |
Flavor Symmetric Sectors and Collider Physics ; We discuss the phenomenology of effective field theories with new scalar or vector representations of the Standard Model quark flavor symmetry group, allowing for large flavor breaking involving the third generation. Such field content can have a relatively low mass scale lesssim TeV and O1 couplings to quarks, while being naturally consistent with both flavor violating and flavor diagonal constraints. These theories therefore have the potential for early discovery at LHC, and provide a flavor safe tool box for addressing anomalies at colliders and low energy experiments. We catalogue the possible flavor symmetric representations, and consider applications to the anomalous Tevatron ttbar forward backward asymmetry and Bs mixing measurements, individually or concurrently. Collider signatures and constraints on flavor symmetric models are also studied more generally. In our examination of the ttbar forward backward asymmetry we determine model independent acceptance corrections appropriate for comparing against CDF data that can be applied to any model seeking to explain the ttbar forward backward asymmetry. |
1,0 superconformal models in six dimensions ; We construct sixdimensional 1,0 superconformal models with nonabelian gauge couplings for multiple tensor multiplets. A crucial ingredient in the construction is the introduction of threeform gauge potentials which communicate degrees of freedom between the tensor multiplets and the YangMills multiplet, but do not introduce additional degrees of freedom. Generically these models provide only equations of motions. For a subclass also a Lagrangian formulation exists, however it appears to exhibit indefinite metrics in the kinetic sector. We discuss several examples and analyze the excitation spectra in their supersymmetric vacua. In general, the models are perturbatively defined only in the spontaneously broken phase with the vev of the tensor multiplet scalars serving as the inverse coupling constants of the YangMills multiplet. We briefly discuss the inclusion of hypermultiplets which complete the field content to that of superconformal 2,0 theories. |
Multistage Kondo effect as a manifestation of dynamical symmetries in the single and twoelectron tunneling ; The concept of dynamical symmetries is used for formulation of the renormalization group approach to the Kondo effect in the Anderson model with repulsive and attractive interaction U. It is shown that the generic local symmetry of the Anderson Hamiltonian is determined by the SU4 Lie group. The Anderson Hamiltonian is rewritten in terms of the GellMann matrices of the 4th rank, which form the set of group generators and the basis for construction of irreducible vector operators describing the excitation spectra in the charge and spin sectors. The multistage Kondo sceening is described in terms of the local SU4 dynamical symmetry. It is shown that the similarity between the conventional Kondo cotunneling effect for spin 12 in the positive U model and the Kondo resonance for pair tunneling in the negative U model is a direct manifestation of implicit SU4 symmetry of the AndersonKondo model. |
Properties of the limit shape for some last passage growth models in random environments Dissertation ; We study directed lastpassage percolation on the planar square lattice whose weights have general distributions, or equivalently, queues in series with general service distributions. Each row of the last passage model has its own randomly chosen weight distribution. We first show the existence of the limiting time constant and list its properties. Next we study the problem for models with Bernoulli and exponential weights, for which we already have more precise results. We then present some universality results about the limiting time constant close to the boundary of the quadrant. Close to the yaxis, where the number of random distributions averaged over stays large, the limiting time constant takes the same universal form as in the homogeneous model. But close to the xaxis we see the effect of the tail of the distribution of the random environment. In particular we will give some estimates of the upper bound in this case. |
A new approach to cosmological perturbations in fR models ; We propose an analytic procedure that allows to determine quantitatively the deviation in the behavior of cosmological perturbations between a given fR modified gravity model and a LCDM reference model. Our method allows to study structure formation in these models from the largest scales, of the order of the Hubble horizon, down to scales deeply inside the Hubble radius, without employing the socalled quasistatic approximation. Although we restrict our analysis here to linear perturbations, our technique is completely general and can be extended to any perturbative order. |
Finite geometry models of electric field noise from patch potentials in ion traps ; We model electric field noise from fluctuating patch potentials on conducting surfaces by taking into account the finite geometry of the ion trap electrodes to gain insight into the origin of anomalous heating in ion traps. The scaling of anomalous heating rates with surface distance, d, is obtained for several generic geometries of relevance to current ion trap designs, ranging from planar to spheroidal electrodes. The influence of patch size is studied both by solving Laplace's equation in terms of the appropriate Green's function as well as through an eigenfunction expansion. Scaling with surface distance is found to be highly dependent on the choice of geometry and the relative scale between the spatial extent of the electrode, the ionelectrode distance, and the patch size. Our model generally supports the d4 dependence currently found by most experiments and models, but also predicts geometrydriven deviations from this trend. |
Effects of fR Model on the Dynamical Instability of Expansionfree Gravitational Collapse ; Dark energy models based on fR theory have been extensively studied in literature to realize the late time acceleration. In this paper, we have chosen a viable fR model and discussed its effects on the dynamical instability of expansionfree fluid evolution generating a central vacuum cavity. For this purpose, contracted Bianchi identities are obtained for both the usual matter as well as dark source. The term dark source is named to the higher order curvature corrections arising from fR gravity. The perturbation scheme is applied and different terms belonging to Newtonian and post Newtonian regimes are identified. It is found that instability range of expansionfree fluid on external boundary as well as on internal vacuum cavity is independent of adiabatic index Gamma but depends upon the density profile, pressure anisotropy and fR model. |
General Quantum Fidelity Susceptibilities for the J1J2 Chain ; We study slightly generalized quantum fidelity susceptibilities where the differential change in the fidelity is measured with respect to a different term than the one used for driving the system towards a quantum phase transition. As a model system we use the spin12 J1J2 antiferromagnetic Heisenberg chain. For this model, we study three fidelity susceptibilities, chip, chiD and chiAF, which are related to the spin stiffness, the dimer order and antiferromagnetic order, respectively. All these groundstate fidelity susceptibilities are sensitive to the phase diagram of the J1J2 model. We show that they all can accurately identify a quantum critical point in this model occurring at J2 0.241J1 between a gapless Heisenberg phase for J2 J2critical and a dimerized phase for J2 J2critical. This phase transition, in the BerezinskiiKosterlitzThouless universality class, is controlled by a marginal operator and is therefore particularly difficult to observe. |
Neutrino masses generation in a Z4 model ; We present a renormalizable flavor model with Z4 as flavor symmetry in both the quark and lepton sectors. The model is constructed with a minimal approach and noright handed neutrinos are introduced. In this approach a minimum number of two SU2 Higgs doublets and one scalar singlet are required in order to obtain the Nearest Neighbor Interaction form for charged fermions and to generate neutrino masses radiatively. For the quark sector we follow the charge assignations made by Branco et. al. in reference 1. All fermion masses and mixing angles in the model are in agreement with current experimental data and only the inverted hierarchy for the neutrino mass spectrum is allowed. Since neutrinos are Majorana the contribution to neutrinoless double beta decay is also analyzed. |
Neutrino Masses in Supersymmetric Economical SU3C X SU3L X U1X Model ; The Rsymmetry formalism is applied for the supersymmetric economical SU3C X SU3L X U1X 331 model. The generalization of the minimal supersymmetric standard model relation among Rparity, spin and matter parity is derived, and discrete symmetries for the proton stability in this model are imposed. We show that in such a case it is able to give leptons masses at just the tree level. A simple mechanism for the mass generation of the neutrinos is explored. With the new Rparity, the neutral fermions get mass matrix with two distinct sectors one light which is identified with neutrino mass matrix, another heavy one which is identified with neutralinos one. The similar situation exists in the charged fermion sector. Some phenomenological consequences such as proton stability, neutrinoless double beta decays are discussed. |
Reconstructing the History of Energy Condition Violation from Observational Data ; We study the likelihood of energy condition violations in the history of the Universe. Our method is based on a set of functions that characterize energy condition violation. FLRW cosmological models are built around these indication functions. By computing the Fisher matrix of model parameters using type Ia supernova and Hubble parameter data, we extract the principal modes of these functions' redshift evolution. These modes allow us to obtain general reconstructions of energy condition violation history independent of the dark energy model. We find that the data suggest a history of strong energy condition violation, but the null and dominant energy conditions are likely to be fulfilled. Implications for dark energy models are discussed. |
Flavour Violation in charged leptons Present and Future ; In the absence of a fundamental principle preventing charged lepton flavour violation, one expects that extensions of the Standard Model accommodating neutrino masses and mixings should also allow for charged lepton flavour violating processes such as elli to elljgamma, elli to ellj ellk ellm and mu e conversion in nuclei, for which the rates depend in general on the mechanism of neutrino mass generation. In addition to lowenergy experiments, there are also searches for lepton flavour violation at colliders, where new physics can be directly probed through flavour violating production andor decays of heavy states. In a model independent way, we briefly use effective operators responsible for these processes to derive information about the underlying framework of new physics. We then consider some specific classes of models supersymmetry, extra dimensions, grand unified theories that account for rich scenarios of charged lepton flavour violation. We also comment on the role of charged lepton flavour violation in disentangling models of new physics. |
Geometric and thermodynamic properties in GaussBonnet gravity ; In this paper, the generalized second law GSL of thermodynamics and entropy is revisited in the context of cosmological models in GaussBonnet gravity with the boundary of the universe is assumed to be enclosed by the dynamical apparent horizon. The model is best fitted with the observational data for distance modulus. The best fitted geometric and thermodynamic parameters such as equation of state parameter, deceleration parameter and entropy are derived. To link between thermodynamic and geometric parameters, the entropy rate of change multiplied by the temperature as a model independent thermodynamic state parameter is also derived. The results show that the model is in good agreement with the observational analysis. |
Uselessness for an Oracle Model with Internal Randomness ; We consider a generalization of the standard oracle model in which the oracle acts on the target with a permutation selected according to internal random coins. We describe several problems that are impossible to solve classically but can be solved by a quantum algorithm using a single query; we show that such infinityvsone separations between classical and quantum query complexities can be constructed from much weaker separations. We also give conditions to determine when oracle problemseither in the standard model, or in any of the generalizations we considercannot be solved with success probability better than random guessing would achieve. In the oracle model with internal randomness where the goal is to gain any nonzero advantage over guessing, we prove roughly speaking that k quantum queries are equivalent in power to 2k classical queries, thus extending results of Meyer and Pommersheim. |
A Tool for ModelBased Language Specification ; Formal languages let us define the textual representation of data with precision. Formal grammars, typically in the form of BNFlike productions, describe the language syntax, which is then annotated for syntaxdirected translation and completed with semantic actions. When, apart from the textual representation of data, an explicit representation of the corresponding data structure is required, the language designer has to devise the mapping between the suitable data model and its proper language specification, and then develop the conversion procedure from the parse tree to the data model instance. Unfortunately, whenever the format of the textual representation has to be modified, changes have to propagated throughout the entire language processor tool chain. These updates are timeconsuming, tedious, and errorprone. Besides, in case different applications use the same language, several copies of the same language specification have to be maintained. In this paper, we introduce a modelbased parser generator that decouples language specification from language processing, hence avoiding many of the problems caused by grammardriven parsers and parser generators. |
Viscous dark fluid Universe a unified model of the dark sector ; The Universe is modeled as consisting of pressureless baryonic matter and a bulk viscous fluid which is supposed to represent a unified description of the dark sector. In the homogeneous and isotropic background the textittotal energy density of this mixture behaves as a generalized Chaplygin gas. The perturbations of this energy density are intrinsically nonadiabatic and source relative entropy perturbations. The resulting baryonic matter power spectrum is shown to be compatible with the 2dFGRS and SDSS DR7 data. A joint statistical analysis, using also Hubblefunction and supernovae Ia data, shows that, different from other studies, there exists a maximum in the probability distribution for a negative present value of the deceleration parameter. Moreover, the unified model presented here favors a matter content that is of the order of the baryonic matter abundance suggested by bigbang nucleosynthesis. A problem of simple bulk viscous models, however, is the behavior of the gravitational potential and the reproduction of the CMB power spectrum. |
Solving the TTC 2011 Compiler Optimization Task with metatools ; The authors' metatools are a collection of tools for generic programming. This includes generating Java sources from mathematically wellfounded specifications, as well as the creation of strictly typed document object models for XML encoded texts. In this context, almost every computerinternal structure is treated as a model, and every computation is a kind of model transformation. This concept differs significantly from classical model transformation executed by specialized tools and languages. Therefore it seemed promising to the organizers of the TTC 2011, as well as to the authors, to apply metatools to one of the challenges, namely to the compiler optimization task. This is a report on the resulting experiences. |
Extended nonlocal chiralquark model for the D and Bmeson weakdecay constants ; In this work, we construct a phenomenological effective model for the heavylight quark systems, which consist of u,d,c,b quarks, i.e. extended nonlocal chiralquark model ExNLChQM to compute the heavymeson weakdecay constants fD and fB. ExNLChQM is based on the heavyquark effective field theory as well as the dilute instantonvacuum configuration. In ExNLChQM, a certain portion of the heavymeson mass is considered to be generated from the nontrivial QCD vacuum contribution, being similar to that for the light quarks in usual instanton approaches. Hence, the effective heavy and lightquark masses become momentumdependent and play the role of a smooth UV regulator. Employing a generic externalfield method applied to the effective action from ExNLChQM, we obtain fD 169.28 234.57 MeV and fB 165.41 229.21 MeV from the numerical results, depending on different model parameters. These values are in relatively good agreement with experimental data and various theoretical estimations. We also discuss the heavyquark effects on the QCD vacuum, and the decay constants fD and fB in terms of the heavyquark spin symmetry. |