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Efficient Bayesian analysis of multiple changepoint models with dependence across segments ; We consider Bayesian analysis of a class of multiple changepoint models. While there are a variety of efficient ways to analyse these models if the parameters associated with each segment are independent, there are few general approaches for models where the parameters are dependent. Under the assumption that the dependence is Markov, we propose an efficient online algorithm for sampling from an approximation to the posterior distribution of the number and position of the changepoints. In a simulation study, we show that the approximation introduced is negligible. We illustrate the power of our approach through fitting piecewise polynomial models to data, under a model which allows for either continuity or discontinuity of the underlying curve at each changepoint. This method is competitive with, or outperforms, other methods for inferring curves from noisy data; and uniquely it allows for inference of the locations of discontinuities in the underlying curve.

Multiscale modeling of polymers at interfaces ; A brief review of modeling and simulation methods for a study of polymers at interfaces is provided. When studying truly multiscale problems as provided by realistic polymer systems, coarse graining is practically unavoidable. In this process, degrees of freedom on smaller scales are eliminated to the favor of a model suitable for efficient study of the system behavior on larger length and time scales. We emphasize the need to distinguish between dynamic and static properties regarding the model validation. A model which accurately reproduces static properties may fail completely, when it comes to the dynamic behavior of the system. Furthermore, we comment on the use of Monte Carlo method in polymer science as compared to molecular dynamics simulations. Using the latter approach, we also discuss results of recent computer simulations on the properties of polymers close to solid substrates. This includes both generic features as also observed in the case of simpler molecular models as well as polymer specific properties. Predictive power of computer simulations is highlighted by providing experimental evidence for these observations. Some important implications of these results for an understanding of mechanical properties of thin polymer films and coatings are also worked out.

Causal Inference on Discrete Data using Additive Noise Models ; Inferring the causal structure of a set of random variables from a finite sample of the joint distribution is an important problem in science. Recently, methods using additive noise models have been suggested to approach the case of continuous variables. In many situations, however, the variables of interest are discrete or even have only finitely many states. In this work we extend the notion of additive noise models to these cases. We prove that whenever the joint distribution probX,Y admits such a model in one direction, e.g. YfXN, N independent X, it does not admit the reversed model XgYtilde N, tilde N independent Y as long as the model is chosen in a generic way. Based on these deliberations we propose an efficient new algorithm that is able to distinguish between cause and effect for a finite sample of discrete variables. In an extensive experimental study we show that this algorithm works both on synthetic and real data sets.

Mapping Complex Networks Exploring Boolean Modeling of Signal Transduction Pathways ; In this study, we explored the utility of a descriptive and predictive bionetwork model for phospholipase Ccoupled calcium signaling pathways, built with nonkinetic experimental information. Boolean models generated from these data yield oscillatory activity patterns for both the endoplasmic reticulum resident inositol1,4,5trisphosphate receptor IP3R and the plasmamembrane resident canonical transient receptor potential channel 3 TRPC3. These results are specific as randomization of the Boolean operators ablates oscillatory pattern formation. Furthermore, knockout simulations of the IP3R, TRPC3, and multiple other proteins recapitulate experimentally derived results. The potential of this approach can be observed by its ability to predict previously undescribed cellular phenotypes using in vitro experimental data. Indeed our cellular analysis of the developmental and calciumregulatory protein, DANGER1a, confirms the counterintuitive predictions from our Boolean models in two highly relevant cellular models. Based on these results, we theorize that with sufficient legacy knowledge andor computational biology predictions, Boolean networks provide a robust method for predictivemodeling of any biological system.

The Unifying Dark Fluid Model ; The standard model of cosmology relies on the existence of two components, dark matter and dark energy, which dominate the expansion of the Universe. There is no direct proof of their existence, and their nature is still unknown. Many alternative models suggest other cosmological scenarios, and in particular the dark fluid model replace the dark matter and dark energy components by a unique dark component able to mimic the behaviour of both components. The current cosmological constraints on the unifying dark fluid model is discussed, and a dark fluid model based on a complex scalar field is presented. Finally the consequences of quantum corrections on the scalar field potential are investigated.

A minimal model of Lorentz gauge gravity with dynamical torsion ; A new Lorentz gauge gravity model with R2type Lagrangian is proposed. In the absence of classical torsion the model admits a topological phase with an arbitrary metric. We analyze the equations of motion in constant curvature spacetime background using the Lagrange formalism and demonstrate that the model possesses a minimal set of dynamic degrees of freedom for the torsion. Surprisingly, the number of torsion dynamic degrees of freedom equals the number of physical degrees of freedom for the metric tensor. An interesting feature of the model is that the spin two mode of torsion becomes dynamical essentially due to the nonlinear structure of the theory. We perform covariant oneloop quantization of the model for a special case of constant curvature spacetime background. We treat the contortion as a quantum field variable whereas the metric tensor is kept as a classical object. We discuss a possible mechanism of an emergent Einstein gravity as a part of the effective theory induced due to quantum dynamics of torsion.

Lepton Flavor Violation in Models with A4 and S4 Flavor Symmetries ; The lepton flavor violation muto egamma, tauto egamma, tautomugamma, muto3e, tauto3e, tauto3mu and mue conversion in Al and Ti are studied in both the AltarelliFeruglio A4 model and the S4 model of Ding. The rates of these lepton flavor violation process for the inverted hierarchy neutrino mass spectrum are enhanced considerably by the next to leading order contributions. For both models, we find that the mue conversion in Ti is within the precision of next generation experiments in all the parameter space considered, the mue conversion in Al should be observable at least in a very significant part of the parameter space, whereas tauto egamma, tautomugamma, tauto3e and tauto3mu are below the expected future sensitivity. The detectability of muto egamma and muto3e in near future depends on the models and the neutrino mass spectrum. We suggest that a comprehensive consideration of the lepton flavor violation processes is important to test and distinguish both discrete flavor symmetry models.

Probing the primordial power spectra with inflationary priors ; We investigate constraints on power spectra of the primordial curvature and tensor perturbations with priors based on singlefield slowroll inflation models. We stochastically draw the Hubble slowroll parameters and generate the primordial power spectra using the inflationary flow equations. Using data from recent observations of CMB and several measurements of geometrical distances in the late Universe, Bayesian parameter estimation and model selection are performed for models that have separate priors on the slowroll parameters. The same analysis is also performed adopting the standard parameterization of the primordial power spectra. We confirmed that the scaleinvariant HarrisonZel'dovich spectrum is disfavored with increased significance from previous studies. While current observations appear to be optimally modeled with some simple models of singlefield slowroll inflation, data is not enough constraining to distinguish these models.

A bijection between paths for the Mp,2p1 minimal model Virasoro characters ; The states in the irreducible modules of the minimal models can be represented by infinite lattice paths arising from consideration of the corresponding RSOS statistical models. For the Mp,2p1 models, a completely different path representation has been found recently, this one on a halfinteger lattice; it has no known underlying statisticalmodel interpretation. The correctness of this alternative representation has not yet been demonstrated, even at the level of the generating functions, since the resulting fermionic characters differ from the known ones. This gap is filled here, with the presentation of two versions of a bijection between the two path representations of the Mp,2p1 states. In addition, a halflattice path representation for the Mp1,2p1 models is stated, and other generalisations suggested.

The dynamical behavior of the Extended Holographic Dark Energy with Hubble Horizon ; The extended holographic dark energy model with the Hubble horizon as the infrared cutoff avoids the problem of the circular reasoning of the holographic dark energy model. Unfortunately, it is hit with the nogo theorem. In this paper, we consider the extended holographic dark energy model with a potential, Vphi, for the BransDicke scalar field. With the addition of a potential for the BransDicke scalar field, the extended holographic dark energy model using the Hubble horizon as the infrared cutoff is a viable dark energy model, and the model has the dark energy dominated attractor solution.

FroggattNielsen models from E8 in Ftheory GUTs ; This paper studies Ftheory SU5 GUT models where the three generations of the standard model come from three different curves. All the matter is taken to come from curves intersecting at a point of enhanced E8 gauge symmetry. Giving a vev to some of the GUT singlets naturally implements a FroggattNielsen approach to flavour structure. A scan is performed over all possible models and the results are filtered using phenomenological constraints. We find a unique model that fits observations of quark and lepton masses and mixing well. This model suffers from two drawbacks Rparity must be imposed by hand and there is a doublettriplet splitting problem.

Accomplishments in GenomeScale In Silico Modeling for Industrial and Medical Biotechnology ; Driven by advancements in highthroughput biological technologies and the growing number of sequenced genomes, the construction of in silico models at the genome scale has provided powerful tools to investigate a vast array of biological systems and applications. Here, we review comprehensively the uses of such models in industrial and medical biotechnology, including biofuel generation, food production, and drug development. While the use of in silico models is still in its early stages for delivering to industry, significant initial successes have been achieved. For the cases presented here, genomescale models predict engineering strategies to enhance properties of interest in an organism or to inhibit harmful mechanisms of pathogens. Going forward, genomescale in silico models promise to extend their application and analysis scope to become a transformative tool in biotechnology.

1D LiebLiniger Bose Gas as NonRelativistic Limit of the SinhGordon Model ; The repulsive LiebLiniger model can be obtained as the nonrelativistic limit of the SinhGordon model all physical quantities of the latter model Smatrix, Lagrangian and operators can be put in correspondence with those of the former. We use this mapping, together with the Thermodynamical Bethe Ansatz equations and the exact form factors of the SinhGordon model, to set up a compact and general formalism for computing the expectation values of the LiebLiniger model both at zero and finite temperature. The computation of onepoint correlators is thoroughly detailed and, when possible, compared with known results in the literature.

Branchingtime model checking of onecounter processes ; Onecounter processes OCPs are pushdown processes which operate only on a unary stack alphabet. We study the computational complexity of model checking computation tree logic CTL over OCPs. A PSPACE upper bound is inherited from the modal mucalculus for this problem. First, we analyze the periodic behaviour of CTL over OCPs and derive a model checking algorithm whose running time is exponential only in the number of control locations and a syntactic notion of the formula that we call leftward until depth. Thus, model checking fixed OCPs against CTL formulas with a fixed leftward until depth is in P. This generalizes a result of the first author, Mayr, and To for the expression complexity of CTL's fragment EF. Second, we prove that already over some fixed OCP, CTL model checking is PSPACEhard. Third, we show that there already exists a fixed CTL formula for which model checking of OCPs is PSPACEhard. For the latter, we employ two results from complexity theory i Converting a natural number in Chinese remainder presentation into binary presentation is in logspaceuniform NC1 and ii PSPACE is AC0serializable. We demonstrate that our approach can be used to answer further open questions.

Likelihoodfree Bayesian inference for alphastable models ; alphastable distributions are utilised as models for heavytailed noise in many areas of statistics, finance and signal processing engineering. However, in general, neither univariate nor multivariate alphastable models admit closed form densities which can be evaluated pointwise. This complicates the inferential procedure. As a result, alphastable models are practically limited to the univariate setting under the Bayesian paradigm, and to bivariate models under the classical framework. In this article we develop a novel Bayesian approach to modelling univariate and multivariate alphastable distributions based on recent advances in likelihoodfree inference. We present an evaluation of the performance of this procedure in 1, 2 and 3 dimensions, and provide an analysis of real daily currency exchange rate data. The proposed approach provides a feasible inferential methodology at a moderate computational cost.

Dynamical transitions and sliding friction of the phasefieldcrystal model with pinning ; We study the nonlinear driven response and sliding friction behavior of the phasefieldcrystal PFC model with pinning including both thermal fluctuations and inertial effects. The model provides a continuous description of adsorbed layers on a substrate under the action of an external driving force at finite temperatures, allowing for both elastic and plastic deformations. We derive general stochastic dynamical equations for the particle and momentum densities including both thermal fluctuations and inertial effects. The resulting coupled equations for the PFC model are studied numerically. At sufficiently low temperatures we find that the velocity response of an initially pinned commensurate layer shows hysteresis with dynamical melting and freezing transitions for increasing and decreasing applied forces at different critical values. The main features of the nonlinear response in the PFC model are similar to the results obtained previously with molecular dynamics simulations of particle models for adsorbed layers.

Skewness of maximum likelihood estimators in dispersion models ; We introduce the dispersion models with a regression structure to extend the generalized linear models, the exponential family nonlinear models Cordeiro and Paula, 1989 and the proper dispersion models Jorgensen, 1997a. We provide a matrix expression for the skewness of the maximum likelihood estimators of the regression parameters in dispersion models. The formula is suitable for computer implementation and can be applied for several important submodels discussed in the literature. Expressions for the skewness of the maximum likelihood estimators of the precision and dispersion parameters are also derived. In particular, our results extend previous formulas obtained by Cordeiro and Cordeiro 2001 and Cavalcanti et al. 2009. A simulation study is perfomed to show the practice importance of our results.

Bayesian posterior probabilities revisited ; Huelsenbeck and Rannala 2004, Systematic Biology 53, 904913 presented a series of simulations in order to assess the extent to which the bayesian posterior probabilities associated with phylogenetic trees represent the standard frequentist statistical interpretation. They concluded that when the analysis model matches the generating model then the bayesian posterior probabilities are correct, but that the probabilities are much too large when the model is underspecified and slightly too small when the model is overspecified. Here, I take issue with the first conclusion, and instead contend that their simulation data show that the posterior probabilities are still slightly too large even when the models match. Furthermore, I suggest that the data show that the degree of this overestimation increases as the sequence length increases, and that it might increase as model complexity increases. I also provide some comments on the authors' conclusions concerning whether bootstrap proportions over or underestimate the true probabilities.

Quantum Integrable Model of an Arrangement of Hyperplanes ; The goal of this paper is to give a geometric construction of the Bethe algebra of Hamiltonians of a Gaudin model associated to a simple Lie algebra. More precisely, in this paper a quantum integrable model is assigned to a weighted arrangement of affine hyperplanes. We show under certain assumptions that the algebra of Hamiltonians of the model is isomorphic to the algebra of functions on the critical set of the corresponding master function. For a discriminantal arrangement we show under certain assumptions that the symmetric part of the algebra of Hamiltonians is isomorphic to the Bethe algebra of the corresponding Gaudin model. It is expected that this correspondence holds in general without the assumptions. As a byproduct of constructions we show that in a Gaudin model associated to an arbitrary simple Lie algebra, the Bethe vector, corresponding to an isolated critical point of the master function, is nonzero.

Rewriting Constraint Models with Metamodels ; An important challenge in constraint programming is to rewrite constraint models into executable programs calculat ing the solutions. This phase of constraint processing may require translations between constraint programming lan guages, transformations of constraint representations, model optimizations, and tuning of solving strategies. In this paper, we introduce a pivot metamodel describing the common fea tures of constraint models including different kinds of con straints, statements like conditionals and loops, and other firstclass elements like object classes and predicates. This metamodel is general enough to cope with the constructions of many languages, from objectoriented modeling languages to logic languages, but it is independent from them. The rewriting operations manipulate metamodel instances apart from languages. As a consequence, the rewriting operations apply whatever languages are selected and they are able to manage model semantic information. A bridge is created between the metamodel space and languages using parsing techniques. Tools from the software engineering world can be useful to implement this framework.

Interacting entropycorrected new agegraphic tachyon, Kessence and dilaton scalar field models of dark energy in nonflat universe ; We present the new agegraphic dark energy model by introducing the quantum corrections to the entropyarea relation in the setup of loop quantum gravity. Employing this new form of dark energy, we investigate the model of interacting dark energy and derive its equation of state. We study the correspondence between the tachyon, Kessence and dilaton scalar field models with the interacting entropycorrected new agegraphic dark energy model in the nonflat FRW universe. Moreover, we reconstruct the corresponding scalar potentials which describe the dynamics of the scalar field models.

Cosmic microwave background constraints on cosmological models with largescale isotropy breaking ; Several anomalies appear to be present in the largeangle cosmic microwave background CMB anisotropy maps of WMAP, including the alignment of largescale multipoles. Models in which isotropy is spontaneously broken e.g., by a scalar field have been proposed as explanations for these anomalies, as have models in which a preferred direction is imposed during inflation. We examine models inspired by these, in which isotropy is broken by a multiplicative factor with dipole andor quadrupole terms. We evaluate the evidence provided by the multipole alignment using a Bayesian framework, finding that the evidence in favor of the model is generally weak. We also compute approximate changes in estimated cosmological parameters in the brokenisotropy models. Only the overall normalization of the power spectrum is modified significantly.

Agegraphic Dark Energy Model in NonFlat Universe Statefinder Diagnostic and wwprime Analysis ; We study the interacting agegraphic dark energy ADE model in nonflat universe by means of statefinder diagnostic and wwprime analysis. First, the evolution of EoS parameter wd and deceleration parameter q in terms of scale factor for interacting ADE model in nonflat universe are calculated. Dependence of wd on the ADE model parameters n and alpha in different spatial curvatures is investigated. We show that the evolution of q is dependent on the type of spatial curvature, beside of dependence on parameters n and alpha. The accelerated expansion takes place sooner in open universe and later in closed universe compare with flat universe. Then, we plot the evolutionary trajectories of the interacting ADE model for different values of the parameters n and alpha as well as for different contributions of spatial curvature, in the statefinder parameters plane. In addition to statefinder, we also investigate the ADE model in nonflat universe with wwprime analysis.

The WN minimal model classification ; We first rigourously establish, for any N, that the toroidal modular invariant partition functions for the not necessarily unitary WNp,q minimal models biject onto a welldefined subset of those of the SUNxSUN WessZuminoWitten theories at level pN,qN. This permits considerable simplifications to the proof of the CappelliItzyksonZuber classification of Virasoro minimal models. More important, we obtain from this the complete classification of all modular invariants for the W3p,q minimal models. All should be realised by rational conformal field theories. Previously, only those for the unitary models, i.e. W3p,p1, were classified. For all N our correspondence yields for free an extensive list of WNp,q modular invariants. The W3 modular invariants, like the Virasoro minimal models, all factorise into SU3 modular invariants, but this fails in general for larger N. We also classify the SU3xSU3 modular invariants, and find there a new infinite series of exceptionals.

Interacting entropycorrected holographic scalar field models in nonflat universe ; In this work we establish a correspondence between the tachyon, Kessence and dilaton scalar field models with the interacting entropycorrected holographic dark ECHD model in nonflat FRW universe. The reconstruction of potentials and dynamics of these scalar fields according to the evolutionary behavior of the interacting ECHDE model are be done. It has been shown that the phantom divide can not be crossed in ECHDE tachyon model while it is achieved for ECHDE Kessence and ECHDE dilaton scenarios. At last we calculate the limiting case of interacting ECHDE model, without entropycorrection.

Highway Mobility and Vehicular AdHoc Networks in NS3 ; The study of vehicular adhoc networks VANETs requires efficient and accurate simulation tools. As the mobility of vehicles and driver behavior can be affected by network messages, these tools must include a vehicle mobility model integrated with a quality network simulator. We present the first implementation of a wellknown vehicle mobility model to ns3, the next generation of the popular ns2 networking simulator. Vehicle mobility and network communication are integrated through events. Usercreated event handlers can send network messages or alter vehicle mobility each time a network message is received and each time vehicle mobility is updated by the model. To aid in creating simulations, we have implemented a straight highway model that manages vehicle mobility, while allowing for various user customizations. We show that the results of our implementation of the mobility model matches that of the model's author and provide an example of using our implementation in ns3.

Boundary WessZuminoNovikovWitten Model from the Pairing Hamiltonian ; Correlation functions of primary fields in the WessZuminoNovikovWitten WZNW model are known to satisfy a system of KnizhnikZamolodchikov KZ equations, which involve constants of motion of the exactlysolvable Gaudin magnet. We modify the KZ equations by replacing these Gaudin operators with constants of motion of the closelyrelated Richardson pairing Hamiltonian and reconstruct a deformed WZNW model, whose correlators satisfy these equations. This modified theory, dubbed here the boundary WZNW model, contains a term that breaks translational symmetry and therefore represents a generalized boundary operator. The corresponding correlators of the boundary WZNW model are calculated and are shown to acquire exponential prefactors, in contrast to the bulk WZNW theories. The solution also establishes a connection between correlation functions of the WZNW model and the spectrum of the reduced pairing Hamiltonian.

Bandwidth Modeling and Estimation in Peer to Peer Networks ; Recent studies have shown that the majority of today's internet traffic is related to Peer to Peer P2P traffic. The study of bandwidth in P2P networks is very important. Because it helps us in more efficient capacity planning and QoS provisioning when we would like to design a large scale computer networks. In this paper motivated by the behavior of peers sources or seeds that is modeled by Ornstein Uhlenbeck OU process, we propose a model for bandwidth in P2P networks. This model is represented with a stochastic integral. We also model the bandwidth when we have multiple downloads or uploads. The autocovariance structure of bandwidth in either case is studied and the statistical parameters such as mean, variance and autocovariance are obtained. We then study the queue length behavior of the bandwidth model. The methods for generating synthetic bandwidth process and estimation of the bandwidth parameters using maximum likehood estimation are presented.

Twosided estimates for stock price distribution densities in jumpdiffusion models ; We consider uncorrelated SteinStein, Heston, and HullWhite models and their perturbations by compound Poisson processes with jump amplitudes distributed according to a double exponential law. Similar perturbations of the BlackScholes model were studied by S. Kou. For perturbed stochastic volatility models, we obtain twosided estimates for the stock price distribution density and compare the tail behavior of this density before and after perturbation. It is shown that if the value of the parameter, characterizing the right tail of the double exponential law, is small, then the stock price density in the perturbed model decays slower than the density in the original model. On the other hand, if the value of this parameter is large, then there are no significant changes in the behavior of the stock price distribution density.

Szekeres SwissCheese model and supernova observations ; We use different particular classes of axially symmetric Szekeres Swisscheese models for the study of the apparent dimming of the supernovae of type Ia. We compare the results with those obtained in the corresponding LemaitreTolman Swisscheese models. Although the quantitative picture is different the qualitative results are comparable, i.e, one cannot fully explain the dimming of the supernovae using small scale 50 Mpc inhomogeneities. To fit successfully the data we need structures of order of 500 Mpc size or larger. However, this result might be an artifact due to the use of axial light rays in axially symmetric models. Anyhow, this work is a first step in trying to use Szekeres Swisscheese models in cosmology and it will be followed by the study of more physical models with still less symmetry.

A lattice study of N2 LandauGinzburg model using a Nicolai map ; It has been conjectured that the twodimensional N2 WessZumino model with a quasihomogeneous superpotential provides the LandauGinzburg description of the N2 superconformal minimal models. For the cubic superpotential Wlambda Phi33, it is expected that the WessZumino model describes A2 model and the chiral superfield Phi shows the conformal weight h,barh16,16 at the IR fixed point. We study this conjecture by a lattice simulation, extracting the weight from the finite volume scaling of the susceptibility of the scalar component in Phi. We adopt a lattice model with the overlap fermion, which possesses a Nicolai map and a discrete Rsymmetry. We set alambda0.3 and generate the scalar field configurations by solving the Nicolai map on L times L lattices in the range L18 32. To solve the map, we use the NewtonRaphson algorithm with various initial configurations. The result is 1hbarh0.660 pm0.011, which is consistent with the conjecture within the statistical error, while a systematic error is estimated as less than 0.5 .

The TuttePotts connection in the presence of an external magnetic field ; The classical relationship between the Tutte polynomial of graph theory and the Potts model of statistical mechanics has resulted in valuable interactions between the disciplines. Unfortunately, it does not include the external magnetic fields that appear in most Potts model applications. Here we define the Vpolynomial, which lifts the classical relationship between the Tutte polynomial and the zero field Potts model to encompass external magnetic fields. The Vpolynomial generalizes Nobel and Welsh's Wpolynomial, which extends the Tutte polynomial by incorporating vertex weights and adapting contraction to accommodate them. We prove that the variable field Potts model partition function with its many specializations is an evaluation of the Vpolynomial, and hence a polynomial with deletioncontraction reduction and FortuinKasteleyn type representation. This unifies an important segment of Potts model theory and brings previously successful combinatorial machinery, including complexity results, to bear on a wider range of statistical mechanics models.

Global SO10 Ftheory GUTs ; Making use of toric geometry we construct a class of global Ftheory GUT models. The base manifolds are blowups of Fano threefolds and the CalabiYau fourfold is a complete intersection of two hypersurfaces. We identify possible GUT divisors and construct SO10 models on them using the spectral cover construction. We use a split spectral cover to generate chiral matter on the 10 curves in order to get more degrees of freedom in phenomenology. We use abelian flux to break SO10 to SU5times U1 which is interpreted as a flipped SU5 model. With the GUT Higgses in the SU5times U1 model it is possible to further break the gauge symmetry to the Standard Model. We present several phenomenologically attractive examples in detail.

Information theoretic model validation for clustering ; Model selection in clustering requires i to specify a suitable clustering principle and ii to control the model order complexity by choosing an appropriate number of clusters depending on the noise level in the data. We advocate an information theoretic perspective where the uncertainty in the measurements quantizes the set of data partitionings and, thereby, induces uncertainty in the solution space of clusterings. A clustering model, which can tolerate a higher level of fluctuations in the measurements than alternative models, is considered to be superior provided that the clustering solution is equally informative. This tradeoff between emphinformativeness and emphrobustness is used as a model selection criterion. The requirement that data partitionings should generalize from one data set to an equally probable second data set gives rise to a new notion of structure induced information.

Parameter identifiability in a class of random graph mixture models ; We prove identifiability of parameters for a broad class of random graph mixture models. These models are characterized by a partition of the set of graph nodes into latent unobservable groups. The connectivities between nodes are independent random variables when conditioned on the groups of the nodes being connected. In the binary random graph case, in which edges are either present or absent, these models are known as stochastic blockmodels and have been widely used in the social sciences and, more recently, in biology. Their generalizations to weighted random graphs, either in parametric or nonparametric form, are also of interest in many areas. Despite a broad range of applications, the parameter identifiability issue for such models is involved, and previously has only been touched upon in the literature. We give here a thorough investigation of this problem. Our work also has consequences for parameter estimation. In particular, the estimation procedure proposed by Frank and Harary for binary affiliation models is revisited in this article.

Beyond MFV in family symmetry theories of fermion masses ; Minimal Flavour Violation MFV postulates that the only source of flavour changing neutral currents and CP violation, as in the Standard Model, is the CKM matrix. However it does not address the origin of fermion masses and mixing and models that do usually have a structure that goes well beyond the MFV framework. In this paper we compare the MFV predictions with those obtained in models based on spontaneously broken horizontal family symmetries, both Abelian and nonAbelian. The generic suppression of flavour changing processes in these models turns out to be weaker than in the MFV hypothesis. Despite this, in the supersymmetric case, the suppression may still be consistent with a solution to the hierarchy problem, with masses of superpartners below 1 TeV. A comparison of FCNC and CP violation in processes involving a variety of different family quantum numbers should be able to distinguish between various family symmetry models and models satisfying the MFV hypothesis.

Open system dynamics of simple collision models ; A simple collision model is employed to introduce elementary concepts of open system dynamics of quantum systems. In particular, within the framework of collision models we introduce the quantum analogue of thermalization process called quantum homogenization and simulate quantum decoherence processes. These dynamics are driven by partial swaps and controlled unitary collisions, respectively. We show that collision models can be used to prepare multipartite entangled states. Partial swap dynamics generates Wtype of entanglement saturating the CKW inequalities, whereas the decoherence collision models creates GHZtype of entangled states. The considered evolution of a system in a sequence of collisions is described by a discrete semigroup E1,...,En. Interpolating this discrete points within the set of quantum channels we derive for both processes the corresponding Lindblad master equations. In particular, we argue that collision models can be used as simulators of arbitrary Markovian dynamics, however, the inverse is not true.

Optimal timedependent lattice models for nonequilibrium dynamics ; Lattice models are abundant in theoretical and condensedmatter physics. Generally, lattice models contain timeindependent hopping and interaction parameters that are derived from the Wannier functions of the noninteracting problem. Here, we present a new concept based on timedependent Wannier functions and the variational principle that leads to optimal timedependent lattice models. As an application, we use the BoseHubbard model with timedependent Wannier functions to study a quench scenario involving higher bands. We find a separation of times scales in the dynamics and show that under some circumstances the multiband nonequilibrium dynamics of a quantum system can be obtained essentially at the cost of a singleband model.

Duality of parity doublets of helicity pm 2 in D21 ; In D21 dimensions there are two dual descriptions of parity singlets of helicity pm 1, namely the selfdual model of firstorder in derivatives and the MaxwellChernSimons theory of secondorder. Correspondingly, for helicity pm 2 there are four models SSDpmr describing parity singlets of helicities pm 2. They are of first, second,third and fourthorder r1,2,3,4 respectively. Here we show that the generalized soldering of the opposite helicity models SSD4 and SSD4 leads to the linearized form of the new massive gravity suggested by Bergshoeff, Hohm and Townsend BHT similarly to the soldering of SSD3 and SSD3. We argue why in both cases we have the same result. We also find out a triple master action which interpolates between the three dual models linearized BHT theory, SSD3 SSD3 and SSD4 SSD4. By comparing gauge invariant correlation functions we deduce dual maps between those models. In particular, we learn how to decompose the field of the linearized BHT theory in helicity eigenstates of the dual models up to gauge transformations.

Modeling the Nonlinear Viscoelastic Response of High Temperature Polyimides ; A constitutive model is developed to predict the viscoelastic response of polyimide resins that are used in high temperature applications. This model is based on a thermodynamic framework that uses the notion that the natural configuration' of a body evolves as the body undergoes a process and the evolution is determined by maximizing the rate of entropy production in general and the rate of dissipation within purely mechanical considerations. We constitutively prescribe forms for the specific Helmholtz potential and the rate of dissipation which is the product of density, temperature and the rate of entropy production, and the model is derived by maximizing the rate of dissipation with the constraint of incompressibility, and the reduced energy dissipation equation is also regarded as a constraint in that it is required to be met in every process that the body undergoes. The efficacy of the model is ascertained by comparing the predictions of the model with the experimental data for PMR15 and HFPEII52 polyimide resins.

Modeling Dynamical Influence in Human Interaction Patterns ; How can we model influence between individuals in a social system, even when the network of interactions is unknown In this article, we review the literature on the influence model, which utilizes independent time series to estimate how much the state of one actor affects the state of another actor in the system. We extend this model to incorporate dynamical parameters that allow us to infer how influence changes over time, and we provide three examples of how this model can be applied to simulated and real data. The results show that the model can recover known estimates of influence, it generates results that are consistent with other measures of social networks, and it allows us to uncover important shifts in the way states may be transmitted between actors at different points in time.

Dimensional reduction in quantum field theories at finite temperature and density ; In this work we present two correspondences between the massless GrossNeveu model with one or two coupling constants in 11 dimensions and nonrelativistic field theories in 31 dimensions. It is shown that on a meanfield level the massless GrossNeveu model can be mapped onto BCS theory provided that translational invariance of the condensate is assumed. The generalized massless GrossNeveu model with two coupling constants is mapped onto a quasi onedimensional extended Hubbard model used in the description of spinPeierls systems. It is shown that the particle hole symmetry of the Hubbard model implies selfconsistency of the condensate. The dimensional reduction allows an identification of the phase diagrams of the models.

Identification of discrete concentration graph models with one hidden binary variable ; Conditions are presented for different types of identifiability of discrete variable models generated over an undirected graph in which one node represents a binary hidden variable. These models can be seen as extensions of the latent class model to allow for conditional associations between the observable random variables. Since local identification corresponds to full rank of the parametrization map, we establish a necessary and sufficient condition for the rank to be full everywhere in the parameter space. The condition is based on the topology of the undirected graph associated to the model. For nonfull rank models, the obtained characterization allows us to find the subset of the parameter space where the identifiability breaks down.

Condensed Groundstates of Frustrated BoseHubbard Models ; We study theoretically the groundstates of twodimensional BoseHubbard models which are frustrated by gauge fields. Motivated by recent proposals for the implementation of optically induced gauge potentials, we focus on the situation in which the imposed gauge fields give rise to a pattern of staggered fluxes, of magnitude alpha and alternating in sign along one of the principal axes. For alpha12 this model is equivalent to the case of uniform flux per plaquette nphi12, which, in the hardcore limit, realizes the fully frustrated spin12 XY model. We show that the meanfield groundstates of this frustrated BoseHubbard model typically break translational symmetry. We introduce a general numerical technique to detect broken symmetry condensates in exact diagonalization studies. Using this technique we show that, for all cases studied, the groundstate of the BoseHubbard model with staggered flux alpha is condensed, and we obtain quantitative determinations of the condensate fraction. We discuss the experimental consequences of our results. In particular, we explain the meaning of gaugeinvariance in ultracold atom systems subject to optically induced gauge potentials, and show how the ability to imprint phase patterns prior to expansion can allow very useful additional information to be extracted from expansion images.

Towards Quality of Service and Resource Aware Robotic Systems through ModelDriven Software Development ; Engineering the software development process in robotics is one of the basic necessities towards industrialstrength service robotic systems. A major challenge is to make the step from codedriven to modeldriven systems. This is essential to replace handcrafted singleunit systems by systems composed out of components with explicitly stated properties. Furthermore, this fosters reuse by separating robotics knowledge from shortcycled implementational technologies. Altogether, this is one but important step towards able robots. This paper reports on a modeldriven development process for robotic systems. The process consists of a robotics metamodel with first explications of nonfunctional properties. A modeldriven toolchain based on Eclipse provides the model transformation and code generation steps. It also provides design time analysis of resource parameters e.g. schedulability analysis of realtime tasks as a first step towards overall resource awareness in the development of integrated robotic systems. The overall approach is underpinned by several real world scenarios.

Phase diagram of the ABC model with nonconserving processes ; The three species ABC model of driven particles on a ring is generalized to include vacancies and particlenonconserving processes. The model exhibits phase separation at high densities. For equal average densities of the three species, it is shown that although the dynamics is it local, it obeys detailed balance with respect to a Hamiltonian with it longrange interactions, yielding a nonadditive free energy. The phase diagrams of the conserving and nonconserving models, corresponding to the canonical and grandcanonical ensembles, respectively, are calculated in the thermodynamic limit. Both models exhibit a transition from a homogeneous to a phaseseparated state, although the phase diagrams are shown to differ from each other. This conforms with the expected inequivalence of ensembles in equilibrium systems with longrange interactions. These results are based on a stability analysis of the homogeneous phase and exact solution of the hydrodynamic equations of the models. They are supported by MonteCarlo simulations. This study may serve as a useful starting point for analyzing the phase diagram for unequal densities, where detailed balance is not satisfied and thus a Hamiltonian cannot be defined.

A Simple Abstraction for Data Modeling ; The problems that scientists face in creating well designed databases intersect with the concerns of data curation. Entityrelationship modeling and its variants have been the basis of most relational data modeling for decades. However, these abstractions and the relational model itself are intricate and have proved not to be very accessible among scientists with limited resources for data management. This paper explores one aspect of relational data models, the meaning of foreign key relationships. We observe that a foreign key produces a table relationship that generally references either an entity or repeating attributes. This paper proposes constructing foreign keys based on these two cases, and suggests that the method promotes intuitive data modeling and normalization.

Dark Energy Model in Anisotropic Bianchi TypeIII SpaceTime with Variable EoS Parameter ; A new dark energy model in anisotropic Bianchi typeIII spacetime with variable equation of state EoS parameter has been investigated in the present paper. To get the deterministic model, we consider that the expansion theta in the model is proportional to the eigen value sigma22 of the shear tensor sigmaji. The EoS parameter omega is found to be time dependent and its existing range for this model is in good agreement with the recent observations of SNe Ia data Knop et al. 2003 and SNe Ia data with CMBR anisotropy and galaxy clustering statistics Tegmark et al. 2004. It has been suggested that the dark energy that explains the observed accelerating expansion of the universe may arise due to the contribution to the vacuum energy of the EoS in a time dependent background. Some physical aspects of dark energy model are also discussed.

A nonparametric urnbased approach to interacting failing systems with an application to credit risk modeling ; In this paper we propose a new nonparametric approach to interacting failing systems FS, that is systems whose probability of failure is not negligible in a fixed time horizon, a typical example being firms and financial bonds. The main purpose when studying a FS is to calculate the probability of default and the distribution of the number of failures that may occur during the observation period. A model used to study a failing system is defined default model. In particular, we present a general recursive model constructed by the means of inter acting urns. After introducing the theoretical model and its properties we show a first application to credit risk modeling, showing how to assess the idiosyncratic probability of default of an obligor and the joint probability of failure of a set of obligors in a portfolio of risks, that are divided into reliability classes.

A New Non Linear, Time Stamped Feed Back Model Based Encryption Mechanism with Acknowledgement Support ; In this work a model is going to be used which develops data distributed over a identified value which is used as nonce IV. The model considers an equilibrium equation which is a function of non linear relationships, time variant and nonce variant values and takes the feed back of earlier round as input to the present round. The process is repeated for different timings which are used as time stamps in the encryption mechanism. Thus this model generates a distributed sequence which is used as sub key. This model supports very important parameters in symmetric data encryption schemes like non linear relationships between different values used in the model, variable key length, timeliness of encryption mechanism and also acknowledgement between the participating parties. It also supports feed back mode which provides necessary strength against crypto analysis.

Nonlinear analysis of spacecraft thermal models ; We study the differential equations of lumpedparameter models of spacecraft thermal control. Firstly, we consider a satellite model consisting of two isothermal parts nodes an outer part that absorbs heat from the environment as radiation of various types and radiates heat as a blackbody, and an inner part that just dissipates heat at a constant rate. The resulting system of two nonlinear ordinary differential equations for the satellite's temperatures is analyzed with various methods, which prove that the temperatures approach a steady state if the heat input is constant, whereas they approach a limit cycle if it varies periodically. Secondly, we generalize those methods to study a manynode thermal model of a spacecraft this model also has a stable steady state under constant heat inputs that becomes a limit cycle if the inputs vary periodically. Finally, we propose new numerical analyses of spacecraft thermal models based on our results, to complement the analyses normally carried out with commercial software packages.

Uncovering Mechanisms of Coronal Magnetism via Advanced 3D Modeling of Flares and Active Regions ; The coming decade will see the routine use of solar data of unprecedented spatial and spectral resolution, time cadence, and completeness. To capitalize on the new or soon to be available facilities such as SDO, ATST and FASR, and the challenges they present in the visualization and synthesis of multiwavelength datasets, we propose that realistic, sophisticated, 3D active region and flare modeling is timely and critical, and will be a forefront of coronal studies over the coming decade. To make such modeling a reality, a broad, concerted effort is needed to capture the wealth of information resulting from the data, develop a synergistic modeling effort, and generate the necessary visualization, interpretation and modeldata comparison tools to accurately extract the key physics.

Asymptotic law of likelihood ratio for multilayer perceptron models ; We consider regression models involving multilayer perceptrons MLP with one hidden layer and a Gaussian noise. The data are assumed to be generated by a true MLP model and the estimation of the parameters of the MLP is done by maximizing the likelihood of the model. When the number of hidden units of the true model is known, the asymptotic distribution of the maximum likelihood estimator MLE and the likelihood ratio LR statistic is easy to compute and converge to a chi2 law. However, if the number of hidden unit is overestimated the Fischer information matrix of the model is singular and the asymptotic behavior of the MLE is unknown. This paper deals with this case, and gives the exact asymptotic law of the LR statistics. Namely, if the parameters of the MLP lie in a suitable compact set, we show that the LR statistics is the supremum of the square of a Gaussian process indexed by a class of limit score functions.

Different SO10 Paths to Fermion Masses and Mixings ; Recently SO10 models with typeII seesaw dominance have been proposed as a promising framework for obtaining Grand Unification theories with approximate Tribimaximal TB mixing in the neutrino sector. We make a general study of SO10 models with typeII seesaw dominance and show that an excellent fit can be obtained for fermion masses and mixings, also including the neutrino sector. To make this statement more significant we compare the performance of typeII seesaw dominance models in fitting the fermion masses and mixings with more conventional models which have no builtin TB mixing in the neutrino sector. For a fair comparison the same input data and fitting procedure is adopted for all different theories. We find that the typeII dominance models lead to an excellent fit, comparable with the best among the available models, but the tight structure of this framework implies a significantly larger amount of fine tuning with respect to other approaches.

A mathematical model for networks with structures in the mesoscale ; The new concept of multilevel network is introduced in order to embody some topological properties of complex systems with structures in the mesoscale which are not completely captured by the classical models. This new model, which generalizes the hypernetwork and hyperstructure models, fits perfectly with several reallife complex systems, including social and public transportation networks. We present an analysis of the structural properties of the multilevel network, including the clustering and the metric structures. Some analytical relationships amongst the efficiency and clustering coefficient of this new model and the corresponding parameters of the underlying network are obtained. Finally some random models for multilevel networks are given to illustrate how different multilevel structures can produce similar underlying networks and therefore that the mesoscale structure should be taken into account in many applications.

Aging and stationary properties of nonequilibrium symmetrical threestate models ; We consider a nonequilibrium threestate model whose dynamics is Markovian and displays the same symmetry as the threestate Potts model, i.e., the transition rates are invariant under the permutation of the states. Unlike the Potts model, detailed balance is in general not satisfied. The aging and the stationary properties of the model defined on a square lattice are obtained by means of largescale Monte Carlo simulations. We show that the phase diagram presents a critical line, belonging to the threestate Potts universality class, that ends at a point whose universality class is that of the voter model. Aging is considered on the critical line, at the voter point and in the ferromagnetic phase.

Vortex and gap generation in gauge models of graphene ; Effective quantum field theoretical continuum models for graphene are investigated. The models include a complex scalar field and a vector gauge field. Different gauge theories are considered and their gap patterns for the scalar, vector, and fermion excitations are investigated. Different gauge groups lead to different relations between the gaps, which can be used to experimentally distinguish the gauge theories. In this class of models the fermionic gap is a dynamic quantity. The finiteenergy vortex solutions of the gauge models have the flux of the magnetic field quantized, making the BohmAharonov effect active even when external electromagnetic fields are absent. The flux comes proportional to the scalar field angular momentum quantum number. The zero modes of the Dirac equation show that the gauge models considered here are compatible with fractionalization.

Quantum deformation of two fourdimensional spin foam models ; We construct the qdeformed version of two fourdimensional spin foam models, the Euclidean and Lorentzian versions of the EPRL model. The qdeformed models are based on the representation theory of two copies of Uqsu2 at a root of unity and on the quantum Lorentz group with a real deformation parameter. For both models we give a definition of the quantum EPRL intertwiners, study their convergence and braiding properties and construct an amplitude for the foursimplexes. We find that both of the resulting models are convergent.

Weak Gravity Conjecture and HolographicAgegraphic Dark Energy ; A criterion that should be satisfied in the inflation and quintessence models is motivated from the weak gravity conjecture WGC by Huang. However, it is found that the criterion is inconsistent with the Holographic dark energy HDE and new agegraphic dark energy NADE models. In the note, we firstly show that in the HDE and NADE models the criterion should be be replaced respectively by two new criterions. Secondly, we apply the new criterions indicated by WGC to survey the two models. We find that the contradiction between WGC and the NADE model is removed when the new criterion is used. In the HDE model, we find the effects of the spatial curvature and the interaction should be considered in order to match the new criterion.

Modeling heterogeneity in ranked responses by nonparametric maximum likelihood How do Europeans get their scientific knowledge ; This paper is motivated by a Eurobarometer survey on science knowledge. As part of the survey, respondents were asked to rank sources of science information in order of importance. The official statistical analysis of these data however failed to use the complete ranking information. We instead propose a method which treats ranked data as a set of paired comparisons which places the problem in the standard framework of generalized linear models and also allows respondent covariates to be incorporated. An extension is proposed to allow for heterogeneity in the ranked responses. The resulting model uses a nonparametric formulation of the random effects structure, fitted using the EM algorithm. Each mass point is multivalued, with a parameter for each item. The resultant model is equivalent to a covariate latent class model, where the latent class profiles are provided by the mass point components and the covariates act on the class profiles. This provides an alternative interpretation of the fitted model. The approach is also suitable for paired comparison data.

DirectLiNGAM A direct method for learning a linear nonGaussian structural equation model ; Structural equation models and Bayesian networks have been widely used to analyze causal relations between continuous variables. In such frameworks, linear acyclic models are typically used to model the datagenerating process of variables. Recently, it was shown that use of nonGaussianity identifies the full structure of a linear acyclic model, i.e., a causal ordering of variables and their connection strengths, without using any prior knowledge on the network structure, which is not the case with conventional methods. However, existing estimation methods are based on iterative search algorithms and may not converge to a correct solution in a finite number of steps. In this paper, we propose a new direct method to estimate a causal ordering and connection strengths based on nonGaussianity. In contrast to the previous methods, our algorithm requires no algorithmic parameters and is guaranteed to converge to the right solution within a small fixed number of steps if the data strictly follows the model.

Holographic unification of dark matter and dark energy ; Using a new version of the holographic principle, a constant term was introduced, which conduces to the description of the standard cosmological LCDM model, and unifies under the same concept the dark matter and dark energy phenomena. The obtained model improves the results of previously considered holographic models based on local quantities. The inclusion of constant term is interpreted as a natural first approximation for the infrared cutoff which is associated with the vacuum energy, and the additional terms guarantee an appropriate evolutionary scenario that fits the astrophysical observations. The model allows to reproduce the standard LCDM model without explicitly introducing matter content, and using only geometrical quantities. It is also obtained that the model may describe the dark energy beyond the standard LCDM.

Crossing w1 by a single scalar field coupling with matter and the observational constraints ; Motivated by YangMills dark energy model, we propose a new model by introducing a logarithmic correction. we find that this model can avoid the coincidence problem naturally and gives an equation of state w smoothly crossing 1 if an interaction between dark energy and dark matter exists. It has a stable tracker solution as well. To confront with observations based on the combined data of SNIa, BAO, CMB and Hubble parameter, we obtain the best fit values of the parameters with 1sigma, 2sigma, 3sigma errors for the noncoupled model Omegam0.276pm0.0080.0160.0240.0150.022, h0.699pm0.003pm0.006pm0.008, and for the coupled model with a decaying rate gamma0.2 Omegam0.291pm0.0040.0080.0120.0070.011, h0.701pm0.002pm0.005pm0.007. In particular, it is found that the noncoupled model has a dynamic evolution almost undistinguishable to LambdaCDM at the latetime Universe.

Model of the electroweak, gravitational and strong interactions in the Otheory ; Based on the matrix representation of octonion algebra, supplied with specific multiplication rule, the model of electroweak and gravitational interactions is built up. While electroweak interaction in this model is induced by charged Wbosons, other two forces appear to have slightly more complicated nature. Gravitational interaction coincides in the model with dipole interaction of a pair of charged bosons. The dipole consists of a charged vector bosons pair from the major octonion algebra fields. When the charged dipole pair interacts with the neutral bosons pair from the major octonion algebra fields, the charged bosons pair misses its mass. The drop in mass leads to appearance of farranging forces of gravitational interaction. Finally, strong interaction appears in the model as internal gravitational solution of 'black whole' type with the peculiar 'gravitational' constant. The solution is a product of interaction of major vector fields pair with charged Wbosons pair. It is inferred from the model that the state space is tendimensional. The space is built as a module of the matrix representation of octonion algebra over the particles field Omodule. Similarly to the Standard WeinbergSalam theory, the particle mass here appears as the product of interaction of massless spinor fields and Higgs field from Omodule representation.

Scalable Approach to Uncertainty Quantification and Robust Design of Interconnected Dynamical Systems ; Development of robust dynamical systems and networks such as autonomous aircraft systems capable of accomplishing complex missions faces challenges due to the dynamically evolving uncertainties coming from model uncertainties, necessity to operate in a hostile cluttered urban environment, and the distributed and dynamic nature of the communication and computation resources. Modelbased robust design is difficult because of the complexity of the hybrid dynamic models including continuous vehicle dynamics, the discrete models of computations and communications, and the size of the problem. We will overview recent advances in methodology and tools to model, analyze, and design robust autonomous aerospace systems operating in uncertain environment, with stress on efficient uncertainty quantification and robust design using the case studies of the mission including modelbased target tracking and search, and trajectory planning in uncertain urban environment. To show that the methodology is generally applicable to uncertain dynamical systems, we will also show examples of application of the new methods to efficient uncertainty quantification of energy usage in buildings, and stability assessment of interconnected power networks.

Conditional Density Estimation by Penalized Likelihood Model Selection and Applications ; In this technical report, we consider conditional density estimation with a maximum likelihood approach. Under weak assumptions, we obtain a theoretical bound for a KullbackLeibler type loss for a single model maximum likelihood estimate. We use a penalized model selection technique to select a best model within a collection. We give a general condition on penalty choice that leads to oracle type inequality for the resulting estimate. This construction is applied to two examples of partitionbased conditional density models, models in which the conditional density depends only in a piecewise manner from the covariate. The first example relies on classical piecewise polynomial densities while the second uses Gaussian mixtures with varying mixing proportion but same mixture components. We show how this last case is related to an unsupervised segmentation application that has been the source of our motivation to this study.

Anthropic versus cosmological solutions to the coincidence problem ; In this paper we investigate possible solutions to the coincidence problem in flat phantom dark energy models with a constant dark energy equation of state and quintessence models with a linear scalar field potential. These models are representative of a broader class of cosmological scenarios in which the universe has a finite lifetime. We show that, in the absence of anthropic constraints, including a prior probability for the models inversely proportional to the total lifetime of the universe excludes models very close to the Lambda rm CDM model. This relates a cosmological solution to the coincidence problem with a dynamical dark energy component having an equation of state parameter not too close to 1 at the present time. We further show, that anthropic constraints, if they are sufficiently stringent, may solve the coincidence problem without the need for dynamical dark energy.

The Genesis of the BigBang and Inflation ; The standard model of cosmology posits that some time in the remote past, labelled as t0, a BigBang occurred. However, it does not tell what caused the BigBang and subsequently the Inflation. In the present work the cause of the BigBang and Inflation is suggested on the basis of the hints provided by the experimental findings at CERN and RHIC. The model used is singularity free Newtonian, i.e., nonrelativistic, oscillatory model of the universe in which the space does not expand whereas all the relativistic cosmological models of the universe including the standard model, except the now discredited Einstein's static model, imply that apart from the matter and the radiation in the universe the space is also expanding. However, there is no observational evidence whatsoever of the expansion of the space and as such, in all probability, the space is not at all expanding. A critique of the singularity theorems is also given on the basis of the experimental findings at CERN and RHIC and it is emphasized that no gravitationally collapsing object can collapse to a singularity, if it does, the time honoured Pauli's exclusion principle would be violated.

Supergroup extended super Liouville correspondence ; We derive a relation between correlation functions of supergroup WZNW models and conformal field theories with extended superconformal symmetry. The supergroups considered have a bosonic subgroup of the form SL2 x A for some Lie group A. The corresponding conformal field theory is a super Liouville field theory coupled with the WZNW model on A. An example is a correspondence between the PSU1,12 WZNW model and small N4 super Liouville field theory. The OSPn2 WZNW model is related to a superconformal field theory with SOn extended superconformal symmetry of the KnizhnikBershadsky type. In the case n4 this is simply the large N4,4 superconformal symmetry. Besides these two examples we make a general derivation encompassing the WZNW models on supergroups SL2n, D2,1;alpha, OSP42n, F4 and G3 and their relation to models with extended superconformal algebras as symmetry.

Autoassociative models, nonlinear Principal component analysis, manifolds and projection pursuit ; In this paper, autoassociative models are proposed as candidates to the generalization of Principal Component Analysis. We show that these models are dedicated to the approximation of the dataset by a manifold. Here, the word manifold refers to the topology properties of the structure. The approximating manifold is built by a projection pursuit algorithm. At each step of the algorithm, the dimension of the manifold is incremented. Some theoretical properties are provided. In particular, we can show that, at each step of the algorithm, the mean residuals norm is not increased. Moreover, it is also established that the algorithm converges in a finite number of steps. Some particular autoassociative models are exhibited and compared to the classical PCA and some neural networks models. Implementation aspects are discussed. We show that, in numerous cases, no optimization procedure is required. Some illustrations on simulated and real data are presented.

Natural human mobility patterns and spatial spread of infectious diseases ; We investigate a model for spatial epidemics explicitly taking into account bidirectional movements between base and destination locations on individual mobility networks. We provide a systematic analysis of generic dynamical features of the model on regular and complex metapopulation network topologies and show that significant dynamical differences exist to ordinary reactiondiffusion and effective force of infection models. On a lattice we calculate an expression for the velocity of the propagating epidemic front and find that in contrast to the diffusive systems, our model predicts a saturation of the velocity with increasing traveling rate. Furthermore, we show that a fully stochastic system exhibits a novel threshold for attack ratio of an outbreak absent in diffusion and force of infection models. These insights not only capture natural features of human mobility relevant for the geographical epidemic spread, they may serve as a starting point for modeling important dynamical processes in human and animal epidemiology, population ecology, biology and evolution.

Fractal Systems of Central Places Based on Intermittency of Spacefilling ; The central place models are fundamentally important in theoretical geography and city planning theory. The texture and structure of central place networks have been demonstrated to be selfsimilar in both theoretical and empirical studies. However, the underlying rationale of central place fractals in the real world has not yet been revealed so far. This paper is devoted to illustrating the mechanisms by which the fractal patterns can be generated from central place systems. The structural dimension of the traditional central place models is d2 indicating no intermittency in the spatial distribution of human settlements. This dimension value is inconsistent with empirical observations. Substituting the complete space filling with the incomplete space filling, we can obtain central place models with fractional dimension Dd2 indicative of spatial intermittency. Thus the conventional central place models are converted into fractal central place models. If we further integrate the chance factors into the improved central place fractals, the theory will be able to well explain the real patterns of urban places. As empirical analyses, the US cities and towns are employed to verify the fractalbased models of central places.

Theoretical light curves of type Ia supernovae ; Aims. We present the first theoretical SN Ia light curves calculated with the timedependent version of the general purpose model atmosphere code PHOENIX. Our goal is to produce light curves and spectra of hydro models of all types of supernovae. Methods. We extend our model atmosphere code PHOENIX to calculate type Ia supernovae light curves. A simple solver was imple mented which keeps track of energy conservation in the atmosphere during the free expansion phase. Results. The correct operation of the new additions to PHOENIX were verified in test calculations. Furthermore, we calculated theo retical light curves and compared them to the observed SN Ia light curves of SN 1999ee and SN 2002bo. We obtained LTE as well as NLTE model light curves. Conclusions. We have verified the correct operation of our extension into the time domain. We have calculated the first SN Ia model light curves using PHOENIX in both LTE and NLTE. For future work the infrared model light curves need to be further investigated.

Degenerate random environments ; We consider connectivity properties of certain i.i.d. random environments on Zd, where at each location some steps may not be available. Site percolation and oriented percolation can be viewed as special cases of the models we consider. In such models, one of the quantities most often studied is the random set of vertices that can be reached from the origin by following a connected path. More generally, for the models we consider, multiple different types of connectivity are of interest, including the set of vertices that can be reached from the origin; the set of vertices from which the origin can be reached; the intersection of the two. As with percolation models, many of the models we consider admit, or are expected to admit phase transitions. Among the main results of the paper is a proof of the existence of phase transitions for some twodimensional models that are nonmonotone in their underlying parameter, and an improved bound on the critical value for oriented site percolation on the triangular lattice. The connectivity of the random directed graphs provides a foundation for understanding the asymptotic properties of random walks in these random environments, which we study in a second paper.

CP Violation in D0D0bar Mixing and Electric Dipole Moments in SUSY Alignment Models ; We report on a study of CP Violation in D0D0bar mixing and Electric Dipole Moments in the framework of supersymmetric alignment models. Both classes of observables are strongly suppressed in the Standard Model and highly sensitive to new sources of flavor and CP violation that can be present in models of New Physics. Supersymmetric alignment models generically predict large nonstandard effects in D0D0bar mixing and we show that visible CP violation in D0D0bar mixing implies lower bounds for the EDMs of hadronic systems, like the neutron EDM and the mercury EDM, in the reach of future experimental sensitivities. We also give updated constraints on the mass insertions of the Minimal Supersymmetric Standard Model using the current data on D0D0bar mixing.

A holographic approach to lowenergy weak interactions of hadrons ; We apply the doubletrace formalism to incorporate nonleptonic weak interactions of hadrons into holographic models of the strong interactions. We focus our attention upon Delta S1 nonleptonic kaon decays. By working with a YangMillsChernSimons 5dimensional action, we explicitly show how, at low energies, one recovers the Delta S1 weak chiral Lagrangian for both the anomalous and nonanomalous sectors. We provide definite predictions for the low energy coefficients in terms of the AdS metric and argue that the doubletrace formalism is a 5dimensional avatar of the Weak Deformation Model introduced long ago by Ecker et al. As a significant phenomenological application, we reassess the Kto 3pi decays in the light of the holographic model. Previous models found a finetuned cancellation of resonance exchange in these decays, which was both conceptually puzzling and quantitatively in disagreement with experimental results. The holographic model we build is an illustrative counterexample showing that the cancellation encountered in the literature is not generic but a modeldependent statement and that agreement with experiment can be obtained.

Ising Models for Inferring Network Structure From Spike Data ; Now that spike trains from many neurons can be recorded simultaneously, there is a need for methods to decode these data to learn about the networks that these neurons are part of. One approach to this problem is to adjust the parameters of a simple model network to make its spike trains resemble the data as much as possible. The connections in the model network can then give us an idea of how the real neurons that generated the data are connected and how they influence each other. In this chapter we describe how to do this for the simplest kind of model an Ising network. We derive algorithms for finding the best model connection strengths for fitting a given data set, as well as faster approximate algorithms based on mean field theory. We test the performance of these algorithms on data from model networks and experiments.

Multigraph limit of the dense configuration model and the preferential attachment graph ; The configuration model is the most natural model to generate a random multigraph with a given degree sequence. We use the notion of dense graph limits to characterize the special form of limit objects of convergent sequences of configuration models. We apply these results to calculate the limit object corresponding to the dense preferential attachment graph and the edge reconnecting model. Our main tools in doing so are 1 the relation between the theory of graph limits and that of partially exchangeable random arrays 2 an explicit construction of our random graphs that uses urn models.

Twofluid dark matter models ; We investigate the possibility that dark matter is a mixture of two noninteracting perfect fluids, with different fourvelocities and thermodynamic parameters. The twofluid model can be described as an effective single anisotropic fluid, with distinct radial and tangential pressures. The basic equations describing the equilibrium structure of the twofluid dark matter model, and of the tangential velocity of test particles in stable circular orbits, are obtained for the case of a spherically symmetric static geometry. By assuming a nonrelativistic kinetic model for the dark matter particles, the density profile and the tangential velocity of the dark matter mixture are obtained by numerically integrating the gravitational field equations. The cosmological implications of the model are also briefly considered, and it is shown that the anisotropic twofluid model isotropizes in the large time limit.

An Analysis of Phase Transition in NK Landscapes ; In this paper, we analyze the decision version of the NK landscape model from the perspective of threshold phenomena and phase transitions under two random distributions, the uniform probability model and the fixed ratio model. For the uniform probability model, we prove that the phase transition is easy in the sense that there is a polynomial algorithm that can solve a random instance of the problem with the probability asymptotic to 1 as the problem size tends to infinity. For the fixed ratio model, we establish several upper bounds for the solubility threshold, and prove that random instances with parameters above these upper bounds can be solved polynomially. This, together with our empirical study for random instances generated below and in the phase transition region, suggests that the phase transition of the fixed ratio model is also easy.

Structure and Dynamics of Polynomial Dynamical Systems ; Discrete models have a long tradition in engineering, including finite state machines, Boolean networks, Petri nets, and agentbased models. Of particular importance is the question of how the model structure constrains its dynamics. This paper discusses an algebraic framework to study such questions. The systems discussed here are given by mappings on an affine space over a finite field, whose coordinate functions are polynomials. They form a general class of models which can represent many discrete model types. Assigning to such a system its dependency graph, that is, the directed graph that indicates the variable dependencies, provides a mapping from systems to graphs. A basic property of this mapping is derived and used to prove that dynamical systems with an acyclic dependency graph can only have a unique fixed point in their phase space and no periodic orbits. This result is then applied to a published model of in vitro virus competition.

Bayes Variable Selection in Semiparametric Linear Models ; There is a rich literature proposing methods and establishing asymptotic properties of Bayesian variable selection methods for parametric models, with a particular focus on the normal linear regression model and an increasing emphasis on settings in which the number of candidate predictors p diverges with sample size n. Our focus is on generalizing methods and asymptotic theory established for mixtures of gpriors to semiparametric linear regression models having unknown residual densities. Using a Dirichlet process location mixture for the residual density, we propose a semiparametric gprior which incorporates an unknown matrix of cluster allocation indicators. For this class of priors, posterior computation can proceed via a straightforward stochastic search variable selection algorithm. In addition, Bayes factor and variable selection consistency is shown to result under various cases including proper and improper priors on g and pn, with the models under comparison restricted to have model dimensions diverging at a rate less than n.

Meanfield critical behaviour and ergodicity break in a nonequilibrium onedimensional RSOS growth model ; We investigate the nonequilibrium roughening transition of a onedimensional restricted solidonsolid model by directly sampling the stationary probability density of a suitable order parameter as the surface adsorption rate varies. The shapes of the probability density histograms suggest a typical GinzburgLandau scenario for the phase transition of the model, and estimates of the magnetic exponent seem to confirm its meanfield critical behaviour. We also found that the flipping times between the metastable phases of the model scale exponentially with the system size, signaling the breaking of ergodicity in the thermodynamic limit. Incidentally, we discovered that a closely related model not considered before also displays a phase transition with the same critical behaviour as the original model. Our results support the usefulness of offcritical histogram techniques in the investigation of nonequilibrium phase transitions. We also briefly discuss in an appendix a good and simple pseudorandom number generator used in our simulations.

Every FormulaBased Logic Program Has a Least InfiniteValued Model ; Every definite logic program has as its meaning a least Herbrand model with respect to the programindependent ordering setinclusion. In the case of normal logic programs there do not exist least models in general. However, according to a recent approach by Rondogiannis and Wadge, who consider infinitevalued models, every normal logic program does have a least model with respect to a programindependent ordering. We show that this approach can be extended to formulabased logic programs i.e., finite sets of rules of the form AleftarrowF where A is an atom and F an arbitrary firstorder formula. We construct for a given program P an interpretation MP and show that it is the least of all models of P. Keywords Logic programming, semantics of programs, negationasfailure, infinitevalued logics, set theory

Mathematical Analysis of the BIBEE Approximation for Molecular Solvation Exact Results for Spherical Inclusions ; We analyze the mathematically rigorous BIBEE boundaryintegral based electrostatics estimation approximation of the mixeddielectric continuum model of molecular electrostatics, using the analytically solvable case of a spherical solute containing an arbitrary charge distribution. Our analysis, which builds on Kirkwood's solution using spherical harmonics, clarifies important aspects of the approximation and its relationship to Generalized Born models. First, our results suggest a new perspective for analyzing fast electrostatic models the separation of variables between material properties the dielectric constants and geometry the solute dielectric boundary and charge distribution. Second, we find that the eigenfunctions of the reactionpotential operator are exactly preserved in the BIBEE model for the sphere, which supports the use of this approximation for analyzing chargecharge interactions in molecular binding. Third, a comparison of BIBEE to the recent GBepsilon theory suggests a modified BIBEE model capable of predicting electrostatic solvation free energies to within 4 of a full numerical Poisson calculation. This modified model leads to a projectionframework understanding of BIBEE and suggests opportunities for future improvements.

SingletDoublet Dark Matter ; In light of recent data from direct detection experiments and the Large Hadron Collider, we explore models of dark matter in which an SU2 doublet is mixed with a Standard Model singlet. We impose a thermal history. If the new particles are fermions, this model is already constrained due to null results from XENON100. We comment on remaining regions of parameter space and assess prospects for future discovery. We do the same for the model where the new particles are scalars, which at present is less constrained. Much of the remaining parameter space for both models will be probed by the next generation of direct detection experiments. For the fermion model, DeepCore may also play an important role.

Bianchi VI0 in Scalar and ScalarTensor Cosmologies ; We study several cosmological models with Bianchi textrmVI0 symmetries under the selfsimilar approach. In order to study how the textquotedblleft constantstextquotedblright G and Lambda may vary, we propose three scenarios where such constants are considered as time functions. The first model is a perfect fluid. We find that the behavior of G and Lambda are related. If G behaves as a growing time function then Lambda is a positive decreasing time function but if G is decreasing then Lambda is negative. For this model we have found a new solution. The second model is a scalar field, where in a phenomenological way, we consider a modification of the KleinGordon equation in order to take into account the variation of G. Our third scenario is a scalartensor model. We find three solutions for this models where G is growing, constant or decreasing and Lambda is a positive decreasing function or vanishes. We put special emphasis on calculating the curvature invariants in order to see if the solutions isotropize.

A Simple EnergyDependent Model for GRB Pulses with Interesting Physical Implications ; A simple mathematical model for GRB pulses is postulated in both time and energy. The model breaks GRB pulses up into component functions, one general light curve function exclusively in the time dimension and four component functions exclusively in the energy dimension. Each component function of energy is effectively orthogonal to the other energycomponent functions. The model is a good statistical fit to several of the most fluent separable GRB pulses known. Even without theoretical interpretation, the model may be immediately useful for fitting prompt emission from GRB pulses across energy channels with a minimal number of free parameters, sometimes far fewer than freshly fitting a GRB pulse in every energy band separately. Some theoretical implications of the model might be particularly interesting, however, as the temporal component e.g. the shape of the light curve is well characterized mathematically by the well known Planck distribution.

Kinetic limits for pairinteraction driven master equations and biological swarm models ; We consider a class of stochastic processes modeling binary interactions in an Nparticle system. Examples of such systems can be found in the modeling of biological swarms. They lead to the definition of a class of master equations that we call pair interaction driven master equations. We prove a propagation of chaos result for this class of master equations which generalizes Mark Kac's well know result for the Kac model in kinetic theory. We use this result to study kinetic limits for two biological swarm models. We show that propagation of chaos may be lost at large times and we exhibit an example where the invariant density is not chaotic.

Colored Tensor Models a Review ; Colored tensor models have recently burst onto the scene as a promising conceptual and computational tool in the investigation of problems of random geometry in dimension three and higher. We present a snapshot of the cutting edge in this rapidly expanding research field. Colored tensor models have been shown to share many of the properties of their direct ancestor, matrix models, which encode a theory of fluctuating twodimensional surfaces. These features include the possession of Feynman graphs encoding topological spaces, a 1N expansion of graph amplitudes, embedded matrix models inside the tensor structure, a resumable leading order with critical behavior and a continuum large volume limit, SchwingerDyson equations satisfying a Lie algebra akin to the Virasoro algebra in two dimensions, nontrivial classical solutions and so on. In this review, we give a detailed introduction of colored tensor models and pointers to current and future research directions.

Posterior convergence rates in nonlinear latent variable models ; Nonlinear latent variable models have become increasingly popular in a variety of applications. However, there has been little study on theoretical properties of these models. In this article, we study rates of posterior contraction in univariate density estimation for a class of nonlinear latent variable models where unobserved U0,1 latent variables are related to the response variables via a random nonlinear regression with an additive error. Our approach relies on characterizing the space of densities induced by the above model as kernel convolutions with a general class of continuous mixing measures. The literature on posterior rates of contraction in density estimation almost entirely focuses on finite or countably infinite mixture models. We develop approximation results for our class of continuous mixing measures. Using an appropriate Gaussian process prior on the unknown regression function, we obtain the optimal frequentist rate up to a logarithmic factor under standard regularity conditions on the true density.

A Complexity Separation Between the CacheCoherent and Distributed Shared Memory Models ; We consider asynchronous multiprocessor systems where processes communicate by accessing shared memory. Exchange of information among processes in such a multiprocessor necessitates costly memory accesses called emphremote memory references RMRs, which generate communication on the interconnect joining processors and main memory. In this paper we compare two popular shared memory architecture models, namely the emphcachecoherent CC and emphdistributed shared memory DSM models, in terms of their power for solving synchronization problems efficiently with respect to RMRs. The particular problem we consider entails one process sending a signal to a subset of other processes. We show that a variant of this problem can be solved very efficiently with respect to RMRs in the CC model, but not so in the DSM model, even when we consider amortized RMR complexity. To our knowledge, this is the first separation in terms of amortized RMR complexity between the CC and DSM models. It is also the first separation in terms of RMR complexity for asynchronous systems that does not rely in any way on waitfreedomthe requirement that a process makes progress in a bounded number of its own steps.

Fault Tolerant Boolean Satisfiability ; A deltamodel is a satisfying assignment of a Boolean formula for which any small alteration, such as a single bit flip, can be repaired by flips to some small number of other bits, yielding a new satisfying assignment. These satisfying assignments represent robust solutions to optimization problems e.g., scheduling where it is possible to recover from unforeseen events e.g., a resource becoming unavailable. The concept of deltamodels was introduced by Ginsberg, Parkes and Roy AAAI 1998, where it was proved that finding deltamodels for general Boolean formulas is NPcomplete. In this paper, we extend that result by studying the complexity of finding deltamodels for classes of Boolean formulas which are known to have polynomial time satisfiability solvers. In particular, we examine 2SAT, HornSAT, AffineSAT, dualHornSAT, 0valid and 1valid SAT. We see a wide variation in the complexity of finding deltamodels, e.g., while 2SAT and AffineSAT have polynomial time tests for deltamodels, testing whether a HornSAT formula has one is NPcomplete.

Evaluating the SharedCanvas Manuscript Data Model in CATCHPlus ; In this paper, we present the SharedCanvas model for describing the layout of culturally important, handwritten objects such as medieval manuscripts, which is intended to be used as a common input format to presentation interfaces. The model is evaluated using two collections from CATCHPlus not consulted during the design phase, each with their own complex requirements, in order to determine if further development is required or if the model is ready for general usage. The model is applied to the new collections, revealing several new areas of concern for user interface production and discovery of the constituent resources. However, the fundamental information modelling aspects of SharedCanvas and the underlying Open Annotation Collaboration ontology are demonstrated to be sufficient to cover the challenging new requirements. The distributed, Linked Open Data approach is validated as an important methodology to seamlessly allow simultaneous interaction with multiple repositories, and at the same time to facilitate both scholarly commentary and crowdsourcing of the production of transcriptions.

Bridge Copula Model for Option Pricing ; In this paper we present a new multiasset pricing model, which is built upon newly developed families of solvable multiparameter singleasset diffusions with a nonlinear smileshaped volatility and an affine drift. Our multiasset pricing model arises by employing copula methods. In particular, all discounted singleasset price processes are modeled as martingale diffusions under a riskneutral measure. The price processes are socalled UOU diffusions and they are each generated by combining a variable Ito transformation with a measure change performed on an underlying OrnsteinUhlenbeck Gaussian process. Consequently, we exploit the use of a normal bridge copula for coupling the singleasset dynamics while reducing the distribution of the multiasset price process to a multivariate normal distribution. Such an approach allows us to simulate multidimensional price paths in a precise and fast manner and hence to price pathdependent financial derivatives such as Asianstyle and Bermudan options using the Monte Carlo method. We also demonstrate how to successfully calibrate our multiasset pricing model by fitting respective equity option and asset market prices to the singleasset models and their return correlations i.e. the copula function using the leastsquare and maximumlikelihood estimation methods.

Renormalisation group improved leptogenesis in family symmetry models ; We study renormalisation group RG corrections relevant for leptogenesis in the case of family symmetry models such as the AltarelliFeruglio A4 model of tribimaximal lepton mixing or its extension to trimaximal mixing. Such corrections are particularly relevant since in large classes of family symmetry models, to leading order, the CP violating parameters of leptogenesis would be identically zero at the family symmetry breaking scale, due to the form dominance property. We find that RG corrections violate form dominance and enable such models to yield viable leptogenesis at the scale of righthanded neutrino masses. More generally, the results of this paper show that RG corrections to leptogenesis cannot be ignored for any family symmetry model involving sizeable neutrino and tau Yukawa couplings.

An Extended Excursion Set Approach to Structure Formation in Chameleon Models ; In attempts to explain dark energy, a number of models have been proposed in which the formation of largescale structure depends on the local environment. These models are highly nonlinear and difficult to analyse analytically. Nbody simulations have therefore been used to study their nonlinear evolution. Here we extend excursion set theory to incorporate environmental effects on structure formation. We apply the method to a chameleon model and calculate observables such as the nonlinear mass function at various redshifts. The method can be generalized to study other obervables and other models of environmentally dependent interactions. The analytic methods described here should prove useful in delineating which models deserve more detailed study with Nbody simulations.

Z' boson decay in the SU3L otimes U1N electroweak model with heavy leptons ; Based on the expectation generated by the discovery of new particles by current colliders, we analyze the decay of the Z' boson in the frame of one of the SU3L otimes U1N electroweak extensions of the standard model. The main objective is calculate the decay rate of this exotic boson in the aforementioned model at the tree level. With this purpose we need to develop the gauge sector, where we find thirtythree interaction terms. Mentioned particle Z' has not yet been observed experimentally, but a large number of models predict its existence. This boson exhibits a variety of decay channels, but we will concentrate on the bosonic sector, in particular in the new charged vector bosons V pm and doubly charged U pmpm as final products, because these are special features of the model. On the other hand, we would like to remark that this model does not account for the Z' W W vertex although this decay channel is considered one of the main ways to detect the Z' boson in the Tevatron.

Effect of discrete time observations on synchronization in Chua model and applications to data assimilation ; Recent studies show indication of the effectiveness of synchronization as a data assimilation tool for small or mesoscale forecast when less number of variables are observed frequently. Our main aim here is to understand the effects of changing observational frequency and observational noise on synchronization and prediction in a low dimensional chaotic system, namely the Chua circuit model. We perform it identical twin experiments in order to study synchronization using discreteintime observations generated from independent model run and coupled unidirectionally to the model through x, y and z separately. We observe synchrony in a finite range of coupling constant when coupling the x and y variables of the Chua model but not when coupling the z variable. This range of coupling constant decreases with increasing levels of noise in the observations. The Chua system does not show synchrony when the time gap between observations is greater than about oneseventh of the Lyapunov time. Finally, we also note that prediction errors are much larger when noisy observations are used than when using observations without noise.

A Method to Control Order of Phase Transition Invisible States in Discrete Spin Models ; It is an important topic to investigate nature of the phase transition in wide area of science such as statistical physics, materials science, and computational science. Recently it has been reported the efficiency of quantum adiabatic evolutionquantum annealing for systems which exhibit a phase transition, and we cannot obtain a good solution in such systems. Thus, to control the nature of the phase transition has been also attracted attention in quantum information science. In this paper we review nature of the phase transition and how to control the order of the phase transition. We take the Ising model, the standard Potts model, the BlumeCapel model, the WajnflaszPick model, and the Potts model with invisible states for instance. Until now there is no general method to avoid the difficulty of annealing method in systems which exhibit a phase transition. It is a challenging problem to propose a method how to erase or how to control the nature of the phase transition in the target system.