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Heston Stochastic VolofVol Model for Joint Calibration of VIX and SP 500 Options ; A parsimonious generalization of the Heston model is proposed where the volatilityofvolatility is assumed to be stochastic. We follow the perturbation technique of Fouque et al 2011, CUP to derive a first order approximation of the price of options on a stock and its volatility index. This approximation is given by Heston's quasiclosed formula and some of its Greeks. It can be very efficiently calculated since it requires to compute only Fourier integrals and the solution of simple ODE systems. We exemplify the calibration of the model with SP 500 and VIX data.

Dynamical features of an anisotropic cosmological model ; The dynamical features of Bianchi type VIh BVIh universe are investigated in fR,T theory of gravity. The field equations and the physical properties of the model are derived considering a power law expansion of the universe. The effect of anisotropy on the dynamics of the universe as well on the energy conditions are studied. The assumed anisotropy of the model is found to have substantial effects on the energy condition and dynamical parameters.

Highergenus wallcrossing in the gauged linear sigma model ; We introduce a technique for proving allgenus wallcrossing formulas in the gauged linear sigma model as the stability parameter varies, without assuming factorization properties of the virtual class. We implement this technique explicitly for the hybrid model, which generalizes our previous work to the LandauGinzburg phase.

Analytic Solution of the Starobinsky Model for Inflation ; We prove that the field equations of the Starobinsky model for inflation in a FriedmannLemaitreRobertsonWalker constitute an integrable system as the field equations pass the singularity test. The analytical solution in terms of a Painlev'e Series for the Starobinsky model is presented for the case of zero and nonzero spatial curvature. In both cases the leadingorder term describes the radiation era provided by the corresponding higherorder theory.

Learning Knowledge Graph Embeddings with Type Regularizer ; Learning relations based on evidence from knowledge bases relies on processing the available relation instances. Many relations, however, have clear domain and range, which we hypothesize could help learn a better, more generalizing, model. We include such information in the RESCAL model in the form of a regularization factor added to the loss function that takes into account the types categories of the entities that appear as arguments to relations in the knowledge base. We note increased performance compared to the baseline model in terms of mean reciprocal rank and hitsN, N 1, 3, 10. Furthermore, we discover scenarios that significantly impact the effectiveness of the type regularizer.

Occupationconstrained interband dynamics of a nonhermitian twoband BoseHubbard Hamiltonian ; The interband dynamics of a twoband BoseHubbard model is studied with strongly correlated bosons forming singlesite double occupancies referred to as doublons. Our model for resonant doublon interband coupling exhibits interesting dynamical features such as quantum Zeno effect, the generation of states such as a twoband Belllike state and an upperband Mottlike state. The evolution of the asymptotic state is controlled here by the effective opening of one or both of the two bands, which models decay channels.

Wormhole solutions of RDM model ; The model of a spiral galaxy with radially directed flows of dark matter is extended by exotic matter, in a form of a perfect fluid with a linear anisotropic equation of state. The exotic matter is collected in the minimum of gravitational potential and opens a wormhole in the center of the galaxy. The flows of dark matter pass through the wormhole and form a mirror galaxy on the other side. The influence of model parameters to the shape of solution is studied, a solution matching parameters of Milky Way galaxy is computed.

Auxiliary Objectives for Neural Error Detection Models ; We investigate the utility of different auxiliary objectives and training strategies within a neural sequence labeling approach to error detection in learner writing. Auxiliary costs provide the model with additional linguistic information, allowing it to learn generalpurpose compositional features that can then be exploited for other objectives. Our experiments show that a joint learning approach trained with parallel labels on indomain data improves performance over the previous best error detection system. While the resulting model has the same number of parameters, the additional objectives allow it to be optimised more efficiently and achieve better performance.

Bulk viscous cosmological model in Brans Dicke theory with new form of time varying deceleration parameter ; In this article we have presented FRW cosmological model in the framework of BransDicke theory. This paper deals with a new proposed form of deceleration parameter and cosmological constant. The effect of bulk viscosity is also studied in the presence of modified Chaplygin gas equation of state. Further, we have discussed the physical behaviors of the models.

Minimal NonAbelian Supersymmetric Twin Higgs ; We propose a minimal supersymmetric Twin Higgs model that can accommodate tuning of the electroweak scale for heavy stops better than 10 with high mediation scales of supersymmetry breaking. A crucial ingredient of this model is a new SU2X gauge symmetry which provides a Dterm potential that generates a large SU4 invariant coupling for the Higgs sector and only small set of particles charged under SU2X, which allows the model to be perturbative around the Planck scale. The new gauge interaction drives the top yukawa coupling small at higher energy scales, which also reduces the tuning.

Fast and accurate modelling of nonlinear pulse propagation in gradedindex multimode fibers ; We develop a model for the description of nonlinear pulse propagation in multimode optical fibers with a parabolic refractive index profile. It consists in a 11D generalized nonlinear Schrodinger equation with a periodic nonlinear coefficient, which can be solved in an extremely fast and efficient way. The model is able to quantitatively reproduce recently observed phenomena like geometric parametric instability and broadband dispersive wave emission. We envisage that our equation will represent a valuable tool for the study of spatiotemporal nonlinear dynamics in the growing field of multimode fiber optics.

HierarchicallyAttentive RNN for Album Summarization and Storytelling ; We address the problem of endtoend visual storytelling. Given a photo album, our model first selects the most representative summary photos, and then composes a natural language story for the album. For this task, we make use of the Visual Storytelling dataset and a model composed of three hierarchicallyattentive Recurrent Neural Nets RNNs to encode the album photos, select representative summary photos, and compose the story. Automatic and human evaluations show our model achieves better performance on selection, generation, and retrieval than baselines.

Light of Planck2015 on NonCanonical Inflation ; Slowroll inflationary scenario is considered in noncanonical scalar field model supposing a powerlaw function for kinetic term, and using two formalisms. In the first approach, the potential is considered as a powerlaw function, that is the most common approach in studying inflation. HamiltonJacobi approach is selected as the second formalism, so that the Hubble parameter is introduced as a function of scalar field instead of the potential. Employing the last observational data, the free parameters of the model are constrained, and the predicted form of the potential and attractor behavior of the model are considered in detail.

Boltzmann machines and energybased models ; We review Boltzmann machines and energybased models. A Boltzmann machine defines a probability distribution over binaryvalued patterns. One can learn parameters of a Boltzmann machine via gradient based approaches in a way that log likelihood of data is increased. The gradient and Hessian of a Boltzmann machine admit beautiful mathematical representations, although computing them is in general intractable. This intractability motivates approximate methods, including Gibbs sampler and contrastive divergence, and tractable alternatives, namely energybased models.

Gravitational baryogenesis of vacuum Inflation ; We show that in the vacuum inflation model, the gravitational baryogenesis mechanism will produce the baryon asymmetry. We analyze the evolution of entropy and baryon number in the vacuum inflation model. The comparison between dilution speed and the chemical potential may give a natural interpretation for decouple temperature of the gravitational baryogenesis interaction. From the result, the mechanism can give acceptable baryontoentropy ratio in the vacuum inflation model.

Lattice Models of Finite Fields ; Finite fields form an important chapter in abstract algebra, and mathematics in general. We aim to provide a geometric and intuitive model for finite fields, involving algebraic numbers, in order to make them accessible and interesting to a much larger audience. Such lattice models of finite fields provide a good basis for later developing the theory in a more concrete way, including Frobenius elements, all the way to Artin reciprocity law. Examples are provided, intended for an undergraduate audience in the first place.

Extending Yagil exchange ratio determination model to the case of stochastic dividends ; This article extends, in a stochastic environment, the Yagil 1987 model which establishes, in a deterministic dividend discount model, a range for the exchange ratio in a stockforstock merger agreement. Here, we generalize Yagil's work letting both pre and postmerger dividends grow randomly over time. If Yagil focuses only on changes in stock prices before and after the merger, our stochastic environment allows to keep in account both shares' expected values and variance, letting us to identify a more complex bargaining region whose shape depends on mean and standard deviation of the dividends' growth rate.

Dynamical and observational analysis of interacting models ; We investigate the dynamical behaviour of a general class of interacting models in the dark sector in which the phenomenological coupling between cold dark matter and dark energy is a power law of the cosmic scale factor. From numerical simulations we show that, in this background, dark energy always dominates the current composition cosmic. This behaviour may alleviate substantially the coincidence problem. By using current type Ia supernovae, baryonic acoustic oscillations and cosmic microwave background data, we perform a joint statistical analysis and obtain constraints on free parameters of this class of model.

Active Exploration for Learning Symbolic Representations ; We introduce an online active exploration algorithm for dataefficiently learning an abstract symbolic model of an environment. Our algorithm is divided into two parts the first part quickly generates an intermediate Bayesian symbolic model from the data that the agent has collected so far, which the agent can then use along with the second part to guide its future exploration towards regions of the state space that the model is uncertain about. We show that our algorithm outperforms random and greedy exploration policies on two different computer game domains. The first domain is an Asteroidsinspired game with complex dynamics but basic logical structure. The second is the Treasure Game, with simpler dynamics but more complex logical structure.

Pure radiation in spacetime models that admit integration of the eikonal equation by the separation of variables method ; We consider spacetime models with pure radiation, which admit integration of the eikonal equation by the method of separation of variables. For all types of these models, the equations of the energymomentum conservation law were integrated. The resulting form of metric, energy density and wave vectors of radiation as functions of metric for all types of spaces under consideration is presented. The solutions obtained can be used for any metric theories of gravitation.

Modeling Quantum Behavior in the Framework of Permutation Groups ; Quantummechanical concepts can be formulated in constructive finite terms without loss of their empirical content if we replace a general unitary group by a unitary representation of a finite group. Any linear representation of a finite group can be realized as a subrepresentation of a permutation representation. Thus, quantummechanical problems can be expressed in terms of permutation groups. This approach allows us to clarify the meaning of a number of physical concepts. Combining methods of computational group theory with Monte Carlo simulation we study a model based on representations of permutation groups.

Game Theory Models for the Verification of the Collective Behaviour of Autonomous Cars ; The collective of autonomous cars is expected to generate almost optimal traffic. In this position paper we discuss the multiagent models and the verification results of the collective behaviour of autonomous cars. We argue that noncooperative autonomous adaptation cannot guarantee optimal behaviour. The conjecture is that intention aware adaptation with a constraint on simultaneous decision making has the potential to avoid unwanted behaviour. The online routing game model is expected to be the basis to formally prove this conjecture.

Modeling differential rotations of compact stars in equilibriums ; Outcomes of numerical relativity simulations of massive core collapses or binary neutron star mergers with moderate masses suggest formations of rapidly and differentially rotating neutron stars. Subsequent fall back accretion may also amplify the degree of differential rotations. We propose new formulations for modeling differential rotations of those compact stars, and present selected solutions of differentially rotating, stationary, and axisymmetric compact stars in equilibriums. For the cases when rotating stars reach breakup velocities, the maximum masses of such rotating models are obtained.

Interactions and oscillations of coherent flavor eigenstates in beta decay ; The theory pioneered by Blasone and Vitiello describes massive neutrinos as generalized coherent flavor eigenstates within the extended Standard Model. In this paper, we compute the neutron beta decay spectrum for the BlasoneVitiello theory in a model with two neutrinos. For relativistic neutrinos, the obtained spectrum is in agreement with the Standard Model. However, there are discrepancies when the kinetic energy of the electron is close to the end point energy. The possibility of measuring the discrepancies in future experiments is discussed.

Equilibrium fluctuations for the weakly asymmetric discrete Atlas model ; This contribution aims at presenting and generalizing a recent work of Hernandez, Jara and Valentim DOI10.1016j.spa.2016.06.026. We consider the weakly asymmetric version of the socalled discrete Atlas model, which has been introduced there. Precisely, we look at some equilibrium fluctuation field of a weakly asymmetric zerorange process which evolves on a discrete halfline, with a source of particles at the origin. We prove that its macroscopic evolution is governed by a stochastic heat equation with Neumann or Robin boundary conditions, depending on the range of the parameters of the model.

Is uniform persisitence a robust property in almost periodic models A wellbehaved family almost periodic Nicholson systems ; Using techniques of nonautonomous dynamical systems, we completely characterize the persistence properties of an almost periodic Nicholson system in terms of some numerically computable exponents. Although similar results hold for a class of cooperative and sublinear models, in the general nonautonomous setting one has to consider persistence as a collective property of the family of systems over the hull the reason is that uniform persistence is not a robust property in models given by almost periodic differential equations.

Sentence Correction Based on Largescale Language Modelling ; With the further development of informatization, more and more data is stored in the form of text. There are some loss of text during their generation and transmission. The paper aims to establish a language model based on the largescale corpus to complete the restoration of missing text. In this paper, we introduce a novel measurement to find the missing words, and a way of establishing a comprehensive candidate lexicon to insert the correct choice of words. The paper also introduces some effective optimization methods, which largely improve the efficiency of the text restoration and shorten the time of dealing with 1000 sentences into 3.6 seconds. keywords language model, sentence correction, word imputation, parallel optimization

Multiway Interacting Regression via Factorization Machines ; We propose a Bayesian regression method that accounts for multiway interactions of arbitrary orders among the predictor variables. Our model makes use of a factorization mechanism for representing the regression coefficients of interactions among the predictors, while the interaction selection is guided by a prior distribution on random hypergraphs, a construction which generalizes the Finite Feature Model. We present a posterior inference algorithm based on Gibbs sampling, and establish posterior consistency of our regression model. Our method is evaluated with extensive experiments on simulated data and demonstrated to be able to identify meaningful interactions in applications in genetics and retail demand forecasting.

Quasirandom Monte Carlo application in CGE systematic sensitivity analysis ; The uncertainty and robustness of Computable General Equilibrium models can be assessed by conducting a Systematic Sensitivity Analysis. Different methods have been used in the literature for SSA of CGE models such as Gaussian Quadrature and Monte Carlo methods. This paper explores the use of Quasirandom Monte Carlo methods based on the Halton and Sobol' sequences as means to improve the efficiency over regular Monte Carlo SSA, thus reducing the computational requirements of the SSA. The findings suggest that by using lowdiscrepancy sequences, the number of simulations required by the regular MC SSA methods can be notably reduced, hence lowering the computational time required for SSA of CGE models.

Model category structures and spectral sequences ; Let k be a commutative ring with unit. We endow the categories of filtered complexes and of bicomplexes of kmodules, with cofibrantly generated model structures, where the class of weak equivalences is given by those morphisms inducing a quasiisomorphism at a certain fixed stage of the associated spectral sequence. For filtered complexes, we relate the different model structures obtained, when we vary the stage of the spectral sequence, using the functors shift and d'ecalage.

On the dilemma of fractal or fractional kinetics in drug release studies A comparison between Weibull and MittagLeffler functions ; We compare two of the most successful models for the description and analysis of drug release data. The fractal kinetics approach leading to release profiles described by a Weibull function and the fractional kinetics approach leading to release profiles described by a MittagLeffler function. We used Monte Carlo simulations to generate artificial release data from euclidean and fractal substrates. We have also used real release data from the literature and found that both models are capable in describing release data up to roughly 85 of the release. For larger times both models systematically overestimate the number of particles remaining in the release device.

Modeling of graphene Hall effect sensors for microbead detection ; This paper deals with the modeling of sensitivity of epitaxial graphene Hall bars, from submicrometer to micrometer size, to the stray field generated by a magnetic microbead. To demonstrate experiment feasibility, the model is first validated by comparison to measurement results, considering an acdc detection scheme. Then, an exhaustive numerical analysis is performed to investigate signal detriment caused by material defects, saturation of bead magnetization at high fields, increment of bead distance from sensor surface and device width increase.

Cosmological Model Independent Time Delay Method ; We propose a Cosmological Model Independent Time Delay CMITD method where the Lorentz invariance violation LIV variable Kz is constructed by observational data instead of cosmological model. The simulated time delay data show the CMITD method could present the validity of LIV test. And, the errors in the propagating process is critical for the existence and magnitude of LIV.

Supersymmetric Preons and the Standard Model ; The experimental fact that standard model superpartners have not been observed compels one to consider an alternative implementation for supersymmetry. The basic supermultiplet proposed here consists of a photon and a charged spin 12 preon field, and their superpartners. These fields are shown to yield the standard model fermions, Higgs fields and gauge symmetries. Supersymmetry is defined for unbound preons only. Quantum group SLq2 representations are introduced to classify topologically scalars, preons, quarks and leptons.

Image reconstruction in quantitative photoacoustic tomography with the simplified P2 approximation ; Photoacoustic tomography PAT is a hybrid imaging modality that intends to construct highresolution images of optical properties of heterogeneous media from measured acoustic data generated by the photoacoustic effect. To date, most of the modelbased quantitative image reconstructions in PAT are performed with either the radiative transport equation or its classical diffusion approximation as the model of light propagation. In this work, we study quantitative image reconstructions in PAT using the simplified P2 equations as the light propagation model. We provide numerical evidences on the feasibility of this approach and derive some stability results as theoretical justifications.

Classifying medical relations in clinical text via convolutional neural networks ; Deep learning research on relation classification has achieved solid performance in the general domain. This study proposes a convolutional neural network CNN architecture with a multipooling operation for medical relation classification on clinical records and explores a loss function with a categorylevel constraint matrix. Experiments using the 2010 i2b2VA relation corpus demonstrate these models, which do not depend on any external features, outperform previous singlemodel methods and our best model is competitive with the existing ensemblebased method.

BirnbaumSaunders Distribution A Review of Models, Analysis and Applications ; Birnbaum and Saunders introduced a twoparameter lifetime distribution to model fatigue life of a metal, subject to cyclic stress. Since then, extensive work has been done on this model providing different interpretations, constructions, generalizations, inferential methods, and extensions to bivariate, multivariate and matrixvariate cases. More than two hundred papers and one research monograph have already appeared describing all these aspects and developments. In this paper, we provide a detailed review of all these developments and at the same time indicate several open problems that could be considered for further research.

Anisotropic Stars in the Nonminimal YRF2 Gravity ; We investigate anisotropic compact stars in the nonminimal YRF2 model of gravity which couples an arbitrary function of curvature scalar YR to the electromagnetic field invariant F2. After we obtain exact anisotropic solutions to the field equations of the model, we apply the continuity conditions to the solutions at the boundary of the star. Then we find the mass, electric charge, and surface gravitational redshift by the parameters of the model and radius of the star.

Aff2Vec AffectEnriched Distributional Word Representations ; Human communication includes information, opinions, and reactions. Reactions are often captured by the affectivemessages in written as well as verbal communications. While there has been work in affect modeling and to some extent affective content generation, the area of affective word distributions in not well studied. Synsets and lexica capture semantic relationships across words. These models however lack in encoding affective or emotional word interpretations. Our proposed model, Aff2Vec provides a method for enriched word embeddings that are representative of affective interpretations of words. Aff2Vec outperforms the stateoftheart in intrinsic wordsimilarity tasks. Further, the use of Aff2Vec representations outperforms baseline embeddings in downstream natural language understanding tasks including sentiment analysis, personality detection, and frustration prediction.

Sensitivity of Regular Estimators ; This paper studies local asymptotic relationship between two scalar estimates. We define sensitivity of a target estimate to a control estimate to be the directional derivative of the target functional with respect to the gradient direction of the control functional. Sensitivity according to the information metric on the model manifold is the asymptotic covariance of regular efficient estimators. Sensitivity according to a general policy metric on the model manifold can be obtained from influence functions of regular efficient estimators. Policy sensitivity has a local counterfactual interpretation, where the ceteris paribus change to a counterfactual distribution is specified by the combination of a control parameter and a Riemannian metric on the model manifold.

An infiniteserver queueing model MMAPkGk in semiMarkov random environment with marked MAP arrival and subject to catastrophes ; In the present paper the infiniteserver MMAPkGk queueing model with random resource vector of customers, marked MAP arrival and semiMarkov SM arrival of catastrophes is considered. The joint generating functions PGF of transient and stationary distributions of number of busy servers and numbers of different types served customers, as well as Laplace transformations LT of joint distributions of total accumulated resources in the model at moment and total accumulated resources of served customers during time interval are found. The basic differential and renewal equations for transient and stationary PGF of queue sizes of customers are found.

Mathematical Analysis of Chemical Reaction Systems ; The use of mathematical methods for the analysis of chemical reaction systems has a very long history, and involves many types of models deterministic versus stochastic, continuous versus discrete, and homogeneous versus spatially distributed. Here we focus on mathematical models based on deterministic massaction kinetics. These models are systems of coupled nonlinear differential equations on the positive orthant. We explain how mathematical properties of the solutions of massaction systems are strongly related to key properties of the networks of chemical reactions that generate them, such as specific versions of reversibility and feedback interactions.

Learning Tree Distributions by Hidden Markov Models ; Hidden tree Markov models allow learning distributions for tree structured data while being interpretable as nondeterministic automata. We provide a concise summary of the main approaches in literature, focusing in particular on the causality assumptions introduced by the choice of a specific tree visit direction. We will then sketch a novel nonparametric generalization of the bottomup hidden tree Markov model with its interpretation as a nondeterministic tree automaton with infinite states.

Data Augmentation for Neural Online Chat Response Selection ; Data augmentation seeks to manipulate the available data for training to improve the generalization ability of models. We investigate two data augmentation proxies, permutation and flipping, for neural dialog response selection task on various models over multiple datasets, including both Chinese and English languages. Different from standard data augmentation techniques, our method combines the original and synthesized data for prediction. Empirical results show that our approach can gain 1 to 3 recallat1 points over baseline models in both fullscale and smallscale settings.

Codeswitched Language Models Using Dual RNNs and SameSource Pretraining ; This work focuses on building language models LMs for codeswitched text. We propose two techniques that significantly improve these LMs 1 A novel recurrent neural network unit with dual components that focus on each language in the codeswitched text separately 2 Pretraining the LM using synthetic text from a generative model estimated using the training data. We demonstrate the effectiveness of our proposed techniques by reporting perplexities on a MandarinEnglish task and derive significant reductions in perplexity.

Deeply Learning Derivatives ; This paper uses deep learning to value derivatives. The approach is broadly applicable, and we use a call option on a basket of stocks as an example. We show that the deep learning model is accurate and very fast, capable of producing valuations a million times faster than traditional models. We develop a methodology to randomly generate appropriate training data and explore the impact of several parameters including layer width and depth, training data quality and quantity on model speed and accuracy.

Systemic Risk and the Dependence Structures ; We propose a dynamic model of dependence structure between financial institutions within a financial system and we construct measures for dependence and financial instability. Employing Markov structures of joint credit migrations, our model allows for contagious simultaneous jumps in credit ratings and provides flexibility in modeling dependence structures. Another key aspect is that the proposed measures consider the interdependence and reflect the changing economic landscape as financial institutions evolve over time. In the final part, we give several examples, where we study various dependence structures and investigate their systemic instability measures. In particular, we show that subject to the same pool of Markov chains, the simulated Markov structures with distinct dependence structures generate different sequences of systemic instability.

Malliavin Calculus and Density for Singular Stochastic Partial Differential Equations ; We study Malliavin differentiability of solutions to subcritical singular parabolic stochastic partial differential equations SPDEs and we prove the existence of densities for a class of singular SPDEs. Both of these results are implemented in the setting of regularity structures. For this we construct renormalized models in situations where some of the driving noises are replaced by deterministic CameronMartin functions, and we show Lipschitz continuity of these models with respect to the CameronMartin norm. In particular, in many interesting situations we obtain a convergence and stability result for lifts of L2functions to models, which is of independent interest. The proof also involves two separate algebraic extensions of the regularity structure which are carried out in rather large generality.

Critical Percolation on Random Networks with Prescribed Degrees ; Random graphs have played an instrumental role in modelling realworld networks arising from the internet topology, social networks, or even proteininteraction networks within cells. Percolation, on the other hand, has been the fundamental model for understanding robustness and spread of epidemics on these networks. From a mathematical perspective, percolation is one of the simplest models that exhibits phase transition, and fascinating features are observed around the critical point. In this thesis, we prove limit theorems about structural properties of the connected components obtained from percolation on random graphs at criticality. The results are obtained for random graphs with general degree sequence, and we identify different universality classes for the critical behavior based on moment assumptions on the degree distribution.

On 2d CFTs that interpolate between minimal models ; We investigate exactly solvable twodimensional conformal field theories that exist at generic values of the central charge, and that interpolate between Aseries or Dseries minimal models. When the central charge becomes rational, correlation functions of these CFTs may tend to correlation functions of minimal models, or diverge, or have finite limits which can be logarithmic. These results are based on analytic relations between fourpoint structure constants and residues of conformal blocks.

Nonstandard microinertia terms in the relaxed micromorphic model wellposedness for dynamics ; We study the existence of solutions arising from the modelling of elastic materials using generalized theories of continua. In view of some evidence from physics of metamaterials we focus our effort on two recent nonstandard relaxed micromorphic models including novel microinertia terms. These novel microinertia terms are needed to better capture the bandgap response. The existence proof is based on the Banach fixed point theorem.

Derivation of a heteroepitaxial thinfilm model ; A variational model for epitaxiallystrained thin films on rigid substrates is derived both by Gammaconvergence from a transitionlayer setting, and by relaxation from a sharpinterface description available in the literature for regular configurations. The model is characterized by a configurational energy that accounts for both the competing mechanisms responsible for the film shape. On the one hand, the lattice mismatch between the film and the substrate generate large stresses, and corrugations may be present because film atoms move to release the elastic energy. On the other hand, flatter profiles may be preferable to minimize the surface energy. Some first regularity results are presented for energeticallyoptimal film profiles.

MASON A Model AgnoStic ObjectNess Framework ; This paper proposes a simple, yet very effective method to localize dominant foreground objects in an image, to pixellevel precision. The proposed method 'MASON' ModelAgnoStic ObjectNess uses a deep convolutional network to generate categoryindependent and modelagnostic heat maps for any image. The network is not explicitly trained for the task, and hence, can be used offtheshelf in tandem with any other network or task. We show that this framework scales to a wide variety of images, and illustrate the effectiveness of MASON in three varied application contexts.

Some asymptotic properties of SEIRS models with nonlinear incidence and random delays ; TThis paper presents the dynamics of mosquitoes and humans, with general nonlinear incidence rate and multiple distributed delays for the disease. The model is a SEIRS system of delay differential equations. The normalized dimensionless version is derived; analytical techniques are applied to find conditions for deterministic extinction and permanence of disease. The BRN R0 and ESPR EemuvT1mu T2 are computed. Conditions for deterministic extinction and permanence are expressed in terms of R0 and EemuvT1mu T2, and applied to a P.vivax malaria scenario. Numerical results are given.

BerryEsseen bounds in the inhomogeneous CurieWeiss model with external field ; We study the inhomogeneous CurieWeiss model with external field, where the inhomogeneity is introduced by adding a positive weight to every vertex and letting the interaction strength between two vertices be proportional to the product of their weights. In this model, the sum of the spins obeys a central limit theorem outside the critical line. We derive a BerryEsseen rate of convergence for this limit theorem using Stein's method for exchangeable pairs. For this, we, amongst others, need to generalize this method to a multidimensional setting with unbounded random variables.

Convergence rate of Markov chains and hybrid numerical schemes to jumpdiffusions with application to the Bates model ; We study the rate of weak convergence of Markov chains to diffusion processes under suitable but quite general assumptions. We give an example in the financial framework, applying the convergence analysis to a multiple jumps tree approximation of the CIR process. Then, we combine the Markov chain approach with other numerical techniques in order to handle the different components in jumpdiffusion coupled models. We study the speed of convergence of this hybrid approach and we provide an example in finance, applying our results to a treefinite difference approximation in the Heston or Bates model.

Face Recognition Based on Sequence of Images ; This paper presents a face recognition method based on a sequence of images. Face shape is reconstructed from images using a combination of structurefrommotion and multiview stereo methods. The reconstructed 3D face model is compared against models held in a gallery. The novel element in the presented approach is the fact, that the reconstruction is based only on input images and doesn't require a generic, deformable face model. Experimental verification of the proposed method is also included.

On existence and uniqueness of solution for a hydrodynamic problem related to water artificial circulation in a lake ; In this work we introduce a wellposed mathematical model for the processes involved in the artificial circulation of water, in order to avoid eutrophication phenomena, for instance, in a lake. This novel and general formulation is based on the modified NavierStokes equations following the Smagorinsky model of turbulence, and presenting a suitable nonhomogeneous Dirichlet boundary condition. For the analytical study of the problem, we prove several theoretical results related to existence, uniqueness and smoothness for the solution of this recirculation model.

A Stochastic Approach to Eulerian Numbers ; We examine the aggregate behavior of onedimensional random walks in a model known as onedimensional Internal Diffusion Limited Aggregation. In this model, a sequence of n particles perform random walks on the integers, beginning at the origin. Each particle walks until it reaches an unoccupied site, at which point it occupies that site and the next particle begins its walk. After all walks are complete, the set of occupied sites is an interval of length n containing the origin. We show the probability that k of the occupied sites are positive is given by an Eulerian probability distribution. Having made this connection, we use generating function techniques to compute the expected run time of the model.

Truthpreservation under fuzzy ppformulas ; How can nonclassical logic contribute to the analysis of complexity in computer science In this paper, we give a step towards this question, taking a logical modeltheoretic approach to the analysis of complexity in fuzzy constraint satisfaction. We study fuzzy positiveprimitive sentences, and we present an algebraic characterization of classes axiomatized by this kind of sentences in terms of homomorphisms and direct products. The ultimate goal is to study the expressiveness and reasoning mechanisms of nonclassical languages, with respect to constraint satisfaction problems and, in general, in modelling decision scenarios. fuzzy constraint satisfaction, fuzzy logics, model theory.

Unitarity of SinghHagen model in D dimensions ; The particle content of the SinghHagen model SH in D dimensions is revisited. We suggest a complete set of spinprojection operators acting on totally symmetric rank3 fields. We give a general expression for the propagator and determine the coefficients of the SH model confirming previous results of the literature. Adding totally symmetric source terms we provide an unitarity analysis in D dimensions.

Lorentz violation and Gravitoelectromagnetism Casimir effect and StefanBoltzmann law at Finite temperature ; The standard model and general relativity are local Lorentz invariants. However it is possible that at Planck scale there may be a breakdown of Lorentz symmetry. Models with Lorentz violation are constructed using Standard Model Extension SME. Here gravitational sector of the SME is considered to analyze the Lorentz violation in Gravitoelectromagnetism GEM. Using the energymomentum tensor, the StefanBoltzmann law and Casimir effect are calculated at finite temperature to ascertain the level of local Lorentz violation. Thermo Field Dynamics TFD formalism is used to introduce temperature effects.

Stueckelberg Bosons as an Ultralight Dark Matter Candidate ; In this letter, we propose a new model of fuzzy dark matter based on Stueckelberg theory. Dark matter is treated as a BoseEinstein condensate of Stueckelberg particles and the resulting cosmological effects are analyzed. Fits are understood for the density and halo sizes of such particles and comparison with existing models is made. Certain attractive properties of the model are demonstrated and lines for future work are laid out.

Qualitative description of the universe in the interacting fluids scheme ; In this work we present a qualitative description of the evolution of a curved universe when we consider the interacting scheme for the constituents of the dark sector. The resulting dynamics can be modeled by a set of LotkaVolterra type equations. For this model a future singularity is allowed, therefore the cyclic behavior for the energy interchange between the components of the universe is present only at some stage of the cosmic evolution. Due to the presence of the future singularity, the model exhibits global instability.

Irreversibility and typicality A simple analytical result for the Ehrenfest model ; With the aid of simple analytical computations for the Ehrenfest model, we clarify some basic features of macroscopic irreversibility. The stochastic character of the model allows us to give a nonambiguous interpretation of the general idea that irreversibility is a typical property for the vast majority of the realizations of the stochastic process, a single trajectory of a macroscopic observable behaves irreversibly, remaining very close to the deterministic evolution of its ensemble average, which can be computed using probability theory. The validity of the above scenario is checked through simple numerical simulations and a rigorous proof of the typicality is provided in the thermodynamic limit.

A robust KalmanBucy filtering problem ; A generalized KalmanBucy model under model uncertainty and a corresponding robust problem are studied in this paper. We find that this robust problem is equivalent to an estimate problem under a sublinear operator. By Girsanov transformation and the minimax theorem, we prove that this problem can be reformulated as a classical KalmanBucy filtering problem under a new probability measure. The equation which governs the optimal estimator is obtained. Moreover, the optimal estimator can be decomposed into the classical optimal estimator and a term related to model uncertainty.

Momentum sections in Hamiltonian mechanics and sigma models ; We show a constrained Hamiltonian system and a gauged sigma model have a structure of a momentum section and a Hamiltonian Lie algebroid theory recently introduced by Blohmann and Weinstein. We propose a generalization of a momentum section on a premultisymplectic manifold by considering gauged sigma models on a higher dimensional manifold.

Inflationary tensor fossils deformed by solid matter scalar field interaction ; We study effect of superhorizon tensor perturbations on scalar perturbations, so called effect of clustering fossils, in cosmological model in which inflation is driven by both solid matter and scalar field. The effect deforms primordial scalar power spectrum causing asymmetry in it, which leaves imprint on CMB anisotropies and the cosmic structure. Parameter space of this combined model allows for enhancement of logarithmic scale dependence of this deformation, as opposed to simpler models in which such scale dependence is suppressed by slowroll parameters.

Emergent gauge bosons and dynamical symmetry breaking in a fourfermion Lifshitz model ; We consider the fourfermion Lifshitz model, introduce in this model an auxiliary vector field, and generate an effective dynamics for this field. We explicitly demonstrate that within this dynamics, the effective bumblebee potential for the vector field naturally arises as a oneloop correction and allows for the dynamical breaking of the rotational symmetry.

How to FineTune BERT for Text Classification ; Language model pretraining has proven to be useful in learning universal language representations. As a stateoftheart language model pretraining model, BERT Bidirectional Encoder Representations from Transformers has achieved amazing results in many language understanding tasks. In this paper, we conduct exhaustive experiments to investigate different finetuning methods of BERT on text classification task and provide a general solution for BERT finetuning. Finally, the proposed solution obtains new stateoftheart results on eight widelystudied text classification datasets.

Optical excitation of surface plasmons and terahertz emission from metals ; We propose a microscopic theory of terahertz THz radiation generation on metal gratings under the action of femtosecond laser pulses. In contrast to previous models, only lowfrequency currents inside the metal are considered without involving electron emission. The presented model is based on plasmonenhanced thermal effects and explains the resonant character of opticaltoTHz conversion giving an adequate estimation for the full signal energy. Numerical modeling reproduces specific experimental features like delayed character of THz response and low conversion efficiency when the grating depth is too large.

Kessence and kinetic gravity braiding models in twofield measure theory ; We show that, in the context of the twofield measure theory, any kessence model leads to the existence of a fluid made of nonrelativistic matter and cosmological constant that would explain the dark matter and dark energy problem at the same time. On the other hand, kinetic gravity braiding models can lead to different behaviors, such as phantom dark energy, stiff matter, and a cosmological constant. For stiff matter, there even exists the case where the scalar field does not have any effect in the dynamics of the Universe.

A Case Study Exploiting Neural Machine Translation to Translate CUDA to OpenCL ; The sequencetosequence seq2seq model for neural machine translation has significantly improved the accuracy of language translation. There have been new efforts to use this seq2seq model for program language translation or program comparisons. In this work, we present the detailed steps of using a seq2seq model to translate CUDA programs to OpenCL programs, which both have very similar programming styles. Our work shows i a training input set generation method, ii prepost processing, and iii a case study using Polybenchgpu1.0, NVIDIA SDK, and Rodinia benchmarks.

Robustness of ANCOVA in randomised trials with unequal randomisation ; Randomised trials with continuous outcomes are often analysed using ANCOVA, with adjustment for prognostic baseline covariates. In an article published recently, Wang etal proved that in this setting the model based standard error estimator for the treamtent effect is consistent under outcome model misspecification, provided the probability of randomisation to each treatment is 12. In this article, we extend their results allowing for unequal randomisation. These demonstrate that the model based standard error is in general inconsistent when the randomisation probability differs from 12. In contrast, the sandwich standard error can provide asymptotically valid inferences under misspecification when randomisation probabilities are not equal, and is therefore recommended when randomisation is unequal.

General theory of charge regulation within the PoissonBoltzmann framework study of a stickycharged wall model ; This work introduces a stickycharge wall model as a simple and intuitive representation of charge regulation. Implemented within the meanfield level of description, the model modifies the boundary conditions without affecting the underlying PoissonBoltzmann PB equation of an electrolyte. Employing various modified PB equations, we are able to assess how various structural details of an electrolyte influence charge regulation.

Scene Induced MultiModal Trajectory Forecasting via Planning ; We address multimodal trajectory forecasting of agents in unknown scenes by formulating it as a planning problem. We present an approach consisting of three models; a goal prediction model to identify potential goals of the agent, an inverse reinforcement learning model to plan optimal paths to each goal, and a trajectory generator to obtain future trajectories along the planned paths. Analysis of predictions on the Stanford drone dataset, shows generalizability of our approach to novel scenes.

Exploring Evolving Plants as Interacting Particles in a Randomly Generated Heterogeneous Environment ; We model evolution of plants in a world, made up of different locations, with multiple environments mutually exclusive and collectively exhaustive subsets of locations. Each environment landmass has temperature, rainfall, and other attributes that directly affect plant growth and reproduction. Each plant has preferences for environment attributes. Depending on how suitable the environment is to the plants, seeds are released or death occurs. With every reproductive cycle, genetic mutations occur. To model competition, plants in compete for survival, and success is stochastically dependent on environmental fitness. Our model determines whether and how evolution occurs, and how the attributes of plants change and possibly converge over time in relation to the attributes of the environment.

Polynomial Scaling of Numerical Diagonalization of the 1D Transverse Field Ising Model into a Commuting Basis using the Pauli Product Representation ; We report numerical results on the diagonalization of 1D transverse field Ising model. Numerical simulations using the Pauli product representation yield diagonalization from 3 spins to 22 spins in the transverse field Ising model with the number of global Jacobi unitary transformations and number of final terms in diagonalized spin z representation both grew polynomial with the number of spins. These results computed on a classical computer show promise in constructing a quantum circuit to simulate diagonalized generic manyparticle Hamiltonians using polynomial number of gates.

Homogenization of twophase flow in porous media from Pore to Darcy Scale A phasefield approach ; We extend the twoscale expansion approach of periodic homogenization to include time scales and thus can tackle the full instationary NavierStokesCahnHilliard model at the pore scale as microscale. Time scale separation allows us to keep microscale dynamics, responsible e.g. for hysteresis, and arrive at a numerically tractable micromacro model including coupled generalized Darcy's laws.

Global stability of a Caputo fractional SIRS model with general incidence rate ; We introduce a fractional order SIRS model with nonlinear incidence rate. Existence of a unique positive solution to the model is proved. Stability analysis of the disease free equilibrium and positive fixed points are investigated. Finally, a numerical example is presented.

Nonlocality of Observables in QuasiHermitian Quantum Theory ; Explicit construction of local observable algebras in quasiHermitian quantum theories is derived in both the tensor product model of locality and in models of free fermions. The latter construction is applied to several cases of a mathcalPTsymmetric toy model of particleconserving free fermions on a 1dimensional lattice, with nearest neighbour interactions and open boundary conditions. Despite the locality of the Hamiltonian, local observables do not exist in generic collections of sites in the lattice. The collections of sites which do contain nontrivial observables strongly depends on the complex potential.

Investigating Simple Object Representations in ModelFree Deep Reinforcement Learning ; We explore the benefits of augmenting stateoftheart modelfree deep reinforcement algorithms with simple object representations. Following the Frostbite challenge posited by Lake et al. 2017, we identify object representations as a critical cognitive capacity lacking from current reinforcement learning agents. We discover that providing the Rainbow model Hessel et al.,2018 with simple, featureengineered object representations substantially boosts its performance on the Frostbite game from Atari 2600. We then analyze the relative contributions of the representations of different types of objects, identify environment states where these representations are most impactful, and examine how these representations aid in generalizing to novel situations.

A4 realization of leftright symmetric linear seesaw ; We explore an A4symmetric flavor based leftright symmetric model with linear seesaw mechanism and study the associated neutrino phenomenology. The framework offers the advantage of studying neutrino mass, nonunitarity effects in lepton sector, lepton flavour violation and CP violation. The fermion content of the model includes usual quarks, leptons along with additional sterile fermion per generation while the scalar content includes Higgs doublets and scalar bidoublet. We study analytically as well as numerically the correlation between different model parameters and their dependence on experimentally determined neutrino observables.

Gradient Boosting Neural Networks GrowNet ; A novel gradient boosting framework is proposed where shallow neural networks are employed as weak learners''. General loss functions are considered under this unified framework with specific examples presented for classification, regression, and learning to rank. A fully corrective step is incorporated to remedy the pitfall of greedy function approximation of classic gradient boosting decision tree. The proposed model rendered outperforming results against stateoftheart boosting methods in all three tasks on multiple datasets. An ablation study is performed to shed light on the effect of each model components and model hyperparameters.

Emergent Planck mass and dark energy from affine gravity ; We introduce a novel model of affine gravity, which implements the noscale scenario. Namely, Planck mass and Hubble constant emerge dynamically, through the mechanism of spontaneous breaking of scaleinvariance. Moreover, in our model the time direction and nondegenerate metric emerge dynamically as well. This naturally gives rise to the inflation and may server as a starting point for the birth of the Universe. We show that our model is phenomenologically viable, both from the perspective of the direct tests of gravity and cosmological evolution.

Stochastic Pore Collapse Models in Granular Materials ; Stochastic models for pore collapse in granular materials are developed. First, a general fluctuating stressstrain relation for a plastic flow rule is derived. The fluctuations account for nonassociativity in plastic deformations typically observed in heterogeneous materials. Second, an axisymmetric spherical shell compaction model is extended to account for fluctuations in the material microstructure due to granular interactions at the pore scale. This changes the stressstrain constitutive equation determining the dynamics of pore collapse. Results show that stochastic differential equations can account for multiscale interactions in a statistical sense.

A gravity term from spontaneous symmetry breaking ; In this model, the gravity term in the Lagrangean comes from spontaneous symmetry breaking of an additional scalar quadruplet field Upsilon. The resulting gravitational field is approximate to one of the models of coframe gravity with parameters rho1 4 rho2 0, rho3 0. This article includes an exact solution of coframe gravity with model parameters rho1 neq 0, rho2 any, rho3 0, which is Newtonian at infinity. An iteration process is given to construct a solution for a given matterradiation stressenergy tensor.

Musings on Firewalls and the Information Paradox ; The past year has seen an explosion of new and old ideas about black hole physics. Prior to the firewall paper, the dominant picture was the thermofield model apparently implied by ADSCFT dualitycitemal2. While some seek a narrow responce to Almheiri, Marolf, Polchinski, and Sully,AMPSciteamps, there are a number of competing models. One problem in the field is the ambiguity of the competing proposals. Some are equivalent while others incompatible. This paper will attempt to define and classify a few models representative of the current discussions.

Inflationary Baryogenesis in a Model with Gauged Baryon Number ; We argue that inflationary dynamics may support a scenario where significant matterantimatter asymmetry is generated from initially smallscale quantum fluctuations that are subsequently stretched out over large scales. This scenario can be realised in extensions of the Standard Model with an extra gauge symmetry having mixed anomalies with the electroweak gauge symmetry. Inflationary baryogenesis in a model with gauged baryon number is considered in detail.

Vector inflation by kinetic coupled gravity ; Vector inflation is a newly established model where inflation is driven by nonminimally coupled massive vector fields with a potential term. This model is similar to the model of chaotic inflation with scalar fields, except that for vector fields the isotropy of expansion is achieved either by considering a triplet of orthogonal vector fields or N randomly oriented independent vector fields. We introduce a new version of vector inflation where the vector field has no potential term but is nonminimally coupled to gravity through the kinetic term. The nonminimal coupling is established by introducing the Einstein tensor besides the metric tensor within the kinetic term of the vector field.

Validation of Compton Scattering Monte Carlo Simulation Models ; Several models for the Monte Carlo simulation of Compton scattering on electrons are quantitatively evaluated with respect to a large collection of experimental data retrieved from the literature. Some of these models are currently implemented in general purpose Monte Carlo systems; some have been implemented and evaluated for possible use in Monte Carlo particle transport for the first time in this study. Here we present first and preliminary results concerning total and differential Compton scattering cross sections.

Natural models of theories of green points ; We explicitly present expansions of the complex field which are models of the theories of green points in the multiplicative group case and in the case of an elliptic curve without complex multiplication defined over mathbbR. In fact, in both cases we give families of structures depending on parameters and prove that they are all models of the theories, provided certain instances of Schanuel's conjecture or an analogous conjecture for the exponential map of the elliptic curve hold. In the multiplicative group case, however, the results are unconditional for generic choices of the parameters.

Analysis of Probabilistic Basic Parallel Processes ; Basic Parallel Processes BPPs are a wellknown subclass of Petri Nets. They are the simplest common model of concurrent programs that allows unbounded spawning of processes. In the probabilistic version of BPPs, every process generates other processes according to a probability distribution. We study the decidability and complexity of fundamental qualitative problems over probabilistic BPPs in particular reachability with probability 1 of different classes of target sets e.g. upwardclosed sets. Our results concern both the Markovchain model, where processes are scheduled randomly, and the MDP model, where processes are picked by a scheduler.

Propositional dynamic logic for searching games with errors ; We investigate some finitelyvalued generalizations of propositional dynamic logic with tests. We start by introducing the n1valued Kripke models and a corresponding language based on a modal extension of Lukasiewicz manyvalued logic. We illustrate the definitions by providing a framework for an analysis of the R'enyi Ulam searching game with errors. Our main result is the axiomatization of the theory of the n1valued Kripke models. This result is obtained through filtration of the canonical model of the smallest n1valued propositional dynamic logic.

Stable Exact Cosmological Solutions in Induced Gravity Models ; We study dynamics of induced gravity cosmological models with sixth degree potential, that have found using the superpotential method. The important property of these models are existence of exact cosmological solutions that tend to fixed points. The stability of these cosmological solutions have been obtained. In particular, we find conditions under which solutions with a nonmonotonic Hubble parameter that tend to a fixed point are attractors.

On estimation states of hidden markov models in condition of unknown transition matrix ; In this paper, we develop methods of nonlinear filtering and prediction of an unobservable Markov chain with a finite set of states. This Markov chain controls coefficients of ARp model. Using observations generated by ARp model we have to estimate the state of Markov chain in the case of an unknown probability transition matrix. Comparison of proposed nonparametric algorithms with the optimal methods in the case of the known transition matrix is carried out by simulating.

Form factors of local operators in a onedimensional twocomponent Bose gas ; We consider a onedimensional model of a twocomponent Bose gas and study form factors of local operators in this model. For this aim we use an approach based on the algebraic Bethe ansatz. We show that the form factors under consideration can be reduced to those of the monodromy matrix entries in a generalized GL3invariant model. In this way we derive determinant representations for the form factors of local operators.

Approximate likelihood inference in generalized linear latent variable models based on integral dimension reduction ; Latent variable models represent a useful tool for the analysis of complex data when the constructs of interest are not observable. A problem related to these models is that the integrals involved in the likelihood function cannot be solved analytically. We propose a computational approach, referred to as Dimension Reduction Method DRM, that consists of a dimension reduction of the multidimensional integral that makes the computation feasible in situations in which the quadrature based methods are not applicable. We discuss the advantages of DRM compared with other existing approximation procedures in terms of both computational feasibility of the method and asymptotic properties of the resulting estimators.

Nongeometric CalabiYau compactifications and fractional mirror symmetry ; We construct a wide class of nongeometric compactifications of type II superstring theories preserving N1 spacetime supersymmetry in four dimensions, starting from CalabiYau compactifications at Gepner points. Particular examples of this construction provide quantum equivalences between CalabiYau compactifications and nonCalabiYau ones, generalizing mirror symmetry. The associated LandauGinzburg models involve both chiral and twisted chiral multiplets hence cannot be lifted to ordinary CalabiYau gauged linear sigmamodels.

Hypergeometric analytic continuation of the strongcoupling perturbation series for the 2d BoseHubbard model ; We develop a scheme for analytic continuation of the strongcoupling perturbation series of the pure BoseHubbard model beyond the Mott insulatortosuperfluid transition at zero temperature, based on hypergeometric functions and their generalizations. We then apply this scheme for computing the critical exponent of the order parameter of this quantum phase transition for the twodimensional case, which falls into the universality class of the threedimensional XY model. This leads to anontrivial test of the universality hypothesis.