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Nonlocal Solutions to Dynamic Equilibrium Models The Approximate Stable Manifolds Approach ; This study presents a method for constructing a sequence of approximate solutions of increasing accuracy to general equilibrium models on nonlocal domains. The method is based on a technique originated from dynamical systems theory. The approximate solutions are constructed employing the Contraction Mapping Theorem and the fact that solutions to general equilibrium models converge to a steady state. The approach allows deriving the a priori and a posteriori approximation errors of the solutions. Under certain nonlocal conditions we prove the convergence of the approximate solutions to the true solution and hence the Stable Manifold Theorem. We also show that the proposed approach can be treated as a rigorous proof of convergence for the extended path algorithm to the true solution in a class of nonlinear rational expectation models.

Weak Gravity Strongly Constrains LargeField Axion Inflation ; Models of largefield inflation based on axionlike fields with shift symmetries can be simple and natural, and make a promising prediction of detectable primordial gravitational waves. The Weak Gravity Conjecture is known to constrain the simplest case in which a single compact axion descends from a gauge field in an extra dimension. We argue that the Weak Gravity Conjecture also constrains a variety of theories of multiple compact axions including Nflation and some alignment models. We show that other alignment models entail surprising consequences for how the mass spectrum of the theory varies across the axion moduli space, and hence can be excluded if further conjectures hold. In every case that we consider, plausible assumptions lead to field ranges that cannot be parametrically larger than the Planck scale. Our results are strongly suggestive of a general inconsistency in models of largefield inflation based on compact axions, and possibly of a more general principle forbidding superPlanckian field ranges.

TreeCut for Probabilistic Image Segmentation ; This paper presents a new probabilistic generative model for image segmentation, i.e. the task of partitioning an image into homogeneous regions. Our model is grounded on a midlevel image representation, called a region tree, in which regions are recursively split into subregions until superpixels are reached. Given the region tree, image segmentation is formalized as sampling cuts in the tree from the model. Inference for the cuts is exact, and formulated using dynamic programming. Our treecut model can be tuned to sample segmentations at a particular scale of interest out of many possible multiscale image segmentations. This generalizes the common notion that there should be only one correct segmentation per image. Also, it allows moving beyond the standard singlescale evaluation, where the segmentation result for an image is averaged against the corresponding set of coarse and fine human annotations, to conduct a scalespecific evaluation. Our quantitative results are comparable to those of the leading gPbowtucm method, with the notable advantage that we additionally produce a distribution over all possible treeconsistent segmentations of the image.

On the accuracy of selfnormalized loglinear models ; Calculation of the lognormalizer is a major computational obstacle in applications of loglinear models with large output spaces. The problem of fast normalizer computation has therefore attracted significant attention in the theoretical and applied machine learning literature. In this paper, we analyze a recently proposed technique known as selfnormalization, which introduces a regularization term in training to penalize log normalizers for deviating from zero. This makes it possible to use unnormalized model scores as approximate probabilities. Empirical evidence suggests that selfnormalization is extremely effective, but a theoretical understanding of why it should work, and how generally it can be applied, is largely lacking. We prove generalization bounds on the estimated variance of normalizers and upper bounds on the loss in accuracy due to selfnormalization, describe classes of input distributions that selfnormalize easily, and construct explicit examples of highvariance input distributions. Our theoretical results make predictions about the difficulty of fitting selfnormalized models to several classes of distributions, and we conclude with empirical validation of these predictions.

Doubly RobustBased Generalized Estimating Equations for the Analysis of Longitudinal Ordinal Missing Data ; Generalized Estimation Equations GEE are a wellknown method for the analysis of nonGaussian longitudinal data. This method has computational simplicity and marginal parameter interpretation. However, in the presence of missing data, it is only valid under the strong assumption of missing completely at random MCAR. Some corrections can be done when the missing data mechanism is missing at random MAR inverse probability weighting WGEE and multiple imputation MIGEE. In order to obtain consistent estimates, it is necessary the correct specification of the weight model for WGEE or the imputation model for the MIGEE. A recent method combining ideas of these two approaches has doubly robust property. For consistency, it requires only the weight or the imputation model to be correct. In this work it is assumed a proportional odds model and it is proposed a doubly robust estimator for the analysis of ordinal longitudinal data with intermittently missing response and covariate under the MAR mechanism. Simulation results revealed better performance of the proposed method compared to WGEE and MIGEE. The method is applied to a data set related to Analgesia Pain in Childbirth study.

Higher dimensional Loop Quantum Cosmology ; Loop quantum cosmologyLQC is the symmetric model of loop quantum gravity. In this paper, we generalize the structure of loop quantum cosmology to the theories with arbitrary spacetime dimensions. The isotropic and homogenous cosmological model in n1 dimensions is quantized by the loop quantization method. Interestingly, we find that the underlying quantum theories are divided into two qualitatively different sectors according to spacetime dimensions. The effective Hamiltonian and modified dynamical equations of n1 dimensional LQC are obtained. Moreover, our results indicate that the classical big bang singularity is resolved in arbitrary spacetime dimensions by a quantum bounce. We also briefly discuss the similarities and differences between the n1 dimensional model and the 31 dimensional one. Our model serves as a first example of higher dimensional loop quantum cosmology and offers possibility to investigate quantum gravity effects in higher dimensional cosmology.

pyMOR Generic Algorithms and Interfaces for Model Order Reduction ; Reduced basis methods are projectionbased model order reduction techniques for reducing the computational complexity of solving parametrized partial differential equation problems. In this work we discuss the design of pyMOR, a freely available software library of model order reduction algorithms, in particular reduced basis methods, implemented with the Python programming language. As its main design feature, all reduction algorithms in pyMOR are implemented generically via operations on welldefined vector array, operator and discretization interface classes. This allows for an easy integration with existing opensource highperformance partial differential equation solvers without adding any model reduction specific code to these solvers. Besides an indepth discussion of pyMOR's design philosophy and architecture, we present several benchmark results and numerical examples showing the feasibility of our approach.

Scientific Modelling with CoalgebraAlgebra Homomorphisms ; Many recursive functions can be defined elegantly as the unique homomorphisms, between two algebras, two coalgebras, or one each, that are induced by some universal property of a distinguished structure. Besides the wellknown applications in recursive functional programming, several basic modes of reasoning about scientific models have been demonstrated to admit such an exact metatheory. Here we explore the potential of coalgebraalgebra homomorphism that are not a priori unique, for capturing more loosely specifying patterns of scientific modelling. We investigate a pair of dual techniques that leverage comonadic structure to obtain reasonable genericity even when no universal properties are given. We show the general applicability of the approach by discussing a surprisingly broad collection of instances from realworld modelling practice.

Embed to Control A Locally Linear Latent Dynamics Model for Control from Raw Images ; We introduce Embed to Control E2C, a method for model learning and control of nonlinear dynamical systems from raw pixel images. E2C consists of a deep generative model, belonging to the family of variational autoencoders, that learns to generate image trajectories from a latent space in which the dynamics is constrained to be locally linear. Our model is derived directly from an optimal control formulation in latent space, supports longterm prediction of image sequences and exhibits strong performance on a variety of complex control problems.

Standing Waves Braneworlds ; The class of nonstationary braneworld models generated by the coupled gravitational and scalar fields is reviewed. The model represents a brane in a spacetime with single time and one large infinite and several small compact spacelike extra dimensions. In some particular cases the model has the solutions corresponding to the bulk graviscalar standing waves bounded by the brane. Pure gravitational localization mechanism of matter particles on the node of standing waves, where the brane is placed, is discussed. Cosmological applications of the model also considered.

The model of the black hole enclosed in dust. The flat space case ; In this work the model is constructed to describe the black hole enclosed in the dust cosmological background in case of zero spatial curvature. This model is based on our exact solution of the class of LTB inhomogeneous solutions. We considered the properties of the model and built the RTstructure of the resulting spacetime. It was shown that central region includes the Schwarzchildlike black hole. We derived the equations of motion of the test particle from the point of view of the observer comoving with cosmological expansion. We found analytical expressions for observable orbital and radial velocities of the particle and plotted the surface profile of the total velocity in this case. In comoving coordinate frame it is impossible to study the questions concerning the black hole horizon but one can observe the local motion of the particles influenced by the cosmological expansion.

A Flippon Related Singlet at the LHC II ; We consider the 750 GeV diphoton resonance at the 13 TeV LHC in the cal FSU5 model with a Standard Model SM singlet field which couples to TeVscale vectorlike particles, dubbed flippons. This singlet field assumes the role of the 750 GeV resonance, with production via gluon fusion and subsequent decay to a diphoton via the vectorlike particle loops. We present a numerical analysis showing that the observed 8 TeV and 13 TeV diphoton production crosssections can be generated in the model space with realistic electric charges and Yukawa couplings for light vectorlike masses. We further discuss the experimental viability of light vectorlike masses in a General NoScale cal FSU5 model, offering a few benchmark scenarios in this consistent GUT that can satisfy all experimental constraints imposed by the LHC and other essential experiments.

Using particle swarm optimization to search for locally Doptimal designs for mixed factor experiments with binary response ; Identifying optimal designs for generalized linear models with a binary response can be a challenging task, especially when there are both continuous and discrete independent factors in the model. Theoretical results rarely exist for such models, and the handful that do exist come with restrictive assumptions. This paper investigates the use of particle swarm optimization PSO to search for locally Doptimal designs for generalized linear models with discrete and continuous factors and a binary outcome and demonstrates that PSO can be an effective method. We provide two real applications using PSO to identify designs for experiments with mixed factors one to redesign an odor removal study and the second to find an optimal design for an electrostatic discharge study. In both cases we show that the Defficiencies of the designs found by PSO are much better than the implemented designs. In addition, we show PSO can efficiently find Doptimal designs on a prototype or an irregularly shaped design space, provide insights on the existence of minimally supported optimal designs, and evaluate sensitivity of the Doptimal design to misspecifications in the link function.

A Generalized Ising Model for studying Alloy Evolution under Irradiation and its use in Kinetic Monte Carlo Simulations ; We derive an Ising Hamiltonian for kinetic simulations involving interstitial and vacancy defects in binary alloys. Our model, which we term ABVI', incorporates solute transport by both interstitial defects and vacancies into a mathematicallyconsistent framework , and thus represents a generalization to the widelyused ABV model for alloy evolution simulations. The Hamiltonian captures the three possible interstitial configurations in a binary alloy AA, AB, and BB, which makes it particularly useful for irradiation damage simulations. All the constants of the Hamiltonian are expressed in terms of bond energies that can be computed using firstprinciples calculations. We implement our ABVI model in kinetic Monte Carlo simulations and perform a verification exercise by comparing our results to published irradiation damage simulations in simple binary systems with Frenkel pair defect production and several microstructural scenarios, with matching agreement found.

Heterotic free fermionic and symmetric toroidal orbifold models ; Free fermionic models and symmetric heterotic toroidal orbifolds both constitute exact backgrounds that can be used effectively for phenomenological explorations within string theory. Even though it is widely believed that for Z2xZ2 orbifolds the two descriptions should be equivalent, a detailed dictionary between both formulations is still lacking. This paper aims to fill this gap We give a detailed account of how the input data of both descriptions can be related to each other. In particular, we show that the generalized GSO phases of the free fermionic model correspond to generalized torsion phases used in orbifold model building. We illustrate our translation methods by providing free fermionic realizations for all Z2xZ2 orbifold geometries in six dimensions.

Classifying the behavior of noncanonical quintessence ; We derive general conditions for the existence of stable scaling solutions for the evolution of noncanonical quintessence, with a Lagrangian of the form mathcalLX,phiXalphaVphi, for powerlaw and exponential potentials when the expansion is dominated by a background barotropic fluid. Our results suggest that in most cases, noncanonical quintessence with such potentials does not yield interesting models for the observed dark energy. When the scaling solution is not an attractor, there is a wide range of model parameters for which the evolution asymptotically resembles a zeropotential solution with equation of state parameter w 12alpha 1, and oscillatory solutions are also possible for positive powerlaw potentials; we derive the conditions on the model parameters which produce both types of behavior. We investigate thawing noncanonical models with a nearlyflat potential and derive approximate expressions for the evolution of wa. These forms for wa differ in a characteristic way from the corresponding expressions for canonical quintessence.

A Convex Polynomial ForceMotion Model for Planar Sliding Identification and Application ; We propose a polynomial forcemotion model for planar sliding. The set of generalized friction loads is the 1sublevel set of a polynomial whose gradient directions correspond to generalized velocities. Additionally, the polynomial is confined to be convex evendegree homogeneous in order to obey the maximum work inequality, symmetry, shape invariance in scale, and fast invertibility. We present a simple and statisticallyefficient model identification procedure using a sumofsquares convex relaxation. Simulation and robotic experiments validate the accuracy and efficiency of our approach. We also show practical applications of our model including stable pushing of objects and free sliding dynamic simulations.

Sharp detection in PCA under correlations all eigenvalues matter ; Principal component analysis PCA is a widely used method for dimension reduction. In high dimensional data, the signal eigenvalues corresponding to weak principal components PCs do not necessarily separate from the bulk of the noise eigenvalues. Therefore, popular tests based on the largest eigenvalue have little power to detect weak PCs. In the special case of the spiked model, certain tests asymptotically equivalent to linear spectral statistics LSSaveraging effects over all eigenvalueswere recently shown to achieve some power. We consider a nonparametric, nonGaussian generalization of the spiked model to the setting of Marchenko and Pastur 1967. This allows a general bulk of the noise eigenvalues, accomodating correlated variables even under the null hypothesis of no significant PCs. We develop new tests based on LSS to detect weak PCs in this model. We show using the CLT for LSS that the optimal LSS satisfy a Fredholm integral equation of the first kind. We develop algorithms to solve it, building on our recent method for computing the limit empirical spectrum. In contrast to the standard spiked model, we find that under widely spread null eigenvalue distributions, the new tests have a lot of power.

Dimensional reduction for the general Markov model on phylogenetic trees ; We present a method of dimensional reduction for the general Markov model of sequence evolution on a phylogenetic tree. We show that taking certain linear combinations of the associated random variables site pattern counts reduces the dimensionality of the model from exponential in the number of extant taxa, to quadratic in the number of taxa, while retaining the ability to statistically identify phylogenetic divergence events. A key feature is the identification of an invariant subspace which depends only bilinearly on the model parameters, in contrast to the usual multilinear dependence in the full space. We discuss potential applications including the computation of split edge weights on phylogenetic trees from observed sequence data.

Radiative Neutrino Mass in Alternative LeftRight Model ; We propose a radiative seesaw model in alternative leftright model without any bidoublet scalar fields, in which all the fermion masses in the standard model are generated through a canonical seesaw mechanism at the tree level. On the other hand the observed neutrino masses are generated at twoloop level. In this paper we focus on the neutrino sector and show how to induce the active neutrino masses. Then we discuss the observed neutrino oscillation, constraints from lepton flavor violations, new sources of muon anomalous magnetic moment, a longlived dark matter candidate with keV scale mass, and collider physics.

A Structured Variational Autoencoder for Learning Deep Hierarchies of Sparse Features ; In this note we present a generative model of natural images consisting of a deep hierarchy of layers of latent random variables, each of which follows a new type of distribution that we call rectified Gaussian. These rectified Gaussian units allow spikeandslab type sparsity, while retaining the differentiability necessary for efficient stochastic gradient variational inference. To learn the parameters of the new model, we approximate the posterior of the latent variables with a variational autoencoder. Rather than making the usual meanfield assumption however, the encoder parameterizes a new type of structured variational approximation that retains the prior dependencies of the generative model. Using this structured posterior approximation, we are able to perform joint training of deep models with many layers of latent random variables, without having to resort to stacking or other layerwise training procedures.

Baryogenesis and Dark Matter in U1 Extensions ; A brief review is given of some recent works where baryogenesis and dark matter have a common origin within the U1 extensions of the standard model and of the minimal supersymmetric standard model. The models considered generate the desired baryon asymmetry and the dark matter to baryon ratio. In one model all of the fundamental interactions do not violate lepton number, and the total BL in the Universe vanishes. In addition, one may also generate a normal hierarchy of neutrino masses and mixings in conformity with the current data. Specifically one can accommodate theta13sim 9circ consistent with the data from Daya Bay reactor neutrino experiment.

Price Dynamics Via Expectations, and the Role of Money Therein ; Beyond its obvious macroeconomic relevance, fiat money has important microeconomic implications. They matter for addressing No. 8 in Smale's Mathematical Problems for the Next Century extend the mathematical model of general equilibrium theory to include price adjustments. In the canonical ArrowDebreu framework, equilibrium prices are set by a fictitious auctioneer. Removing that fiction raises the question of how prices are set and adjusted by decentralised actors with incomplete information. We investigate this question through a very basic model where a unique factor of production, labour, produces a single consumption good, called jelly for brevity. The point of the model is to study a price dynamics based on the firm's expectations about jelly demand and labour supply. The system tends towards economic equilibrium, however, depending on the initial conditions it might not get there. In different model versions, different kinds of money are introduced. Compared to the case of no money, the introduction of money as a store of value facilitates the system reaching economic equilibrium. If money is introduced as a third commodity, i.e. there is also a demand for money, the system dynamics in general becomes more complex.

Deep Amortized Inference for Probabilistic Programs ; Probabilistic programming languages PPLs are a powerful modeling tool, able to represent any computable probability distribution. Unfortunately, probabilistic program inference is often intractable, and existing PPLs mostly rely on expensive, approximate samplingbased methods. To alleviate this problem, one could try to learn from past inferences, so that future inferences run faster. This strategy is known as amortized inference; it has recently been applied to Bayesian networks and deep generative models. This paper proposes a system for amortized inference in PPLs. In our system, amortization comes in the form of a parameterized guide program. Guide programs have similar structure to the original program, but can have richer data flow, including neural network components. These networks can be optimized so that the guide approximately samples from the posterior distribution defined by the original program. We present a flexible interface for defining guide programs and a stochastic gradientbased scheme for optimizing guide parameters, as well as some preliminary results on automatically deriving guide programs. We explore in detail the common machine learning pattern in which a 'local' model is specified by 'global' random values and used to generate independent observed data points; this gives rise to amortized local inference supporting global model learning.

Systems of Delay Differential Equations Analysis of a model with feedback ; Selfregulatory models are common in nature, as described e.g. in citemur, citeha and citeGb. Let us consider a system made up of a number of glands as a motivation. Each gland secretes a hormone that allows secretion in the next gland, which successively generates another hormone to stimulate the next one and so on. In the end, a final hormone is released which, by increasing its concentration, will inhibit the secretion of previous hormones that allowed the production process. This generates the decay of this hormone to a minimum threshold that reactivates the cycle again. This behavior can be seen in other biochemical processes, such as enzymatic or bacterial models. Topological degree is a useful tool to find stable equilibria in a wide variety of models with constant parameters and, furthermore, allows to deduce the existence of periodic solutions when the constant parameters are replaced by periodic functions.

Sufficient conditions for existence of positive periodic solution of a generalized nonresident computer virus model ; In this paper, we introduce a nonresident computer virus model and prove the existence of at least one positive periodic solution. The proposed model is based on a biological approach and is obtained by considering that all rates rates that the computers are disconnected from the Internet, the rate that the computers are cured, etc are time dependent real functions. Assuming that the initial condition is a positive vector and the coefficients are positive omegaperiodic and applying the topological degree arguments we deduce that generalized nonresident computer virus model has at least one positive omegaperiodic solution. The proof consists of two big parts. First, an appropriate change of variable which conserves the periodicity property and implies the positive behavior. Second, a reformulation of transformed system as an operator equation which is analyzed by applying the continuation theorem of the coincidence degree theory.

Gibbs Measures with memory of length 2 on an arbitrary order Cayley tree ; In this paper, we consider the IsingVanniminus model on an arbitrary order Cayley tree. We generalize the results conjectured in Chinese Journal of Physics, 54 4, 635649 2016 and International Journal of Modern Physics, arXiv1608.06178 for an arbitrary order Cayley tree. We establish existence and a full classification of translation invariant Gibbs measures with memory of length 2 associated with the model on arbitrary order Cayley tree. We construct the recurrence equations corresponding generalized ANNNI model. We satisfy the Kolmogorov emphconsistency condition. We propose a rigorous measuretheoretical approach to investigate the Gibbs measures with memory of length 2 for the model. We explain whether the number of branches of tree does not change the number of Gibbs measures. Also we take up with trying to determine when phase transition does occur.

Backlund Transformation and QuasiIntegrable Deformation of Mixed FermiPastaUlam and FrenkelKontorova Models ; In this paper we study a nonlinear partial differential equation PDE, proposed by N. Kudryashov arXiv1611.06813v1nlin.SI, using continuum limit approximation of mixed FermiPastaUlam and FrenkelKontorova Models. This generalized semidiscrete equation can be considered as a model for the description of nonlinear dislocation waves in crystal lattice and the corresponding continuous system can be called mixed generalized potential KdV and sineGordon equation. We obtain the Backlund transformation of this equation in Riccati form in inverse method. We further study the quasiintegrable deformation of this model.

Zitterbewegung and the Electron ; Starting from a statistical model of the electron, which explains spin and spin measurements in terms of a probability density distribution resulting from a rapidly changing angular momentum during an extended Zitterbewegung, a lightlike model of electron and Fermions is formulated. This model describes individual particles in terms of paths of a moving quantum. It is shown that this description allows one to reproduce observable properties as pathaverages over a period of the fast extended Zitterbewegung in elementary calculations. The general topology of the paths may be described as a helical path, with a helix axis forming a circle around a fixed point in space. The radius of the helix and of the circle are equal and given by half the reduced Compton wave length of a photon of energy equal to the rest energy of the particle described. The paths depend on the relative velocity between the described entity and the observer, and represent the De Broglie wave. The merits of the proposed model are summarized and its role in relation to the established description by quantum mechanics discussed. It is concluded that it supports the existence of the proposed extended Zitterbewegung, and offers a description of quantum behaviour without quantum mechanics.

SpaceTime Graph Modeling of Ride Requests Based on RealWorld Data ; This paper focuses on modeling ride requests and their variations over location and time, based on analyzing extensive realworld data from a ridesharing service. We introduce a graph model that captures the spatial and temporal variability of ride requests and the potentials for ride pooling. We discover these ride request graphs exhibit a well known property called densification power law often found in real graphs modelling human behaviors. We show the pattern of ride requests and the potential of ride pooling for a city can be characterized by the densification factor of the ride request graphs. Previous works have shown that it is possible to automatically generate synthetic versions of these graphs that exhibit a given densification factor. We present an algorithm for automatic generation of synthetic ride request graphs that match quite well the densification factor of ride request graphs from actual ride request data.

Training Group Orthogonal Neural Networks with Privileged Information ; Learning rich and diverse representations is critical for the performance of deep convolutional neural networks CNNs. In this paper, we consider how to use privileged information to promote inherent diversity of a single CNN model such that the model can learn better representations and offer stronger generalization ability. To this end, we propose a novel group orthogonal convolutional neural network GoCNN that learns untangled representations within each layer by exploiting provided privileged information and enhances representation diversity effectively. We take image classification as an example where image segmentation annotations are used as privileged information during the training process. Experiments on two benchmark datasets ImageNet and PASCAL VOC clearly demonstrate the strong generalization ability of our proposed GoCNN model. On the ImageNet dataset, GoCNN improves the performance of stateoftheart ResNet152 model by absolute value of 1.2 while only uses privileged information of 10 of the training images, confirming effectiveness of GoCNN on utilizing available privileged knowledge to train better CNNs.

Convex Hull of the Quadratic Branch AC Power Flow Equations and Its Application in Radial Distribution Networks ; A branch flow model BFM is used to formulate the AC power flow in general networks. For each branchline, the BFM contains a nonconvex quadratic equality. A mathematical formulation of its convex hull is proposed, which is the tightest convex relaxation of this quadratic equation. The convex hull formulation consists of a second order cone inequality and a linear inequality within the physical bounds of power flows. The convex hull formulation is analytically proved and geometrically validated. An optimal scheduling problem of distributed energy storage DES in radial distribution systems with high penetration of photovoltaic resources is investigated in this paper. To capture the performance of both the battery and converter, a secondorder DES model is proposed. Following the convex hull of the quadratic branch flow equation, the convex hull formulation of the nonconvex constraint in the DES model is also derived. The proposed convex hull models are used to generate a tight convex relaxation of the DES optimal scheduling DESOS problem. The proposed approach is tested on several radial systems. A discussion on the extension to meshed networks is provided.

Numerical Study of Nonlinear Dynamics of a Population System with Time Delay ; Mathematical models of interacting populations are often constructed as systems of differential equations, which describe how populations change with time. Below we study one such model connected to the nonlinear dynamics of a system of populations in presence of time delay. The consequence of the presence of the time delay is that the nonlinear dynamics of the studied system become more rich, e.g., new orbits in the phase space of the system arise which are dependent on the timedelay parameters. In more detail we introduce a time delay and generalize the model system of differential equations for the interaction of three populations based on generalized Volterra equations in which the growth rates and competition coefficients of populations depend on the number of members of all populations citeDimitrova2001a,citeDimitrova2001b and then numerically solve the system with and without time delay. We use a modification of the method of Adams for the numerical solution of the system of model equations with time delay. By appropriate selection of the parameters and initial conditions we show the impact of the delay time on the dynamics of the studied population system.

TransformationBased Models of Video Sequences ; In this work we propose a simple unsupervised approach for next frame prediction in video. Instead of directly predicting the pixels in a frame given past frames, we predict the transformations needed for generating the next frame in a sequence, given the transformations of the past frames. This leads to sharper results, while using a smaller prediction model. In order to enable a fair comparison between different video frame prediction models, we also propose a new evaluation protocol. We use generated frames as input to a classifier trained with ground truth sequences. This criterion guarantees that models scoring high are those producing sequences which preserve discriminative features, as opposed to merely penalizing any deviation, plausible or not, from the ground truth. Our proposed approach compares favourably against more sophisticated ones on the UCF101 data set, while also being more efficient in terms of the number of parameters and computational cost.

An alternative approach to modelling a cosmic void and its effect on the cosmic microwave background ; We apply our tetradbased approach for constructing sphericallysymmetric solutions in general relativity to modelling a void, and compare it with the standard LemaitreTolmanBondi LTB formalism. In particular, we construct models for the void observed in the direction of Draco in the WISE2MASS galaxy survey, and a corresponding cosmic microwave background CMB temperature decrement in the Planck data in the same direction. We find that the presentday density and velocity profiles of the void are not well constrained by the existing data, so that void models produced from the two approaches can differ substantially while remaining broadly consistent with the observations. We highlight the importance of considering the velocity as well as the density profile in constraining voids.

Closed trapping horizons without singularity ; In gravitational collapse leading to black hole formation, trapping horizons typically develop inside the contracting matter. Classically, an ingoing trapping horizon moves towards the centre where it reaches a curvature singularity, while an outgoing horizon moves towards the surface of the star where it becomes an isolated, null horizon. However, strong quantum effects at high curvature close to the centre could modify the classical picture substantially, e.g. by deflecting the ingoing horizon to larger radii, until it eventually reunites with the outgoing horizon. We here analyse some existing models of regular black holes of finite lifespan formed out of ingoing null shells collapsing from mathscrI, after giving general conditions for the existence of singularityfree closed trapping horizons. We study the energymomentum tensor of such models by solving Einstein's equations in reverse and give an explicit form of the metric to model a Hawking radiation reaching mathscrI. A major flaw of the models aiming at describing the formation of black holes with a Vaidya limit on mathscrI as well as their evaporation is finally exhibited they necessarily violate the null energy condition up to mathscrI, i.e. in a noncompact region of spacetime.

Generative models for local network community detection ; Local network community detection aims to find a single community in a large network, while inspecting only a small part of that network around a given seed node. This is much cheaper than finding all communities in a network. Most methods for local community detection are formulated as adhoc optimization problems. In this work, we instead start from a generative model for networks with community structure. By assuming that the network is uniform, we can approximate the structure of unobserved parts of the network to obtain a method for local community detection. We apply this local approximation technique to two variants of the stochastic block model. To our knowledge, this results in the first local community detection methods based on probabilistic models. Interestingly, in the limit, one of the proposed approximations corresponds to conductance, a popular metric in this field. Experiments on real and synthetic datasets show comparable or improved results compared to stateoftheart local community detection algorithms.

NonStandard Neutrino Interactions in a Modified 2HDM ; In the traditional neutrinophilic twoHiggs doublet model nu2HDM, there is no nonstandard neutrino interaction NSI as the interactions between the Standard Model fermions with neutrinos are negligibly small due to the tiny mixing of the two scalar doublets. In this work, we propose that if nu2HDM is modified by considering the righthanded electron, eR is negatively charged under a global U1symmetry then one can generate significant amount of NSI along with the tiny Dirac neutrino mass. Depending on different constraints from the LEP experiment, tree level lepton flavor violating processes, bigbang neucleosynthesis etc., we observe that this model significantly restricts the range of permissible NSI parameters, putting a strict upper bound on different NSIs. Furthermore, considering these modeldependent NSIs, we study their impact on the nextgeneration superbeam experiment, DUNE. We present a detailed discussion on the mass hierarchy sensitivity and the CPviolation discovery study considering the impact of both diagonal as well as offdiagonal NSIs.

Resonant properties of finite cracks and their acoustic emission spectra ; In this paper, the acoustic emission accompanying the formation of brittle cracks of finite length is investigated theoretically using the approach based on the application of Huygens' principle for elastic solids. In the framework of this approach, the main input information required for calculations of acoustic emission spectra is the normal displacements of the crack edges as a function of frequency and wavenumber. Two simple approximate models defining this function are used in this paper for calculations of the acoustic emission spectra and directivity functions of a crack of finite length. The simplest model considers a crack that opens monotonously to its static value. The more refined model accounts for oscillations during crack opening and considers a crack of finite size as a resonator for symmetric modes of Rayleigh waves propagating along the crack edges and partly reflecting from the crack tips. Analytical solutions for generated acoustic emission spectra are obtained for both models and compared with each other. It is shown that resonant properties of a crack are responsible for the appearance of noticeable peaks in the frequency spectra of generated acoustic emission signals that can be used for evaluation of crack sizes. The obtained analytical results are illustrated by numerical calculations.

Primordial Black Holes from Higgs Vacuum Instability Avoiding Finetuning through an Ultraviolet Safe Mechanism ; We have recently proposed the idea that dark matter in our universe is formed by primordial black holes generated by Standard Model Higgs fluctuations during inflation and thanks to the fact that the Standard Model Higgs potential develops an instability at a scale of the order of 1011 GeV. In this sense, dark matter does not need any physics beyond the Standard Model, although the mechanism needs finetuning to avoid the overshooting of the Higgs into the dangerous AdS vacuum. We show how such finetuning can be naturally avoided by coupling the Higgs to a very heavy scalar with mass gg 1011 GeV that stabilises the potential in the deep ultraviolet, but preserving the basic feature of the mechanism which is built within the Standard Model.

Conditional heteroskedasticity in cryptoasset returns ; This paper examines the time series properties of cryptocurrency assets, such as Bitcoin, using established econometric inference techniques, namely models of the GARCH family. The contribution of this study is twofold. I explore the time series properties of cryptocurrencies, a new type of financial asset on which there appears to be little or no literature. I suggest an improved econometric specification to that which has been recently proposed in Chu et al 2017, the first econometric study to examine the price dynamics of the most popular cryptocurrencies. Questions regarding the reliability of their study stem from the authors misdiagnosing the distribution of GARCH innovations. Checks are performed on whether innovations are Gaussian or GED by using Kolmogorov type nonparametric tests and Khmaladze's martingale transformation. Null of gaussianity is strongly rejected for all GARCHp,q models, with p,q in 1,ldots,5 , for all cryptocurrencies in sample. For tests of normality, I make use of the GaussKronrod quadrature. Parameters of GARCH models are estimated with generalized error distribution innovations using maximum likelihood. For calculating Pvalues, the parametric bootstrap method is used. Arguing against Chu et al 2017, I show that there is a strong empirical argument against modelling innovations under some common assumptions.

COBAIN generalized 3D radiative transfer code for contact binary atmospheres ; Contact binary stars have been known to have a peculiar and somewhat mysterious hydro and thermodynamical structure since their discovery, which directly affects the radiation distribution in their atmospheres. Over the past several decades, however, observational data of contact binaries have been modeled through a simplified approach, involving the artificial concatenation of the two components of the contact envelope and populating their respective surfaces with either blackbody atmospheres or planeparallel model atmospheres of single stars. We show the implications this approach has on the reliability of the system parameter values and propose a method to overcome these issues with a new generalized radiative transfer code, COBAIN COntact Binary Atmospheres with INterpolation. The basic principles of COBAIN are outlined and their application to different geometries and polytropic stellar structures is discussed. We present initial tests on single nonrotating, uniformly rotating and differentially rotating stars, as well as on simplified polytropic structural models of contact binaries. We briefly discuss the final goal of this ambitious project, which is the computation of model atmosphere tables under the correct assumptions for contact binary stars, to be used in modern binary star analysis codes.

A connection between linearized GaussBonnet gravity and classical electrodynamics ; A connection between linearized GaussBonnet gravity and classical electrodynamics is found by developing a procedure which can be used to derive completely gauge invariant models. The procedure involves building the most general Lagrangian for a particular order of derivatives N and rank of tensor potential M, then solving such that the model is completely gauge invariant the Lagrangian density, equation of motion and energymomentum tensor are all gauge invariant. In the case of N 1 order of derivatives and M 1 rank of tensor potential, electrodynamics is uniquely derived from the procedure. In the case of N 2 order of derivatives and M 2 rank of symmetric tensor potential, linearized GaussBonnet gravity is uniquely derived from the procedure. The natural outcome of the models for classical electrodynamics and linearized GaussBonnet gravity from a common set of rules provides an interesting connection between two well explored physical models.

Global Aerodynamic Design Optimization via PrimalDual Aggregation Method ; Global aerodynamic design optimization using Euler or NavierStokes equations requires very reliable surrogate modeling techniques since the computational effort for the underlying flow simulations is usually high. In general, for such problems, the number of samples that can be generated to train the surrogate models is very limited due to restricted computational resources. On the other hand, recent developments in adjoint methods enable nowadays evaluation of gradient information at a reasonable computational cost for a wide variety of engineering problems. Therefore, a much richer data set can be collected using an adjoint solver in a Design of Experiment framework. In the present work, we present a novel aggregation method, which enables the state of the art surrogate models to incorporate extra gradient information without causing overfitting problems. Therefore, accurate surrogate models with relatively large number of design parameters can be trained from a small set of samples. We also present results two well known benchmark design optimization problems showing efficiency and robustness of the new method.

Deep Structured Prediction with Nonlinear Output Transformations ; Deep structured models are widely used for tasks like semantic segmentation, where explicit correlations between variables provide important prior information which generally helps to reduce the data needs of deep nets. However, current deep structured models are restricted by oftentimes very local neighborhood structure, which cannot be increased for computational complexity reasons, and by the fact that the output configuration, or a representation thereof, cannot be transformed further. Very recent approaches which address those issues include graphical model inference inside deep nets so as to permit subsequent nonlinear output space transformations. However, optimization of those formulations is challenging and not well understood. Here, we develop a novel model which generalizes existing approaches, such as structured prediction energy networks, and discuss a formulation which maintains applicability of existing inference techniques.

Light vectors coupled to bosonic currents ; New spin1 particles with masses below the weak scale are present in many theories of beyond Standard Model SM physics. In this work, we extend previous analyses by systematically considering the couplings of such a vector to the bosonic sector of the SM, focusing on models that lead to massmixing with the Z boson. These couplings generically lead to enhanced emission of the vector's longitudinal mode, both in Higgs decays and in flavor changing meson decays. We present bounds in the SMX effective theory and investigate their modeldependence. For the case of Higgs decays, we point out that treelevel vector emission is, depending on the model, not always enhanced, affecting the constraints. For meson decays, which are the dominant constraints at small vector masses, we find that while B decay constraints can be weakened by finetuning UV parameters, it is generically difficult to suppress the stringent constraints from kaon decays.

Learning to Rank Query Graphs for Complex Question Answering over Knowledge Graphs ; In this paper, we conduct an empirical investigation of neural query graph ranking approaches for the task of complex question answering over knowledge graphs. We experiment with six different ranking models and propose a novel selfattention based slot matching model which exploits the inherent structure of query graphs, our logical form of choice. Our proposed model generally outperforms the other models on two QA datasets over the DBpedia knowledge graph, evaluated in different settings. In addition, we show that transfer learning from the larger of those QA datasets to the smaller dataset yields substantial improvements, effectively offsetting the general lack of training data.

MultiView Networks For MultiChannel Audio Classification ; In this paper we introduce the idea of multiview networks for sound classification with multiple sensors. We show how one can build a multichannel sound recognition model trained on a fixed number of channels, and deploy it to scenarios with arbitrary and potentially dynamically changing number of input channels and not observe degradation in performance. We demonstrate that at inference time you can safely provide this model all available channels as it can ignore noisy information and leverage new information better than standard baseline approaches. The model is evaluated in both an anechoic environment and in rooms generated by a room acoustics simulator. We demonstrate that this model can generalize to unseen numbers of channels as well as unseen room geometries.

Improving ZeroShot Translation of LowResource Languages ; Recent work on multilingual neural machine translation reported competitive performance with respect to bilingual models and surprisingly good performance even on zeroshot translation directions not observed at training time. We investigate here a zeroshot translation in a particularly lowresource multilingual setting. We propose a simple iterative training procedure that leverages a duality of translations directly generated by the system for the zeroshot directions. The translations produced by the system suboptimal since they contain mixed language from the shared vocabulary, are then used together with the original parallel data to feed and iteratively retrain the multilingual network. Over time, this allows the system to learn from its own generated and increasingly better output. Our approach shows to be effective in improving the two zeroshot directions of our multilingual model. In particular, we observed gains of about 9 BLEU points over a baseline multilingual model and up to 2.08 BLEU over a pivoting mechanism using two bilingual models. Further analysis shows that there is also a slight improvement in the nonzeroshot language directions.

Time will tell Recovering Preferences when Choices are Noisy ; The ability to uncover preferences from choices is fundamental for both positive economics and welfare analysis. Overwhelming evidence shows that choice is stochastic, which has given rise to random utility models as the dominant paradigm in applied microeconomics. However, as is well known, it is not possible to infer the structure of preferences in the absence of assumptions on the structure of noise. This makes it impossible to empirically test the structure of noise independently from the structure of preferences. Here, we show that the difficulty can be bypassed if data sets are enlarged to include response times. A simple condition on response time distributions a weaker version of first order stochastic dominance ensures that choices reveal preferences without assumptions on the structure of utility noise. Sharper results are obtained if the analysis is restricted to specific classes of models. Under symmetric noise, response times allow to uncover preferences for choice pairs outside the data set, and if noise is Fechnerian, even choice probabilities can be forecast out of sample. We conclude by showing that standard random utility models from economics and standard driftdiffusion models from psychology necessarily generate data sets fulfilling our sufficient condition on response time distributions.

Neutrino predictions from a leftright symmetric flavored extension of the standard model ; We propose a leftright symmetric electroweak extension of the Standard Model based on the Delta left 27right family symmetry. The masses of all electrically charged Standard Model fermions lighter than the top quark are induced by a Universal Seesaw mechanism mediated by exotic fermions. The top quark is the only Standard Model fermion to get mass directly from a tree level renormalizable Yukawa interaction, while neutrinos are unique in that they get calculable radiative masses through a lowscale seesaw mechanism. The scheme has generalized mutau symmetry and leads to a restricted range of neutrino oscillations parameters, with a nonzero neutrinoless double beta decay amplitude lying at the upper ranges generically associated to normal and inverted neutrino mass ordering.

The arbitrariness of potentials in interacting quintessence models ; We study the interacting quintessence model with two different types of interaction by introducing a general parameterization of the quintessence potentials. The form of the quintessence potentials is arbitrary as the recent cosmological observations failed to constrain any particular form of the potentials. We explore the interacting quintessence models and investigate if an introduction of interaction between the dark sectors can constrain any particular form of the potential. Our findings reconfirm the arbitrariness of the quintessence potentials even for the interacting dark energy models. As a result, it is shown that the current observations are able to put an upper bound to the interaction parameter for both of the interactions we consider, although it is not possible to constrain the form of the potentials.

Learning Dense Stereo Matching for Digital Surface Models from Satellite Imagery ; Digital Surface Model generation from satellite imagery is a difficult task that has been largely overlooked by the deep learning community. Stereo reconstruction techniques developed for terrestrial systems including self driving cars do not translate well to satellite imagery where image pairs vary considerably. In this work we present neural network tailored for Digital Surface Model generation, a ground truthing and training scheme which maximizes available hardware, and we present a comparison to existing methods. The resulting models are smooth, preserve boundaries, and enable further processing. This represents one of the first attempts at leveraging deep learning in this domain.

The lowenergy TQFT of the generalized double semion model ; The generalized double semion GDS model, introduced by Freedman and Hastings, is a lattice system similar to the toric code, with a gapped Hamiltonian whose definition depends on a triangulation of the ambient manifold M, but whose space of ground states does not depend on the triangulation, but only on the underlying manifold. In this paper, we use topological quantum field theory TQFT to investigate the lowenergy limit of the GDS model. We define and study a functorial TQFT ZmathrmGDS in every dimension n such that for every closed n 1manifold M, ZmathrmGDSM is isomorphic to the space of ground states of the GDS model on M; the isomorphism can be chosen to intertwine the actions of the mapping class group of M that arise on both sides. Throughout this paper, we compare our constructions and results with their known analogues for the toric code.

Systematical study of pulsar light curves with special relativistic effects ; We systematically study pulsar light curves, taking into account the special relativistic effect, i.e., the Doppler factor due to the fast spin of the neutron stars, together with the time delay, which comes from the difference of the travel times depending on the position of the spots. For this purpose, first we derive the basic equations with the general expression of the metric for the static, spherically symmetric spacetime, where for simplicity we adopt the pointlike spot approximation for the antipodal spots associated with the magnetic polar cap model. Then, we calculate the light curves from the neutron star models in general relativity, with various angle between rotational and magnetic axes and the inclination angle. As the results, unlike the case for a slowly rotating stellar model, we find that the light curve from a fast rotating stellar model depends not only the stellar compactness but also the stellar radius. We also find that the amplitude of the light curve becomes larger as the stellar radius increases and as the stellar compactness decreases. Thus, via careful observations of the light curves from the rotating neutron star, one would determine the stellar compactness together with the stellar radius, if it rotates fast enough.

Interaction between active particles and quantum vortices leading to Kelvin wave generation ; One of the main features of superfluids is the presence of topological defects with quantised circulation. These objects are known as quantum vortices and exhibit a hydrodynamic behaviour. Nowadays, particles are the main experimental tool used to visualise quantum vortices and to study their dynamics. We use a selfconsistent model based on the threedimensional GrossPitaevskii GP equation to explore theoretically and numerically the attractive interaction between particles and quantised vortices at very low temperature. Particles are described as localised potentials depleting the superfluid and following Newtonian dynamics. We are able to derive analytically a reduced centralforce model that only depends on the classical degrees of freedom of the particle. Such model is found to be consistent with the GP simulations. We then generalised the model to include deformations of the vortex filament. The resulting longrange mutual interaction qualitatively reproduces the observed generation of a cusp on the vortex filament during the particle approach. Moreover, we show that particles can excite Kelvin waves on the vortex filament through a resonance mechanism even if they are still far from it.

GWarm inflation Intermediate model ; A warmintermediate inflationary universe model is studied in the presence of the Galileon coupling Gphi,XgphiX. General conditions required for successful inflation are deduced and discussed from the background and cosmological perturbations under slowroll approximation. In our analyze we assume that the dynamics of our model evolves accordingly two separate regimes, namely 3gdotphiHgg 1R, i.e., when the Galileon term dominates over the standard kinetic term and the dissipative ratio, and secondly in the regime where both 3gdotphiH and R become of the same order than unity. For these regimes and assuming that the coupling parameter gg0 constant, we consider two different dissipative coefficients Gamma; one constant and the other being a function of the inflaton field. Furthermore, we find the allowed range in the space of parameters for our Gwarm model by considering the latest data of Planck and also the BICEP2KeckArray data from the rrns plane, in combination with the conditions in which the Galileon term dominates and the thermal fluctuations of the inflaton field predominate over the quantum ones.

A domain agnostic measure for monitoring and evaluating GANs ; Generative Adversarial Networks GANs have shown remarkable results in modeling complex distributions, but their evaluation remains an unsettled issue. Evaluations are essential for i relative assessment of different models and ii monitoring the progress of a single model throughout training. The latter cannot be determined by simply inspecting the generator and discriminator loss curves as they behave nonintuitively. We leverage the notion of duality gap from game theory to propose a measure that addresses both i and ii at a low computational cost. Extensive experiments show the effectiveness of this measure to rank different GAN models and capture the typical GAN failure scenarios, including mode collapse and nonconvergent behaviours. This evaluation metric also provides meaningful monitoring on the progression of the loss during training. It highly correlates with FID on natural image datasets, and with domain specific scores for text, sound and cosmology data where FID is not directly suitable. In particular, our proposed metric requires no labels or a pretrained classifier, making it domain agnostic.

Interpolative Fusions I ; We define the interpolative fusion Tcup of a family Tii in I of firstorder theories over a common reduct Tcap, a notion that generalizes many examples of random or generic structures in the modeltheoretic literature. When each Ti is modelcomplete, Tcup coincides with the model companion of Tcup bigcupi in I Ti. By obtaining sufficient conditions for the existence of Tcup, we develop new tools to show that theories of interest have model companions.

Switchbased Active Deep DynaQ Efficient Adaptive Planning for TaskCompletion Dialogue Policy Learning ; Training taskcompletion dialogue agents with reinforcement learning usually requires a large number of real user experiences. The DynaQ algorithm extends Qlearning by integrating a world model, and thus can effectively boost training efficiency using simulated experiences generated by the world model. The effectiveness of DynaQ, however, depends on the quality of the world model or implicitly, the prespecified ratio of real vs. simulated experiences used for Qlearning. To this end, we extend the recently proposed Deep DynaQ DDQ framework by integrating a switcher that automatically determines whether to use a real or simulated experience for Qlearning. Furthermore, we explore the use of active learning for improving sample efficiency, by encouraging the world model to generate simulated experiences in the stateaction space where the agent has not fully explored. Our results show that by combining switcher and active learning, the new framework named as Switchbased Active Deep DynaQ SwitchDDQ, leads to significant improvement over DDQ and Qlearning baselines in both simulation and human evaluations.

Adjustable Realtime Style Transfer ; Artistic style transfer is the problem of synthesizing an image with content similar to a given image and style similar to another. Although recent feedforward neural networks can generate stylized images in realtime, these models produce a single stylization given a pair of stylecontent images, and the user doesn't have control over the synthesized output. Moreover, the style transfer depends on the hyperparameters of the model with varying optimum for different input images. Therefore, if the stylized output is not appealing to the user, shehe has to try multiple models or retrain one with different hyperparameters to get a favorite stylization. In this paper, we address these issues by proposing a novel method which allows adjustment of crucial hyperparameters, after the training and in realtime, through a set of manually adjustable parameters. These parameters enable the user to modify the synthesized outputs from the same pair of stylecontent images, in search of a favorite stylized image. Our quantitative and qualitative experiments indicate how adjusting these parameters is comparable to retraining the model with different hyperparameters. We also demonstrate how these parameters can be randomized to generate results which are diverse but still very similar in style and content.

Enhanced correlations and superconductivity in weakly interacting partially flat band systems a determinantal quantum Monte Carlo study ; Motivated by recent experiments realizing correlated phenomena and superconductivity in 2D van der Waals devices, we consider the general problem of whether correlation effects may be enhanced by modifying band structure while keeping a fixed weak interaction strength. Using determinantal quantum Monte Carlo, we study the 2D Hubbard model for two different band structures a regular nearestneighbor tightbinding model, and a partially flat band structure containing a nondispersing region, with identical total noninteracting bandwidth W. For both repulsive and attractive weak interactions U ll W, correlated phenomena are significantly stronger in the partially flat model. In the repulsive case, even with U an order of magnitude smaller than W, we find the presence of a Mott insulating state near halffilling of the flat region in momentum space. In the attractive case, where generically the ground state is superconducting, the partially flat model exhibits significantly enhanced superconducting transition temperatures. These results suggest the possibility of engineering correlation effects in materials by tuning the noninteracting electronic dispersion.

Towards models with a unified dynamical mechanism for elementary particle masses ; Numerical evidence for a new dynamical mechanism of elementary particle mass generation has been found by lattice simulation in a simple, yet highly nontrivial SU3 gauge model where a SU2 doublet of strongly interacting fermions is coupled to a complex scalar field doublet via a Yukawa and a Wilsonlike term. We point out that if, as a next step towards the construction of a realistic beyondtheStandardModel model, weak interactions are introduced, then also weak bosons get a mass by the very same nonperturbative mechanism. In this scenario fermion mass hierarchy can be naturally understood owing to the peculiar gauge coupling dependence of the nonperturbatively generated masses. Hence, if the phenomenological value of the mass of the top quark or the weak bosons has to be reproduced, the RGI scale of the theory must be much larger than LambdaQCD. This feature hints at the existence of new strong interactions and particles at a scale LambdaT of a few TeV. In such a speculative framework the electroweak scale can be derived from the basic scale LambdaT and the Higgs boson should arise as a bound state in the WWZZ channel.

Bilateral Adversarial Training Towards Fast Training of More Robust Models Against Adversarial Attacks ; In this paper, we study fast training of adversarially robust models. From the analyses of the stateoftheart defense method, i.e., the multistep adversarial training, we hypothesize that the gradient magnitude links to the model robustness. Motivated by this, we propose to perturb both the image and the label during training, which we call Bilateral Adversarial Training BAT. To generate the adversarial label, we derive an closedform heuristic solution. To generate the adversarial image, we use onestep targeted attack with the target label being the most confusing class. In the experiment, we first show that random start and the most confusing target attack effectively prevent the label leaking and gradient masking problem. Then coupled with the adversarial label part, our model significantly improves the stateoftheart results. For example, against PGD100 whitebox attack with crossentropy loss, on CIFAR10, we achieve 63.7 versus 47.2; on SVHN, we achieve 59.1 versus 42.1. At last, the experiment on the very computationally challenging ImageNet dataset further demonstrates the effectiveness of our fast method.

Understanding the uninterpretability of natural image distributions using generative models ; Probability density estimation is a classical and well studied problem, but standard density estimation methods have historically lacked the power to model complex and highdimensional image distributions. More recent generative models leverage the power of neural networks to implicitly learn and represent probability models over complex images. We describe methods to extract explicit probability density estimates from GANs, and explore the properties of these image density functions. We perform sanity check experiments to provide evidence that these probabilities are reasonable. However, we also show that density functions of natural images are difficult to interpret and thus limited in use. We study reasons for this lack of interpretability, and show that we can get interpretability back by doing density estimation on latent representations of images.

Memory Augmented Deep Generative models for Forecasting the Next Shot Location in Tennis ; This paper presents a novel framework for predicting shot location and type in tennis. Inspired by recent neuroscience discoveries we incorporate neural memory modules to model the episodic and semantic memory components of a tennis player. We propose a Semi Supervised Generative Adversarial Network architecture that couples these memory models with the automatic feature learning power of deep neural networks and demonstrate methodologies for learning player level behavioural patterns with the proposed framework. We evaluate the effectiveness of the proposed model on tennis tracking data from the 2012 Australian Tennis open and exhibit applications of the proposed method in discovering how players adapt their style depending on the match context.

Option Pricing in Illiquid Markets with Jumps ; The classical linear BlackScholes model for pricing derivative securities is a popular model in financial industry. It relies on several restrictive assumptions such as completeness, and frictionless of the market as well as the assumption on the underlying asset price dynamics following a geometric Brownian motion. The main purpose of this paper is to generalize the classical BlackScholes model for pricing derivative securities by taking into account feedback effects due to an influence of a large trader on the underlying asset price dynamics exhibiting random jumps. The assumption that an investor can trade large amounts of assets without affecting the underlying asset price itself is usually not satisfied, especially in illiquid markets. We generalize the FreyStremme nonlinear option pricing model for the case the underlying asset follows a Levy stochastic process with jumps. We derive and analyze a fully nonlinear parabolic partialintegro differential equation for the price of the option contract. We propose a semiimplicit numerical discretization scheme and perform various numerical experiments showing influence of a large trader and intensity of jumps on the option price.

Matter Power Spectra in Viable fR Gravity Models with Dynamical Background ; We study the matter power spectra in the viable fR gravity models with the dynamical background evolution and linear perturbation theory by using the CosmoMC package. We show that these viable fR models generally shorten the age of the universe and suppress the matter density fluctuation. We examine the allowed ranges of the model parameters and the constraints of the cosmological variables from the current observational data, and find that the dynamical evolution of rhoDEz plays an important role to constrain the neutrino masses.

Power Allocation in MultiUser Cellular Networks Deep Reinforcement Learning Approaches ; The modelbased power allocation algorithm has been investigated for decades, but it requires the mathematical models to be analytically tractable and it usually has high computational complexity. Recently, the datadriven modelfree machine learning enabled approaches are being rapidly developed to obtain nearoptimal performance with affordable computational complexity, and deep reinforcement learning DRL is regarded as of great potential for future intelligent networks. In this paper, the DRL approaches are considered for power control in multiuser wireless communication cellular networks. Considering the crosscell cooperation, the offlineonline centralized training and the distributed execution, we present a mathematical analysis for the DRLbased toplevel design. The concrete DRL design is further developed based on this foundation, and policybased REINFORCE, valuebased deep Q learning DQL, actorcritic deep deterministic policy gradient DDPG algorithms are proposed. Simulation results show that the proposed datadriven approaches outperform the stateofart modelbased methods on sumrate performance, with good generalization power and faster processing speed. Furthermore, the proposed DDPG outperforms the REINFORCE and DQL in terms of both sumrate performance and robustness, and can be incorporated into existing resource allocation schemes due to its generality.

The autofeat Python Library for Automated Feature Engineering and Selection ; This paper describes the autofeat Python library, which provides scikitlearn style linear regression and classification models with automated feature engineering and selection capabilities. Complex nonlinear machine learning models, such as neural networks, are in practice often difficult to train and even harder to explain to nonstatisticians, who require transparent analysis results as a basis for important business decisions. While linear models are efficient and intuitive, they generally provide lower prediction accuracies. Our library provides a multistep feature engineering and selection process, where first a large pool of nonlinear features is generated, from which then a small and robust set of meaningful features is selected, which improve the prediction accuracy of a linear model while retaining its interpretability.

SemiSupervised ImagetoImage Translation ; Imagetoimage translation is a longestablished and a difficult problem in computer vision. In this paper we propose an adversarial based model for imagetoimage translation. The regular deep neuralnetwork based methods perform the task of imagetoimage translation by comparing gram matrices and using image segmentation which requires human intervention. Our generative adversarial network based model works on a conditional probability approach. This approach makes the image translation independent of any local, global and content or style features. In our approach we use a bidirectional reconstruction model appended with the affine transform factor that helps in conserving the content and photorealism as compared to other models. The advantage of using such an approach is that the imagetoimage translation is semisupervised, independant of image segmentation and inherits the properties of generative adversarial networks tending to produce realistic. This method has proven to produce better results than Multimodal Unsupervised Imagetoimage translation.

Incorporating energy storage and user experience in isolated microgrid dispatch using a multiobjective model ; In order to coordinate multiple different scheduling objectives from the perspectives of economy, environment and users, a practical multiobjective dynamic optimal dispatch model incorporating energy storage and user experience is proposed for isolated microgrids. In this model, besides Microturbine units, energy storage is employed to provide spinning reserve services for microgirds; and furthermore, from the perspective of demand side management, a consumer satisfaction indicator is developed to measure the quality of user experience. A twostep solution methodology incorporating multiobjective optimization MOO and decision analysis is put forward to address this model. First, a powerful heuristic optimization algorithm, called the thetadominance based evolutionary algorithm, is used to find a welldistributed set of Paretooptimal solutions of the problem. And thereby, the best compromise solutions BCSs are identified from the entire solutions with the use of decision analysis by integrating fuzzy Cmeans clustering and grey relation projection. The simulation results on the modified Oak Ridge National Laboratory Distributed Energy Control and Communication lab microgrid test system demonstrate the effectiveness of the proposed approach.

Phenomenology of an extended IDM with loopgenerated fermion mass hierarchies ; We perform a comprehensive analysis of the most distinctive and important phenomenological implications of the recently proposed mechanism of sequential loop generation of strong hierarchies in the Standard Model SM fermion mass spectra. This mechanism is consistently realized at the level of renormalizable interactions in an extended variant of the Inert Higgs Doublet model, possessing the additional Z21times Z22 discrete and U1X gauge family symmetries, while the matter sectors of the SM are extended by means of SU2Lsinglet scalars, heavy vectorlike leptons and quarks, as well as righthanded neutrinos. We thoroughly analyze the most stringent constraints on the model parameter space, coming from the Zprime collider searches, related to the anomaly in lepton universality, and the muon anomalous magnetic moment, as well as provide benchmark points for further tests of the model and discuss possible standard candle signatures relevant for future explorations.

NAOMI NonAutoregressive Multiresolution Sequence Imputation ; Missing value imputation is a fundamental problem in spatiotemporal modeling, from motion tracking to the dynamics of physical systems. Deep autoregressive models suffer from error propagation which becomes catastrophic for imputing longrange sequences. In this paper, we take a nonautoregressive approach and propose a novel deep generative model NonAutOregressive Multiresolution Imputation NAOMI to impute longrange sequences given arbitrary missing patterns. NAOMI exploits the multiresolution structure of spatiotemporal data and decodes recursively from coarse to finegrained resolutions using a divideandconquer strategy. We further enhance our model with adversarial training. When evaluated extensively on benchmark datasets from systems of both deterministic and stochastic dynamics. NAOMI demonstrates significant improvement in imputation accuracy reducing average prediction error by 60 compared to autoregressive counterparts and generalization for long range sequences.

Exploring the context of recurrent neural network based conversational agents ; Conversational agents have begun to rise both in the academic in terms of research and commercial in terms of applications world. This paper investigates the task of building a nongoal driven conversational agent, using neural network generative models and analyzes how the conversation context is handled. It compares a simpler EncoderDecoder with a Hierarchical Recurrent EncoderDecoder architecture, which includes an additional module to model the context of the conversation using previous utterances information. We found that the hierarchical model was able to extract relevant context information and include them in the generation of the output. However, it performed worse 3540 than the simple EncoderDecoder model regarding both grammatically correct output and meaningful response. Despite these results, experiments demonstrate how conversations about similar topics appear close to each other in the context space due to the increased frequency of specific topicrelated words, thus leaving promising directions for future research and how the context of a conversation can be exploited.

Model Independent Explorations of Majorana Neutrino Mass Origins ; The scale of neutrino mass generation may be too large to explore directly, but useful information may still be extracted from independent experimental channels. Here I survey various model independent probes of Majorana neutrino mass origins. An introduction to the concepts relevant to the analysis is followed by a discussion of the physical ranges of neutrino parameters within the context of standard and nonstandard interactions. Armed with this, I move on to systematically analyze the properties of radiatively generated neutrino masses induced by nonrenormalizable lepton number violating effective operators of mass dimensions five through eleven. By fitting these to the observed light mass scale, I extract predictions for neutrino mixing as well as neutrinoless double beta decay, rare mesontau decays and collider phenomenology. I find that many such models are already constrained by current data and many more will be probed in the near future. I then move on demonstrate the utility of a low scale seesaw mechanism via a viable sterile neutrino model that satisfies all oscillation data as well as solves problems associated with supernova kicks and heavy element nucleosynthesis. From this I extract predictions for tritium and neutrinoless double beta decay searches.

Frustration and entanglement in the t2g spinorbital model on a triangular lattice valencebond and generalized liquid states ; We consider the spinorbital model for a magnetic system with singly occupied but triply degenerate t2g orbitals coupled into a planar, triangular lattice, as would be exemplified by NaTiO2. We investigate the ground states of the model for interactions which interpolate between the limits of pure superexchange and purely direct exchange interactions. By considering ordered and dimerized states at the meanfield level, and by interpreting the results from exact diagonalization calculations on selected finite systems, we demonstrate that orbital interactions are always frustrated, and that orbital correlations are dictated by the spin state, manifesting an intrinsic entanglement of these degrees of freedom. In the absence of Hund coupling, the ground state changes from a highly resonating, dimerbased, symmetryrestored spin and orbital liquid phase, to one based on completely static, spinsinglet valence bonds. The generic properties of frustration and entanglement survive even when spins and orbitals are nominally decoupled in the ferromagnetic phases stabilized by a strong Hund coupling. By considering the same model on other lattices, we discuss the extent to which frustration is attributable separately to geometry and to interaction effects.

Dynamic Model and Phase Transitions for Liquid Helium ; This article presents a phenomenological dynamic phase transition theory modeling and analysis for superfluids. As we know, although the timedependent GinzburgLandau model has been successfully used in superconductivity, and the classical GinzburgLandau free energy is still poorly applicable to liquid helium in a quantitative sense. The study in this article is based on 1 a new dynamic classification scheme of phase transitions, 2 new timedependent GinzburgLandau models for general equilibrium transitions, and 3 the general dynamic transition theory. The results in this article predict the existence of a unstable region H, where both solid and liquid He II states appear randomly depending on fluctuations and the existence of a switch point M on the lambdacurve, where the transitions changes types.

Vector Field Models of Inflation and Dark Energy ; We consider several new classes of viable vector field alternatives to the inflaton and quintessence scalar fields. Spatial vector fields are shown to be compatible with the cosmological anisotropy bounds if only slightly displaced from the potential minimum while dominant, or if driving an anisotropic expansion with nearly vanishing quadropole today. The Bianchi I model with a spatial field and an isotropic fluid is studied as a dynamical system, and several types of scaling solutions are found. On the other hand, timelike fields are automatically compatible with largescale isotropy. We show that they can be dynamically important if nonminimal gravity couplings are taken into account. As an example, we reconstruct a vectorGaussBonnet model which generates the concordance model acceleration at late times and supports an inflationary epoch at high curvatures. The evolution of vortical perturbations is considered.

Modelling and optimization of photon pair sources based on spontaneous parametric downconversion ; We address the problem of efficient modelling of photon pairs generated in spontaneous parametric downconversion and coupled into singlemode fibers. It is shown that when the range of relevant transverse wave vectors is restricted by the pump and fiber modes, the computational complexity can be reduced substantially with the help of the paraxial approximation, while retaining the full spectral characteristics of the source. This approach can serve as a basis for efficient numerical calculations, or can be combined with analytically tractable approximations of the phase matching function. We introduce here a cosinegaussian approximation of the phase matching function which works for a broader range of parameters than the gaussian model used previously. The developed modelling tools are used to evaluate characteristics of the photon pair sources such as the pair production rate and the spectral purity quantifying frequency correlations. Strategies to generate spectrally uncorrelated photons, necessary in multiphoton interference experiments, are analyzed with respect to tradeoffs between parameters of the source.

Loop Corrections to Cosmological Perturbations in Multifield Inflationary Models ; We investigate oneloop quantum corrections to the power spectrum of adiabatic perturbation from entropy modesadiabatic mode crossinteractions in multiple DBI inflationary models. We find that due to the noncanonical kinetic term in DBI models, the loop corrections are enhanced by slowvarying parameter epsilon and small sound speed cs. Thus, in general the loopcorrections in multiDBI models can be large. Moreover, we find that the loopcorrections from adiabaticentropy crossinteraction vertices are IR finite.

Capture and Indirect Detection of Inelastic Dark Matter ; We compute the capture rate for Dark Matter in the Sun for models where the dominant interaction with nuclei is inelastic the Dark Matter upscatters to a nearby dark partner state with a small splitting of order a 100 keV. Such models have previously been shown to be compatible with DAMALIBRA data, as well as data from all other direct detection experiments. The kinematics of inelastic Dark Matter ensures that the dominant contribution to capture occurs from scattering off of iron. We give a prediction for neutrino rates for current and future neutrino telescopes based on the results from current direct detection experiments. Current bounds from SuperKamiokande and IceCube22 significantly constrain these models, assuming annihilations are into twobody Standard Model final states, such as WW, ttbar, bbbar or tautau. Annihilations into first and second generation quarks and leptons are generally allowed, as are annihilations into new force carriers which decay dominantly into ee, mumu and pipi.

A mathematical model for Tsunami generation using a conservative velocitypressure hyperbolic system ; By using the Hugoniot curve in detonics as a Riemann invariant of a velocitypressure model, we get a conservative hyperbolic system similar to the Euler equations. The only differences are the larger value of the adiabatic constant 8.678 instead of 1.4 for gas dynamics and the mass density replaced by a strain density depending on the pressure. The model is not homogeneous since it involves a gravity and a friction term. After the seismic wave reaches up the bottom of the ocean, one gets a pressure wave propagating toward the surface, which is made of a frontal shock wave followed by a regular decreasing profile. Since this regular profile propagates faster than the frontal shock waves, the amplitude of the pressure wave is strongly reduced when reaching the surface. Only in the case of a strong earth tremor the residual pressure wave is still sufficient to generate a water elevation with a sufficient wavelengths enable to propagate as a SaintVenant water wave and to become a tsunami when reaching the shore. We describe the construction of the model and the computation of the wave profile and discuss about the formation or not of a wave.

An ObjectOriented and Fast Lexicon for Semantic Generation ; This paper is about the technical design of a large computational lexicon, its storage, and its access from a Prolog environment. Traditionally, efficient access and storage of data structures is implemented by a relational database management system. In Delilah, a lexiconbased NLP system, efficient access to the lexicon by the semantic generator is vital. We show that our highly detailed HPSGstyle lexical specifications do not fit well in the Relational Model, and that they cannot be efficiently retrieved. We argue that they fit more naturally in the ObjectOriented Model. Although storage of objects is redundant, we claim that efficient access is still possible by applying indexing, and compression techniques from the Relational Model to the ObjectOriented Model. We demonstrate that it is possible to implement objectoriented storage and fast access in ISO Prolog.

The AwRascleZhang model with constraints ; The thesis deals with the AwRascleZhang model for traffic. We have applied the model to describe the influence of a large and slow vehicle a bus or a truck on the traffic. The trajectory of the bus is given by an ODE. The model can also be applied to the case of a fixed constraint, like a traffic light or a toll gate. We define two different Riemann solvers the first one conserves both the number of cars and the generalized momentum, while the second conserves only the number of cars. We characterize the invariant domains for these Riemann solvers. We study two numerical methods based on the Godunov method to capture the proposed solutions and we track the bus trajectory with a fronttracking technique. The first method is based on conservation and captures exactly the solution corresponding to the first Riemann solver. The second method is based on a nonuniform mesh. Both methods fail to capture the solutions corresponding to the second Riemann solver for general initial data. Finally, we prove the existence of solutions for the Cauchy problem for the second Riemann solver in the case of a fixed constraint, applying the wavefront tracking method.

A Generic Minimal Discrete Model for Toroidal Moments and Its Experimental Realization ; It is well known that a closed loop of magnetic dipoles can give rise to the rather elusive toroidal moment. However, artificial structures required to generate the necessary magnetic moments are typically optically large, complex to make and easily compromised by the kinetic inductance at high frequencies. Instead of using magnetic dipoles, we propose a minimal model based on just three aligned discrete electric dipoles in which the occurrence of resonant toroidal modes is guaranteed by symmetry. The advantage of this model is its simplicity and the same model supports toroidal moments from the microwave regime up to optical frequencies as exemplified by a threeantenna array and a system consisting of three nanosized plasmonic particles. Both the microwave and highfrequency configurations exhibit nonradiating anapoles. Experiments in the microwave regime confirm the theoretical predictions.

EcoStrategy Towards a New Generation Managerial Model Based on Green IT and CSR ; The sustainable development strategy in the management of information and communication technology ICT is an advanced research sector which provides a theoretical framework for integrating social and environmental responsibilities of business in the development and implementation of the management strategy. This article offers an original management model that integrates the Corporate Social Responsibility CSR approach and Green IT, which enables decision makers, governance and strategic alignment of ICT, business and sustainability. The model offers a new vision of decision making through economic opportunities and increasing pressure from stakeholders. This paper reveals the strategic relevance of the model, on the basis of a literature review, and provides guidelines for sustainable business development of effective management systems, and improvement of the economic, social and environmental performance of companies. The proposed framework provides a new generation managerial approach to ICT management strategy that we call EcoStrategy.

Interparticle potential energy for Ddimensional electromagnetic models from the corresponding scalar ones ; Using a method based on the generating functional plus a kind of correspondence principle which acts as a bridge between the electromagnetic and scalar fields it is shown that the interparticle potential energy concerning a given Ddimensional electromagnetic model can be obtained in a simple way from that related to the corresponding scalar system. The Ddimensional electromagnetic potential for a general model containing higher derivatives is then found from the corresponding scalar one and the behavior of the former is analyzed at large as well as small distances. In addition, we investigate the presence of ghosts in the fourdimensional version of the potential associated with the model above and analyze the reason why the Coulomb singularity is absent from this system. The nogo theorem by Ostrogradski is demystified as well.

Generalized Galileons instabilities of bouncing and Genesis cosmologies and modified Genesis ; We study spatially flat bouncing cosmologies and models with the earlytime Genesis epoch in a popular class of generalized Galileon theories. We ask whether there exist solutions of these types which are free of gradient and ghost instabilities. We find that irrespectively of the forms of the Lagrangian functions, the bouncing models either are plagued with these instabilities or have singularities. The same result holds for the original Genesis model and its variants in which the scale factor tends to a constant as tto infty. The result remains valid in theories with additional matter that obeys the Null Energy Condition and interacts with the Galileon only gravitationally. We propose a modified Genesis model which evades our nogo argument and give an explicit example of healthy cosmology that connects the modified Genesis epoch with kination the epoch still driven by the Galileon field, which is a conventional massless scalar field at that stage.

Vacuum self similar anisotropic cosmologies in FRgravity ; The implications from the existence of a proper Homothetic Vector Field HVF on the dynamics of vacuum anisotropic models in FR gravitational theory are studied. The fact that emphevery Spatially Homogeneous vacuum model is equivalent, formally, with a flux free anisotropic fluid model in standard gravity and the induced powerlaw form of the functional FR due to selfsimilarity enable us to close the system of equations. We found some new exact anisotropic solutions that arise as fixed points in the associated dynamical system. The nonexistence of Kasnerlike Bianchi type I solutions in proper FRgravity i.e. Rneq 0 strengthens the belief that curvature corrections will prevent the shear influence into the past thus permitting an isotropic singularity. We also discuss certain issues regarding the lack of vacuum models of type III, IV, VIIh in comparison with the corresponding results in standard gravity.

Smallsignal model for frequency analysis of thermoelectric systems ; We show how smallsignal analysis, a standard method in electrical engineering, may be applied to thermoelectric device performance measurement by extending a dc model to the dynamical regime. We thus provide a physical ground to textitadhoc models used to interpret impedance spectroscopy of thermoelectric elements from an electrical circuit equivalent for thermoelectric systems in the frequency domain. We particularly stress the importance of the finite thermal impedance of the thermal contacts between the thermoelectric system and the thermal reservoirs in the derivation of such models. The expression for the characteristic angular frequency of the thermoelectric system we obtain is a generalization of the expressions derived in previous studies. In particular, it allows to envisage impedance spectroscopy measurements beyond the restrictive case of adiabatic boundary conditions often difficult to achieve experimentally, and hence emphinsitu characterization of thermoelectric generators.

Naturally Small Dirac Neutrino Mass with Intermediate SU2L Multiplet Fields ; If neutrinos are Dirac fermions, certain new physics beyond the standard model should exist to account for the smallness of neutrino mass. With two additional scalars and a heavy intermediate fermion, in this paper, we systematically study the general mechanism that can natrally generate the tiny Dirac neutrino mass at tree and in oneloop level. For tree level models, we focus on natural ones, in which the additional scalars develop small vacuum expectation values without finetuning. For oneloop level models, we explore those having dark matter candidates under Z2D symmetry. In both cases, we concentrate on SU2L multiplet scalars no larger than quintuplet, and derive the complete sets of viable models. Phenomenologies, such as lepton flavor violation, leptogenesis, and LHC signatures are briefly discussed.

A parallel workload has extreme variability ; In both highperformance computing HPC environments and the public cloud, the duration of time to retrieve or save your results is simultaneously unpredictable and important to your over all resource budget. It is generally accepted Google Taming the Long Latency Tail When More Machines Equals Worse Results, Todd Hoff, highscalability.com 2012, but without a robust explanation, that identical parallel tasks do take different durations to complete a phenomena known as variability. This paper advances understanding of this topic. We carefully choose a model from which systemlevel complexity emerges that can be studied directly. We find that a generalized extreme value GEV model for variability naturally emerges. Using the public cloud, we find realworld observations have excellent agreement with our model. Since the GEV distribution is a limit distribution this suggests a universal property of parallel systems gated by the slowest communication element of some sort. Hence, this model is applicable to a variety of processing and IO tasks in parallel environments. These findings have important implications, ranging from characterizing ideal performance for parallel codes to detecting degraded behaviour at extreme scales.

SIR Asymptotics in General Network Models ; In the performance analyses of wireless networks, asymptotic quantities and properties often pro vide useful results and insights. The asymptotic analyses become especially important when complete analytical expressions of the performance metrics of interest are not available, which is often the case if one departs from very specific modeling assumptions. In this paper, we consider the asymptotics of the SIR distribution in general wireless network models, including ad hoc and cellular networks, simple and nonsimple point processes, and singular and bounded path loss models, for which, in most cases, finding analytical expressions of the complete SIR distribution seems hopeless. We show that the lower tails of the SIR distributions decay polynomially with the order solely determined by the path loss exponent or the fading parameter, while the upper tails decay exponentially, with the exception of cellular networks with singular path loss. In addition, we analyze the impact of the nearest interferer on the asymptotic properties of the SIR distributions, and we formulate three crisp conjectures that if true determine the asymptotic behavior in many cases based on the largescale path loss properties of the desired signal andor nearest interferer only.

Living on the Edge A Toy Model for Holographic Reconstruction of Algebras with Centers ; We generalize the PastawskiYoshidaHarlowPreskill HaPPY holographic quantum errorcorrecting code to provide a toy model for bulk gauge fields or linearized gravitons. The key new elements are the introduction of degrees of freedom on the links edges of the associated tensor network and their connection to further copies of the HaPPY code by an appropriate isometry. The result is a model in which boundary regions allow the reconstruction of bulk algebras with central elements living on the interior edges of the greedy entanglement wedge, and where these central elements can also be reconstructed from complementary boundary regions. In addition, the entropy of boundary regions receives both RyuTakayanagilike contributions and further corrections that model the fracdelta textArea4GN term of Faulkner, Lewkowycz, and Maldacena. Comparison with YangMills theory then suggests that this fracdelta textArea4GN term can be reinterpreted as a part of the bulk entropy of gravitons under an appropriate extension of the physical bulk Hilbert space.

Exact Model Reduction by a SlowFast Decomposition of Nonlinear Mechanical Systems ; We derive conditions under which a general nonlinear mechanical system can be exactly reduced to a lowerdimensional model that involves only the most flexible degrees of freedom. This SlowFast Decomposition SFD enslaves exponentially fast the stiff degrees of freedom to the flexible ones as all oscillations converge to the reduced model defined on a slow manifold. We obtain an expression for the domain boundary beyond which the reduced model ceases to be relevant due to a generic loss of stability of the slow manifold. We also find that near equilibria, the SFD gives a mathematical justification for two modalreduction methods used in structural dynamics static condensation and modal derivatives. These formal reduction procedures, however, are also found to return incorrect results when the SFD conditions do not hold. We illustrate all these results on mechanical examples.

Integrable model of nonlinear dislocations ; Using the continuous limit approximation in the dynamical system we study a nonlinear partial differential equation which corresponds to the generalization of both the FermiPastaUlam and the FrenkelKontorova models. This generalized model can be considered as a model for the description nonlinear dislocation waves in the crystal lattice. We obtain the nonlinear partial differential equation for the description of dislocations. Taking into account the wave moving in one direction we obtain another nonlinear evolution equation. Using the Painlev'e test we analyze the integrability of this equation. We find that there exist an integrable case of the partial differential equation for nonlinear dislocations. The Lax pair for the solution of the Cauchy problem is found. The solution of the Cauchy problem for nonlinear evolution equation is discussed. One and the twosoliton solutions for the nonlinear evolution equation are presented. The influence of parameters on the propagation of one and the twosoliton solutions is analyzed and demonstrated.

Universality in generalized models of inflation ; We discuss the cosmological evolution of a scalar field with non standard kinetic term in terms of a Renormalization Group Equation RGE. In this framework inflation corresponds to the slow evolution in a neighborhood of a fixed point and universality classes for inflationary models naturally arise. Using some examples we show the application of the formalism. The predicted values for the speed of sound cs and for the amount of nonGaussianities produced in these models are discussed. In particular, we show that it is possible to introduce models with cs2 neq 1 that can be in agreement with present cosmological observations.

NeighborhoodHistory Quantum Walk ; History dependent discrete time quantum walks QWs are often studied for their lattice traversal properties. A particular model in the literature uses the state of a memory qubit at each site to record visits and to control the dynamics of the walk. We generalize this model to the neighborhoodhistory quantum walk NHQW, in which the walk dynamics and the state of the memory qubits in a neighborhood of the particle's position are interdependent. To demonstrate it, we construct an NHQW on a onedimensional lattice, with a simple neighborhood. Several dynamically interesting history dependent QWs can be realized as singleparticle sectors of quantum lattice gas automata QLGA. In contrast, the NHQW constructed in this paper is realized as a singleparticle sector of the more general quantum cellular automaton QCA. The complexity of the NHQW dynamics presents a promising avenue toward richer walk strategies and a potentially useful model of QWs for the Noisy IntermediateScale Quantum NISQ era of quantum computing. It also modifies QWs to conceivably allow for modeling fundamental physics incorporating quantum field interactions with particles.

Learning Generic Sentence Representations Using Convolutional Neural Networks ; We propose a new encoderdecoder approach to learn distributed sentence representations that are applicable to multiple purposes. The model is learned by using a convolutional neural network as an encoder to map an input sentence into a continuous vector, and using a long shortterm memory recurrent neural network as a decoder. Several tasks are considered, including sentence reconstruction and future sentence prediction. Further, a hierarchical encoderdecoder model is proposed to encode a sentence to predict multiple future sentences. By training our models on a large collection of novels, we obtain a highly generic convolutional sentence encoder that performs well in practice. Experimental results on several benchmark datasets, and across a broad range of applications, demonstrate the superiority of the proposed model over competing methods.