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Geometrothermodynamic model for the evolution of the Universe ; Using the formalism of geometrothermodynamics to derive a fundamental thermodynamic equation, we construct a cosmological model in the framework of relativistic cosmology. In a first step, we describe a system without thermodynamic interaction, and show it to be equivalent to the standard LambdaCDM paradigm. The second step includes thermodynamic interaction and produces a model consistent with the main features of inflation. With the proposed fundamental equation we are thus able to describe all the known epochs in the evolution of our Universe, starting from the inflationary phase.

Topological Network Entanglement as Order Parameter for the Emergence of Geometry ; We show that, in discrete models of quantum gravity, emergent geometric space can be viewed as the entanglement pattern in a mixed quantum state of the universe, characterized by a universal topological network entanglement. As a concrete example we analyze the recently proposed model in which geometry emerges due to the condensation of 4cycles in random regular bipartite graphs, driven by the combinatorial OllivierRicci curvature. Using this model we show that the emergence of geometric order decreases the entanglement entropy of random configurations. The lowest geometric entanglement entropy is realized in four dimensions.

An Optimized Microeconomic Modeling System for Analyzing Industrial Externalities in NonOECD Countries ; In this paper, we provide an integrated systems modeling approach to analyzing global externalities from a microeconomic perspective. Various forms of policy fiscal, monetary, etc. have addressed flaws and market failures in models, but few have been able to successfully eliminate modern externalities that remain an environmental and human threat. We assess three primary global industries pollution, agriculture, and energy with respect to nonOECD entities through both qualitative and quantitative studies. By combining key mutual points of specific externalities present within each respective industry, we are able to propose an alternative and optimized solution to internalizing them via incentives and cooperative behavior rather than by traditional Pigouvian taxes and subsidies.

LinXGBoost Extension of XGBoost to Generalized Local Linear Models ; XGBoost is often presented as the algorithm that wins every ML competition. Surprisingly, this is true even though predictions are piecewise constant. This might be justified in high dimensional input spaces, but when the number of features is low, a piecewise linear model is likely to perform better. XGBoost was extended into LinXGBoost that stores at each leaf a linear model. This extension, equivalent to piecewise regularized leastsquares, is particularly attractive for regression of functions that exhibits jumps or discontinuities. Those functions are notoriously hard to regress. Our extension is compared to the vanilla XGBoost and Random Forest in experiments on both synthetic and realworld data sets.

DeBroglieBohm interpretation of a HoravaLifshitz quantum cosmology model ; In the present letter, we consider the DeBroglieBohm interpretation of a HovravaLifshitz quantum cosmology model in the presence of a radiation perfect fluid. We compute the Bohm's trajectories for the scale factor and show that it never goes to zero. That result gives a strong indication that this model is free from singularities, at the quantum level. We also compute the quantum potential. That quantity helps understanding why the scale factor never vanishes.

A 3D Human Body Blockage Model for Outdoor MillimeterWave Cellular Communication ; Blocking is one of the most important challenges in exploiting millimeterwave for fifthgeneration 5G cellular communication systems. Compared to blockages caused by buildings or terrains, human body blockage exhibits a higher complexity due to the mobility and dynamic statistics of humans. To support development of outdoor millimeterwave cellular systems, in this paper we present a novel 3D physical model of human body blockage. Based on the proposed model, the impact of human body blockage on framebased data transmission is discussed, with respect to the system specifications and environment conditions.

bridgesampling An R Package for Estimating Normalizing Constants ; Statistical procedures such as Bayes factor model selection and Bayesian model averaging require the computation of normalizing constants e.g., marginal likelihoods. These normalizing constants are notoriously difficult to obtain, as they usually involve highdimensional integrals that cannot be solved analytically. Here we introduce an R package that uses bridge sampling Meng Wong, 1996; Meng Schilling, 2002 to estimate normalizing constants in a generic and easytouse fashion. For models implemented in Stan, the estimation procedure is automatic. We illustrate the functionality of the package with three examples.

Polynomial processes for power prices ; Polynomial processes have the property that expectations of polynomial functions of degree n, say of the future state of the process conditional on the current state are given by polynomials of degree leq n of the current state. Here we explore the application of polynomial processes in the context of structural models for energy prices. We focus on the example of Alberta power prices, derive one and twofactor models for spot prices. We examine their performance in numerical experiments, and demonstrate that the richness of the dynamics they are able to generate makes them well suited for modelling even extreme examples of energy price behaviour.

Exact solutions for silicon photomultipliers models and application to measurements ; Dark count rate and correlated noise rate are among the main parameters that characterize silicon photomultipliers SiPM. Typically, these parameters are evaluated by applying approximate formulas, or by fitting specific models, to the measured SiPM noise spectra. Here a novel approach is presented, where exact formulas are derived from a statistical model of dark counts and correlated noise generation. The method allows one to measure the true value of such parameters from the areas of just the first peaks in the dark spectrum. A numerical analysis shows the accuracy of the method.

Augmented Homotopical Algebraic Geometry ; We develop the framework for augmented homotopical algebraic geometry. This is an extension of homotopical algebraic geometry, which itself is a homotopification of classical algebraic geometry. To do so, we define the notion of augmentation categories, which are a special class of generalised Reedy categories. For an augmentation category, we prove the existence of a closed Quillen model structure on the presheaf category which is compatible with the KanQuillen model structure on simplicial sets. Moreover, we use the concept of augmented hypercovers to define a local model structure on the category of augmented presheaves. We prove that crossed simplicial groups, and the planar rooted tree category are examples of augmentation categories. Finally, we introduce a method for generating new examples from old via a categorical pushout construction.

Dynamics of twoscalarfield cosmological models beyond the exponential potential ; In this paper, we discuss the dynamics of two scalarfield cosmological models. Unlike in the situation of exponential potential, we find that there are latetime attractors in which one scalar field dominates the energy density of universe and the other one decay. We also discuss the possibility of multiple attractors model which is useful to realize the evolution of the universe from a scaling era to recent acceleration era. We also give the conditions of the existence of multiple attractors.

Stability of selfaccelerating Universe in modified gravity with dynamical torsion the case of small background torsion ; We consider the model of modified gravity with dynamical torsion. This model was found to have promising stability properties about various backgrounds. The model admits a selfaccelerating solution. We have shown previously that if the parameters are adjusted in such a way that the torsion is much greater than the effective cosmological constant, the selfaccelerating solution is unstable there are exponentially growing modes. Here we study the scalar perturbations in the case when the torsion is of the order of the effective cosmological constant. We find that there are no exponential instabilities.

Phase space analysis of a FRW cosmology in the MaxwellCattaneo approach ; In this work, we present a phase space analysis of a spatially flat Friedmann RobertsonWalker FRW model in which the dark matter fluid is modeled as an imperfect fluid having bulk viscosity. The bulk viscosity is governed by the MaxwellCattaneo approach. The rest of the components of the model radiation and dark energy are treated as perfect fluids. Imposing a complete cosmological dynamics and taking into account a recent constraint on the dark matter equation of state EOS, we obtain bound on the bulk viscosity. The results point towards the possibility of describing not only the current speed up of the Universe but also the previous matter and radiation dominated eras.

Physical models from noncommutative causality ; We introduced few years ago a new notion of causality for noncommutative spacetimes directly related to the Dirac operator and the concept of Lorentzian spectral triple. In this paper, we review in a nontechnical way the noncommutative causal structure of many toy models as almost commutative spacetimes and the MoyalWeyl spacetime. We show that those models present some unexpected physical interpretations as a geometrical explanation of the Zitterbewegung trembling motion of a fermion as well as some geometrical constraints on translations and energy jumps of wave packets on the Moyal spacetime.

Removing instability of PolonyiStarobinsky supergravity by adding FI term ; PolonyiStarobinsky PS supergravity is the N1 supergravity model of Starobinsky inflation with spontaneous supersymmetry breaking after inflation due to Polonyi superfield, and inflaton belonging to a massive vector supermultiplet. The PS model is used for an explicit realization of the superheavy gravitino dark matter scenario in cosmology. We find a potential instability in this model, and offer a mechanism for its removal by adding a FayetIliopoulos FI term.

Minimal time synthesis for a kinematic drone model ; In this paper, we consider a rough kinematic model for a UAV flying at constant altitude moving forward with positive lower and upper bounded linear velocities and positive minimum turning radius.For this model, we consider the problem of minimizing the time travelled by the UAV starting from a general configuration to connect a specified target being a fixed circle of minimum turning radius.The timeoptimal synthesis is presented as a partition of the state space which defines a unique optimal path such that the target can be reached optimally.

On Gravitational Energy in Conformal Teleparallel Gravity ; The paper deals with the definition of gravitational energy in conformal teleparallel gravity. The total energy is defined by means of the field equations which allow a local conservation law. Then such an expression is analyzed for a homogeneous and isotropic Universe. This model is implemented by the FriedmannRobertsonWalker FRW line element. The energy of the universe in the absence of matter is identified with the dark energy, however it can be expanded for curved models defining such an energy as the difference between the total energy and the energy of the perfect fluid which is the matter field in the FRW model.

Radiative Dirac neutrino mass, DAMPE dark matter and leptogenesis ; We explain the electronpositron excess reported by the DAMPE collaboration recently in a radiative Dirac seesaw model where a dark U1X gauge symmetry can i forbid the treelevel Yukawa couplings of three righthanded neutrinos to the standard model lepton and Higgs doublets, ii predict the existence of three dark fermions for the gauge anomaly cancellation, iii mediate a testable scattering of the lightest dark fermion off the nucleons. Our model can also accommodate a successful leptogenesis to generate the cosmic baryon asymmetry.

Sentiment Classification using Images and Label Embeddings ; In this project we analysed how much semantic information images carry, and how much value image data can add to sentiment analysis of the text associated with the images. To better understand the contribution from images, we compared models which only made use of image data, models which only made use of text data, and models which combined both data types. We also analysed if this approach could help sentiment classifiers generalize to unknown sentiments.

Mapping of TwoDimensional Schrodinger Equation under the Point Transformation ; For the twodimensional Schrodinger equation, the general form of the point transformations such that the result can be interpreted as a Schrodinger equation with effective i.e. position dependent mass is studied. A wide class of such models with different forms of mass function is obtained in this way. Starting from the solvable twodimensional model, the variety of solvable partner models with effective mass can be built. Several illustrating examples not amenable to the conventional separation of variables are given.

SpaceTime in the SYK Model ; We consider the question of identifying the bulk spacetime of the SYK model. Focusing on the signature of emergent spacetime of the Euclidean model, we explain the need for nonlocal Radontype transformations on external legs of npoint Green's functions. This results in a dual theory with Euclidean AdS signature with additional legfactors. We speculate that these factors incorporate the coupling of additional bulk states similar to the discrete states of 2d string theory.

Deep Koalarization Image Colorization using CNNs and InceptionResNetv2 ; We review some of the most recent approaches to colorize grayscale images using deep learning methods. Inspired by these, we propose a model which combines a deep Convolutional Neural Network trained from scratch with highlevel features extracted from the InceptionResNetv2 pretrained model. Thanks to its fully convolutional architecture, our encoderdecoder model can process images of any size and aspect ratio. Other than presenting the training results, we assess the public acceptance of the generated images by means of a user study. Finally, we present a carousel of applications on different types of images, such as historical photographs.

From Nontrivial Geometries to Power Spectra and Vice Versa ; We review a recent formalism which derives the functional forms of the primordial tensor and scalar power spectra of scalar potential inflationary models. The formalism incorporates the case of geometries with nonconstant first slowroll parameter. Analytic expressions for the power spectra are given that explicitly display the dependence on the geometric properties of the background. Moreover, we present the full algorithm for using our formalism, to reconstruct the model from the observed power spectra. Our techniques are applied to models possessing features in their potential with excellent agreement.

Information Perspective to Probabilistic Modeling Boltzmann Machines versus Born Machines ; We compare and contrast the statistical physics and quantum physics inspired approaches for unsupervised generative modeling of classical data. The two approaches represent probabilities of observed data using energybased models and quantum states respectively.Classical and quantum information patterns of the target datasets therefore provide principled guidelines for structural design and learning in these two approaches. Taking the restricted Boltzmann machines RBM as an example, we analyze the information theoretical bounds of the two approaches. We verify our reasonings by comparing the performance of RBMs of various architectures on the standard MNIST datasets.

Lepton mixing and the chargedlepton mass ratios ; We construct a class of renormalizable models for lepton mixing that generate predictions given in terms of the chargedlepton mass ratios. We show that one of those models leads, when one takes into account the known experimental values, to almost maximal CPbreaking phases and to almost maximal neutrinoless doublebeta decay. We study in detail the scalar potential of the models, especially the bounds imposed by unitarity on the values of the quartic couplings.

Fast trimers in onedimensional extended FermiHubbard model ; We consider a onedimensional two component extended FermiHubbard model with nearest neighbor interactions and mass imbalance between the two species. We study the stability of trimers, various observables for detecting them, and expansion dynamics. We generalize the definition of the trimer gap to include the formation of different types of clusters originating from nearest neighbor interactions. Expansion dynamics reveal rapidly propagating trimers, with speeds exceeding doublon propagation in strongly interacting regime. We present a simple model for understanding this unique feature of the movement of the trimers, and we discuss the potential for experimental realization.

Dwell time for local stability of switched systems with application to nonspiking neuron models ; For switched systems that switch between distinct globally stable equilibria, we offer closedform formulas that lock oscillations in the required neighborhood of the equilibria. Motivated by nonspiking neuron models, the main focus of the paper is on the case of planar switched affine systems, where we use properties of nested cylinders coming from quadratic Lyapunov functions. In particular, for the first time ever, we use the dwelltime concept in order to give an explicit condition for nonspiking of linear neuron models with periodically switching current. An extension to the general nonlinear case is also given.

Syntactic Forcing Models for Coherent Logic ; We present three syntactic forcing models for coherent logic. These are based on sites whose underlying category only depends on the signature of the coherent theory, and they do not presuppose that the logic has equality. As an application we give a coherent theory T and a sentence psi which is Tredundant for any geometric implication phi, possibly with equality, if T psi proves phi, then T proves phi, yet false in the generic model of T. This answers in the negative a question by Wraith.

Exact Calculation of Normalized Maximum Likelihood Code Length Using Fourier Analysis ; The normalized maximum likelihood code length has been widely used in model selection, and its favorable properties, such as its consistency and the upper bound of its statistical risk, have been demonstrated. This paper proposes a novel methodology for calculating the normalized maximum likelihood code length on the basis of Fourier analysis. Our methodology provides an efficient nonasymptotic calculation formula for exponential family models and an asymptotic calculation formula for general parametric models with a weaker assumption compared to that in previous work.

Factor graph fragmentization of expectation propagation ; Expectation propagation is a general approach to fast approximate inference for graphical models. The existing literature treats models separately when it comes to deriving and coding expectation propagation inference algorithms. This comes at the cost of similar, longwinded algebraic steps being repeated and slowing down algorithmic development. We demonstrate how factor graph fragmentization can overcome this impediment. This involves adoption of the message passing on a factor graph approach to expectation propagation and identification of factor graph subgraphs, which we call fragments, that are common to wide classes of models. Key fragments and their corresponding messages are catalogued which means that their algebra does not need to be repeated. This allows compartmentalization of coding and efficient software development.

Mathematical foundations of Accelerated Molecular Dynamics methods ; The objective of this review article is to present recent results on the mathematical analysis of the Accelerated Dynamics algorithms introduced by A.F. Voter in collaboration with D. Perez and M. Sorensen. Using the notion of quasistationary distribution, one is able to rigorously justify the fact that the exit event from a metastable state for the Langevin or overdamped Langevin dynamics can be modeled by a kinetic Monte Carlo model. Moreover, under some geometric assumptions, one can prove that this kinetic Monte Carlo model can be parameterized using EyringKramers formulas. These are the building blocks required to analyze the Accelerated Dynamics algorithms, to understand their efficiency and their accuracy, and to improve and generalize these techniques beyond their original scope.

Shortterm atthemoney asymptotics under stochastic volatility models ; A smalltime Edgeworth expansion of the density of an asset price is given under a general stochastic volatility model, from which asymptotic expansions of put option prices and atthemoney implied volatilities follow. A limit theorem for atthemoney implied volatility skew and curvature is also given as a corollary. The rough Bergomi model is treated as an example.

Modeling and stabilization of a rotating mechanical system with elastic plates ; A mechanical system consisting of a rigid body and attached Kirchhoff plates under the action of three independent controls torques is considered. The equations of motion of such model are derived in the form of a system of coupled nonlinear ordinary and partial differential equations. The operator form of this system is represented as an abstract differential equation in a Hilbert space. A feedback control law is constructed such that the corresponding infinitesimal generator is dissipative.

Detecting noncausal artifacts in multivariate linear regression models ; We consider linear models where d potential causes X1,...,Xd are correlated with one target quantity Y and propose a method to infer whether the association is causal or whether it is an artifact caused by overfitting or hidden common causes. We employ the idea that in the former case the vector of regression coefficients has 'generic' orientation relative to the covariance matrix SigmaXX of X. Using an ICA based model for confounding, we show that both confounding and overfitting yield regression vectors that concentrate mainly in the space of low eigenvalues of SigmaXX.

Toward Coordinated Transmission and Distribution Operations ; Proliferation of smart grid technologies has enhanced observability and controllability of distribution systems. If coordinated with the transmission system, resources of both systems can be used more efficiently. This paper proposes a model to operate transmission and distribution systems in a coordinated manner. The proposed model is solved using a Surrogate Lagrangian Relaxation SLR approach. The computational performance of this approach is compared against existing methods e.g. subgradient method. Finally, the usefulness of the proposed model and solution approach is demonstrated via numerical experiments on the illustrative example and IEEE benchmarks.

On singularityresolution in mimetic gravity ; Recently, it was shown that modified mimetic gravity, with a fsquarephi term, results in a singularityfree model of gravity, for both cosmological and black hole spacetimes 1, 2. In this work, we analyze this model further and show that, since the function f was tuned to vanish rapidly for small values of the argument, the nonsingular bounce relies heavily on a subtle branch changing mechanism for the multivalued function f. Furthermore, this mechanism has interesting implications for the proposed link between this model and loop quantum cosmology.

Partially Linear Spatial Probit Models ; A partially linear probit model for spatially dependent data is considered. A triangular array setting is used to cover various patterns of spatial data. Conditional spatial heteroscedasticity and nonidentically distributed observations and a linear process for disturbances are assumed, allowing various spatial dependencies. The estimation procedure is a combination of a weighted likelihood and a generalized method of moments. The procedure first fixes the parametric components of the model and then estimates the nonparametric part using weighted likelihood; the obtained estimate is then used to construct a GMM parametric component estimate. The consistency and asymptotic distribution of the estimators are established under sufficient conditions. Some simulation experiments are provided to investigate the finite sample performance of the estimators.

A Review of MixedEffect Modeling in the Longitudinal Studies Using Medical Images of Patients ; In this review paper, some applications of the mixed effect modeling in medial image processing and longitudinal analysis is studied. For this purpose, a general structure is extracted from some of the researches in the literature. This structure includes a number of essential elements, each of which having a few design choices, namely 1 tracked features, 2 models mathematical expression and random effects and finally 3 response prediction. Two research study examples in Alzheimers disease and prostate tomography are also briefly introduced to further discuss the above design choices.

Influence of the ZZ' mixing on the Z' production cross section in the modelindependent approach ; The new module SMZp is developed for the MonteCarlo generator Sherpa that extends simulations of the Standard model SM processes with the Abelian Z' boson in the modelindependent approach. The special derived earlier relations between the Z' couplings to the SM fields proper to the renormalizable theories are taken into account. Using this module, dependence of the Z' production cross section on the ZZ' mixing angle theta0 in the DrellYan process is investigated within the range of 1 TeV leq mZ' leq 5 TeV. It is shown that if it is essential to keep the Z' theory renormalizable, theta0 cannot be neglected as it is often done, even if it is small.

Detecting Adversarial Perturbations with Saliency ; In this paper we propose a novel method for detecting adversarial examples by training a binary classifier with both origin data and saliency data. In the case of image classification model, saliency simply explain how the model make decisions by identifying significant pixels for prediction. A model shows wrong classification output always learns wrong features and shows wrong saliency as well. Our approach shows good performance on detecting adversarial perturbations. We quantitatively evaluate generalization ability of the detector, showing that detectors trained with strong adversaries perform well on weak adversaries.

Stochastic Model of Breakdown Nucleation under Intense Electric Fields ; Plastic response due to dislocation activity under intense electric fields is proposed as a source of breakdown. A model is formulated based on stochastic multiplication and arrest under the stress generated by the field. A critical transition in the dislocation population is suggested as the cause of protrusion formation leading to subsequent arcing. The model is studied using Monte Carlo simulations and theoretical analysis, yielding a simplified dependence of the breakdown rates on the electric field. These agree with experimental observations of field and temperature breakdown dependencies.

Study of Twist2 GTMDs in scalardiquark model ; We investigate the Generalized Transverse Momentumdependent Distributions GTMDs describing the parton structure of proton using the lightfront scalardiquark model. In particular, we study the Wigner distributions for unpolarized quark in unpolarized, longitudinallypolarized and transverselypolarized proton. We also investigate the twist2 GTMDs for unpolarized quark Gammagamma in scalardiquark model.

On q,tdeformation of Gaussian matrix model ; The recently discovered general formulas for perturbative correlators in basic matrix models can be interpreted as the Schurpreservation property of Gaussian measures. Then substitution of Schur by, say, Macdonald polynomials, defines a q,tdeformation of the matrix model. Eigenvalue integral representations and Virasorolike constraints are immediate consequences.

Quantum description of timingjitter for single photon ONOFF detectors ; In the context of ultrafast quantum communication and random number generation, detection timingjitters represent a strong limitation as they can introduce major timetagging errors and affect the quality of timecorrelated photon counting or quantum state engineering. Despite their importance in emerging photonic quantum technologies, no detector model including such effects has been developed so far. We propose here an operational theoretical model based on POVM density formalism able to explicitly quantify the effect of timingjitter for a typical class of single photon detector. We apply our model to some common experimental situations.

AffineGoldstonequartetmetric gravity emergent vs. existent ; As a grouptheoretic foundation of gravity, it is considered an affineGoldstone nonlinear model based upon the nonlinear realization of the global affine symmetry spontaneously broken at the Planck scale to the Poincare symmetry. It is shown that below this scale the model justifies and elaborates an earlier introduced effective field theory of the quartetmetric gravity incorporating the gravitational dark substances emerging in addition to the tensor graviton. The prospects for subsequent going beyond the nonlinear model above the Planck scale are indicated.

Random Polymers and Generalized Urn Processes ; We describe a microcanonical approach for polymer models that combines atmospheric methods with urn theory. We show that Large Deviation Properties of urn models can provide quite deep mathematical insight by analyzing the Random Walk Range problem in mathbbZd. We also provide a new mean field theory for the Range Problem that is exactly solvable by analogy with the BagchiPal urn model.

Semantic Search by Latent Ontological Features ; Both named entities and keywords are important in defining the content of a text in which they occur. In particular, people often use named entities in information search. However, named entities have ontological features, namely, their aliases, classes, and identifiers, which are hidden from their textual appearance. We propose ontologybased extensions of the traditional Vector Space Model that explore different combinations of those latent ontological features with keywords for text retrieval. Our experiments on benchmark datasets show better search quality of the proposed models as compared to the purely keywordbased model, and their advantages for both text retrieval and representation of documents and queries.

Logoptimal portfolio without NFLVR existence, complete characterization, and duality ; This paper addresses the logoptimal portfolio for a general semimartingale model. The most advanced literature on the topic elaborates existence and characterization of this portfolio under nofreelunchwithvanishingrisk assumption NFLVR. There are many financial models violating NFLVR, while admitting the logoptimal portfolio on the one hand. On the other hand, for financial markets under progressively enlargement of filtration, NFLVR remains completely an open issue, and hence the literature can be applied to these models. Herein, we provide a complete characterization of logoptimal portfolio and its associated optimal deflator, necessary and sufficient conditions for their existence, and we elaborate their duality as well without NFLVR.

A Hybrid of Deep Audio Feature and ivector for Artist Recognition ; Artist recognition is a task of modeling the artist's musical style. This problem is challenging because there is no clear standard. We propose a hybrid method of the generative model ivector and the discriminative model deep convolutional neural network. We show that this approach achieves stateoftheart performance by complementing each other. In addition, we briefly explain the advantages and disadvantages of each approach.

Iterative evaluation of LSTM cells ; In this work we present a modification in the conventional flow of information through a LSTM network, which we consider well suited for RNNs in general. The modification leads to a iterative scheme where the computations performed by the LSTM cell are repeated over a constant input and cell state values, while updating the hidden state a finite number of times. We provide theoretical and empirical evidence to support the augmented capabilities of the iterative scheme and show examples related to language modeling. The modification yields an enhancement in the model performance comparable with the original model augmented more than 3 times in terms of the total amount of parameters.

A maximum entropy network reconstruction of macroeconomic models ; In this article the problem of reconstructing the pattern of connection between agents from partial empirical data in a macroeconomic model is addressed, given a set of behavioral equations. This systemic point of view puts the focus on distributional and network effects, rather than timedependence. Using the theory of complex networks we compare several models to reconstruct both the topology and the flows of money of the different types of monetary transactions, while imposing a series of constraints related to national accounts, and to empirical network sparsity. Some properties of reconstructed networks are compared with their empirical counterpart.

FLRW accelerating universe with interactive dark energy ; We have developed an accelerating cosmological model for the present universe which is phantom for the period 0 leq z leq 1.99 and quintessence phase for 1.99 leq z leq 2.0315. The universe is assumed to be filled with barotropic and dark energyDE perfect fluid in which DE interact with matter. For a deceleration parameterDP having deceleratingaccelerating transition phase of universe, we assume hybrid expansion law for scale factor. The transition red shift for the model is obtained as zt 0.956. The model satisfies current observational constraints.

Integrals of motion for nonaxisymmetric potentials ; Context The modelling of stationary galactic stellar populations can be performed using distribution functions. Aims This paper aims to write explicit integrals of motion and distribution functions. Methods We propose an analytic formulation of the integrals of motion with an explicit dependence on potential. This formulation applies to potentials with rotational symmetry or triaxial symmetry. It is exact for Stackel potentials and approximate for other potentials. Results Modelling a stationary stellar population using these integrals of motion allows the force field to be found with satisfactory accuracy. On the other hand, the mass density distribution that generates the force field and the gravitational potential is recovered with less accuracy due to lower precision in modelling boxtype orbits.

BPS solutions for generalised WessZumino models and their applications ; We present BPS solutions to a general class of WessZumino models which extend previous results in the literature. We discuss their relation to amplitudes on threshold, and their application to scalar domain walls in Supersymmetric QCD. We also find partial expressions for WessZumino models with softly broken supersymmetry.

Robust Neural Machine Translation with Doubly Adversarial Inputs ; Neural machine translation NMT often suffers from the vulnerability to noisy perturbations in the input. We propose an approach to improving the robustness of NMT models, which consists of two parts 1 attack the translation model with adversarial source examples; 2 defend the translation model with adversarial target inputs to improve its robustness against the adversarial source inputs.For the generation of adversarial inputs, we propose a gradientbased method to craft adversarial examples informed by the translation loss over the clean inputs.Experimental results on ChineseEnglish and EnglishGerman translation tasks demonstrate that our approach achieves significant improvements 2.8 and 1.6 BLEU points over Transformer on standard clean benchmarks as well as exhibiting higher robustness on noisy data.

Scale Factors of Homogeneous Anisotropic Cosmological Models with Perfect Fluid ; The article is devoted to cosmology. It deals with homogeneous anisotropic cosmological models. Scale factors have been evaluated for the multicomponent models with perfect fluid, taking account of its expansion, rotation and shear. The cosmological fluid components are as follows phantom matter, de Sitter vacuum, domain walls, strings, dust, radiation, perfect gas, stiff matter and ekpyrotic matter. The scale factor dependences on the equation of state and kinematic invariants of the perfect fluid have been analysed. The paper is aimed at finding exact solutions of Friedmann and Raychaudhuri equations for different combination of matter components and kinematic invariants.

Neural Spline Flows ; A normalizing flow models a complex probability density as an invertible transformation of a simple base density. Flows based on either coupling or autoregressive transforms both offer exact density evaluation and sampling, but rely on the parameterization of an easily invertible elementwise transformation, whose choice determines the flexibility of these models. Building upon recent work, we propose a fullydifferentiable module based on monotonic rationalquadratic splines, which enhances the flexibility of both coupling and autoregressive transforms while retaining analytic invertibility. We demonstrate that neural spline flows improve density estimation, variational inference, and generative modeling of images.

Establishing a relativistic model for atomic gravimeters ; This work establishes a highprecision relativistic theoretical model start from studying finite speed of light effect based on a coordinate transformation, and further extend the research methods to analyze the overall relativistic effects. This model promotes the development of testing General Relativity with atomic interferometry.

Character ngram Embeddings to Improve RNN Language Models ; This paper proposes a novel Recurrent Neural Network RNN language model that takes advantage of character information. We focus on character ngrams based on research in the field of word embedding construction Wieting et al. 2016. Our proposed method constructs word embeddings from character ngram embeddings and combines them with ordinary word embeddings. We demonstrate that the proposed method achieves the best perplexities on the language modeling datasets Penn Treebank, WikiText2, and WikiText103. Moreover, we conduct experiments on application tasks machine translation and headline generation. The experimental results indicate that our proposed method also positively affects these tasks.

A coreflection of cubical sets into simplicial sets with applications to model structures ; We show that the category of simplicial sets is a coreflective subcategory of the category of cubical sets with connections, with the inclusion given by a version of the straightening functor. We show that using the coreflector, one can transfer any cofibrantly generated model structure in which cofibrations are monomorphisms to cubical sets, thus obtaining cubical analogues of the Quillen and Joyal model structures.

Warm Quintessential Inflation ; We introduce warm quintessential inflation and study it in the weak dissipative regime. We consider the original quintessential inflation model, which approximates quartic chaotic inflation at early times and thawing quartic inversepowerlaw quintessence at present. We find that the model successfully accounts for both inflation and dark energy observations, while it naturally reheats the Universe, thereby overcoming a major problem of quintessential inflation modelbuilding.

Branched splines ; Spline functions have long been used in numerical solution of differential equations. Recently it revives as isogeometric analysis, which offers integration of finite element analysis and NURBS based CAD into a single unified process. Usually many NURBS pieces are needed to build geometrically continuous CAD models. In this paper, we introduce some splines defined on branched covering of sphere, torus or general domains of R2, which are called branched splines in this paper. A single piece of such splines is enough to build some complex CAD models. Multiresolution analysis on surfaces of high genus built from such splines can be carried out naturally. CAD and FEA are integrated directly on such models. A theoretical framework is presented in this paper, together with some simple examples.

Realworld forward rate dynamics with affine realizations ; We investigate the existence of affine realizations for L'evy driven interest rate term structure models under the realworld probability measure, which so far has only been studied under an assumed riskneutral probability measure. For models driven by Wiener processes, all results obtained under the riskneutral approach concerning the existence of affine realizations are transferred to the general case. A similar result holds true for models driven by compound Poisson processes with finite jump size distributions. However, in the presence of jumps with infinite activity we obtain severe restrictions on the structure of the market price of risk; typically, it must even be constant.

Towards implications of asymptotically safe gravity for particle physics ; We review aspects of the interplay of asymptotically safe gravity with matter, focusing on the potential predictive power of the quantum scalesymmetry underlying the asymptotically safe fixed point. We explain how an asymptotically safe fixed point for the Standard Model, induced by quantumgravity fluctuations, might i render the Standard Model ultraviolet complete and ii allow us to calculate the values of some of the StandardModel couplings. In particular, we highlight that such a fixed point might explain the massdifference between the top and bottom quark.

On Cyclic FiniteState Approximation of DataDriven Systems ; In this document, some novel theoretical and computational techniques for constrained approximation of datadriven systems, are presented. The motivation for the development of these techniques came from structurepreserving matrix approximation problems that appear in the fields of system identification and model predictive control, for datadriven systems and processes. The research reported in this document is focused on finitestate approximation of datadriven systems. Some numerical implementations of the aforementioned techniques in the simulation and model predictive control of some generic datadriven systems, that are related to electrical signal transmission models, are outlined.

On the Lperror of the Grenandertype estimator in the Cox model ; We consider the Cox regression model and study the asymptotic global behavior of the Grenandertype estimator for a monotone baseline hazard function. This model is not included in the general setting of Durot 2007. However, we show that a similar central limit theorem holds for Lperror of the Grenandertype estimator. We also propose a test procedure for a Weibull baseline distribution, based on the Lpdistance between the Grenander estimator and a parametric estimator of the baseline hazard. Simulation studies are performed to investigate the performance of this test.

Unified Interpretation of Scalegenesis in Conformally Extended Standard Models ; We present a universal interpretation for a class of conformal extended standard models including Higgs portal interactions realized in lowenergy effective theories. The scale generation mechanism in this class scalegenesis arises along the nearly conformalflat direction for the scale symmetry breaking, where the electroweaksymmetry breaking structure is achieved in a similar way to the standard model's. A dynamical origin for the Higgs portal coupling can provide the discriminator for the lowenergy universality class'', to be probed in forthcoming collider experiments.

Spectral Visualization Sharpening ; In this paper, we propose a perceptuallyguided visualization sharpening technique. We analyze the spectral behavior of an established comprehensive perceptual model to arrive at our approximated model based on an adapted weighting of the bandpass images from a Gaussian pyramid. The main benefit of this approximated model is its controllability and predictability for sharpening colormapped visualizations. Our method can be integrated into any visualization tool as it adopts generic imagebased postprocessing, and it is intuitive and easy to use as viewing distance is the only parameter. Using highly diverse datasets, we show the usefulness of our method across a wide range of typical visualizations.

Unsupervised Separation of Dynamics from Pixels ; We present an approach to learn the dynamics of multiple objects from image sequences in an unsupervised way. We introduce a probabilistic model that first generate noisy positions for each object through a separate linear statespace model, and then renders the positions of all objects in the same image through a highly nonlinear process. Such a linear representation of the dynamics enables us to propose an inference method that uses exact and efficient inference tools and that can be deployed to query the model in different ways without retraining.

jiant A Software Toolkit for Research on GeneralPurpose Text Understanding Models ; We introduce jiant, an open source toolkit for conducting multitask and transfer learning experiments on English NLU tasks. jiant enables modular and configurationdriven experimentation with stateoftheart models and implements a broad set of tasks for probing, transfer learning, and multitask training experiments. jiant implements over 50 NLU tasks, including all GLUE and SuperGLUE benchmark tasks. We demonstrate that jiant reproduces published performance on a variety of tasks and models, including BERT and RoBERTa. jiant is available at httpsjiant.info.

Safe Mission Planning under Dynamical Uncertainties ; This paper considers safe robot mission planning in uncertain dynamical environments. This problem arises in applications such as surveillance, emergency rescue, and autonomous driving. It is a challenging problem due to modeling and integrating dynamical uncertainties into a safe planning framework, and finding a solution in a computationally tractable way. In this work, we first develop a probabilistic model for dynamical uncertainties. Then, we provide a framework to generate a path that maximizes safety for complex missions by incorporating the uncertainty model. We also devise a Monte Carlo method to obtain a safe path efficiently. Finally, we evaluate the performance of our approach and compare it to potential alternatives in several case studies.

Wellposedness of the free boundary hard phase fluids in Minkowski background and its Newtonian limit ; The hard phase model describes a relativistic barotropic irrotational fluid with sound speed equal to the speed of light. In this paper, we prove the local wellposedness for this model in the Minkowski background with free boundary. Moreover, we show that as the speed of light tends to infinity, the solution of this model converges to the solution of the corresponding Newtonian free boundary problem for incompressible fluids. In the appendix we explain how to extend our proof to the general barotropic fluid free boundary problem.

Learning Optimal Control of Water Distribution Networks through Sequential Modelbased Optimization ; Sequential Modelbased Bayesian Optimization has been successfully applied to several application domains, characterized by complex search spaces, such as Automated Machine Learning and Neural Architecture Search. This paper focuses on optimal control problems, proposing a Sequential Modelbased Bayesian Optimization framework to learn optimal control strategies. A quite general formalization of the problem is provided, along with a specific instance related to optimization of pumping operations in an urban Water Distribution Network. Relevant results on a reallife Water Distribution Network are reported, comparing different possible choices for the proposed framework.

Vacuum Decay in the Standard Model Analytical Results with Running and Gravity ; A tunneling bounce driving the decay of a metastable vacuum must respect an integral constraint dictated by simple scaling arguments that is very useful to determine key properties of the bounce. After illustrating how this works in a simple toy model, the Standard Model Higgs potential is considered, including quartic coupling running and gravitational corrections as sources of scale invariance breaking. This approach clarifies the existence of the bounce and leads to simple and accurate analytical results in an expansion in the breaking parameters. Using the socalled tunnelingpotential approach generalized for nonminimal coupling to gravity the integral constraint and the tunneling action are extended to second order in perturbations.

An R Package for generating covariance matrices for maximumentropy sampling from precipitation chemistry data ; We present an opensource R package MESgenCov v 0.1.0 for temporally fitting multivariate precipitation chemistry data and extracting a covariance matrix for use in the MESP maximumentropy sampling problem. We provide multiple functionalities for modeling and model assessment. The package is tightly coupled with NADPNTN National Atmospheric Deposition Program National Trends Network data from their set of 379 monitoring sites, 1978present. The user specifies the sites, chemicals, and time period desired, fits an appropriate userspecified univariate model for each site and chemical selected, and the package produces a covariance matrix for use by MESP algorithms.

A Hedonic Metric Approach to Estimating the Demand for Differentiated Products An Application to Retail Milk Demand ; This article introduces the Hedonic Metric HM approach as an original method to model the demand for differentiated products. Using this approach, initially, we create an ndimensional hedonic space based on the characteristic information available to consumers. Next, we allocate products into this space and estimate the elasticities using distances. Our model makes it possible to estimate a large number of differentiated products in a single demand system. We applied our model to estimate the retail demand for fluid milk products.

Hierarchical Models Intrinsic Separability in High Dimensions ; It has long been noticed that high dimension data exhibits strange patterns. This has been variously interpreted as either a blessing or a curse, causing uncomfortable inconsistencies in the literature. We propose that these patterns arise from an intrinsically hierarchical generative process. Modeling the process creates a web of constraints that reconcile many different theories and results. The model also implies high dimensional data posses an innate separability that can be exploited for machine learning. We demonstrate how this permits the openset learning problem to be defined mathematically, leading to qualitative and quantitative improvements in performance.

Multiscale global sensitivity analysis for stochastic chemical systems ; Sensitivity analysis is routinely performed on simplified surrogate models as the cost of such analysis on the original model may be prohibitive. Little is known in general about the induced bias on the sensitivity results. Within the framework of chemical kinetics, we provide a full justification of the above approach in the case of variance based methods provided the surrogate model results from the original one through the thermodynamic limit. We also provide illustrative numerical examples in context of a MichaelisMenten system and a biochemical reaction network describing a genetic oscillator.

Large longdistance contributions to the electric dipole moments of charged leptons in the standard model ; We reevaluate the electric dipole moment EDM of charged leptons in the standard model using hadron effective models. We find unexpectedly large EDM generated by the hadron level longdistance effect, de 5.8 times 1040 , dmu 1.4 times 1038, and dtau 7.3 times 1038 ecm, with an error bar of 70, exceeding the conventionally known fourloop level elementary contribution by several orders of magnitude.

Statistical Indicators of the Scientific Publications Importance a Stochastic Model and Critical Look ; A model of scientific citation distribution is given. We apply it to understand the role of the Hirsch index as an indicator of scientific publication importance in Mathematics and some related fields. The proposed model is based on a generalization of such wellknown distributions as geometric and Sibuja laws included now in a family of distributions. Real data analysis of the Hirsch index and corresponding citation numbers is given.

Supersaturation model for InN PAMOCVD ; We developed a thermodynamic supersaturation model for plasmaassisted metalorganic chemical vapor deposition of InN. The model is based on the chemical combination of indium with plasmagenerated atomic nitrogen ions. Indium supersaturation was analyzed for InN films grown by PAMOCVD with varying input flow of indium precursor. Raman spectroscopy, Xray diffraction, and atomic force microscopy provided feedback on structural properties and surface morphology of grown films. Growth parameter variation effect on In supersaturation was analyzed. InN films grown at varying growth parameters resulting in the same In supersaturation value exhibit similar structural properties and surface morphology.

SusceptibleInfectedRecovered SIR Dynamics of COVID19 and Economic Impact ; I estimate the SusceptibleInfectedRecovered SIR epidemic model for Coronavirus Disease 2019 COVID19. The transmission rate is heterogeneous across countries and far exceeds the recovery rate, which enables a fast spread. In the benchmark model, 28 of the population may be simultaneously infected at the peak, potentially overwhelming the healthcare system. The peak reduces to 6.2 under the optimal mitigation policy that controls the timing and intensity of social distancing. A stylized asset pricing model suggests that the stock price temporarily decreases by 50 in the benchmark case but shows a Wshaped, moderate but longer bear market under the optimal policy.

Twinlike models for parametrized dark energy ; We study cosmological models involving a single real scalar field that has an equation of state parameter which evolves with cosmic time. We highlight some common parametrizations for the equation of state as a function of redshift in the context of twinlike theories. The procedure is used to introduce different models that have the same acceleration parameter, with the very same energy densities and pressure in flat spacetime.

IIB matrix model Extracting the spacetime points ; Assuming that the largeN master field of the Lorentzian IIB matrix model has been obtained, we go through the procedure of how the coordinates of emerging spacetime points can be extracted. Explicit calculations with test master fields suggest that the genuine IIBmatrixmodel master field may have a finestructure that is essential for producing the spacetime points of an expanding universe.

Several amazing discoveries about compact metrizable spaces in ZF ; In the absence of the axiom of choice, the settheoretic status of many natural statements about metrizable compact spaces is investigated. Some of the statements are provable in mathbfZF, some are shown to be independent of mathbfZF. For independence results, distinct models of mathbfZF and permutation models of mathbfZFA with transfer theorems of Pincus are applied. New symmetric models are constructed in each of which the power set of mathbbR is wellorderable, the Continuum Hypothesis is satisfied but a denumerable family of nonempty finite sets can fail to have a choice function, and a compact metrizable space need not be embeddable into the Tychonoff cube 0, 1mathbbR.

Extrapolating false alarm rates in automatic speaker verification ; Automatic speaker verification ASV vendors and corpus providers would both benefit from tools to reliably extrapolate performance metrics for large speaker populations without collecting new speakers. We address false alarm rate extrapolation under a worstcase model whereby an adversary identifies the closest impostor for a given target speaker from a large population. Our models are generative and allow sampling new speakers. The models are formulated in the ASV detection score space to facilitate analysis of arbitrary ASV systems.

A new method to calculate a 2d ising universality transition point application near the ashkinteller multicritical point ; We propose a new method to numerically calculate transition points that belongs to 2D Ising universality class for quantum spin models. Generally, near the multicritical point, in conventional methods, a finite size correction becomes very large. To suppress the effect of the multicritical point, we use a zaxis twisted boundary condition and a yaxis twisted boundary condition. We apply our method to an S 12 bondalternating XXZ model. The multicritical point of this model has a BKT transition, where the correlation length diverges singularly. However, with our method, the convergence of calculation is highly improved, thus we can calculate the transition point even near the multicritical point.

mlr3proba An R Package for Machine Learning in Survival Analysis ; As machine learning has become increasingly popular over the last few decades, so too has the number of machine learning interfaces for implementing these models. Whilst many R libraries exist for machine learning, very few offer extended support for survival analysis. This is problematic considering its importance in fields like medicine, bioinformatics, economics, engineering, and more. mlr3proba provides a comprehensive machine learning interface for survival analysis and connects with mlr3's general model tuning and benchmarking facilities to provide a systematic infrastructure for survival modeling and evaluation.

On the minimal drift for recurrence in the frog model on dary trees ; We study the recurrence of onepersite frog model textFMd, p on a dary tree with drift parameter pin 0,1, which determines the bias of frogs' random walks. We are interested in the minimal drift pd so that the frog model is recurrent. Using a coupling argument together with a generating function technique, we prove that for all d ge 2, pdle 13, which is the optimal universal upper bound.

Filling random cycles ; We compute the asymptotic behavior of the averagecase filling volume for certain models of random Lipschitz cycles in the unit cube and sphere. For example, we estimate the minimal area of a Seifert surface for a model of random knots first studied by Millett. This is a generalization of the classical AjtaiKoml'osTusn'ady optimal matching theorem from combinatorial probability. The author hopes for applications to the topology of random links, random maps between spheres, and other models of random geometric objects.

Prediction of Hilbertian autoregressive processes a Recurrent Neural Network approach ; The autoregressive Hilbertian model ARH was introduced in the early 90's by Denis Bosq. It was the subject of a vast literature and gave birth to numerous extensions. The model generalizes the classical multidimensional autoregressive model, widely used in Time Series Analysis. It was successfully applied in numerous fields such as finance, industry, biology. We propose here to compare the classical prediction methodology based on the estimation of the autocorrelation operator with a neural network learning approach. The latter is based on a popular version of Recurrent Neural Networks the Long Short Term Memory networks. The comparison is carried out through simulations and real datasets.

Counterfactual and Welfare Analysis with an Approximate Model ; We propose a conceptual framework for counterfactual and welfare analysis for approximate models. Our key assumption is that model approximation error is the same magnitude at new choices as the observed data. Applying the framework to quasilinear utility, we obtain bounds on quantities at new prices using an approximate law of demand. We then bound utility differences between bundles and welfare differences between prices. All bounds are computable as linear programs. We provide detailed analytical results describing how the data map to the bounds including shape restrictions that provide a foundation for plugin estimation. An application to gasoline demand illustrates the methodology.

Possible Controllability of Control Argumentation Frameworks Extended Version ; The recent Control Argumentation Framework CAF is a generalization of Dung's Argumentation Framework which handles argumentation dynamics under uncertainty; especially it can be used to model the behavior of an agent which can anticipate future changes in the environment. Here we provide new insights on this model by defining the notion of possible controllability of a CAF. We study the complexity of this new form of reasoning for the four classical semantics, and we provide a logical encoding for reasoning with this framework.

Modeling networks of probabilistic memristors in SPICE ; Efficient simulation of probabilistic memristors and their networks requires novel modeling approaches. One major departure from the conventional memristor modeling is based on a master equation for the occupation probabilities of network states arXiv2003.11011 2020. In the present article, we show how to implement such master equations in SPICE a generalpurpose circuit simulation program. In the case studies, we simulate the dynamics of acdriven probabilistic binary and multistate memristors, and dcdriven networks of probabilistic binary and multistate memristors. Our SPICE results are in perfect agreement with known analytical solutions. Examples of LTspice codes are included.

Machine learningbased EDFA Gain Model Generalizable to Multiple Physical Devices ; We report a neuralnetwork based erbiumdoped fiber amplifier EDFA gain model built from experimental measurements. The model shows low gainprediction error for both the same device used for training MSE leq 0.04 dB2 and different physical units of the same make generalization MSE leq 0.06 dB2.

IIB matrix model and regularized big bang ; The largeN master field of the Lorentzian IIB matrix model can, in principle, give rise to a particular degenerate metric relevant to a regularized big bang. The length parameter of this degenerate metric is then calculated in terms of the IIBmatrixmodel length scale.

Noisy SelfKnowledge Distillation for Text Summarization ; In this paper we apply selfknowledge distillation to text summarization which we argue can alleviate problems with maximumlikelihood training on single reference and noisy datasets. Instead of relying on onehot annotation labels, our student summarization model is trained with guidance from a teacher which generates smoothed labels to help regularize training. Furthermore, to better model uncertainty during training, we introduce multiple noise signals for both teacher and student models. We demonstrate experimentally on three benchmarks that our framework boosts the performance of both pretrained and nonpretrained summarizers achieving stateoftheart results.

BornOppenheimer approximation in optical cavities from success to breakdown ; The coupling of a molecule and a cavity induces nonadiabaticity in the molecule which makes the description of its dynamics complicated. For polyatomic molecules, reduceddimensional models and the use of the BornOppenheimer approximation BOA may remedy the situation. It is demonstrated that contrary to expectation, BOA may even fail in a onedimensional model and generally expected to fail in two or moredimensional models due to the appearance of conical intersections induced by the cavity.

Comments on old and recent experiments of stickiness of a soft solid to a rough hard surface ; The old asperity model of Fuller and Tabor had demonstrated almost 50 years ago surprisingly good correlation with respect to quite a few experiments on the pulloff decay due to roughness of rubber spheres against roughened Perspex plates. We revisit here some features of the Fuller and Tabor model in view of the more recent theories and experiments, finding good correlation can be obtained only at intermediate resolutions, as perhaps in stylus profilometers. In general we confirm the predictions of the Persson Tosatti and Bearing Area Model of Ciavarella, as stickiness depends largely on the long wavelength content of roughness, and not the fine features. Therefore, multiinstruments measurements should hopefully not be needed.

Isobaric analog state energy in deformed nuclei a toy model ; A formula to evaluate the effects of a general deformation on the Coulomb direct contribution to the energy of the Isobaric Analog State IAS is presented and studied via a simple yet physical model. The toy model gives a reasonable account of microscopic deformed HartreeFockBogolyubov HFB calculations in a test case, and provides a guidance when predicting unknown IAS energies. Thus, deformed HFB calculations, to predict the IAS energies, are performed for several neutrondeficient mediummass and heavy nuclei which are now planned to be studied experimentally.