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Few-Shot Adversarial Learning of Realistic Neural Talking Head ModelsMay 20 2019Several recent works have shown how highly realistic human head images can be obtained by training convolutional neural networks to generate them. In order to create a personalized talking head model, these works require training on a large dataset of ... More

Parsing Images of Overlapping Organisms with Deep Singling-Out NetworksDec 19 2016This work is motivated by the mostly unsolved task of parsing biological images with multiple overlapping articulated model organisms (such as worms or larvae). We present a general approach that separates the two main challenges associated with such ... More

Instance Segmentation of Biological Images Using Harmonic EmbeddingsApr 10 2019We present a new instance segmentation approach tailored to biological images, where instances may correspond to individual cells, organisms or plant parts. Unlike instance segmentation for user photographs or road scenes, in biological data object instances ... More

Aggregating Deep Convolutional Features for Image RetrievalOct 26 2015Several recent works have shown that image descriptors produced by deep convolutional neural networks provide state-of-the-art performance for image classification and retrieval problems. It has also been shown that the activations from the convolutional ... More

Learning Deep Embeddings with Histogram LossNov 02 2016We suggest a loss for learning deep embeddings. The new loss does not introduce parameters that need to be tuned and results in very good embeddings across a range of datasets and problems. The loss is computed by estimating two distribution of similarities ... More

Fast ConvNets Using Group-wise Brain DamageJun 08 2015Dec 07 2015We revisit the idea of brain damage, i.e. the pruning of the coefficients of a neural network, and suggest how brain damage can be modified and used to speedup convolutional layers. The approach uses the fact that many efficient implementations reduce ... More

Instance Segmentation by Deep ColoringJul 26 2018We propose a new and, arguably, a very simple reduction of instance segmentation to semantic segmentation. This reduction allows to train feed-forward non-recurrent deep instance segmentation systems in an end-to-end fashion using architectures that have ... More

Multiregion Bilinear Convolutional Neural Networks for Person Re-IdentificationDec 16 2015Jul 29 2016In this work we explore the applicability of the recently proposed CNN architecture, called Bilinear CNN, and its new modification that we call multi-region Bilinear CNN to the person re-identification problem. Originally, Bilinear CNNs were introduced ... More

Instance Normalization: The Missing Ingredient for Fast StylizationJul 27 2016Sep 20 2016It this paper we revisit the fast stylization method introduced in Ulyanov et. al. (2016). We show how a small change in the stylization architecture results in a significant qualitative improvement in the generated images. The change is limited to swapping ... More

End-to-end Learning of Cost-Volume Aggregation for Real-time Dense StereoNov 17 2016We present a new deep learning-based approach for dense stereo matching. Compared to previous works, our approach does not use deep learning of pixel appearance descriptors, employing very fast classical matching scores instead. At the same time, our ... More

Pairwise QuantizationJun 05 2016We consider the task of lossy compression of high-dimensional vectors through quantization. We propose the approach that learns quantization parameters by minimizing the distortion of scalar products and squared distances between pairs of points. This ... More

Learnable Visual MarkersOct 28 2016We propose a new approach to designing visual markers (analogous to QR-codes, markers for augmented reality, and robotic fiducial tags) based on the advances in deep generative networks. In our approach, the markers are obtained as color images synthesized ... More

Deep Image PriorNov 29 2017Apr 05 2018Deep convolutional networks have become a popular tool for image generation and restoration. Generally, their excellent performance is imputed to their ability to learn realistic image priors from a large number of example images. In this paper, we show ... More

Impostor Networks for Fast Fine-Grained RecognitionJun 13 2018In this work we introduce impostor networks, an architecture that allows to perform fine-grained recognition with high accuracy and using a light-weight convolutional network, making it particularly suitable for fine-grained applications on low-power ... More

Latent Convolutional ModelsJun 16 2018Nov 02 2018We present a new latent model of natural images that can be learned on large-scale datasets. The learning process provides a latent embedding for every image in the training dataset, as well as a deep convolutional network that maps the latent space to ... More

Texture Networks: Feed-forward Synthesis of Textures and Stylized ImagesMar 10 2016Gatys et al. recently demonstrated that deep networks can generate beautiful textures and stylized images from a single texture example. However, their methods requires a slow and memory-consuming optimization process. We propose here an alternative approach ... More

Learnable Triangulation of Human PoseMay 14 2019We present two novel solutions for multi-view 3D human pose estimation based on new learnable triangulation methods that combine 3D information from multiple 2D views. The first (baseline) solution is a basic differentiable algebraic triangulation with ... More

Speeding-up Convolutional Neural Networks Using Fine-tuned CP-DecompositionDec 19 2014Apr 24 2015We propose a simple two-step approach for speeding up convolution layers within large convolutional neural networks based on tensor decomposition and discriminative fine-tuning. Given a layer, we use non-linear least squares to compute a low-rank CP-decomposition ... More

Neural Codes for Image RetrievalApr 07 2014Jul 07 2014It has been shown that the activations invoked by an image within the top layers of a large convolutional neural network provide a high-level descriptor of the visual content of the image. In this paper, we investigate the use of such descriptors (neural ... More

Hyperbolic Image EmbeddingsApr 03 2019Computer vision tasks such as image classification, image retrieval and few-shot learning are currently dominated by Euclidean and spherical embeddings, so that the final decisions about class belongings or the degree of similarity are made using linear ... More

Image Manipulation with Perceptual DiscriminatorsSep 05 2018Systems that perform image manipulation using deep convolutional networks have achieved remarkable realism. Perceptual losses and losses based on adversarial discriminators are the two main classes of learning objectives behind these advances. In this ... More

DeepWarp: Photorealistic Image Resynthesis for Gaze ManipulationJul 25 2016Jul 26 2016In this work, we consider the task of generating highly-realistic images of a given face with a redirected gaze. We treat this problem as a specific instance of conditional image generation and suggest a new deep architecture that can handle this task ... More

Coordinate-based Texture Inpainting for Pose-Guided Image GenerationNov 28 2018We present a new deep learning approach to pose-guided resynthesis of human photographs. At the heart of the new approach is the estimation of the complete body surface texture based on a single photograph. Since the input photograph always observes only ... More

Set2Model Networks: Learning Discriminatively To Learn Generative ModelsDec 22 2016Oct 27 2017We present a new "learning-to-learn"-type approach that enables rapid learning of concepts from small-to-medium sized training sets and is primarily designed for web-initialized image retrieval. At the core of our approach is a deep architecture (a Set2Model ... More

Domain-Adversarial Training of Neural NetworksMay 28 2015May 26 2016We introduce a new representation learning approach for domain adaptation, in which data at training and test time come from similar but different distributions. Our approach is directly inspired by the theory on domain adaptation suggesting that, for ... More

Large-Scale 3D Shape Reconstruction and Segmentation from ShapeNet Core55Oct 17 2017Oct 27 2017We introduce a large-scale 3D shape understanding benchmark using data and annotation from ShapeNet 3D object database. The benchmark consists of two tasks: part-level segmentation of 3D shapes and 3D reconstruction from single view images. Ten teams ... More

Exact and approximate analytical solutions of Weiss equation of ferromagnetism and their experimental relevanceFeb 14 2017The recent progress in the theory of generalized Lambert functions makes possible to solve exactly the Weiss equation of ferromagnetism. However, this solution is quite inconvenient for practical purposes. Precise approximate analytical solutions are ... More

Reply to Paris's Comments on Exactification of Stirling's Approximation for the Logarithm of the Gamma FunctionAug 07 2014In a recent paper [arXiv:1406.1320] Paris has made several comments concerning the author's recent work on the exactification of Stirling's approximation for the logarithm of the gamma function, $\ln \Gamma(z)$. Despite acknowledging that the calculations ... More

Exactification of Stirling's Approximation for the Logarithm of the Gamma FunctionApr 10 2014Exactification is the process of obtaining exact values of a function from its complete asymptotic expansion. Here Stirling's approximation for the logarithm of the gamma function or $\ln \Gamma(z)$ is derived completely whereby it is composed of the ... More

Reynolds number of transition and large-scale properties of strong turbulenceSep 14 2014A turbulent flow is characterized by velocity fluctuations excited in an extremely broad interval of wave numbers $k> \Lambda_{f}$ where $\Lambda_{f}$ is a relatively small set of the wave-vectors where energy is pumped into fluid by external forces. ... More

Reynolds Number of Transition as a Dynamic Constraint on Statistical Theory of TurbulenceAug 20 2013Iterative coarse-graining procedure based on Wyld's perturbation expansion is applied to the problem of Navier-Stokes turbulence. It is shown that the low-order calculation gives the fixed-point Reynolds number $ Re_{fp}$ (coupling constant) almost identical ... More

Statistics of Transverse Velocity Differences in TurbulenceSep 09 1999An unusual symmetry of the equation for the generating function of transverse velocity differences $\Delta v=v(x+r)-v(x)$ is used to obtain a closed equation for the probability density function $P(\Delta v,r)$ in strong three-dimensional turbulence. ... More

Tensor categories (after P. Deligne)Jan 25 2004These notes give an exposition of Deligne's theorem on the existense of super fiber functor.

Asymptotics of the ground state energy of heavy molecules and related topics. IIOct 04 2012Jan 23 2013We consider asymptotics of the ground state energy of heavy atoms and molecules in the strong external magnetic field and derive it including Schwinger and Dirac corrections (if magnetic field is not too strong). We also consider related topics: an excessive ... More

Asymptotics of the ground state energy of heavy molecules and related topicsOct 03 2012We consider asymptotics of the ground state energy of heavy atoms and molecules and derive it including Schwinger and Dirac corrections. We consider also related topics: an excessive negative charge, ionization energy and excessive negative charge when ... More

Déformations isospectrales non compactes et théorie quantique des champsJul 21 2005Nov 02 2005The aim of this thesis is to study the isopectral deformations from the point of view of Alain Connes' noncommutative geometry. This class of quantum spaces constituts a curved space generalisation of Moyal planes and noncommutative tori. First of all, ... More

Heat-Kernel Approach to UV/IR Mixing on Isospectral Deformation ManifoldsDec 20 2004May 23 2005We work out the general features of perturbative field theory on noncommutative manifolds defined by isospectral deformation. These (in general curved) `quantum spaces', generalizing Moyal planes and noncommutative tori, are constructed using Rieffel's ... More

New Barr-Zee contributions to $\mathbf{(g-2)_μ}$ in two-Higgs-doublet modelsFeb 14 2015May 18 2015We study the contribution of new sets of two-loop Barr-Zee type diagrams to the anomalous magnetic moment of the muon within the two-Higgs-doublet model framework. We show that some of these contributions can be quite sizeable for a large region of the ... More

Implicit Function Theorem for systems of polynomial equations with vanishing Jacobian and its application to flexible polyhedra and frameworksJun 19 2000We study the existence problem for a local implicit function determined by a system of nonlinear algebraic equations in the particular case when the determinant of its Jacobian matrix vanishes at the point under consideration. We present a system of sufficient ... More

The Dehn invariants of the Bricard octahedraJan 20 2009We prove that the Dehn invariants of any Bricard octahedron remain constant during the flex and that the Strong Bellows Conjecture holds true for the Steffen flexible polyhedron.

On the Boundedness of The Bilinear Hilbert Transform along "non-flat" smooth curvesOct 16 2011Dec 31 2015We are proving $L^2(\R)\times L^2(\R)\,\rightarrow\,L^1(\R)$ bounds for the bilinear Hilbert transform $H_{\Gamma}$ along curves $\Gamma=(t,-\gamma(t))$ with $\gamma$ being a smooth "non-flat" curve near zero and infinity.

The Polynomial Carleson OperatorMay 19 2011We prove that the generalized Carleson operator with polynomial phase function is of strong type $(p,p)$ for $1<p<\infty$, thus answering a question asked by E. Stein. A key ingredient in this proof is the further extension of the relational time-frequency ... More

Groupoids and the integration of Lie algebroidsApr 13 2000We show that a Lie algebroid on a stratified manifold is integrable if, and only if, its restriction to each strata is integrable. These results allow us to construct a large class of algebras of pseudodifferential operators.

Bethe anzats derivation of the Tracy-Widom distribution for one-dimensional directed polymersMar 25 2010The distribution function of the free energy fluctuations in one-dimensional directed polymers with $\delta$-correlated random potential is studied by mapping the replicated problem to a many body quantum boson system with attractive interactions. Performing ... More

Non-perturbative phenomena in the three-dimensional random field Ising modelMar 27 2006The systematic approach for the calculations of the non-perturbative contributions to the free energy in the ferromagnetic phase of the random field Ising model is developed. It is demonstrated that such contributions appear due to localized in space ... More

Universal RandomnessSep 16 2010Jun 30 2011During last two decades it has been discovered that the statistical properties of a number of microscopically rather different random systems at the macroscopic level are described by {\it the same} universal probability distribution function which is ... More

Griffiths singularity in the random Ising ferromagnetMay 10 2005The explicit form of the Griffiths singularity in the random ferromagnetic Ising model in external magnetic field is derived. In terms of the continuous random temperature Ginzburg-Landau Hamiltonian it is shown that in the paramagnetic phase away from ... More

Stochastic effects in the growth of dropletsMay 30 2005The effects of stochastic absorption and ejection of molecules by growing droplets have been considered. Both analytical and numerical approaches have been used. They demonstrate the satisfactory coincidence. It is proved that in general case corresponding ... More

Perturbative theory approaches to the metastable phase decayDec 31 2007The perturbative theory of the nucleation kinetics is analyzed. A new improvement is suggested and compared with numerical calculations.

Different scenarios of the late stages of condensationDec 31 2007The late stages of the nucleation have been described analytically. The approximate solution of the Zel'dowich-Folmer-Frenkel equation has been constructed.

Stratified Picard--Lefschetz theoryMay 11 1995The monodromy action in the homology of level sets of Morse functions on stratified singular analytic varieties is studied. The local variation operators in both the standard and the intersection homology groups defined by the loops around the critical ... More

A Note On Higher Order GrammarOct 03 2009Both syntax-phonology and syntax-semantics interfaces in Higher Order Grammar (HOG) are expressed as axiomatic theories in higher-order logic (HOL), i.e. a language is defined entirely in terms of provability in the single logical system. An important ... More

Isospectral commuting variety and the Harish-Chandra D-moduleFeb 17 2010Feb 25 2010Let g be a complex reductive Lie algebra with Cartan algebra h. Hotta and Kashiwara defined a holonomic D-module M, on g x h, called Harish-Chandra module. We give an explicit description of gr(M), the associated graded module with respect to a canonical ... More

Variations on themes of KostantOct 08 2007Jan 09 2008Let g be a complex semisimple Lie algebra and let G' be the Langlands dual group. We give a description of the cohomology algebra of an arbitrary spherical Schubert variety in the loop Grassmannian for G' as a quotient of the form Sym(g^e)/J. Here, J ... More

Fermionization Transform for Certain Higher-Dimensional Quantum Spin ModelsMar 19 2010Proposed is a generalization of Jordan-Wigner transform that allows to exactly fermionize a large family of quantum spin Hamiltonians in dimensions higher than one. The key new steps are to enlarge the Hilbert space of the original model by adding to ... More

A two-parameter generalization of the complete elliptic integral of second kindAug 17 2007A two-parameter generalization of the complete elliptic integral of second kind is expressed in terms of the Appell function $F_{4}$. This function is further reduced to a quite simple bilinear form in the complete elliptic integrals $K$ and $E$. The ... More

Calculation of the D and B Meson LifetimesJul 22 1994Aug 30 1994Using the expansions of the heavy meson decay widths in the heavy quark mass and QCD sum rules for estimates of corresponding matrix elements,\, we calculate the $D^{\pm,o,s}$ decay widths and the $B^{\pm,o,s}$ lifetime differences. The results for D ... More

Integer conversions and estimation of the number of integer solutions of algebraic Diophantine equationsNov 17 2016The paper assesses the top number of integer solutions of algebraic Diophantine Thue diagonal equation with the degree $n \geq 2$ and number of variables $k > 2$ and equations with explicit variable in the case when the coefficients of the equation have ... More

Quantum mechanics of time-dependent systems. Construction of pure statesApr 03 1995For time-dependent systems the wavefunction depends explicitly on time and it is not a pure state of the Hamiltonian. We construct operators for which the above wavefunction is a pure state. The method is based on the introduction of conserved quantities ... More

On measures which generate the scalar product in a space of rational functionsFeb 07 2016Feb 12 2016Let $z_1,z_2,\,\ldots\,,z_n$ be pairwise different points of the unit disc and $\mathscr{L}(z_1,z_2,\,\ldots\,z_n)$ be the linear space generated by the rational fractions $\frac{1}{t-z_1} , \frac{1}{t-z_2} , \cdots\ , \frac{1}{t-z_n}\cdot$ Every non-negative ... More

Econophysics of Business Cycles: Aggregate Economic Fluctuations, Mean Risks and Mean Square RisksAug 31 2017This paper presents hydrodynamic-like model of business cycles aggregate fluctuations of economic and financial variables. We model macroeconomics as ensemble of economic agents on economic space and agent's risk ratings play role of their coordinates. ... More

Non-Local Macroeconomic Transactions and Credits-Loans Surface-Like WavesMay 29 2017This paper describes surface-like waves of macroeconomic Credits-Loans transactions on economic space. We use agent's risk ratings as their coordinates and describe evolution of macro variables by transactions between agents. Aggregations of agent's variables ... More

Teichmuller TQFT vs Chern-Simons TheoryOct 12 2017Oct 19 2017Teichm\"uller TQFT is a unitary 3d topological theory whose Hilbert spaces are spanned by Liouville conformal blocks. It is related but not identical to PSL(2,R) Chern-Simons theory. To physicists, it is known in particular in the context of 3d-3d correspondence ... More

Asymptotic of summation arithmetic functions, the limit for which is the law of normal distributionFeb 08 2019Feb 13 2019Summation arithmetic functions with asymptotically independent terms are studied in the paper, the limit of which is the law of normal distribution. Assertions about the asymptotic behavior of the indicated functions are proved.

Rational points near manifolds and metric Diophantine approximationApr 02 2009Jun 03 2009This work is motivated by problems on simultaneous Diophantine approximation on manifolds, namely, establishing Khintchine and Jarnik type theorems for submanifolds of R^n. These problems have attracted a lot of interest since Kleinbock and Margulis proved ... More

On the Properties of the Cayley Graph of Richard Thompson's Group FNov 26 2002We study some properties of the Cayley graph of the R.Thompson's group F in generators $x_0$, $x_1$. We show that the density of this graph, that is, the least upper bound of the average vertex degree of its finite subgraphs is at least 3. It is known ... More

Galois descent of determinants in the ramified caseOct 30 2010In the local, unramified case the determinantal functions associated to the group-ring of a finite group satisfy Galois descent. This note examines the obstructions to Galois determinantal descent in the ramified case.

Sharp Spectral Asymptotics for Operators with Irregular Coefficients. V. Multidimensional Schroedinger operator with a strong magnetic field. Non-Full-rank caseOct 16 2005Aug 02 2011Sharp spectral asymptotics for multidimensional Schroedinger operators with the strong magnetic field are derived under rather weak smoothness conditions. I assume that magnetic intensity matrix has constant defect r>0 at each point. In comparison with ... More

Sharp Spectral Asymptotics for Operators with Irregular Coefficients. III. Schroedinger operator with a strong magnetic fieldOct 16 2005Apr 01 2011Sharp spectral asymptotics for 2- and 3-dimensional Schroedinger operators with strong magnetic field are derived under rather weak smoothness conditions. In comparison with version 1 of 2005 new results are added and minor errors corrected.

Sinai's condition for real valued Lévy processesMay 24 2005We prove that the upward ladder height subordinator $H$ associated to a real valued L\'{e}vy process $\xi$ has Laplace exponent $\phi$ that varies regularly at $\infty$ (resp. at 0) if and only if the underlying L\'{e}vy process $\xi$ satisfies Sinai's ... More

On Transformation of Potapov's Fundamental Matrix InequalityJun 13 2007According to V.P.Potapov, a classical interpolation problem can be reformulated in terms of a so-called Fundamental Matrix Inequality (FMI). To show that every solution of the FMI satisfies the interpolation problem, we usualy have to transform the FMI ... More

Automorphisms of local fields of period $p^M$ and nilpotent class $<p$May 20 2015May 23 2016Suppose $K$ is a finite extension of $\mathbb{Q}_p$ containing a $p^M$-th primitive root of unity. For $1\leqslant s<p$ denote by $K[s,M]$ the maximal $p$-extension of $K$ with the Galois group of period $p^M$ and nilpotent class $s$. We apply the nilpotent ... More

Automorphisms of local fields of period $p$ and nilpotent class $<p$Mar 17 2014Jan 09 2017Suppose $K$ is a finite field extension of $\mathbb{Q} _p$ containing a primitive $p$-th root of unity. Let $\Gamma _{<p}$ be the Galois group of a maximal $p$-extension of $K$ with the Galois group of period $p$ and nilpotent class $<p$. In the paper ... More

Modified proof of a local analogue of the Grothendieck conjectureJul 17 2009A local analogue of the Grothendieck Conjecture is an equivalence of the category of complete discrete valuation fields $K$ with finite residue fields of characteristic $p\ne 0$ and the category of absolute Galois groups of fields $K$ together with their ... More

The Erdős-Selfridge and the Schinzel-Tijdeman theorems hold in $PA^-$Oct 30 2014Mar 14 2015We show that "The product of consecutive integers is never a power" and several results by Schinzel and Tijdeman on the solutions of the equation $y^m=P(x)$, for $m>1$, $y>1$, and $P(x)$ a polynomial with rational coefficients and with at least two distinct ... More

Physical applications of a new method of solving the quintic equationOct 15 2009Oct 27 2009Some physical applications of the Passare-Tsikh solution of a principal quintic equation are discussed. As an example, a quintic equation of state is solved in detail. This approach provides analytical approximations for several problems admitting until ... More

On filtered multiplicative bases of group algebras IIFeb 13 2001We give an explicit list of all p-groups G with a cyclic subgroup of index p^2, such that the group algebra KG over the field K of characteristic p has a filtered multiplicative K-basis. We also proved that such a K-basis does not exist for the group ... More

On the group of automorphisms of Shimura curves and applicationsJun 10 2002Let V_D be the Shimura curve over \Q attached to the indefinite rational quaternion algebra of discriminant D. In this note we investigate the group of automorphisms of V_D and prove that, in many cases, it is the Atkin-Lehner group. Moreover, we determine ... More

On the Boundedness of The Bilinear Hilbert Transform along "non-flat" smooth curves. The Banach triangle case ($L^r,\: 1\leq r<\infty$)Dec 31 2015Apr 27 2016We show that the bilinear Hilbert transform $H_{\Gamma}$ along curves $\Gamma=(t,-\gamma(t))$ with $\gamma\in\mathcal{N}\mathcal{F}^{C}$ is bounded from $L^{p}(\mathbb{R})\times L^{q}(\mathbb{R})\,\rightarrow\,L^{r}(\mathbb{R})$ where $p,\,q,\,r$ are ... More

A functional model for the Fourier--Plancherel operator truncated on the positive half-axisOct 30 2017Jul 17 2018The truncated Fourier operator $\mathscr{F}_{\mathbb{R^{+}}}$, $$ (\mathscr{F}_{\mathbb{R^{+}}}x)(t)=\frac{1}{\sqrt{2\pi}} \int\limits_{\mathbb{R^{+}}}x(\xi)e^{it\xi}\,d\xi\,,\ \ \ t\in{}{\mathbb{R^{+}}}, $$ is studied. The operator $\mathscr{F}_{\mathbb{R^{+}}}$ ... More

A. Cormack's last inversion formula and a FBP reconstructionJul 31 2014A reconstruction of a function from integrals over the family of confocal paraboloids is given by a FBP formula.

Dyer-Lashof-Cohen operations in Hochschild cohomologyApr 01 2005Apr 17 2009We give explicit formulae for operations in Hochschild cohomology which are analogous to the operations in the homology of double loop spaces. As a corollary we obtain that any brace algebra in finite characteristic is always a restricted Lie algebra. ... More

On the Pauli principle violation in QFTJun 27 2007We propose a new mechanism for a ''small" violation of Pauli Principle in the framework of Quantum Field Theory. Instead of modification of algebra - commutation relations for fields - we introduce spontaneous violation of Pauli Principle which is proportional ... More

Estimating of the number of integer (natural) solutions of inhomogeneous algebraic Diophantine diagonal equations with integer coefficientsAug 11 2016Aug 12 2016This paper investigates the upper bound of the number of integer (natural) solutions of inhomogeneous algebraic Diophantine diagonal equations with integer coefficients without a free member via the circle method of Hardy and Littlewood. Author found ... More

Extremal quantile regressionMay 30 2005Quantile regression is an important tool for estimation of conditional quantiles of a response Y given a vector of covariates X. It can be used to measure the effect of covariates not only in the center of a distribution, but also in the upper and lower ... More

An analogue of a van der Waerden's theorem and its application to two-distance preserving mappingsApr 15 2015Apr 17 2015The van der Waerden's theorem reads that an equilateral pentagon in Euclidean 3-space $\Bbb E^3$ with all diagonals of the same length is necessarily planar and its vertex set coincides with the vertex set of some convex regular pentagon. We prove the ... More

Asymptotics of the ground state energy of heavy atoms and molecules in combined magnetic fieldDec 29 2013Mar 27 2014We consider asymptotics of the ground state energy of heavy atoms and molecules in the self-generatedl magnetic field. Namely, we consider $$H=((D-A)\cdot\boldsymbol{\sigma})^2-V$$ with $$V=\sum_{1\le m\le M} \frac{Z_m}{|x-y_m|}$$ and a corresponding ... More

Asymptotics of the ground state energy of heavy molecules and related topics. IIOct 04 2012Mar 28 2017We consider asymptotics of the ground state energy of heavy atoms and molecules in the strong external magnetic field and derive it including Schwinger and Dirac corrections (if magnetic field is not too strong). We also consider related topics: an excessive ... More

Asymptotics of the ground state energy in the relativistic settingsJul 21 2017Aug 23 2017The purpose of this paper is to derive sharp asymptotics of the ground state energy for the heavy atoms and molecules in the relativistic settings, and, in particular, to derive relativistic Scott correction term and also Dirac, Schwinger and relativistic ... More

Local trace asymptotics in the self-generated magnetic fieldAug 21 2011Dec 23 2011We consider a semiclassical asymptotics of local trace for the 3D-Schroedinger operator with self-generated magnetic field; it is given by Weyl expression with O(h^{-1}) error and under standard condition to Hamiltonian trajectories even o(h^{-1}). In ... More

Short Loops and Pointwise Spectral AsymptoticsMay 05 2010We consider pointwise semiclassical spectral asymptotics i.e. asymptotics of $e(x,x,0)$ as $h\to +0$ where $e(x,y,\tau)$ is the Schwartz kernel of the spectral projector and consider two cases when schort loops give contribution above $O(h^{1-d})$: (i) ... More

Cell decompositions of double Bott-Samelson varietiesOct 17 2013Nov 18 2013Let G be a connected complex semisimple Lie group. Webster and Yakimov have constructed partitions of the double flag variety G/B x G/B_, where (B, B_) is a pair of opposite Borel subgroups of G, generalizing the Deodhar decompositions of G/B. We show ... More

An analytical approach to the Rational Simplex ProblemApr 28 2013May 08 2013In 1973, J. Cheeger and J. Simons raised the following question that still remains open and is known as the Rational Simplex Problem: Given a geodesic simplex in the spherical 3-space so that all of its interior dihedral angles are rational multiples ... More

Hodge decomposition in the homology of long knotsDec 01 2008Dec 06 2008The paper describes a natural splitting in the rational homology and homotopy of the spaces of long knots. This decomposition presumably arises from the cabling maps in the same way as a natural decomposition in the homology of loop spaces arises from ... More

A countable series of bisimple $\mathcal{H}$-trivial finitely presented congruence-free monoidsJan 22 2013We provide a countable series of bisimple $\mathcal{H}$-trivial finitely presented congruence-free monoids.

Generalized Cosecant Numbers and the Hurwitz Zeta FunctionFeb 14 2017Aug 09 2018This announcement paper summarises recent development concerning the generalized cosecant numbers $c_{\rho,k}$, which represent the coefficients of the power series expansion for the important fundamental function $z^{\rho}/\sin^{\rho} z$. These coefficients ... More

On symmetric units in group algebrasSep 01 2000Let $U(KG)$ be the group of units of the group ring $KG$ of the group $G$ over a commutative ring $K$. The anti-automorphism $g\mapsto g\m1$ of $G$ can be extended linearly to an anti-automorphism $a\mapsto a^*$ of $KG$. Let $S_*(KG)=\{x\in U(KG) \mid ... More

Exponential scaling limit of the single-particle Anderson model via adaptive feedback scalingMar 09 2015Aug 12 2015We propose a reformulation of the bootstrap version of the Multi-Scale Analysis (BMSA), developed by Germinet and Klein, to make explicit the fact that BMSA implies asymptotically exponential decay of eigenfunctions (EFs) and of EF correlators (EFCs), ... More

Matrix products with constraints on the sliding block relative frequencies of different factorsMar 20 2014May 28 2014One of fundamental results of the theory of joint/generalized spectral radius, the Berger-Wang theorem, establishes equality between the joint and generalized spectral radii of a set of matrices. Generalization of this theorem on products of matrices ... More

Hourglass alternative and the finiteness conjecture for the spectral characteristics of sets of non-negative matricesJul 02 2015Oct 19 2015Recently Blondel, Nesterov and Protasov proved that the finiteness conjecture holds for the generalized and the lower spectral radii of the sets of non-negative matrices with independent row/column uncertainty. We show that this result can be obtained ... More