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LSALSA: efficient sparse coding in single and multiple dictionary settingsFeb 13 2018We propose an efficient sparse coding (SC) framework for obtaining sparse representation of data. The proposed framework is very general and applies to both the single dictionary setting, where each data point is represented as a sparse combination of ... More

Invertible Autoencoder for domain adaptationFeb 10 2018The unsupervised image-to-image translation aims at finding a mapping between the source ($A$) and target ($B$) image domains, where in many applications aligned image pairs are not available at training. This is an ill-posed learning problem since it ... More

Semistochastic Quadratic Bound MethodsSep 05 2013Feb 17 2014Partition functions arise in a variety of settings, including conditional random fields, logistic regression, and latent gaussian models. In this paper, we consider semistochastic quadratic bound (SQB) methods for maximum likelihood inference based on ... More

Logarithmic Time Online Multiclass predictionJun 06 2014Nov 14 2015We study the problem of multiclass classification with an extremely large number of classes (k), with the goal of obtaining train and test time complexity logarithmic in the number of classes. We develop top-down tree construction approaches for constructing ... More

Stochastic Bound MajorizationSep 22 2013Recently a majorization method for optimizing partition functions of log-linear models was proposed alongside a novel quadratic variational upper-bound. In the batch setting, it outperformed state-of-the-art first- and second-order optimization methods ... More

VisualBackProp for learning using privileged information with CNNsMay 24 2018In many machine learning applications, from medical diagnostics to autonomous driving, the availability of prior knowledge can be used to improve the predictive performance of learning algorithms and incorporate `physical,' `domain knowledge,' or `common ... More

Skin Lesion Segmentation and Classification with Deep Learning SystemFeb 16 2019Melanoma is one of the ten most common cancers in the US. Early detection is crucial for survival, but often the cancer is diagnosed in the fatal stage. Deep learning has the potential to improve cancer detection rates, but its applicability to melanoma ... More

Notes on using Determinantal Point Processes for Clustering with Applications to Text ClusteringOct 26 2014In this paper, we compare three initialization schemes for the KMEANS clustering algorithm: 1) random initialization (KMEANSRAND), 2) KMEANS++, and 3) KMEANSD++. Both KMEANSRAND and KMEANS++ have a major that the value of k needs to be set by the user ... More

On the boosting ability of top-down decision tree learning algorithm for multiclass classificationMay 17 2016We analyze the performance of the top-down multiclass classification algorithm for decision tree learning called LOMtree, recently proposed in the literature Choromanska and Langford (2014) for solving efficiently classification problems with very large ... More

Deep learning with Elastic Averaging SGDDec 20 2014Oct 25 2015We study the problem of stochastic optimization for deep learning in the parallel computing environment under communication constraints. A new algorithm is proposed in this setting where the communication and coordination of work among concurrent processes ... More

Simultaneous Learning of Trees and Representations for Extreme Classification and Density EstimationOct 14 2016Mar 02 2017We consider multi-class classification where the predictor has a hierarchical structure that allows for a very large number of labels both at train and test time. The predictive power of such models can heavily depend on the structure of the tree, and ... More

Simultaneous Learning of Trees and Representations for Extreme Classification, with Application to Language ModelingOct 14 2016This paper addresses the problem of multi-class classification with an extremely large number of classes, where the class predictor is learned jointly with the data representation, as is the case in language modeling problems. The predictor admits a hierarchical ... More

Differentially- and non-differentially-private random decision treesOct 26 2014Feb 05 2015We consider supervised learning with random decision trees, where the tree construction is completely random. The method is popularly used and works well in practice despite the simplicity of the setting, but its statistical mechanism is not yet well-understood. ... More

Entropy-SGD: Biasing Gradient Descent Into Wide ValleysNov 06 2016This paper proposes a new optimization algorithm called Entropy-SGD for training deep neural networks that is motivated by the local geometry of the energy landscape at solutions found by gradient descent. Local extrema with low generalization error have ... More

Entropy-SGD: Biasing Gradient Descent Into Wide ValleysNov 06 2016Dec 05 2016This paper proposes a new optimization algorithm called Entropy-SGD for training deep neural networks that is motivated by the local geometry of the energy landscape at solutions found by gradient descent. Local extrema with low generalization error have ... More

Entropy-SGD: Biasing Gradient Descent Into Wide ValleysNov 06 2016Nov 13 2016This paper proposes a new optimization algorithm called Entropy-SGD for training deep neural networks that is motivated by the local geometry of the energy landscape at solutions found by gradient descent. Local extrema with low generalization error have ... More

Binary embeddings with structured hashed projectionsNov 16 2015Jul 01 2016We consider the hashing mechanism for constructing binary embeddings, that involves pseudo-random projections followed by nonlinear (sign function) mappings. The pseudo-random projection is described by a matrix, where not all entries are independent ... More

VisualBackProp: visualizing CNNs for autonomous drivingNov 16 2016This paper proposes a new method, that we call VisualBackProp, for visualizing which sets of pixels of the input image contribute most to the predictions made by the convolutional neural network (CNN). The method heavily hinges on exploring the intuition ... More

Explaining How a Deep Neural Network Trained with End-to-End Learning Steers a CarApr 25 2017As part of a complete software stack for autonomous driving, NVIDIA has created a neural-network-based system, known as PilotNet, which outputs steering angles given images of the road ahead. PilotNet is trained using road images paired with the steering ... More

VisualBackProp: efficient visualization of CNNsNov 16 2016May 19 2017This paper proposes a new method, that we call VisualBackProp, for visualizing which sets of pixels of the input image contribute most to the predictions made by the convolutional neural network (CNN). The method heavily hinges on exploring the intuition ... More

The Loss Surfaces of Multilayer NetworksNov 30 2014Jan 21 2015We study the connection between the highly non-convex loss function of a simple model of the fully-connected feed-forward neural network and the Hamiltonian of the spherical spin-glass model under the assumptions of: i) variable independence, ii) redundancy ... More

Adversarial Learning-Based On-Line Anomaly Monitoring for Assured AutonomyNov 12 2018The paper proposes an on-line monitoring framework for continuous real-time safety/security in learning-based control systems (specifically application to a unmanned ground vehicle). We monitor validity of mappings from sensor inputs to actuator commands, ... More

Entropy-SGD: Biasing Gradient Descent Into Wide ValleysNov 06 2016Apr 21 2017This paper proposes a new optimization algorithm called Entropy-SGD for training deep neural networks that is motivated by the local geometry of the energy landscape. Local extrema with low generalization error have a large proportion of almost-zero eigenvalues ... More

A Deep Unsupervised Learning Approach Toward MTBI Identification Using Diffusion MRIFeb 08 2018Apr 11 2018Mild traumatic brain injury is a growing public health problem with an estimated incidence of over 1.7 million people annually in US. Diagnosis is based on clinical history and symptoms, and accurate, concrete measures of injury are lacking. This work ... More

Structured adaptive and random spinners for fast machine learning computationsOct 19 2016Nov 26 2016We consider an efficient computational framework for speeding up several machine learning algorithms with almost no loss of accuracy. The proposed framework relies on projections via structured matrices that we call Structured Spinners, which are formed ... More

A Deep Unsupervised Learning Approach Toward MTBI Identification Using Diffusion MRIFeb 08 2018Mild traumatic brain injury (mTBI) is a growing public health problem with an estimated incidence of one million people annually in US. Neurocognitive tests have been used to both assess the patient condition and to monitor the patient progress. This ... More

Structured adaptive and random spinners for fast machine learning computationsOct 19 2016Oct 28 2016We consider an efficient computational framework for speeding up several machine learning algorithms with almost no loss of accuracy. The proposed framework relies on projections via structured matrices that we call Structured Spinners, which are formed ... More

Structured adaptive and random spinners for fast machine learning computationsOct 19 2016We consider an efficient computational framework for speeding up several machine learning algorithms with almost no loss of accuracy. The proposed framework relies on projections via structured matrices that we call Structured Spinners, which are formed ... More

Beyond Backprop: Online Alternating Minimization with Auxiliary VariablesJun 24 2018Feb 01 2019We propose a novel online alternating minimization (AltMin) algorithm for training deep neural networks, provide theoretical convergence guarantees and demonstrate its advantages on several classification tasks as compared both to standard backpropagation ... More

Correlated radiative electron capture in ion-atom collisionsAug 30 2010Radiative double electron capture (RDEC) is a one-step process where two free (or quasi-free) target electrons are captured into a bound state of the projectile, e.g. into an empty K-shell, and the energy excess is released as a single photon. This process ... More

On the numbers of 1-factors and 1-factorizations of hypergraphsMar 28 2015Dec 14 2015A hypergraph $G=(X,W)$ is called $d$-uniform if each hyperedge $w$ is a set of $d$ vertices. A 1-factor of a hypergraph $G$ is a set of hyperedges such that every vertex of the hypergraph is incident to exactly one hyperedge from the set. A 1-factorization ... More

Lie Bialgebra Structures for Centrally Extended Two- Dimensional Galilei Algebra and their Lie-Poisson CounterpartsOct 23 1997Jan 16 1998All bialgebra structures for centrally extended Galilei algebra are classified. The corresponding Lie-Poisson structures on centrally extended Galilei group are found.

Iterated identities and iterational depth of groupsSep 21 2014Given word on $n$ letters, we study groups which satisfiy "iterated identity" $w$, meaning that for all $x_1, \dots, x_n$ there exists $m$ such that $m$-the iteration of $w$ of Engel type, applied to $x_1, \dots, x_n$, is equal to the identity. We define ... More

Modeling IR SED of AGN with Spitzer and Herschel dataJan 21 2013One of the remaining open issues in the context of the analysis of Active Galactic Nuclei (AGN) is the evidence that nuclear gravitational accretion is often accompanied by a concurrent starburst (SB) activity. What is, in this picture, the role played ... More

On Orbital variety closures in sl_n. III Geometric propertiesJul 25 2005This is the third paper in the series. Here we define a few combinatorial orders on Young tableaux. The first order is obtained from induced Duflo order by the extension with the help of Vogan T_{\alpha, \beta} procedure. We call it Duflo-Vogan order. ... More

The Finite Temperature Effective Potential for Local Composite OperatorsApr 04 1997The method of the effective action for the composite operators $\Phi^2(x)$ and $\Phi^4(x)$ is applied to the termodynamics of the scalar quantum field with $\lambda\Phi^4$ interaction. An expansion of the finite temperature effective potential in powers ... More

Goldstone Bosons in the Gaussian ApproximationAug 18 1995Aug 31 1995The O(N) symmetric scalar quantum field theory with \lambda\Phi^4 interaction is discussed in the Gaussian approximation. It is shown that the Goldstone theorem is fulfilled for arbitrary N.

Gaussian approximation to the condensation of the interacting Bose gasSep 29 2003The effective action formalism of quantum field theory is used to study the properties of the non-relativistic interacting Bose gas. The Gaussian approximation is formulated by calculating the effective action to the first order of the optimized expansion. ... More

Multi-particle States from the Effective Action for Local Composite Operators: Anharmonic OscillatorDec 15 1995Dec 19 1995The effective action for the local composite operator $\Phi^2(x)$ in the scalar quantum field theory with $\lambda\Phi^4$ interaction is obtained in the expansion in two-particle-point-irreducible (2PPI) diagrams up to five-loops. The effective potential ... More

Exploring the Universe with Metal-Poor StarsAug 23 2011The early chemical evolution of the Galaxy and the Universe is vital to our understanding of a host of astrophysical phenomena. Since the most metal-poor Galactic stars (with metallicities down to [Fe/H]\sim-5.5) are relics from the high-redshift Universe, ... More

An embedding resultDec 29 2013In unbounded subset $\Omega$ in $R^n$ we study the operator $u\rightarrow gu$ as an operator defined in the Sobolev space $W^{r,p}(\Omega)$ and which takes values in $L^p(\Omega)$. The functions $g$ belong to wider spaces of $L^p$ connected with the Morrey ... More

Exact Solutions to SupergravityJun 11 1996We find a general p-1-brane solution to supergravity coupled to a p+1-form field strength using the ``standard ansatz'' for the fields. In addition to the well-known elementary and solitonic p-1-brane solutions, which are the only ones preserving half ... More

String Solutions to SupergravityOct 23 1996We find the comlete solution to ten-dimensional supergravity coupled to a three-form field strength, given the ``standard ansatz" for the fields, and show that in addition to the well-known elementary and solitonic (heterotic) string solutions, one of ... More

A construction of a nonparametric quantum information manifoldNov 21 2005We present a construction of a Banach manifold on the set of faithful normal states of a von Neumann algebra, where the underlying Banach space is a quantum analogue of an Orlicz space. On the manifold, we introduce the exponential and mixture connections ... More

Teichmuller geodesics that do not have a limit in PMFOct 31 2005Nov 17 2010We construct a Teichmuller geodesic which does not have a limit on the Thurston boundary of the Teichmuller space.

Weakly Interacting, Dilute Bose Gases in 2DJun 01 2005Jun 27 2006This article surveys a number of theoretical problems and open questions in the field of two-dimensional dilute Bose gases with weak repulsive interactions. In contrast to three dimensions, in two dimensions the formation of long-range order is prohibited ... More

Classification of isoparametric hypersurfaces in spheres with $(g,m)=(6,1)$Mar 15 2015Aug 05 2015We classify isoparametric hypersurfaces in spheres with $(g,m)=(6,1)$ and thereby reprove a result of Dorfmeister and Neher.

Harmonic Self-maps of $\mbox{SU}(3)$Dec 22 2015By constructing solutions of a singular boundary value problem we prove the existence of a countably infinite family of harmonic self-maps of $\mbox{SU}(3)$ with non-trivial, i.e. $\neq 0,\pm 1$, Brouwer degree.

Compactifying the Space of Length Functions of a Right-angled Artin GroupOct 20 2015Culler and Morgan proved that the length function of a minimal action of a group on a tree completely determines the action. As a consequence the space of minimal actions of a free group on trees, up to scaling (also known as Outer Space), embeds in infinite ... More

Improving LHC searches for strong EW symmetry breaking resonancesMay 18 2015Sep 05 2016Composite Higgs models generically predict the existence of heavy spin-1 resonances with the same quantum numbers as electroweak gauge bosons. The effective lagrangian description of these resonances is presented, pointing out the origin of their interactions ... More

On the numbers of 1-factors and 1-factorizations of hypergraphsMar 28 2015Dec 04 2016A 1-factor of a hypergraph $G=(X,W)$ is a set of hyperedges such that every vertex of $G$ is incident to exactly one hyperedge from the set. A 1-factorization is a partition of all hyperedges of $G$ into disjoint 1-factors. The adjacency matrix of a $d$-uniform ... More

Symmetric waves are traveling waves for a shallow water equation for surface waves of moderate amplitudeFeb 01 2016Following a general principle introduced by Ehrnstr\"{o}m et.al. we prove that for an equation modeling the free surface evolution of moderate amplitude waves in shallow water, all symmetric waves are traveling waves.

Cyclic anamorphic cosmologyOct 10 2016Cyclic models of the universe have the advantage of avoiding initial conditions problems related to postulating any sort of beginning in time. To date, the only known viable examples of cyclic models have been ekpyrotic. In this paper, we show that the ... More

Transversals, plexes, and multiplexes in iterated quasigroupsSep 10 2017A $d$-ary quasigroup of order $n$ is a $d$-ary operation over a set of cardinality $n$ such that the Cayley table of the operation is a $d$-dimensional latin hypercube of the same order. Given a binary quasigroup $G$, the $d$-iterated quasigroup $G^{\left[d\right]}$ ... More

Representations and geometric structuresFeb 10 2016This note summarizes in an informal way some geometric properties of Anosov representations into the symplectic group, which were presented in a talk at the conference What is Next. The mathematical legacy of Bill Thurston, held in June 2014 in Cornell. ... More

Bounded Cohomology and GeometryJan 17 2005This work deals with relations between a bounded cohomological invariant and the geometry of Hermitian symmetric spaces of noncompact type. The invariant, obtained from the K\"ahler class, is used to define and characterize a special class of totally ... More

Kronecker limit formulas and scattering constants for Fermat curvesNov 04 2011Eisenstein series are real analytic functions which play a central role in spectral theory of the hyperbolic Laplacian. Kronecker limit formulas determine their connection to modular forms. The main result of this work is Theorem 7.2 in which a Kronecker ... More

Geometric construction of spinors in orthogonal modular categoriesOct 16 2002Oct 09 2003A geometric construction of Z_2-graded orthogonal modular categories is given. Their 0-graded parts coincide with categories previously obtained by Blanchet and the author from the category of tangles modulo the Kauffman skein relations. Quantum dimensions ... More

On the determinant of hexagonal grids $H_{k,n}$Aug 31 2013Feb 15 2014We analyse the problem of singularity of graphs for hexagonal grid graphs. We introduce methods for transforming weighted graph, which do not change the determinant of adjacency matrix. We use these methods to calculate the determinant of all hexagonal ... More

Generalised global supersolutions with mass control for systems with taxisJun 15 2018The existence of generalised global supersolutions with a control upon the total muss is established for a wide family of parabolic-parabolic chemotaxis systems and general integrable initial data in any space dimension. It is verified that as long as ... More

Lyapunov theorem for q-concave Banach spacesOct 17 2013Generalization of Lyapunov convexity theorem is proved for vector measure with values in Banach spaces with unconditional bases, which are q-concave for some $q<\infty.$

Woronowicz construction of compact quantum groups for functions on permutations. Classification result for N=3Jan 28 2014We provide a classification of compact quantum groups, which can be obtained by the Woronowicz construction, when the arrays used in the twisted determinant condition are extensions of functions on permutations. General properties of such quantum groups ... More

On $S_n$-invariant conformal blocks vector bundles of rank one on $\overline M_{0,n}$Apr 23 2014For any simple Lie algebra, a positive integer, and tuple of compatible weights, the conformal blocks bundle is a globally generated vector bundle on the moduli space of pointed rational curves. We classify all $S_n$-invariant vector bundles of conformal ... More

Ecology of galaxy stellar populations from optical spectroscopic surveysOct 12 2009The age and chemical composition of the stars in present-day galaxies carry important clues about their star formation processes. The latest generation of population synthesis models have allowed to derive age and stellar metallicity estimates for large ... More

Refined invariants and TQFT's from Homfly skein theoryJun 17 1998Jul 03 1998We work in the reduced SU(N,K) modular category as constructed recently by Blanchet. We define spin type and cohomological refinements of the Turaev-Viro invariants of closed oriented 3-manifolds and give a formula relating them to Blanchet's invariants. ... More

Rook numbers and the normal ordering problemFeb 23 2004Jul 15 2004For an element $w$ in the Weyl algebra generated by $D$ and $U$ with relation $DU=UD+1$, the normally ordered form is $w=\sum c_{i,j}U^iD^j$. We demonstrate that the normal order coefficients $c_{i,j}$ of a word $w$ are rook numbers on a Ferrers board. ... More

On orbital variety closures in sl(n). II. Descendants of a Richardson orbital varietyNov 26 2003For a semisimple Lie algebra g the orbit method attempts to assign representations of g to (coadjoint) orbits in g*. Orbital varieties are particular Lagrangian subvarieties of such orbits leading to highest weight representations of g. In sl(n) orbital ... More

Comparison of quantum binary experimentsOct 21 2011Jun 21 2012A quantum binary experiment consists of a pair of density operators on a finite dimensional Hilbert space. An experiment E is called \epsilon-deficient with respect to another experiment F if, up to \epsilon, its risk functions are not worse than the ... More

Affine connections, duality and divergences for a von Neumann algebraNov 05 2003On the predual of a von Neumann algebra, we define a differentiable manifold structure and affine connections by embeddings into non-commutative L_p-spaces. Using the geometry of uniformly convex Banach spaces and duality of the L_p and L_q spaces for ... More

Base norms and discrimination of generalized quantum channelsAug 19 2013We introduce and study norms in the space of hermitian operators, obtained from base norms in positively generated subspaces. These norms are closely related to discrimination of so-called generalized quantum channels, including quantum states, channels ... More

Stellar Archaeology -- Exploring the Universe with Metal-Poor StarsJun 11 2010The abundance patterns of the most metal-poor stars in the Galactic halo and small dwarf galaxies provide us with a wealth of information about the early Universe. In particular, these old survivors allow us to study the nature of the first stars and ... More

The Effective Action for Local Composite Operators $Φ^2(x)$ and $Φ^4(x)$Jun 13 1996The generating functionals for the local composite operators, $\Phi^2(x)$ and $\Phi^4(x)$, are used to study excitations in the scalar quantum field theory with $\lambda \Phi^4$ interaction. The effective action for the composite operators is obtained ... More

Dynamical Simulations with Smeared Link Staggered FermionsNov 04 2002One of the most serious problems of the staggered fermion lattice action is flavor symmetry violation. Smeared link staggered fermions can improve flavor symmetry by an order of magnitude relative to the standard thin link action. Over the last few years ... More

Topological Susceptibility on Dynamical Staggered Fermion ConfigurationsApr 30 2001The topological susceptibility is one of the few physical quantities that directly measure the properties of the QCD vacuum. Chiral perturbation theory predicts that in the small quark mass limit the topological susceptibility depends quadratically on ... More

New Results from the MINOS Experiment - EPS 2011 conference proceedingsJan 17 2012The MINOS experiment is a long-baseline neutrino experiment designed to study neutrino behaviour, in particular the phenomenon of neutrino oscillations. MINOS sends the NuMI neutrino beam through two detectors, a Near Detector 1 km downstream from the ... More

On partitions of the unit interval generated by Brocot sequencesDec 27 2005Dec 15 2007Let $ p_{i, n}, i=1,..., N(n)=2^{n-1} $ be the lengths of intervals between the neighboring fractions of Brocot sequence $ F_n $. We obtain an asymptotic formula for $\sigma_{\beta}(F_n)=\sum_{i=1}^{N(n)} p_{i, n}^{\beta} $,which improves known estimates. ... More

Spectral Stieltjes-Type Integration and Some ApplicationsNov 25 2005Mar 06 2011This paper presents Stieltjes-type integration for operator-valued functions with respect to spectral families. The relation between Riemann-Stieltjes integrals associated with some classes of spectral families including, in particular, those that arise ... More

Infinite families of harmonic self-maps of spheresJan 25 2015Oct 16 2015For each of the spheres $\mathbb{S}^{n}$, $n\geq 5$, we construct a new infinite family of harmonic self-maps, and prove that their members have Brouwer degree $\pm1$ or $\pm3$. These self-maps are obtained by solving a singular boundary value problem. ... More

Trace formulas for tuples of commuting contractionsSep 18 2013Sep 22 2013This paper extends the trace formulas of [5] with perturbations in normed ideals of $B(H)$ to multivariate functions of commuting contractions admitting a dilation to commuting normal contractions.

Multiple operator integrals and spectral shiftJul 02 2009Mar 06 2011Multiple scalar integral representations for traces of operator derivatives are obtained and applied in the proof of existence of the higher order spectral shift functions.

Higher order spectral shift, II. Unbounded caseJan 16 2009Jul 01 2009We construct higher order spectral shift functions, which represent the remainders of Taylor-type approximations for the value of a function at a perturbed self-adjoint operator by derivatives of the function at an initial unbounded operator. In the particular ... More

Rarefaction waves in nonlocal convection-diffusion equationsMar 29 2013Apr 16 2013We consider the "convection-diffussion" equation $u_t=J*u-u-uu_x,$ where $J$ is a probability density. We supplement this equation with step-like initial conditions and prove a convergence of corresponding solution towards a rarefaction wave, i.e. a unique ... More

Stochastic Volterra convolution with Lévy processNov 07 2004Nov 29 2004In the paper we study stochastic convolution appearing in Volterra equation driven by so called L\'evy process. By L\'evy process we mean a process with homogeneous independent increments, continuous in probability and cadlag.

Whittaker functions on metaplectic covers of GL(r)May 17 2016This paper establishes a combinatorial link between different approaches to constructing Whittaker functions on a metaplectic group over a non-archimedean local field. We prove a metaplectic analogue of Tokuyama's Theorem and give a crystal description ... More

Generating the Ideals Defining Unions of Schubert VarietiesMay 12 2014This note computes a Gr\"obner basis for the ideal defining a union of Schubert varieties. More precisely, it computes a Gr\"obner basis for unions of schemes given by northwest rank conditions on the space of all matrices of a fixed size. Schemes given ... More

Levi-Civita connections of flag manifoldsDec 05 2005For any flag manifold G/T we obtain an explicit expression of its Levi-Civita connection with respect to any invariant Riemannian metric.

Almost Kähler 4-dimensional Lie groups with $J$-invariant Ricci tensorAug 03 2003The aim of this paper is to determine left-invariant strictly almost K\"ahler structures on 4-dimensional Lie groups $(g, J, \Omega)$ such that the Ricci tensor is $J$-invariant.

Generalised supersolutions with mass control for the Keller-Segel system with logarithmic sensitivityApr 15 2018The existence of generalised global supersolutions with a control upon the total muss is established for the parabolic-parabolic Keller-Segel system with logarithmic sensitivity for any space dimension. It is verified that smooth supersolutions of this ... More

CLT for linear eigenvalue statistics for a tensor product version of sample covariance matricesFeb 27 2016Jan 26 2017For $k,m,n\in \mathbb{N}$, we consider $n^k\times n^k$ random matrices of the form $$ \mathcal{M}_{n,m,k}(\mathbf{y})=\sum_{\alpha=1}^m\tau_\alpha {Y_\alpha}Y_\alpha^T,\quad Y_\alpha=\mathbf{y}_\alpha^{(1)}\otimes...\otimes\mathbf{y}_\alpha^{(k)}, $$ ... More

Bayesian Approach to Handling Informative SamplingJan 27 2015In the case of informative sampling the sampling scheme explicitly or implicitly depends on the response variable. As a result, the sample distribution of response variable can- not be used for making inference about the population. In this research I ... More

The Malliavin derivative and compactness: application to a degenerate PDE-SDE couplingSep 06 2016Jun 29 2017Compactness is one of the most versatile tools in the analysis of nonlinear PDEs and systems. Usually, compactness is established by means of some embedding theorem between functional spaces. Such theorems, in turn, rely on appropriate estimates for a ... More

Stochastic Integral with respect to Cylindrical Wiener ProcessNov 21 2005This paper is devoted to a construction of the stochastic It\^o integral with respect to infinite dimensional cylindrical Wiener process. The construction given is an alternative one to that introduced by DaPrato and Zabczyk [3]. The connection of the ... More

Non-Discrete Complex Hyperbolic Triangle Groups of Type (m,m,infinity)Apr 30 2010In this note we prove that a complex hyperbolic triangle group of type (m,m,infinity), i.e. a group of isometries of the complex hyperbolic plane, generated by complex reflections in three complex geodesics meeting at angles Pi/m, Pi/m and 0, is not discrete ... More

Bifractional Brownian motion for $H>1$ and $2HK\le 1$Feb 25 2019Bifractional Brownian motion on $\mathbb{R}_+$ is a two parameter centered Gaussian process with covariance function: $$ R_{H,K} (t,s)=\frac 1{2^K}\left(\left(t^{2H}+s^{2H}\right)^K-\vert t-s\vert^{2HK}\right), \qquad s,t\ge 0. $$ This process has been ... More

Maximally informative ensembles for SIC-POVMs in dimension 3Apr 30 2014Nov 16 2014In order to find out for which initial states of the system the uncertainty of the measurement outcomes will be minimal, one can look for the minimizers of the Shannon entropy of the measurement. In case of group covariant measurements this question becomes ... More

Strong electroweak symmetry breaking (or, if no SM Higgs, then what?)Jun 08 2012While the LHC takes on the challenge of experimentally exploring the electroweak symmetry breaking sector, it is not only interesting but also crucial to explore alternatives to the Standard Model scenario with an elementary scalar Higgs boson. The idea ... More

Two-weight norm inequalities for potential type and maximal operators in a metric spaceMay 13 2011Dec 31 2012We characterize two-weight norm inequalities for potential type integral operators in terms of Sawyer-type testing conditions. Our result is stated in a space of homogeneous type with no additional geometric assumptions, such as group structure or non-empty ... More

Gauss diagrams of 3-manifoldsAug 06 2003We present a simple combinatorial method to encode 3-dimensional manifolds, based on their Heegaard diagrams. The notion of a Gauss diagram of a 3-manifold is introduced. We check the conditions for a Gauss diagram to represent a closed manifold and a ... More

A counterpart of the Verlinde algebra for the small quantum groupJul 19 2001May 07 2002Let $\bar{Pr}$ denote the ideal spanned by the characters of projective modules in the Grothendieck ring of the category of finite dimensional modules over the small quantum group $u_l$. We show that $\bar{Pr}$ admits a description completely parallel ... More

B-orbits of nilpotent order 2 and link patternsMar 13 2007Sep 03 2008In this paper we describe geometry of orbits of upper triangular matrices of nilpotent order 2 under conjugation by the group of upper triangular invertible matrices in terms of link patterns. Further we apply this description to the computations of the ... More