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A generalized Sard theorem on real closed fieldsMar 14 2015We work with semi-algebraic functions on arbitrary real closed fields. We generalize the notion of critical values and prove a Sard type theorem in our framework.

Geometry of polynomial mappings at infinity via intersection homologyJul 14 2010For given polynomial map $F:\C^2\to\C^2$ with nonvanishing jacobian we associate a variety whose homology or intersection homology describes the geometry of singularities at infinity of this map.

Efroymson's approximation theorem for globally subanalytic functionsMay 14 2019Efroymson's approximation theorem asserts that if $f$ is a $\mathcal{C}^0$ semialgebraic mapping on a $\mathcal{C}^\infty$ semialgebraic submanifold $M$ of $\mathbb{R}^n$ and if $\varepsilon:M\to \mathbb{R}$ is a positive continuous semialgebraic function ... More

On a singular variety associated to a polynomial mappingDec 28 2012In the paper "Geometry of polynomial mapping at infinity via intersection homology" the second and third authors associated to a given polynomial mapping $F : \C^2 \to \C^2$ with nonvanishing jacobian a variety whose homology or intersection homology ... More

The Mayer-Vietoris Sequence for Graphs of Groups, Property (T), and the First $\ell^2$-Betti NumberDec 11 2014Sep 12 2016We explore the Mayer-Vietoris sequence developed by Chiswell for the fundamental group of a graph of groups when vertex groups satisfy some vanishing assumption on the first cohomology (e.g. property (T), or vanishing of the first $\ell^2$-Betti number). ... More

Unbounded symmetric operators in $K$-homology and the Baum-Connes ConjectureDec 18 2004Using the unbounded picture of analytical K-homology, we associate a well-defined K-homology class to an unbounded symmetric operator satisfying certain mild technical conditions. We also establish an ``addition formula'' for the Dirac operator on the ... More

$L^1$ cohomology of bounded subanalytic manifoldsNov 09 2010We prove some de Rham theorems on bounded subanalytic submanifolds of $\R^n$ (not necessarily compact). We show that the $L^1$ cohomology of such a submanifold is isomorphic to its singular homology. In the case where the closure of the underlying manifold ... More

$L^\infty$ cohomology is intersection cohomologyDec 03 2009Jul 06 2012Let $X$ be any subanalytic compact pseudomanifold. We show a De Rham theorem for $L^\infty$ forms. We prove that the cohomology of $L^\infty$ forms is isomorphic to intersection cohomology in the maximal perversity.

More on the New Large $D$ Limit of Matrix ModelsOct 19 2017In this paper, we extend the recent analysis of the new large $D$ limit of matrix models to the cases where the action contains arbitrary multi-trace interaction terms as well as to arbitrary correlation functions. We discuss both the cases of complex ... More

Le problème de Kadison-Singer (The Kadison-Singer problem)Sep 20 2014In 1959, R.V. Kadison and I.M. Singer asked whether each pure state of the algebra of bounded diagonal operators on $\ell^2$, admits a unique state extension to $B(\ell^2)$. The positive answer was given in June 2013 by A. Marcus, D. Spielman and N. Srivastava, ... More

Toward an Anthropocentric Approach for Hybrid Control Architectures: Case of a Furniture FactoryDec 14 2018Typology of goods and services' consumption has changed. In order to adapt to this change, it is relevant for a company to turn toward new ways of production and management. Slowly, the concept of industry 4.0 starts to set up in manufacturing companies. ... More

A Lefschetz duality intersection homologyDec 13 2010Apr 20 2011We prove a Lefschetz duality result for intersection homology. Usually, this result applies to pseudomanifolds with boundary which are assumed to have a "collared neighborhood of their boundary". Our duality does not need this assumption and is a generalization ... More

The Baum-Connes conjecture: an extended surveyMay 24 2019We present a history of the Baum-Connes conjecture, the methods involved, the current status, and the mathematics it generated.

Vanishing homologyJan 14 2008In this paper we introduce a new homology theory devoted to the study of families such as semi-algebraic or subanalytic families and in general to any family definable in an o-minimal structure (such as Denjoy-Carleman definable or $ln-exp$ definable ... More

The Howe-Moore property for real and p-adic groupsMar 07 2010We consider in this paper a relative version of the Howe-Moore Property, about vanishing at infinity of coefficients of unitary representations. We characterize this property in terms of ergodic measure-preserving actions. We also characterize, for linear ... More

Locally compact groups with every isometric action bounded or properMay 02 2017A locally compact group $G$ has property PL if every isometric $G$-action either has bounded orbits or is (metrically) proper. For $p>1$, say that $G$ has property $BP_{L^p}$ if the same alternative holds for the smaller class of affine isometric actions ... More

On 1-cocycles induced by a positive definite function on a locally compact abelian groupMar 18 2013For $\varphi$ a normalized positive definite function on a locally compact abelian group $G$, we consider on the one hand the unitary representation $\pi_\varphi$ associated to $\varphi$ by the GNS construction, on the other hand the probability measure ... More

Expanders and box spacesSep 04 2015We consider box spaces of finitely generated, residually finite groups $G$, and try to distinguish them up to coarse equivalence. We show that, for $n\geq 2$, the group $SL_n(\mathbb{Z})$ has a continuum of box spaces which are pairwise non-coarsely equivalent ... More

Anomalous Hall and Nernst effects in a two-dimensional electron gas with an anisotropic cubic Rashba spin-orbit interactionJun 28 2019The anomalous Hall and Nernst effects are considered theoretically within Matsubara-Green's function formalism. The effective Hamiltonian of a magnetized two-dimensional electron gas with cubic Rashba spin-orbit interaction may describe transport properties ... More

Whitney stratifications and the continuity of local Lipschitz Killing curvaturesJul 05 2015We prove that local Lipschitz Killing curvatures of definable sets in a polynomially bounded o-minimal structure are continuous along strata of Whitney stratifications and locally Lipschitz if the stratifications are (w)- regular.

Wreath products with the integers, proper actions and Hilbert space compressionMar 20 2006Mar 29 2006We prove that the properties of acting metrically properly on some space with walls or some CAT(0) cube complex are closed by taking the wreath product with \Z. We also give a lower bound for the (equivariant) Hilbert space compression of H\wr\Z in terms ... More

De Rham Theorem for L^\infty forms and homology on singular spacesFeb 22 2010We introduce smooth L^\infty differential forms on a singular (semialgebraic) set X in R^n. Roughly speaking, a smooth L^\infty differential form is a certain class of equivalence of 'stratified forms', that is, a collection of smooth forms on disjoint ... More

Flat currents on definable pseudomanifoldsOct 05 2016We show that the cohomology of flat currents on definable pseudomanifolds in polynomially bounded o-minimal structures is isomorphic to its intersection cohomology in the top perversity.

Spectral element modeling of three dimensional wave propagation in a self-gravitating Earth with an arbitrarily stratified outer coreAug 27 2003This paper deals with the spectral element modeling of seismic wave propagation at the global scale. Two aspects relevant to low-frequency studies are particularly emphasized. First, the method is generalized beyond the Cowling approximation in order ... More

K-theory for the $C^*$-algebras of the solvable Baumslag-Solitar groupsApr 19 2016We provide a new computation of the K-theory of the group $C^*$-algebra of the solvable Baumslag-Solitar group $BS(1,n)\;(n\neq 1)$; our computation is based on the Pimsner-Voiculescu 6-terms exact sequence, by viewing $BS(1,n)$ as a semi-direct product ... More

On equivariant embeddings of generalized Baumslag-Solitar groupsDec 30 2012Let G be a group acting cocompactly without inversion on a tree X, with all vertex and edge stabilizers isomorphic to the same free abelian group Z^n. We prove that G has the Haagerup Property if and only if G is weakly amenable, and we give a necessary ... More

Reduced 1-cohomology and relative property (T)Dec 06 2009Shalom characterized property (T) in terms of the vanishing of all reduced first cohomology. We characterize group pairs having the property that the restriction map on all first reduced cohomology vanishes. We show that, in a strong sense, this is inequivalent ... More

On the local geometry of definably stratified setsJan 18 2017We prove that a theorem of Pawlucki, showing that Whitney regularity for a subanalytic set with a smooth singular locus of codimension one implies the set is a finite union of differentiable manifolds with boundary, applies to definable sets in polynomially ... 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

Towards an exact adaptive algorithm for the determinant of a rational matrixMay 31 2007In this paper we propose several strategies for the exact computation of the determinant of a rational matrix. First, we use the Chinese Remaindering Theorem and the rational reconstruction to recover the rational determinant from its modular images. ... 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.

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

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

B0943+10: low-frequency study of subpulse periodicity in the Bright mode with LOFAROct 16 2017We utilise broadband sensitive LOFAR observations in 25-80 MHz frequency range to study the single-pulse emission properties of the mode-switching pulsar PSR B0943+10. We review the derivation of magnetospheric geometry, originally based on low-frequency ... More

Rényi relative entropies and noncommutative $L_p$-spacesSep 27 2016Jun 30 2017We propose an extension of the sandwiched R\'enyi relative $\alpha$-entropy to normal positive functionals on arbitrary von Neumann algebras, for the values $\alpha>1$. For this, we use Kosaki's definition of noncommutative $L_p$-spaces with respect to ... More

Positiveness of the permanent of 4-dimensional polystochastic matrices of order 4Jan 31 2018A nonnegative multidimensional matrix is called polystochastic if the sum of its entries over each line is equal to one. We prove that the permanent of every $4$-dimensional polystochastic matrix of order $4$ is positive.

Torsion and Linking number for a surface diffeomorphismJan 23 2018For a $\mathcal{C}^1$ diffeomorphism $f:\mathbb{R}^2\rightarrow\mathbb{R}^2$ isotopic to the identity, we prove that for any value $l\in\mathbb{R}$ of the linking number at finite time of the orbits of two points there exists at least a point whose torsion ... More

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.

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

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

Generalised global supersolutions with mass control for systems with taxisJun 15 2018Mar 27 2019The 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

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

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

A minimal scale invariant axion solution to the strong CP-problemMay 30 2017Dec 07 2017We present a scale invariant extension of the Standard model allowing for the Kim-Shifman-Vainstein-Zakharov (KSVZ) axion solution of the strong CP problem in QCD. We add the minimal number of new particles and show that the Peccei-Quinn scalar might ... More

Ranks and Symmetric Ranks of Cubic SurfacesJan 16 2018We study cubic surfaces as symmetric tensors of format $4 \times 4 \times 4$. We consider the non-symmetric tensor rank and the symmetric Waring rank of cubic surfaces, and show that the two notions coincide over the complex numbers. The corresponding ... 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

Generalised global supersolutions with mass control for systems with taxisJun 15 2018Apr 10 2019The 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

On quantum quasi-relative entropySep 30 2018Jan 27 2019We consider a quantum quasi-relative entropy $S_f^K$ for an operator $K$ and an operator convex function $f$. We show how to obtain the error bounds for the monotonicity and joint convexity inequalities from the recent results for the $f$-divergences ... More

RG Smoothing Algorithm Which Makes Data CompressionJun 05 2018I describe a new method for smoothing a one-dimensional curve in Euclidian space with an arbitrary number of dimensions. The basic idea is borrowed from renormalization group theory which previously was applied to biological macromolecules. There are ... More

A Riemann-Hilbert problem for uncoupled BPS structuresFeb 21 2018May 22 2019We study the Riemann-Hilbert problem attached to an uncoupled BPS structure proposed by Bridgeland in "Riemann-Hilbert problems from Donaldson-Thomas theory". We show that it has "essentially" unique meromorphic solutions given by a product of Gamma functions. ... More

Contribution of Cosmic Rays from Sources with a Monoenergetic Proton Spectrum to the Extragalactic Diffuse Gamma-Ray EmissionDec 30 2018The extragalactic sources of ultra-high-energy (E > 4x10^19 eV) cosmic rays that make a small contribution to the flux of particles recorded by ground-based arrays are discussed. We show that cosmic rays from such sources can produce a noticeable diffuse ... 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.

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

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

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

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

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

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

Note about Stiefel-Whitney classes on real Bott manifoldsAug 24 2018Real Bott manifolds is a class of flat manifolds with holonomy group $\mathbb Z_2^k$ of diagonal type. In this paper we want to show how we can compute even Stiefel - Whitney classes on real Bott manifolds. This paper is an answer to the question of professor ... More

Quelques méthodes pour les mots sturmiensJan 07 2019May 13 2019In this book chapter, written in French, we consider the classical family of Sturmian words, defined as the aperiodic infinite words containing only $n+1$ factors of a length $n$, which is the minimal possible value. We will discuss several techniques ... 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

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

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

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

Entanglement rates for bipartite open systemsMay 03 2015Aug 10 2015We provide upper bound on the maximal rate at which irreversible quantum dynamics can generate entanglement in a bipartite system. The generator of irreversible dynamics consists of a Hamiltonian and dissipative terms in Lindblad form. The relative entropy ... More

Decomposing almost complete graphs by random treesDec 01 2015Dec 07 2015An old conjecture of Ringel states that every tree with $m$ edges decomposes the complete graph $K_{2m+1}$. The best known lower bound for the order of a complete graph which admits a decomposition by every given tree with $m$ edges is $O(m^3)$. We show ... More

Comparison of quantum channels and statistical experimentsDec 22 2015Apr 24 2016For a pair of quantum channels with the same input space, we show that the possibility of approximation of one channel by post-processings of the other channel can be characterized by comparing the success probabilities for the two ensembles obtained ... More

Improved gradient flow for step scaling function and scale settingJan 30 2015The gradient flow renormalized coupling offers a simple and relatively inexpensive way to calculate the step scaling function and the lattice scale, but both applications can be hindered by large lattice artifacts. Recently we introduced an empirical ... More

Non-classical features in general probabilistic theoriesMay 22 2017Jan 23 2018We study incompatibility of measurements and its relation to steering and nonlocality in finite dimensional general probabilistic theories (GPT). The basic idea is to represent finite collections of measurements as affine maps of a state space into a ... More

CoVaR-based portfolio selectionMar 04 2017We consider the portfolio optimization with risk measured by conditional value-at-risk, based on the stress event of chosen asset being equal to the opposite of its value-at-risk level, under the normality assumption. Solvability conditions are given ... 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.

The culmination of an inverse cascade: mean flow and fluctuationsOct 25 2017Feb 01 2018Two dimensional turbulence has a remarkable tendency to self-organize into large, coherent structures, forming a mean flow. The purpose of this paper is to elucidate how these structures are sustained, and what determines them and the fluctuations around ... More

Development of novel plastic scintillators based on polyvinyltoluene for the hybrid J-PET/MR tomographOct 23 2017A novel plastic scintillator, referred to as J-PET scintillator, has been developed for the application in the digital positron emission tomography (PET). The novelty of the concept lies in application of the 2-(4-styrylphenyl)benzoxazole as a wavelength ... More

Space-time slicing in Horndeski theories and its implications for non-singular bouncing solutionsOct 16 2017Jan 27 2018In this paper, we show how the proper choice of gauge is critical in analyzing the stability of non-singular cosmological bounce solutions based on Horndeski theories. We show that it is possible to construct non-singular cosmological bounce solutions ... 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

Recent results from the ARIANNA neutrino experimentSep 23 2016The ARIANNA experiment is currently taking data in its pilot-phase on the Ross ice-shelf. Fully autonomous stations measure radio signals in the frequency range from 100 MHz to 1 GHz. The seven station HRA was completed in December 2014, and augmented ... 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

A Riemann-Hilbert problem for uncoupled BPS structuresFeb 21 2018We study the Riemann-Hilbert problem attached to an uncoupled BPS structure proposed by Bridgeland in [3]. We show that it has "essentially" unique meromorphic solutions given by a product of Gamma functions. We reconstruct the corresponding connection. ... More

Transversals in completely reducible multiary quasigroups and in multiary quasigroups of order 4Dec 06 2016Sep 11 2017An $n$-ary quasigroup $f$ of order $q$ is an $n$-ary operation over a set of cardinality $q$ such that the Cayley table of the operation is an $n$-dimensional latin hypercube of order $q$. A transversal in a quasigroup $f$ (or in the corresponding latin ... 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.