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A Novel Landau-de Gennes Model with Quartic Elastic TermsJun 21 2019Within the framework of the generalized Landau-de Gennes theory, we identify a $Q$-tensor-based energy that reduces to the four-constant Oseen-Frank energy when it is considered over orientable uniaxial nematic states. Although the commonly considered ... More

Polygonization of carbon nanotubesNov 12 2007We use a multiscale procedure to derive a simple continuum model of multiwalled carbon nanotubes that takes into account both strong covalent bonds within graphene layers and weak bonds between atoms in different layers. The model predicts polygonization ... More

On Minimizers of the Landau-de Gennes Energy Functional on Planar DomainsJul 16 2013Mar 27 2014We study tensor-valued minimizers of the Landau-de Gennes energy functional on a simply-connected planar domain $\Omega$ with non-contractible boundary data. Here the tensorial field represents the second moment of a local orientational distribution of ... More

Two-parametric $δ'$-interactions: approximation by Schrödinger operators with localized rank-two perturbationsJan 29 2018Apr 01 2018We construct a norm resolvent approximation to the family of point interactions $f(+0)=\alpha f(-0)+\beta f'(-0)$, $f'(+0)=\alpha^{-1}f'(-0)$ by Schr\"odinger operators with localized rank-two perturbations coupled with short range potentials. In particular, ... More

On coupling constant thresholds in one dimensionMay 26 2019The threshold behaviour of negative eigenvalues for Schr\"{o}dinger operators of the type $$ H_\lambda=-\frac{d^2}{dx^2}+U(x)+\lambda\alpha_\lambda V(\alpha_\lambda x) $$ is considered. The potentials $U$ and $V$ are real-valued bounded functions of compact ... More

Dimension reduction for the Landau-de Gennes model in planar nematic thin filmsJan 29 2015May 22 2015We use the method of $\Gamma$-convergence to study the behavior of the Landau-de Gennes model for a nematic liquid crystalline film in the limit of vanishing thickness. In this asymptotic regime, surface energy plays a greater role and we take particular ... More

Dimension reduction for the Landau-de Gennes model on curved nematic thin filmsNov 09 2016We use the method of $\Gamma$-convergence to study the behavior of the Landau-de Gennes model for a nematic liquid crystalline film attached to a general fixed surface in the limit of vanishing thickness. This paper generalizes the approach that we used ... More

Thin Film Liquid Crystals with Oblique Anchoring and BoojumsJul 10 2019We study a two-dimensional variational problem which arises as a thin-film limit of the Landau-de Gennes energy of nematic liquid crystals. We impose an oblique angle condition for the nematic director on the boundary, via boundary penalization (weak ... More

A Discrete-to-Continuum Model of Weakly Interacting Incommensurate ChainsApr 28 2017Aug 22 2017In this paper we use a formal discrete-to-continuum procedure to derive a continuum variational model for two chains of atoms with slightly incommensurate lattices. The chains represent a cross-section of a three-dimensional system consisting of a graphene ... More

Dimension reduction for the Landau-de Gennes model on curved nematic thin filmsNov 09 2016Apr 15 2017We use the method of $\Gamma$-convergence to study the behavior of the Landau-de Gennes model for a nematic liquid crystalline film attached to a general fixed surface in the limit of vanishing thickness. This paper generalizes the approach that we used ... More

Asymptotic analysis of vibrating system containing stiff-heavy and flexible-light partsDec 05 2007A model of strongly inhomogeneous medium with simultaneous perturbation of rigidity and mass density is studied. The medium has strongly contrasting physical characteristics in two parts with the ratio of rigidities being proportional to a small parameter ... More

Low and high frequency approximations to eigenvibrations of string with double contrastsApr 16 2008Sep 13 2009We study eigenvibrations for inhomogeneous string consisting of two parts with strongly contrasting stiffness and mass density. In this work we treat a critical case for the high frequency approximations, namely the case when the order of mass density ... More

Capacity of a multiply-connected domain and nonexistence of Ginzburg-Landau minimizers with prescribed degrees on the boundaryJan 01 2006Apr 21 2006Suppose that $\omega\subset\Omega\subset R^2$. In the annular domain $A=\Omega\setminus\bar\omega$ we consider the class $J$ of complex valued maps having degree 1 on $\partial \Omega$ and on $\partial\omega$. It was conjectured by Berlyand and Mironescu ... More

Approximating points of a Banach space by points of an operator imageJan 30 2019Answering one problem that has its origins in quantum mechanics, we prove that for any sequence $(A_n)_{n\in\mathbb N}$ of convex nowhere dense sets in a Banach space $X$ and any sequence $(\varepsilon_n)_{n=1}^\infty$ of positive real numbers with $\lim_{n\to\infty}\varepsilon_n=0$, ... More

A Model Problem for Nematic-Isotropic Transitions with Highly Disparate Elastic ConstantsNov 30 2018We analyze a model problem based on highly disparate elastic constants that we propose in order to understand corners and cusps that form on the boundary between the nematic and isotropic phases in a liquid crystal. For a bounded planar domain $\Omega$ ... More

Euler elastica as a $Γ$-Limit of discrete bending energies of one-dimensional chains of atomsApr 26 2016This work is motivated by discrete-to-continuum modeling of the mechanics of a graphene sheet, which is a single-atom thick macromolecule of carbon atoms covalently bonded to form a hexagonal lattice. The strong covalent bonding makes the sheet essentially ... More

A Discrete-to-Continuum Model of Weakly Interacting Incommensurate Two-Dimensional LatticesAug 03 2017In this paper we propose a continuum variational model for a two-dimensional deformable lattice of atoms interacting with a two-dimensional rigid lattice. The two lattices have slightly different lattice parameters and there is a small relative rotation ... More

Effective models for nematic liquid crystals composites with ferromagnetic inclusionsJan 16 2013Molecules of a nematic liquid crystal respond to an applied magnetic field by reorienting themselves in the direction of the field. Since the dielectric anisotropy of a nematic is small, it takes relatively large fields to elicit a significant liquid ... More

Existence of superconducting solutions for a reduced Ginzburg-Landau model in the presence of strong electric currentsNov 08 2016Jan 31 2019In this work we consider a reduced Ginzburg-Landau model in which the magnetic field is neglected and the magnitude of the current density is significantly stronger than that considered in a recent work by the same authors. We prove the existence of a ... More

Radially symmetric minimizers for a $p$-Ginzburg Landau type energy in $\R^2$Nov 10 2010Dec 30 2010We consider the minimization of a p-Ginzburg-Landau energy functional over the class of radially symmetric functions of degree one. We prove the existence of a unique minimizer in this class, and show that its modulus is monotone increasing and concave. ... More

Existence of superconducting solutions for a reduced {G}inzburg-{L}andau model in the presence of strong electric currentsNov 08 2016In this work we consider a reduced Ginzburg-Landau model in which the magnetic field is neglected and the magnitude of the current density is significantly stronger than that considered in a recent work by the same authors. We prove the existence of a ... More

Modeling of nematic electrolyte and nonlinear electroosmosisJan 11 2016Jun 06 2016We derive a mathematical model of a nematic electrolyte based on the Leslie-Ericksen theory of liquid crystal flow. Our goal is to investigate the nonlinear electrokinetic effects that occur because the nematic matrix is anisotropic, in particular, transport ... More

A non-traditional view on the modeling of nematic disclination dynamicsMar 06 2016Nonsingular disclination dynamics in a uniaxial nematic liquid crystal is modeled within a mathematical framework where the kinematics is a direct extension of the classical way of identifying these line defects with singularities of a unit vector field ... More

Existence and stability of superconducting solutions for the Ginzburg-Landau equations in the presence of weak electric currentsSep 07 2014For a reduced Ginzburg-Landau model in which the magnetic field is neglected, we prove, for weak electric currents, the existence of a steady-state solution in a vicinity of the purely superconducting state. We further show that this solution is linearly ... More

Solvable models for the Schrodinger operators with $δ'$-like potentialsSep 05 2009Jun 07 2011We turn back to the well known problem of interpretation of the Schrodinger operator with the pseudopotential being the first derivative of the Dirac function. We show that the problem in its conventional formulation contains hidden parameters and the ... More

Phase Transitions in Nematics: Textures with Tactoids and DisclinationsFeb 17 2019We demonstrate that a first order isotropic-to-nematic phase transition in liquid crystals can be succesfully modeled within the generalized Landau-de Gennes theory by selecting an appropriate combination of elastic constants. The numerical simulations ... More

Numerical analysis of the vertex models for simulating grain boundary networksOct 21 2014Feb 20 2015Polycrystalline materials undergoing coarsening can be represented as evolving networks of grain boundaries, whose statistical characteristics determine macroscopic materials properties. The process of formation of various statistical distributions is ... More

Strongly nonlinear asymptotic model of cellular instabilities in premixed flames with stepwise ignition temperature kineticsDec 20 2016Mar 31 2017In this paper we consider ignition-temperature, first-order reaction model of thermo-diffusive combustion that describes dynamics of thick flames arising in a theory of combustion of hydrogen-oxygen and ethylene-oxygen mixtures. These flames often assume ... More

Electro-osmosis in nematic liquid crystalsApr 05 2016Jun 15 2016We derive a mathematical model of a nematic electrolyte based on a variational formulation of nematodynamics. Extending our previous work, we consider a general setup which incorporates dielectric anisotropy of the liquid-crystalline matrix and the full ... More

Some remarks on 1D Schrödinger operators with localized magnetic and electric potentialsNov 17 2018One-dimensional Schr\"odinger operators with singular perturbed magnetic and electric potentials are considered. We study the strong resolvent convergence of two families of the operators with potentials shrinking to a point. Localized $\delta$-like magnetic ... More

1D Schrödinger operators with short range interactions: two-scale regularization of distributional potentialsFeb 21 2012Oct 23 2012For real bounded functions \Phi and \Psi of compact support, we prove the norm resolvent convergence, as \epsilon and \nu tend to 0, of a family of one-dimensional Schroedinger operators on the line of the form S_{\epsilon, \nu}= -D^2+\alpha\epsilon^{-2}\Phi(\epsilon^{-1}x)+\beta\nu^{-1}\Psi(\nu^{-1}x), ... More

Schroedinger operators with singularly scaled magnetic and electric potentialsJun 09 2012Sep 02 2013The norm resolvent convergence of a family of one-dimensional Schroedinger operators with singular magnetic and electric potentials of small support is studied.

Q-tensor model for electrokinetics in nematic liquid crystalsDec 11 2016Apr 15 2017We use a variational principle to derive a mathematical model for a nematic electrolyte in which the liquid crystalline component is described in terms of a second-rank order tensor. The model extends the previously developed director-based theory and ... More

Schrödinger operators with Coulomb-like and $δ'$-like potentialsJan 22 2019We study the convergence of Schr\"odinger operators $$ H_\varepsilon= -\frac{d^2}{dx^2}+Q_\varepsilon(x)+\varepsilon^{-2}U(\varepsilon^{-1}x) +\varepsilon^{-1}V(\varepsilon^{-1}x) $$ as $\varepsilon\to 0$, where $Q_\varepsilon$ is a regularization of ... More

Schroedinger operators with (αδ'+βδ)-like potentials: norm resolvent convergence and solvable modelsJan 12 2012Jan 25 2012For real functions \Phi and \Psi that are integrable and compactly supported, we prove the norm resolvent convergence, as \epsilon\ goes to 0, of a family S(\epsilon) of one-dimensional Schroedinger operators on the line of the form S(\epsilon)= -D^2 ... More

Schrödinger operators with singular rank-two perturbations and point interactionsApr 01 2018Jun 30 2018Norm resolvent approximation for a wide class of point interactions in one dimension is constructed. To analyse the limit behaviour of Schr\"odinger operators with localized singular rank-two perturbations coupled with {\delta}-like potentials as the ... More

Schrödinger operators with Coulomb-like potentialsJan 22 2019Apr 07 2019We study the convergence of 1D Schr\"odinger ope\-rators $H_\varepsilon$ with the potentials which are regularizations of a class of pseudo-potentials having in particular the form $$ \alpha \delta'(x)+\beta \delta(x)+\gamma/|x|\quad\text{or}\quad \alpha ... More

Macroscopic two-state systems in trapped atomic condensatesSep 09 2010We consider a macroscopic two-sate system based on persistent current states of a Bose-Einstein condensate (BEC) of interacting neutral atoms confined in a ring with a weak Josephson link. We demonstrate that macroscopic superpositions of different BEC ... More

Quantum Nucleation and Macroscopic Quantum Tunneling in Cold-Atom Boson-Fermion MixturesOct 17 2008Kinetics of phase separation transition in boson-fermion cold atom mixtures is investigated. We identify the parameters at which the transition is governed by quantum nucleation mechanism, responsible for the formation of critical nuclei of a stable phase. ... More

Metastable states and macroscopic quantum tunneling in a cold atom Josephson ringSep 18 2009We study macroscopic properties of a system of weakly interacting neutral bosons confined in a ring-shaped potential with a Josephson junction. We derive an effective low energy action for this system and evaluate its properties. In particular we find ... More

Coherent phase slips in superconducting nanoringsJul 15 2011We study quantum fluctuations of persistent current in a small superconducting ring. Based on a microscopic model of the ring we argue that under certain conditions such ring will exhibit coherent quantum phase slips, similar to those in a flux qubit. ... More

Kinetics of the Phase Separation Transition in Cold-Atom Boson-Fermion MixturesDec 04 2007Apr 16 2008We study the kinetics of the first order phase separation transition in boson-fermion cold-atom mixtures. At sufficiently low temperatures such a transition is driven by quantum fluctuations responsible for the formation of critical nuclei of a stable ... More

Cold Atom QubitsMay 29 2010Dec 20 2010We discuss a laser-trapped cold-atom superfluid qubit system. Each qubit is proposed as a macroscopic two-state system based on a set of Bose-Einstein condensate (BEC) currents circulating in a ring, cut with a Josephson barrier. We review the effective ... More

Singularly perturbed hyperbolic problems on metric graphs: asymptotics of solutionsOct 20 2016We are interested in evolution phenomena on star-like networks composed of several branches which vary considerably in physical properties. The initial boundary value problem for singularly perturbed hyperbolic differential equation on a metric graph ... More

Complete WKB asymptotics of high frequency vibrations in a stiff problemOct 01 2008Asymptotic behaviour of eigenvalues and eigenfunctions of a stiff problem is described in the case of the fourth-order ordinary differential operator. Considering the stiffness coefficient that depends on a small parameter epsilon and vanishes as epsilon ... More

Quantum Money with Classical VerificationSep 02 2011Mar 15 2012We propose and construct a quantum money scheme that allows verification through classical communication with a bank. This is the first demonstration that a secure quantum money scheme exists that does not require quantum communication for coin verification. ... More

A Note on Shared Randomness and Shared Entanglement in CommunicationMay 12 2005Aug 06 2005We consider several models of 1-round classical and quantum communication, some of these models have not been defined before. We "almost separate" the models of simultaneous quantum message passing with shared entanglement and the model of simultaneous ... More

Instabilities of dispersion-managed solitons in the normal dispersion regimeMar 13 2000Dispersion-managed solitons are reviewed within a Gaussian variational approximation and an integral evolution model. In the normal regime of the dispersion map (when the averaged path dispersion is negative), there are two solitons of different pulse ... More

Translationally invariant nonlinear Schrodinger latticesMar 10 2006Persistence of stationary and traveling single-humped localized solutions in the spatial discretizations of the nonlinear Schrodinger (NLS) equation is addressed. The discrete NLS equation with the most general cubic polynomial function is considered. ... More

Free energy in the Potts spin glassDec 01 2015Dec 28 2015We study the Potts spin glass model, which generalizes the Sherrington-Kirkpatrick model to the case when spins take more than two values but their interactions are counted only if the spins are equal. We obtain the analogue of the Parisi variational ... More

Recombination formulae for the spectrum of curve singularities and some applicationsMar 23 2014May 16 2014We obtain some recombination formulae for the spectra of (complex, reduced) plane curve singularities. As an application we prove: a generalization of Durfee's bound; a generalization of Givental's bound; the multiplicity of the curve singularity is determined ... More

QR-submanifolds and Riemannian metrics with $G_2$ holonomyApr 26 2011Jul 05 2011In this note we prove that QR-submanifolds of the hyper-Kahler manifolds under some conditions admit the $G_2$ holonomy. We give simplest examples of such QR-submanifolds namely tori. We conjecture that all $G_2$ holonomy manifolds arise in this way.

2D Ising model: correlation functions at criticality via Riemann-type boundary value problemsMay 29 2016Sep 30 2016In this note we overview recent convergence results for correlations in the critical planar nearest-neighbor Ising model. We start with a short discussion of the combinatorics of the model and a definition of fermionic and spinor observables. After that, ... More

Del Pezzo singularities and SUSY breakingMay 23 2007Aug 25 2007An analytic construction of compact Calabi-Yau manifolds with del Pezzo singularities is found. We present complete intersection CY manifolds for all del Pezzo singularities and study the complex deformations of these singularities. An example of the ... More

Non RG logarithms via RG equationsFeb 10 2004We compute complete leading logarithms in $\Phi^4$ theory with the help of Connes and Kreimer RG equations. These equations are defined in the Lie algebra dual to the Hopf algebra of graphs. The results are compared with calculations in parquet approximation. ... More

On discrepancy between ATIC and Fermi dataMay 18 2009Jul 04 2009Either ATIC or Fermi-LAT data can be fitted together with the PAMELA data by three components: primary background ~ E^{-3.3}, secondary background ~ E^{-3.6}, and an additional source of electrons ~ E^{-g_a} Exp(-E/E_{cut}). We find that the best fits ... More

Twitter as a Transport Layer PlatformSep 23 2015Internet messengers and social networks have become an integral part of modern digital life. We have in mind not only the interaction between individual users but also a variety of applications that exist in these applications. Typically, applications ... More

Composition series for degenerate principal series of GL(n)Oct 18 2015In this note we consider representations of the group GL(n,F), where F is the field of real or complex numbers or, more generally, an arbitrary local field, in the space of equivariant line bundles over Grassmannians over the same field F. We study reducibility ... More

Development of the method of quaternion typification of Clifford algebra elements using k-fold commutators and anticommutatorsMar 20 2009In this paper we further develop the method of quaternion typification of Clifford algebra elements suggested by the author in the previous paper. On the basis of new classification of Clifford algebra elements it is possible to find out and prove a number ... More

Integer properties of a composition of exponential generating functionsNov 09 2012In this paper, we study a composition of exponential generating functions. We obtain new properties of this composition, which allow to distinguish prime numbers from composite numbers. Using the result of paper we get the known properties of the Bell ... More

Beam-Beam Resonances for Different Collision SchemesJun 25 2008One of the main advantages of proposed by P. Raimondi "Crab Waist" collision scheme is a strong suppression of betatron resonances excited by beam-beam interaction. Some qualitative explanations with numerical examples, describing beam-beam resonances ... More

Courant algebroids, derived brackets and even symplectic supermanifoldsOct 15 1999In this dissertation we study Courant algebroids, objects that first appeared in the work of T. Courant on Dirac structures; they were later studied by Liu, Weinstein and Xu who used Courant algebroids to generalize the notion of the Drinfeld double to ... More

Improved bounds for arithmetic progressions in product setsFeb 12 2015Let $B$ be a set of natural numbers of size $n$. We prove that the length of the longest arithmetic progression contained in the product set $B.B = \{bb'| \, b, b' \in B\}$ cannot be greater than $O(n \log n)$ which matches the lower bound provided in ... More

On limit cycles appearing by polynomial perturbation of Darbouxian integrable systemsApr 24 2007We prove an existential finiteness Varchenko-Khovanskii type result for integrals of rational 1-forms over the level curves of Darbouxian integrals.

Diophantine exponents of measures: a dynamical approachJun 24 2005We place the theory of metric Diophantine approximation on manifolds into a broader context of studying Diophantine properties of points generic with respect to certain measures on $\Bbb R^n$. The correspondence between multidimensional Diophantine approximation ... More

The transversality conditions for infinite-horizon optimal control problem with a free right endpoint and the stability of the adjoint variable (in Russian)May 16 2011An infinite-horizon optimal control problem with a free right endpoint is considered. In this paper we proved that Lyapunov stability of the adjoint variable implying the vanishing of the adjoint variable at infinity along optimal solution.

On a criterion of properness of multimapsNov 09 2009The close relation between properness and closedness of maps is well-known. For instance, for Fredholm mappings of infinite dimensional Banach manifolds, these properties are equivalent. On the other hand, properness of maps plays an important role for ... More

A note on the residue Chern characterNov 09 2005The aim of this note is to improve upon our earlier result which translates Weyl's (curvature) formulation of Chern character of a smooth vector bundle into the language of residues. The dualized Chern character is the functional on smooth differential ... More

On transversality condition for overtaking optimality in infinite horizon control problemApr 10 2017In this paper we investigate necessary conditions of optimality for infinite-horizon optimal control problems with overtaking optimality as an optimality criterion. For the case of local Lipschitz continuity of the payoff function, we construct a boundary ... More

Deviation inequality for monotonic Boolean functions with application to a number of k-cycles in a random graphMay 18 2004Using Talagrand's concentration inequality on the discrete cube {0,1}^m we show that given a real-valued function Z(x)on {0,1}^m that satisfies certain monotonicity conditions one can control the deviations of Z(x) above its median by a local Lipschitz ... More

Variational solutions to the abstract Euler equationMay 15 2019We study a class of nonlinear evolutionary equations of a certain structure reminiscent of the incompressible Euler equations. This includes, in particular, the ideal MHD, multidimensional Camassa-Holm, EPDiff, Euler-alpha and Korteweg-de Vries equations, ... More

Badly approximable systems of affine formsAug 12 1998Jan 20 1999We prove an inhomogeneous analogue of W. M. Schmidt's (1969) theorem on Hausdorff dimension of the set of badly approximable systems of linear forms. The proof is based on ideas and methods from the theory of dynamical systems, in particular, on abundance ... More

An extension of quantitative nondivergence and applications to Diophantine exponentsAug 25 2005May 19 2008We present a sharpening of nondivergence estimates for unipotent (or more generally polynomial-like) flows on homogeneous spaces. Applied to metric Diophantine approximation, it yields precise formulas for Diophantine exponents of affine subspaces of ... More

Betti numbers of small covers and their two-fold coveringsSep 20 2017We point out a gap in the proof of the Davis--Januszkiewicz theorem on cohomology of small covers of simple polytopes, and give a correction to this proof. We use this theorem to compute explicitly the Betti numbers for a wide class of two-fold coverings ... More

A Note on Moments of Limit Log Infinitely Divisible Stochastic Measures of Bacry and MuzySep 02 2016A multiple integral representation of single and joint moments of the total mass of the limit log-infinitely divisible stochastic measure of Bacry and Muzy [$\textit{Comm. Math. Phys.}$ ${\bf 236}$: 449-475, 2003] is derived. The covariance structure ... More

A new lower bound for reset threshold of synchronizing automata with sink stateJan 27 2017We present a new series of examples of binary slowly synchronizing automata with sink state. The reset threshold of the $n$-state automaton in this series is $\frac{n^2}{4}+2n-9$. This improves on the previously known lower bound for the maximum reset ... More

On weak Lie 2-algebrasDec 20 2007A Lie 2-algebra is a linear category equipped with a functorial bilinear operation satisfying skew-symmetry and Jacobi identity up to natural transformations which themselves obey coherence laws of their own. Functors and natural transformations between ... More

Singularities of integrable Hamiltonian systems: a criterion for non-degeneracy, with an application to the Manakov topSep 04 2010Oct 28 2011Let (M,\omega) be a symplectic 2n-manifold and h_1,...,h_n be functionally independent commuting functions on M. We present a geometric criterion for a singular point P\in M (i.e. such that {dh_i(P)}_{i=1}^n are linearly dependent) to be non-degenerate ... More

Example of a diffeomorphism for which the special ergodic theorem doesn't holdDec 27 2011Aug 20 2012In this work we present an example of C^\infty-diffeomorphism of a compact 4-manifold such that it admits a global SRB measure \mu but for which the special ergodic theorem doesn't hold. Namely, for this transformation there exist a continuous function ... More

Embedding 3-manifolds with boundary into closed 3-manifoldsMar 15 2010Apr 17 2011We prove that there is an algorithm which determines whether or not a given 2-polyhedron can be embedded into some integral homology 3-sphere. This is a corollary of the following main result. Let $M$ be a compact connected orientable 3-manifold with ... More

Algebraization of a Cartier divisorOct 15 2012We extend to pairs classical results of R. Elkik on lifting of homomorphisms and algebraization. In particular, we establish algebraization of an affine rig-smooth formal variety with a rig-smooth closed subvariety. This solves affirmatively a problem ... More

Hölder properties of Weierstrass-like solutions of $θ$-twisted cohomological equationsJul 31 2015It is proved that bounded solutions of modified ($\theta$-twisted) cohomological equations for expanding circle maps are $\theta$-H\"{o}lder continuous but are not $(\theta+\gamma)$-H\"{o}lder continuous for every $\gamma>0$ at almost every point. This ... More

Free energy in the Potts spin glassDec 01 2015Nov 11 2016We study the Potts spin glass model, which generalizes the Sherrington-Kirkpatrick model to the case when spins take more than two values but their interactions are counted only if the spins are equal. We obtain the analogue of the Parisi variational ... More

On Riemann zeroes, Lognormal Multiplicative Chaos, and Selberg IntegralJun 21 2015Nov 29 2015Rescaled Mellin-type transforms of the exponential functional of the Bourgade-Kuan-Rodgers statistic of Riemann zeroes are conjecturally related to the distribution of the total mass of the limit lognormal stochastic measure of Mandelbrot-Bacry-Muzy. ... More

Free energy in the mixed p-spin models with vector spinsDec 14 2015Dec 27 2015Using the synchronization mechanism developed in the previous work on the Potts spin glass model, arXiv:1512.00370, we obtain the analogue of the Parisi formula for the free energy in the mixed even $p$-spin models with vector spins, which include the ... More

Exponential energy growth due to slow parameter oscillations in quantum mechanical systemsJan 09 2016It is shown that a periodic emergence and destruction of an additional quantum number leads to an exponential growth of energy of a quantum mechanical system subjected to a slow periodic variation of parameters. The main example is given by systems (e.g., ... More

Spectral components analysis of diffuse emission processesFeb 06 2012We develop a novel method to separate the components of a diffuse emission process based on an association with the energy spectra. Most of the existing methods use some information about the spatial distribution of components, e.g., closeness to an external ... More

Cayley Automatic Groups and Numerical Characteristics of Turing TransducersJun 27 2016This paper is devoted to the problem of finding characterizations for Cayley automatic groups. The concept of Cayley automatic groups was recently introduced by Kharlampovich, Khoussainov and Miasnikov. We address this problem by introducing three numerical ... More

Dual Graph Polynomials and a 4-face FormulaAug 14 2015We study the dual graph polynomials and the case when a Feynman graph has no triangles but has a 4-face. This leads to the proof of the duality-admissibility of all graphs up to 18 loops. As a consequence, the $c_2$ invariant is the same for all 4 Feynman ... More

Tight Lower Bounds for the Longest Common Extension ProblemNov 09 2016We prove that in the non-uniform cell probe model the trade-off $S(n)T(n) = \Omega(n\log n)$ holds for any data structure solving the longest common extension problem on strings of length $n$ in $S(n) = \Omega(n)$ bits of space with queries working in ... More

Accurate solution of near-colliding Prony systems via decimation and homotopy continuationDec 31 2014Oct 21 2016We consider polynomial systems of Prony type, appearing in many areas of mathematics. Their robust numerical solution is considered to be difficult, especially in "near-colliding" situations. We consider a case when the structure of the system is a-priori ... More

Faster Lightweight Lempel-Ziv ParsingApr 25 2015Jun 08 2015We present an algorithm that computes the Lempel-Ziv decomposition in $O(n(\log\sigma + \log\log n))$ time and $n\log\sigma + \epsilon n$ bits of space, where $\epsilon$ is a constant rational parameter, $n$ is the length of the input string, and $\sigma$ ... More

QCD measurements at the TevatronNov 30 2011Dec 30 2011Selected quantum chromodynamics (QCD) measurements performed at the Fermilab Run II Tevatron ppbar collider running at sqrt{s} = 1.96 TeV by CDF and D0 Collaborations are presented. The inclusive jet, dijet production and three-jet cross section measurements ... More

Elimination of generalised imaginaries and Galois cohomologyDec 08 2013Nov 12 2014The objective of this article is to characterise elimination of finite generalised imaginaries (as defined by Hrushovski) in terms of group cohomology. As an application, I consider series of Zariski geometries constructed by Hrushovski and Zilber, and ... More

Quantum Predictive Learning and Communication Complexity with Single InputDec 17 2008Mar 15 2012We define a new model of quantum learning that we call Predictive Quantum (PQ). This is a quantum analogue of PAC, where during the testing phase the student is only required to answer a polynomial number of testing queries. We demonstrate a relational ... More

On the Role of Shared EntanglementApr 08 2006Aug 22 2006Despite the apparent similarity between shared randomness and shared entanglement in the context of Communication Complexity, our understanding of the latter is not as good as of the former. In particular, there is no known "entanglement analogue" for ... More

A question about Parisi functionalDec 22 2004We conjecture that the Parisi functional in the SK model is convex in the functional order parameter and prove a partial result that shows the convexity along one-sided directions. A consequence of this result is log-convexity of L_1 norm for a class ... More

A central limit theorem for weighted averages of spins in the high temperature region of the Sherrington-Kirkpatrick modelMay 18 2004In this paper we prove that in the high temperature region of the Sherrington-Kirkpatrick model for a typical realization of the disorder the weighted average of spins $\sum_{i\leq N} t_i \sigma_i$ will be approximately Gaussian provided that $\max_{i\leq ... More

The free energy in a multi-species Sherrington-Kirkpatrick modelOct 24 2013Dec 22 2015The authors of [Ann. Henri Poincar\'{e} 16 (2015) 691-708] introduced a multi-species version of the Sherrington-Kirkpatrick model and suggested the analogue of the Parisi formula for the free energy. Using a variant of Guerra's replica symmetry breaking ... More

On solutions of the reduced model for the dynamical evolution of contact linesFeb 05 2013We solve the linear advection-diffusion equation with a variable speed on a semi-infinite line. The variable speed is determined by an additional condition at the boundary, which models the dynamics of a contact line of a hydrodynamic flow at a 180 contact ... More