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Fast Prediction of New Feature UtilityJun 18 2012We study the new feature utility prediction problem: statistically testing whether adding a new feature to the data representation can improve predictive accuracy on a supervised learning task. In many applications, identifying new informative features ... More

Semi-derived and derived Hall algebras for stable categoriesSep 24 2014Given a Frobenius category $\mathcal{F}$ satisfying certain finiteness conditions, we consider the localization of its Hall algebra $\mathcal{H(F)}$ at the classes of all projective-injective objects. We call it the {\it "semi-derived Hall algebra"} $\mathcal{SDH(F, ... More

Spectral analysis for differential systems with a singularityJun 05 2016We consider the differential system $y'-x^{-1}Ay-q(x)y=\rho By $ with $n\times n$ matrices $A,B, q(x)$, where $A,B$ are constant, $B$ is diagonal, $A$ and $q(x)$ are off-diagonal, $q(\cdot)\in W^1_1[0,\infty)$. Some distinguished fundamental system of ... More

Forward sum rule for the $2γ$-exchange correction to the charge radius extraction from elastic electron scatteringJun 06 2014Nov 14 2014Two-photon exchange (TPE) contributions to elastic electron-proton scattering in the forward regime and in leading log $\sim t\ln|t|$ approximation in the momentum transfer $|t|$ are considered. The imaginary part of TPE amplitude in these kinematics ... More

Dispersive contributions to $e^+p/e^-p$ cross section ratio in forward regimeOct 27 2006Two-photon exchange (TPE) contributions to elastic electron-proton scattering in the forward regime are considered. The imaginary part of TPE amplitude in these kinematics is related to the DIS nucleon structure functions. The real part of the TPE amplitude ... More

Beam normal spin asymmetry in the quasi-RCS approximationDec 08 2005Dec 16 2005The two-photon exchange contribution to the single spin asymmetries with the spin orientation normal to the reaction plane is discussed for elastic electron-proton scattering in the equivalent photon approximation. In this case, hadronic part of the two-photon ... More

Nucleon EDM and rare decays of eta mesonsMar 19 2008I consider rare CP-violating decay modes $\eta(\eta')\to\pi\pi$ and note that an interaction that leads to such decays would necessarily induce a nucleon electric dipole moment (EDM). The experimental limits for the corresponding branching ratios are ... More

Community-level cohesion without cooperationJun 04 2015Mar 10 2016Recent work draws attention to community-community encounters ("coalescence") as likely an important factor shaping natural ecosystems. This work builds on MacArthur's classic model of competitive coexistence to investigate such community-level competition ... More

Free Lie algebroids and the space of pathsFeb 20 2007Jul 17 2007We construct algebraic and algebro-geometric models for the spaces of unparametrized paths. This is done by considering a path as a holonomy functional on indeterminate connections. For a manifold X, we construct a Lie algebroid P which serves as the ... More

Invitation to higher local fields, Part II, section 5: Harmonic analysis on algebraic groups over two-dimensional local fields of equal characteristicDec 18 2000This work introduces author's approach to harmonic analysis on algebraic groups over functional two-dimensional local fields. For a two-dimensional local field a Hecke algebra which is formed by operators which integrate pro-locally-constant complex functions ... More

Noncommutative geometry based on commutator expansionsFeb 07 1998We develop an approach to noncommutative algebraic geometry ``in the perturbative regime" around ordinary commutative geometry. Let R be a noncommutative algebra and A=R/[R,R] its commutativization. We describe what should be the formal neighborhood of ... More

Real mixed Hodge structuresFeb 03 2008Jul 10 2010We identify the category of real mixed Hodge structures with the category of vector bundles with connections (not necessarily flat) on C, equivariant with respect to C^*. Here C is the complex plane considered as a 2-dimensional real manifold, and C^* ... More

Selected problemsJan 25 2005This is a renovated list of open problems, to appear in: "Affine Algebraic Geometry" conference Proceedings volume in Contemporary Mathematics series of the Amer. Math. Soc. Ed. by Jaime Gutierrez, Vladimir Shpilrain, and Jie-Tai Yu.

A representation of isometries on function spacesDec 06 1995The main result says that every surjective isometry between two ideal Banach function spaces satisfying certain conditions can be presented as a composition of a measurable transformation of a variable and multiplication by a function.

On the Lebesgue measure of the Julia set of a quadratic polynomialMay 28 1991The goal of this note is to prove the following theorem: Let $p_a(z) = z^2+a$ be a quadratic polynomial which has no irrational indifferent periodic points, and is not infinitely renormalizable. Then the Lebesgue measure of the Julia set $J(p_a)$ is equal ... More

The complement of a $σ$-compact subset of a space with a $π$-tree also has a $π$-treeDec 08 2015Sep 19 2016We prove that the complement of a $\sigma$-compact subset of a topological space that has a $\pi$-tree also has a $\pi$-tree. To do this, we construct the foliage hybrid operation, which deals with foliage trees (that is, set-theoretic trees with a `leaf' ... More

Moments of lepton spectrum in B decays and the $m_b - m_c$ quark mass differenceNov 14 1994Nov 18 1994It is argued that the quark mass difference $m_b-m_c$ can be extracted with a high accuracy from experimental data on ratia of moments of lepton energy spectrum in semileptonic decays of $B$ mesons. Theoretical expressions for the moments are presented, ... More

Hidden nonlinear supersymmetries in pure parabosonic systemsMar 15 1999Nov 26 1999The existence of intimate relation between generalized statistics and supersymmetry is established by observation of hidden supersymmetric structure in pure parabosonic systems. This structure is characterized generally by a nonlinear superalgebra. The ... More

Universality of the R-deformed Heisenberg algebraMay 07 1997We show that deformed Heisenberg algebra with reflection emerging in parabosonic constructions is also related to parafermions. This universality is discussed in different algebraic aspects and is employed for the description of spin-j fields, anyons ... More

Deformed Heisenberg algebra with reflectionJan 19 1997A universality of deformed Heisenberg algebra involving the reflection operator is revealed. It is shown that in addition to the well-known infinite-dimensional representations related to parabosons, the algebra has also finite-dimensional representations ... More

R-deformed Heisenberg algebraJan 14 1997It is shown that the deformed Heisenberg algebra involving the reflection operator R (R-deformed Heisenberg algebra) has finite-dimensional representations which are equivalent to representations of paragrassmann algebra with a special differentiation ... More

Comment on "The relativistic particle with curvature and torsion of world trajectory"Oct 14 1998Gogilidze and Surovtsev have claimed recently (hep-th/9809191) that the tachyonic sector can be removed from the spectrum of the relativistic particle with curvature and torsion by a proper gauge choice. We show that the mass-spin dependence obtained ... More

Integrals of motion, supersymmetric quantum mechanics and dynamical supersymmetryAug 20 1998Aug 22 1998The class of relativistic spin particle models reveals the `quantization' of parameters already at the classical level. The special parameter values emerge if one requires the maximality of classical global continuous symmetries. The same requirement ... More

R-deformed Heisenberg algebra, anyons and d=2+1 supersymmetryMay 06 1997Jun 19 1997A universal minimal spinor set of linear differential equations describing anyons and ordinary integer and half-integer spin fields is constructed with the help of deformed Heisenberg algebra with reflection. The construction is generalized to some d=2+1 ... More

Estimates related to Shirshov height theorem (PhD Thesis)Nov 15 2015In 1993 E. I. Zelmanov asked the following question in Dniester Notebook: $"$Suppose that $F_{2,m}$ is a $2$-generated associative ring with the identity $x^m=0$. Is it true, that the nilpotency degree of $F_{2,m}$ has exponential growth?$"$ We show that ... More

Manifestation of the Nuclear Anapole Moment in M1 Transitions in ThalliumApr 28 2002We calculate nuclear spin-dependent parity non-conserving $E1$-amplitudes for optical transition $6p_{1/2,F} -> 6p_{3/2,F'}$ and for hyperfine transition $6p_{1/2,F} -> 6p_{1/2,F'}$ in Tl. Experimental limit on the former amplitude placed by Vetter et ... More

Biphoton ququarts as either pure or mixed states, features and reconstruction from coincidence measurementsSep 17 2012Features of biphoton polarization-frequency ququarts are considered. Their wave functions are defined as functions of both polarization and frequency variables of photons with the symmetry obligatory for two-boson states taken into account. In experiments, ... More

On the Yang-Yau inequality for the first Laplace eigenvalueFeb 09 2019In a seminal paper published in 1980, P. C. Yang and S.-T. Yau proved an inequality bounding the first eigenvalue of the Laplacian on an orientable Riemannian surface in terms of its genus $\gamma$ and the area. The equality in Yang-Yau's estimate is ... More

Population protocols with unreliable communicationFeb 26 2019Population protocols are a model of distributed computation intended for the study of networks of independent computing agents with dynamic communication structure. Each agent has a finite number of states, and communication opportunities occur nondeterministically, ... More

Estimates for character sums in finite fields of order $p^2$ and $p^3$Jun 12 2018Let $p$ be a prime number, $\mathbb{F}_{p^n}$ be the finite field of order $p^n$, and $\{\omega_1,\ldots\omega_n\}$ be a basis of $\mathbb{F}_{p^n}$ over $\mathbb{F}_p$. Let, further, $N_i,H_i$ be integers such that $1\leq H_i\leq p$, $\,\,i=1,\ldots,n$. ... More

Approximation beats concentration? An approximation view on inference with smooth radial kernelsJan 10 2018Aug 02 2018Positive definite kernels and their associated Reproducing Kernel Hilbert Spaces provide a mathematically compelling and practically competitive framework for learning from data. In this paper we take the approximation theory point of view to explore ... More

Ordered Dags: HypercubeSortOct 03 2017We generalise the insertion into a binary heap to any directed acyclic graph (DAG) with one source vertex. This lets us formulate a general method for converting any such DAG into a data structure with priority queue interface. We apply our method to ... More

Modeling solid-state dewetting of a single-crystal binary alloy thin filmsJan 02 2018Dewetting of a binary alloy thin film is studied using a continuum many-parameter model that accounts for the surface and bulk diffusion, the bulk phase separation, the surface segregation and the particles formation. Analytical solution is found for ... More

Wealth dynamics in a sentiment-driven marketMay 19 2017We study dynamics of a simulated world with stock and money, driven by the externally given processes which we refer to as sentiments. The considered sentiments influence the buy/sell stock trading attitude, the perceived price uncertainty, and the trading ... More

Statistics of narrow-band partially polarized lightJan 31 2017A complete single-point statistical description of a narrow-band partially polarized optical field is developed in terms of the 2-D Period-Averaged Probability Density Function (PA-PDF) of the electrical field vector. This statistic can be measured using ... More

Description of Glass Transition kinetics in 3D XY-model in terms of Gauge Field TheoryOct 02 2018We consider a gauge theory of the glass transition in the frustrated XY model being simplest model containing topologically nontrivial excitations. We describe the transition kinetics and find that the three-dimensional system exhibits the Vogel-Fulcher-Tamman ... More

Short survey about combinatorics on words and algorithmic methods in a ring (draft)Dec 12 2016A short survey about combinatorics on words and algorithmic methods in a ring. Special attention is given to Shirshov's results. Adopted for undegraduate students.

Set avoiding squares in $\mathbb{Z}_m$Oct 16 2016We prove that for all squarefree $m$ and any set $A\subset\mathbb{Z}_m$ such that $A-A$ does not contain non-zero squares the bound $|A|\leq m^{1/2}(3n)^{1.5n}$ holds, where $n$ denotes the number of odd prime divisors of $m$.

Conjoint axiomatization of the Choquet integral for heterogeneous product setsMar 26 2016We propose an axiomatization of the Choquet integral model for the general case of a heterogeneous product set $X = X_1 \times \ldots \times X_n$. In MCDA elements of $X$ are interpreted as alternatives, characterized by criteria taking values from the ... More

Einstein-Yang-Mills Black Hole Interiors: Serious Problems But Simple SolutionApr 29 1997Jun 11 1997Recently E. E. Donets, D. V. Galtsov, and the author reported the results of numerical and analytical investigation of the SU(2) Einstein-Yang-Mills black hole interior solutions (gr-qc/9612067). It was shown that a generic interior solution develops ... More

Propagating Cosmic Rays with exact Solution of Fokker-Planck EquationMar 07 2017Shortfalls in cosmic ray (CR) propagation models obscure the CR sources and acceleration mechanisms. This problem became particularly obvious after the Fermi, Pamela, and AMS-02 have discovered the electron/positron and $p/$He spectral anomalies. Most ... More

Schmidt-mode analysis of quadrature entanglement in superpositions of two-mode multiphoton statesMay 13 2019The Schmidt-decomposition formalism is proposed to be used for evaluation of the degree of quadrature entanglement in two-mode multiphoton states.

Model of pathogenesis of psoriasis. Part 2. Local processesJan 13 2012Apr 14 2012Analytical research of results of experimental and theoretical studies on pathogenesis of psoriatic disease is carried out. The new model of pathogenesis - skin reaction to systemic psoriatic process SPP is formulated. ... Psoriatic inflammation is regarded ... More

New generation electron-positron factoriesJun 27 2011In 2010 we celebrated 50 years since commissioning of the first particle storage ring ADA in Frascati (Italy) that also became the first electron-positron collider in 1964. After that date the particle colliders have increased their intensity, luminosity ... More

On Hamiltonian minimality of isotropic non-homogeneous tori in $\mathbb{H}^n$ and $\mathbb{C} \mathrm{P}^{2n+1}$Jun 13 2019We construct a family of flat isotropic non-homogeneous tori in $\mathbb{H}^n$ and $\mathbb{C} \mathrm{P}^{2n+1}$ and find necessary and sufficient conditions for their Hamiltonian minimality.

On equations over Brandt semigroupsSep 23 2017In this paper, we study equations over Brandt semigroup $B_n$. We compute that the number of unsolvable equations in one variable asymptotically equals $\frac{2}{n^2}$, and the average number of solutions of these equations asymptotically equals $n^2$. ... More

Liouville's equation for curvature and systolic defectMay 03 2011Jun 12 2011We analyze the probabilistic variance of a solution of Liouville's equation for curvature, given suitable bounds on the Gaussian curvature. The related systolic geometry was recently studied by Horowitz, Katz, and Katz, where we obtained a strengthening ... More

Sensitivity of DANSS detector to short range neutrino oscillationsDec 02 2014DANSS is a highly segmented $1m^3$ plastic scintillator detector. Its 2500 scintillator strips have a Gd loaded reflective cover. Light is collected with 3 wave length shifting fibers per strip and read out with 50 PMTs and 2500 SiPMs. The DANSS will ... More

Galois cohomology of reductive algebraic groups over the field of real numbersJan 23 2014We describe functorially the first Galois cohomology set of a connected reductive algebraic group over the field R of real numbers in terms of a certain action of the Weyl group on the real points of order dividing 2 of the maximal torus containing a ... More

Resolution of the Cauchy problem for the Toda lattice with non-stabilized initial dataOct 26 2001This paper is the continuation of the work "On an inverse problem for finite-difference operators of second order". We consider the Cauchy problem for the Toda lattice in the case when the corresponding L-operator is a Jacobi matrix with bounded elements, ... More

Morse groups in symmetric spaces corresponding to the symmetric groupFeb 18 1998We describe the Morse groups of the nearby cycles sheaves on the nilcones in three classical symmetric spaces.

A bijective proof of Loehr-Warrington's formulas for the statistics $\mbox{ctot}_{\frac{q}{p}}$ and $\mbox{midd}_{\frac{q}{p}}$Jan 30 2013Dec 07 2013Loehr and Warrington introduced partitional statistics $\mbox{ctot}_{\frac{q}{p}}(D)$ and $\mbox{midd}_{\frac{q}{p}}(D)$ and provided formulas for these statistics in terms of the boundary graph of the Young diagram $D$. In this paper we give a bijective ... More

Local calibration of mass and systolic geometryApr 14 2002We prove the simultaneous (k,n-k)-systolic freedom, for a pair of adjacent integers k smaller than n/2, of a simply connected n-manifold X. Our construction, related to recent results of I. Babenko, is concentrated in a neighborhood of suitable k-dimensional ... More

Singular sets and parameters of generalized triangle orbifoldsMar 03 2001Oct 19 2016We study groups generated by three half-turns in the Lobachevsky $3$-space and their quotient orbifolds. These generalized triangle groups are closely related to the arbitrary 2-generator Kleinian groups. Our main result is a classification of the singular ... More

Gradient-like flows and self-indexing in stratified Morse theoryJun 21 2000Sep 12 2000We develop the idea of self-indexing and the technology of gradient-like vector fields in the setting of Morse theory on a complex algebraic stratification. Our main result is the local existence, near a Morse critical point, of gradient-like vector fields ... More

On spectra of hyperbolic surfaces without thin handlesJan 05 2019We obtain a sharp lower estimate on eigenvalues of Laplace--Beltrami operator on a hyperbolic surface with injectivity radius bounded from the below.

Fractional Derivatives of Convex Lyapunov Functions and Control Problems in Fractional Order SystemsOct 19 2017The paper is devoted to the development of control procedures with a guide for conflict-controlled dynamical systems described by ordinary fractional differential equations with the Caputo derivative of an order $\alpha \in (0, 1).$ For the case when ... More

On maxispaces of nonparametric testsAug 16 2017May 17 2018For the problems of nonparametric hypothesis testing we introduce the notion of maxisets and maxispace. We point out the maxisets of $\chi^2-$tests, Cramer-von Mises tests, tests generated $\mathbb{L}_2$- norms of kernel estimators and tests generated ... More

Schmidt decomposition for non-collinear biphoton angular wave functionsNov 08 2014Schmidt modes of non-collinear biphoton angular wave functions are found analytically. The experimentally realizable procedure is described for their separation. Parameters of the Schmidt decomposition are used for evaluation of the degree of biphoton's ... More

Data-driven goodness-of-fit testsAug 01 2007Dec 18 2007We introduce a new general class of statistical tests. The class contains Neyman's smooth tests and data-driven efficient score tests as special examples. We prove general consistency theorems for the tests from the class. The paper shows that the tests ... More

A question by Alexei Aleksandrov and logarithmic determinantsAug 28 2001We answer negatively to the question posed by Aleksandrov concerning analytic functions of Smirnov's class in the unit disk with pure imaginary boundary values. We also find new sufficient conditions for representations of functions of Smirnov's class ... More

Zeros of Gaussian Analytic FunctionsJul 06 2000We prove and discuss three results on zero distribution of gaussian analytic functions: (i) the Edeleman-Kostlan formula for the expectation of the counting measure; (ii) a variation on the theme of Calabi's rigidity theorem; (iii) Offord's estimate of ... More

Extending the exact sequence of nonabelian $H^1$, using nonabelian $H^2$ with coefficients in crossed modulesAug 26 2016In this note, following Dedecker and Debremaeker, we extend the cohomology exact sequence for nonabelian $H^1$, using nonabelian $H^2$ with coefficients in crossed modules.

Marketing features of dropshipping in system of e-commerceMay 10 2015Today dropshipping wins the Internet promptly and transformed to one of the basic tools of marketing in e-commerce. Marketing features, mechanisms and value dropshipping in the conditions of network economy of the XXI century reveal in article. The author ... More

Mathematics of Knowledge Refinement: Probabilistic Arithmetic, with no unknowns and no infinity. Part I. Generalized Probabilistic Arithmetic. Basic definitions and propertiesNov 01 2011May 22 2012An approach to build Probabilistic Arithmetic in which initial values of all correlated random variables are known, but with varying degrees of accuracy. As a result of the proposed Probabilistic Arithmetic operations, variable values, degrees of their ... More

QUBIC ExperimentMay 16 2016QUBIC is a ground-based experiment, currently under construction, that uses the novel bolometric interferometry technology. It is dedicated to measure the primordial B-modes of CMB. As a bolometric interferometer, QUBIC has high sensitivity and good systematics ... More

Surfaces containing two circles through each pointDec 30 2015We find all analytic surfaces in space $\mathbb{R}^3$ such that through each point of the surface one can draw two transversal circular arcs fully contained in the surface. The problem of finding such surfaces traces back to the works of Darboux from ... More

Quasiparticle approach to molecules interacting with quantum solventsOct 05 2016Understanding the behavior of molecules interacting with superfluid helium represents a formidable challenge and, in general, requires approaches relying on large-scale numerical simulations. Here we demonstrate that experimental data collected over the ... More

Dynamics of quadratic polynomials, I: Combinatorics and geometry of the Yoccoz puzzleMar 01 1995This work studies combinatorics and geometry of the Yoccoz puzzle for quadratic polynomials. It is proven that the moduli of the ``principal nest'' of annuli grow at linear rate. As a corollary we obtain complex a priori bounds and local connectivity ... More

On exotic algebraic structures on affine spacesJun 02 1995By an exotic algebraic structure on the affine space ${\bf C}^n$ we mean a smooth affine algebraic variety which is diffeomorphic to ${\bf R}^{2n}$ but not isomorphic to ${\bf C}^n$. This is a survey of the recent developement on the subject, which emphasizes ... More

On 2-systoles of hyperbolic 3-manifoldsMay 23 2012Jul 08 2012We investigate the geometry of $\pi_1$-injective surfaces in closed hyperbolic 3-manifolds. First we prove that for any $e>0$, if the manifold $M$ has sufficiently large systole $\sys_1(M)$, the genus of any such surface in $M$ is bounded below by $\exp((1/2-e)\sys_1(M))$. ... More

Geodesics, volumes and Lehmer's conjectureJun 09 2011In this report I discuss the relations between systoles and volumes of hyperbolic manifolds and a conjecture of Lehmer about the Mahler measure of non-cyclotomic polynomials.

Enhancement of the electric dipole moment of the electron in the YbF moleculeMay 27 1997We calculate an effective electric field on the unpaired electron in the YbF molecule. This field determines sensitivity of the molecular experiment to the electric dipole moment of the electron. We use experimental value of the spin-doubling constant ... More

Nonlinear electromagnetic response and Higgs mode excitation in BCS superconductors with impuritiesFeb 05 2019Feb 12 2019We reveal that due to the presence of disorder oscillations of the order parameter amplitude called the Higgs mode can be effectively excited by the external electromagnetic radiation in usual BCS superconductors. This mechanism works for superconductors ... More

Parallel Algorithm for Frequent Itemset Mining on Intel Many-core SystemsDec 28 2018Frequent itemset mining leads to the discovery of associations and correlations among items in large transactional databases. Apriori is a classical frequent itemset mining algorithm, which employs iterative passes over database combining with generation ... More

$γW$-box Inside-Out: Nuclear Polarizabilities Distort the Beta Decay SpectrumDec 11 2018Mar 06 2019I consider the $\gamma W$-box correction to superallowed nuclear $\beta$-decays in the framework of dispersion relations. I address a novel effect of a distortion of the emitted electron energy spectrum by nuclear polarizabilities and show that this effect, ... More

Steklov problem on differential formsMay 24 2017In this paper we study spectral properties of Dirichlet-to-Neumann map on differential forms obtained by a slight modification of the definition due to Belishev and Sharafutdinov. The resulting operator $\Lambda$ is shown to be self-adjoint on the subspace ... More

Arithmetic Kleinian groups generated by elements of finite orderOct 19 2016Jul 07 2017We show that up to commensurability there are only finitely many cocompact arithmetic Kleinian groups generated by rotations. This implies, in particular, that there exist only finitely many conjugacy classes of cocompact two generated arithmetic Kleinian ... More

On evolutionary selection of blackjack strategiesNov 16 2017We apply the approach of evolutionary programming to the problem of optimization of the blackjack basic strategy. We demonstrate that the population of initially random blackjack strategies evolves and saturates to a profitable performance in about one ... More

Dimension Theory Approach to the Complexity of Almost Periodic TrajectoriesOct 09 2017We introduce and study a dimensional-like characteristic of an uniformly almost periodic function, which we call the Diophantine dimension. By definition, it is the exponent in the asymptotic behavior of the inclusio length. Diophantine dimension is connected ... More

Fluctuations of the aperture-averaged orbital angular momentum after propagation through turbulenceJan 05 2018Jan 09 2018In the recent paper [1] it was shown that for paraxial propagation of scalar waves, the transverse linear momentum and orbital angular momentum (OAM) are related to the wave coherence function. Although both of these quantities are conserved during free-space ... More

Busy beavers and Kolmogorov complexityMar 15 2017The idea to find the "maximal number that can be named" can be traced back to Archimedes (see his Psammit). From the viewpoint of computation theory the natural question is "which number can be described by at most n bits"? This question led to the definition ... More

Derivation of Schrodinger's equationFeb 07 2017In this article, a model of a material particle in chaotic motion (while maintaining a definite size and trajectory) is presented. On the basis of this model, the following is achieved: --to express Planck's constant through the main features of a stationary ... More

Population protocols with unreliable communicationFeb 26 2019Mar 06 2019Population protocols are a model of distributed computation intended for the study of networks of independent computing agents with dynamic communication structure. Each agent has a finite number of states, and communication opportunities occur nondeterministically, ... More

Hopfological algebra and categorification at a root of unity: the first stepsSep 04 2005Mar 25 2006Any finite-dimensional Hopf algebra H is Frobenius and the stable category of H-modules is triangulated monoidal. To H-comodule algebras we assign triangulated module-categories over the stable category of H-modules. These module-categories are generalizations ... More

Phenomenological implications of an alternative Hamiltonian constraint for quantum cosmologyNov 02 2005In this paper we review a model based on loop quantum cosmology that arises from a symmetry reduction of the self dual Plebanski action. In this formulation the symmetry reduction leads to a very simple Hamiltonian constraint that can be quantized explicitly ... More

Discriminant and Hodge classes on the space of Hitchin's coversMar 31 2019We continue the study of the rational Picard group of the moduli space of Hitchin's spectral covers started in P. Zograf's and D. Korotkin's work [11]. In the first part of the paper we expand the ``boundary'', ``Maxwell stratum'' and ``caustic'' divisors ... More

On the class of caustic on the moduli space of odd spin curvesSep 08 2015Jan 20 2019Let $C$ be a smooth projective curve of genus $g\geq 3$ and let $\eta$ be an odd theta characteristic on it such that $h^0(C,\eta) = 1$. Pick a point $p$ from the support of $\eta$ and consider the one-dimensional linear system $|\eta + p|$. In general ... More

A sequence of connections and a characterization of Kähler manifoldsSep 29 1998We study a sequence of connections which is associated with a Riemannian metric and an almost symplectic structure on a manifold. We prove that if this sequence is trivial (i.e. constant) or 2-periodic, then the manifold has a canonical K\"ahler structure. ... More

Proof of Gal's conjecture for the D series of generalized associahedraJun 09 2011In this short note we consider generalized associahedra of type D_n. We prove that these simple flag polytopes are not nestohedra for n > 3, but the statement of Gal's conjecture holds for them.

The defect of weak approximation for homogeneous spaces. IIApr 30 2008May 10 2008Let X be a homogeneous space of a connected linear algebraic group G' over a number field k, containing a k-point x. Assume that the stabilizer of x in G' is connected. Using the notion of a quasi-trivial group, recently introduced by Colliot-Th\'el\`ene, ... More

Existence of perfect Morse functions on spaces with semi-free circle actionFeb 15 2002Apr 01 2003Let $M$ be a compact oriented simply-connected manifold of dimension at least 8. Assume $M$ is equipped with a torsion-free semi-free circle action with isolated fixed points. We prove $M$ has a perfect invariant Morse-Smale function. The major ingredient ... More

Continuity of the Mixing OperatorAug 16 2005Oct 03 2005Mixed distributions are considered as a results of application of a linear operator, which maps mixing measures to mixed measures. The main result is a proof of continuity of this mixing operator. Corollaries for parametric families of distributions (usually ... More

KISS approach to credit portfolio modelingJul 11 2011A simple, yet reasonably accurate, analytical technique is proposed for multi-factor structural credit portfolio models. The accuracy of the technique is demonstrated by benchmarking against Monte Carlo simulations. The approach presented here may be ... More

Convolution equations on lattices: periodic solutions with values in a prime characteristic fieldJun 29 2006Feb 13 2007These notes are inspired by the theory of cellular automata. A linear cellular automaton on a lattice of finite rank or on a toric grid is a discrete dinamical system generated by a convolution operator with kernel concentrated in the nearest neighborhood ... More

The Sharp Lower Bound of Asymptotic Efficiency of Estimators in the Zone of Moderate Deviation ProbabilitiesJun 07 2012For the zone of moderate deviation probabilities the local asymptotic minimax lower bound of asymptotic efficiency of estimators is established. The estimation parameter is multidimensional. The lower bound admits the interpretation as the lower bound ... More

Metric spaces nonembeddable into Banach spaces with the Radon-Nikodým property and thick families of geodesicsDec 19 2013Apr 04 2014We show that a geodesic metric space which does not admit bilipschitz embeddings into Banach spaces with the Radon-Nikod\'ym property does not necessarily contain a bilipschitz image of a thick family of geodesics. This is done by showing that any thick ... More

Link homology and categorificationMay 12 2006Sep 01 2006This is a short survey of algebro-combinatorial link homology theories which have the Jones polynomial and other link polynomials as their Euler characteristics.

Heisenberg algebra and a graphical calculusSep 16 2010A new calculus of planar diagrams involving diagrammatics for biadjoint functors and degenerate affine Hecke algebras is introduced. The calculus leads to an additive monoidal category whose Grothendieck ring contains an integral form of the Heisenberg ... More

Parshin Residues via Coboundary OperatorsJul 25 2007Dec 05 2010The article consist of two main parts: an analog of the Leray Theory for Singular Varieties and its application to the Theory of Parshin's Residues. The first part is independent from the second. It uses the theory of Whitney stratifications. The second ... More