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Clustering to Given ConnectivitiesMar 26 2018Apr 20 2018We define a general variant of the graph clustering problem where the criterion of density for the clusters is (high) connectivity. In {\sc Clustering to Given Connectivities}, we are given an $n$-vertex graph $G$, an integer $k$, and a sequence $\Lambda=\langle ... More

On the Parameterized Complexity of Graph Modification to First-Order Logic PropertiesMay 11 2018Feb 26 2019We consider the problems of deciding whether an input graph can be modified by removing/adding at most k vertices/edges such that the result of the modification satisfies some property definable in first-order logic. We establish a number of sufficient ... More

Low-rank binary matrix approximation in column-sum normApr 12 2019We consider $\ell_1$-Rank-$r$ Approximation over GF(2), where for a binary $m\times n$ matrix ${\bf A}$ and a positive integer $r$, one seeks a binary matrix ${\bf B}$ of rank at most $r$, minimizing the column-sum norm $||{\bf A} -{\bf B}||_1$. We show ... More

Variants of Plane Diameter CompletionSep 02 2015The {\sc Plane Diameter Completion} problem asks, given a plane graph $G$ and a positive integer $d$, if it is a spanning subgraph of a plane graph $H$ that has diameter at most $d$. We examine two variants of this problem where the input comes with another ... More

Finding Connected Secluded SubgraphsOct 30 2017Problems related to finding induced subgraphs satisfying given properties form one of the most studied areas within graph algorithms. Such problems have given rise to breakthrough results and led to development of new techniques both within the traditional ... More

Linear-Time Algorithms for Scattering Number and Hamilton-Connectivity of Interval GraphsJan 25 2013Hung and Chang showed that for all k>=1 an interval graph has a path cover of size at most k if and only if its scattering number is at most k. They also showed that an interval graph has a Hamilton cycle if and only if its scattering number is at most ... More

Editing to a Connected Graph of Given DegreesAug 08 2013Jun 04 2014The aim of edge editing or modification problems is to change a given graph by adding and deleting of a small number of edges in order to satisfy a certain property. We consider the Edge Editing to a Connected Graph of Given Degrees problem that asks ... More

Editing to a Graph of Given DegreesNov 19 2013Dec 23 2014We consider the Editing to a Graph of Given Degrees problem that asks for a graph G, non-negative integers d,k and a function \delta:V(G)->{1,...,d}, whether it is possible to obtain a graph G' from G such that the degree of v is \delta(v) for any vertex ... More

Graph Editing to a Given Degree SequenceJan 13 2016We investigate the parameterized complexity of the graph editing problem called Editing to a Graph with a Given Degree Sequence, where the aim is to obtain a graph with a given degree sequence \sigma by at most k vertex or edge deletions and edge additions. ... More

Long Circuits and Large Euler SubgraphsApr 21 2013An undirected graph is Eulerian if it is connected and all its vertices are of even degree. Similarly, a directed graph is Eulerian, if for each vertex its in-degree is equal to its out-degree. It is well known that Eulerian graphs can be recognized in ... More

Enumeration and Maximum Number of Minimal Connected Vertex Covers in GraphsFeb 24 2016Connected Vertex Cover is one of the classical problems of computer science, already mentioned in the monograph of Garey and Johnson. Although the optimization and decision variants of finding connected vertex covers of minimum size or weight are well ... More

A Linear Kernel for Finding Square Roots of Almost Planar GraphsAug 22 2016A graph H is a square root of a graph G if G can be obtained from H by the addition of edges between any two vertices in H that are of distance 2 from each other. The Square Root problem is that of deciding whether a given graph admits a square root. ... More

On the tractability of optimization problems on H-graphsSep 27 2017Apr 25 2018For a graph $H$, a graph $G$ is an $H$-graph if it is an intersection graph of connected subgraphs of some subdivision of $H$. $H$-graphs naturally generalize several important graph classes like interval or circular-arc graph. This class was introduced ... More

Approximating acyclicity parameters of sparse hypergraphsSep 22 2008The notions of hypertree width and generalized hypertree width were introduced by Gottlob, Leone, and Scarcello in order to extend the concept of hypergraph acyclicity. These notions were further generalized by Grohe and Marx, who introduced the fractional ... More

Spanning Circuits in Regular MatroidsJul 19 2016We consider the fundamental Matroid Theory problem of finding a circuit in a matroid spanning a set T of given terminal elements. For graphic matroids this corresponds to the problem of finding a simple cycle passing through a set of given terminal edges ... More

Covering vectors by spaces: Regular matroidsOct 06 2017Seymour's decomposition theorem for regular matroids is a fundamental result with a number of combinatorial and algorithmic applications. In this work we demonstrate how this theorem can be used in the design of parameterized algorithms on regular matroids. ... More

Obtaining Planarity by Contracting Few EdgesApr 23 2012The Planar Contraction problem is to test whether a given graph can be made planar by using at most k edge contractions. This problem is known to be NP-complete. We show that it is fixed-parameter tractable when parameterized by k.

Structured Connectivity AugmentationJun 13 2017We initiate the algorithmic study of the following "structured augmentation" question: is it possible to increase the connectivity of a given graph G by superposing it with another given graph H? More precisely, graph F is the superposition of G and H ... More

Minimizing Rosenthal Potential in Multicast GamesSep 26 2013A multicast game is a network design game modelling how selfish non-cooperative agents build and maintain one-to-many network communication. There is a special source node and a collection of agents located at corresponding terminals. Each agent is interested ... More

The Parameterized Complexity of Graph CyclabilityDec 12 2014Jan 25 2016The cyclability of a graph is the maximum integer $k$ for which every $k$ vertices lie on a cycle. The algorithmic version of the problem, given a graph $G$ and a non-negative integer $k,$ decide whether the cyclability of $G$ is at least $k,$ is {\sf ... More

On the Parameterized Complexity of Graph Modification to First-Order Logic PropertiesMay 11 2018Oct 30 2018We consider the problems of deciding whether an input graph can be modified by removing/adding at most k vertices/edges such that the result of the modification satisfies some property definable in first-order logic. We establish a number of sufficient ... More

Finding vertex-surjective graph homomorphismsApr 10 2012The Surjective Homomorphism problem is to test whether a given graph G called the guest graph allows a vertex-surjective homomorphism to some other given graph H called the host graph. The bijective and injective homomorphism problems can be formulated ... More

Parameterized Low-Rank Binary Matrix ApproximationMar 16 2018We provide a number of algorithmic results for the following family of problems: For a given binary m\times n matrix A and integer k, decide whether there is a "simple" binary matrix B which differs from A in at most k entries. For an integer r, the "simplicity" ... More

Parameterized k-Clustering: The distance matters!Feb 22 2019We consider the $k$-Clustering problem, which is for a given multiset of $n$ vectors $X\subset \mathbb{Z}^d$ and a nonnegative number $D$, to decide whether $X$ can be partitioned into $k$ clusters $C_1, \dots, C_k$ such that the cost \[\sum_{i=1}^k \min_{c_i\in ... More

Induced Disjoint Paths in Circular-Arc Graphs in Linear TimeMar 04 2014The Induced Disjoint Paths problem is to test whether a graph G with k distinct pairs of vertices (s_i,t_i) contains paths P_1,...,P_k such that P_i connects s_i and t_i for i=1,...,k, and P_i and P_j have neither common vertices nor adjacent vertices ... More

Preventing Unraveling in Social Networks Gets HarderApr 23 2013The behavior of users in social networks is often observed to be affected by the actions of their friends. Bhawalkar et al. \cite{bhawalkar-icalp} introduced a formal mathematical model for user engagement in social networks where each individual derives ... More

Generating All Minimal Edge Dominating Sets with Incremental-Polynomial DelayAug 27 2012Oct 23 2012For an arbitrary undirected simple graph G with m edges, we give an algorithm with running time O(m^4 |L|^2) to generate the set L of all minimal edge dominating sets of G. For bipartite graphs we obtain a better result; we show that their minimal edge ... More

On the parameterized complexity of cutting a few vertices from a graphApr 23 2013Oct 01 2013We study the parameterized complexity of separating a small set of vertices from a graph by a small vertex-separator. That is, given a graph $G$ and integers $k$, $t$, the task is to find a vertex set $X$ with $|X| \le k$ and $|N(X)| \le t$. We show that ... More

Parameterized Complexity of the Anchored k-Core Problem for Directed GraphsApr 22 2013Sep 17 2013Bhawalkar, Kleinberg, Lewi, Roughgarden, and Sharma [ICALP 2012] introduced the Anchored k-Core problem, where the task is for a given graph G and integers b, k, and p to find an induced subgraph H with at least p vertices (the core) such that all but ... More

Induced Disjoint Paths in Claw-Free GraphsFeb 20 2012Mar 06 2014Paths P1,...,Pk in a graph G=(V,E) are said to be mutually induced if for any 1 <= i < j <= k, Pi and Pj have neither common vertices nor adjacent vertices (except perhaps their end-vertices). The Induced Disjoint Paths problem is to test whether a graph ... More

A Survey on the Computational Complexity of Colouring Graphs with Forbidden SubgraphsJul 06 2014Feb 15 2016For a positive integer $k$, a $k$-colouring of a graph $G=(V,E)$ is a mapping $c: V\rightarrow\{1,2,...,k\}$ such that $c(u)\neq c(v)$ whenever $uv\in E$. The Colouring problem is to decide, for a given $G$ and $k$, whether a $k$-colouring of $G$ exists. ... More

Code loops in dimension at most 8Dec 18 2017Code loops are certain Moufang $2$-loops constructed from doubly even binary codes that play an important role in the construction of local subgroups of sporadic groups. More precisely, code loops are central extensions of the group of order $2$ by an ... More

Going Far From DegeneracyFeb 07 2019An undirected graph G is d-degenerate if every subgraph of G has a vertex of degree at most d. By the classical theorem of Erd\H{o}s and Gallai from 1959, every graph of degeneracy d>1 contains a cycle of length at least d+1. The proof of Erd\H{o}s and ... More

Parameterized Algorithms for Finding Square RootsOct 21 2013We show that the following two problems are fixed-parameter tractable with parameter k: testing whether a connected n-vertex graph with m edges has a square root with at most n-1+k edges and testing whether such a graph has a square root with at least ... More

Output-Polynomial Enumeration on Graphs of Bounded (Local) Linear MIM-WidthSep 12 2015Sep 15 2015The linear induced matching width (LMIM-width) of a graph is a width parameter defined by using the notion of branch-decompositions of a set function on ternary trees. In this paper we study output-polynomial enumeration algorithms on graphs of bounded ... More

Numerical simulation of the stress-strain state of the dental systemSep 17 2015We present mathematical models, computational algorithms and software, which can be used for prediction of results of prosthetic treatment. More interest issue is biomechanics of the periodontal complex because any prosthesis is accompanied by a risk ... More

Hadwiger number of graphs with small chordalityJun 15 2014The Hadwiger number of a graph G is the largest integer h such that G has the complete graph K_h as a minor. We show that the problem of determining the Hadwiger number of a graph is NP-hard on co-bipartite graphs, but can be solved in polynomial time ... More

How to Hunt an Invisible Rabbit on a GraphFeb 19 2015Feb 20 2015We investigate Hunters & Rabbit game, where a set of hunters tries to catch an invisible rabbit that slides along the edges of a graph. We show that the minimum number of hunters required to win on an (n\times m)-grid is \lfloor min{n,m}/2\rfloor+1. We ... More

Squares of Low Maximum DegreeAug 22 2016Aug 27 2016A graph H is a square root of a graph G if G can be obtained from H by adding an edge between any two vertices in H that are of distance 2. The Square Root problem is that of deciding whether a given graph admits a square root. This problem is only known ... More

Editing to a Planar Graph of Given DegreesAug 11 2015We consider the following graph modification problem. Let the input consist of a graph $G=(V,E)$, a weight function $w\colon V\cup E\rightarrow \mathbb{N}$, a cost function $c\colon V\cup E\rightarrow \mathbb{N}$ and a degree function $\delta\colon V\rightarrow ... More

Covering Vectors by Spaces in Perturbed Graphic Matroids and Their DualsFeb 19 2019Perturbed graphic matroids are binary matroids that can be obtained from a graphic matroid by adding a noise of small rank. More precisely, r-rank perturbed graphic matroid M is a binary matroid that can be represented in the form I +P, where I is the ... More

Going Far From DegeneracyFeb 07 2019Feb 14 2019An undirected graph G is d-degenerate if every subgraph of G has a vertex of degree at most d. By the classical theorem of Erd\H{o}s and Gallai from 1959, every graph of degeneracy d>1 contains a cycle of length at least d+1. The proof of Erd\H{o}s and ... More

Editing to Eulerian GraphsOct 25 2014We investigate the problem of modifying a graph into a connected graph in which the degree of each vertex satisfies a prescribed parity constraint. Let $ea$, $ed$ and $vd$ denote the operations edge addition, edge deletion and vertex deletion respectively. ... More

Parameterized Complexity of Superstring ProblemsFeb 05 2015In the Shortest Superstring problem we are given a set of strings $S=\{s_1, \ldots, s_n\}$ and integer $\ell$ and the question is to decide whether there is a superstring $s$ of length at most $\ell$ containing all strings of $S$ as substrings. We obtain ... More

Metric Dimension of Bounded Tree-length GraphsFeb 08 2016The notion of resolving sets in a graph was introduced by Slater (1975) and Harary and Melter (1976) as a way of uniquely identifying every vertex in a graph. A set of vertices in a graph is a resolving set if for any pair of vertices x and y there is ... More

Parameterized Complexity of Secluded Connectivity ProblemsFeb 13 2015Apr 21 2015The Secluded Path problem models a situation where a sensitive information has to be transmitted between a pair of nodes along a path in a network. The measure of the quality of a selected path is its exposure, which is the total weight of vertices in ... More

Algorithms for outerplanar graph roots and graph roots of pathwidth at most 2Mar 15 2017Oct 06 2018Deciding whether a given graph has a square root is a classical problem that has been studied extensively both from graph theoretic and from algorithmic perspectives. The problem is NP-complete in general, and consequently substantial effort has been ... More

Parameterized Aspects of Strong Subgraph ClosureFeb 28 2018Motivated by the role of triadic closures in social networks, and the importance of finding a maximum subgraph avoiding a fixed pattern, we introduce and initiate the parameterized study of the Strong F-closure problem, where F is a fixed graph. This ... More

Approximation Schemes for Low-Rank Binary Matrix Approximation ProblemsJul 18 2018We provide a randomized linear time approximation scheme for a generic problem about clustering of binary vectors subject to additional constrains. The new constrained clustering problem encompasses a number of problems and by solving it, we obtain the ... More

Partial complementation of graphsApr 29 2018A partial complement of the graph $G$ is a graph obtained from $G$ by complementing all the edges in one of its induced subgraphs. We study the following algorithmic question: for a given graph $G$ and graph class $\mathcal{G}$, is there a partial complement ... More

Path-space variational inference for non-equilibrium coarse-grained systemsAug 02 2015Jan 11 2016In this paper, we discuss information-theoretic tools for obtaining optimized coarse-grained molecular models for both equilibrium and non-equilibrium molecular dynamics. The latter are ubiquitous in physicochemical and biological applications, where ... More

Density Fluctuations in the Solar Wind Driven by Alfvén Wave Parametric DecayDec 23 2017Feb 06 2018Measurements and simulations of inertial compressive turbulence in the solar wind are characterized by anti-correlated magnetic fluctuations parallel to the mean field and density structures. This signature has been interpreted as observational evidence ... More

Domain decomposition methods with overlapping subdomains for time-dependent problemsJan 04 2014Jul 10 2014Domain decomposition (DD) methods for solving time-dependent problems can be classified by (i) the method of domain decomposition used, (ii) the choice of decomposition operators (exchange of boundary conditions), and (iii) the splitting scheme employed. ... More

A Simpler Self-reduction Algorithm for Matroid Path-widthMay 31 2016Apr 18 2018Path-width of matroids naturally generalizes the better known parameter of path-width for graphs, and is NP-hard by a reduction from the graph case. While the term matroid path-width was formally introduced by Geelen-Gerards-Whittle [JCTB 2006] in pure ... More

Reactor Neutrinos: Toward OscillationsFeb 08 2019I shall sketch the history of reactor neutrino physics over five decades since the Reines-Cowan proof of neutrino existence in the late 50s, till the advent of the present era of precision reactor neutrino oscillation experiments. There are three chapters ... More

Reciprocal link among the Qiao-Liu peakon equation and the modified Korteweg-de Vries equationOct 10 2010Oct 17 2010This paper has been withdrawn by the author. The result is already known.

Combinatorial polarization, code loops, and codes of high levelJan 24 2007We first find the combinatorial degree of any map $f:V\to F$ where $F$ is a finite field and $V$ is a finite-dimensional vector space over $F$. We then simplify and generalize a certain construction due to Chein and Goodaire that was used in characterizing ... More

Kochen-Specker sets and Hadamard matricesDec 09 2016Dec 01 2017We introduce a new class of complex Hadamard matrices which have not been studied previously. We use these matrices to construct a new infinite family of parity proofs of the Kochen-Specker theorem. We show that the recently discovered simple parity proof ... More

On complete integrability of the Mikhailov-Novikov-Wang systemMay 12 2010Oct 12 2010We obtain compatible Hamiltonian and symplectic structure for a new two-component fifth-order integrable system recently found by Mikhailov, Novikov and Wang (arXiv:0712.1972), and show that this system possesses a hereditary recursion operator and infinitely ... More

Rankin-Cohen brackets for orthogonal Lie algebras and bilinear conformally invariant differential operatorsJan 12 2013Based on the Lie theoretical methods of algebraic Fourier transformation, we classify singular vectors of diagonally embedded generalized Verma modules for orthogonal Lie algebra and its conformal parabolic subalgebra with commutative nilradical, thereby ... More

Generalized subresultants and generalized subresultant algorithmSep 29 2006Oct 04 2006In this paper we present the notions of trail (pseudo-)division, generalized subresultants and generalized subresultant algorithm.

Limiting measure and stationarity of solutions to stochastic evolution equations with Volterra noiseJun 18 2017Large-time behaviour of solutions to stochastic evolution equations driven by two-sided regular Volterra processes is studied. The solution is understood in the mild sense and takes values in a separable Hilbert space. Sufficient conditions for the existence ... More

Surjective H-Colouring: New Hardness ResultsJan 09 2017Mar 26 2017A homomorphism from a graph G to a graph H is a vertex mapping f from the vertex set of G to the vertex set of H such that there is an edge between vertices f(u) and f(v) of H whenever there is an edge between vertices u and v of G. The H-Colouring problem ... More

Theory of Spin Hall Magnetoresistance from a Microscopic PerspectiveMar 25 2019We present a theory of the spin Hall magnetoresistance of metals in contact with magnetic insulators. We express the spin-mixing conductances, which govern the phenomenology of the effect, in terms of the microscopic parameters of the interface and the ... More

Characterization of self-adjoint extensions for discrete symplectic systemsAug 28 2016All self-adjoint extensions of minimal linear relation associated with the discrete symplectic system are characterized. Especially, for the scalar case on a finite discrete interval some equivalent forms and the uniqueness of the given expression are ... More

You Are How You Walk: Uncooperative MoCap Gait Identification for Video Surveillance with Incomplete and Noisy DataJun 28 2017Jul 27 2017This work offers a design of a video surveillance system based on a soft biometric -- gait identification from MoCap data. The main focus is on two substantial issues of the video surveillance scenario: (1) the walkers do not cooperate in providing learning ... More

Walker-Independent Features for Gait Recognition from Motion Capture DataSep 22 2016Aug 24 2017MoCap-based human identification, as a pattern recognition discipline, can be optimized using a machine learning approach. Yet in some applications such as video surveillance new identities can appear on the fly and labeled data for all encountered people ... More

Learning Robust Features for Gait Recognition by Maximum Margin CriterionSep 14 2016Aug 24 2017In the field of gait recognition from motion capture data, designing human-interpretable gait features is a common practice of many fellow researchers. To refrain from ad-hoc schemes and to find maximally discriminative features we may need to explore ... More

On Move Pattern Trends in a Large Go Games CorpusSep 24 2012We process a large corpus of game records of the board game of Go and propose a way of extracting summary information on played moves. We then apply several basic data-mining methods on the summary information to identify the most differentiating features ... More

Simulation of the electrical conductivity of two-dimensional films with aligned rod-like conductive fillers: effect of the filler length dispersityAug 07 2018Using Monte Carlo simulation, we studied the electrical conductivity of two-dimensional films. The films consisted of a poorly conductive host matrix and highly conductive rod-like fillers (rods). The rods were of various lengths fitting a log-normal ... More

Using Neural Network Formalism to Solve Multiple-Instance ProblemsSep 23 2016Many objects in the real world are difficult to describe by a single numerical vector of a fixed length, whereas describing them by a set of vectors is more natural. Therefore, Multiple instance learning (MIL) techniques have been constantly gaining on ... More

A numerical study of the homogeneous elliptic equation with fractional order boundary conditionsFeb 21 2017We consider the homogeneous equation ${\mathcal A} u=0$, where ${\mathcal A}$ is a symmetric and coercive elliptic operator in $H^1(\Omega)$ with $\Omega$ bounded domain in ${{\mathbb R}}^d$. The boundary conditions involve fractional power $\alpha$, ... More

Averaging in LRS class II spacetimesDec 22 2014We generalize Buchert's averaged equations [Gen. Rel. Grav. 32, 105 (2000); Gen. Rel. Grav. 33, 1381 (2001)] to LRS class II dust model in the sense that all Einstein equations are averaged, not only the trace part. We derive the relevant averaged equations ... More

Steady State Sensitivity Analysis of Continuous Time Markov ChainsApr 02 2018Jan 21 2019In this paper we study Monte Carlo estimators based on the likelihood ratio approach for steady-state sensitivity. We first extend the result of Glynn and Olvera-Cravioto [doi:doi: 10.1287/stsy.2018.002] to the setting of continuous time Markov chains ... More

Quasi-Euclidean subrings of Q[x]Oct 24 2014Using a nonstandard model of Peano arithmetic, we show that there are quasi-Euclidean subrings of Q[x] which are not k-stage Euclidean for any norm and positive integer k. These subrings can be either PID or non-UFD, depending on the choice of parameters ... More

The minimum principle for affine functions with the point of continuity property and isomorphisms of spaces of continuous affine functionJan 24 2018Let X be a compact convex set and let ext X stand for the set of extreme points of X. We show that an affine function with the point of continuity property on X satisfies the minimum principle. As a corollary we obtain a generalization of a theorem by ... More

Two-level schemes for the advection equationNov 19 2017The advection equation is the basis for mathematical models of continuum mechanics. In the approximate solution of nonstationary problems it is necessary to inherit main properties of the conservatism and monotonicity of the solution. In this paper, the ... More

High order numerical schemes for solving fractional powers of elliptic operatorsJan 01 2019In many recent applications when new materials and technologies are developed it is important to describe and simulate new nonlinear and nonlocal diffusion transport processes. A general class of such models deals with nonlocal fractional power elliptic ... More

Evolutionary, symmetric p-Laplacian. Interior regularity of time derivatives and its consequencesSep 25 2015Dec 02 2016We consider the evolutionary symmetric $p$-Laplacian with safety $1$. By symmetric we mean that the full gradient of $p$-Laplacian is replaced by its symmetric part, which causes breakdown of the Uhlenbeck structure. We derive the interior regularity ... More

Mazur intersection property for Asplund spacesApr 03 2008The main result of the present note states that it is consistent with the ZFC axioms of set theory (relying on Martin's Maximum MM axiom), that every Asplund space of density character $\omega_1$ has a renorming with the Mazur intersection property. Combined ... More

Approximation by amplitude and frequency operatorsSep 15 2014Mar 06 2016We study Pad\'{e} interpolation at the node $z=0$ of functions $f(z)=\sum_{m=0}^{\infty} f_m z^m$, analytic in a neighbourhood of this node, by amplitude and frequency operators (sums) of the form $$ \sum_{k=1}^n \mu_k h(\lambda_k z), \qquad \mu_k,\lambda_k\in ... More

New solvable sigma models in plane--parallel wave backgroundAug 01 2013Mar 19 2014We explicitly solve the classical equations of motion for strings in backgrounds obtained as non-abelian T-duals of a homogeneous isotropic plane-parallel wave. To construct the dual backgrounds, semi-abelian Drinfeld doubles are used which contain the ... More

A Simulator for LLVM BitcodeApr 18 2017In this paper, we introduce an interactive simulator for programs in the form of LLVM bitcode. The main features of the simulator include precise control over thread scheduling, automatic checkpoints and reverse stepping, support for source-level information ... More

Scattering polarization in solar flaresOct 11 2013There is an ongoing debate about the origin and even the very existence of a high degree of linear polarization of some chromospheric spectral lines observed in solar flares. The standard explanation of these measurements is in terms of the impact polarization ... More

Graded contractions of the Gell-Mann graded sl(3,C)Aug 19 2013The Gell-Mann grading, one of the four gradings of sl(3,C) that cannot be further refined, is considered as the initial grading for the graded contraction procedure. Using the symmetries of the Gell-Mann grading, the system of contraction equations is ... More

On tensor rank of conditional probability tables in Bayesian networksSep 22 2014A difficult task in modeling with Bayesian networks is the elicitation of numerical parameters of Bayesian networks. A large number of parameters is needed to specify a conditional probability table (CPT) that has a larger parent set. In this paper we ... More

Numerical solving the boundary value problem for fractional powers of elliptic operatorsFeb 07 2014A boundary value problem for a fractional power of the second-order elliptic operator is considered. It is solved numerically using a time-dependent problem for a pseudo-parabolic equation. For the auxiliary Cauchy problem, the standard two-level schemes ... More

Bisimulation Equivalence of First-Order Grammars is ACKERMANN-CompleteJan 22 2019Checking whether two pushdown automata with restricted silent actions are weakly bisimilar was shown decidable by S\'enizergues (1998, 2005). We provide the first known complexity upper bound for this famous problem, in the equivalent setting of first-order ... More

Higher symmetries of symplectic Dirac operatorMar 19 2018We construct in projective differential geometry of the real dimension $2$ higher symmetry algebra of the symplectic Dirac operator ${D}\kern-0.5em\raise0.22ex\hbox{/}_s$ acting on symplectic spinors. The higher symmetry differential operators correspond ... More

Fundamental mode exact schemes for unsteady problemsMay 19 2017The problem of increasing the accuracy of an approximate solution is considered for boundary value problems for parabolic equations. For ordinary differential equations (ODEs), nonstandard finite difference schemes are in common use for this problem. ... More

Iterative computational identification of a spacewise dependent the source in a parabolic equationsApr 15 2016Coefficient inverse problems related to identifying the right-hand side of an equation with use of additional information is of interest among inverse problems for partial differential equations. When considering non-stationary problems, tasks of recovering ... More

Approximating the extreme Ritz values and upper bounds for the $A$-norm of the error in CGOct 04 2018In practical conjugate gradient (CG) computations it is important to monitor the quality of the approximate solution to $Ax=b$ so that the CG algorithm can be stopped when the required accuracy is reached. The relevant convergence characteristics, like ... More

Fermat's Last Theorem and Catalan's Conjecture in Weak Exponential ArithmeticsFeb 11 2016Nov 14 2016We study Fermat's Last Theorem and Catalan's conjecture in the context of weak arithmetics with exponentiation. We deal with expansions (B,e) of models of arithmetical theories (in the language L=(0,1,+,x,<)) by a binary (partial or total) function e ... More

Emergent Gravity at a Lifshitz Point from a Bose Liquid on the LatticeMar 01 2010We propose a model with quantum bosons on the fcc lattice, which has a stable algebraic Bose liquid phase at low energy. We show that this phase is described by emergent quantum gravity at the Gaussian z = 3 Lifshitz fixed point in 3+1 dimensions. The ... More

Control Explicit---Data Symbolic Model Checking: An IntroductionMar 29 2013A comprehensive verification of parallel software imposes three crucial requirements on the procedure that implements it. Apart from accepting real code as program input and temporal formulae as specification input, the verification should be exhaustive, ... More

Survey of an approach to quantum measurement, classical properties and realist interpretation problemsAug 15 2010Feb 23 2011The paper gives a systematic review of the basic ideas of (non-relativistic) quantum mechanics including all changes that result from previous work of the authors. This shows that the new theory is self-consistent and (in certain sense) complete. The ... More

Note on Undecidability of Bisimilarity for Second-Order Pushdown ProcessesMar 04 2013Broadbent and G\"oller (FSTTCS 2012) proved the undecidability of bisimulation equivalence for processes generated by epsilon-free second-order pushdown automata. We add a few remarks concerning the used proof technique, called Defender's forcing, and ... More

Computational identification of the lowest space-wise dependent coefficient of a parabolic equationApr 09 2018In the present work, we consider a nonlinear inverse problem of identifying the lowest coefficient of a parabolic equation. The desired coefficient depends on spatial variables only. Additional information about the solution is given at the final time ... More

Two-component domain decomposition scheme with overlapping subdomains for parabolic equationsMay 09 2017An iteration-free method of domain decomposition is considered for approximate solving a boundary value problem for a second-order parabolic equation. A standard approach to constructing domain decomposition schemes is based on a partition of unity for ... More

Remarks on the convergence of pseudospectraAug 14 2014We establish the convergence of pseudospectra in Hausdorff distance for closed operators acting in different Hilbert spaces and converging in the generalised norm resolvent sense. As an assumption, we exclude the case that the limiting operator has constant ... More