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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 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

Hitting Topological Minor Models in Planar Graphs is Fixed Parameter TractableJul 05 2019For a finite collection of graphs ${\cal F}$, the ${\cal F}$-TM-Deletion problem has as input an $n$-vertex graph $G$ and an integer $k$ and asks whether there exists a set $S \subseteq V(G)$ with $|S| \leq k$ such that $G \setminus S$ does not contain ... More

Refined Complexity of PCA with OutliersMay 10 2019Principal component analysis (PCA) is one of the most fundamental procedures in exploratory data analysis and is the basic step in applications ranging from quantitative finance and bioinformatics to image analysis and neuroscience. However, it is well-documented ... 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

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

Planar Disjoint Paths in Linear TimeJul 12 2019The Disjoint Paths problem asks whether a fixed number of pairs of terminals in a graph $G$ can be linked by pairwise disjoint paths. In the context of this problem, Robertson and Seymour introduced the celebrated irrelevant vertex technique that has ... More

Planar Disjoint Paths in Linear TimeJul 12 2019Jul 17 2019The Disjoint Paths problem asks whether a fixed number of pairs of terminals in a graph $G$ can be linked by pairwise disjoint paths. In the context of this problem, Robertson and Seymour introduced the celebrated irrelevant vertex technique that has ... 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

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

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

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

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

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.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Parallelization, processor communication and error analysis in lattice kinetic Monte CarloAug 05 2012In this paper we study from a numerical analysis perspective the Fractional Step Kinetic Monte Carlo (FS-KMC) algorithms proposed in [1] for the parallel simulation of spatially distributed particle systems on a lattice. FS-KMC are fractional step algorithms ... More

Error analysis of coarse-grained kinetic Monte Carlo methodSep 09 2005In this paper we investigate the approximation properties of the coarse-graining procedure applied to kinetic Monte Carlo simulations of lattice stochastic dynamics. We provide both analytical and numerical evidence that the hierarchy of the coarse models ... More

Spatial multi-level interacting particle simulations and information theory-based error quantificationAug 03 2012We propose a hierarchy of multi-level kinetic Monte Carlo methods for sampling high-dimensional, stochastic lattice particle dynamics with complex interactions. The method is based on the efficient coupling of different spatial resolution levels, taking ... More

Yang-Mills detour complexes and conformal geometryJun 16 2006Mar 25 2008Working over a pseudo-Riemannian manifold, for each vector bundle with connection we construct a sequence of three differential operators which is a complex (termed a Yang-Mills detour complex) if and only if the connection satisfies the full Yang-Mills ... 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

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

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

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

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

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

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

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

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

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

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

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 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

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

Multilevel coarse graining and nano--pattern discovery in many particle stochastic systemsSep 02 2011In this work we propose a hierarchy of Monte Carlo methods for sampling equilibrium properties of stochastic lattice systems with competing short and long range interactions. Each Monte Carlo step is composed by two or more sub - steps efficiently coupling ... 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

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

Noncommutative Geometry of Quantized CoveringsApr 30 2019May 21 2019This research is devoted to the noncommutative generalization of topological coverings. Otherwise since topological coverings are related to the set of geometric constructions one can obtain noncommutative generalizations of these constructions. Here ... 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

Species OrthogonalizationSep 17 2001We discuss general formation of complementary behaviors, functions and forms in biological species competing for resources. We call orthogonalization the related processes on macro and micro-level of a self-organized formation of correlations in the species ... More

A new family of singular integral operators whose $L^2$-boundedness implies rectifiabilityJan 27 2016Sep 12 2017Let $E \subset \mathbb{C}$ be a Borel set such that $0<\mathcal{H}^1(E)<\infty$. David and L\'eger proved that the Cauchy kernel $1/z$ (and even its coordinate parts $\textrm{Re}\, z/|z|^2$ and $\textrm{Im}\, z/|z|^2$, $z\in \mathbb{C}\setminus\{0\}$) ... More

A Short Proof of Euler--Poincaré FormulaDec 05 2016Feb 23 2017We provide a short self-contained inductive proof of the famous generalized Euler-Poincar\'e Formula for the numbers of faces of a convex polytope in every dimension. Our proof is elementary and it does not use shellability of polytopes.

Discrete trigonometric and hyperbolic systems: An overviewJun 17 2016Aug 22 2016In this paper we present an overview of results for discrete trigonometric and hyperbolic systems. These systems are discrete analogues of trigonometric and hyperbolic linear Hamiltonian systems. We show results which can be viewed as discrete n-dimensional ... More

Random generators of given orders and the smallest simple Moufang loopJan 24 2007The probability that $m$ randomly chosen elements of a finite power associative loop $C$ have prescribed orders and generate $C$ is calculated in terms of certain constants related to the action of $Aut(C)$ on the subloop lattice of $C$. As an illustration, ... More

Surprising spectra of PT-symmetric point interactionsJun 01 2009Spectra of the second derivative operators corresponding to the special PT-symmetric point interactions are studied. The results are partly the completion of those obtained in [1]. The particular PT-symmetric point interactions causing unusual spectral ... More

Optimal statistical decision for Gaussian graphical model selectionJan 09 2017Gaussian graphical model is a graphical representation of the dependence structure for a Gaussian random vector. It is recognized as a powerful tool in different applied fields such as bioinformatics, error-control codes, speech language, information ... More

A note on the problem of prisoners and hatsJan 03 2018We study the famous mathematical puzzle of prisoners and hats. We introduce a framework in which various variants of the problem can be formalized. We examine three particular versions of the problem (each one in fact a class of problems) and completely ... 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

Combinatorial aspects of code loopsJan 24 2007The existence and uniqueness (up to equivalence) of code loops was first established by R. Griess. Nevertheless, the explicit construction of code loops remained open until T. Hsu introduced the notion of symplectic cubic spaces and their Frattini extensions, ... More

On the uniqueness of loops M(G,2)Jan 24 2007Let $G$ be a finite group and $C_2$ the cyclic group of order 2. Consider the 8 multiplicative operations $(x,y)\mapsto (x^iy^j)^k$, where $i$, $j$, $k\in\{-1, 1\}$. Define a new multiplication on $G\times C_2$ by assigning one of the above 8 multiplications ... 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.

Hypergeometric form of Fundamental theorem of calculusAug 14 2018We introduce a natural method of computing antiderivatives of a large class of functions which stems from the observation that the series expansion of an antiderivative differs from the series expansion of the corresponding integrand by just two Pochhammer ... More

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

Electrostatic doping of graphene through ultrathin hexagonal boron nitride filmsNov 10 2011When combined with graphene, hexagonal boron nitride (h-BN) is an ideal substrate and gate dielectric with which to build metalh-BN|graphene field-effect devices. We use first-principles density functional theory (DFT) calculations for Cu|h-BN|graphene ... More

Coarse-graining schemes and a posteriori error estimates for stochastic lattice systemsAug 01 2006The primary objective of this work is to develop coarse-graining schemes for stochastic many-body microscopic models and quantify their effectiveness in terms of a priori and a posteriori error analysis. In this paper we focus on stochastic lattice systems ... More

Interferometric observations of the multiple stellar system delta VelorumMar 30 2007delta Velorum is a nearby (24pc) triple stellar system, containing a close, eclipsing binary (Aa, Ab) discovered in 2000. Multiple systems provide an opportunity to determine the set of fundamental parameters (mass, luminosity, size and chemical composition) ... More

Stochastic Combinatorial Ensembles for Defending Against Adversarial ExamplesAug 20 2018Sep 08 2018Many deep learning algorithms can be easily fooled with simple adversarial examples. To address the limitations of existing defenses, we devised a probabilistic framework that can generate an exponentially large ensemble of models from a single model ... More

Exact Crossing Number Parameterized by Vertex CoverJun 14 2019We prove that the exact crossing number of a graph can be efficiently computed for simple graphs having bounded vertex cover. In more precise words, Crossing Number is in FPT when parameterized by the vertex cover size. This is a notable advance since ... More

Symplectic twistor operator and its solution space on ${\mathbb R}^2$Jan 12 2013Jan 05 2016We introduce the symplectic twistor operator $T_s$ in symplectic spin geometry, as a symplectic analogue of the twistor operator in Riemannian spin geometry. We focus on the real dimension 2 and compute the space of its solutions on ${\mathbb R}^2$. Our ... More

Kochen-Specker sets in four-dimensional spacesMay 23 2019For the first time we construct an infinite family of Kochen-Specker sets in a space of fixed dimension, namely in R^4. While most of the previous constructions of Kochen-Specker sets have been based on computer search, our construction is analytical ... More

A priori estimation of a time step for numerically solving parabolic problemsNov 12 2013This work deals with the problem of choosing a time step for the numerical solution of boundary value problems for parabolic equations. The problem solution is derived using the fully implicit scheme, whereas a time step is selected via explicit calculations. ... 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

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

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

Characterization of half-radial matricesApr 27 2018Sep 06 2018Numerical radius $r(A)$ is the radius of the smallest ball with the center at zero containing the field of values of a given square matrix $A$. It is well known that $r(A)\leq \|A\| \leq 2r(A)$, where $\| \cdot \|$ is the matrix 2-norm. Matrices attaining ... 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

Equivalent formulation of Thomassen's conjecture using Tutte paths in claw-free graphsJul 18 2019We continue studying Thomassen's conjecture (every 4-connected line graph has a Hamilton cycle) in the direction of a recently shown equivalence with Jackson's conjecture (every 2-connected claw-free graph has a Tutte cycle), and we extend the equivalent ... More

Dynamical Generation of Synthetic Electric Fields for Photons in the Quantum RegimeFeb 02 2019Jun 21 2019Optomechanics offers a natural way to implement synthetic dynamical gauge fields, leading to synthetic electric fields for phonons and, as a consequence, to unidirectional light transport. Here we investigate the quantum dynamics of synthetic gauge fields ... More

On (alpha,beta,gamma)-derivations of Lie algebras and corresponding invariant functionsMar 18 2008We consider finite-dimensional complex Lie algebras. We generalize the concept of Lie derivations via certain complex parameters and obtain various Lie and Jordan operator algebras as well as two one-parametric sets of linear operators. Using these parametric ... More

Multi-step nucleation of nanocrystals in aqueous solutionMay 16 2016Nucleation and growth of solids from solutions impacts many natural processes and are fundamental to applications in materials engineering and medicine. For a crystalline solid, the nucleus is a nanoscale cluster of ordered atoms, which forms through ... 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

Dynamical Generation of Synthetic Electric Fields for Photons in the Quantum RegimeFeb 02 2019Optomechanics offers a natural way to implement synthetic dynamical gauge fields, leading to synthetic electric fields for phonons and, as a consequence, to unidirectional light transport. Here we investigate the quantum dynamics of synthetic gauge fields ... More

On extremal properties of Jacobian elliptic functions with complex modulusDec 18 2015A thorough analysis of values of the function $m\mapsto\mbox{sn}(K(m)u\mid m)$ for complex parameter $m$ and $u\in (0,1)$ is given. First, it is proved that the absolute value of this function never exceeds 1 if $m$ does not belong to the region in $\mathbb{C}$ ... 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

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