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A polynomial version of Cereceda's conjectureMar 13 2019Let $k$ and $d$ be such that $k \ge d+2$. Consider two $k$-colourings of a $d$-degenerate graph $G$. Can we transform one into the other by recolouring one vertex at each step while maintaining a proper coloring at any step? Cereceda et al. answered that ... More
Discrete Spectra of Convolutions on Disks using Sturm-Liouville TheoryJan 15 2019This paper presents a systematic study for analytic aspects of discrete spectra methods for convolution of functions supported on disks, according to the Sturm-Liouville theory. We then investigate different aspects of the presented theory in the cases ... More
Near actionsJan 14 2019A near permutation of a set is a bijection between two cofinite subsets, modulo coincidence on smaller cofinite subsets. Near permutations of a set form its near symmetric group. In this monograph, we define near actions as homomorphisms into this group, ... More
Fourier-Zernike Series of Convolutions on DisksOct 29 2018This paper presents a systematic study for analytic aspects of Fourier-Zernike series of convolutions of functions supported on disks. We then investigate different aspects of the presented theory in the cases of zero-padded functions.
Inductive limits of semiprojective C*-algebrasApr 13 2018Feb 18 2019We prove closure properties for the class of C*-algebras that are inductive limits of semiprojective C*-algebras. Most importantly, we show that this class is closed under shape domination, and so in particular under shape and homotopy equivalence. It ... More
Near critical preferential attachment networks have small giant componentsDec 01 2017Preferential attachment networks with power law exponent $\tau>3$ are known to exhibit a phase transition. There is a value $\rho_{\rm c}>0$ such that, for small edge densities $\rho\leq \rho_c$ every component of the graph comprises an asymptotically ... More
Contrast in Greyscales of GraphsDec 22 2016Jan 11 2018A greyscale $f$ of a graph $G(V,E)$ is a mapping from $V$ to the interval $[0,1]$ such that $\{0, 1\} \subseteq Im(f)$. This function $f$ induces another mapping $\widehat{f}$ on $E$ by assigning to each edge the non-negative difference of the values ... More
Smooth Factors of Projective Actions of Higher Rank Lattices and RigiditySep 22 2016We study smooth factors of the standard actions of lattices in higher rank semisimple Lie groups on flag manifolds. Under a mild condition on existence of a single differentiable sink, we show that these factors are $C^{\infty}$-conjugate to the standard ... More
Exponential Mixing and Smooth Classification of Commuting Expanding MapsAug 08 2016We show that genuinely higher rank expanding actions of abelian semi-groups on compact manifolds are $C^{\infty}$-conjugate to affine actions on infra-nilmanifolds. This is based on the classification of expanding diffeomorphisms up to \holder conjugacy ... More
Three-coloring triangle-free graphs on surfaces VII. A linear-time algorithmJan 06 2016We give a linear-time algorithm to decide 3-colorability of a triangle-free graph embedded in a fixed surface, and a quadratic-time algorithm to output a 3-coloring in the affirmative case. The algorithms also allow to prescribe the coloring for a bounded ... More
Using tropical optimization to solve constrained minimax single-facility location problems with rectilinear distanceNov 24 2015Nov 28 2015We consider a constrained minimax single-facility location problem with addends on the plane with rectilinear distance. The problem is first formulated in a standard form, and then represented in terms of tropical mathematics as a constrained optimization ... More
Using tropical optimization to solve constrained minimax single-facility location problems with rectilinear distanceNov 24 2015Sep 07 2017The aim of this paper is twofold: first, to extend the area of applications of tropical optimization by solving new constrained location problems, and second, to offer new closed-form solutions to general problems that are of interest to location analysis. ... More
Interpolation by periods in planar domainNov 22 2015Let $\Omega\subset\mathbb R^2$ be a countably connected domain. To any closed differential form of degree $1$ in $\Omega$ with components in $L^2(\Omega)$ one associates the sequence of its periods around holes in $\Omega$, that is around bounded connected ... More
Three-coloring triangle-free graphs on surfaces VI. 3-colorability of quadrangulationsSep 03 2015We give a linear-time algorithm to decide 3-colorability (and find a 3-coloring, if it exists) of quadrangulations of a fixed surface. The algorithm also allows to prescribe the coloring for a bounded number of vertices.
Fast and accurate computation of the logarithmic capacity of compact setsJul 21 2015Oct 19 2016We present a numerical method for computing the logarithmic capacity of compact subsets of $\mathbb{C}$, which are bounded by Jordan curves and have finitely connected complement. The subsets may have several components and need not have any special symmetry. ... More
Groups with infinitely many ends acting analytically on the circleJun 11 2015Sep 28 2015This article takes the inspiration from two milestones in the study of non minimal actions of groups on the circle: Duminy's theorem about the number of ends of semi-exceptional leaves and Ghys' freeness result in analytic regularity. Our first result ... More
Groups with infinitely many ends acting analytically on the circleJun 11 2015Nov 28 2018This article takes the inspiration from two milestones in the study of non minimal actions of groups on the circle: Duminy's theorem about the number of ends of semi-exceptional leaves and Ghys' freeness result in analytic regularity. Our first result ... More
Ability to Count Is Worth $Θ(Δ)$ RoundsMay 09 2015Hella et al. (PODC 2012, Distributed Computing 2015) identified seven different models of distributed computing - one of which is the port-numbering model - and provided a complete classification of their computational power relative to each other. However, ... More
Search algorithms for efficient logistics chainsApr 09 2015Logistics networks arise whenever there is a transfer of material substance or objects (such as checked baggage on international flights) as well as energy, information, or finance through links (channels). A general concept of logistics network is suggested ... More
Conjugate Function Method and Conformal Mappings in Multiply Connected DomainsFeb 06 2015Oct 13 2015In this paper, we present a generalization of the conjugate function method, an algorithm for numerical computation of conformal mappings for simply and doubly connected domains, on multiply connected domains. The key challenge addressed here is the construction ... More
Conjugate Function Method and Conformal Mappings in Multiply Connected DomainsFeb 06 2015Jul 05 2017The conjugate function method is an algorithm for numerical computation of conformal mappings for simply and doubly connected domains. In this paper the conjugate function method is generalized for multiply connected domains. The key challenge addressed ... More
An on-line competitive algorithm for coloring bipartite graphs without long induced pathsFeb 03 2015The existence of an on-line competitive algorithm for coloring bipartite graphs remains a tantalizing open problem. So far there are only partial positive results for bipartite graphs with certain small forbidden graphs as induced subgraphs. We propose ... More
Metric spaces admitting low-distortion embeddings into all $n$-dimensional Banach spacesDec 24 2014Aug 18 2015For a fixed $K\gg 1$ and $n\in\mathbb{N}$, $n\gg 1$, we study metric spaces which admit embeddings with distortion $\le K$ into each $n$-dimensional Banach space. Classical examples include spaces embeddable into $\log n$-dimensional Euclidean spaces, ... More
Rainbow Colouring of Split GraphsApr 17 2014A rainbow path in an edge coloured graph is a path in which no two edges are coloured the same. A rainbow colouring of a connected graph G is a colouring of the edges of G such that every pair of vertices in G is connected by at least one rainbow path. ... More
List-coloring apex-minor-free graphsJan 07 2014A graph H is t-apex if H-X is planar for some set X\subset V(H) of size t. For any integer t>=0 and a fixed t-apex graph H, we give a polynomial-time algorithm to decide whether a (t+3)-connected H-minor-free graph is colorable from a given assignment ... More
List-coloring apex-minor-free graphsJan 07 2014Dec 26 2016A graph H is t-apex if H-X is planar for some subset X of V(H) of size t. For any integer t>=0 and a fixed t-apex graph H, we give a polynomial-time algorithm to decide whether a (t+3)-connected H-minor-free graph is colorable from a given assignment ... More
On the ergodic theory of free group actions by real-analytic circle diffeomorphismsDec 15 2013Nov 02 2016We consider finitely generated groups of real-analytic circle diffeomorphisms. We show that if such a group admits an exceptional minimal set (i.e., a minimal invariant Cantor set), then its Lebesgue measure is zero; moreover, there are only finitely ... More
Towards the solution of some fundamental questions concerning group actions on the circle and codimension-one foliationsDec 15 2013Sep 07 2014We consider finitely generated groups of real-analytic circle diffeomorphisms. We show that if such a group admits an exceptional minimal set (i.e., a minimal invariant Cantor set), then its Lebesgue measure is zero; moreover, there are only finitely ... More
Complete solution of a constrained tropical optimization problem with application to location analysisNov 12 2013Apr 16 2014We present a multidimensional optimization problem that is formulated and solved in the tropical mathematics setting. The problem consists of minimizing a nonlinear objective function defined on vectors over an idempotent semifield by means of a conjugate ... More
Direct solutions to tropical optimization problems with nonlinear objective functions and boundary constraintsNov 10 2013We examine two multidimensional optimization problems that are formulated in terms of tropical mathematics. The problems are to minimize nonlinear objective functions, which are defined through the multiplicative conjugate vector transposition on vectors ... More
Random spanning forests, Markov matrix spectra and well distributed pointsOct 07 2013Jan 29 2016This paper is a variation on the uniform spanning tree theme. We use random spanning forests to solve the following problem: for a Markov process on a finite set of size $n$, find a probability law on the subsets of any given size $m \leq n$ with the ... More
Minimum Distance Estimation of Milky Way Model Parameters and Related InferenceSep 03 2013Aug 15 2014We propose a method to estimate the location of the Sun in the disk of the Milky Way using a method based on the Hellinger distance and construct confidence sets on our estimate of the unknown location using a bootstrap based method. Assuming the Galactic ... More
Weighted energy problem on the unit circleJul 20 2013We solve the weighted energy problem on the unit circle, by finding the extremal measure and describing its support. Applications to polynomial and exponential weights are also included.
The $κ_r$-version of the WRT$_r$-invariants, monochromatic 3-connected blinks and evidence for a conjecture on their induced 3-manifoldsJul 08 2013Feb 24 2014A {\em blink} is a plane graph with a bipartition (black, gray) of its edges. Subtle classes of blinks are in 1-1 correspondence with closed, oriented and connected 3-manifolds up to orientation preserving homeomorphisms \cite{lins2013B}. Switching black ... More
Conditionally strictly negative definite kernelsJul 06 2013Mar 24 2014In this note we refine the notion of conditionally negative definite kernels to the notion of conditionally strictly negative definite kernels and study its properties. We show that the class of these kernels carries some surprising rigidity, in particular, ... More
Vulnerability of robust preferential attachment networksJun 14 2013Aug 22 2013Scale-free networks with small power law exponent are known to be robust, meaning that their qualitative topological structure cannot be altered by random removal of even a large proportion of nodes. By contrast, it has been argued in the science literature ... More
Closed oriented 3-manifolds are subtle equivalence classes of plane graphsMay 20 2013Jul 09 2013A {\em blink} is a plane graph with an arbitrary bipartition of its edges. As a consequence of a recent result of Martelli, I show that the homeomorphisms classes of closed oriented 3-manifolds are in 1-1 correspondence with specific classes of blinks. ... More
Closed oriented 3-manifolds are subtle equivalence classes of plane graphsMay 20 2013Dec 07 2016A {\em blink} is a plane graph with an arbitrary bipartition of its edges. As a consequence of a recent result of Martelli, I show that the homeomorphisms classes of closed oriented 3-manifolds are in 1-1 correspondence with specific classes of blinks. ... More
Non-commutative localizations of additive categories and weight structures; applications to birational motivesApr 22 2013Sep 15 2014In this paper we demonstrate that 'non-commutative localizations' of arbitrary additive categories (generalizing those defined by Cohn for rings) are closely (and naturally) related with weight structures. Localizing an arbitrary triangulated $C$ by a ... More
Complete monotonicity for inverse powers of some combinatorially defined polynomialsJan 11 2013Jan 06 2014We prove the complete monotonicity on $(0,\infty)^n$ for suitable inverse powers of the spanning-tree polynomials of graphs and, more generally, of the basis generating polynomials of certain classes of matroids. This generalizes a result of Szego and ... More
A tropical extremal problem with nonlinear objective function and linear inequality constraintsDec 26 2012We consider a multidimensional extremal problem formulated in terms of tropical mathematics. The problem is to minimize a nonlinear objective function, which is defined on a finite-dimensional semimodule over an idempotent semifield, subject to linear ... More
Algebraic solution to a constrained rectilinear minimax location problem on the planeDec 25 2012We consider a constrained minimax single facility location problem on the plane with rectilinear distance. The feasible set of location points is restricted to rectangles with sides oriented at a 45 degrees angle to the axes of Cartesian coordinates. ... More
Algebraic solutions to multidimensional minimax location problems with Chebyshev distanceDec 25 2012Multidimensional minimax single facility location problems with Chebyshev distance are examined within the framework of idempotent algebra. A new algebraic solution based on an extremal property of the eigenvalues of irreducible matrices is given. The ... More
List-coloring embedded graphsOct 29 2012For any fixed surface Sigma of genus g, we give an algorithm to decide whether a graph G of girth at least five embedded in Sigma is colorable from an assignment of lists of size three in time O(|V(G)|). Furthermore, we can allow a subgraph (of any size) ... More
Rainbow Colouring of Split and Threshold GraphsMay 08 2012A rainbow colouring of a connected graph is a colouring of the edges of the graph, such that every pair of vertices is connected by at least one path in which no two edges are coloured the same. Such a colouring using minimum possible number of colours ... More
Topological generators of abelian Lie groups and hypercyclic finitely generated abelian semigroups of matricesAug 04 2011In this paper we bring together results about the density of subsemigroups of abelian Lie groups, the minimal number of topological generators of abelian Lie groups and a result about actions of algebraic groups. We find the minimal number of generators ... More
Algebraic/combinatorial proofs of Cayley-type identities for derivatives of determinants and pfaffiansMay 31 2011Dec 31 2012The classic Cayley identity states that \det(\partial) (\det X)^s = s(s+1)...(s+n-1) (\det X)^{s-1} where X=(x_{ij}) is an n-by-n matrix of indeterminates and \partial=(\partial/\partial x_{ij}) is the corresponding matrix of partial derivatives. In this ... More
Conjugate Function Method for Numerical Conformal MappingsMar 25 2011Jun 26 2012We present a method for numerical computation of conformal mappings from simply or doubly connected domains onto so-called canonical domains, which in our case are rectangles or annuli. The method is based on conjugate harmonic functions and properties ... More
A Coloring Algorithm for Triangle-Free GraphsJan 29 2011We give a randomized algorithm that properly colors the vertices of a triangle-free graph G on n vertices using O(\Delta(G)/ log \Delta(G)) colors, where \Delta(G) is the maximum degree of G. The algorithm takes O(n\Delta2(G)log\Delta(G)) time and succeeds ... More
"On the engineers' new toolbox" or Analog Circuit Design, using Symbolic Analysis, Computer Algebra, and Elementary Network TransformationsDec 31 2010In this paper, by way of three examples - a fourth order low pass active RC filter, a rudimentary BJT amplifier, and an LC ladder - we show, how the algebraic capabilities of modern computer algebra systems can, or in the last example, might be brought ... More
Rainbow Connection Number and RadiusNov 02 2010Sep 11 2012The rainbow connection number, rc(G), of a connected graph G is the minimum number of colours needed to colour its edges, so that every pair of its vertices is connected by at least one path in which no two edges are coloured the same. In this note we ... More
The geometry of oriented cubesAug 10 2010This reports on the fundamental objects revealed by Ross Street, which he called `orientals'. Street's work was in part inspired by Robert's attempts to use N-category ideas to construct nets of C*-algebras in Minkowski space for applications to relativistic ... More
Zero forcing parameters and minimum rank problemsMar 10 2010The zero forcing number Z(G), which is the minimum number of vertices in a zero forcing set of a graph G, is used to study the maximum nullity / minimum rank of the family of symmetric matrices described by G. It is shown that for a connected graph of ... More
Birth of a strongly connected giant in an inhomogeneous random digraphNov 16 2009We present and investigate a general model for inhomogeneous random digraphs with labeled vertices, where the arcs are generated independently, and the probability of inserting an arc depends on the labels of its endpoints and its orientation. For this ... More
When is a Riesz distribution a complex measure?Jun 16 2009Feb 06 2012Let R_\alpha be the Riesz distribution on a simple Euclidean Jordan algebra, parametrized by the complex number \alpha. I give an elementary proof of the necessary and sufficient condition for R_\alpha to be a locally finite complex measure (= complex ... More
Candy-passing Games on General Graphs, IIJul 29 2008We give a new proof that any candy-passing game on a graph G with at least 4|E(G)|-|V(G)| candies stabilizes. (This result was first proven in arXiv:0807.4450.) Unlike the prior literature on candy-passing games, we use methods from the general theory ... More
Harmonic analysis of finite lamplighter random walksJan 22 2007Recently, several papers have been devoted to the analysis of lamplighter random walks, in particular when the underlying graph is the infinite path $\mathbb{Z}$. In the present paper, we develop a spectral analysis for lamplighter random walks on finite ... More
New results on generalized graph coloringJun 10 2003For graph classes $P_1,...,P_k$, Generalized Graph Coloring is the problem of deciding whether the vertex set of a given graph $G$ can be partitioned into subsets $V_1,...,V_k$ so that $V_j$ induces a graph in the class $P_j$ $(j=1,2,...,k)$. If $P_1 ... More
Vertex-partitioning into fixed additive induced-hereditary properties is NP-hardJun 10 2003Can the vertices of a graph $G$ be partitioned into $A \cup B$, so that $G[A]$ is a line-graph and $G[B]$ is a forest? Can $G$ be partitioned into a planar graph and a perfect graph? The NP-completeness of these problems are just special cases of our ... More
A connection between multiresolution wavelet theory of scale N and representations of the Cuntz algebra O_NDec 19 1996In this paper we give a short survey of a connection between the theory of wavelets in L^2(R) and certain representations of the Cuntz algebra on L^2(T).
Isometries, shifts, Cuntz algebras and multiresolution wavelet analysis of scale NDec 17 1996In this paper we show how wavelets originating from multiresolution analysis of scale N give rise to certain representations of the Cuntz algebras O_N, and conversely how the wavelets can be recovered from these representations. The representations are ... More
Iterated function systems and permutation representations of the Cuntz algebraDec 17 1996We study a class of representations of the Cuntz algebras O_N, N=2,3,..., acting on L^2(T) where T=R/2\pi Z. The representations arise in wavelet theory, but are of independent interest. We find and describe the decomposition into irreducibles, and show ... More