total 384took 0.10s

Finding non-minority balls with majority and plurality queriesDec 20 2018Given a set of $n$ colored balls, a \textit{majority, non-minority or plurality ball} is one whose color class has size more than $n/2$, at least $n/2$ or larger than any other color class, respectively. We describe linear time algorithms for finding ... More

t-wise Berge and t-heavy hypergraphsFeb 08 2019In many proofs concerning extremal parameters of Berge hypergraphs one starts with analyzing that part of that shadow graph which is contained in many hyperedges. Capturing this phenomenon we introduce two new types of hypergraphs. A hypergraph $\mathcal{H}$ ... More

Large B_d-free and union-free subfamiliesDec 17 2010For a property $\Gamma$ and a family of sets $\cF$, let $f(\cF,\Gamma)$ be the size of the largest subfamily of $\cF$ having property $\Gamma$. For a positive integer $m$, let $f(m,\Gamma)$ be the minimum of $f(\cF,\Gamma)$ over all families of size $m$. ... More

Avoider-Enforcer star gamesFeb 11 2013Jan 30 2015In this paper, we study $(1 : b)$ Avoider-Enforcer games played on the edge set of the complete graph on $n$ vertices. For every constant $k\geq 3$ we analyse the $k$-star game, where Avoider tries to avoid claiming $k$ edges incident to the same vertex. ... More

Two-part set systemsOct 01 2011The two part Sperner theorem of Katona and Kleitman states that if $X$ is an $n$-element set with partition $X_1 \cup X_2$, and $\cF$ is a family of subsets of $X$ such that no two sets $A, B \in \cF$ satisfy $A \subset B$ (or $B \subset A$) and $A \cap ... More

On the number of maximal intersecting k-uniform families and further applications of Tuza's set pair methodJan 04 2015Mar 12 2015We study the function $M(n,k)$ which denotes the number of maximal $k$-uniform intersecting families $F\subseteq \binom{[n]}{k}$. Improving a bound of Balogh at al. on $M(n,k)$, we determine the order of magnitude of $\log M(n,k)$ by proving that for ... More

Nonrepetitive colorings of lexicographic product of graphsOct 20 2012Sep 16 2013A coloring $c$ of the vertices of a graph $G$ is nonrepetitive if there exists no path $v_1v_2\ldots v_{2l}$ for which $c(v_i)=c(v_{l+i})$ for all $1\le i\le l$. Given graphs $G$ and $H$ with $|V(H)|=k$, the lexicographic product $G[H]$ is the graph obtained ... More

Invariant formulation of the Functional Renormalisation Group method for $U(n)\times U(n)$ symmetric matrix modelsOct 24 2012The Local Potential Approximation (LPA) to the Wetterich-equation is formulated explicitly in terms of operators, which are invariant under the $U(n)\times U(n)$ symmetry group. Complete formulas are presented for the two-flavor ($U(2)\times U(2)$) case. ... More

Search Problems in Vector SpacesSep 26 2013Jan 30 2014We consider the following $q$-analog of the basic combinatorial search problem: let $q$ be a prime power and $\GF(q)$ the finite field of $q$ elements. Let $V$ denote an $n$-dimensional vector space over $\GF(q)$ and let $\mathbf{v}$ be an unknown 1-dimensional ... More

An improvement on the maximum number of $k$-Dominating Independent SetsSep 14 2017Erd\H{o}s and Moser raised the question of determining the maximum number of maximal cliques or equivalently, the maximum number of maximal independent sets in a graph on $n$ vertices. Since then there has been a lot of research along these lines. A $k$-dominating ... More

On the number of cycles in a graph with restricted cycle lengthsOct 11 2016Let $L$ be a set of positive integers. We call a (directed) graph $G$ an $L$\emph{-cycle graph} if all cycle lengths in $G$ belong to $L$. Let $c(L,n)$ be the maximum number of cycles possible in an $n$-vertex $L$-cycle graph (we use $\vec{c}(L,n)$ for ... More

Line Percolation in Finite Projective PlanesAug 01 2016We study combinatorial parameters of a recently introduced bootstrap percolation problem in finite projective planes. We present sharp results on the size of the minimum percolating sets and the maximal non-percolating sets. Additional results on the ... More

Majority and Plurality ProblemsMar 07 2012Given a set of n balls each colored with a color, a ball is said to be majority, k-majority, plurality if its color class has size larger than half of the number of balls, has size at least k, has size larger than any other color class; respectively. ... More

Cross-Sperner familiesApr 20 2011A pair of families $(\cF,\cG)$ is said to be \emph{cross-Sperner} if there exists no pair of sets $F \in \cF, G \in \cG$ with $F \subseteq G$ or $G \subseteq F$. There are two ways to measure the size of the pair $(\cF,\cG)$: with the sum $|\cF|+|\cG|$ ... More

The minimum number of vertices in uniform hypergraphs with given domination numberMar 11 2016Jul 16 2016The \textit{domination number} $\gamma(\mathcal{H})$ of a hypergraph $\mathcal{H}=(V(\mathcal{H}),E(\mathcal{H})$ is the minimum size of a subset $D\subset V(\mathcal{H}$ of the vertices such that for every $v\in V(\mathcal{H})\setminus D$ there exist ... More

Weak Coupling Phase Structureof the Abelian Higgs Model at Finite TemperatureMay 03 1993Using the 1-loop reduced 3D action of the Abelian Higgs-model we discuss the order of its finite temperature phase transition. A two-variable saddle point approximation is proposed for the evaluation of the effective potential. The strength of the first ... More

On the ratio of maximum and minimum degree in maximal intersecting familiesSep 06 2011To study how balanced or unbalanced a maximal intersecting family $\mathcal{F}\subseteq \binom{[n]}{r}$ is we consider the ratio $\mathcal{R}(\mathcal{F})=\frac{\Delta(\mathcal{F})}{\delta(\mathcal{F})}$ of its maximum and minimum degree. We determine ... More

Domination game on uniform hypergraphsOct 01 2017In this paper we introduce and study the domination game on hypergraphs. This is played on a hypergraph $\mathcal{H}$ by two players, namely Dominator and Staller, who alternately select vertices such that each selected vertex enlarges the set of vertices ... More

Finding a non-minority ball with majority answersSep 28 2015Sep 28 2016Suppose we are given a set of $n$ balls $\{b_1,\ldots,b_n\}$ each colored either red or blue in some way unknown to us. To find out some information about the colors, we can query any triple of balls $\{b_{i_1},b_{i_2},b_{i_3}\}$. As an answer to such ... More

From Floquet to Dicke: quantum spin-Hall insulator interacting with quantum lightMay 28 2015Sep 15 2015Time-periodic perturbations due to classical electromagnetic fields are useful to engineer the topological properties of matter using the Floquet theory. Here we investigate the effect of quantized electromagnetic fields by focusing on the quantized light-matter ... More

Collective modes for quantum spin Hall insulator interacting with quantum lightFeb 12 2019We investigate the light-matter interaction between the edge state of a 2D topological insulator and quantum electromagnetic field. The interaction originates from the Zeeman term between the spin of the edge electrons and the magnetic field, and also ... More

Saturating Sperner familiesMay 23 2011A family $\cF \subseteq 2^{[n]}$ saturates the monotone decreasing property $\cP$ if $\cF$ satisfies $\cP$ and one cannot add any set to $\cF$ such that property $\cP$ is still satisfied by the resulting family. We address the problem of finding the minimum ... More

Grundy dominating sequences and zero forcing setsFeb 02 2017In a graph $G$ a sequence $v_1,v_2,\dots,v_m$ of vertices is Grundy dominating if for all $2\le i \le m$ we have $N[v_i]\not\subseteq \cup_{j=1}^{i-1}N[v_j]$ and is Grundy total dominating if for all $2\le i \le m$ we have $N(v_i)\not\subseteq \cup_{j=1}^{i-1}N(v_j)$. ... More

Dominating sequences in grid-like and toroidal graphsJul 01 2016A longest sequence $S$ of distinct vertices of a graph $G$ such that each vertex of $S$ dominates some vertex that is not dominated by its preceding vertices, is called a Grundy dominating sequence; the length of $S$ is the Grundy domination number of ... More

Escort distribution function of work done and diagonal entropies in quenched Luttinger liquidsSep 17 2014We study the escort probability distribution function of work done during an interaction quantum quench of Luttinger liquids. It crosses over from the thermodynamic to the small system limit with increasing $a$, the order of the escort distribution, and ... More

Local phonon mode in a fermionic bath, and its relation to Kondo effectNov 07 2006Jun 06 2007We have studied the interplay of a local phonon mode embedded in a metallic host (Holstein impurity model) using Abelian bosonization. The phonon frequency softens, which takes place in two steps: first, their frequency starts softening, and acquires ... More

Drude weight, Meissner weight, rotational inertia of bosonic superfluids: how are they distinguished?Oct 15 2013Feb 25 2014The Drude weight, the quantity which distinguishes metals from insulators, is proportional to the second derivative of the ground state energy with respect to a flux at zero flux. The same expression also appears in the definition of the Meissner weight, ... More

On some non-linear projections of self-similar sets in $\mathbb{R}^3$Mar 03 2015Apr 26 2016In the last years considerable attention has been paid for the orthogonal and non-linear projections of self-similar sets. In this paper we consider orthogonal transformation-free self-similar sets in $\mathbb{R}^3$, i.e. the generating IFS has the form ... More

Forbidding rank-preserving copies of a posetOct 25 2017The maximum size, $La(n,P)$, of a family of subsets of $[n]=\{1,2,...,n\}$ without containing a copy of $P$ as a subposet, has been intensively studied. Let $P$ be a graded poset. We say that a family $\mathcal{F}$ of subsets of $[n]=\{1,2,...,n\}$ contains ... More

Local Classical and Quantum Criticality due to Electron-Vibration InteractionApr 09 2009We study the local classical and quantum critical properties of electron-vibration interaction, represented by the Yu-Anderson model. It exhibits an instability, similar to the Wentzel-Bardeen singularity, whose nature resembles to weakly first order ... More

The Wiedemann-Franz law in the SU(N) Wolff modelFeb 16 2006We study the electrical and thermal transport through the SU(N) Wolff model with the use of bosonization. The Wilson ratio reaches unity as N grows to infinity. The electric conductance is dominated by the charge channel, and decreases monotonically with ... More

Algebraic degrees of pseudo-Anosov stretch factorsJun 21 2015Oct 26 2016The main result is that the possible algebraic degrees of pseudo-Anosov stretch factors on the closed orientable surface of genus $g$ are the even integers between 2 and $6g-6$ and the odd integers between 3 and $3g-3$. There is an analogous result for ... More

Covering Paths and Trees for Planar GridsNov 03 2013Given a set of points in the plane, a covering path is a polygonal path that visits all the points. In this paper we consider covering paths of the vertices of an n x m grid. We show that the minimal number of segments of such a path is $2\min(n,m)-1$ ... More

Spin supplementary conditions for spinning compact binariesSep 06 2016We consider the different spin supplementary conditions (SSC) for a spinning compact binary with the leading-order spin-orbit (SO) interaction. The Lagrangian of the binary system can be constructed but it is acceleration-dependent in two cases of SSC. ... More

Retarded cosmological gravity and Mach's principle in flat FRW universesFeb 19 2013The retarded gravitation produced by the matter and energy content of the observable universe is formulated and shown how this cosmological gravity gives rise to inertial forces in accelerated frames of reference. The model is developed for spatially ... More

On the Ledrappier-Young formula for self-affine measuresMar 03 2015Jun 02 2015Ledrappier and Young introduced a relation between entropy, Lyapunov exponents and dimension for invariant measures of diffeomorphisms on compact manifolds. In this paper, we show that a self-affine measure on the plane satisfies the Ledrappier-Young ... More

Characterizations and Properties of Graphs of Baire FunctionsNov 02 2016Let $X$ be a paracompact topological space and $Y$ be a Banach space. In this paper, we will characterize the Baire-1 functions $f:X\rightarrow{Y}$ by their graph: namely, we will show that $f$ is a Baire-1 function if and only if its graph $gr(f)$ is ... More

Algebraic degrees of pseudo-Anosov stretch factorsJun 21 2015Nov 19 2016The motivation for this paper is to justify a remark of Thurston that the algebraic degree of stretch factors of pseudo-Anosov maps on a surface $S$ can be as high as the dimension of the Teichm\"uller space of $S$. In addition to proving this, we completely ... More

Mixing time of an unaligned Gibbs sampler on the squareJun 27 2017Oct 06 2018The paper concerns a particular example of the Gibbs sampler and its mixing efficiency. Coordinates of a point are rerandomized in the unit square $[0,1]^2$ to approach a stationary distribution with density proportional to $\exp(-A^2(u-v)^2)$ for $(u,v)\in ... More

Baire categorical aspects of first passage percolationNov 21 2017In the previous decades, the theory of first passage percolation became a highly important area of probability theory. In this work, we will observe what can be said about the corresponding structure if we forget about the probability measure defined ... More

RENORMALISATION GROUP AIDED FINITE TEMPERATURE REDUCTION OF QUANTUM FIELD THEORIESMay 03 1995Dimensional reduction of finite temperature quantum field theories can be improved with help of continous renormalisation group steps. The method is applied to the integration of the lowest non-static ($n=\pm 1$) modes of the finite temperature $\Phi^4$-theory. ... More

A Hierarchy of Effective Field Theories of Hot Electroweak MatterDec 30 1993Abst\-ract: A hierarchy of effective three-dimensional theories of finite temperature electroweak matter is studied. First an integration over non-static modes leads to an effective theory containing a gauge field $A_{i}^{a}$, an adjoint Higgs field $A_{0}^a$ ... More

An implementation of the relational k-means algorithmApr 25 2013A C# implementation of a generalized k-means variant called relational k-means is described here. Relational k-means is a generalization of the well-known k-means clustering method which works for non-Euclidean scenarios as well. The input is an arbitrary ... More

The Fermi edge singularity in the SU(N) Wolff modelSep 15 2005The low temperature properties of the SU(N) Wolff impurity model are studied via Abelian bosonization. The path integral treatment of the problem allows for an exact evaluation of low temperature properties of the model. The single particle Green's function ... More

Large-N limit of a magnetic impurity in unconventional density wavesJul 15 2004We investigate the effect of unconventional density wave (UDW) condensate on an Anderson impurity using large-N technique at T=0. In accordance with previous treatments of a Kondo impurity in pseudogap phases, we find that Kondo effect occurs only in ... More

Finite volume form factors and correlation functions at finite temperatureJul 24 2009In this thesis we investigate finite size effects in 1+1 dimensional integrable QFT. In particular we consider matrix elements of local operators (finite volume form factors) and vacuum expectation values and correlation functions at finite temperature. ... More

Galois conjugates of pseudo-Anosov stretch factors are dense in the complex planeFeb 17 2017Aug 16 2017In this paper, we study the Galois conjugates of stretch factors of pseudo-Anosov elements of the mapping class group of a surface. We show that - except in low-complexity cases - these conjugates are dense in the complex plane. For this, we use Penner's ... More

Mixing times of Markov chains on a cycle with additional long range connectionsJan 08 2014Jun 25 2015We develop Markov chain mixing time estimates for a class of Markov chains with restricted transitions. We assume transitions may occur along a cycle of $n$ nodes and on $n^\gamma$ additional edges, where $\gamma < 1$. We find that the mixing times of ... More

Algebraic degrees of pseudo-Anosov stretch factorsJun 21 2015Oct 16 2018The motivation for this paper is to justify a remark of Thurston that the algebraic degree of stretch factors of pseudo-Anosov maps on a surface $S$ can be as high as the dimension of the Teichm\"uller space of $S$. In addition to proving this, we completely ... More

Fibrations of 3-manifolds and asymptotic translation length in the arc complexOct 16 2018Given a 3-manifold $M$ fibering over the circle, we investigate how the asymptotic translation lengths of pseudo-Anosov monodromies in the arc complex vary as we vary the fibration. We formalize this problem by defining normalized asymptotic translation ... More

Baire categorical aspects of first passage percolation IINov 11 2018In this paper we continue our earlier work about topological first passage percolation and answer certain questions asked in our previous paper. Notably, we prove that apart from trivialities, in the generic configuration there exists exactly one geodesic ... More

Algebraic degrees and Galois conjugates of pseudo-Anosov stretch factorsJun 21 2015Nov 10 2015We show that every even positive integer at most the dimension of Teichm\"uller space occurs as the degree of the minimal polynomial of a pseudo-Anosov stretch factor on an orientable surface. By Thurston's upper bound on the degree, these are all the ... More

Boundary effect on CDW: Friedel oscillations, STM imageMar 17 2005We study the effect of open boundary condition on charge density waves (CDW). The electron density oscillates rapidly close to the boundary, and additional non-oscillating terms (~ln(r)) appear. The Friedel oscillations survive beyond the CDW coherence ... More

Coloring half-planes and bottomless rectanglesMay 01 2011We prove lower and upper bounds for the chromatic number of certain hypergraphs defined by geometric regions. This problem has close relations to conflict-free colorings. One of the most interesting type of regions to consider for this problem is that ... More

Computing arbitrary Lagrangian Eulerian maps for evolving surfacesDec 06 2016The good mesh quality of an evolving discretized surface or domain is often compromised during time evolution. In recent years this phenomena have been overcome in a couple of ways, one of them uses arbitrary Lagrangian Eulerian maps. However, the numerical ... More

Lifts of pseudo-Anosov homeomorphisms of nonorientable surfaces have vanishing SAF invariantApr 19 2016Aug 03 2016We show that any pseudo-Anosov map that is a lift of pseudo-Anosov homeomorphism of a nonorientable surface has vanishing SAF invariant. We also provide a criterion to certify that a pseudo-Anosov map is not such a lift.

The variety of domination gamesJul 07 2018Domination game [SIAM J.\ Discrete Math.\ 24 (2010) 979--991] and total domination game [Graphs Combin.\ 31 (2015) 1453--1462] are by now well established games played on graphs by two players, named Dominator and Staller. In this paper, Z-domination ... More

On Grundy total domination number in product graphsDec 23 2017A longest sequence $(v_1,\ldots,v_k)$ of vertices of a graph $G$ is a Grundy total dominating sequence of $G$ if for all $i$, $N(v_i) \setminus \bigcup_{j=1}^{i-1}N(v_j)\not=\emptyset$. The length $k$ of the sequence is called the Grundy total domination ... More

Effective Models of the Electroweak Phase TransitionJun 06 1995The consecutive integration over the distinct mass scales ${\cal O}(T),{\cal O}(gT)$ leads to a hierarchy of effective models for the electroweak phase transition. Different techniques for the realisation of such strategy are reviewed. Advantages and ... More

Quantum quench in the Luttinger model with finite temperature initial stateJul 29 2013Oct 07 2013We study the non-equilibrium dynamics of the Luttinger model after a quantum quench, when the initial state is a finite temperature thermal equilibrium state. The diagonal elements of the density matrix in the steady state show thermal features for high ... More

Magnetotransport and thermoelectricity in disordered grapheneJan 29 2007We have studied the electric and thermal response of two-dimensional Dirac-fermions in a quantizing magnetic field in the presence of localized disorder. The electric and heat current operators in the presence of magnetic field are derived. The self-energy ... More

NMR relaxation rate and static spin susceptibility in grapheneFeb 17 2008The NMR relaxation rate and the static spin susceptibility in graphene are studied within a tight-binding description. At half filling, the NMR relaxation rate follows a power law as $T^2$ on the particle-hole symmetric side, while with a finite chemical ... More

Improved mixing rates of directed cycles by added connectionSep 04 2015Sep 16 2015We provide bounds on the mixing rate of a Markov chain whose mixing properties are improved by a combination of adding long distance edges and introducing non-reversibility. Our model is built on a cycle graph and involves selecting a sublinear number ... More

The Robustness and the Doubly-Preferential Attachment Simulation of the Consensus Connectome Dynamics of the Human BrainOct 14 2016The increasing quantity and quality of the publicly available human cerebral diffusion MRI data make possible the study of the brain as it was unimaginable before. The Consensus Connectome Dynamics (CCD) is a remarkable phenomenon that was discovered ... More

Hopf bifurcation and period functions for Wright type delay differential equationsJan 12 2018We present the simplest criterion that determines the direction of the Hopf bifurcations of the delay differential equation $x'(t)=-\mu f(x(t-1))$, as the parameter $\mu$ passes through the critical values $\mu_k$. We give a complete classification of ... More

Harmonic Manifolds and the Volume of Tubes about CurvesJun 08 2015Oct 03 2016H. Hotelling proved that in the n-dimensional Euclidean or spherical space, the volume of a tube of small radius about a curve depends only on the length of the curve and the radius. A. Gray and L. Vanhecke extended Hotelling's theorem to rank one symmetric ... More

On the dimension of self-similar measures with complicated overlapsFeb 11 2019In this paper, we investigate the Hausdorff dimension of the invariant measures of the iterated function system (IFS) $\{\alpha x, \beta x, \gamma x+(1-\gamma)\}$. We provide an "almost every" type result by a direct application of the results of Feng ... More

Topological insulation in a ladder model with particle-hole and reflection symmetriesJan 30 2018Feb 19 2018A two-legged ladder model, one dimensional, exhibiting the parity anomaly is constructed. The model belongs to the $C$ and $CI$ symmetry classes, depending on the parameters, but, due to reflection, it exhibits topological insulation. The model consists ... More

Critical Higgs Mass and Temperature Dependence of Gauge Boson Masses in the SU(2) Gauge-Higgs ModelAug 15 1996We study the effective 3-D SU(2) Gauge-Higgs model at finite temperature for Higgs-masses in the range from $60$ GeV up to $100$ GeV. The first order electroweak phase transition weakens with increasing Higgs-mass and terminates at a critical end-point. ... More

Gauge Boson Masses in the 3-d, SU(2) Gauge-Higgs ModelMar 05 1996We study gauge boson propagators in the symmetric and symmetry broken phases of the 3-d, $SU(2)$ gauge-Higgs model. Correlation functions for the gauge fields are calculated in Landau gauge. They are found to decay exponentially at large distances leading ... More

Reentrant Kondo effect in Landau quantized grapheneMay 14 2007We have studied the interplay of an Anderson impurity in Landau quantized graphene, with special emphasis on the influence of the chemical potential. Within the slave-boson mean-field theory, we found reentrant Kondo behaviour by varying the chemical ... More

Luttinger liquid with complex forward scattering: robustness and Berry phaseOct 06 2015Luttinger liquids (LLs) are one dimensional systems with well-understood instabilities due to umklapp or backscattering. We study a generalization of the Luttinger model, which incorporates a time reversal symmetry breaking interaction producing a complex ... More

AMS-02 fits Dark MatterSep 07 2015May 10 2016In this work we perform a comprehensive statistical analysis of the AMS-02 electron, positron fluxes and the antiproton-to-proton ratio in the context of a simplified dark matter model. We include known, standard astrophysical sources and a dark matter ... More

Generalized eccentric vs. true anomaly parametrizations in the perturbed Keplerian motionOct 10 2006The angular and the radial parts of the dynamics of the perturbed Kepler motion are separable in many important cases. In this paper we study the radial motion and its parametrizations. We develop in detail a generalized eccentric anomaly parametrization ... More

More on Decomposing Coverings by OctantsMar 05 2015Nov 17 2015In this note we improve our upper bound given earlier by showing that every 9-fold covering of a point set in the space by finitely many translates of an octant decomposes into two coverings, and our lower bound by a construction for a 4-fold covering ... More

Convex Polygons are Self-CoverableJul 09 2013Mar 14 2014We introduce a new notion for geometric families called self-coverability and show that homothets of convex polygons are self-coverable. As a corollary, we obtain several results about coloring point sets such that any member of the family with many points ... More

Path-search in the pyramid and in other graphsApr 27 2011We are given an acyclic directed graph with one source, and a subset of its edges which contains exactly one outgoing edge for every non-sink vertex. These edges determine a unique path from the source to a sink. We can think of it as a switch in every ... More

Octants are Cover DecomposableJan 19 2011Jan 20 2011We prove that octants are cover-decomposable, i.e., any 12-fold covering of any subset of the space with a finite number of translates of a given octant can be decomposed into two coverings. As a corollary, we obtain that any 12-fold covering of any subset ... More

Limits of compact decorated graphsOct 25 2010Following a general program of studying limits of discrete structures, and motivated by the theory of limit objects of converge sequences of dense simple graphs, we study the limit of graph sequences such that every edge is labeled by an element of a ... More

Regularity partitions and the topology of graphonsFeb 23 2010We highlight a topological aspect of the graph limit theory. Graphons are limit objects for convergent sequences of dense graphs. We introduce the representation of a graphon on a unique metric space and we relate the dimension of this metric space to ... More

On the Question of Validity of the Anthropic PrinciplesSep 18 2006During the last centuries of human history, many questions was repeated in connection with the great problems of the existence and origin of human beings, and also of the Universe. The old questions of common sense and philosophy have not been solved ... More

Temperature dependent conductances of deformable molecular devicesJun 04 2009Transport through a molecular device coupled to a vibrational mode is studied. By mapping it to the Yu-Anderson model in the large contact broadening limit, the zero bias electric and heat conductances are evaluated non-perturbatively. These exhibit a ... More

Stochastic integration based on simple, symmetric random walksDec 23 2007Jul 06 2009A new approach to stochastic integration is described, which is based on an a.s. pathwise approximation of the integrator by simple, symmetric random walks. Hopefully, this method is didactically more advantageous, more transparent, and technically less ... More

The graph theoretic moment problemOct 25 2010We study an analogue of the classical moment problem in the framework where moments are indexed by graphs instead of natural numbers. We study limit objects of graph sequences where edges are labeled by elements of a topological space. Among other things ... More

Random Graphons and a Weak Positivstellensatz for GraphsFeb 08 2009In an earlier paper the authors proved that limits of convergent graph sequences can be described by various structures, including certain 2-variable real functions called graphons, random graph models satisfying certain consistency conditions, and normalized, ... More

Improved mixing rates of directed cycles by added connectionSep 04 2015Feb 10 2018We investigate the mixing rate of a Markov chain where a combination of long distance edges and non-reversibility is introduced: as a first step, we focus here on the following graphs: starting from the cycle graph, we select random nodes and add all ... More

Stable and convergent fully discrete interior-exterior coupling of Maxwell's equationsMay 13 2016Jan 25 2017Maxwell's equations are considered with transparent boundary conditions, for initial conditions and inhomogeneity having support in a bounded, not necessarily convex three-dimensional domain or in a collection of such domains. The numerical method only ... More

Absence of orthogonality catastrophe after a spatially inhomogeneous interaction quench in Luttinger liquidsOct 22 2014Aug 29 2015We investigate the Loschmidt echo, the overlap of the initial and final wavefunctions of Luttinger liquids after a spatially inhomogeneous interaction quench. In studying the Luttinger model, we obtain an analytic solution of the bosonic Bogoliubov-de ... More

Electron spin dynamics in strongly correlated metalsJan 28 2009The temperature dependence of the electron spin life-time, T_1 and the g-factor are anomalous in alkali fullerides (K,Rb)_3C_60, which cannot be explained by the canonical Elliott-Yafet theory. These materials are archetypes of strongly correlated and ... More

Unusual hyperfine interaction of Dirac electrons and NMR spectroscopy in grapheneApr 01 2009Theory of nuclear magnetic resonance (NMR) in graphene is presented. The canonical form of the electron-nucleus hyperfine interaction is strongly modified by the linear electronic dispersion. The NMR shift and spin-lattice relaxation time are calculated ... More

Ledrappier-Young formula and exact dimensionality of self-affine measuresNov 18 2015Nov 28 2016In this paper, we solve the long standing open problem on exact dimensionality of self-affine measures on the plane. We show that every self-affine measure on the plane is exact dimensional regardless of the choice of the defining iterated function system. ... More

Human Sexual Dimorphism of the Relative Cerebral Area Volumes in the Data of the Human Connectome ProjectApr 20 2016The average human brain volume of the males is larger than that of the females. Several MRI voxel-based morphometry studies show that the gray matter/white matter ratio is larger in females. Here we have analyzed the recent public release of the Human ... More

Dimension maximizing measures for self-affine systemsJul 10 2015Apr 26 2016In this paper we study the dimension theory of planar self-affine sets satisfying dominated splitting in the linear parts and strong separation condition. The main results of this paper is the existence of dimension maximizing Gibbs measures (K\"aenm\"aki ... More

On the transience of random interlacementsFeb 23 2011Jul 17 2011We consider the interlacement Poisson point process on the space of doubly-infinite Z^d-valued trajectories modulo time-shift, tending to infinity at positive and negative infinite times. The set of vertices and edges visited by at least one of these ... More

Proper Coloring of Geometric HypergraphsDec 07 2016We study whether for a given planar family F there is an m such that any finite set of points can be 3-colored such that any member of F that contains at least m points contains two points with different colors. We conjecture that if F is a family of ... More

Minimal Penner dilatations on nonorientable surfacesJul 24 2018For any nonorientable closed surface, we determine the minimal dilatation among pseudo-Anosov mapping classes arising from Penner's construction. We deduce that the sequence of minimal Penner dilatations has exactly two accumulation points, in contrast ... More

Harmonic Manifolds and TubesApr 30 2017Jul 23 2017The authors showed in a preceding paper that in a connected locally harmonic manifold, the volume of a tube of small radius about a regularly parameterized simple arc depends only on the length of the arc and the radius. In this paper, we show that this ... More

Radon induced hyperplasia: effective adaptation reducing the local doses in the bronchial epitheliumMar 03 2016There is experimental and histological evidence that chronic irritation and cell death may cause hyperplasia in the exposed tissue. As the heterogeneous deposition of inhaled radon progeny results in high local doses at the peak of the bronchial bifurcations, ... More

Numerical analysis of parabolic problems with dynamic boundary conditionsJan 08 2015Space and time discretizations of parabolic differential equations with dynamic boundary conditions are studied in a weak formulation that fits into the standard abstract formulation of parabolic problems, just that the usual L^2(\Omega) inner product ... More

Inelastic Scattering from Local Vibrational ModesJun 10 2008We study a nonuniversal contribution to the dephasing rate of conduction electrons due to local vibrational modes. The inelastic scattering rate is strongly influenced by multiphonon excitations, exhibiting oscillatory behaviour. For higher frequencies, ... More