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Edge-ordered Ramsey numbersJun 20 2019We introduce and study a variant of Ramsey numbers for edge-ordered graphs, that is, graphs with linearly ordered sets of edges. The edge-ordered Ramsey number $\overline{R}_e(\mathfrak{G})$ of an edge-ordered graph $\mathfrak{G}$ is the minimum positive ... More

Coloring points with respect to squaresDec 07 2015We consider the problem of $2$-coloring geometric hypergraphs. Specifically, we show that there is a constant $m$ such that any finite set $\mathcal{S}$ of points in the plane can be $2$-colored such that every axis-parallel square that contains at least ... More

On the maximum size of connected hypergraphs without a path of given lengthOct 23 2017In this note we asymptotically determine the maximum number of hyperedges possible in an $r$-uniform, connected $n$-vertex hypergraph without a Berge path of length $k$, as $n$ and $k$ tend to infinity. We show that, unlike in the graph case, the multiplicative ... More

Majority problems of large query sizeOct 28 2016The aim of this paper is twofold: we present improvements of results of De Marco and Kranakis [6] on majority models, and we also survey recent results concerning the generalizations of the pairing model with query size k, and also provide bounds on their ... More

Rounds in a combinatorial search problemNov 30 2016We consider the following combinatorial search problem: we are given some excellent elements of $[n]$ and we should find at least one, asking questions of the following type: "Is there an excellent element in $A \subset [n]$?". G.O.H. Katona proved sharp ... More

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

Regular graphs are antimagicApr 30 2015In this note we prove - with a slight modification of an argument of Cranston et al. \cite{cranston} - that $k$-regular graphs are antimagic for $k\ge 2$.

Coloring points with respect to squaresDec 07 2015Jun 12 2017We consider the problem of $2$-coloring geometric hypergraphs. Specifically, we show that there is a constant $m$ such that any finite set of points in the plane $\mathcal{S} \subset {\mathbb R}^2$ can be $2$-colored such that every axis-parallel square ... More

A plurality problem with three colors and query size threeAug 19 2017The Plurality problem - introduced by Aigner \cite{A2004} - has many variants. In this article we deal with the following version: suppose we are given $n$ balls, each of them colored by one of three colors. A \textit{plurality ball} is one such that ... More

Regular graphs are antimagicApr 30 2015Jan 09 2019An undirected simple graph $G=(V,E)$ is called antimagic if there exists an injective function $f:E\rightarrow\{1,\dots,|E|\}$ such that $\sum_{e\in E(u)} f(e)\neq\sum_{e\in E(v)} f(e)$ for any pair of different nodes $u,v\in V$. In a previous version ... More

A note on $\mathtt{V}$-free $2$-matchingsMay 14 2015Motivated by a conjecture of Liang [Y.-C. Liang. {\em Anti-magic labeling of graphs}. PhD thesis, National Sun Yat-sen University, 2013.], we introduce a restricted path packing problem in bipartite graphs that we call a $\mathtt{V}$-free $2$-matching. ... More

A discrete isodiametric result: the Erdős-Ko-Rado theorem for multisetsDec 05 2012Mar 09 2014There are many generalizations of the Erd\H{o}s-Ko-Rado theorem. We give new results (and problems) concerning families of $t$-intersecting $k$-element multisets of an $n$-set and point out connections to coding theory and classical geometry. We establish ... 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

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

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

Correlation bound for distant parts of factor of IID processesMar 28 2016Apr 08 2016We study factor of i.i.d. processes on the $d$-regular tree for $d \geq 3$. We show that if such a process is restricted to two distant connected subgraphs of the tree, then the two parts are basically uncorrelated. More precisely, any functions of the ... More

On the discrete Fuglede and Pompeiu problemsJul 08 2018Dec 17 2018We investigate the discrete Fuglede's conjecture and Pompeiu problem on finite abelian groups and develop a strong connection between the two problems. We give a geometric condition under which a multiset of a finite abelian group has the discrete Pompeiu ... 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

Ramsey problems for Berge hypergraphsAug 30 2018Dec 17 2018For a graph $G$, a hypergraph $\mathcal{H}$ is a Berge copy of $G$ (or a Berge-$G$ in short), if there is a bijection $f : E(G) \rightarrow E(\mathcal{H})$ such that for each $e \in E(G)$ we have $e \subset f(e)$. We denote the family of $r$-uniform hypergraphs ... 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

Stability results on vertex Turán problems in Kneser graphsApr 11 2018Apr 20 2018The vertex set of the Kneser graph $K(n,k)$ is $V = \binom{[n]}{k}$ and two vertices are adjacent if the corresponding sets are disjoint. For any graph $F$, the largest size of a vertex set $U \subseteq V$ such that $K(n,k)[U]$ is $F$-free, was recently ... More

On Clique Coverings of Complete Multipartite GraphsSep 05 2018A clique covering of a graph $G$ is a set of cliques of $G$ such that any edge of $G$ is contained in one of these cliques, and the weight of a clique covering is the sum of the sizes of the cliques in it. The sigma clique cover number $scc(G)$ of a graph ... More

On the maximum number of copies of H in graphs with given size and orderOct 01 2018We study the maximum number $ex(n,e,H)$ of copies of a graph $H$ in graphs with given number of vertices and edges. We show that for any fixed graph $H$, $ex(n,e,H)$ is asymptotically realized by the quasi-clique provided that the edge density is sufficiently ... More

Stability results on vertex Turán problems in Kneser graphsApr 11 2018Mar 07 2019The vertex set of the Kneser graph $K(n,k)$ is $V = \binom{[n]}{k}$ and two vertices are adjacent if the corresponding sets are disjoint. For any graph $F$, the largest size of a vertex set $U \subseteq V$ such that $K(n,k)[U]$ is $F$-free, was recently ... 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

On the discrete Fuglede and Pompeiu problemsJul 08 2018Apr 11 2019We investigate the discrete Fuglede's conjecture and Pompeiu problem on finite abelian groups and develop a strong connection between the two problems. We give a geometric condition under which a multiset of a finite abelian group has the discrete Pompeiu ... More

Nondivergence form quasilinear heat equations driven by space-time white noiseFeb 20 2019We give a Wong-Zakai type characterisation of the solutions of quasilinear heat equations driven by space-time white noise in $1+1$ dimensions. In order to show that the renormalisation counterterms are local in the solution, a careful arrangement of ... More

A Potts Model for Night Light and Human PopulationJan 17 2015The Potts model was one of the most popular physics models of the twentieth century in an interdisciplinary context. It has been applied to a large variety of problems. Many generalizations exists and a whole range of models were inspired by this statistical ... More

$n$-fold unbiased bases: an extension of the MUB conditionJun 14 2017I introduce a new notion, that extends the mutually unbiased bases (MUB) conditons to more than two bases. These, I call the nUB conditions, and the corresponding bases $n$-fold unbiased. They naturally appear while optimizing generic $n$-to-one quantum ... More

Boundary regularity of stochastic PDEsMay 15 2017May 21 2018The boundary behaviour of solutions of stochastic PDEs with Dirichlet boundary conditions can be surprisingly - and in a sense, arbitrarily - bad: as shown by Krylov, for any $\alpha>0$ one can find a simple $1$-dimensional constant coefficient linear ... More

On the number of containments in $P$-free familiesApr 04 2018A subfamily $\{F_1,F_2,\dots,F_{|P|}\}\subseteq \mathcal F$ is a copy of the poset $P$ if there exists a bijection $i:P\rightarrow \{F_1,F_2,\dots,F_{|P|}\}$ such that $p\le_P q$ implies $i(p)\subseteq i(q)$. A family $\mathcal F$ is $P$-free, if it does ... 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

Rainbow Ramsey problems for the Boolean latticeSep 23 2018We address the following rainbow Ramsey problem: For posets $P,Q$ what is the smallest number $n$ such that any coloring of the elements of the Boolean lattice $B_n$ either admits a monochromatic copy of $P$ or a rainbow copy of $Q$. We consider both ... 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

Vertex Turán problems for the oriented hypercubeJul 18 2018In this short note we consider the oriented vertex Tur\'an problem in the hypercube: for a fixed oriented graph $\overrightarrow{F}$, determine the maximum size $ex_v(\overrightarrow{F}, \overrightarrow{Q_n})$ of a subset $U$ of the vertices of the oriented ... More

On the Turán number of some ordered even cyclesOct 20 2017Jul 17 2018A classical result of Bondy and Simonovits in extremal graph theory states that if a graph on $n$ vertices contains no cycle of length $2k$ then it has at most $O(n^{1+1/k})$ edges. However, matching lower bounds are only known for $k=2,3,5$. In this ... 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

A universal linear algebraic model for conformal geometriesMar 22 2016Sep 08 2016This article describes an entirely algebraic model for conformal geometries, which include the Euclidean, spherical and hyperbolic geometries. On one hand, their relationship is usually shown analytically, through systematic comparison of the measurement ... More

Homological codes and abelian anyonsMay 05 2015We study a generalization of Kitaev's abelian toric code model defined on CW complexes. In this model qudits are attached to n dimensional cells and the interaction is given by generalized star and plaquette operators. These are defined in terms of coboundary ... More

Towards a classification of $6\times 6$ complex Hadamard matricesFeb 02 2007Complex Hadamard matrices have received considerable attention in the past few years due to their appearance in quantum information theory. While a complete characterization is currently available only up to order 5 (in \cite{haagerup}), several new constructions ... More

Localization errors in solving stochastic partial differential equations in the whole spaceAug 22 2015Apr 23 2017Cauchy problems with SPDEs on the whole space are localized to Cauchy problems on a ball of radius $R$. This localization reduces various kinds of spatial approximation schemes to finite dimensional problems. The error is shown to be exponentially small. ... More

The Hamiltonian brain: efficient probabilistic inference with excitatory-inhibitory neural circuit dynamicsJul 03 2014Dec 31 2016Probabilistic inference offers a principled framework for understanding both behaviour and cortical computation. However, two basic and ubiquitous properties of cortical responses seem difficult to reconcile with probabilistic inference: neural activity ... More

Homological codes and abelian anyonsMay 05 2015Jan 19 2017We study a generalization of Kitaev's abelian toric code model defined on CW complexes. In this model qudits are attached to $n$ dimensional cells and the interaction is given by generalized star and plaquette operators. These are defined in terms of ... More

Qudit homological product codesMay 28 2015Jan 24 2017In this note we show that the random homological product code construction of Bravyi and Hastings can be extended to qudits of dimension D with D an odd prime. While the result is not surprising, the proof does require new ideas.

On the regularisation of the noise for the Euler-Maruyama scheme with irregular driftDec 11 2018The strong rate of convergence of the Euler-Maruyama scheme for nondegenerate SDEs with irregular drift coefficients is considered. In the case of $\alpha$-H\"older drift in recent literature the rate $\alpha/2$ was proved in many related situations. ... More

On the boundedness of solutions of SPDEsDec 13 2013Jan 03 2015In this paper estimates for the uniform norm of solutions of parabolic SPDEs are derived. The result is obtained through iteration techniques, motivated by the work of Moser in deterministic settings. As an application of the main result, solvability ... More

The Fuglede conjecture for convex domains is true in all dimensionsApr 28 2019Jul 19 2019A set $\Omega \subset \mathbb{R}^d$ is said to be spectral if the space $L^2(\Omega)$ has an orthogonal basis of exponential functions. A conjecture due to Fuglede (1974) stated that $\Omega$ is a spectral set if and only if it can tile the space by translations. ... 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

Localization errors in solving stochastic partial differential equations in the whole spaceAug 22 2015Cauchy problems with SPDEs on the whole space are localized to Cauchy problems on a ball of radius $R$. This localization reduces various kinds of spatial approximation schemes to finite dimensional problems. The error is shown to be exponentially small. ... More

On the density of planar sets without unit distancesSep 14 2018We improve the upper bound of the density of a planar, measurable set containing no two points at distance 1 to 0:25688 by involving higher order convolutions of the autocorrelation function of the set.

Self-testing mutually unbiased bases in the prepare-and-measure scenarioMar 01 2018Mar 21 2019Mutually unbiased bases (MUBs) constitute the canonical example of incompatible quantum measurements. One standard application of MUBs is the task known as quantum random access code (QRAC), in which classical information is encoded in a quantum system, ... More

Recursive ECF identification of linear systems driven by Lévy processesApr 11 2014In the literature the empirical characteristic function method is presented as an off-line identification method. While the results of the off-line methods are attractive, the proposed algorithms are ill-conditioned in many cases so that they requires ... More

Characterizing variability in nonlinear recurrent neuronal networksOct 10 2016In this note, we develop semi-analytical techniques to obtain the full correlational structure of a stochastic network of nonlinear neurons described by rate variables. Under the assumption that pairs of membrane potentials are jointly Gaussian -- which ... More

A Feynman-Kac formula for stochastic Dirichlet problemsNov 13 2016A representation formula for solutions of stochastic partial differential equations with Dirichlet boundary conditions is proved. The scope of our setting is wide enough to cover the general situation when the backward characteristics that appear in the ... More

Geometry of Permutation LimitsSep 13 2016Nov 01 2018This paper initiates a limit theory of permutation valued processes, building on the recent theory of permutons. We apply this to study the asymptotic behaviour of random sorting networks. We prove that the Archimedean path, the conjectured limit of random ... More

Qudit homological product codesMay 28 2015In this note we show that the random homological product code construction of Bravyi and Hastings can be extended to qudits of dimension D with D an odd prime. While the result is not surprising, the proof does require new ideas.

The Hamiltonian BrainJul 03 2014Jul 04 2014A venerable history of models have shown that simple and complex cell responses in the primary visual cortex (V1) are adapted to the statistics of natural images. These models are based, either explicitly or implicitly, on the assumption that neural responses ... More

The Fuglede conjecture for convex domains is true in all dimensionsApr 28 2019Let $\Omega$ be a convex body in $\mathbb{R}^d$. We say that $\Omega$ is spectral if the space $L^2(\Omega)$ has an orthogonal basis of exponential functions. There is a conjecture going back to Fuglede (1974) which states that $\Omega$ is spectral if ... More

Observables from a perturbative, accelerating solution of relativistic hydrodynamicsOct 12 2018The discovery of the almost perfect fluid like nature of the strongly interacting quark-gluon plasma was one of the most important discoveries of heavy-ion physics in recent decades. The experimental results are well described by hydrodynamical models. ... More

Finite difference schemes for stochastic partial differential equations in Sobolev spacesAug 21 2013Jan 28 2015We discuss $L_p$-estimates for finite difference schemes approximating parabolic, possibly degenerate, SPDEs, with initial conditions from $W^m_p$ and free terms taking values in $W^m_p.$ Consequences of these estimates include an asymptotic expansion ... More

Local $L_\infty$-estimates, weak Harnack inequality, and stochastic continuity of solutions of SPDEsMar 15 2015Oct 17 2016We consider stochastic partial differential equations under minimal assumptions: the coefficients are merely bounded and measurable and satisfy the stochastic parabolicity condition. In particular, the diffusion term is allowed to be scaling-critical. ... More

Character tables and the problem of existence of finite projective planesSep 18 2017Recently, the authors of the present work (together with M. N. Kolountzakis) introduced a new version of the non-commutative Delsarte scheme and applied it to the problem of mutually unbiased bases. Here we use this method to investigate the existence ... More

On the size of planarly connected crossing graphsSep 08 2015Aug 30 2016We prove that if an $n$-vertex graph $G$ can be drawn in the plane such that each pair of crossing edges is independent and there is a crossing-free edge that connects their endpoints, then $G$ has $O(n)$ edges. Graphs that admit such drawings are related ... More

Geometry of Permutation LimitsSep 13 2016Sep 27 2016We investigate the limit theory of permutation valued stochastic processes with the goal of understanding geometric behaviour of large random sorting networks. The theory builds on the limit theory of permutations, called permutons. We use the limit theory ... More

Search for methane isotope fractionation due to Rayleigh distillation on TitanApr 08 2016We search for meridional variation in the abundance of CH$_3$D relative to CH$_4$ on Titan using near-IR spectra obtained with NIRSPAO at Keck, which have a photon-limited signal-to-noise ratio of $\sim$50. Our observations can rule out a larger than ... More

On the real linear polarization constant problemDec 01 2006The present paper deals with lower bounds for the norm of products of linear forms. It has been proved by J. Arias-de-Reyna \cite{ARIAS}, that %for ${\mathbb C}^n$, the so-called $n^{\rm th}$ linear polarization constant $c_n({\mathbb C}^n)$ is $n^{n/2}$, ... More

Slowly decaying averages and fat towersSep 18 2016Let $(X,\Sigma,m,\tau)$ be an ergodic system, that is, $(X, \Sigma, m)$ is a probability space and $\tau: X \to X$ is an invertible ergodic $m$-preserving transformation. For a function $f:X\to\mathbb R$, let $A_Nf$ denote the $N$th ergodic average, $A_Nf(x)=\frac{1}{N}\cdot ... More

Fast electron spin flips via strong subcycle electric excitationMar 13 2018An important goal in quantum information processing is to reduce the duration of quantum-logical operations. Motivated by this, we provide a theoretical analysis of electrically induced fast dynamics of a single-electron spin-orbit qubit. We study the ... More

Adaptive Majority Problems for Restricted Query Graphs and for Weighted SetsMar 20 2019Suppose that the vertices of a graph $G$ are colored with two colors in an unknown way. The color that occurs on more than half of the vertices is called the majority color (if it exists), and any vertex of this color is called a majority vertex. We study ... More

Incompatibility robustness of quantum measurements: a unified frameworkJun 02 2019In quantum mechanics performing a measurement is an invasive process which generally disturbs the system. Due to this phenomenon, there exist incompatible quantum measurements, i.e., measurements that cannot be simultaneously performed on a single copy ... More

Incompatibility robustness of quantum measurements: a unified frameworkJun 02 2019Jun 21 2019In quantum mechanics performing a measurement is an invasive process which generally disturbs the system. Due to this phenomenon, there exist incompatible quantum measurements, i.e., measurements that cannot be simultaneously performed on a single copy ... More

ECF identification of GARCH systems driven by Lévy processesApr 11 2014L\'evy processes are widely used in financial mathematics, telecommunication, economics, queueing theory and natural sciences for modelling. We propose an essentially asymptotically efficient estimation method for the system parameters of general autoregressive ... More

Asymptotic scaling properties of the posterior mean and variance in the Gaussian scale mixture modelJun 03 2017Nov 28 2017The Gaussian scale mixture model (GSM) is a simple yet powerful probabilistic generative model of natural image patches. In line with the well-established idea that sensory processing is adapted to the statistics of the natural environment, the GSM has ... More

Consensus time in a voter model with concealed and publicly expressed opinionsMay 16 2018The voter model is a simple agent-based model to mimic opinion dynamics in social networks: a randomly chosen agent adopts the opinion of a randomly chosen neighbour. This process is repeated until a consensus emerges. Although the basic voter model is ... More

On the solvability of degenerate stochastic partial differential equations in Sobolev spacesApr 16 2014Systems of parabolic, possibly degenerate parabolic SPDEs are considered. Existence and uniqueness are established in Sobolev spaces. Similar results are obtained for a class of equations generalizing the deterministic first order symmetric hyperbolic ... More

Under recurrence in the Khintchine recurrence theoremMar 24 2016May 23 2016The Khintchine recurrence theorem asserts that on a measure preserving system, for every set $A$ and $\varepsilon>0$, we have $\mu(A\cap T^{-n}A)\geq \mu(A)^2-\varepsilon$ for infinitely many $n\in \mathbb{N}$. We show that there are systems having under-recurrent ... More

The changing rotational excitation of C_3 in comet 9P/Tempel 1 during Deep ImpactJul 05 2012The 4050\AA\ band of C$_3$ was observed with Keck/HIRES echelle spectrometer during the {\em Deep Impact} encounter. We perform a 2-dimensional analysis of the exposures in order to study the spatial, spectral, and temporal changes in the emission spectrum ... More

X-ray Ionization of Heavy Elements Applied to Protoplanetary DisksMay 17 2011The consequences of the Auger effect on the population of heavy element ions are analyzed for the case of relatively cool gas irradiated by keV X-rays, with intended applications to the accretion disks of young stellar ob jects. Highly charged ions are ... More

An application of positive definite functions to the problem of MUBsDec 28 2016We present a new approach to the problem of mutually unbiased bases (MUBs), based on positive definite functions on the unitary group. The method provides a new proof of the fact that there are at most $d+1$ MUBs in ${\mathbb C}^d$. It may also lead to ... More

Random differences in Szemerédi's theorem and related resultsJul 07 2013May 06 2014We introduce a new, elementary method for studying random differences in arithmetic progressions and convergence phenomena along random sequences of integers. We apply our method to obtain significant improvements on previously known results.

Under recurrence in the Khintchine recurrence theoremMar 24 2016Dec 07 2016The Khintchine recurrence theorem asserts that on a measure preserving system, for every set $A$ and $\varepsilon>0$, we have $\mu(A\cap T^{-n}A)\geq \mu(A)^2-\varepsilon$ for infinitely many $n\in \mathbb{N}$. We show that there are systems having under-recurrent ... More

Constructions of complex Hadamard matrices via tiling Abelian groupsJul 11 2006Oct 05 2006Applications in quantum information theory and quantum tomography have raised current interest in complex Hadamard matrices. In this note we investigate the connection between tiling Abelian groups and constructions of complex Hadamard matrices. First, ... More

On Convergence of Modulated Ergodic Hilbert TransformsOct 17 2016Let $p(t)$ be a Hardy field function which grows "super-linearly" and stays "sufficiently far" from polynomials. We show that for each measure-preserving system, $(X,\Sigma,\mu,\tau)$, with $\tau$ a measure-preserving $\mathbb{Z}$-action, the modulated ... More

Fast sampling for Bayesian inference in neural circuitsApr 14 2014Apr 23 2014Time is at a premium for recurrent network dynamics, and particularly so when they are stochastic and correlated: the quality of inference from such dynamics fundamentally depends on how fast the neural circuit generates new samples from its stationary ... More

Higher order anisotropies in the Buda-Lund model: Disentangling flow and density field anisotropiesApr 25 2016Oct 12 2016The Buda-Lund hydro model describes an expanding ellipsoidal fireball, and fits the observed elliptic flow and oscillating HBT radii successfully. Due to fluctuations in energy depositions, the fireball shape however fluctuates on an event-by-event basis. ... More

On the role of time in perceptual decision makingFeb 10 2015According to the dominant view, time in perceptual decision making is used for integrating new sensory evidence. Based on a probabilistic framework, we investigated the alternative hypothesis that time is used for gradually refining an internal estimate ... More

Transfer matrix approach for the Kerr and Faraday rotation in layered nanostructuresMar 07 2016To study the optical rotation of the polarization of light incident on multilayer systems consisting of atomically thin conductors and dielectric multilayers we present a general method based on transfer matrices. The transfer matrix of the atomically ... More

Robustness of flight leadership relations in pigeonsOct 25 2016Collective animal movements produce spectacular natural phenomena that arise from simple local interactions among group members. Flocks of homing pigeons, Columba livia, provide a useful model for the study of collective motion and decision making. During ... More

The biased odd cycle gameOct 16 2012Apr 11 2013In this paper we consider biased Maker-Breaker games played on the edge set of a given graph $G$. We prove that for every $\delta>0$ and large enough $n$, there exists a constant $k$ for which if $\delta(G)\geq \delta n$ and $\chi(G)\geq k$, then Maker ... More

Kerr-de Sitter Quasinormal Modes via Accessory Parameter ExpansionNov 29 2018Feb 06 2019Quasinormal modes are characteristic oscillatory modes that control the relaxation of a perturbed physical system back to its equilibrium state. In this work, we calculate QNM frequencies and angular eigenvalues of Kerr--de Sitter black holes using a ... More

Optical phonons for Peierls chains with long-range Coulomb interactionsNov 14 2016We consider a chain of atoms that are bound together by a harmonic force. Spin-1/2 electrons that move between neighboring chain sites (H\"uckel model) induce a lattice dimerization at half band filling (Peierls effect). We supplement the H\"uckel model ... More

FUV Irradiated Disk Atmospheres: Ly$α$ and the Origin of Hot H$_2$ EmissionDec 14 2015Protoplanetary disks are strongly irradiated by a stellar FUV spectrum that is dominated by Ly$\alpha$ photons. We investigate the impact of stellar Ly$\alpha$ irradiation on the terrestrial planet region of disks ($\lesssim 1$AU) using an updated thermal-chemical ... More

Identifying codes and searching with balls in graphsMay 29 2014Jun 02 2014Given a graph $G$ and a positive integer $R$ we address the following combinatorial search theoretic problem: What is the minimum number of queries of the form "does an unknown vertex $v \in V(G)$ belong to the ball of radius $r$ around $u$?" with $u ... More

Self-organized UAV Traffic in Realistic EnvironmentOct 29 2016We investigated different dense multirotor UAV traffic simulation scenarios in open 2D and 3D space, under realistic environments with the presence of sensor noise, communication delay, limited communication range, limited sensor update rate and finite ... More

Hückel--Hubbard-Ohno modeling of $\boldsymbolπ$-bonds in ethene and ethyne with application to trans-polyacetyleneDec 10 2015Quantum chemistry calculations provide the potential energy between two carbon atoms in ethane (H$_3$C$-$CH$_3$), ethene (H$_2$C$=$CH$_2$), and ethyne (HC$\equiv$CH) as a function of the atomic distance. Based on the energy function for the $\sigma$-bond ... More

Kerr-de Sitter Quasinormal Modes via Accessory Parameter ExpansionNov 29 2018May 09 2019Quasinormal modes are characteristic oscillatory modes that control the relaxation of a perturbed physical system back to its equilibrium state. In this work, we calculate QNM frequencies and angular eigenvalues of Kerr--de Sitter black holes using a ... More

How (not) to assess the importance of correlations for the matching of spontaneous and evoked activityJan 28 2013Mar 27 2013A comment on `Population rate dynamics and multineuron firing patterns in sensory cortex' by Okun et al. Journal of Neuroscience 32(48):17108-17119, 2012 and our response to the corresponding reply by Okun et al's (arXiv, 2013).

Static and dynamic shear viscosity of a single layer complex plasmaMar 01 2011Jun 24 2011We measured the static and dynamic (complex) shear viscosity of a single layer complex plasma by applying, respectively, a stationary and a periodically modulated shear stress induced by the light pressure of manipulating laser beams. Under static conditions ... More

Thermal soaring flight of birds and unmanned aerial vehiclesDec 02 2010Thermal soaring saves much energy, but flying large distances in this form represents a great challenge for birds, people and Unmanned Aerial Vehicles (UAVs). The solution is to make use of so-called thermals, which are localized, warmer regions in the ... More