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Fractional Local DimensionJun 13 2019The original notion of dimension for posets was introduced by Dushnik and Miller in 1941 and has been studied extensively in the literature. In 1992, Brightwell and Scheinerman developed the notion of fractional dimension as the natural linear programming ... More

The Communication Complexity of OptimizationJun 13 2019We consider the communication complexity of a number of distributed optimization problems. We start with the problem of solving a linear system. Suppose there is a coordinator together with $s$ servers $P_1, \ldots, P_s$, the $i$-th of which holds a subset ... More

Querying a Matrix through Matrix-Vector ProductsJun 13 2019We consider algorithms with access to an unknown matrix $M\in\mathbb{F}^{n \times d}$ via matrix-vector products, namely, the algorithm chooses vectors $\mathbf{v}^1, \ldots, \mathbf{v}^q$, and observes $M\mathbf{v}^1,\ldots, M\mathbf{v}^q$. Here the ... More

Post-Processing of High-Dimensional DataJun 13 2019Scientific computations or measurements may result in huge volumes of data. Often these can be thought of representing a real-valued function on a high-dimensional domain, and can be conceptually arranged in the format of a tensor of high degree in some ... More

A Turing Kernelization Dichotomy for Structural Parameterizations of $\mathcal{F}$-Minor-Free DeletionJun 13 2019For a fixed finite family of graphs $\mathcal{F}$, the $\mathcal{F}$-Minor-Free Deletion problem takes as input a graph $G$ and an integer $\ell$ and asks whether there exists a set $X \subseteq V(G)$ of size at most $\ell$ such that $G-X$ is $\mathcal{F}$-minor-free. ... More

Binomial edge ideals of cographsJun 13 2019We determine the Castelnuovo--Mumford regularity of binomial edge ideals of complement reducible graphs (cographs). On $n$ vertices the maximum regularity is essentially $2n/3$. Independently of the number of vertices, we also bound the regularity by ... More

Fast, reliable and unrestricted iterative computation of Gauss--Hermite and Gauss--Laguerre quadraturesJun 12 2019Methods for the computation of classical Gaussian quadrature rules are described which are effective both for small and large degree. These methods are reliable because the iterative computation of the nodes has guaranteed convergence, and they are fast ... More

Nonintrusive proper generalised decomposition for parametrised incompressible flow problems in OpenFOAMJun 12 2019The computational cost of parametric studies currently represents the major limitation to the application of simulation-based engineering techniques in a daily industrial environment. This work presents the first nonintrusive implementation of the proper ... More

The Tandem Duplication Distance is NP-hardJun 12 2019In computational biology, tandem duplication is an important biological phenomenon which can occur either at the genome or at the DNA level. A tandem duplication takes a copy of a genome segment and inserts it right after the segment - this can be represented ... More

Multicolor Ramsey numbers of cycles in Gallai coloringsJun 12 2019For a graph $H$ and an integer $k\ge1$, the $k$-color Ramsey number $R_k(H)$ is the least integer $N$ such that every $k$-coloring of the edges of the complete graph $K_N$ contains a monochromatic copy of $H$. Let $C_m$ denote the cycle on $m\ge4 $ vertices. ... More

Virtual classes of parabolic $\mathrm{SL}_2(\mathbb{C})$-character varietiesJun 12 2019In this paper, we compute the virtual classes in the Grothendieck ring of algebraic varieties of $\mathrm{SL}_2(\mathbb{C})$-character varieties over compact orientable surfaces with parabolic points of semi-simple type. When the parabolic punctures are ... More

Sorted Top-k in RoundsJun 12 2019We consider the sorted top-$k$ problem whose goal is to recover the top-$k$ items with the correct order out of $n$ items using pairwise comparisons. In many applications, multiple rounds of interaction can be costly. We restrict our attention to algorithms ... More

Approximating the Orthogonality Dimension of Graphs and HypergraphsJun 12 2019A $t$-dimensional orthogonal representation of a hypergraph is an assignment of nonzero vectors in $\mathbb{R}^t$ to its vertices, such that every hyperedge contains two vertices whose vectors are orthogonal. The orthogonality dimension of a hypergraph ... More

Prophet Inequalities on the Intersection of a Matroid and a GraphJun 12 2019We consider prophet inequalities in a setting where agents correspond to both elements in a matroid and vertices in a graph. A set of agents is feasible if they form both an independent set in the matroid and an independent set in the graph. Our main ... More

Homological Connectivity in Random Čech ComplexesJun 11 2019Jun 13 2019We study the homology of random \v{C}ech complexes generated by a homogeneous Poisson process. We focus on 'homological connectivity' - the stage where the random complex is dense enough, so that its homology "stabilizes" and becomes isomorphic to that ... More

Homological Connectivity in Čech ComplexesJun 11 2019We study the homology of random \v{C}ech complexes generated by a homogeneous Poisson process. We focus on 'homological connectivity' - the stage where the random complex is dense enough, so that its homology "stabilizes" and becomes isomorphic to that ... More

Discrepancy, Coresets, and Sketches in Machine LearningJun 11 2019This paper defines the notion of class discrepancy for families of functions. It shows that low discrepancy classes admit small offline and streaming coresets. We provide general techniques for bounding the class discrepancy of machine learning problems. ... More

Similarity Problems in High DimensionsJun 11 2019The main contribution of this dissertation is the introduction of new or improved approximation algorithms and data structures for several similarity search problems. We examine the furthest neighbor query, the annulus query, distance sensitive membership, ... More

Weighted, Bipartite, or Directed Stream Graphs for the Modeling of Temporal NetworksJun 11 2019We recently introduced a formalism for the modeling of temporal networks, that we call stream graphs. It emphasizes the streaming nature of data and allows rigorous definitions of many important concepts generalizing classical graphs. This includes in ... More

UnLimited TRAnsfers for Multi-Modal Route Planning: An Efficient SolutionJun 11 2019We study a multi-modal route planning scenario consisting of a public transit network and a transfer graph representing a secondary transportation mode (e.g., walking or taxis). The objective is to compute all journeys that are Pareto-optimal with respect ... More

Lyapunov Differential Equation Hierarchy and Polynomial Lyapunov Functions for Switched Linear SystemsJun 11 2019In this work, we address the problem of searching for homogeneous polynomial Lyapunov functions for stable switched linear systems. Specifically, we show an equivalence between polynomial Lyapunov functions for switched linear systems and quadratic Lyapunov ... More

The Prolog debugger and declarative programmingJun 11 2019Logic programming is a declarative programming paradigm. Programming language Prolog makes logic programming possible, at least to a substantial extent. However the Prolog debugger works solely in terms of the operational semantics. So it is incompatible ... More

Communication and Memory Efficient Testing of Discrete DistributionsJun 11 2019We study distribution testing with communication and memory constraints in the following computational models: (1) The {\em one-pass streaming model} where the goal is to minimize the sample complexity of the protocol subject to a memory constraint, and ... More

Faster Algorithms for High-Dimensional Robust Covariance EstimationJun 11 2019We study the problem of estimating the covariance matrix of a high-dimensional distribution when a small constant fraction of the samples can be arbitrarily corrupted. Recent work gave the first polynomial time algorithms for this problem with near-optimal ... More

New dynamic and verifiable multi-secret sharing schemes based on LFSR public key cryptosystemJun 11 2019A verifiable multi-secret sharing (VMSS) scheme enables the dealer to share multiple secrets, and the deception of both participants and the dealer can be detected. After analyzing the security of VMSS schemes proposed by Mashhadi and Dehkordi in 2015, ... More

A Linear Algorithm for Minimum Dominator Colorings of Orientations of PathsJun 11 2019In this paper we present an algorithm for finding a minimum dominator coloring of orientations of paths. To date this is the first algorithm for dominator colorings of digraphs in any capacity. We prove that the algorithm always provides a minimum dominator ... More

Using Hoare logic in a process algebra settingJun 11 2019This paper concerns the relation between process algebra and Hoare logic. We introduce an extension of ACP (Algebra of Communicating Processes) with features that are relevant to processes in which data are involved, present a Hoare logic for the processes ... More

Rearrangement operations on unrooted phylogenetic networksJun 11 2019Rearrangement operations transform a phylogenetic tree into another one and hence induce a metric on the space of phylogenetic trees. Popular operations for unrooted phylogenetic trees are NNI (nearest neighbour interchange), SPR (subtree prune and regraft), ... More

Almost Optimal Semi-streaming Maximization for k-Extendible SystemsJun 11 2019In this paper we consider the problem of finding a maximum weight set subject to a $k$-extendible constraint in the data stream model. The only non-trivial algorithm known for this problem to date---to the best of our knowledge---is a semi-streaming $k^2(1 ... More

Shape versus timing: linear responses of a limit cycle with hard boundaries under instantaneous and static perturbationJun 11 2019When dynamical systems producing rhythmic behavior operate within hard limits, they may exhibit limit cycles with sliding components, that is, closed isolated periodic orbits that make and break contact with a constraint surface. Examples include heel-ground ... More

Gait modeling and optimization for the perturbed Stokes regimeJun 11 2019Many forms of locomotion, both natural and artificial, are dominated by viscous friction in the sense that without power expenditure they quickly come to a standstill. From geometric mechanics, it is known that for swimming at the "Stokesian" (viscous; ... More

Ultra Fast Medoid Identification via Correlated Sequential HalvingJun 11 2019The medoid of a set of $n$ points is the point in the set that minimizes the sum of distances to other points. Computing the medoid can be solved exactly in $O(n^2)$ time by computing the distances between all pairs of points. Previous work shows that ... More

Meta-Learning Neural Bloom FiltersJun 10 2019There has been a recent trend in training neural networks to replace data structures that have been crafted by hand, with an aim for faster execution, better accuracy, or greater compression. In this setting, a neural data structure is instantiated by ... More

Independence in Arithmetic: The Method of $(\mathcal L, n)$-ModelsJun 10 2019I develop in depth the machinery of $(\mathcal L, n)$-models originally introduced by Shelah \cite{ShelahPA} and, independently in a slightly different form by Kripke (cf \cite{put2000}, \cite{quin80}). This machinery allows fairly routine constructions ... More

Pure entropic regularization for metrical task systemsJun 10 2019We show that on every $n$-point HST metric, there is a randomized online algorithm for metrical task systems (MTS) that is $1$-competitive for service costs and $O(\log n)$-competitive for movement costs. In general, these refined guarantees are optimal ... More

Sequential Source Coding for Stochastic Systems Subject to Finite Rate ConstraintsJun 10 2019In this paper, we apply a sequential source coding framework to analyze fundamental performance limitations of stochastic control systems subject to feedback data-rate constraints. We first show that the characterization of the rate-distortion region ... More

The Demand Query Model for Bipartite MatchingJun 10 2019We introduce a `concrete complexity' model for studying algorithms for matching in bipartite graphs. The model is based on the "demand query" model used for combinatorial auctions. Most (but not all) known algorithms for bipartite matching seem to be ... More

Transfer operator for ultradifferentiable expanding maps of the circleJun 10 2019Given a $\mathcal{C}^\infty$ expanding map $T$ of the circle, we construct a Hilbert space $\mathcal{H}$ of smooth functions on which the transfer operator $\mathcal{L}$ associated to $T$ acts as a compact operator. This result is made quantitative (in ... More

Parallel Streaming Random SamplingJun 10 2019This paper investigates parallel random sampling from a potentially-unending data stream whose elements are revealed in a series of element sequences (minibatches). While sampling from a stream was extensively studied sequentially, not much has been explored ... More

A Dijkstra-Based Efficient Algorithm for Finding a Shortest Non-zero Path in Group-Labeled GraphsJun 10 2019The parity constrained shortest path problem is a well-known variant that is tractable via weighted matching if a graph is undirected and has nonnegative edge length. As a generalization, we focus on the problem of finding a shortest non-zero path between ... More

Weighted Quasi Interpolant Spline Approximation of 3D point clouds via local refinementJun 10 2019We present a new surface approximation, the Weighted Quasi Interpolant Spline Approximation (w-QISA), to approximate very large and noisy point clouds. We adopt local implicit representations based on three key ingredients: 1) a local mesh for the piecewise ... More

Big Ramsey degrees of 3-uniform hypergraphsJun 10 2019Given a countably infinite hypergraph $\mathcal R$ and a finite hypergraph $\mathcal A$, the big Ramsey degree of $\mathcal A$ in $\mathcal R$ is the least number $L$ such that, for every finite $k$ and every $k$-colouring of the embeddings of $\mathcal ... More

Symmetry Properties of Nested Canalyzing FunctionsJun 10 2019Many researchers have studied symmetry properties of various Boolean functions. A class of Boolean functions, called nested canalyzing functions (NCFs), has been used to model certain biological phenomena. We identify some interesting relationships between ... More

Prokhorov-like conditions for weak compactness of sets of bounded Radon measures on different topological spacesJun 09 2019The paper presents some weak compactness criterion for a subset $M$ of the set $\mathfrak{RM}_b(T,\mathcal{G})$ of all positive bounded Radon measures on a Hausdorff topological space $(T,\mathcal{G})$ similar to the Prokhorov criterion for a complete ... More

Corrected overlap weight and clustering coefficientJun 09 2019We discuss two well known network measures: the overlap weight of an edge and the clustering coefficient of a node. For both of them it turns out that they are not very useful for data analytic task to identify important elements (nodes or links) of a ... More

Ping-pong partitions and locally discrete groups of real-analytic circle diffeomorphisms, I: ConstructionJun 09 2019Following the recent advances in the study of groups of circle diffeomorphisms, we classify the topological dynamics of locally discrete, finitely generated, virtually free subgroups of the group $\mathsf{Diff}^\omega_+(\mathbb S^1)$ of orientation preserving ... More

Families of periodic orbits: closed 1-forms and global continuabilityJun 08 2019We investigate global continuation of periodic orbits of a differential equation depending on a parameter, assuming that a closed 1-form satisfying certain properties exists. We begin by extending the global continuation theory of Alexander, Alligood, ... More

Finding a Generator Matrix of a Multidimensional Cyclic CodeJun 08 2019We generalize Sepasdar's method for finding a generator matrix of two-dimensional cyclic codes to find an independent subset of a general multicyclic code, which may form a basis of the code as a vector subspace. A generator matrix can be then constructed ... More

Antipodes, preantipodes and Frobenius functorsJun 08 2019We prove that a quasi-bialgebra admits a preantipode if and only if the associated free quasi-Hopf bimodule functor is Frobenius, if and only if the relative (opmonoidal) monad is a Hopf monad. The same results hold in particular for a bialgebra, tightening ... More

On the Triangles in Certain Types of Line ArrangementsJun 08 2019In this article we combinatorially describe the triangles that are present in two types of line arrangements, those which have global cyclicity and those which are infinity type line arrangements. A combinatorial nomenclature has been described for both ... More

Study of Compressed Randomized UTV Decompositions for Low-Rank Matrix Approximations in Data ScienceJun 08 2019In this work, a novel rank-revealing matrix decomposition algorithm termed Compressed Randomized UTV (CoR-UTV) decomposition along with a CoR-UTV variant aided by the power method technique is proposed. CoR-UTV computes an approximation to a low-rank ... More

Adversarial Examples for Non-Parametric Methods: Attacks, Defenses and Large Sample LimitsJun 07 2019Adversarial examples have received a great deal of recent attention because of their potential to uncover security flaws in machine learning systems. However, most prior work on adversarial examples has been on parametric classifiers, for which generic ... More

Multiplicity of subharmonics in a class of periodic predator-prey Volterra modelsJun 07 2019This paper ascertains the global topological structure of the set of subharmonics of arbitrary order of the periodic predator-prey model introduced in L\'opez-G\'omez, Ortega and Tineo in 1996. By constructing the iterates of the monodromy operator of ... More

Zooming Cautiously: Linear-Memory Heuristic Search With Node Expansion GuaranteesJun 07 2019We introduce and analyze two parameter-free linear-memory tree search algorithms. Under mild assumptions we prove our algorithms are guaranteed to perform only a logarithmic factor more node expansions than A* when the search space is a tree. Previously, ... More

Invariant Schreier decorations of unimodular random networksJun 07 2019We prove that every $2d$-regular unimodular random network carries an invariant random Schreier decoration. Equivalently, it is the Schreier coset graph of an invariant random subgroup of the free group $F_d$. As a corollary we get that every $2d$-regular ... More

Optimal algebraic Breadth-First Search for sparse graphsJun 07 2019There has been a rise in the popularity of algebraic methods for graph algorithms given the development of the GraphBLAS library and other sparse matrix methods. These are useful in practice because many graph algorithms are amenable to sparse matrix ... More

A local version of the Myers-Steenrod TheoremJun 07 2019We prove the Myers-Steenrod theorem for local topological groups of isometries acting on pointed $\mathcal{C}^{k,\alpha}$-Riemannian manifolds, with $k+\alpha>0$. As an application, we infer a new regularity result for a certain class of locally homogeneous ... More

Three real Artin-Tate motivesJun 07 2019We analyze the spectrum of the tensor-triangulated category of Artin-Tate motives over the base field R of real numbers, with integral coefficients. Away from 2, we obtain the same spectrum as for complex Tate motives, previously studied by the second-named ... More

Explicit logarithmic formulas of special values of hypergeometric functions 3F2Jun 07 2019In a joint paper [4] by Otsubo, Terasoma and the first author, we proved that the special value 3F2(a,b,q;a+b,q;1) of the generalized hypergeometric function is a linear combination of log of algebraic numbers if the triplet (a,b,q) of rational numbers ... More

Cross sections to flows via intrinsically harmonic formsJun 06 2019We establish a new criterion for the existence of a global cross section to a non-singular volume-preserving flow on a compact manifold. Namely, if $\Phi$ is a non-singular smooth flow on a compact, connected manifold $M$ with a smooth invariant volume ... More

Auslander-Reiten conjecture for non-Gorenstein Cohen-Macaulay ringsJun 06 2019Let $R$ be a Cohen-Macaulay local ring and $Q$ be a parameter ideal of $R$. Due to M. Auslander, S. Ding, and \O. Solberg, the Auslander-Reiten conjecture holds for $R$ if and only if it holds for the residue ring $R/Q$. In the former part of this paper, ... More

Near Neighbor: Who is the Fairest of Them All?Jun 06 2019$\newcommand{\ball}{\mathbb{B}}\newcommand{\dsQ}{{\mathcal{Q}}}\newcommand{\dsS}{{\mathcal{S}}}$In this work we study a fair variant of the near neighbor problem. Namely, given a set of $n$ points $P$ and a parameter $r$, the goal is to preprocess the ... More

An efficient data-driven solver for Fokker-Planck equations: algorithm and analysisJun 06 2019Computing the invariant probability measure of a randomly perturbed dynamical system usually means solving the stationary Fokker-Planck equation. This paper studies several key properties of a novel data-driven solver for low-dimensional Fokker-Planck ... More

Model predictive control with stage cost shaping inspired by reinforcement learningJun 06 2019This work presents a suboptimality study of a particular model predictive control with a stage cost shaping based on the ideas of reinforcement learning. The focus of the suboptimality study is to derive quantities relating the infinite-horizon cost function ... More

Ihara Zeta EntropyJun 06 2019In this article, we introduce an entropy based on the formal power series expansion of the Ihara Zeta function. We find a number of inequalities based on the values of the Ihara zeta function. These new entropies are applicable in symbolic dynamics and ... More

The route to chaos in routing games: Population increase drives period-doubling instability, chaos & inefficiency with Price of Anarchy equal to oneJun 06 2019We study a learning dynamic model of routing (congestion) games to explore how an increase in the total demand influences system performance. We focus on non-atomic routing games with two parallel edges of linear cost, where all agents evolve using Multiplicative ... More

On $3$-dimensional foliated dynamical systems and Hilbert type reciprocity lawJun 06 2019We show some fundamental results concerning $3$-dimensional foliated dynamical systems (FDS$^3$ for short) introduced by Deninger. Firstly, we give a decomposition theorem for an FDS$^3$, which yields a classification of FDS$^3$'s. Secondly, for each ... More

On some ideals with linear free resolutionsJun 06 2019Given $\Sigma\subset\mathbb K[x_1,\ldots,x_k]$, any finite collection of linear forms, some possibly proportional, and any $1\leq a\leq |\Sigma|$, it has been conjectured that $I_a(\Sigma)$, the ideal generated by all $a$-fold products of $\Sigma$, has ... More

Virial inversion and density functionalsJun 05 2019We prove a novel inversion theorem for functionals given as power series in infinite-dimensional spaces and apply it to the inversion of the density-activity relation for inhomogeneous systems. This provides a rigorous framework to prove convergence for ... More

Greed is Not Always Good: On Submodular Maximization over Independence SystemsJun 05 2019In this work, we consider the maximization of submodular functions constrained by independence systems. Because of the wide applicability of submodular functions, this problem has been extensively studied in the literature. When the independence system ... More

A Note on Submodular Maximization over Independence SystemsJun 05 2019Jun 07 2019In this work, we consider the maximization of submodular functions constrained by independence systems. Because of the wide applicability of submodular functions, this problem has been extensively studied in the literature, on specialized independence ... More

Quantum Algorithms for Solving Dynamic Programming ProblemsJun 05 2019We present quantum algorithms for solving finite-horizon and infinite-horizon dynamic programming problems. The infinite-horizon problems are studied using the framework of Markov decision processes. We prove query complexity lower bounds for classical ... More

Signaletic operadsJun 05 2019We introduce $k$-signaletic operads and their Koszul duals, generalizing the dendriform, diassociative and duplicial operads (which correspond to the $k=1$ case). We show that the Koszul duals of the $k$-signaletic operads act on multipermutations and ... More

Fair Distributions from Biased Samples: A Maximum Entropy Optimization FrameworkJun 05 2019One reason for the emergence of bias in AI systems is biased data -- datasets that may not be true representations of the underlying distributions -- and may over or under-represent groups with respect to protected attributes such as gender or race. We ... More

Distributed Weighted Matching via Randomized Composable CoresetsJun 05 2019Maximum weight matching is one of the most fundamental combinatorial optimization problems with a wide range of applications in data mining and bioinformatics. Developing distributed weighted matching algorithms is challenging due to the sequential nature ... More

Conditions for discreteness of the spectrum to multi-dimensional Schrödinger operatorJun 05 2019This work is a continuation of our previos paper \cite{Zel1}, where for the the Schr\"odinger operator $H=-\Delta+ V(\e)\cdot$ $(V(\e)\ge 0)$, acting in the space $L_2(\R^d)\,(d\ge 3)$, some constructive sufficient conditions for discreteness of its spectrum ... More

On a functional inequality stemming from the Grüss-type inequalitiesJun 05 2019We study functional inequality of the form $$|T(f,h)-T(f,g)T(g,h)| \leq F(f,g)F(g,h) -F(f,h)$$ where $T$ is a complex-valued functional and $F$ is a real-valued map. Motivation for our studies comes from some generalizations of Gr\"uss inequality.

Fair Near Neighbor Search: Independent Range Sampling in High DimensionsJun 05 2019Similarity search is a fundamental algorithmic primitive, widely used in many computer science disciplines. There are several variants of the similarity search problem, and one of the most relevant is the $r$-near neighbor ($r$-NN) problem: given a radius ... More

On the computability properties of topological entropy: a general approachJun 04 2019The dynamics of symbolic systems, such as multidimensional subshifts of finite type or cellular automata, are known to be closely related to computability theory. In particular, the appropriate tools to describe and classify topological entropy for this ... More

Scalable Spatial Scan Statistics for TrajectoriesJun 04 2019We define several new models for how to define anomalous regions among enormous sets of trajectories. These are based on spatial scan statistics, and identify a geometric region which captures a subset of trajectories which are significantly different ... More

Counting independent sets in unbalanced bipartite graphsJun 04 2019We give an FPTAS for approximating the partition function of the hard-core model for bipartite graphs when there is sufficient imbalance in the degrees or fugacities between the sides $(L,R)$ of the bipartition. This includes, among others, the biregular ... More

Mean field approximation of a heterogeneous population of plants in competitionJun 04 2019The processes of interplant competition within a field are still poorly understood. However, they explain a large part of the heterogeneity in a field and may have longer-term consequences, especially in mixed stands. Modeling can help to better understand ... More

Vertical Vafa-Witten invariantsJun 04 2019We show that \emph{vertical} contributions to (possibly semistable) Tanaka-Thomas-Vafa-Witten invariants are well defined for surfaces with $p_g(S)>0$, partially proving conjectures of \cite{TT2} and \cite{T}. Moreover, we show that such contributions ... More

Uncertainty Principles for the Continuous Shearlet Transforms in Arbitrary Space DimensionsJun 04 2019The aim of this article is to formulate some novel uncertainty principles for the continuous shearlet transforms in arbitrary space dimensions. Firstly, we derive an analogue of the Pitt's inequality for the continuous shearlet transforms, then we formulate ... More

On Expansions and Nodes for Sparse Grid Collocation of Lognormal Elliptic PDEsJun 04 2019This work is a follow-up on a previous contribution (`Convergence of sparse collocation for functions of countably many Gaussian random variables (with application to elliptic PDEs)' SIAM Journal of Numerical Analysis 2018), and contains further insights ... More

A deterministic algorithm for counting colorings with $2Δ$ colorsJun 04 2019Jun 06 2019We give a polynomial time deterministic approximation algorithm (an FPTAS) for counting the number of $q$-colorings of a graph of maximum degree $\Delta$, provided only that $q\ge 2\Delta$. This substantially improves on previous deterministic algorithms ... More

A deterministic algorithm for counting colorings with $2Δ$ colorsJun 04 2019We give a polynomial time deterministic approximation algorithm (an FPTAS) for counting the number of $q$-colorings of a graph of maximum degree $\Delta$, provided only that $q\ge 2\Delta$. This substantially improves on previous deterministic algorithms ... More

Implication Avoiding Dynamics for Externally Observed NetworksJun 03 2019Previous network models have imagined that connections change to promote structural balance, or to reflect hierarchies. We propose a model where agents adjust their connections to appear credible to an external observer. In particular, we envision a signed, ... More

On Romeo and Juliet Problems: Minimizing Distance-to-SightJun 03 2019We introduce a variant of the watchman route problem, which we call the quickest pair-visibility problem. Given two persons standing at points $s$ and $t$ in a simple polygon $P$ with no holes, we want to minimize the distance they travel in order to ... More

Induction of $\mathbb{Z}^2$-actions and of partitions of the 2-torusJun 03 2019Sturmian sequences are the most simple aperiodic sequences. A result of Morse, Hedlund (1940) and Coven, Hedlund (1970) is that a biinfinite binary sequence is sturmian if and only if it is obtained as the coding of an irrational rotation on the circle ... More

Cores and Other Dense Structures in Complex NetworksJun 03 2019Complex networks are a powerful paradigm to model complex systems. Specific network models, e.g., multilayer networks, temporal networks, and signed networks, enrich the standard network representation with additional information to better capture real-world ... More

Transient amplifiers of selection and reducers of fixation for death-Birth updating on graphsJun 03 2019The spatial structure of an evolving population affects which mutations become fixed. Some structures amplify selection, increasing the likelihood that beneficial mutations become fixed while deleterious mutations do not. Other structures suppress selection, ... More

Optimal reporter placement in sparsely measured genetic networks using the Koopman operatorJun 03 2019Optimal sensor placement is an important yet unsolved problem in control theory. In this paper, we make use of the Koopman observability gramian to develop an algorithm for optimal sensor placement of discrete time autonomous nonlinear dynamical systems. ... More

A $2$-compact group as a spetsJun 03 2019Jun 12 2019In 1998 Malle introduced spetses which are mysterious objects with non-real Weyl groups. In algebraic topology, a $p$-compact group $\mathbf{X}$ is a space which is a homotopy-theoretic $p$-local analogue of a compact Lie group. A connected $p$-compact ... More

A $2$-compact group as a spetsJun 03 2019In 1999 Brou\'{e}, Malle and Michel introduced the concept of a ``spets'' which is a mysterious object with a non-real Weyl group. In algebraic topology, a $p$-compact group $X$ is a space which is a homotopy-theoretic $p$-local analogue of a compact ... More

Rpair: Rescaling RePair with RsyncJun 03 2019Data compression is a powerful tool for managing massive but repetitive datasets, especially schemes such as grammar-based compression that support computation over the data without decompressing it. In the best case such a scheme takes a dataset so big ... More

A Direct $\tilde{O}(1/ε)$ Iteration Parallel Algorithm for Optimal TransportJun 03 2019Optimal transportation, or computing the Wasserstein or ``earth mover's'' distance between two distributions, is a fundamental primitive which arises in many learning and statistical settings. We give an algorithm which solves this problem to additive ... More

Direct Linear Time Construction of Parameterized Suffix and LCP Arrays for Constant AlphabetsJun 03 2019We present the first worst-case linear time algorithm that directly computes the parameterized suffix and LCP arrays for constant sized alphabets. Previous algorithms either required quadratic time or the parameterized suffix tree to be built first. More ... More

Descent Data and Absolute Kan ExtensionsJun 03 2019Jun 06 2019The fundamental construction underlying descent theory, the lax descent category, comes with a functor that forgets the \textit{descent data}. We prove that, in any $2$-category with lax descent objects, the forgetful morphisms create all absolute Kan ... More

Descent Data and Absolute Kan ExtensionsJun 03 2019The fundamental construction underlying descent theory, the lax descent category, comes with a functor that forgets the \textit{descent data}. We prove that, in any $2$-category with lax descent objects, the forgetful morphisms create all absolute Kan ... More