Latest in cs.ds

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Generalized semimodularity: order statisticsFeb 14 2019A notion of generalized $n$-semimodularity is introduced, which extends that of (sub/super)mod\-ularity in four ways at once. The main result of this paper, stating that every generalized $(n\colon\!2)$-semimodular function on the $n$th Cartesian power ... More
Complexity-Theoretic Aspects of Expanding Cellular AutomataFeb 14 2019The expanding cellular automata (XCA) variant of cellular automata is investigated and characterized from a complexity-theoretical standpoint. The respective polynomial-time complexity class is shown to coincide with ${\le_{tt}^p}(\textbf{NP})$, that ... More
A Broad Class of Discrete-Time Hypercomplex-Valued Hopfield Neural NetworksFeb 14 2019In this paper, we address the stability of a broad class of discrete-time hypercomplex-valued Hopfield-type neural networks. To ensure the neural networks belonging to this class always settle down at a stationary state, we introduce novel hypercomplex ... More
Some Flatness Conditions on Normal Metric Contact PairsFeb 14 2019In this paper the geometry of normal metric contact pair manifolds is studied under the flatness of conformal, concircular and quasi-conformal curvature tensors. It is proved that a conformal flat normal metric contact pair manifold is an Einstein manifold ... More
A linear programming approach to approximating infinite time reachable sets of strictly stable linear control systemsFeb 14 2019We develop a new numerical method for approximating infinite time reachable sets of strictly stable linear control systems. By solving a linear program with a constraint that incorporates the system dynamics, we compute a polytope with fixed facet normals ... More
Conversion from RLBWT to LZ77Feb 14 2019Converting a compressed format of a string into another compressed format without an explicit decompression is one of the central research topics in string processing. We discuss the problem of converting the run-length Burrows-Wheeler Transform (RLBWT) ... More
Network Semantic Segmentation with Application to GitHubFeb 14 2019In this paper we introduce the concept of network semantic segmentation for social network analysis. We consider the GitHub social coding network which has been a center of attention for both researchers and software developers. Network semantic segmentation ... More
A Cross-Repository Model for Predicting Popularity in GitHubFeb 14 2019Social coding platforms, such as GitHub, can serve as natural laboratories for studying the diffusion of innovation through tracking the pattern of code adoption by programmers. This paper focuses on the problem of predicting the popularity of software ... More
On the Structure of Time-delay Embedding in Linear Models of Non-linear Dynamical SystemsFeb 14 2019It is known that for a non-linear dynamical system, periodic and quasi-periodic attractors can be reconstructed in a discrete sense using time-delay embedding. Following this argument, it has been shown that even chaotic non-linear systems can be represented ... More
Space-Efficient Data Structures for LatticesFeb 13 2019A lattice is a partially-ordered set in which every pair of elements has a unique meet (greatest lower bound) and join (least upper bound). We present new data structures for lattices that are simple, efficient, and nearly optimal in terms of space complexity. ... More
Efficient Continuous Multi-Query Processing over Graph StreamsFeb 13 2019Graphs are ubiquitous and ever-present data structures that have a wide range of applications involving social networks, knowledge bases and biological interactions. The evolution of a graph in such scenarios can yield important insights about the nature ... More
Reconstructing Trees from TracesFeb 13 2019We study the problem of learning a node-labeled tree given independent traces from an appropriately defined deletion channel. This problem, tree trace reconstruction, generalizes string trace reconstruction, which corresponds to the tree being a path. ... More
Entropy theory for Delone sets in locally compact abelian groupsFeb 13 2019We extend the notion of patch counting entropy to Delone sets without finite local complexity (FLC). We show that for all Delone sets patch counting entropy equals the topological entropy of the corresponding Delone dynamical systems. Furthermore we present, ... More
New Results on Directed Edge Dominating SetFeb 13 2019We study a family of generalizations of Edge Dominating Set on directed graphs called Directed $(p,q)$-Edge Dominating Set. In this problem an arc $(u,v)$ is said to dominate itself, as well as all arcs which are at distance at most $q$ from $v$, or at ... More
Task-based Augmented Contour Trees with Fibonacci HeapsFeb 13 2019This paper presents a new algorithm for the fast, shared memory, multi-core computation of augmented contour trees on triangulations. In contrast to most existing parallel algorithms our technique computes augmented trees, enabling the full extent of ... More
Constructing Antidictionaries in Output-Sensitive SpaceFeb 13 2019A word $x$ that is absent from a word $y$ is called minimal if all its proper factors occur in $y$. Given a collection of $k$ words $y_1,y_2,\ldots,y_k$ over an alphabet $\Sigma$, we are asked to compute the set $\mathrm{M}^{\ell}_{y_{1}\#\ldots\#y_{k}}$ ... More
Learning and Generalization for Matching ProblemsFeb 13 2019We study a classic algorithmic problem through the lens of statistical learning. That is, we consider a matching problem where the input graph is sampled from some distribution. This distribution is unknown to the algorithm; however, an additional graph ... More
CSPs with Global Modular Constraints: Algorithms and Hardness via Polynomial RepresentationsFeb 13 2019We study the complexity of Boolean constraint satisfaction problems (CSPs) when the assignment must have Hamming weight in some congruence class modulo M, for various choices of the modulus M. Due to the known classification of tractable Boolean CSPs, ... More
Mesh: Compacting Memory Management for C/C++ ApplicationsFeb 13 2019Programs written in C/C++ can suffer from serious memory fragmentation, leading to low utilization of memory, degraded performance, and application failure due to memory exhaustion. This paper introduces Mesh, a plug-in replacement for malloc that, for ... More
Learning Ising Models with Independent FailuresFeb 13 2019We give the first efficient algorithm for learning the structure of an Ising model that tolerates independent failures; that is, each entry of the observed sample is missing with some unknown probability p. Our algorithm matches the essentially optimal ... More
Search and Rescue in the Face of Uncertain ThreatsFeb 13 2019We consider a search problem in which one or more targets must be rescued by a search party, or Searcher. The targets may be survivors of some natural disaster, or prisoners held by an adversary. The targets are hidden among a finite set of locations, ... More
Derivative-based global sensitivity analysis for models with high-dimensional inputs and functional outputsFeb 12 2019We present a framework for derivative-based global sensitivity analysis (GSA) for models with high-dimensional input parameters and functional outputs. We combine ideas from derivative-based GSA, random field representation via Karhunen--Lo\`{e}ve expansions, ... More
Crowdsourced PAC Learning under Classification NoiseFeb 12 2019In this paper, we analyze PAC learnability from labels produced by crowdsourcing. In our setting, unlabeled examples are drawn from a distribution and labels are crowdsourced from workers who operate under classification noise, each with their own noise ... More
Integral and differential structure on the free $C^{\infty}$-ring modalityFeb 12 2019This paper develops an example of an integral category whose integral transformation operates on smooth 1-forms. Further, we revisit the differential structure of this category, and we investigate derivations, coderelictions, and Rota-Baxter algebras ... More
Measure of quality of finite-dimensional linear systems: A frame-theoretic viewFeb 12 2019A measure of quality of a control system is a quantitative extension of the classical binary notion of controllability. In this article we study the quality of linear control systems from a frame-theoretic perspective. We demonstrate that all LTI systems ... More
The Cost of Privacy: Optimal Rates of Convergence for Parameter Estimation with Differential PrivacyFeb 12 2019Privacy-preserving data analysis is a rising challenge in contemporary statistics, as the privacy guarantees of statistical methods are often achieved at the expense of accuracy. In this paper, we investigate the tradeoff between statistical accuracy ... More
Global solutions of continuous coagulation-fragmentation equations with unbounded coefficientsFeb 12 2019In this paper we prove the existence of global classical solutions to continuous coagulation-fragmentation equations with unbounded coefficients under the sole assumption that the coagulation rate is dominated by a power of the fragmentation rate, thus ... More
Compressed Range Minimum QueriesFeb 12 2019Given a string $S$ of $n$ integers in $[0,\sigma)$, a range minimum query $\textsf{RMQ}(i, j)$ asks for the index of the smallest integer in $S[i \dots j]$. It is well known that the problem can be solved with a succinct data structure of size $2n + o(n)$ ... More
Learning interpretable continuous-time models of latent stochastic dynamical systemsFeb 12 2019We develop an approach to learn an interpretable semi-parametric model of a latent continuous-time stochastic dynamical system, assuming noisy high-dimensional outputs sampled at uneven times. The dynamics are described by a nonlinear stochastic differential ... More
Shadowing and structural stability in linear dynamical systemsFeb 12 2019A well-known result in the area of dynamical systems asserts that any invertible hyperbolic operator on any Banach space is structurally stable. This result was originally obtained by P. Hartman in 1960 for operators on finite-dimensional spaces. The ... More
A Theory of Selective PredictionFeb 12 2019We consider a model of selective prediction, where the prediction algorithm is given a data sequence in an online fashion and asked to predict a pre-specified statistic of the upcoming data points. The algorithm is allowed to choose when to make the prediction ... More
How to count the number of zeros that a polynomial has on the unit circle?Feb 12 2019The classical problem of counting the number of real zeros of a real polynomial was solved a long time ago by Sturm. The analogous problem of counting the number of zeros that a polynomial has on the unit circle is, however, still an open problem. In ... More
On the Convergence of Network SystemsFeb 11 2019The apparent disconnection between the microscopic and the macroscopic is a major issue in the understanding of complex systems. To this extend, we study the convergence of repeatedly applying local rules on a network, and touch on the expressive power ... More
Geometric MulticutFeb 11 2019We study the following separation problem: Given a collection of colored objects in the plane, compute a shortest "fence" $F$, i.e., a union of curves of minimum total length, that separates every two objects of different colors. Two objects are separated ... More
Computing Extremely Accurate Quantiles Using t-DigestsFeb 11 2019We present on-line algorithms for computing approximations of rank-based statistics that give high accuracy, particularly near the tails of a distribution, with very small sketches. Notably, the method allows a quantile $q$ to be computed with an accuracy ... More
Statistical instability for contracting Lorenz flowsFeb 11 2019We consider one parameter families of vector fields introduced by Rovella, obtained through modifying the eigenvalues of the geometric Lorenz attractor, replacing the expanding condition on the eigenvalues of the singularity by a contracting one. We show ... More
Uniform convergence in von Neumann's ergodic theorem in absence of a spectral gapFeb 11 2019Von Neumann's original proof of the ergodic theorem is revisited. A convergence rate is established under the assumption that one can control the density of the spectrum of the underlying self-adjoint operator when restricted to suitable subspaces. Explicit ... More
Reconstructing dynamical networks via feature rankingFeb 11 2019Empirical data on real complex systems are becoming increasingly available. Parallel to this is the need for new methods of reconstructing (inferring) the topology of networks from time-resolved observations of their node-dynamics. The methods based on ... More
Flow-Up Bases for Generalized Spline Modules on Arbitrary GraphsFeb 11 2019Let R be a commutative ring with identity. An edge labeled graph is a graph with edges labeled by the ideals of R. A generalized spline over an edge labeled graph is a vertex labeling by the elements of R, such that the labels of adjacent vertices agree ... More
A Minimal Template for Interactive Web-based Demonstrations of Musical Machine LearningFeb 11 2019New machine learning algorithms are being developed to solve problems in different areas, including music. Intuitive, accessible, and understandable demonstrations of the newly built models could help attract the attention of people from different disciplines ... More
Balancing Straight-Line ProgramsFeb 10 2019It is shown that a context-free grammar of size $m$ that produces a single string $w$ (such a grammar is also called a string straight-line program) can be transformed in linear time into a context-free grammar for $w$ of size $\mathcal{O}(m)$, whose ... More
On the Complexity of Exact Pattern Matching in Graphs: Determinism and Zig-Zag MatchingFeb 10 2019Exact pattern matching in labeled graphs is the problem of searching paths of a graph $G=(V,E)$ that spell the same string as the given pattern $P[1..m]$. This basic problem can be found at the heart of more complex operations on variation graphs in computational ... More
Doubly periodic monopoles and $q$-difference modulesFeb 10 2019An interesting theme in complex differential geometry is to find a correspondence between algebraic objects and differential geometric objects. One of the most attractive is the non-abelian Hodge theory of Simpson. In this paper, pursuing an analogue ... More
On modeling hard combinatorial optimization problems as linear programs: Refutations of the "unconditional impossibility" claimsFeb 10 2019There has been a series of developments in the recent literature (by essentially a same "circle" of authors) with the absolute/unconditioned (implicit or explicit) claim that there exists no abstraction of an NP-Complete combinatorial optimization problem ... More
Approximating $k$-connected $m$-dominating setsFeb 10 2019A subset $S$ of nodes in a graph $G$ is a $k$-connected $m$-dominating set ($(k,m)$-cds) if the subgraph $G[S]$ induced by $S$ is $k$-connected and every $v \in V \setminus S$ has at least $m$ neighbors in $S$. In the $k$-Connected $m$-Dominating Set ... More
Set Cover in Sub-linear TimeFeb 10 2019We study the classic set cover problem from the perspective of sub-linear algorithms. Given access to a collection of $m$ sets over $n$ elements in the query model, we show that sub-linear algorithms derived from existing techniques have almost tight ... More
Multi-Dimensional Balanced Graph Partitioning via Projected Gradient DescentFeb 10 2019Motivated by performance optimization of large-scale graph processing systems that distribute the graph across multiple machines, we consider the balanced graph partitioning problem. Compared to the previous work, we study the multi-dimensional variant ... More
Scalable Fair ClusteringFeb 10 2019We study the fair variant of the classic $k$-median problem introduced by Chierichetti et al. [2017]. In the standard $k$-median problem, given an input pointset $P$, the goal is to find $k$ centers $C$ and assign each input point to one of the centers ... More
Metric Curvatures and their Applications 2: Metric Ricci Curvature and FlowFeb 09 2019In this second part of our overview of the different metric curvatures and their various applications, we concentrate on the Ricci curvature and flow for polyhedral surfaces and higher dimensional manifolds, and we largely review our previous studies ... More
Linear Time Algorithms for Multiple Cluster Scheduling and Multiple Strip PackingFeb 09 2019We study the Multiple Cluster Scheduling problem and the Multiple Strip Packing problem. For both problems, there is no algorithm with approximation ratio better than $2$ unless $P = NP$. In this paper, we present an algorithm with approximation ratio ... More
Trajectories of semigroups of holomorphic functions and harmonic measureFeb 09 2019We give an explicit relation between the slope of the trajectory of a semigroup of holomorphic functions and the harmonic measure of the associated planar domain ${\varOmega}$. We use this to construct a semigroup whose slope is an arbitrary interval ... More
Fast Approximation Schemes for Bin PackingFeb 09 2019We present new approximation schemes for bin packing based on the following two approaches: (1) partitioning the given problem into mostly identical sub-problems of constant size and then construct a solution by combining the solutions of these constant ... More
Modular Nekrasov-Okounkov formulasFeb 09 2019Using Littlewood's map, which decomposes a partition into its $r$-core and $r$-quotient, Han and Ji have shown that many well-known hook-length formulas admit modular analogues. In this paper we present a variant of the Han-Ji `multiplication theorem' ... More
Fast Sequence Segmentation using Log-Linear ModelsFeb 08 2019Sequence segmentation is a well-studied problem, where given a sequence of elements, an integer K, and some measure of homogeneity, the task is to split the sequence into K contiguous segments that are maximally homogeneous. A classic approach to find ... More
Faster Repetition-Aware Compressed Suffix Trees based on Block TreesFeb 08 2019Suffix trees are a fundamental data structure in stringology, but their space usage, though linear, is an important problem for its applications. We design and implement a new compressed suffix tree targeted to highly repetitive texts, such as large genomic ... More
Constructing Selections Stepwise Over Cones of Simplicial ComplexesFeb 08 2019It is given a simplified proof of a natural generalisation of Uspenskij's selection characterisation of paracompact $C$-spaces. The method is also applied to give a simplified proof of a similar characterisation of paracompact finite $C$-space. Another ... More
The method of forcingFeb 08 2019The purpose of this article is to give a presentation of the method of forcing aimed at someone with a minimal knowledge of set theory and logic. The emphasis will be on how the method can be used to prove theorems in ZFC.
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
Zeros of irreducible characters lying in a normal subgroupFeb 08 2019Let $N$ be a normal subgroup of a finite group $G$. An element $g\in G$ such that $\chi(g)=0$ for some irreducible character $\chi$ of $G$ is called a vanishing element of $G$. The aim of this paper is to analyse the influence of the $\pi$-elements in ... More
On zeros of irreducible characters lying in a normal subgroupFeb 08 2019Feb 13 2019Let $N$ be a normal subgroup of a finite group $G$. An element $g\in G$ such that $\chi(g)=0$ for some irreducible character $\chi$ of $G$ is called a vanishing element of $G$. The aim of this paper is to analyse the influence of the $\pi$-elements in ... More
Using Background Knowledge to Rank ItemsetsFeb 08 2019Assessing the quality of discovered results is an important open problem in data mining. Such assessment is particularly vital when mining itemsets, since commonly many of the discovered patterns can be easily explained by background knowledge. The simplest ... More
Hyperuniform point sets on flat tori: deterministic and probabilistic aspectsFeb 08 2019In this paper we study hyperuniformity on flat tori. Hyperuniform point sets on the unit sphere have been studied by J.~Brauchart, P.~Grabner, W.~Kusner and J.~Ziefle. It is shown that point sets which are hyperuniform for large balls, small balls or ... More
Are your Items in Order?Feb 08 2019Items in many datasets can be arranged to a natural order. Such orders are useful since they can provide new knowledge about the data and may ease further data exploration and visualization. Our goal in this paper is to define a statistically well-founded ... More
Space-efficient merging of succinct de Bruijn graphsFeb 07 2019We propose a new algorithm for merging succinct representations of de Bruijn graphs introduced in [Bowe et al. WABI 2012]. Our algorithm is inspired by the approach introduced by Holt and McMillan [Bionformatics 2014, ACM-BCB 2014] for merging Burrow-Wheeler ... More
Discovering Descriptive Tile Trees by Mining Optimal Geometric SubtilesFeb 07 2019When analysing binary data, the ease at which one can interpret results is very important. Many existing methods, however, discover either models that are difficult to read, or return so many results interpretation becomes impossible. Here, we study a ... More
The Long and the Short of It: Summarising Event Sequences with Serial EpisodesFeb 07 2019An ideal outcome of pattern mining is a small set of informative patterns, containing no redundancy or noise, that identifies the key structure of the data at hand. Standard frequent pattern miners do not achieve this goal, as due to the pattern explosion ... More
Significance of Episodes Based on Minimal WindowsFeb 07 2019Discovering episodes, frequent sets of events from a sequence has been an active field in pattern mining. Traditionally, a level-wise approach is used to discover all frequent episodes. While this technique is computationally feasible it may result in ... More
Distributed Ledger Privacy: Ring Signatures, Möbius and CryptoNoteFeb 07 2019Distributed ledger and blockchain systems are expected to make financial systems easier to audit, reduce counter-party risk and transfer assets seamlessly. The key concept is a token controlled by a cryptographic private key for spending, and represented ... More
Going Far From DegeneracyFeb 07 2019Feb 14 2019An undirected graph G is d-degenerate if every subgraph of G has a vertex of degree at most d. By the classical theorem of Erd\H{o}s and Gallai from 1959, every graph of degeneracy d>1 contains a cycle of length at least d+1. The proof of Erd\H{o}s and ... More
Going Far From DegeneracyFeb 07 2019An undirected graph G is d-degenerate if every subgraph of G has a vertex of degree at most d. By the classical theorem of Erd\H{o}s and Gallai from 1959, every graph of degeneracy d>1 contains a cycle of length at least d+1. The proof of Erd\H{o}s and ... More
A fast algorithm for constructing balanced binary search treesFeb 07 2019We suggest a new non-recursive algorithm for constructing a binary search tree given an array of numbers. The algorithm has $O(N)$ time and $O(1)$ memory complexities if the given array of $N$ numbers is sorted. The resulting tree is of minimal height ... More
On Mean Estimation for General Norms with Statistical QueriesFeb 07 2019We study the problem of mean estimation for high-dimensional distributions, assuming access to a statistical query oracle for the distribution. For a normed space $X = (\mathbb{R}^d, \|\cdot\|_X)$ and a distribution supported on vectors $x \in \mathbb{R}^d$ ... More
Superposition, reduction of multivariable problems, and approximationFeb 07 2019We study reduction schemes for functions of "many" variables into system of functions in one variable. Our setting includes infinite-dimensions. Following Cybenko-Kolmogorov, the outline for our results is as follows: We present explicit reductions schemes ... More
Finding Good Itemsets by Packing DataFeb 06 2019The problem of selecting small groups of itemsets that represent the data well has recently gained a lot of attention. We approach the problem by searching for the itemsets that compress the data efficiently. As a compression technique we use decision ... More
Some Singular Vector-valued Jack and Macdonald PolynomialsFeb 06 2019For each partition $\tau$ of $N$ there are irreducible modules of the symmetric groups $\mathcal{S}_{N}$ or the corresponding Hecke algebra $\mathcal{H}_{N}\left( t\right) $ whose bases consist of reverse standard Young tableaux of shape $\tau$. There ... More
New Amortized Cell-Probe Lower Bounds for Dynamic ProblemsFeb 06 2019We build upon the recent papers by Weinstein and Yu (FOCS'16), Larsen (FOCS'12), and Clifford et al. (FOCS'15) to present a general framework that gives amortized lower bounds on the update and query times of dynamic data structures. Using our framework, ... More
Toward a Dichotomy for Approximation of $H$-coloringFeb 06 2019The minimum cost homomorphism problem (MinHOM) is a natural optimization problem for homomorphisms to a fixed (di)graph H. Given an input (di)graph G, with a cost associated with mapping any vertex of G to any vertex of H, one seeks to minimize the sum ... More
Ramsey properties of randomly perturbed dense graphsFeb 06 2019We investigate Ramsey properties of a random graph model in which random edges are added to a given dense graph. Specifically, we determine lower and upper bounds on the function $p=p(n)$ that ensures that for any dense graph $G_n$ a.a.s. every 2-colouring ... More
Top Tree Compression of TriesFeb 06 2019We present a compressed representation of tries based on top tree compression [ICALP 2013] that works on a standard, comparison-based, pointer machine model of computation and supports efficient prefix search queries. Namely, we show how to preprocess ... More
Firefighting on TreesFeb 06 2019In the Firefighter problem, introduced by Hartnell in 1995, a fire spreads through a graph while a player chooses which vertices to protect in order to contain it. In this paper, we focus on the case of trees and we consider as well the Fractional Firefighter ... More
An example on Lyapunov stability and linearizationFeb 06 2019The purpose of this paper is to present an example of a C1 (in the Fr\'echet sense) discrete dynamical system in a infinite-dimensional separable Hilbert space for which the origin is an exponentially asymptotically stable fixed point, but such that its ... More
On Quasi Ordinal Diagram SystemsFeb 06 2019The purposes of this note are the following two; we first generalize Okada-Takeuti's well quasi ordinal diagram theory, utilizing the recent result of Dershowitz-Tzameret's version of tree embedding theorem with gap conditions. Second, we discuss possible ... More
Testing Markov Chains without HittingFeb 06 2019We study the problem of identity testing of markov chains. In this setting, we are given access to a single trajectory from a markov chain with unknown transition matrix $Q$ and the goal is to determine whether $Q = P$ for some known matrix $P$ or $\text{Dist}(P, ... More
Fast Mean Estimation with Sub-Gaussian RatesFeb 06 2019We propose an estimator for the mean of a random vector in $\mathbb{R}^d$ that can be computed in time $O(n^4+n^2d)$ for $n$ i.i.d.~samples and that has error bounds matching the sub-Gaussian case. The only assumptions we make about the data distribution ... More
A Composable Coreset for k-Center in Doubling MetricsFeb 05 2019A set of points $P$ in a metric space and a constant integer $k$ are given. The $k$-center problem finds $k$ points as \textit{centers} among $P$, such that the maximum distance of any point of $P$ to their closest centers $(r)$ is minimized. Doubling ... More
Beltrami fields with nonconstant proportionality factorFeb 05 2019We consider the question raised by Enciso and Peralta-Salas in [4] (see arXiv:1402.6825): What nonconstant functions $f$ can occur as the proportionality factor for a Beltrami field $\mathbf{u}$ on an open subset $U \subset \mathbb{R}^3$? We also consider ... More
Average-case complexity of a branch-and-bound algorithm for min dominating setFeb 05 2019The average-case complexity of a branch-and-bound algorithms for Minimum Dominating Set problem in random graphs in the G(n,p) model is studied. We identify phase transitions between subexponential and exponential average-case complexities, depending ... More
Dynamic hierarchies in temporal directed networksFeb 05 2019The outcome of interactions in many real-world systems can be often explained by a hierarchy between the participants. Discovering hierarchy from a given directed network can be formulated as follows: partition vertices into levels such that, ideally, ... More
Rigorous numerics of blow-up solutions for ODEs with exponential nonlinearityFeb 05 2019Our concerns here are blow-up solutions for ODEs with exponential nonlinearity from the viewpoint of dynamical systems and their numerical validations. As an example, the finite difference discretization of $u_t = u_{xx} + e^{u^m}$ with the homogeneous ... More
Inferring the strength of social ties: a community-driven approachFeb 05 2019Online social networks are growing and becoming denser. The social connections of a given person may have very high variability: from close friends and relatives to acquaintances to people who hardly know. Inferring the strength of social ties is an important ... More
Hierarchical Matrix Operations on GPUs: Matrix-Vector Multiplication and CompressionFeb 05 2019Hierarchical matrices are space and time efficient representations of dense matrices that exploit the low rank structure of matrix blocks at different levels of granularity. The hierarchically low rank block partitioning produces representations that ... More
Dynamical systems with fast switching and slow diffusion: Hyperbolic equilibria and stable limit cyclesFeb 05 2019We study the long-term qualitative behavior of randomly perturbed dynamical systems. More specifically, we look at limit cycles of certain stochastic differential equations (SDE) with Markovian switching, in which the process switches at random times ... More
Hamiltonicity below Dirac's conditionFeb 05 2019Dirac's theorem (1952) is a classical result of graph theory, stating that an $n$-vertex graph ($n \geq 3$) is Hamiltonian if every vertex has degree at least $n/2$. Both the value $n/2$ and the requirement for every vertex to have high degree are necessary ... More
Network Resilience Assessment via QoS Degradation Metrics: An Algorithmic ApproachFeb 05 2019This paper focuses on network resilience to perturbation of edge weight. Other than connectivity, many network applications nowadays rely upon some measure of network distance between a pair of connected nodes. In these systems, a metric related to network ... More
Discovering bursts revisited: guaranteed optimization of the model parametersFeb 05 2019One of the classic data mining tasks is to discover bursts, time intervals, where events occur at abnormally high rate. In this paper we revisit Kleinberg's seminal work, where bursts are discovered by using exponential distribution with a varying rate ... More
Rigidity theorems of Lagrangian submanifolds in the homogeneous nearly Kähler $\mathbb{S}^6(1)$Feb 05 2019Feb 10 2019In this paper, we study Lagrangian submanifolds of the homogeneous nearly K\"ahler $6$-dimensional unit sphere $\mathbb{S}^6(1)$. As the main result, we derive a Simons' type integral inequality in terms of the second fundamental form for compact Lagrangian ... More
Rigidity theorems of Lagrangian submanifolds in the homogeneous nearly Kähler $\mathbb{S}^6(1)$Feb 05 2019In this paper, we study Lagrangian submanifolds of the homogeneous nearly K\"ahler $6$-dimensional unit sphere $\mathbb{S}^6(1)$. We derive a Simons' type integral inequality in terms of the second fundamental form for compact Lagrangian submanifolds ... More
Randomized Riemannian Preconditioning for Quadratically Constrained ProblemsFeb 05 2019Optimization problem with quadratic equality constraints are prevalent in machine learning. Indeed, two important examples are Canonical Correlation Analysis (CCA) and Linear Discriminant Analysis (LDA). Unfortunately, methods for solving such problems ... More
A Generalization of Linear Positive SystemsFeb 05 2019The dynamics of linear positive systems maps the positive orthant to itself. In other words, it maps a set of vectors with zero sign variations to itself. This raises the following question: what linear systems map the set of vectors with $k$ sign variations ... More
An Optimal Algorithm for Online Freeze-tagFeb 05 2019In the freeze-tag problem, one active robot must wake up many frozen robots. The robots are considered as points in a metric space, where active robots move at a constant rate and activate other robots by visiting them. In the (time-dependent) online ... More