IA Scholar Query: Connectivity Properties of Random Subgraphs of the Cube.
https://scholar.archive.org/
Internet Archive Scholar query results feedeninfo@archive.orgMon, 10 Oct 2022 00:00:00 GMTfatcat-scholarhttps://scholar.archive.org/help1440NeoCube: Graph-Based Implementation of the M3 Data Model
https://scholar.archive.org/work/cxli5v7uznbmdj2hfmcpokfocm
In this work, we consider metadata-based exploration of media collections using the M3 data model, to support multimedia analytics applications. We propose a new metadata-server implementation based on the Neo4j graph database system, and compare it to the existing, heavily-optimised server based on a relational database system. We show that the graph-based implementation performs well for interactive metadata-space retrieval, albeit not as well as the optimised relational implementation. The graph-based implementation also allows for very efficient updates to the metadata collection, however, which are practically impossible in the optimised relational implementation.Nikolaj Mertz, Björn Þór Jónsson, Aaron Duanework_cxli5v7uznbmdj2hfmcpokfocmMon, 10 Oct 2022 00:00:00 GMTDescriptive Combinatorics and Distributed Algorithms
https://scholar.archive.org/work/pjgjlnfrkzd5vmd7p7c5yr66pe
In this article we shall explore a fascinating area called descriptive combinatorics and its recently discovered connections to distributed algorithms-a fundamental part of computer science that is becoming increasingly important in the modern era of decentralized computation. The interdisciplinary nature of these connections means that there is very little common background shared by the researchers who are interested in them. With this in mind, this article was written under the assumption that the reader would have close to no background in either descriptive set theory or computer science. The reader will judge to what degree this endeavor was successful. The article comprises two parts. In the first part we give a brief introduction to some of the central notions and problems of descriptive combinatorics. The second part is devoted to a survey of some of the results concerning theAnton Bernshteynwork_pjgjlnfrkzd5vmd7p7c5yr66peSat, 01 Oct 2022 00:00:00 GMTHypercontractive Inequalities for the Second Norm of Highly Concentrated Functions, and Mrs. Gerber's-Type Inequalities for the Second Rényi Entropy
https://scholar.archive.org/work/jtfmry2pj5fwbhqcci4efwmt5i
Let Tϵ, 0≤ϵ≤1/2, be the noise operator acting on functions on the boolean cube {0,1}n. Let f be a distribution on {0,1}n and let q>1. We prove tight Mrs. Gerber-type results for the second Rényi entropy of Tϵf which take into account the value of the qth Rényi entropy of f. For a general function f on {0,1}n we prove tight hypercontractive inequalities for the ℓ2 norm of Tϵf which take into account the ratio between ℓq and ℓ1 norms of f.Niv Levhari, Alex Samorodnitskywork_jtfmry2pj5fwbhqcci4efwmt5iTue, 27 Sep 2022 00:00:00 GMTIt's a Wrap! Visualisations that Wrap Around Cylindrical, Toroidal, or Spherical Topologies
https://scholar.archive.org/work/akpvfdnu2fhgdjsfxa25kjeu2a
Traditional visualisations are designed to be shown on a flat surface (screen or page) but most data is not "flat". For example, the surface of the earth exists on a sphere, however, when that surface is presented on a flat map, key information is hidden, such as geographic paths on the spherical surface being wrapped across the boundaries of the flat map. Similarly, cyclical time-series data has no beginning or end. When such cyclical data is presented on a traditional linear chart, the viewer needs to perceive continuity of the visualisation across the chart's boundaries. Mentally reconnecting the chart across such a boundary may induce additional cognitive load. More complex data such as a network diagram with hundreds or thousands of links between data points leads to a densely connected structure that is even less "flat" and needs to wrap around in multiple dimensions. To improve the usability of these visualisations, this thesis explores a novel class of interactive wrapped data visualisations, i.e., visualisations that wrap around continuously when interactively panned on a two-dimensional projection of surfaces of 3D shapes, specifically, cylinder, torus, or sphere. We start with a systematic exploration of the design space of interactive wrapped visualisations, characterising the visualisations that help people understand the relationship within the data. Subsequently, we investigate a series of wrappable visualisations for cyclical time series, network, and geographic data. We show that these interactive visualisations better preserve the spatial relations in the case of geospatial data, and better reveal the data's underlying structure in the case of abstract data such as networks and cyclical time series. Furthermore, to assist future research and development, we contribute layout algorithms and toolkits to help create pannable wrapped visualisations.Kun-Ting Chenwork_akpvfdnu2fhgdjsfxa25kjeu2aTue, 27 Sep 2022 00:00:00 GMTWilson loops in the abelian lattice Higgs model
https://scholar.archive.org/work/chzafi3j4jfpvfi4knsxqonadi
We consider the lattice Higgs model on ℤ^4, with structure group given by ℤ_n for n ≥ 2. We compute the expected value of the Wilson loop observable to leading order when the gauge coupling constant and hopping parameter are both sufficiently large. The leading order term is expressed in terms of a quantity arising from the related but much simpler ℤ_n model, which reduces to the Ising model when n=2. As part of the proof, we construct a coupling between the lattice Higgs model and the ℤ_n model.Malin P. Forsström, Jonatan Lenells, Fredrik Viklundwork_chzafi3j4jfpvfi4knsxqonadiMon, 26 Sep 2022 00:00:00 GMTEdge-fault-tolerance about the SM-λ property of hypercube-like networks
https://scholar.archive.org/work/yu7tnv3rxrbgrhfw6dybnxbto4
The edge-fault-tolerance of networks is of great significance to the design and maintenance of networks. For any pair of vertices u and v of the connected graph G, if they are connected by min{_G(u),_G(v)} edge-disjoint paths, then G is strong Menger edge connected (SM-λ for short). The conditional edge-fault-tolerance about the SM-λ property of G, written sm_λ^r(G), is the maximum value of m such that G-F is still SM-λ for any edge subset F with |F|≤ m and δ(G-F)≥ r, where δ(G-F) is the minimum degree of G-F. Previously, most of the exact value for sm_λ^r(G) is aimed at some well-known networks when r≤ 2, and a few of the lower bounds on some well-known networks for r≥ 3. In this paper, we firstly determine the exact value of sm_λ^r(G) on class of hypercube-like networks (HL-networks for short, including hypercubes, twisted cubes, crossed cubes etc.) for a general r, that is, sm_λ^r(G_n)=2^r(n-r)-n for every G_n∈ HL_n, where n≥ 3 and 1≤ r ≤ n-2.Dong Liu.Pingshan Li, Bicheng Zhangwork_yu7tnv3rxrbgrhfw6dybnxbto4Sun, 25 Sep 2022 00:00:00 GMTA remark on the Ramsey number of the hypercube
https://scholar.archive.org/work/q77643xf3vbntmiz3rcrhhv36e
A well known conjecture of Burr and Erdos asserts that the Ramsey number r(Q_n) of the hypercube Q_n on 2^n vertices is of the order O(2^n). In this paper, we show that r(Q_n)=O(2^2n-c n) for a universal constant c>0, improving upon the previous best known bound r(Q_n)=O(2^2n), due to Conlon, Fox and Sudakov.Konstantin Tikhomirovwork_q77643xf3vbntmiz3rcrhhv36eSat, 24 Sep 2022 00:00:00 GMTLinear Clustering Process on Networks
https://scholar.archive.org/work/4no7cqk5arb5xfw4zu5bi263ta
We propose a linear clustering process on a network consisting of two opposite forces: attraction and repulsion between adjacent nodes. Each node is mapped to a position on a one-dimensional line. The attraction and repulsion forces move the nodal position on the line, depending on how similar or different the neighbourhoods of two adjacent nodes are. Based on each node position, the number of clusters in a network, together with each node's cluster membership, is estimated. The performance of the proposed linear clustering process is benchmarked on synthetic networks against widely accepted clustering algorithms such as modularity, the Louvain method and the non-back tracking matrix. The proposed linear clustering process outperforms the most popular modularity-based methods, such as the Louvain method, while possessing a comparable computational complexity.Ivan Jokić, Piet Van Mieghemwork_4no7cqk5arb5xfw4zu5bi263taFri, 23 Sep 2022 00:00:00 GMT22 Examples of Solution Compression via Derandomization
https://scholar.archive.org/work/3pydj4cpjbgj5nnjaphn42x36i
We provide bounds on the compression size of the solutions to 22 problems in computer science. For each problem, we show that solutions exist with high probability, for some simple probability measure. Once this is proven, derandomization can be used to prove the existence of a simple solution.Samuel Epsteinwork_3pydj4cpjbgj5nnjaphn42x36iFri, 23 Sep 2022 00:00:00 GMTCentral Measures of Continuous Graded Graphs: the Case of Distinct Frequencies
https://scholar.archive.org/work/ks6q4l3s2ba3nok3skoxjlfnbe
We define a class of continuous graded graphs similar to the graph of Gelfand–Tsetlin patterns, and describe the set of all ergodic central measures of discrete type on the path spaces of such graphs. The main observation is that an ergodic central measure on a subgraph of a Pascal-type graph can often be obtained as the restriction of the standard Bernoulli measure to the path space of the subgraph. This observation dramatically changes the approach to finding central measures also on discrete graphs, such as the famous Young graph. The simplest example of this type is given by the theorem on the weak limits of normalized Lebesgue measures on simplices; these are the so-called Cesàro measures, which are concentrated on the sequences with prescribed Cesàro limits (this limit parametrizes the corresponding measure). More complicated examples are the graphs of continuous Young diagrams with fixed number of rows and the graphs of spectra of infinite Hermitian matrices of finite rank. We prove existence and uniqueness theorems for ergodic central measures and describe their structure. In particular, our results 1) give a new spectral description of the so-called infinite-dimensional Wishart measures – ergodic unitarily invariant measures of discrete type on the set of infinite Hermitian matrices; 2) describe the structure of continuous analogs of measures on discrete graded graphs. New problems and connections which appear are to be considered in new publications.A.Vershik, F.Petrovwork_ks6q4l3s2ba3nok3skoxjlfnbeFri, 23 Sep 2022 00:00:00 GMTImplicit Conversion of Manifold B-Rep Solids by Neural Halfspace Representation
https://scholar.archive.org/work/bn4jlgqys5bwjj5rsdir7pvxiu
We present a novel implicit representation -- neural halfspace representation (NH-Rep), to convert manifold B-Rep solids to implicit representations. NH-Rep is a Boolean tree built on a set of implicit functions represented by the neural network, and the composite Boolean function is capable of representing solid geometry while preserving sharp features. We propose an efficient algorithm to extract the Boolean tree from a manifold B-Rep solid and devise a neural network-based optimization approach to compute the implicit functions. We demonstrate the high quality offered by our conversion algorithm on ten thousand manifold B-Rep CAD models that contain various curved patches including NURBS, and the superiority of our learning approach over other representative implicit conversion algorithms in terms of surface reconstruction, sharp feature preservation, signed distance field approximation, and robustness to various surface geometry, as well as a set of applications supported by NH-Rep.Hao-Xiang Guo and Yang Liu and Hao Pan and Baining Guowork_bn4jlgqys5bwjj5rsdir7pvxiuWed, 21 Sep 2022 00:00:00 GMTThe Quantum and Classical Streaming Complexity of Quantum and Classical Max-Cut
https://scholar.archive.org/work/bovqx5yajzblbgglr3pfsneamy
We investigate the space complexity of two graph streaming problems: Max-Cut and its quantum analogue, Quantum Max-Cut. Previous work by Kapralov and Krachun [STOC '19] resolved the classical complexity of the classical problem, showing that any (2 - ε)-approximation requires Ω(n) space (a 2-approximation is trivial with O(log n) space). We generalize both of these qualifiers, demonstrating Ω(n) space lower bounds for (2 - ε)-approximating Max-Cut and Quantum Max-Cut, even if the algorithm is allowed to maintain a quantum state. As the trivial approximation algorithm for Quantum Max-Cut only gives a 4-approximation, we show tightness with an algorithm that returns a (2 + ε)-approximation to the Quantum Max-Cut value of a graph in O(log n) space. Our work resolves the quantum and classical approximability of quantum and classical Max-Cut using o(n) space. We prove our lower bounds through the techniques of Boolean Fourier analysis. We give the first application of these methods to sequential one-way quantum communication, in which each player receives a quantum message from the previous player, and can then perform arbitrary quantum operations on it before sending it to the next. To this end, we show how Fourier-analytic techniques may be used to understand the application of a quantum channel.John Kallaugher, Ojas Parekhwork_bovqx5yajzblbgglr3pfsneamyTue, 20 Sep 2022 00:00:00 GMTLong-range data transmission in a fault-tolerant quantum bus architecture
https://scholar.archive.org/work/rwxljckglfbyhkwqlkrkkyckue
We propose a scheme for fault-tolerant long-range entanglement generation at the ends of a rectangular array of qubits of length R and a square cross section of size d× d with d=O(log R). Up to an efficiently computable Pauli correction, the scheme generates a maximally entangled state of two qubits using a depth-6 circuit consisting of nearest-neighbor Clifford gates and local measurements only. Compared with existing fault-tolerance schemes for quantum communication, the protocol is distinguished by its low latency: starting from a product state, the entangled state is prepared in a time O(t_local) determined only by the local gate and measurement operation time t_local. Furthermore, the requirements on local repeater stations are minimal: Each repeater uses only Θ(log^2 R) qubits with a lifetime of order O(t_local). We prove a converse bound Ω(log R) on the number of qubits per repeater among all low-latency schemes for fault-tolerant quantum communication over distance R. Furthermore, all operations within a repeater are local when the qubits are arranged in a square lattice. The noise-resilience of our scheme relies on the fault-tolerance properties of the underlying cluster state. We give a full error analysis, establishing a fault-tolerance threshold against general (circuit-level) local stochastic noise affecting preparation, entangling operations and measurements. This includes, in particular, errors correlated in time and space. Our conservative analytical estimates are surprisingly optimistic, suggesting that the scheme is suited for long-range entanglement generation both in and between near-term quantum computing devices.Shin Ho Choe, Robert Koenigwork_rwxljckglfbyhkwqlkrkkyckueTue, 20 Sep 2022 00:00:00 GMTAdsorption of Lattice Polymers with Quenched Topologies
https://scholar.archive.org/work/guxgad4z5ndgpl3yp7opyd7v64
We introduce a framework for adsorption of a single polymer in which the topology of the polymer is quenched before adsorption, in contrast to more standard adsorption models having annealed topology. Our "topology" refers either to the precise branching structure of a branched polymer (in any dimension), or else to the knot type of a ring polymer in three dimensions. The quenched topology is chosen uniformly at random from all lattice polymers of a given size in one of four classes (lattice animals, trees, combs, or rings), and we then consider adsorption of the subclass of configurations that have the quenched topology. When the polymer-surface attraction increases without bound, the quenched topological structure keeps a macroscopic fraction of monomers off the surface, in contrast with annealed models that asymptotically have 100% of monomers in the surface. We prove properties of the limiting free energy and the critical point in each model, although important open questions remain. We pay special attention to the class of comb polymers, which admit some rigorous answers to questions that otherwise remain open. Since the class of all combs was not previously examined rigorously in full generality, we also prove the existence of its growth constant and its limiting free energy for annealed adsorption.Neal Madraswork_guxgad4z5ndgpl3yp7opyd7v64Sun, 18 Sep 2022 00:00:00 GMTOn the Whitney near extension problem, BMO, alignment of data, best approximation in algebraic geometry, manifold learning and their beautiful connections: A modern treatment
https://scholar.archive.org/work/ju47ae6twzbfzaxbexq5rsaute
This paper provides fascinating connections between several mathematical problems which lie on the intersection of several mathematics subjects, namely algebraic geometry, approximation theory, complex-harmonic analysis and high dimensional data science. Modern techniques in algebraic geometry, approximation theory, computational harmonic analysis and extensions develop the first of its kind, a unified framework which allows for a simultaneous study of labeled and unlabeled near alignment data problems in of ℝ^D with the near isometry extension problem for discrete and non-discrete subsets of ℝ^D with certain geometries. In addition, the paper surveys related work on clustering, dimension reduction, manifold learning, vision as well as minimal energy partitions, discrepancy and min-max optimization. Numerous open problems are given.Steven B. Damelinwork_ju47ae6twzbfzaxbexq5rsauteSun, 18 Sep 2022 00:00:00 GMTThe Complexity of Finding Fair Independent Sets in Cycles
https://scholar.archive.org/work/ppwm4agkqjew5jdlcjujadc34u
Let G be a cycle graph and let V_1,...,V_m be a partition of its vertex set into m sets. An independent set S of G is said to fairly represent the partition if |S ∩ V_i| ≥1/2· |V_i| -1 for all i ∈ [m]. It is known that for every cycle and every partition of its vertex set, there exists an independent set that fairly represents the partition (Aharoni et al., A Journey through Discrete Math., 2017). We prove that the problem of finding such an independent set is 𝖯𝖯𝖠-complete. As an application, we show that the problem of finding a monochromatic edge in a Schrijver graph, given a succinct representation of a coloring that uses fewer colors than its chromatic number, is 𝖯𝖯𝖠-complete as well. The work is motivated by the computational aspects of the 'cycle plus triangles' problem and of its extensions.Ishay Havivwork_ppwm4agkqjew5jdlcjujadc34uSat, 17 Sep 2022 00:00:00 GMTLocal Central Limit Theorem for Long-Range Two-Body Potentials at Sufficiently High Temperatures
https://scholar.archive.org/work/ncq5nkxrtrdkpho25pjjg7mjgu
Dobrushin and Tirozzi [14] showed that, for a Gibbs measure with the finite-range potential, the Local Central Limit Theorem is implied by the Integral Central Limit Theorem. Campanino, Capocaccia, and Tirozzi [7] extended this result for a family of Gibbs measures for long-range pair potentials satisfying certain conditions. We are able to show for a family of Gibbs measures for long-range pair potentials not satisfying the conditions given in [7], that at sufficiently high temperatures, if the Integral Central Limit Theorem holds for a given sequence of Gibbs measures, then the Local Central Limit Theorem also holds for the same sequence. We also extend [7] when the state space is general, provided that it is equipped with a finite measure.Eric O. Endo, Vlad Margarintwork_ncq5nkxrtrdkpho25pjjg7mjguFri, 16 Sep 2022 00:00:00 GMTMalicious Source Code Detection Using Transformer
https://scholar.archive.org/work/enyted3du5hp5cdvlijsefbqjm
Open source code is considered a common practice in modern software development. However, reusing other code allows bad actors to access a wide developers' community, hence the products that rely on it. Those attacks are categorized as supply chain attacks. Recent years saw a growing number of supply chain attacks that leverage open source during software development, relaying the download and installation procedures, whether automatic or manual. Over the years, many approaches have been invented for detecting vulnerable packages. However, it is uncommon to detect malicious code within packages. Those detection approaches can be broadly categorized as analyzes that use (dynamic) and do not use (static) code execution. Here, we introduce Malicious Source code Detection using Transformers (MSDT) algorithm. MSDT is a novel static analysis based on a deep learning method that detects real-world code injection cases to source code packages. In this study, we used MSDT and a dataset with over 600,000 different functions to embed various functions and applied a clustering algorithm to the resulting vectors, detecting the malicious functions by detecting the outliers. We evaluated MSDT's performance by conducting extensive experiments and demonstrated that our algorithm is capable of detecting functions that were injected with malicious code with precision@k values of up to 0.909.Chen Tsfaty, Michael Firework_enyted3du5hp5cdvlijsefbqjmFri, 16 Sep 2022 00:00:00 GMTThe Use of Computational Geometry Techniques to Resolve the Issues of Coverage and Connectivity in Wireless Sensor Networks
https://scholar.archive.org/work/am5bqiughfa5hkcowa2dpv6txm
Wireless Sensor Networks (WSNs) enhance the ability to sense and control the physical environment in various applications. The functionality of WSNs depends on various aspects like the localization of nodes, the strategies of node deployment, and a lifetime of nodes and routing techniques, etc. Coverage is an essential part of WSNs wherein the targeted area is covered by at least one node. Computational Geometry (CG) -based techniques significantly improve the coverage and connectivity of WSNs. This paper is a step towards employing some of the popular techniques in WSNs in a productive manner. Furthermore, this paper attempts to survey the existing research conducted using Computational Geometry-based methods in WSNs. In order to address coverage and connectivity issues in WSNs, the use of the Voronoi Diagram, Delaunay Triangulation, Voronoi Tessellation, and the Convex Hull have played a prominent role. Finally, the paper concludes by discussing various research challenges and proposed solutions using Computational Geometry-based techniques.Sharmila Devi, Anju Sangwan, Anupma Sangwan, Mazin Abed Mohammed, Krishna Kumar, Jan Nedoma, Radek Martinek, Petr Zmijwork_am5bqiughfa5hkcowa2dpv6txmFri, 16 Sep 2022 00:00:00 GMTCombinatorial geometry of neural codes, neural data analysis, and neural networks
https://scholar.archive.org/work/4hudx3fjozfltjck6hl5tww4pm
This dissertation explores applications of discrete geometry in mathematical neuroscience. We begin with convex neural codes, which model the activity of hippocampal place cells and other neurons with convex receptive fields. In Chapter 4, we introduce order-forcing, a tool for constraining convex realizations of codes, and use it to construct new examples of non-convex codes with no local obstructions. In Chapter 5, we relate oriented matroids to convex neural codes, showing that a code has a realization with convex polytopes iff it is the image of a representable oriented matroid under a neural code morphism. We also show that determining whether a code is convex is at least as difficult as determining whether an oriented matroid is representable, implying that the problem of determining whether a code is convex is NP-hard. Next, we turn to the problem of the underlying rank of a matrix. This problem is motivated by the problem of determining the dimensionality of (neural) data which has been corrupted by an unknown monotone transformation. In Chapter 6, we introduce two tools for computing underlying rank, the minimal nodes and the Radon rank. We apply these to analyze calcium imaging data from a larval zebrafish. In Chapter 7, we explore the underlying rank in more detail, establish connections to oriented matroid theory, and show that computing underlying rank is also NP-hard. Finally, we study the dynamics of threshold-linear networks (TLNs), a simple model of the activity of neural circuits. In Chapter 9, we describe the nullcline arrangement of a threshold linear network, and show that a subset of its chambers are an attracting set. In Chapter 10, we focus on combinatorial threshold linear networks (CTLNs), which are TLNs defined from a directed graph. We prove that if the graph of a CTLN is a directed acyclic graph, then all trajectories of the CTLN approach a fixed point.Caitlin Lienkaemperwork_4hudx3fjozfltjck6hl5tww4pmThu, 15 Sep 2022 00:00:00 GMT