1,003 research outputs found

    Work-preserving real-time emulation of meshes on butterfly networks

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    The emulation of a guest network G on a host network H is work-preserving and real-time if the inefficiency, that is the ratio WG/WH of the amounts of work done in both networks, and the slowdown of the emulation are O(1). In this thesis we show that an infinite number of meshes can be emulated on a butterfly in a work-preserving real-time manner, despite the fact that any emulation of an s x s-node mesh in a butterfly with load 1 has a dilation of Ω(logs). The recursive embedding of a mesh in a butterfly presented by Koch et al. (STOC 1989), which forms the basis for our work, is corrected and generalized by relaxing unnecessary constraints. An algorithm determining the parameter for each stage of the recursion is described and a rigorous analysis of the resulting emulation shows that it is work-preserving and real-time for an infinite number of meshes. Data obtained from simulated embeddings suggests possible improvements to achieve a truly work-preserving emulation of the class of meshes on the class of butterflies

    Satisfiability, sequence niches, and molecular codes in cellular signaling

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    Biological information processing as implemented by regulatory and signaling networks in living cells requires sufficient specificity of molecular interaction to distinguish signals from one another, but much of regulation and signaling involves somewhat fuzzy and promiscuous recognition of molecular sequences and structures, which can leave systems vulnerable to crosstalk. This paper examines a simple computational model of protein-protein interactions which reveals both a sharp onset of crosstalk and a fragmentation of the neutral network of viable solutions as more proteins compete for regions of sequence space, revealing intrinsic limits to reliable signaling in the face of promiscuity. These results suggest connections to both phase transitions in constraint satisfaction problems and coding theory bounds on the size of communication codes

    Complexity Theory, Game Theory, and Economics: The Barbados Lectures

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    This document collects the lecture notes from my mini-course "Complexity Theory, Game Theory, and Economics," taught at the Bellairs Research Institute of McGill University, Holetown, Barbados, February 19--23, 2017, as the 29th McGill Invitational Workshop on Computational Complexity. The goal of this mini-course is twofold: (i) to explain how complexity theory has helped illuminate several barriers in economics and game theory; and (ii) to illustrate how game-theoretic questions have led to new and interesting complexity theory, including recent several breakthroughs. It consists of two five-lecture sequences: the Solar Lectures, focusing on the communication and computational complexity of computing equilibria; and the Lunar Lectures, focusing on applications of complexity theory in game theory and economics. No background in game theory is assumed.Comment: Revised v2 from December 2019 corrects some errors in and adds some recent citations to v1 Revised v3 corrects a few typos in v

    A new-generation class of parallel architectures and their performance evaluation

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    The development of computers with hundreds or thousands of processors and capability for very high performance is absolutely essential for many computation problems, such as weather modeling, fluid dynamics, and aerodynamics. Several interconnection networks have been proposed for parallel computers. Nevertheless, the majority of them are plagued by rather poor topological properties that result in large memory latencies for DSM (Distributed Shared-Memory) computers. On the other hand, scalable networks with very good topological properties are often impossible to build because of their prohibitively high VLSI (e.g., wiring) complexity. Such a network is the generalized hypercube (GH). The GH supports full-connectivity of its nodes in each dimension and is characterized by outstanding topological properties. In addition, low-dimensional GHs have very large bisection widths. We propose in this dissertation a new class of processor interconnections, namely HOWs (Highly Overlapping Windows), that are more generic than the GH, are highly scalable, and have comparable performance. We analyze the communications capabilities of 2-D HOW systems and demonstrate that in practical cases HOW systems perform much better than binary hypercubes for important communications patterns. These properties are in addition to the good scalability and low hardware complexity of HOW systems. We present algorithms for one-to-one, one-to-all broadcasting, all-to-all broadcasting, one-to-all personalized, and all-to-all personalized communications on HOW systems. These algorithms are developed and evaluated for several communication models. In addition, we develop techniques for the efficient embedding of popular topologies, such as the ring, the torus, and the hypercube, into 1-D and 2-D HOW systems. The objective is to show that 2-D HOW systems are not only scalable and easy to implement, but they also result in good embedding of several classical topologies

    A survey of statistical network models

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    Networks are ubiquitous in science and have become a focal point for discussion in everyday life. Formal statistical models for the analysis of network data have emerged as a major topic of interest in diverse areas of study, and most of these involve a form of graphical representation. Probability models on graphs date back to 1959. Along with empirical studies in social psychology and sociology from the 1960s, these early works generated an active network community and a substantial literature in the 1970s. This effort moved into the statistical literature in the late 1970s and 1980s, and the past decade has seen a burgeoning network literature in statistical physics and computer science. The growth of the World Wide Web and the emergence of online networking communities such as Facebook, MySpace, and LinkedIn, and a host of more specialized professional network communities has intensified interest in the study of networks and network data. Our goal in this review is to provide the reader with an entry point to this burgeoning literature. We begin with an overview of the historical development of statistical network modeling and then we introduce a number of examples that have been studied in the network literature. Our subsequent discussion focuses on a number of prominent static and dynamic network models and their interconnections. We emphasize formal model descriptions, and pay special attention to the interpretation of parameters and their estimation. We end with a description of some open problems and challenges for machine learning and statistics.Comment: 96 pages, 14 figures, 333 reference

    Reconstruction of random geometric graphs: breaking the Ω(r) distortion barrier

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    Embedding graphs in a geographical or latent space, i.e. inferring locations for vertices in Euclidean space or on a smooth manifold or submanifold, is a common task in network analysis, statistical inference, and graph visualization. We consider the classic model of random geometric graphs where n points are scattered uniformly in a square of area n, and two points have an edge between them if and only if their Euclidean distance is less than r. The reconstruction problem then consists of inferring the vertex positions, up to the symmetries of the square, given only the adjacency matrix of the resulting graph. We give an algorithm that, if r = n α for any 0 < α < 1/2, with high probability reconstructs the vertex positions with a maximum error of O(n β ) where β = 1/2−(4/3)α, until α ≥ 3/8 where β = 0 and the error becomes O( √ log n). This improves over earlier results, which were unable to reconstruct with error less than r. Our method estimates Euclidean distances using a hybrid of graph distances and short-range estimates based on the number of common neighbors. We extend our results to the surface of the sphere in R 3 and to hypercubes in any constant fixed dimension.Josep Díaz: partially supported by PID-2020-112581GB-C21 (MOTION). Cristopher Moore: partially supported by National Science Foundation grant IIS-1838251.Peer ReviewedPostprint (published version
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