Exact computation of a manifold metric, via Lipschitz Embeddings and Shortest Paths on a Graph

Centrality indices are an essential concept in network analysis. For those based on shortest-path distances the computation is at least quadratic in the number of nodes, since it usually involves solving the single-source shortest-paths (SSSP) problem from every node. Therefore, exact computation is infeasible for many large networks of interest today. Centrality scores can be estimated, however, from a limited number of SSSP computations. We present results from an experimental study of the quality of such estimates under various selection strategies for the source vertices.

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eMap: A Web Application for Identifying and Visualizing Electron or Hole Hopping Pathways in Proteins

10.26434/chemrxiv.7889993 ◽

2019 ◽

Author(s):

Ruslan N. Tazhigulov ◽

James R. Gayvert ◽

Melissa Wei ◽

Ksenia B. Bravaya

Keyword(s):

Web Application ◽

Shortest Paths ◽

Coarse Grained ◽

Decay Parameter ◽

Electron Hole ◽

Web Based ◽

Aromatic Amino Acid Residue ◽

Pathways Model ◽

Visualization Tools ◽

Effective Decay

<p>eMap is a web-based platform for identifying and visualizing electron or hole transfer pathways in proteins based on their crystal structures. The underlying model can be viewed as a coarse-grained version of the Pathways model, where each tunneling step between hopping sites represented by electron transfer active (ETA) moieties is described with one eﬀective decay parameter that describes protein-mediated tunneling. ETA moieties include aromatic amino acid residue side chains and aromatic fragments of cofactors that are automatically detected, and, in addition, electron/hole residing sites that can be speciﬁed by the users. The software searches for the shortest paths connecting the user-speciﬁed electron/hole source to either all surface-exposed ETA residues or to the user-speciﬁed target. The identiﬁed pathways are ranked based on their length. The pathways are visualized in 2D as a graph, in which each node represents an ETA site, and in 3D using available protein visualization tools. Here, we present the capability and user interface of eMap 1.0, which is available at https://emap.bu.edu.</p>

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A Computational Library Using P-adic Arithmetic for Exact Computation With Rational Numbers in Quantum Computing

10.21236/ada456488 ◽

2005 ◽

Author(s):

Chao Lu

Keyword(s):

Quantum Computing ◽

Rational Numbers ◽

Exact Computation

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A Note on Exact Computation of Max Weighted Score Estimators by Mixed Integer Programming

SSRN Electronic Journal ◽

10.2139/ssrn.1007441 ◽

2007 ◽

Cited By ~ 1

Author(s):

Kostas Florios ◽

Spyros Skouras

Keyword(s):

Integer Programming ◽

Mixed Integer Programming ◽

Mixed Integer ◽

Exact Computation ◽

Weighted Score

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Computer algorithms

10.1093/oso/9780198805090.003.0008 ◽

2018 ◽

Author(s):

Mark Newman

Keyword(s):

Data Structures ◽

Analysis Of Algorithms ◽

Shortest Paths ◽

Minimum Cut ◽

Network Data ◽

Computer Algorithms ◽

Breadth First Search ◽

Augmenting Path ◽

Basic Concepts ◽

Maximum Flows

This chapter introduces some of the fundamental concepts of numerical network calculations. The chapter starts with a discussion of basic concepts of computational complexity and data structures for storing network data, then progresses to the description and analysis of algorithms for a range of network calculations: breadth-first search and its use for calculating shortest paths, shortest distances, components, closeness, and betweenness; Dijkstra's algorithm for shortest paths and distances on weighted networks; and the augmenting path algorithm for calculating maximum flows, minimum cut sets, and independent paths in networks.

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