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Physical Sciences and Mathematics Commons™

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Washington University in St. Louis

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2015

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Articles 1 - 21 of 21

Full-Text Articles in Physical Sciences and Mathematics

Pick Interpolation For Free Holomorphic Functions, Jim Agler, John E. Mccarthy Dec 2015

Pick Interpolation For Free Holomorphic Functions, Jim Agler, John E. Mccarthy

Mathematics Faculty Publications

We give necessary and sufficient conditions to solve an interpolation problem for free holomorphic functions bounded in norm on a free polynomial polyhedron. As an application, we prove that every bounded holomorphic function on a polynomial polyhedron extends to a bounded free function.

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Non-Commutative Holomorphic Functions On Operator Domains, Jim Agler, John E. Mccarthy Dec 2015

Non-Commutative Holomorphic Functions On Operator Domains, Jim Agler, John E. Mccarthy

Mathematics Faculty Publications

We characterize functions of d-tuples of bounded operators on a Hilbert space that are uniformly approximable by free polynomials on balanced open sets.

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Faster Maximium Priority Matchings In Bipartite Graphs, Jonathan Turner Dec 2015

Faster Maximium Priority Matchings In Bipartite Graphs, Jonathan Turner

All Computer Science and Engineering Research

A maximum priority matching is a matching in an undirected graph that maximizes a priority score defined with respect to given vertex priorities. An earlier paper showed how to find maximum priority matchings in unweighted graphs. This paper describes an algorithm for bipartite graphs that is faster when the number of distinct priority classes is limited. For graphs with k distinct priority classes it runs in O(kmn1/2) time, where n is the number of vertices in the graph and m is the number of edges.

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The Bounded Edge Coloring Problem And Offline Crossbar Scheduling, Jonathan Turner Dec 2015

The Bounded Edge Coloring Problem And Offline Crossbar Scheduling, Jonathan Turner

All Computer Science and Engineering Research

This paper introduces a variant of the classical edge coloring problem in graphs that can be applied to an offline scheduling problem for crossbar switches. We show that the problem is NP-complete, develop three lower bounds bounds on the optimal solution value and evaluate the performance of several approximation algorithms, both analytically and experimentally. We show how to approximate an optimal solution with a worst-case performance ratio of 3/2 and our experimental results demonstrate that the best algorithms produce results that very closely track a lower bound.

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Integrability And Regularity Of Rational Functions, Greg Knese Dec 2015

Integrability And Regularity Of Rational Functions, Greg Knese

Mathematics Faculty Publications

Motivated by recent work in the mathematics and engineering literature, we study integrability and non-tangential regularity on the two-torus for rational functions that are holomorphic on the bidisk. One way to study such rational functions is to fix the denominator and look at the ideal of polynomials in the numerator such that the rational function is square integrable. A concrete list of generators is given for this ideal as well as a precise count of the dimension of the subspace of numerators with a specified bound on bidegree. The dimension count is accomplished by constructing a natural pair of commuting …

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Maximum Priority Matchings, Jonathan Turner Nov 2015

Maximum Priority Matchings, Jonathan Turner

All Computer Science and Engineering Research

Let G=(V,E) be an undirected graph with n vertices and m edges, in which each vertex u is assigned an integer priority in [1,n], with 1 being the ``highest'' priority. Let M be a matching of G. We define the priority score of M to be an n-ary integer in which the i-th most-significant digit is the number of vertices with priority i that are incident to an edge in M. We describe a variation of the augmenting path method (Edmonds' algorithm) that finds a matching with maximum priority score in O(mn) time.

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Stochastic Models For Plant Microtubule Self-Organization And Structure, Ezgi Can Eren, Ram Dixit, Natarajan Gautam Nov 2015

Stochastic Models For Plant Microtubule Self-Organization And Structure, Ezgi Can Eren, Ram Dixit, Natarajan Gautam

Biology Faculty Publications & Presentations

One of the key enablers of shape and growth in plant cells is the cortical microtubule (CMT) system, which is a polymer array that forms an appropriately-structured scaffolding in each cell. Plant biologists have shown that stochastic dynamics and simple rules of interactions between CMTs can lead to a coaligned CMT array structure. However, the mechanisms and conditions that cause CMT arrays to become organized are not well understood. It is prohibitively time-consuming to use actual plants to study the effect of various genetic mutations and environmental conditions on CMT self-organization. In fact, even computer simulations with multiple replications are …

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Partial Covariance Based Functional Connectivity Computation Using Ledoit-Wolf Covariance Regularization, Matthew R. Brier, Anish Mitra, John E. Mccarthy, Beau M. Ances, Abraham Z. Snyder Nov 2015

Partial Covariance Based Functional Connectivity Computation Using Ledoit-Wolf Covariance Regularization, Matthew R. Brier, Anish Mitra, John E. Mccarthy, Beau M. Ances, Abraham Z. Snyder

Mathematics Faculty Publications

Highlights •We use the well characterized matrix regularization technique described by Ledoit and Wolf to calculate high dimensional partial correlations in fMRI data. •Using this approach we demonstrate that partial correlations reveal RSN structure suggesting that RSNs are defined by widely and uniquely shared variance. •Partial correlation functional connectivity is sensitive to changes in brain state indicating that they contain functional information. Functional connectivity refers to shared signals among brain regions and is typically assessed in a task free state. Functional connectivity commonly is quantified between signal pairs using Pearson correlation. However, resting-state fMRI is a multivariate process exhibiting a …

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Local And Distributed Pib Accumulation Associated With Development Of Preclinical Alzheimer's Disease, Matthew R. Brier, John E. Mccarthy, Tammie L.S. Benzinger, Ari Stern, Yi Su, Karl A. Friedrichsen, John C. Morris, Beau M. Ances, Andrei G. Vlassenko Oct 2015

Local And Distributed Pib Accumulation Associated With Development Of Preclinical Alzheimer's Disease, Matthew R. Brier, John E. Mccarthy, Tammie L.S. Benzinger, Ari Stern, Yi Su, Karl A. Friedrichsen, John C. Morris, Beau M. Ances, Andrei G. Vlassenko

Mathematics Faculty Publications

Amyloid-beta plaques are a hallmark of Alzheimer's disease (AD) that can be assessed by amyloid imaging (e.g., Pittsburgh B compound [PiB]) and summarized as a scalar value. Summary values may have clinical utility but are an average over many regions of interest, potentially obscuring important topography. This study investigates the longitudinal evolution of amyloid topographies in cognitively normal older adults who had normal (N = 131) or abnormal (N = 26) PiB scans at baseline. At 3 years follow-up, 16 participants with a previously normal PiB scan had conversion to PiB scans consistent with preclinical AD. We investigated the multivariate …

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Conflict-Aware Real-Time Routing For Industrial Wireless Sensor-Actuator Networks, Chengjie Wu, Dolvara Gunatilaka, Mo Sha, Chenyang Lu Sep 2015

Conflict-Aware Real-Time Routing For Industrial Wireless Sensor-Actuator Networks, Chengjie Wu, Dolvara Gunatilaka, Mo Sha, Chenyang Lu

All Computer Science and Engineering Research

Process industries are adopting wireless sensor-actuator networks (WSANs) as the communication infrastructure. WirelessHART is an open industrial standard for WSANs that have seen world-wide deployments. Real-time scheduling and delay analysis have been studied for WSAN extensively. End-to-end delay in WSANs highly depends on routing, which is still open problem. This paper presents the first real-time routing design for WSAN. We first discuss end-to-end delays of WSANs, then present our real-time routing design. We have implemented and experimented our routing designs on a wireless testbed of 69 nodes. Both experimental results and simulations show that our routing design can improve the …

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Maximizing Network Lifetime Of Wireless Sensor-Actuator Networks Under Graph Routing, Chengjie Wu, Dolvara Gunatilaka, Abusayeed Saifullah, Mo Sha, Paras Tiwari, Chenyang Lu, Yixin Chen Sep 2015

Maximizing Network Lifetime Of Wireless Sensor-Actuator Networks Under Graph Routing, Chengjie Wu, Dolvara Gunatilaka, Abusayeed Saifullah, Mo Sha, Paras Tiwari, Chenyang Lu, Yixin Chen

All Computer Science and Engineering Research

Process industries are adopting wireless sensor-actuator networks (WSANs) as the communication infrastructure. The dynamics of industrial environments and stringent reliability requirements necessitate high degrees of fault tolerance in routing. WirelessHART is an open industrial standard for WSANs that have seen world-wide deployments. WirelessHART employs graph routing schemes to achieve network reliability through multiple paths. Since many industrial devices operate on batteries in harsh environments where changing batteries are prohibitively labor-intensive, WSANs need to achieve long network lifetime. To meet industrial demand for long-term reliable communication, this paper studies the problem of maximizing network lifetime for WSANs under graph routing. We …

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Mossbauer Effect, Ronald Lovett Sep 2015

Mossbauer Effect, Ronald Lovett

Topics in Quantum Mechanics

No abstract provided.

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Woodstocc: Extracting Latent Parallelism From A Dna Sequence Aligner On A Gpu, Stephen V. Cole, Jacob R. Gardner, Jeremy D. Buhler Sep 2015

Woodstocc: Extracting Latent Parallelism From A Dna Sequence Aligner On A Gpu, Stephen V. Cole, Jacob R. Gardner, Jeremy D. Buhler

All Computer Science and Engineering Research

An exponential increase in the speed of DNA sequencing over the past decade has driven demand for fast, space-efficient algorithms to process the resultant data. The first step in processing is alignment of many short DNA sequences, or reads, against a large reference sequence. This work presents WOODSTOCC, an implementation of short-read alignment designed for Graphics Processing Unit (GPU) architectures. WOODSTOCC translates a novel CPU implementation of gapped short-read alignment, which has guaranteed optimal and complete results, to the GPU. Our implementation combines an irregular trie search with dynamic programming to expose regularly structured parallelism. We first describe this implementation, …

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The Edge Group Coloring Problem With Applications To Multicast Switching, Jonathan Turner Aug 2015

The Edge Group Coloring Problem With Applications To Multicast Switching, Jonathan Turner

All Computer Science and Engineering Research

This paper introduces a natural generalization of the classical edge coloring problem in graphs that provides a useful abstraction for two well-known problems in multicast switching. We show that the problem is NP-hard and evaluate the performance of several approximation algorithms, both analytically and experimentally. We find that for random χ-colorable graphs, the number of colors used by the best algorithms falls within a small constant factor of χ, where the constant factor is mainly a function of the ratio of the number of outputs to inputs. When this ratio is less than 10, the best algorithms produces solutions that …

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Entropy Vs. Energy Waveform Processing: A Comparison Based On The Heat Equation, Michael S. Hughes, John E. Mccarthy, Paul J. Bruillard, Jon N. Marsh, Samuel A. Wickline May 2015

Entropy Vs. Energy Waveform Processing: A Comparison Based On The Heat Equation, Michael S. Hughes, John E. Mccarthy, Paul J. Bruillard, Jon N. Marsh, Samuel A. Wickline

Mathematics Faculty Publications

Virtually all modern imaging devices collect electromagnetic or acoustic waves and use the energy carried by these waves to determine pixel values to create what is basically an “energy” picture. However, waves also carry “information,” as quantified by some form of entropy, and this may also be used to produce an “information” image. Numerous published studies have demonstrated the advantages of entropy, or “information imaging”, over conventional methods. The most sensitive information measure appears to be the joint entropy of the collected wave and a reference signal. The sensitivity of repeated experimental observations of a slowly-changing quantity may be defined …

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Global Holomorphic Functions In Several Noncommuting Variables, Jim Agler, John E. Mccarthy Apr 2015

Global Holomorphic Functions In Several Noncommuting Variables, Jim Agler, John E. Mccarthy

Mathematics Faculty Publications

We define a free holomorphic function to be a function that is locally, with respect to the free topology, a bounded nc-function. We prove that free holomorphic functions are the functions that are locally uniformly approximable by free polynomials. We prove a realization formula and an Oka-Weil theorem for free analytic functions.

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Angular Momentum, Ronald Lovett Mar 2015

Angular Momentum, Ronald Lovett

Topics in Quantum Mechanics

No abstract provided.

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Operators In Quantum Machanics, Ronald Lovett Feb 2015

Operators In Quantum Machanics, Ronald Lovett

Topics in Quantum Mechanics

No abstract provided.

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Grafalgo - A Library Of Graph Algorithms And Supporting Data Structures, Jonathan Turner Jan 2015

Grafalgo - A Library Of Graph Algorithms And Supporting Data Structures, Jonathan Turner

All Computer Science and Engineering Research

This report provides an overview of Grafalgo, an open-source library of graph algorithms and the data structures used to implement them. The programs in this library were originally written to support a graduate class in advanced data structures and algorithms at Washington University. Because the code's primary purpose was pedagogical, it was written to be as straightforward as possible, while still being highly efficient. Grafalgo is implemented in C++ and incorporates some features of C++11. The library is available on an open-source basis and may be downloaded from https://code.google.com/p/grafalgo/. Source code documentation is at www.arl.wustl.edu/~jst/doc/grafalgo. While not designed as production …

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Vector Space Language, Ronald Lovett Jan 2015

Vector Space Language, Ronald Lovett

Topics in Quantum Mechanics

No abstract provided.

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Additional Results For "Joint Entropy Of Continuously Differentiable Ultrasonic Waveforms" [J. Acoust. Soc. Am. 133(1), 283-300 (2013)], M S. Hughes, J N. Marsh, S A. Wickline, John E. Mccarthy Jan 2015

Additional Results For "Joint Entropy Of Continuously Differentiable Ultrasonic Waveforms" [J. Acoust. Soc. Am. 133(1), 283-300 (2013)], M S. Hughes, J N. Marsh, S A. Wickline, John E. Mccarthy

Mathematics Faculty Publications

Previous results on the use of joint entropy for detection of targeted nanoparticles accumulating in the neovasculature of MDA435 tumors [Fig. 7 of M. S. Hughes et al., J. Acoust. Soc. Am. 133, 283–300 (2013)] are extended, with sensitivity improving by nearly another factor of 2. This result is obtained using a “quasi-optimal” reference waveform in the computation of the joint entropy imaging technique used to image the accumulating nanoparticles.

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