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Articles 1 - 6 of 6
Full-Text Articles in Physical Sciences and Mathematics
A Universal Theory Of Pseudocodewords, Nathan Axvig, Emily Price, Eric T. Psota, Deanna Turk, Lance C. Pérez, Judy L. Walker
A Universal Theory Of Pseudocodewords, Nathan Axvig, Emily Price, Eric T. Psota, Deanna Turk, Lance C. Pérez, Judy L. Walker
Department of Mathematics: Faculty Publications
Three types of pseudocodewords for LDPC codes are found in the literature: graph cover pseudocodewords, linear programming pseudocodewords, and computation tree pseudocodewords. In this paper we first review these three notions and known connections between them. We then propose a new decoding rule — universal cover decoding — for LDPC codes. This new decoding rule also has a notion of pseudocodeword attached, and this fourth notion provides a framework in which we can better understand the other three.
Mathematical Analysis Of Pde Systems Which Govern °Uid Structure Interactive Phenomena, George Avalos, Roberto Triggiani
Mathematical Analysis Of Pde Systems Which Govern °Uid Structure Interactive Phenomena, George Avalos, Roberto Triggiani
Department of Mathematics: Faculty Publications
In this paper, we review and comment upon recently derived results for time dependent partial differential equation (PDE) models, which have been used to describe the various fluid-structure interactions which occur in nature. For these fluid-structure PDEs, this survey is particularly focused on the authors' results of (i) semigroup wellposedness, (ii) stability, and (iii) backward uniqueness.
The Time Invariance Principle, Ecological (Non)Chaos, And A Fundamental Pitfall Of Discrete Modeling, Bo Deng
The Time Invariance Principle, Ecological (Non)Chaos, And A Fundamental Pitfall Of Discrete Modeling, Bo Deng
Department of Mathematics: Faculty Publications
This paper is to show that most discrete models used for population dynamics in ecology are inherently pathological that their predications cannot be independently verified by experiments because they violate a fundamental principle of physics. The result is used to tackle an on-going controversy regarding ecological chaos. Another implication of the result is that all continuous dynamical systems must be modeled by differential equations. As a result it suggests that researches based on discrete modeling must be closely scrutinized and the teaching of calculus and differential equations must be emphasized for students of biology.
Characterizations Of Pseudo-Codewords Of Ldpc Codes, Ralf Koetter, Wen-Cheng W. Li, Pascal O. Vontobel, Judy L. Walker
Characterizations Of Pseudo-Codewords Of Ldpc Codes, Ralf Koetter, Wen-Cheng W. Li, Pascal O. Vontobel, Judy L. Walker
Department of Mathematics: Faculty Publications
An important property of high-performance, low complexity codes is the existence of highly efficient algorithms for their decoding. Many of the most efficient, recent graph-based algorithms, e.g. message passing algorithms and decoding based on linear programming, crucially depend on the efficient representation of a code in a graphical model. In order to understand the performance of these algorithms, we argue for the characterization of codes in terms of a so called fundamental cone in Euclidean space which is a function of a given parity check matrix of a code, rather than of the code itself. We give a number of …
Promoting Undergraduate Research In Mathematics At The University Of Nebraska – Lincoln, Judy L. Walker, Glenn Ledder, Richard Rebarber, Gordon S. Woodward
Promoting Undergraduate Research In Mathematics At The University Of Nebraska – Lincoln, Judy L. Walker, Glenn Ledder, Richard Rebarber, Gordon S. Woodward
Department of Mathematics: Faculty Publications
The Department of Mathematics at the University of Nebraska – Lincoln (UNL) has several programs which promote undergraduate research in a variety of ways. Two of these are summer programs which draw from a national applicant pool: The Nebraska REU in Applied Mathematics (Section 1) is a traditional NSF-funded REU site, and Nebraska IMMERSE (Section 2) offers a summer “bridge” program (with a research bent) for students about to start graduate school in mathematics. IMMERSE is a relatively new program, started in 2004 as part of the department’s Mentoring through Critical Transition Points (MCTP) grant from NSF. The MCTP grant …
S-Extremal Additive F4 Codes, Evangeline P. Bautista, Philippe Gaborit, Jon-Lark Kim, Judy L. Walker
S-Extremal Additive F4 Codes, Evangeline P. Bautista, Philippe Gaborit, Jon-Lark Kim, Judy L. Walker
Department of Mathematics: Faculty Publications
Binary self-dual codes and additive self-dual codes over F4 have in common interesting properties, for example, Type I, Type II, shadows, etc. Recently Bachoc and Gaborit introduced the notion of s-extremality for binary self-dual codes, generalizing Elkies' study on the highest possible minimum weight of the shadows of binary self-dual codes. In this paper, we introduce a concept of s-extremality for additive self-dual codes over F4, give a bound on the length of these codes with even distance d, classify them up to minimum distance d = 4, give possible lengths and (shadow) weight …