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- Asymptotics (1)
- Boolean networks (1)
- Buchberger's algorithm (1)
- Canalyzation (1)
- Central Limit Theorem (1)
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- Colon ideal (1)
- F5 algorithm (1)
- Fractal (1)
- Fundamental cone (1)
- Gene networks (1)
- Groebner basis (1)
- Inference (1)
- Infinite Networks (1)
- Iterative decoding (1)
- Jackson Network (1)
- Linear programming (LP) decoding (1)
- Low-density parity-check (LDPC) code (1)
- Markov chain (1)
- Pseudocodewords (1)
- Queueing Theory (1)
- Reversible (1)
- Signature based algorithm (1)
- Syzygy module (1)
- Test statistic (1)
Articles 1 - 6 of 6
Full-Text Articles in Physical Sciences and Mathematics
Bases And Applications Of Riemann-Roch Spaces Of Function Fields With Many Rational Places, Justin Peachey
Bases And Applications Of Riemann-Roch Spaces Of Function Fields With Many Rational Places, Justin Peachey
All Dissertations
Algebraic geometry codes are generalizations of Reed-Solomon codes, which are implemented in nearly all digital communication devices. In ground-breaking work, Tsfasman, Vladut, and Zink showed the existence of a sequence of algebraic geometry codes that exceed the Gilbert-Varshamov bound, which was previously thought unbeatable. More recently, it has been shown that multipoint algebraic geometry codes can outperform comparable one-point algebraic geometry codes. In both cases, it is desirable that these function fields have many rational places. The prototypical example of such a function field is the Hermitian function field which is maximal. In 2003, Geil produced a new family of …
Fractal Jackson Networks, Mahmoud Rezaei
Fractal Jackson Networks, Mahmoud Rezaei
All Dissertations
In this dissertation, Gaussian random measures that arise as limits of Jackson networks. The support of the random measure is a fractal having Hausdorff dimension delta . The variance measure is the Hausdorff measure also of dimension delta.
Inference In Reversible Markov Chains, Tara Steuber
Inference In Reversible Markov Chains, Tara Steuber
All Dissertations
This dissertation describes the research that we have done concerning
reversible Markov chains. We first present definitions for what it means
for a Markov chain to be reversible. We then give applications of where
reversible Markov chains are used and give a brief history of Markov chain
inference. Finally, two journal articles are found in the paper, one that
is already published and another which is currently being submitted.
The first article examines estimation of the one-step-ahead
transition probabilities in a reversible Markov chain on a countable state
space. A symmetrized moment estimator is proposed that exploits the
reversible structure. …
Pseudocodewords Of Parity-Check Codes, Wittawat Kositwattanarerk
Pseudocodewords Of Parity-Check Codes, Wittawat Kositwattanarerk
All Dissertations
The success of modern algorithms for the decoding problem such as message-passing iterative decoding and linear programming decoding lies in their local nature. This feature allows the algorithms to be extremely fast and capable of correcting more errors than guaranteed by the classical minimum distance of the code. Nonetheless, the performance of these decoders depends crucially on the Tanner graph representation of the code. In order to understand this choice of representation, we need to analyze the pseudocodewords of the Tanner graph of a code. These pseudocodewords are outputs of local decoding algorithms which may not be legitimate codewords. In …
New Algorithms For Computing Groebner Bases, Frank Volny
New Algorithms For Computing Groebner Bases, Frank Volny
All Dissertations
In this thesis, we present new algorithms for computing Groebner bases. The first algorithm, G2V, is incremental in the same fashion as F5 and F5C. At a typical step, one is given a Groebner basis G for an ideal I and any polynomial g, and it is desired to compute a Groebner basis for the new ideal , obtained from I by joining g. Let (I : g) denote the colon ideal of I divided by g. Our algorithm computes Groebner bases for I, g and (I : g) simultaneously. In previous algorithms, S-polynomials that reduce to zero are useless, …
Biologically Relevant Classes Of Boolean Functions, Lori Layne
Biologically Relevant Classes Of Boolean Functions, Lori Layne
All Dissertations
A large influx of experimental data has prompted the development of
innovative computational techniques for modeling and reverse
engineering biological networks. While finite dynamical systems,
in particular Boolean networks, have gained attention as relevant
models of network dynamics, not all Boolean functions reflect the
behaviors of real biological systems. In this work, we focus on two
classes of Boolean functions and study their applicability as
biologically relevant network models: the nested and partially nested
canalyzing functions.
We begin by analyzing the nested canalyzing functions} (NCFs),
which have been proposed as gene regulatory network models due to
their stability properties. We …