DRUM Community: College of Computer, Mathematical & Natural Sciences
http://hdl.handle.net/1903/1586
2015-05-29T08:12:50ZOn Number Of Partitions Of An Integer Into A Fixed Number Of Positive Integers
http://hdl.handle.net/1903/16351
Title: On Number Of Partitions Of An Integer Into A Fixed Number Of Positive Integers
Authors: Oruc, A. Yavuz
Abstract: This paper focuses on the number of partitions of a positive integer $n$ into $k$ positive summands, where $k$ is an integer between $1$ and $n$. Recently some upper bounds were reported for this number in [Merca14]. Here, it is shown that these bounds are not as tight as an earlier upper bound proved in [Andrews76-1] for $k\le 0.42n$. A new upper bound for the number of partitions of $n$ into $k$ summands is given, and shown to be tighter than the upper bound in [Merca14] when $k$ is between $O(\frac{\sqrt{n}}{\ln n})$ and $n-O(\frac{\sqrt{n}}{\ln n})$. It is further shown that the new upper bound is also tighter than two other upper bounds previously reported in~[Andrews76-1] and [Colman82]. A generalization of this upper bound to number of partitions of $n$ into at most $k$ summands is also presented.
Description: Submitted to Journal of Number Theory.2015-04-01T00:00:00ZInvestigations of Highly Irregular Primes and Associated Ray Class Fields
http://hdl.handle.net/1903/16321
Title: Investigations of Highly Irregular Primes and Associated Ray Class Fields
Authors: Stern, Morgan Benjamin
Abstract: We investigate properties of the class number of certain ray class fields of prime conductor lying above imaginary quadratic fields. While most previous work in this area restricted to the case of imaginary quadratic fields of class number 1, we deal almost exclusively with class number 2. Our main results include finding 5 counterexamples to a generalization of the famous conjecture of Vandiver that the class number of the pth real cyclotomic field is never divisible by p. We give these counterexamples the name highly irregular primes due to the fact that any counterexample of classical Vandiver is an irregular prime. In addition we explore whether several consequences of Vandiver's conjecture still hold for these highly irregular primes, including the cyclicity of certain class groups.2014-01-01T00:00:00ZLARGE SYSTEMS OF MANY INTERCONNECTED DYNAMICAL UNITS: GENE NETWORK INFERENCE, EPIGENETIC HERITABILITY, AND EMERGENT BEHAVIOR IN OSCILLATOR SYSTEMS
http://hdl.handle.net/1903/16320
Title: LARGE SYSTEMS OF MANY INTERCONNECTED DYNAMICAL UNITS: GENE NETWORK INFERENCE, EPIGENETIC HERITABILITY, AND EMERGENT BEHAVIOR IN OSCILLATOR SYSTEMS
Authors: Ku, Wai Lim
Abstract: In this thesis, which consists of three parts, we investigate problems related to systems biology and collective behavior in complex systems.
The first part studies genetic networks that are inferred using gene expression data. Here we use established transcriptional regulatory interactions (TRIs) in combination with microarray expression data from both <italic>Escherichia coli</italic> (a prokaryote) and <italic>Saccharomyces cerevisiae</italic> (a eukaryote) to assess the accuracy of predictions of coregulated gene pairs and TRIs from observations of coexpressed gene pairs. We find that highly coexpressed gene pairs are more likely to be coregulated than to share a TRI for <italic>Saccharomyces cerevisiae</italic>, while the incidence of TRIs in highly coexpressed gene pairs is higher for <italic>Escherichia coli</italic>. The data processing inequality (DPI) of information theory has previously been applied for the inference of TRIs. We consider the case where a transcription factor gene is known to regulate two genes (one of which is a transcription factor gene) that are known not to regulate one another. According to the DPI if certain conditions hold, the non-interacting gene pairs should have the smallest mutual information among all pairs in the triplets. While we observe that this is sometimes the case for <italic>Escherichia coli</italic>, we find that it is almost always not the case for <italic>Saccharomyces cerevisiae</italic>, thus indicating that the assumed conditions under which the DPI was derived do not hold.
The second part of this dissertation is related to the dynamical process of epigentic heritability. Epigenetic modifications to histones may promote either activation or repression of the transcription of nearby genes. Recent experimental studies show that the promoters of many lineage-control genes in stem cells have "bivalent domains" in which the nucleosomes contain both active (H3K4me3) and repressive (H3K27me3) marks. Here we formulate a mathematical model to investigate the dynamic properties of bivalent histone modification patterns, and we predict some interesting and potentially experimental observable features.
The third part of this dissertation studies dynamical systems in which a large number $N$ of identical Landau-Stuart oscillators are globally coupled via a mean-field. Previously, it has been observed that this type of system can exhibit a variety of different dynamical behaviors including clumped states (in which each oscillator is in one of a small number of groups for which all oscillators in each group have the same state which is different from group to group), as well as extensive chaos (a situation in which all oscillators have different states and the macroscopic dynamics of the mean field is chaotic). One of our foci is the transition between clumped states and extensive chaos as the system is subjected to slow adiabatic parameter change. We observe and analyze explosive discontinuous transitions between the clumped states and the extensively chaotic states. Also, we study the fractal structures of the extensively chaotic attractors.2014-01-01T00:00:00ZFeasibility Study of Scaling an XMT Many-Core
http://hdl.handle.net/1903/16316
Title: Feasibility Study of Scaling an XMT Many-Core
Authors: O'Brien, Sean; Vishkin, Uzi; Edwards, James; Waks, Edo; Yang, Bao
Abstract: The reason for recent focus on communication avoidance is that high rates of data movement become infeasible due to excessive power dissipation. However, shifting the responsibility of minimizing data movement to the parallel algorithm designer comes at significant costs to programmerâ€™s productivity, as well as: (i) reduced speedups and (ii) the risk of repelling application developers from adopting parallelism.
The UMD Explicit Multi-Threading (XMT) framework has demonstrated advantages on ease of parallel programming through its support of PRAM-like programming, combined with strong, often unprecedented speedups. Such programming and speedups involve considerable data movement between processors and shared memory. Another reason that XMT is a good test case for a study of data movement is that XMT permits isolation and direct study of most of its data movement (and its power dissipation).
Our new results demonstrate that an XMT single-chip many-core processor with tens of thousands of cores and a high throughput network on chip is thermally feasible, though at some cost. This leads to a perhaps game-changing outcome: instead of imposing upfront strict restrictions on data movement, as advocated in a recent report from the National Academies, opt for due diligence that accounts for the full impact on cost. For example, does the increased cost due to communication avoidance (including programmerâ€™s productivity, reduced speedups and desertion risk) indeed offset the cost of the solution we present?
More specifically, we investigate in this paper the design of an XMT many-core for 3D VLSI with microfluidic cooling. We used state-of-the-art simulation tools to model the power and thermal properties of such an architecture with 8k to 64k lightweight cores, requiring between 2 and 8 silicon layers. Inter-chip communication using silicon compatible photonics is also considered. We found that, with the use of microfluidic cooling, power dissipation becomes a cost issue rather than a feasibility constraint.
Robustness of the results is also discussed.2015-01-19T00:00:00Z