Physical Sciences and Mathematics Commons^™

Towards A Theory Of Recursive Function Complexity: Sigma Matrices And Inverse Complexity Measures, Bradford M. Fournier

University of New Orleans Theses and Dissertations

This paper develops a data structure based on preimage sets of functions on a finite set. This structure, called the sigma matrix, is shown to be particularly well-suited for exploring the structural characteristics of recursive functions relevant to investigations of complexity. The matrix is easy to compute by hand, defined for any finite function, reflects intrinsic properties of its generating function, and the map taking functions to sigma matrices admits a simple polynomial-time algorithm . Finally, we develop a flexible measure of preimage complexity using the aforementioned matrix. This measure naturally partitions all functions on a finite set by characteristics …

Effects Of Visualization On Algorithm Comprehension, Matthew Mulvey

Theses and Dissertations

Computer science students are expected to learn and apply a variety of core algorithms which are an essential part of the field. Any one of these algorithms by itself is not necessarily extremely complex, but remembering the large variety of algorithms and the differences between them is challenging. To address this challenge, we present a novel algorithm visualization tool designed to enhance students understanding of Dijkstra’s algorithm by allowing them to discover the rules of the algorithm for themselves. It is hoped that a deeper understanding of the algorithm will help students correctly select, adapt and apply the appropriate algorithm …

Data Mining In Computational Proteomics And Genomics, Yang Song

Dissertations

This dissertation addresses data mining in bioinformatics by investigating two important problems, namely peak detection and structure matching. Peak detection is useful for biological pattern discovery while structure matching finds many applications in clustering and classification.

The first part of this dissertation focuses on elastic peak detection in 2D liquid chromatographic mass spectrometry (LC-MS) data used in proteomics research. These data can be modeled as a time series, in which the X-axis represents time points and the Y-axis represents intensity values. A peak occurs in a set of 2D LC-MS data when the sum of the intensity values in a …

Isolation In Synchronized Drone Formations, Andrew P. Brunner

Electronic Theses and Dissertations

This paper expands on a theoretical model that is used for aerial robots that are working cooperatively to complete a task. In certain situations, such as when multiple robots have catastrophic failures, the surviving robots could become isolated so that they never again communicate with another robot. We prove some properties about isolated robots flying in a grid formation, and we present an algorithm that determines how many robots need to fail to isolate at least one robot. Finally, we propose a strategy that eliminates the possibility of isolation altogether.

Novel Computational Methods For Transcript Reconstruction And Quantification Using Rna-Seq Data, Yan Huang

Theses and Dissertations--Computer Science

The advent of RNA-seq technologies provides an unprecedented opportunity to precisely profile the mRNA transcriptome of a specific cell population. It helps reveal the characteristics of the cell under the particular condition such as a disease. It is now possible to discover mRNA transcripts not cataloged in existing database, in addition to assessing the identities and quantities of the known transcripts in a given sample or cell. However, the sequence reads obtained from an RNA-seq experiment is only a short fragment of the original transcript. How to recapitulate the mRNA transcriptome from short RNA-seq reads remains a challenging problem. We …