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Discrete Mathematics and Combinatorics Commons™
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Articles 1 - 9 of 9
Full-Text Articles in Discrete Mathematics and Combinatorics
An Enumeration Of Nested Networks, Nathan Cornelius
An Enumeration Of Nested Networks, Nathan Cornelius
Williams Honors College, Honors Research Projects
Nested networks have several applications in phylogenetics and electrical circuit theory. In many cases, there may exist more than one distinct network which correctly models a given data set. This proposes a combinatorial problem to determine all possible network solutions. In this paper, we partially solve this problem by developing exponential generating functions which enumerate all 1-nested and 2-nested unicyclic networks. We also describe our procedure to directly count all 1-nested and 2-nested networks and provide all 1-nested networks with 7, 8, and 9 terminal nodes.
Sdrap: An Annotation Pipeline For Highly Scrambled Genomes, Jasper Braun
Sdrap: An Annotation Pipeline For Highly Scrambled Genomes, Jasper Braun
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Loop Homology Of Bi-Secondary Structures, Andrei Bura
Loop Homology Of Bi-Secondary Structures, Andrei Bura
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Efficient Reduced Bias Genetic Algorithm For Generic Community Detection Objectives, Aditya Karnam Gururaj Rao
Efficient Reduced Bias Genetic Algorithm For Generic Community Detection Objectives, Aditya Karnam Gururaj Rao
Theses
The problem of community structure identification has been an extensively investigated area for biology, physics, social sciences, and computer science in recent years for studying the properties of networks representing complex relationships. Most traditional methods, such as K-means and hierarchical clustering, are based on the assumption that communities have spherical configurations. Lately, Genetic Algorithms (GA) are being utilized for efficient community detection without imposing sphericity. GAs are machine learning methods which mimic natural selection and scale with the complexity of the network. However, traditional GA approaches employ a representation method that dramatically increases the solution space to be searched by …
Dynamics Of Gene Networks In Cancer Research, Paul Scott
Dynamics Of Gene Networks In Cancer Research, Paul Scott
Electronic Theses and Dissertations
Cancer prevention treatments are being researched to see if an optimized treatment schedule would decrease the likelihood of a person being diagnosed with cancer. To do this we are looking at genes involved in the cell cycle and how they interact with one another. Through each gene expression during the life of a normal cell we get an understanding of the gene interactions and test these against those of a cancerous cell. First we construct a simplified network model of the normal gene network. Once we have this model we translate it into a transition matrix and force changes on …
Network Analytics For The Mirna Regulome And Mirna-Disease Interactions, Joseph Jayakar Nalluri
Network Analytics For The Mirna Regulome And Mirna-Disease Interactions, Joseph Jayakar Nalluri
Theses and Dissertations
miRNAs are non-coding RNAs of approx. 22 nucleotides in length that inhibit gene expression at the post-transcriptional level. By virtue of this gene regulation mechanism, miRNAs play a critical role in several biological processes and patho-physiological conditions, including cancers. miRNA behavior is a result of a multi-level complex interaction network involving miRNA-mRNA, TF-miRNA-gene, and miRNA-chemical interactions; hence the precise patterns through which a miRNA regulates a certain disease(s) are still elusive. Herein, I have developed an integrative genomics methods/pipeline to (i) build a miRNA regulomics and data analytics repository, (ii) create/model these interactions into networks and use optimization techniques, motif …
Exploring The Space Of Rna Secondary Structures, Heather C. Smith
Exploring The Space Of Rna Secondary Structures, Heather C. Smith
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
The Maximum Clique Problem: Algorithms, Applications, And Implementations, John David Eblen
The Maximum Clique Problem: Algorithms, Applications, And Implementations, John David Eblen
Doctoral Dissertations
Computationally hard problems are routinely encountered during the course of solving practical problems. This is commonly dealt with by settling for less than optimal solutions, through the use of heuristics or approximation algorithms. This dissertation examines the alternate possibility of solving such problems exactly, through a detailed study of one particular problem, the maximum clique problem. It discusses algorithms, implementations, and the application of maximum clique results to real-world problems. First, the theoretical roots of the algorithmic method employed are discussed. Then a practical approach is described, which separates out important algorithmic decisions so that the algorithm can be easily …
A Decomposition Of The Pure Parsimony Problem, Allen Holder, Thomas M. Langley
A Decomposition Of The Pure Parsimony Problem, Allen Holder, Thomas M. Langley
Mathematical Sciences Technical Reports (MSTR)
We partially order a collection of genotypes so that we can represent the problem of inferring the least number of haplotypes in terms of substructures we call g-lattices. This representation allows us to prove that if the genotypes partition into chains with certain structure, then the NP-Hard problem can be solved efficiently. Even without the specified structure, the decomposition shows how to separate the underlying integer programming model into smaller models.