72 research outputs found
Even triangulations and commutative groups
No full textTitle: Even triangulations and commutative groups Author: Jan Luber Department: Department of Algebra Supervisor: prof. RNDr. Aleš Drápal, CSc., DSc. Abstract: This thesis takes interest in latin bitrades and triangulations construc- ted from them. Firstly, we introduce needed definitions, properties of the latin bitrades, detailed construction of the triangulation and mainly possibility of em- bedding latin bitrades into abelian groups. These groups are determined by the relations definied on vertices of the triangulation. Then we get concerned with a particular kind of 3-homogeneous latin bitrades which correspond to toroidal tri- angulation whose each vertex has degree six. For these groups we express relation matrix and complement to their torsion ranks. In case of simple triangulations we present explicit description of the groups and with modular arithmetic we get partial description even for more complex triangulations. Keywords: latin bitrade, eulerian triangulation, abelian grou
Hadamard matrices and their applications in cryptography
Get PDFTitle: Hadamard matrices and their applications in cryptography Author: Jan Luber Department: Department of Algebra Supervisor: prof. RNDr. Aleš Drápal, CSc., DSc., Department of Algebra Abstract: This thesis takes interest in Hadamard matrices, their constructions and application in cryptography. Firstly, we introduce basic properties of Hadamard matrices and selected summary of classical constructions is presented. Then we show a table of constructions that can be used to construct Hadamard matrix of given order. In the next part, we get concerned with Hadamard matrices with circulant cores with detailed description of construction Hadamard matrices with two circulant cores from GL-pair. In the end, we present cryptosystem using Hadamard matrices, we show its essential weaknesses and simple attacks. We propose several improvements in the form of adding other security elements. Keywords: Hadamard matrix, Hadamard conjecture, symmetric cryptograph
Even triangulations and commutative groups
Get PDFTitle: Even triangulations and commutative groups Author: Jan Luber Department: Department of Algebra Supervisor: prof. RNDr. Aleš Drápal, CSc., DSc. Abstract: This thesis takes interest in latin bitrades and triangulations construc- ted from them. Firstly, we introduce needed definitions, properties of the latin bitrades, detailed construction of the triangulation and mainly possibility of em- bedding latin bitrades into abelian groups. These groups are determined by the relations definied on vertices of the triangulation. Then we get concerned with a particular kind of 3-homogeneous latin bitrades which correspond to toroidal tri- angulation whose each vertex has degree six. For these groups we express relation matrix and complement to their torsion ranks. In case of simple triangulations we present explicit description of the groups and with modular arithmetic we get partial description even for more complex triangulations. Keywords: latin bitrade, eulerian triangulation, abelian grou
Identifying genome signatures of drug response in patient derived xenografts (PDX): a machine learning approach.
No full textImproved Prediction of Mouse Pathways Related to Bone Maintenance Through Machine Learning Utilizing Diverse Genomic Data
No full textThe genetic cause of osteoporosis is poorly understood, but a wealth of functional genomic data exist from which osteoporosis related pathways could be identified. A machine learning pipeline was created using Support Vector Machines and was first applied using as inputs all available gene expression data and a second time using only bone-related data. In both cases, models were trained using a manually curated training set of gene relationships known to support bone maintenance and development. Each model was used to predict novel pairwise gene relationships, and specific pathways were compared between models to identify relationships supported primarily by data collected in bone-related contexts as opposed to other cellular contexts. Our results indicate a more accurate result was achieved through biologically-motivated feature selection that considers mammalian cellular context. Our results reinforce the observation that if two genes are functionally associated in one context they may not be functionally associated in all contexts, necessitating careful consideration of training sets and input data into functional prediction methods
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Systems Interrogation of Host-Microbiome Immunomodulation and Metabolism
No full textIn this dissertation, I interrogate how scaling computational systems for complex `omics problems efficiently can lead to novel biological discoveries in the context of both how the microbiome modulates host metabolism and how the immune system responds to cancer. In Chapter 2, the method Aether is introduced. Aether is a tool that allows for intelligence bidding on cloud compute to reduce the cost of computational tasks in genomics by up to .7 orders of magnitude. In Chapter 3, Aether is utilized to handle de novo assembled meta`omic data at massive scale to help yield the discovery a novel microbe present in the stomach of professional athletes. Chapter 4 shows how working with complex single cell sequencing data of immune cells at scale can yield novel insight into tumors non-invasively through the creation of machine learning algorithms that can predict whether a CD8+ T cell in blood is in a shared clonal lineage as T cells in tumor. Taken together, these projects demonstrate the power of coupling experimental design with computation at scale.Medical SciencesMedical Science
"Histopathology Slide Indexing and Search: Are We There Yet?" - UCLA Test Slides
No full text<p>In-House UCLA test slides used for the case report in "Histopathology Slide Indexing and Search: Are We There Yet?" submitted to NEJM AI.</p>
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