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Articles 1 - 7 of 7
Full-Text Articles in Physical Sciences and Mathematics
Discrete Models And Algorithms For Analyzing Dna Rearrangements, Jasper Braun
Discrete Models And Algorithms For Analyzing Dna Rearrangements, Jasper Braun
USF Tampa Graduate Theses and Dissertations
In this work, language and tools are introduced, which model many-to-many mappings that comprise DNA rearrangements in nature. Existing theoretical models and data processing methods depend on the premise that DNA segments in the rearrangement precursor are in a clear one-to-one correspondence with their destinations in the recombined product. However, ambiguities in the rearrangement maps obtained from the ciliate species Oxytricha trifallax violate this assumption demonstrating a necessity for the adaptation of theory and practice.
In order to take into account the ambiguities in the rearrangement maps, generalizations of existing recombination models are proposed. Edges in an ordered graph model …
On Some Problems On Polynomial Interpolation In Several Variables, Brian Jon Tuesink
On Some Problems On Polynomial Interpolation In Several Variables, Brian Jon Tuesink
USF Tampa Graduate Theses and Dissertations
Polynomial approximation is a long studied process, with a history dating back to the 1700s, At which time Lagrange, Newton and Taylor developed their famed approximation methods. At that time, it was discovered that every Taylor projection (projector) is the pointwise limit of Lagrange projections. This leaves open a rather large and intriguing question, What happens in several variables?
To this end we define a linear idempotent operator to be an ideal projector whenever its kernel is an ideal. No matter the number of variables, Taylor projections and Lagrange projections are always ideal projectors, and it is well known that …
On The P(X)-Laplace Equation In Carnot Groups, Robert D. Freeman
On The P(X)-Laplace Equation In Carnot Groups, Robert D. Freeman
USF Tampa Graduate Theses and Dissertations
In this thesis, we examine the p(x)-Laplace equation in the context of Carnot groups. The p(x)-Laplace equation is the prototype equation for a class of nonlinear elliptic partial differential equations having so-called nonstandard growth conditions. An important and useful tool in studying these types of equations is viscosity theory. We prove a p()-Poincar´e-type inequality and use it to prove the equivalence of potential theoretic weak solutions and viscosity solutions to the p(x)-Laplace equation. We exploit this equivalence to prove a Rad´o-type removability result for solutions to the p-Laplace equation in the Heisenberg group. Then we extend this result to the …
Clustering Methods For Gene Expression Data Of Oxytricha Trifallax, Kyle Houfek
Clustering Methods For Gene Expression Data Of Oxytricha Trifallax, Kyle Houfek
USF Tampa Graduate Theses and Dissertations
Clustering is a data analysis method which is used in a large variety of research fields. Many different algorithms exist for clustering, and none of them can be considered universally better than the others. Different methods of clustering are expounded upon, including hierarchical clustering and k-means clustering. Topological data analysis is also described, showing how topology can be used to infer structural information about the data set. We discuss how one finds the validity of clusters, as well as an optimal clustering method, and conclude with how we used various clustering methods to analyze transcriptome data from the ciliate Oxytricha …
Global And Stochastic Dynamics Of Diffusive Hindmarsh-Rose Equations In Neurodynamics, Chi Phan
Global And Stochastic Dynamics Of Diffusive Hindmarsh-Rose Equations In Neurodynamics, Chi Phan
USF Tampa Graduate Theses and Dissertations
This dissertation consisting of three parts is the study of the open problems of global dynamics of diffusive Hindmarsh-Rose equations, random dynamics of the stochastic Hindmarsh-Rose equations with multiplicative noise and additive noise respectively, and synchronization of boundary coupled Hindmarsh-Rose neuron networks.
In Part I (Chapters 2, 3 and 4) of this dissertation, we study the global dynamics for the single neuron model of diffusive and partly diffusive Hindmarsh-Rose equations on a three-dimensional bounded domain. The existence of global attractors as well as its regularity and structure are established by showing the absorbing properties and the asymptotically compact characteristics, especially …
Restricted Isometric Projections For Differentiable Manifolds And Applications, Vasile Pop
Restricted Isometric Projections For Differentiable Manifolds And Applications, Vasile Pop
USF Tampa Graduate Theses and Dissertations
The restricted isometry property (RIP) is at the center of important developments in compressive sensing. In RN, RIP establishes the success of sparse recovery via basis pursuit for measurement matrices with small restricted isometry constants δ2s < 1=3. A weaker condition, δ2s < 0:6246, is actually sufficient to guarantee stable and robust recovery of all s-sparse vectors via l1-minimization. In infinite Hilbert spaces, a random linear map satisfies a general RIP with high probability and allow recovering and extending many known compressive sampling results. This thesis extends the known restricted isometric projection of sparse datasets of vectors embedded in the Euclidean spaces RN down into low-dimensional subspaces Rm ,m << N …<>
Non-Associative Algebraic Structures In Knot Theory, Emanuele Zappala
Non-Associative Algebraic Structures In Knot Theory, Emanuele Zappala
USF Tampa Graduate Theses and Dissertations
In this dissertation we investigate self-distributive algebraic structures and their cohomologies, and study their relation to topological problems in knot theory. Self-distributivity is known to be a set-theoretic version of the Yang-Baxter equation (corresponding to Reidemeister move III) and is therefore suitable for producing invariants of knots and knotted surfaces. We explore three different instances of this situation. The main results of this dissertation can be, very concisely, described as follows. We introduce a cohomology theory of topological quandles and determine a class of topological quandles for which the cohomology can be computed, at least in principle, by means of …