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While primary tumors are often treated effectively, they can spawn secondary cancers called metastases which dramatically decrease chances of survival. In order to In this thesis, we will discuss the Cauchy problem for some nonlinear dispersive PDEs with additive space-time white noise forcing. We will focus on two different models: the stochastic nonlinear beam equation SNLB McKean-Vlasov stochastic differential equations MVSDEs are ubiquitous in kinetic theory and in controlled games with a large number of players.

They have been intensively studied since McKean, as they pave a way to Nonlinear stochastic partial differential equations SPDEs are used to model wide variety of phenomena in physics, engineering, finance and economics. In many such models the equations exhibit super-linear growth. This thesis focuses on a class of finite dimensional symmetric algebras arising in geometry, known as contraction algebras. The main results presented here combine to give a complete description of the derived equivalence This thesis addresses the geometric analysis of traveling front propagation in singularly perturbed dynamical systems.

The study of front propagation in reaction-diffusion systems has received a significant amount of This thesis is concerned with the construction and enhancement of algorithms involving probability and statistics. The main motivation for these are problems that appear in finance and more generally in applied science. The automation of specific mathematical tasks such as theorem proving and algebraic manipulation have been much researched.

However, there have only been a few isolated attempts to automate the whole theory formation This thesis discusses the development of statistical theory in Britain in the period to , and attempts to account for this development as an institutional and an intellectual phenomenon. Colliander, James hamiltonian dynamical systems; partial differential equations; harmonic analysis. Cytrynbaum, Eric Bacterial cell division, Microtubule and cellular organization, Wave propagation in excitable media.

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### What makes the program unique?

Doebeli, Michael Walter Mathematical ecology and evolution, evolution of diversity, adaptive speciation, evolution of cooperation, game theory, experimental evolution in microorganisms. Friedlander, Michael numerical optimization, numerical linear algebra, scientific computing, Scientific computing. Frigaard, Ian Fluid mechanics visco-plastic fluids.

Froese, Richard Gerd Mathematics, Mathematical Physics, quantum mechanics, spectral theory, scattering theory. Ghioca, Dragos Drinfeld modules, isotrivial semiabelian varieties, Lehmer inequality. Recent Doctoral Citations Dr. William Christopher Carlquist "Dr. Carlquist developed a method to map experimental measurements onto mathematical models that describe how a system changes in time and space. Applying his method, he unravelled the mechanism underlying dynamic pattern formation in the E.

Laurent Charette "Dr. Charette studied pattern formations on evolving surfaces. He provided new findings on the bifurcations of reaction-diffusion systems and developed a numerical method to demonstrate his findings using the Closest Point Method.

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## Compare 36 PhD Programs in Mathematics

His work can be extended to many other evolving domain problems. Ye Liu "Dr. Liu studied the free-surface flow of non-Newtonian fluids under gravity. His research provides insights in the dynamics of visco-plastic dambreak problems in different contexts. His results can be applied in many industrial and natural processes ranging from cementing to glacier movement. Navid Ghadermarzy "Dr. Ghadermarzy studied the problem of completing multi-dimensional arrays, i.

Tensor completion is applicable whenever the data has missing or corrupted entries which can be the result of a faulty sensor or when taking measurements is too expensive. He proved optimal bound on the minimum required number of measurements for certain classes of tensors.

## Postgraduate Theses in the School of Mathematics and Statistics

Cole Michael John Zmurchok "Dr. Zmurchok used mathematical models to show that links between forces and chemical signalling in cells can lead to cell size fluctuations. His research suggests mechanisms at play in waves of contraction in a developing tissue, highlighting the importance of feedback between forces and signalling in models for cell dynamics. Sample Thesis Submissions Compressed sensing with deterministic measurement matrices.

Embracing nonuniform samples. Enumerative problems in algebraic geometry motivated from physics. Existence and ill-posedness for fluid PDEs with rough data. Configurations in fractal sets in Euclidean and non-Archimedean local fields : [errata]. Theoretical and numerical study of free-surface flow of viscoplastic fluids : 2D dambreaks, axisymmetrical slumps and surges down an inclined slope. Pattern formation on curved surfaces. Deterministic and stochastic modeling of the Min system for cell division : [supplementary material]. Deterministic and stochastic modeling of the Min system for cell division.

A homotopy-minimization method for parameter estimation in differential equations and its application in unraveling the reaction mechanism of the Min system. Near-optimal sample complexity for noisy or 1-bit tensor completion. From signalling to cell behaviour : modelling multi-scale organization in single and collective cellular systems. New solutions to local and non-local elliptic equations.

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Index bounds and existence results for minimal surfaces and harmonic maps. Faculty Overview Faculty of Science. Academic Unit Department of Mathematics. Generic two-phase coexistence in quadratic contact process. Modular Forms and modular symbols for noncongruence groups. Types of convergences of matrices.

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High-resolution alternating evolution schemes for hyperbolic conservation laws and Hamilton-Jacobi equations. Terwilliger algebras of wreath products of association schemes.

Lie algebra decompositions with applications to quantum dynamics. Analysis and finite element approximations of stochastic optimal control problems constrained by stochastic elliptic partial differential equations. Minimum rank of graphs that allow loops. Inverse scattering problems for first-order systems. Development of level set methods for computing semi-classical limit in Schrodinger equations with various potentials. Large time-stepping methods for higher order time-dependent evolution equations.

## phd - Comprehensive Guide for Ph.D. thesis in Mathematics? - Academia Stack Exchange

Modeling and direct numerical simulation of particle-laden turbulent flows. Weak homomorphisms of coalgebras. Topics in Pricing American-type Contracts.

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Boundary value approaches to molecular dynamics simulation. Weak representation theory in the calculus of relations. Analysis and control theory of some cochlear models. A penalty function method for constrained molecular dynamics. A new message authentication code based on the non-associativity of quasigroups. A modular data analysis pipeline for the discovery of novel RNA motifs.