CAS: Mathematics & Statistics: Scholarly Papers
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Enabling adiabatic passages between disjoint regions in parameter space through topological transitions
(AMER PHYSICAL SOC, 20160909)We explore topological transitions in parameter space in order to enable adiabatic passages between regions adiabatically disconnected within a given parameter manifold. To this end, we study the Hamiltonian of two coupled ... 
Large deviations and averaging for systems of slow–fast reaction–diffusion equations
(20171007)We study a large deviation principle for a system of stochastic reactiondiffusion equations (SRDEs) with a separation of fast and slow components and small noise in the slow component. The derivation of the large deviation ... 
Nonlinear stability of source defects in oscillatory media
(20180221)In this paper, we prove the nonlinear stability under localized perturbations of spectrally stable timeperiodic source defects of reactiondiffusion systems. Consisting of a core that emits periodic wave trains to each ... 
Localized radial roll patterns in higher space dimensions
(2018)Localized roll patterns are structures that exhibit a spatially periodic profile in their center. When following such patterns in a system parameter in one space dimension, the length of the spatial interval over which ... 
Rigorous justification of Taylor dispersion via center manifolds and hypocoercivity
(2018)Taylor diffusion (or dispersion) refers to a phenomenon discovered experimentally by Taylor in the 1950s where a solute dropped into a pipe with a background shear flow experiences diffusion at a rate proportional to 1/ν, ... 
Equivalences and counterexamples between several definitions of the uniform large deviations principle
(20180918)This paper explores the equivalences between four definitions of uniform large deviations principles and uniform Laplace principles found in the literature. Counterexamples are presented to illustrate the differences between ... 
Uniform large deviation principles for Banach space valued stochastic differential equations
(20180305)We prove a large deviation principle (LDP) for a general class of Banach space valued stochastic differential equations (SDE) that is uniform with respect to initial conditions in bounded subsets of the Banach space. A key ... 
Local Calabi–Yau manifolds of type A˜ via SYZ mirror symmetry
(Elsevier, 201905)We carry out the SYZ program for the local Calabi–Yau manifolds of type A˜ by developing an equivariant SYZ theory for the toric Calabi–Yau manifolds of infinitetype. Mirror geometry is shown to be expressed in terms of ... 
Assessing dynamics, spatial scale, and uncertainty in taskrelated brain network analyses
The brain is a complex network of interconnected elements, whose interactions evolve dynamically in time to cooperatively perform specific functions. A common technique to probe these interactions involves multisensor ... 
Characterizing the spiking dynamics of subthalamic nucleus neurons in Parkinson's disease using generalized linear models
(Frontiers Media, 20120620)Accurately describing the spiking patterns of neurons in the subthalamic nucleus (STN) of patients suffering from Parkinson's disease (PD) is important for understanding the pathogenesis of the disease and for achieving ...