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In recent work with Will Johnson, we have shown that given a curve C over the rational number field Q with genus at least 2 and C(Q) is empty, the class of fields K of characteristic 0 such that C(K) ...
An LG model (M, f) is given by a noncompact complex manifold M and the holomorphic function f defined on it, which is an important model in string theory. Because of the mirror symmetry conjecture, th...
Generalized pairs are a natural structure in birational geometry that first appeared in Kodaira’s canonical bundle formula for elliptic fibrations. They were formally introduced by Birkar and Zhang in...
In this talk I will review the developments of homogenization theory for a front propagation model. It is described by a first order Hamilton-Jacobi equation with a Hamiltonian that grows linearly wit...
In this talk, we present numerical approximations of a phase-field model for two-phase ferrofluids, which consists of the Navier-Stokes equations, the Cahn-Hilliard equation, the magnetostatic equatio...
In this talk, we investigate a stochastic nutrient-phytoplankton model which incorporates the effect of white noise on phytoplankton growth. The global existence and uniqueness of a positive solution,...
How to select the active variables which have significant impact on the event of interest is a very important and meaningful problem in the statistical analysis of ultrahigh-dimensional data. In many ...
The pathogenesis of breast cancer is not the same in all countries and regions; therefore, some existing breast cancer risk assessment models are not well adapted to all countries and regions, includi...
In this talk, we first briefly review history of the geometric singular perturbation theory, then talk about the traveling pulses for a diffusive Rosenzweig MacArthur model. We show the existence of t...
Extremum seeking control(ESC)is a class of data-driven optimization algorithms which can drive the output of an unknown dynamic system to its optimal value with respect to some cost function by using ...
Complex nonlinear interplays of multiple scales give rise to many interesting physical phenomena and pose major difficulties for the computer simulation of multiscale PDE models in areas such as reser...
Multinational enterprises actively participate in global production networks. However, the current global value chain accounting framework fails to consider the emissions originating from the producti...
In order to study the depinning transition in presence of strong disorder, Derrida and Retaux (J. Stat. Phys. (2014)) introduced a discrete-time max-type recursive model. It is believed that for a lar...
Conformal invariance of critical lattice models in two-dimensional has been vigorously studied for decades. The first example where the conformal invariance was rigorously verified was the planar unif...
Most existing SAR image change detection algorithms only consider single pixel information of different images, and not consider the spatial dependencies of image pixels. So the change detection resul...

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