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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Dean-Kawasaki equation with singular non-local interactions：well-posedness and large deviations
奇异非局部 相互作用 Dean-Kawasaki方程 适定性 大偏差
2023/11/13
The Dean-Kawasaki equation with non-local singular interactions and correlated noise will be introduced, which describes the evolution of the density function for a system of finitely many particles g...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Peakon Models II: Weak-kink, interactions with peakon, and Remedies
Peakon模型 弱扭结 相互作用 补救措施
2023/5/8
In the 2nd part of the series talks, I will introduce the new phenomena of weak-kink and its interaction with regular peakons which we recently developed. Such models include cubic Camassa-Holm (CH) t...
Anisotropic interactions in a first-order aggregation model:a proof of concept
Anisotropy visual perception aggregation models implicit equations regularization relaxation time uniqueness criteria singular perturbation
2015/7/14
We extend a well-studied ODE model for collective behaviour by considering anisotropic interactions among individuals. Anisotropy is modeled by limited sensorial perception of individuals, that depend...
Fractional Factorial Designs With Admissible Sets of Clear Two-Factor Interactions
Fractional Factorial Designs Admissible Sets Clear Two-Factor Interactions
2015/3/20
Fractional Factorial Designs With Admissible Sets of Clear Two-Factor Interactions.
Weights and degrees in a random graph model based on 3-interactions
Martingale random graph preferential attachment scale-free property
2012/6/19
In a random graph model based on 3-interactions we give the joint asymptotic distribution of weights and degrees and prove scale-free property for the model. Moreover, we determine the asymptotics of ...
A class of integrable Hamiltonian systems including scattering of particles on the line with repulsive interactions
class of integrable Hamiltonian systems scattering of particles line repulsive interactions
2012/4/26
The main purpose of this paper is to introduce a new class of Hamiltonian scattering systems of the cone potential type that can be integrated via the asymptotic velocity. For a large subclass, the as...
On Self-Adjointness Of 1-D Schrodinger Operators With $δ$-Interactions
Schrodinger operator local point interaction self-adjoint operator deficiency indices Jacobi matrices
2012/4/23
In the present work we consider in $L^2(\mathbb{R}_+)$ the Schr\"odinger operator $\mathrm{H_{X,\alpha}}=-\mathrm{\frac{d^2}{dx^2}}+\sum_{n=1}^{\infty}\alpha_n\delta(x-x_n)$. We investigate and comple...
Multiple steady states in a mathematical model for interactions between T cells and macrophages
mathematical model T cells and macrophages Cell Behavior
2011/10/9
Abstract: The aim of this paper is to prove results about the existence and stability of multiple steady states in a system of ordinary differential equations introduced by R. Lev Bar-Or to model the ...
Wavelet thresholding estimation in a Poissonian interactions model with application to genomic data
Adaptive estimation interactions model oracle inequalities Poisson process thresholding rule U-statistics wavelets
2011/9/16
Abstract: This paper deals with the study of dependencies between two given events modeled by point processes. In particular, we focus on the context of DNA to detect favored or avoided distances betw...
Approximate tail probabilities of the maximum of a chi-square field on multi-dimensional lattice points and their applications to detection of loci interactions
Approximate tail probabilities a chi-square field multi-dimensional lattice points
2011/1/4
Define a chi-square random field on a multi-dimensional lattice points index set with a direct-product covariance structure, and consider the distribution of the maximum of this random field. We provi...
Scalable Inference of Customer Similarities from Interactions Data using Dirichlet Processes
Scalable Inference Customer Similarities Interactions Data Dirichlet Processes
2011/1/4
Under the sociological theory of homophily, people who are similar to one another are more likely to interact with one another. Marketers often have access to data on interactions among customers from...
It has been shown that the old-fashioned idea of Sakharov’s induced grav-ity and gauge interactions in the “one-loop dominance" version works astonishingly well yielding reasonable parameters.
Suppression of the quantum-mechanical collapse by repulsive interactions in a quantum gas
Quantum Gases (cond-mat.quant-gas) Pattern Formation and Solitons (nlin.PS)
2010/11/11
The quantum-mechanical collapse (alias fall onto the center of particles attracted by potential -1/r^2), or "quantum anomaly", is a well-known issue in the quantum theory. We demonstrate that the mean...
We discuss possible relationships between geometric and topological in-teractions on one side and physical interactions on the other side. This paper is a follow up of [2].
Singular continuous spectrum of one-dimensional Schrödinger operator with point interactions on a sparse set
Singular continuous spectrum one-dimensional Schrö dinger operator
2010/11/18
We say that a discrete set $X =\{x_n\}_{n\in\dN_0}$ on the half-line $$0=x_0 < x_1 infty$$ is sparse in the case the distances $\Delta x_n = x_{n+1} -x_n$ between neighboring p...