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Let G be a connected, reductive group over an algebraically closed field of good characteristic. For uG unipotent, we describe the conjugacy classes in the component group A(u) of the centralizer of u...
We produce several families of solutions for two-component nonlinear Schrödinger/Gross-Pitaevskii equations. These include domain walls and the first example of an antidark or gray soliton in one...
We introduce domain-wall (DW) states in the bimodal discrete nonlinear Schrödinger equation, in which the modes are coupled by cross-phase modulation (XPM). The results apply to an array of nonli...
We demonstrate the possibility of creating domain walls described by a single component Gross–Pitaevskii equation with attractive interactions, in the presence of an optical–lattice potential. While i...
In this work, we systematically generalize the Evans function methodology to address vector systems of discrete equations. We physically motivate and mathematically use as our case example a vector fo...
We introduce a model motivated by studies of Bose–Einstein condensates (BECs) trapped in double-well potentials. We assume that a mixture of two hyperfine states of the same atomic species is loaded i...
We study the interactions between two atomic species in a binary Bose-Einstein condensate to revisit the conditions for miscibility, oscillatory dynamics between the species, steady-state solutions, a...
We report the numerical realization of robust two-component structures in 2D and 3D Bose-Einstein condensates with nontrivial topological charge in one component. We identify a stable symbiotic state ...
Han and Liu (2012) proposed a method named transelliptical component analysis (TCA) for conducting scale-invariant principal component analysis on high dimensional data with transelliptical distributi...
This paper introduces an extension of the Markov switching ARCH model where the volatility in each state is a convex combination of two different ARCH components with time varying weights with differe...
In this paper, we present a unifying framework which reduces the construction of probabilistic component analysis techniques to a mere selection of the latent neighbourhood via the prior, thus providi...
Let $Y\in\R^n$ be a random vector with mean $s$ and covariance matrix $\sigma^2P_n\tra{P_n}$ where $P_n$ is some known $n\times n$-matrix. We construct a statistical procedure to estimate $s$ as well ...
Residual Component Analysis     Residual Component  Analysis       2011/7/6
Probabilistic principal component analysis (PPCA) seeks a low dimensional representation of a data set in the presence of independent spherical Gaussian noise, Sigma = (sigma^2)*I. The maximum likelih...
Sparse non-Gaussian component analysis (SNGCA) is an unsupervised method of extracting a linear structure from a high dimensional data based on estimating a low-dimensional non-Gaussian data component...
For statistical analysis of functional Magnetic Resonance Imaging (fMRI) data sets, we propose a data-driven approach based on Independent Component Analysis (ICA) implemented in a new version of the ...

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