Regularization schemes for regression have been widely studied in learning theory and inverse problems. In this paper, we study distribution (DR) which involves two stages of sampling, aims at regressing from probability measures to real-valued responses over a reproducing kernel Hilbert space (RKHS). Recently, theoretical analysis on DR has carried out via ridge several behaviors observed. How...

Optical solitons are known to be classically stable objects which robust perturbations. In this work, we show that due quantum mechanical effects, an optical soliton is initially in a classical coherent state will shed photons into the continuum and hence decay. The standard formulation of quantized uses linearized version nonlinear Schrodinger equation background soliton, remains approximation...

We study random design linear regression with no assumptions on the distribution of covariates and a heavy-tailed response variable. In this distribution-free setting, we show that boundedness conditional second moment given is necessary sufficient condition for achieving nontrivial guarantees. As starting point, prove an optimal version classical in-expectation bound truncated least squares es...

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 in which a higher-dimensional bright soliton exists even in a homogeneous setting with defocusing interactions, due to the effective potential created by a stable vortex in the other component. The...

 Ambiguity in the inputs of the models is typical especially in portfolio selection problem where the true distribution of random variables is usually unknown. Here we use robust optimization approach to address the ambiguity in conditional-value-at-risk minimization model. We obtain explicit models of the robust conditional-value-at-risk minimization for polyhedral and correlated polyhedral am...

This paper presents a multi-objective model for location-transportation problem under uncertainty that has been developed to respond to crisis. In the proposed model, humanitarian aid distribution centers (HADC), the number and location of them, the amount of relief goods stored in distribution centers, the amount of relief goods sent to the disaster zone, the number of injured people transferr...

One-dimensional hybrid code simulations are presented, carried out in order both to study solitary waves of the slow mode branch in an isotropic, collisionless, medium-β plasma (βi=0.25) and to test the fluid based soliton interpretation of Cluster observed strong magnetic depressions (Stasiewicz et al., 2003; Stasiewicz, 2004) against kinetic theory. In the simulations, a variety of strongly o...

We studied the efficiency of different implementations of the split-step Fourier method for solving the nonlinear Schrödinger equation that employ different step size selection criteria. We compared the performance of the different implementations for a variety of pulse formats and systems including higher-order solitons, collisions of soliton pulses, a single-channel periodically-stationary di...