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Modulational instability of Gross-Pitaevskii-type equations in 1+1 dimensions
The coupling instability nonlinear schrodinger equation matter waves lens type conversion
2014/12/29
The modulational instability of the nonlinear Schrödinger (NLS) equation is examined in the case with a quadratic external potential. This study is motivated by recent experimental results in the...
On quiver varieties and affine Grassmanians of type A
Quiver varieties affine nilpotent orbit duality
2014/12/29
We construct Nakajima's quiver varieties of type A in terms of affine Grassmannians of type A. This gives a compactification of quiver varieties and a decomposition of affine Grassmannians into a disj...
On a class of spatial discretizations of equations of the nonlinear Schrödinger type
Discrete nonlinear schrodinger equation nonlinear discrete model and discrete
2014/12/25
We demonstrate the systematic derivation of a class of discretizations of nonlinear Schrödinger (NLS) equations for general polynomial nonlinearity whose stationary solutions can be found from a ...
WEYL GROUP MULTIPLE DIRICHLET SERIES OF TYPE A2
Dirichlet series rational function gaussian type
2014/12/25
A Weyl group multiple Dirichlet series is a Dirichlet series in several complex variables attached to a root system . The number of variables equals the rank r of the root system, and the series sati...
LITTELMANN PATTERNS AND WEYL GROUP MULTIPLE DIRICHLET SERIES OF TYPE D
Vail group the root type pattern
2014/12/24
We formulate a conjecture for the local parts of Weyl group multiple Dirichlet series attached to root systems of type D. Our conjecture is analogous to the description of the local parts of type A se...
The problem of estimating the number of unique types or distinct species in a group occurs in many fields, but is not a straightforward one. Given an arbitrary probabilistic distribution of entries to...
Testing Exponentiality Based on Rényi Entropy With Progressively Type-II Censored Data
Renyi Entropy hazard function Monte Carlo simulation order statistics Type-II progressively censored data
2013/4/28
We express the joint R\'enyi entropy of progressively censored order statistics in terms of an incomplete integral of the hazard function, and provide a simple estimate of the joint R\'enyi entropy of...
Additive inverse regression models with convolution-type operators
Inverse regression Additive models Convolution-type operators Mathematical subject codes: primary 62G08 secondary 62G15 62G20
2013/4/27
In a recent paper Birke and Bissantz (2008) considered the problem of nonparametric estimation in inverse regression models with convolution-type operators. For multivariate predictors nonparametric m...
Estimation of entropy-type integral functionals
U-statistics estimation of divergence density power divergence asymptotic normality entropy estimation Raenyi entrop
2012/11/22
Integrated powers of densities of one- or two-multidimensional random variables appear in a variety of problems in mathematical statistics, information theory, and computer science. We study U-statist...
On statistical properties of sets fulfilling rolling-type conditions
r-convexity positive reach rolling condition Glivenko-Cantelli classes set estimation boundary length excess mass
2011/6/20
Motivated by set estimation problems, we consider three closely related shape conditions
for compact sets: positive reach, r-convexity and rolling condition. First, the
relations between these shape...
Ornstein-Uhlenbeck type processes with heavy distribution tails
Ornstein-Uhlenbeck process heavy tails regular variation rank cor-relation Gauss copula log returns modelling
2011/3/25
We consider a transformed Ornstein-Uhlenbeck process model that can be a good candidate for modelling real-life processes characterized by a combination of time-reverting behaviour with heavy distribu...
Likelihood ratio type two-sample tests for current status data
Nonparametric two sample tests current status data likelihood ratio Weibull distribu-tions
2011/3/24
We introduce fully nonparametric two sample tests for testing the null hypothesis that the two samples come from the same distribution if the values are only indirectly given via current status censor...
Likelihood ratio type two-sample tests for current status data
Nonparametric two sample tests current status data, likelihood ratio Weibull distribu-tions
2011/3/23
We introduce fully nonparametric two sample tests for testing the null hypothesis that the two samples come from the same distribution if the values are only indirectly given via current status censor...
Adaptive LASSO-type estimation for ergodic diffusion processes
discretely observed diffusion processes model selection oracle proper-ties random fields stochastic differential equations
2010/3/10
The LASSO is a widely used statistical methodology for simultaneous estimation
and variable selection. In the last years, many authors analyzed this technique from
a theoretical and applied point of...
The shortest distance in random multi-type intersection graphs
Intersection graph shortest path branching process approximation Poissonapproximation
2010/3/9
Using an associated branching process as the basis of our approximation, we
show that typical inter-point distances in a multitype random intersection graph
have a defective distribution, which is w...