### Finite time blow up in Kaniadakis-Quarati model of Bose-Einstein particles

, 2010

"... We study a Fokker-Planck equation with linear diffusion and super-linear drift introduced by Kaniadakis and Quarati [11, 12] to describe the evolution of a gas of Bose-Einstein particles. For kinetic equation of this type it is well-known that, in the physical space R 3, the structure of the equilib ..."

Abstract
- Add to MetaCart

We study a Fokker-Planck equation with linear diffusion and super-linear drift introduced by Kaniadakis and Quarati [11, 12] to describe the evolution of a gas of Bose-Einstein particles. For kinetic equation of this type it is well-known that, in the physical space R 3, the structure of the equilibrium Bose-Einstein distribution depends upon a parameter m ∗ , the critical mass. We are able to describe the time-evolution of the solution in two different situations, which correspond to m ≪ m ∗ and m ≫ m ∗ respectively. In the former case, it is shown that the solution remains regular, while in the latter we prove that the solution starts to blow up at some finite time tc, for which we give an upper bound in terms of the initial mass. The results are in favour of the validation of the model, which, in the supercritical regime, could produce in finite time a transition from a normal fluid to one with a condensate component.

### 1C-HiLasso: A Collaborative Hierarchical Sparse Modeling Framework

"... Sparse modeling is a powerful framework for data analysis and processing. Traditionally, encoding in this framework is performed by solving an `1-regularized linear regression problem, commonly referred to as Lasso or Basis Pursuit. In this work we combine the sparsity-inducing property of the Lasso ..."

Abstract
- Add to MetaCart

Sparse modeling is a powerful framework for data analysis and processing. Traditionally, encoding in this framework is performed by solving an `1-regularized linear regression problem, commonly referred to as Lasso or Basis Pursuit. In this work we combine the sparsity-inducing property of the Lasso at the individual feature level, with the block-sparsity property of the Group Lasso, where sparse groups of features are jointly encoded, obtaining a sparsity pattern hierarchically structured. This results in the Hierarchical Lasso (HiLasso), which shows important practical advantages. We then extend this approach to the collaborative case, where a set of simultaneously coded signals share the same sparsity pattern at the higher (group) level, but not necessarily at the lower (inside the group) level, obtaining the collaborative HiLasso model (C-HiLasso). Such signals then share the same active groups, or classes, but not necessarily the same active set. This model is very well suited for applications such as source identification and separation. An efficient optimization procedure, which guarantees convergence to the global optimum, is developed for these new models. The underlying presentation of the framework and optimization approach is complemented by experimental examples and theoretical results regarding recovery guarantees. I.

### Quasi-Monte Carlo sampling for stochastic variational problems

"... • Computational methods for solving stochastic variational problems require (first) a discretization of the underlying probability distribution induced by a numerical integration scheme for the approximate computation of expec-tations and (second) an efficient solver for a (large scale) finite-dimen ..."

Abstract
- Add to MetaCart

• Computational methods for solving stochastic variational problems require (first) a discretization of the underlying probability distribution induced by a numerical integration scheme for the approximate computation of expec-tations and (second) an efficient solver for a (large scale) finite-dimensional

### 1Reduced-Dimension Multiuser Detection

"... We present a reduced-dimension multiuser detector (RD-MUD) structure that significantly decreases the number of required correlation branches at the receiver front-end, while still achieving performance similar to that of the conventional matched-filter (MF) bank. RD-MUD exploits the fact that the n ..."

Abstract
- Add to MetaCart

to determine active users and sign detection for data recovery, and the reduced-dimension decision-feedback (RDDF) detector, which combines decision-feedback orthogonal matching pursuit for active user detection and sign detection for data recovery. We identify conditions such that error is

*dominated*by active### Culture on the Rise: How and Why Cultural Membership Promotes Democratic Politics

"... Abstract Selectively using Tocqueville, many social scientists suggest that civic participation increases democracy. We go beyond this neo-Tocquevillian model in three ways. First, to capture broader political and economic transformations, we consider different types of participation; results chang ..."

Abstract
- Add to MetaCart

the duty-based and of the identity

*norms*of citizenship, as well as of social and political trust. Cultural membership in class politics contexts,*dominated*by hierarchical institutions and materialist concerns, seems to have somewhat mixed political consequences-if it fosters voting (and, to a lesser### IEEE TRANSACTIONS ON SIGNAL PROCESSING 1 Hidden Relationships: Bayesian Estimation with Partial Knowledge

"... Abstract—We address the problem of Bayesian estimation where the statistical relation between the signal and measure-ments is only partially known. We propose modeling partial Bayesian knowledge by using an auxiliary random vector called instrument. The statistical relations between the instrument a ..."

Abstract
- Add to MetaCart

Abstract—We address the problem of Bayesian estimation where the statistical relation between the signal and measure-ments is only partially known. We propose modeling partial Bayesian knowledge by using an auxiliary random vector called instrument. The statistical relations between the instrument and the signal, and between the instrument and the measurements, are known. However, the joint probability function of the signal and measurements is unknown. Two types of statistical relations are considered, corresponding to second-order moment and complete distribution function knowledge. We propose two approaches for estimation in partial knowledge scenarios. The first is based on replacing the orthogonality principle by an oblique counterpart, and is proven to coincide with the method of instrumental variables from statistics, although developed in a different context. The second is based on a worst-case design strategy and is shown to be advantageous in many aspects. We provide a thorough analysis showing in which situations each of the methods is preferable and propose a non-parametric method for approximating the estimators from a set of examples. Finally, we demonstrate our approach in the context of enhancement of facial images that have undergone unknown degradation and image zooming. Index Terms—Bayesian estimation, minimax regret, partial knowledge, instrumental variables, nonparametric regression. I.

### Approved as to style and content by:

, 2014

"... This Open Access Dissertation is brought to you for free and open access by the Dissertations and Theses at ScholarWorks@UMass Amherst. It has ..."

Abstract
- Add to MetaCart

This Open Access Dissertation is brought to you for free and open access by the Dissertations and Theses at ScholarWorks@UMass Amherst. It has