The majority of microarray studies evaluate gene expression differences between various specimens or conditions. However, the causes of this variability often remain unknown. Our aim is to identify underlying causes of these patterns, a process that would eventually enable a mechanistic understanding of the deregulation of gene expression in cancer. The procedure consists of three phases: pre-p...

Effective Brain-Computer Interfaces (BCIs) require that the time-varying activation patterns of 2-D neural ensembles be modelled. The cluster variation method (CVM) offers a means for the characterization of 2-D local pattern distributions. This paper provides neuroscientists and BCI researchers with a CVM tutorial that will help them to understand how the CVM statistical thermodynamics formula...

In this paper, we apply the Variation of Parameters Method (VPM) for solving initial and boundary value problems of diversified physical nature. The analytical results are calculated in terms of convergent series with easily computable components. The proposed VPM is applied without any discretization, perturbation, transformation or restrictive assumptions and is free from round off errors and...

Total Variation denoising, proposed by Rudin, Osher and Fatemi in [22], is an image processing variational technique that has attracted considerable attention in the past fifteen years. It is an advantageous technique for preserving image edges but tends to sharpen excessively smooth transitions. With the purpose of alleviating this staircase effect some generalizations of Total Variation denoi...

For fuel economy of power system, Plug-in Hybrid Electric Vehicle (PHEV) should be charged late at night to level a load curve. This paper proposes an electricity pricing algorithm for load leveling, using variation method. Variation method is a mathematical technique that can bring a value of integral functional to the extreme value. We formulate a cost minimization problem of PHEV owners, reg...

In this paper, we introduce a novel hybrid variational model which generalizes the classical total variation method and the wavelet shrinkage method. An alternating minimization direction algorithm is then employed. We also prove that it converges strongly to the minimizer of the proposed hybrid model. Finally, some numerical examples illustrate clearly that the new model outperforms the standa...

Image restoration is one of classical inverse problems in image processing and computer vision, which consists of the recovering information about the original image from incomplete or degraded data. In this paper, we consider the problem of reduction of ringing that appears after image resampling. We introduce a novel method for image restoration, based on a quasi-solution method for a compact...

BACKGROUND Results on sera and calibrators vary 1.4- to 2.3-fold among commercial human chorionic gonadotropin (hCG) assays. The relative contributions of calibrators, standards, hCG charge isoforms, and major structural variants to this variation have not been quantified. METHODS Purified hCG was separated by isoelectric focusing into four fractions with pI ranges of 3-4, 4-5, 5-6, and 6-7. ...

We introduce a new iterative regularization procedure for inverse problems based on the use of Bregman distances, with particular focus on problems arising in image processing. We are motivated by the problem of restoring noisy and blurry images via variational methods, by using total variation regularization. We obtain rigorous convergence results, and effective stopping criteria for the gener...

In this paper we present an efficient algorithm for variation-aware interconnect extraction. The problem we are addressing can be formulated mathematically as the solution of linear systems with matrix coefficients that are dependent on a set of random variables. Our algorithm is based on representing the solution vector as a summation of terms. Each term is a product of an unknown vector in th...