Sparsity and Independence: Balancing Two Objectives in Optimization for Source Separation with Application to fMRI Analysis

Because of its wide applicability in various disciplines, blind source separation (BSS), has been an active area of research. For a given dataset, BSS provides useful decompositions under minimum assumptions typically by making use of statistical properties—types of diversity—of the data. Two popular types of diversity that have proven useful for many applications are statistical independence and sparsity. Although many methods have been proposed for the solution of the BSS problem that take either the statistical independence or the sparsity of the data into account, there is no unified method that can take into account both types of diversity simultaneously. In this work, we provide a mathematical framework that enables direct control over the influence of these two types of diversity and apply the proposed framework to the development of an effective ICA algorithm that can jointly exploit independence and sparsity. In addition, due to its importance in biomedical applications, we propose a new model reproducibility framework for the evaluation of the proposed algorithm. Using simulated functional magnetic resonance imaging (fMRI) data, we study the trade-offs between the use of sparsity versus independence in terms of the separation accuracy and reproducibility of the algorithm and provide guidance on how to balance these two objectives in real world applications where the ground truth is not available.     

Evaluation of Energy Saving Operational Modes for Industrial Fracture Connected Processes on the Basis of Incubation Time Fracture Criterion

A problem for a central crack in a plate subjected to plane strain conditions is investigated.Mode Ⅰ crack loading is created by a dynamic pressure pulse applied at a large distance from the crack.It was found that for a certain combination of amplitude and duration of the pulse applied,the energy transmitted to the sample has a strongly marked minimum,meaning that with the pulse amplitude or duration moving away from the optimal values,minimum energy required for initiation of crack growth increases rapidly.The results obtained indicate a possibility to optimise energy consumption of different industrial processes connected with fracture.Much could be gained in,for example,drilling or rock pounding where energy input accounts for the largest part of the process cost.Presumably further investigation of the effect observed can make it possible to predict optimal energy saving parameters,i.e.frequency and amplitude of impacts,for industrial devices,e.g.bores,grinding machines,and hence significantly reduce the process cost.The prediction can be given based on the parameters of the media fractured (material parameters,prevalent crack length and orientation,etc.).