Parametric dictionary design for sparse coding

Abstract—This paper introduces a new dictionary design method for sparse coding of a class of signals. It has been shown that one can sparsely approximate some natural signals using an overcomplete set of parametric functions, e.g. [1], [2]. A problem in using these parametric dictionaries is how to choose the parameters. In practice these parameters have been chosen by an expert or through a set of experiments. In the sparse approximation context, it has been shown that an incoherent dictionary is appropriate for the sparse approximation methods. In this paper we first characterize the dictionary design problem, subject to a constraint on the dictionary. Then we briefly explain that equiangular tight frames have minimum coherence. The complexity of the problem does not allow it to be solved exactly. We introduce a practical method to approximately solve it. Some experiments show the advantages one gets by using these dictionaries

A new effective weighted modified perturbation technique for solving a class of hypersingular integral equations

This paper is an attempt to solve an important class of hypersingular integral equations of the second kind. To this end, we apply a new weighted and modified perturbation method which includes some special cases of the Adomian decomposition method. To justify the efficiency and applicability of the proposed method, we examine some examples. The principal aspects of this method are its simplicity along with fast computations

Constrained Overcomplete Analysis Operator Learning for Cosparse Signal Modelling

We consider the problem of learning a low-dimensional signal model from a collection of training samples. The mainstream approach would be to learn an overcomplete dictionary to provide good approximations of the training samples using sparse synthesis coefficients. This famous sparse model has a less well known counterpart, in analysis form, called the cosparse analysis model. In this new model, signals are characterised by their parsimony in a transformed domain using an overcomplete (linear) analysis operator. We propose to learn an analysis operator from a training corpus using a constrained optimisation framework based on L1 optimisation. The reason for introducing a constraint in the optimisation framework is to exclude trivial solutions. Although there is no final answer here for which constraint is the most relevant constraint, we investigate some conventional constraints in the model adaptation field and use the uniformly normalised tight frame (UNTF) for this purpose. We then derive a practical learning algorithm, based on projected subgradients and Douglas-Rachford splitting technique, and demonstrate its ability to robustly recover a ground truth analysis operator, when provided with a clean training set, of sufficient size. We also find an analysis operator for images, using some noisy cosparse signals, which is indeed a more realistic experiment. As the derived optimisation problem is not a convex program, we often find a local minimum using such variational methods. Some local optimality conditions are derived for two different settings, providing preliminary theoretical support for the well-posedness of the learning problem under appropriate conditions.Comment: 29 pages, 13 figures, accepted to be published in TS

Modeling of Size Effects in Metallic Samples of Confined Volumes

In material science, size effects is described as the variation of material properties as the sample size changes. In this dissertation, the size dependency of the material strength is addressed as size effects. The size effects underlying mechanisms depend on the nature of the considered material. In the case of crystalline metals, size effects in crystalline metals are governed by the dislocations, as the primary deformation mechanism, and their interactions with one another and other defects such as grain boundaries. In this dissertation, the size and strain rate effects of fcc metallic samples of confined volumes are investigated during the nanoindentation and pillar compression experiments using large scale atomistic simulations. Examples of possible benefits include better understanding, controlling, and accelerating the development in new micro- and nano- technology such as microelectromechanical systems (MEMES), nano-coatings, thin films, nanocomposites, ultrafine grain bulk materials, and multilayer systems. First, the effects of different boundary conditions on the simulation of nanoindentation are investigated using Molecular Dynamics (MD). Next, the available theoretical models of size effects during nanoindentation are evaluated using atomistic simulation. In the next step, the MD simulation is incorporated to investigate the governing mechanism of size effects in a nanoscale single crystal Ni thin film during indentation. The effects of grain boundary (GB) on the sources of size effects are then investigated during the nanoindentation test. In the next step, the different mechanisms of size effects in fcc metallic samples of confined volumes are studied during high rate compression tests using large scale atomistic simulation. Different mechanisms of size effects, including the dislocation starvation, source exhaustion, and dislocation source length effect are investigated for pillars with different sizes. Furthermore, the size and strain rate effects are then investigated using the observed dislocation length distribution. Finally, the hardening mechanisms in fcc metallic structures during high rate deformations are studied by incorporating the dislocation network properties

Effect of Human HSP90 on Secondary and Tertiary Structures of Core Protein of Hepatitis C Virus and HbsAg of Hepatitis B Virus

The secondary structure of recombinant proteins can change through complex formation with other proteins. Here, we have determined the spatial structure of two proteins, including core protein of hepatitis C virus and HbsAg of hepatitis B virus, without the effect of human HSP90 as well as with the effect of this recombinant chaperone. As a result, the increase in intensity from 297.5 to 346.64 was accompanied by different folding and being non-polar protein in complex with the chaperone. HbsAg protein, combined with HSP90, showed a reduction in the maximum peak wavelength from 385 to 369.07 nm. The property of protein of being non-polar and hydrophobic, as well as having an increase in intensity from 200 to 219, indicates the protein folding. The shift from 342 to 337 nm along with blue shift indicates hydrophobic properties and the removal of protein from the water environment

Key indicators for organizational performance measurement

Each organization for assessing the amount of utility and desirability of their activities, especially in complex and dynamic environments, requires determining and ranking the vital performance indicators. Indicators provide essential links among strategy, execution and ultimate value creation. The aim of this paper is to develop a framework, which identifies and prioritizes Key Performance Indicators (KPIs) that a company should focus on them to define and measure progress towards organizational objectives. For this purpose, an applied research was conducted in 2013 in an Iranian telecommunication company. We first determined the objectives of the company with respect to four perspectives of BSC (Balanced Scorecard) framework. Next, performance indicators were listed and paired wise comparisons were accomplished by company's high-ranked employees through standard Analytic Hierarchy Process (AHP) questionnaires. This helped us establish the weight of each indicator and to rank them, accordingly