Wavelet Analysis of Big Data Contaminated by Large Noise in an fMRI Study of Neuroplasticity

Functional magnetic resonance imaging (fMRI) allows researchers to analyze brain activity on a voxel level, but using this ability is complicated by dealing with Big Data and large noise. A traditional remedy is averaging over large parts of brain in combination with more advanced technical innovations in reducing fMRI noise. In this paper a novel statistical approach, based on a wavelet analysis of standard fMRI data, is proposed and its application to an fMRI study of neuron plasticity of 24 healthy adults is presented. The aim of that study was to recognize changes in connectivity between left and right motor cortices (the neuroplasticity) after button clicking training sessions. A conventional method of the data analysis, based on averaging images, has implied that for the group of 24 participants the connectivity increased after the training. The proposed wavelet analysis suggests to analyze pathways between left and right hemispheres on a voxel-to-voxel level and for each participant via estimation of corresponding cross-correlations. This immediately necessitates statistical analysis of large-p-small-n correlation matrices contaminated by large noise. Furthermore, distributions that we are dealing in the analysis are neither Gaussian nor sub-Gaussian but sub-exponential. The paper explains how the problem may be solved and presents results of a dynamic analysis of the ability of a human brain to reorganize itself for 24 healthy adults. Results show that the ability of a brain to reorganize itself varies widely even among healthy individuals, and this observation is important for our understanding of a human brain and treatment of brain diseases.     

Comparison of Multivariate Matching Methods: Structures,Distances, and Algorithms

Abstract

A comparison and evaluation is made of recent proposals for multivariate matched sampling in observational studies, where the following three questions are answered: (1) Algorithms: In current statistical practice, matched samples are formed using “nearest available” matching, a greedy algorithm. Greedy matching does not minimize the total distance within matched pairs, though good algorithms exist for optimal matching that do minimize the total distance. How much better is optimal matching than greedy matching? We find that optimal matching is sometimes noticeably better than greedy matching in the sense of producing closely matched pairs, sometimes only marginally better, but it is no better than greedy matching in the sense of producing balanced matched samples. (2) Structures: In common practice, treated units are matched to one control, called pair matching or 1–1 matching, or treated units are matched to two controls, called 1–2 matching, and so on. It is known, however, that the optimal structure is a full matching in which a treated unit may have one or more controls or a control may have one or more treated units. Optimal 1 — k matching is compared to optimal full matching, finding that optimal full matching is often much better. (3) Distances: Matching involves defining a distance between covariate vectors, and several such distances exist. Three recent proposals are compared. Practical advice is summarized in a final section.     

Acoustic metamaterial with negative density

We fabricated a one-dimensional acoustic metamaterial with negative effective density using an array of very thin elastic membranes. We observed acoustic equivalence of the plasma oscillation at ωc=735 Hz. The metamaterial was opaque in the frequency range from 0 to 735 Hz, and was transparent above 735 Hz. We report direct observation of negative acceleration in this acoustic medium below 735 Hz. The frequency characteristics of the metamaterial have the same form as that of metals with negative permittivity. We also provide a simple theory to explain the experimental results.     

Oracle Inequalities for Efromovich–Pinsker Blockwise Estimates

Oracle inequality is a relatively new statistical tool for the analysis of nonparametric adaptive estimates. Oracle is a good pseudo-estimate that is based on both data and an underlying estimated curve. An oracle inequality shows how well an adaptive estimator mimics the oracle for a particular underlying curve. The most advanced oracle inequalities have been recently obtained by Cavalier and Tsybakov (2001) for Stein type blockwise estimates used in filtering a signal from a stationary white Gaussian process. The authors also conjecture that a similar result can be obtained for Efromovich–Pinsker (EP) type blockwise estimators where their approach, based on Stein's formula for risk calculation, does not work. This article proves the conjecture and extends it upon more general models which include not stationary and dependent processes. Other possible extensions, a discussion of practical implications and a numerical study are also presented.     

Topology control in the mobile ad hoc networks in order to intensify energy conservation

Although studied for years, due to their dynamic nature, research in the field of mobile ad hoc networks (MANETs) has remained a vast area of interest. Since once distributed, there will be less to no plausibility of recharge, energy conservation has become one of the pressing concerns regarding this particular type of network. In fact, one of the main obligations of designers is to make efficient use of these scarce resources. There has been tremendous work done in different layers of protocol stack in order to intensify energy conservation. To date, numerous topology control algorithms have been proposed, however, only a few have used meta-heuristics such as genetic algorithms, neural networks and/or learning automata to overcome this issue. On the other hand, since nodes are mobile and thus in a different spatial position, as time varies, we can expect that by regulating time intervals between topology controls, one may prolong the network’s lifetime. The main initiative of this paper is to intensify energy conservation in a mobile ad hoc network by using weighted and learning automata based algorithms. The learning automata, regulates time intervals between which the topology controls are done. The represented learning automata based algorithm uses its learning ability to find appropriate time-intervals so that the nodes would regulate the energy needed in order to exchange the information to their neighbors, accordingly. Moreover, at first we have represented two weighted based algorithms which extend two prominent protocols, namely K-Neigh and LMST. Then these algorithms are combined with a learning based algorithm which regulates time intervals between which the topology controls are done. In comparison with approaches that are based on periodic topology controls, proposed approach shows enhanced results. On the other hand, considering the learning ability of the learning automata based algorithms, composition of the aforementioned algorithms has been proven to be enhanced, in the respect of energy consumed per data transmitted, over those compared with.     

‘Excellent’ primary mathematics teachers’ espoused and enacted values of effective lessons

This paper reports a study that explored the characteristics of mathematics lessons that were espoused as effective by six ??excellent?? mathematics teachers and how they enacted their values in their classroom practice. In this study, we define espoused values as values that we want other people to believe we hold, and enacted values as values that we actually practice. Qualitative data were collected through video-recorded lesson observations (3 lessons for each teacher) and in-depth interviews with teachers after each observation. At the end of the project, stimulated-recall focus group interviews were used to allow teachers to define the meaning of an effective mathematics lesson as well as to recall and reflect on a 10-min edited video clip of one of their teaching lessons. The findings showed that these teachers shared five common characteristics of effective mathematics lessons: achieving teaching objectives; pupils?? cognitive development; affective achievement of pupils; focus on low-attaining pupils; and active participation of pupils in mathematics activities. These values were espoused explicitly as well as enacted in the lessons observed.