Statistical-based monitoring of multivariate non-Gaussian systems

The monitoring of multivariate systems that exhibit non-Gaussian behavior is addressed. Existing work advocates the use of independent component analysis (ICA) to extract the underlying non-Gaussian data structure. Since some of the source signals may be Gaussian, the use of principal component analysis (PCA) is proposed to capture the Gaussian and non-Gaussian source signals. A subsequent application of ICA then allows the extraction of non-Gaussian components from the retained principal components (PCs). A further contribution is the utilization of a support vector data description to determine a confidence limit for the non-Gaussian components. Finally, a statistical test is developed for determining how many non-Gaussian components are encapsulated within the retained PCs, and associated monitoring statistics are defined. The utility of the proposed scheme is demonstrated by a simulation example, and the analysis of recorded data from an industrial melter.

Statistical theory of finite Fermi systems with chaotic excited eigenstates

A theory of strongly interacting Fermi systems of a few particles is developed. At high excit at ion energies (a few times the single-parti cle level spacing) these systems are characterized by an extreme degree of complexity due to strong mixing of the shell-model-based many-part icle basis st at es by the residual two- body interaction. This regime can be described as many-body quantum chaos. Practically, it occurs when the excitation energy of the system is greater than a few single-particle level spacings near the Fermi energy. Physical examples of such systems are compound nuclei, heavy open shell atoms (e.g. rare earths) and multicharged ions, molecules, clusters and quantum dots in solids. The main quantity of the theory is the strength function which describes spreading of the eigenstates over many-part icle basis states (determinants) constructed using the shell-model orbital basis. A nonlinear equation for the strength function is derived, which enables one to describe the eigenstates without diagonalization of the Hamiltonian matrix. We show how to use this approach to calculate mean orbital occupation numbers and matrix elements between chaotic eigenstates and introduce typically statistical variable s such as t emperature in an isolated microscopic Fermi system of a few particles.

Rise time and formant transition duration in the discrimination of speech sounds: The Ba–Wa distinction in developmental dyslexia

Across languages, children with developmental dyslexia have a specific difficulty with the neural representation of the sound structure (phonological structure) of speech. One likely cause of their difficulties with phonology is a perceptual difficulty in auditory temporal processing (Tallal, 1980). Tallal (1980) proposed that basic auditory processing of brief, rapidly successive acoustic changes is compromised in dyslexia, thereby affecting phonetic discrimination (e.g. discriminating /b/ from /d/) via impaired discrimination of formant transitions (rapid acoustic changes in frequency and intensity). However, an alternative auditory temporal hypothesis is that the basic auditory processing of the slower amplitude modulation cues in speech is compromised (Goswami , 2002). Here, we contrast children's perception of a synthetic speech contrast (ba/wa) when it is based on the speed of the rate of change of frequency information (formant transition duration) versus the speed of the rate of change of amplitude modulation (rise time). We show that children with dyslexia have excellent phonetic discrimination based on formant transition duration, but poor phonetic discrimination based on envelope cues. The results explain why phonetic discrimination may be allophonic in developmental dyslexia (Serniclaes , 2004), and suggest new avenues for the remediation of developmental dyslexia. © 2010 Blackwell Publishing Ltd.

On Entropy-Based Molecular Descriptors: Statistical Analysis of Real and Synthetic Chemical Structures

This paper presents an analysis of entropy-based molecular descriptors. Specifically, we use real chemical structures, as well as synthetic isomeric structures, and investigate properties of and among descriptors with respect to the used data set by a statistical analysis. Our numerical results provide evidence that synthetic chemical structures are notably different to real chemical structures and, hence, should not be used to investigate molecular descriptors. Instead, an analysis based on real chemical structures is favorable. Further, we find strong hints that molecular descriptors can be partitioned into distinct classes capturing complementary information.