Use of Mel Frequency Cepstral Coefficients for Automatic Pathology Detection on Sustained Vowel Phonations: Mathematical and Statistical Justification

This paper presents a justification for the use of MFCC parameters in automatic pathology detection on speech. While such an application has produced good results up to now, only partial explanations to this good performance had been given before. The herein exposed explanation consists of an interpretation of the mathematical transformations involved in MFCC calculation and a statistical analysis that confirms the conclusions drawn from the theoretical reasoning

Analysis of distribution of DNA methylation in kidney-renal-clear-cell-carcinoma specific genes using entropy

AbstractDNA Methylation is an epigenetic phenomenon in which methyl groups are added to the cytosines, thereby altering the physio-chemical properties of the DNA region and influencing gene expression. Aberrant DNA methylation in a set of genes or across the genome results in many epigenetic diseases including cancer. In this paper, we use entropy to analyze the extent and distribution of DNA methylation in Tumor Suppressor Genes (TSG's) and Oncogenes related to a specific type of cancer (viz.) KIRC (Kidney-renal-clear-cell-carcinoma). We apply various mathematical transformations to enhance the different regions in DNA methylation distribution and compare the resultant entropies for healthy and tumor samples. We also obtain the sensitivity and specificity of classification for the different mathematical transformations. Our findings show that it is not just the measure of methylation, but the distribution of the methylation levels in the genes that are significant in cancer

Recognition system for facial expression by processing images with deep learning neural network

The recognition systems of patterns in images are mechanisms that filter the information that provides an image to highlight the area of interest for the user. Usually, these mechanisms are based on mathematical transformations that allow the processor to perform interpretations based on the geometry or shape of the image. However, the strategies that implement mathematical transformations are limited, since the effectiveness of these techniques is reduced by changing the morphology or resolution of the image. This paper presents a partial solution to this limitation with a digital image processing technique based on a deep learning neural network (DNN). This technique incorporates a mechanism that allows the DNN to determine the facial expression of a person, based on the segmented information of the image of their face. By segmenting the image and processing its characteristics in parallel, the proposed technique increases the effectiveness of recognizing facial gestures in different images even when modifying their characteristics

Parametric Representations of Facial Expressions on PDE-Based Surfaces

NoParameterisation of facial expressions on PDE surface representations of human faces are presented in this work. Taking advantage of the boundary-value approach inherent to Bloor-Wilson PDE method, facial expressions are achieved by manipulating the original boundary curves. Such curves are responsible for generating a surface representation of a human face in its neutral configuration, so that regions on these curves represent a given facial expression in a fast and realistic manner. Additionally, the parameterisation proposed here is carried out by applying different mathematical transformations to the affected curves according to the corresponding facial expression. Full analytic expressions parameterising some of the most common facial expressions such as smiling and eyebrow raising are in this work. Some graphical examples of these facial expressions are used to illustrate the results obtained using Bloor-Wilson PDE method as the foundations of the parameterisation scheme proposed here. Thus, it is shown that an efficient, intuitive and realistic parameterisation of facial expressions is attainable using Bloor-Wilson PDE method in along with a suitable mathematical expression

Comparison of different electrocardiography with vectorcardiography transformations

This paper deals with transformations from electrocardiographic (ECG) to vectorcardiographic (VCG) leads. VCG provides better sensitivity, for example for the detection of myocardial infarction, ischemia, and hypertrophy. However, in clinical practice, measurement of VCG is not usually used because it requires additional electrodes placed on the patient's body. Instead, mathematical transformations are used for deriving VCG from 12-leads ECG. In this work, Kors quasi-orthogonal transformation, inverse Dower transformation, Kors regression transformation, and linear regression-based transformations for deriving P wave (PLSV) and QRS complex (QLSV) are implemented and compared. These transformation methods were not yet compared before, so we have selected them for this paper. Transformation methods were compared for the data from the Physikalisch-Technische Bundesanstalt (PTB) database and their accuracy was evaluated using a mean squared error (MSE) and a correlation coefficient (R) between the derived and directly measured Frank's leads. Based on the statistical analysis, Kors regression transformation was significantly more accurate for the derivation of the X and Y leads than the others. For the Z lead, there were no statistically significant differences in the medians between Kors regression transformation and the PLSV and QLSV methods. This paper thoroughly compared multiple VCG transformation methods to conventional VCG Frank's orthogonal lead system, used in clinical practice.Web of Science1914art. no. 307

Spin dynamics of an ultra-small nanoscale molecular magnet

We present mathematical transformations which allow us to calculate the spin dynamics of an ultra-small nanoscale molecular magnet consisting of a dimer system of classical (high) Heisenberg spins. We derive exact analytic expressions (in integral form) for the time-dependent spin autocorrelation function and several other quantities. The properties of the time-dependent spin autocorrelation function in terms of various coupling parameters and temperature are discussed in detail

Morphing: A Guide to Mathematical Transformations for Architects and Designers

Review of Morphing: A Guide to Mathematical Transformations for Architects and Designers, Reviewed July 2015 by Barbara Opar, Architecture Librarian, Syracuse University Libraries, [email protected]

Засоби автоматизації генерації електронних документів в системах організаційного управління

Аналізується проблема програмної підтримки автоматизації генерації електронних документів, розглядаються основні підходи до автоматизації генерації електронних документів в системах організаційного керування, запропоновано метод математичних перетворень для розв’язання деяких специфічних задач проблемної області та варіант реалізації інструментальних засобів.The problem of software support for automatic generation of electronic documents is analyzed. Basic approaches to automation of generation of electronic documents in the organizational control systems are examined, the method of mathematical transformations for solving some specific tasks in problem area and variant of implementation of tools are proposed