Determinant Of Matrix Research Articles

Some algebraic properties on rough neutrosophic matrix and its application to multi-criteria decision-making

<abstract><p>Rough set theory is a method of information processing for database systems. The neutrosophic matrix is a generalization of the fuzzy matrix, especially in handling indeterminacy situations. The concept of matrix theory and its energy in the neutrosophic environment help to determine the value of the uncertain matrix. In this paper, we correlate the rough set theory with the neutrosophic matrix theory to introduce the rough neutrosophic matrix (RNM). In this structure, lower and upper approximation neutrosophic matrices are used to deal with uncertain situations. We demonstrate that the given matrix plays a different role in decision-making situations and defined the proposed matrix's determinant, adjoint, algebraic properties and operations. Finally, derived the ranking function for a rough neutrosophic matrix's energy. The new multi-criteria decision-making (MCDM) approach was presented with the ranking formula, which was utilized to rank the alternatives, and numerical examples were provided to show how the proposed matrix and its energy could be applied to an MCDM problem.</p></abstract>

Detection of epileptic seizures from compressively sensed EEG signals for wireless body area networks

Wireless body area networks (WBANs) are gaining popularity for tele-monitoring of biomedical signals such as the electroencephalogram (EEG), with diagnosing and monitoring of epileptic seizures being one of the most important applications. Most seizure-detection algorithms cannot be applied directly to the compressed data in WBANs as they require full reconstruction of original EEG signals. In this study, we propose a novel feature for real-time automatic single-channel seizure detection which does not require complete reconstruction of original EEGs. The feature is based on iteratively applying the orthogonal matching pursuit (OMP) algorithm on the compressed EEG data and computing the rate by which the energies of partially reconstructed signals are increased. The feature, i.e. partial energy difference (PED), is then used for classifying seizure and non-seizure states. We also extend this method to the case for multichannel EEG. In multichannel case, the simultaneous OMP (SOMP) with a low number of iterations (1 and 15 iteration) is applied to the compressed data and the difference between the Frobenius norms of partially reconstructed signals is used as a multivariate feature for the classification of seizure and non-seizure states. The proposed features are used to detect seizure intervals in the EEG database provided by the University of Bonn and the CHB-MIT database. The results show that the proposed features can classify seizure epochs from non-seizures even for compression ratios as small as 0.05. The results also show that the proposed single-channel method achieves improvement of up to 4% for the area under the curve (AUC) with significantly less execution time compared to the benchmark matrix determinant (MD) classification approach. The results of applying the proposed multivariate feature to seizure and non-seizure segments of length 5 s from the CHB-MIT database show that it achieves mean AUC values of 0.941, 0.941, and 0.939 with mean execution times of 9.5, 10.7, and 13.1 s for compression ratios of 0.05, 0.1, and 0.2, respectively. Applying a threshold to the PED in a leave-one-out cross-validation (LOO-CV) scenario generates a sensitivity of 0.873,specificity of 0.710, and accuracy of 0.791 at the compression ratio of 0.05. The proposed single- and multichannel features have the potential for deployment in WBANs for the real-time tele-monitoring of epilepsy patients in healthcare applications.

Adaptive median feature baseline correction for improving recognition of epileptic seizures in ICU EEG

Automated classification of epileptic seizures surrogates the manual interventions required for analyzing long-term electroencephalographic (EEG) signals and helps to speed up the treatment in epilepsy patients. Developing a patient independent algorithm is a great challenge due to the differences in EEG characteristics. Feature distribution among many subjects results in inter-subject variability, which leads to poor classification performance. Therefore, in order to overcome this limitation, we have proposed a novel adaptive median feature baseline correction (AM-FBC) method to update the feature distribution. Two recently proposed features referred to as successive decomposition index (SDI) and matrix determinant (MD) were extracted from 40 intensive care unit patients EEG at a segmentation length of 4 s with 50% overlap. We have investigated the influence of outliers removal and correction, AM-FBC, and post-processing of classifier output to improve the seizure detection results. The classification was performed using a support vector machine classifier with leave-one-subject-out cross-validation. With the application of above-mentioned methods, the highest area under the curve (AUC) of 0.9663 (sensitivity S+ = 0.9661, specificity (S− = 0.8446) and 0.9812 S+ = 0.9822, S− = 0.8705) was achieved using SDI and MD features respectively. Further, the AUC of 0.9593 (S+ = 0.9069, S− = 0.8695) was achieved when both SDI and MD features were used with the application of the outliers correction method. The findings of the study suggest (1) Outliers correction method does not improve results (2) AM-FBC enhances the results (3) Post-processing method improved the classification results at least 2 to 5% and reduced false detections (4) Lowering the outlier removal factor showed good AUC at the cost of loss of feature samples.

Common-Mode Stability Test and Design Guidelines for a Transformer-Based Push-Pull Power Amplifier

We report design guidelines for a transformer-based push-pull power amplifier (PA) with a systematic stability test carried out in the complex frequency domain. By detecting the right half-plane zeros of the impedance matrix's determinant, the common-mode (CM) instability in a differential PA were accurately estimated with the established frequencies from the analysis. In the stability test, the parasitic series coupling capacitance of the input transformer and the parasitic inductance from the gate (base) biasing line were identified as the two primary mechanisms of the CM instability in a transformer-based PA contingent on stability. Based on the analysis of the instability mechanisms, useful stabilization methods were proposed and discussed for a robust push-pull PA design with a well-balanced performance. An onboard transformer-based push-pull PA was implemented for the verification purpose, and the effects of parasitic inductance on the stability had been investigated. The simulated and measured results corresponded well with the proposed analysis.

Great Matrix Equations

This paper is devoted to some identities of matrix and determinants. In this article, matrices inequalities are widely used. Matrices are non-optimistic. The matrix's determinants have been proven. In addition to the left module and the right module descriptions in this article. In general, this article is devoted to matrix approximation.

ANALYTICAL POLE RESIDUE CALCULATION IN SPECTRAL METHOD OF MOMENTS FORMULATIONS FOR PERIODIC STRUCTURES

An analytical method for evaluating pole-residues in spectral method of moments (MoM) formulations is presented. Spectral integral formulations for periodic structures involve the inverse of the MoM matrix, which exhibits a periodic set of pole singularities, corresponding to the zeros of the matrix's determinant. So far, these singularities have not been extracted and the corresponding pole-residues were calculated directly from the difierential or integral deflnitions of the residue. In this work, we consider an analytical expression for the solution to the MoM matrix equation, which enables the extraction of pole singularities and the analytical evaluation of pole-residues. We also present a comparison to previous methods.

Déterminants of Japanese Foreign Direct Investment. Locational Attractiveness of European Countries to Japanese Multinationals

Determinants of Japanese Foreign Direct Investment. Locational Attractiveness of European Countries to Japanese Multinational ; ; L'article examine l'importance des strategies de « diversification » et de « globalisation » des firmes multinationales japonaises dans la determination de leurs investissements directs en Europe. ; A la fin des annees quatre-vingt, les multinationales japonaises qui ont implante leurs filiales en Europe, ont non seulement transfere leur production et leur reseau commercial, mais elles ont egalement etabli un systeme de management concerte, incluant aussi des elements financiers, de distribution et de R&D associes a cette production.