scholarly journals Matrix Expression of Convolution and Its Generalized Continuous Form

Symmetry ◽  
2020 ◽  
Vol 12 (11) ◽  
pp. 1791
Author(s):  
Young Hee Geum ◽  
Arjun Kumar Rathie ◽  
Hwajoon Kim
Keyword(s):  
Neural Networks ◽  
Integral Transforms ◽  
Main Process ◽  
Continuous Form ◽  
Core Technology ◽  
New Variant ◽  
The Matrix ◽  
Matrix Expression ◽  
Almost All ◽  
Laplace Type

In this paper, we consider the matrix expression of convolution, and its generalized continuous form. The matrix expression of convolution is effectively applied in convolutional neural networks, and in this study, we correlate the concept of convolution in mathematics to that in convolutional neural network. Of course, convolution is a main process of deep learning, the learning method of deep neural networks, as a core technology. In addition to this, the generalized continuous form of convolution has been expressed as a new variant of Laplace-type transform that, encompasses almost all existing integral transforms. Finally, we would, in this paper, like to describe the theoretical contents as detailed as possible so that the paper may be self-contained.

scholarly journals Characterization of Relationships Between the Domains of Two Linear Matrix-Valued Functions with Applications

2020 ◽  
Author(s):  
Yongge Tian
Keyword(s):  
Linear Matrix ◽  
Reduced Equations ◽  
Special Cases ◽  
Matrix Rank Method ◽  
The Matrix ◽  
Independent Variable ◽  
Matrix Expression ◽  
Almost All ◽  
Linear Matrix Equations

One of the typical forms of linear matrix expressions (linear matrix-valued functions) is given by $A + B_1X_1C_1 + \cdots + B_kX_kC_k$, where $X_1, \ldots, X_k$ are independent variable matrices of appropriate sizes, which include almost all matrices with unknown entries as its special cases. The domain of the matrix expression is defined to be all possible values of the matrix expressions with respect to $X_1, \ldots, X_k$. I this article, we approach some problems on the relationships between the domains of two linear matrix expressions by means of the block matrix method (BMM), the matrix rank method (MRM), and the matrix equation method (MEM). As application, we discuss some topics on the relationships among general solutions of some linear matrix equations and their reduced equations.

Modeling of Distributed Parameter Processes with Neural Networks

2014 ◽  
Vol 555 ◽  
pp. 530-540
Author(s):  
Honoriu Vălean ◽  
Mihail Abrudean ◽  
Mihaela Ligia Ungureşan ◽  
Iulia Clitan ◽  
Vlad Mureşan
Keyword(s):  
Neural Networks ◽  
Simulation Method ◽  
Distributed Parameter ◽  
Hearth Furnace ◽  
Original Solution ◽  
Steel Pipes ◽  
The Matrix ◽  
The Neural Networks ◽  
Derivatives Of ◽  
Seamless Steel

In this paper an original solution for the modeling of distributed parameter processes using neural networks is presented. The proposed method represents a particular alternative to a very accurate modeling-simulation method for this kind of processes, the method based on the matrix of partial derivatives of the state vector (Mpdx), associated with Taylor series. In order to compare the performances generated by the two methods, a distributed parameter thermal process associated to a rotary hearth furnace (R.H.F) from the technological flow of producing seamless steel pipes is considered. The main similarities and differences between the two methods are highlighted in the paper. The treated solution represents a premise for the usage of the neural networks in the automatic control of the distributed parameter processes domain.

Entropy estimation of the fragments of chest X-ray images

2021 ◽  
pp. 20-26
Author(s):  
Aleksei Aleksandrovich Rumyantsev ◽  
Farkhad Mansurovich Bikmuratov ◽  
Nikolai Pavlovich Pashin
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Binary Classification ◽  
Statistical Characteristics ◽  
Type I ◽  
Deep Convolutional Neural Networks ◽  
Preliminary Calculation ◽  
X Ray ◽  
The Matrix ◽  
Chest X Ray

The subject of this research is medical chest X-ray images. After fundamental pre-processing, the accumulated database of such images can be used for training deep convolutional neural networks that have become one of the most significant innovations in recent years. The trained network carries out preliminary binary classification of the incoming images and serve as an assistant to the radiotherapist. For this purpose, it is necessary to train the neural network to carefully minimize type I and type II errors. Possible approach towards improving the effectiveness of application of neural networks, by the criteria of reducing computational complexity and quality of image classification, is the auxiliary approaches: image pre-processing and preliminary calculation of entropy of the fragments. The article provides the algorithm for X-ray image pre-processing, its fragmentation, and calculation of the entropy of separate fragments. In the course of pre-processing, the region of lungs and spine is selected, which comprises approximately 30-40% of the entire image. Then the image is divided into the matrix of fragments, calculating the entropy of separate fragments in accordance with Shannon’s formula based pm the analysis of individual pixels. Determination of the rate of occurrence of each of the 255 colors allows calculating the total entropy. The use of entropy for detecting pathologies is based on the assumption that its values differ for separate fragments and overall picture of its distribution between the images with the norm and pathologies. The article analyzes the statistical values: standard deviation of error, dispersion. A fully connected neural network is used for determining the patterns in distribution of entropy and its statistical characteristics on various fragments of the chest X-ray image.

scholarly journals Characterization by TGA, SEM, and EDX of Polymeric Matrices Used as Cocaine Camouflages

2018 ◽  
Vol 12 (12) ◽  
pp. 119
Author(s):  
Carlos A. Díaz V ◽  
William F. Garzón M ◽  
Juan C. Higuita V ◽  
Elisabeth. Restrepo-Parra
Keyword(s):  
Surface Morphology ◽  
Thermo Gravimetric Analysis ◽  
Soxhlet Extraction ◽  
Structural Type ◽  
Extraction Process ◽  
Gravimetric Analysis ◽  
Before And After ◽  
The Matrix ◽  
Morphological Differences ◽  
Almost All

In this work, a study of samples that contained cocaine camouflaged inside unidentified polymers was performed. Samples were seized at the Dorado International airport in Colombia. Cocaine was adsorbed or occluded within the matrix. The objective of this research was to extract cocaine from the matrices using soxhlet extraction method. Thereafter matrices were analyzed to determine the surface morphology before and after the extraction. Several morphological differences were exhibited between samples including both adsorbed and occluded cocaine. Moreover, changes in the surface morphology were also observed before and after cocaine extraction. The chemical elemental composition of matrices was also studied using energy dispersive spectroscopy, observing that the alkaloid was totally removed in almost all samples after the extraction process. On the other hand, Thermo gravimetric analysis also allows comparing the results obtained for the samples with patterns of pure cocaine and other polymers as CMC, PVA and HEC, finding several similarities of structural type.

scholarly journals Investigating Musicians’ Mindfulness through a Phenomenological Matrix

2019 ◽  
Author(s):  
Frank Diaz ◽  
Jason Silveira ◽  
Katherine Strand
Keyword(s):  
Music Education ◽  
Personal Growth ◽  
Cognitive Outcomes ◽  
First Year ◽  
First Year College ◽  
Introductory Course ◽  
The Matrix ◽  
College Music ◽  
Neurophysiological Mechanisms ◽  
Almost All

We investigated the efficacy of a phenomenological matrix of mindfulness as a framework for examining expectations, formal meditation experiences, and appraisals of first-year college music students (N = 18) who participated in a 5-day mindfulness module offered through an introductory course in music education. Participants expressed hopes that meditation would help them manage stress and anxiety, improve their focus and relationships, and support their personal growth and motivation. With respect to lived experiences of formal meditation, we found that without explicit prompting, approximately 86% percent of coded phrases reflected dimensions of experience that could be mapped within the matrix, suggesting its efficacy for coding. Furthermore, almost all participants attributed mindfulness to improving their general wellness, with dereification, breathing, and non-aversive affect frequently mentioned as key factors leading to these improvements. Additionally, consistent with the neurophenomenological aims of the matrix, we list cognitive outcomes and neurophysiological mechanisms potentially attributable to the nature of selected appraisal statements by participants.

Finding Cut-Edges and the Minimum Spanning Tree via Semi-Tensor Product Approach

2018 ◽  
Vol 6 (5) ◽  
pp. 459-472
Author(s):  
Xujiao Fan ◽  
Yong Xu ◽  
Xue Su ◽  
Jinhuan Wang
Keyword(s):  
Tensor Product ◽  
Spanning Tree ◽  
Minimum Spanning Tree ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
The Matrix ◽  
Product Approach ◽  
Matrix Expression ◽  
Necessary And Sufficient ◽  
Logical Functions

Abstract Using the semi-tensor product of matrices, this paper investigates cycles of graphs with application to cut-edges and the minimum spanning tree, and presents a number of new results and algorithms. Firstly, by defining a characteristic logical vector and using the matrix expression of logical functions, an algebraic description is obtained for cycles of graph, based on which a new necessary and sufficient condition is established to find all cycles for any graph. Secondly, using the necessary and sufficient condition of cycles, two algorithms are established to find all cut-edges and the minimum spanning tree, respectively. Finally, the study of an illustrative example shows that the results/algorithms presented in this paper are effective.

scholarly journals Determination of Organochlorines in Soil of a Suburban Area of São Paulo Brazil

2020 ◽  
Vol 17 (16) ◽  
pp. 5666
Author(s):  
Justine P. R. O. Varca ◽  
Elâine A. J. Martins ◽  
Gustavo H. C. Varca ◽  
Renato L. Romano ◽  
Daniel T. Lebre ◽  
...  
Keyword(s):  
Validation Study ◽  
Heptachlor Epoxide ◽  
Soil Extraction ◽  
Optimum Result ◽  
Industrial Soil ◽  
Technological Advances ◽  
The Matrix ◽  
Contamination Levels ◽  
Almost All ◽  
Cis And Trans

Technological advances have promoted improvements in several science fields, especially related to environmental and analytical areas with the improvement of detection and development of environmentally friendly extraction techniques. This study applied Quick, Easy, Cheap, Effective, Rugged and Safe method (QuEChERS) for soil extraction and assessed its performance through a validation study using samples from the soil of a contaminated area in Caieiras, SP, Brazil. Nine organochlorine pesticides, including the isomers alpha, beta, gamma and delta- hexachlorocyclohexane; cis- and trans-heptachlor epoxide; cis- and trans-chlordane and heptachlor were analyzed by gas chromatography coupled to electron capture detector. The method was validated according to ISO 5725-4 (2020), EURACHEM (2014) and DOQ-CGCRE-008 (2016). The limits of detection and quantification of the method for the nine organochlorines were α-HCH (1.2 and 12.6 µg kg−1), β-HCH (1.7 and 12.0 µg kg−1), γ-HCH (1.5 and 11.6 µg kg−1), δ-HCH (0.8 and 11.6 µg kg−1), heptachlor (1.0 and 10.8 µg kg−1), cis-heptachlor epoxide (0.9 and 11.5 µg kg−1), trans-heptachlor epoxide (0.9 and 11.5 µg kg−1), cis-chlordane (0.4 and 7.9 µg kg−1) and trans-chlordane (0.5 and 10.9 µg kg−1), respectively, and all of them were within the maximum limits recommended by the EPA for the compounds α-HCH (86.0 and 360.0 µg kg−1), β-HCH (300.0 and 1.3 × 103 µg kg−1), γ-HCH (570.0 and 2.5 × 103 µg kg−1), δ-HCH (not defined), heptachlor (130.0 and 630.0 µg kg−1), cis-/trans-heptachlor epoxide (7.0 and 330.0 µg kg−1), cis-/trans-chlordane (1.77 × 103 and 7.7 × 103 µg kg−1) in residential and industrial soil, respectively. Recovery results were between 65% and 105% for almost all compounds, which is an optimum result for multi-residue analytical methods, considering the complexity of the matrix used in the study. Caieiras presented contamination levels of α-HCH in the range of 2.0 to 66.0 µg g−1, which was higher than the limits established by EPA, corresponding to 0.077 µg g−1 for residential soil and 0.27 µg g−1 for industrial soil. According to the validation study, the analytical method proposed was reliable for organochlorine quantification, and the QuEChERS was considered efficient for organochlorine extraction from soil.

scholarly journals Locally adaptive activation functions with slope recovery for deep and physics-informed neural networks

2020 ◽  
Vol 476 (2239) ◽  
pp. 20200334 ◽  
Author(s):  
Ameya D. Jagtap ◽  
Kenji Kawaguchi ◽  
George Em Karniadakis
Keyword(s):  
Neural Networks ◽  
Adaptive Learning ◽  
Gradient Descent ◽  
Activation Function ◽  
Stochastic Gradient Descent ◽  
Activation Functions ◽  
Gradient Descent Algorithm ◽  
Locally Adaptive ◽  
The Matrix ◽  
Base Method

We propose two approaches of locally adaptive activation functions namely, layer-wise and neuron-wise locally adaptive activation functions, which improve the performance of deep and physics-informed neural networks. The local adaptation of activation function is achieved by introducing a scalable parameter in each layer (layer-wise) and for every neuron (neuron-wise) separately, and then optimizing it using a variant of stochastic gradient descent algorithm. In order to further increase the training speed, an activation slope-based slope recovery term is added in the loss function, which further accelerates convergence, thereby reducing the training cost. On the theoretical side, we prove that in the proposed method, the gradient descent algorithms are not attracted to sub-optimal critical points or local minima under practical conditions on the initialization and learning rate, and that the gradient dynamics of the proposed method is not achievable by base methods with any (adaptive) learning rates. We further show that the adaptive activation methods accelerate the convergence by implicitly multiplying conditioning matrices to the gradient of the base method without any explicit computation of the conditioning matrix and the matrix–vector product. The different adaptive activation functions are shown to induce different implicit conditioning matrices. Furthermore, the proposed methods with the slope recovery are shown to accelerate the training process.

scholarly journals Metabolic Responses of Lactobacillus plantarum Strains during Fermentation and Storage of Vegetable and Fruit Juices

2014 ◽  
Vol 80 (7) ◽  
pp. 2206-2215 ◽  
Author(s):  
P. Filannino ◽  
G. Cardinali ◽  
C. G. Rizzello ◽  
S. Buchin ◽  
M. De Angelis ◽  
...  
Keyword(s):  
Amino Acids ◽  
Lactobacillus Plantarum ◽  
Malic Acid ◽  
Gamma Aminobutyric Acid ◽  
Content Type ◽  
Growth And Survival ◽  
The Matrix ◽  
Cell Densities ◽  
Almost All ◽  
And Storage

ABSTRACTStrains ofLactobacillus plantarumwere grown and stored in cherry (ChJ), pineapple (PJ), carrot (CJ), and tomato (TJ) juices to mimic the chemical composition of the respective matrices. Wheat flour hydrolysate (WFH), whey milk (W), and MRS broth were also used as representatives of other ecosystems. The growth rates and cell densities ofL. plantarumstrains during fermentation (24 h at 30°C) and storage (21 days at 4°C) differed only in part, being mainly influenced by the matrix. ChJ and PJ were the most stressful juices for growth and survival. Overall, the growth in juices was negatively correlated with the initial concentration of malic acid and carbohydrates. The consumption of malic acid was noticeable for all juices, but mainly during fermentation and storage of ChJ. Decreases of branched-chain amino acids (BCAA)—with the concomitant increase of their respective branched alcohols—and His and increases of Glu and gamma-aminobutyric acid (GABA) were the main traits of the catabolism of free amino acids (FAA), which were mainly evident under less acidic conditions (CJ and TJ). The increase of Tyr was found only during storage of ChJ. Some aldehydes (e.g., 3-methyl-butanal) were reduced to the corresponding alcohols (e.g., 3-methyl-1-butanol). After both fermentation and storage, acetic acid increased in all fermented juices, which implied the activation of the acetate kinase route. Diacetyl was the ketone found at the highest level, and butyric acid increased in almost all fermented juices. Data were processed through multidimensional statistical analyses. Except for CJ, the juices (mainly ChJ) seemed to induce specific metabolic traits, which differed in part among the strains. This study provided more in-depth knowledge on the metabolic mechanisms of growth and maintenance ofL. plantarumin vegetable and fruit habitats, which also provided helpful information to select the most suitable starters for fermentation of targeted matrices.

scholarly journals The Stability Cone for a Difference Matrix Equation with Two Delays

2011 ◽  
Vol 2011 ◽  
pp. 1-19 ◽  
Author(s):  
S. A. Ivanov ◽  
M. M. Kipnis ◽  
V. V. Malygina
Keyword(s):  
Neural Networks ◽  
Difference Equations ◽  
Matrix Equation ◽  
Geometric Algorithms ◽  
Difference Matrix ◽  
The Matrix ◽  
Two Delays ◽  
Matrix Difference Equations ◽  
The Stability

We provide geometric algorithms for checking the stability of matrix difference equations with two delays such that the matrix is nilpotent. We give examples of how our results can be applied to the study of the stability of neural networks.

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