Search results for: positive matrix factorization

Authors: Kazuyoshi Mori

Abstract:

Examples of parameterization of stabilizing controllers that require only one of right-/left-coprime factorizations are presented. One parameterization method requires one side coprime factorization. The other requires no coprime factorization. The methods are based on the factorization approach so that a number of models can be applied the method we use in this paper.

Keywords: parametrization, coprime factorization, factorization approach, linear systems

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Authors: Ana Serafimovic, Karthik Devarajan

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Non-negative matrix factorization approximates a high dimensional non-negative matrix V as the product of two non-negative matrices, W and H, and allows only additive linear combinations of data, enabling it to learn parts with representations in reality. It has been successfully applied in the analysis and interpretation of high dimensional data arising in neuroscience, computational biology, and natural language processing, to name a few. The objective of this paper is to assess a hybrid algorithm for non-negative matrix factorization with multiplicative updates. The method aims to minimize the symmetric version of Kullback-Leibler divergence known as intrinsic information and assumes that the noise is signal-dependent and that it originates from an arbitrary distribution from the exponential family. It is a generalization of currently available algorithms for Gaussian, Poisson, gamma and inverse Gaussian noise. We demonstrate the potential usefulness of the new generalized algorithm by comparing its performance to the baseline methods which also aim to minimize symmetric divergence measures.

Keywords: non-negative matrix factorization, dimension reduction, clustering, intrinsic information, symmetric information divergence, signal-dependent noise, exponential family, generalized Kullback-Leibler divergence, dual divergence

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Authors: Hironori Karachi, Haruka Yamashita

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Recently, the system of quick response (QR) code is getting popular. Many companies introduce new QR code payment services and the services are competing with each other to increase the number of users. For increasing the number of users, we should grasp the difference of feature of the demographic information, usage information, and value of users between services. In this study, we conduct an analysis of real-world data provided by Nomura Research Institute including the demographic data of users and information of users’ usages of two services; LINE Pay, and PayPay. For analyzing such data and interpret the feature of them, Nonnegative Matrix Factorization (NMF) is widely used; however, in case of the target data, there is a problem of the missing data. EM-algorithm NMF (EMNMF) to complete unknown values for understanding the feature of the given data presented by matrix shape. Moreover, for comparing the result of the NMF analysis of two matrices, there is Discriminant NMF (DNMF) shows the difference of users features between two matrices. In this study, we combine EMNMF and DNMF and also analyze the target data. As the interpretation, we show the difference of the features of users between LINE Pay and Paypay.

Keywords: data science, non-negative matrix factorization, missing data, quality of services

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Authors: Adel Mohsen

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A direct method based on the good Broyden's updates for evaluating the inverse of a nonsingular square matrix of full rank and solving related system of linear algebraic equations is studied. For a matrix A of order n whose LU-decomposition is A = LU, the multiplication count is O (n3). This includes the evaluation of the LU-decompositions of the inverse, the lower triangular decomposition of A as well as a “reduced matrix inverse”. If an explicit value of the inverse is not needed the order reduces to O (n3/2) to compute to compute inv(U) and the reduced inverse. For a symmetric matrix only O (n3/3) operations are required to compute inv(L) and the reduced inverse. An example is presented to demonstrate the capability of using the reduced matrix inverse in treating ill-conditioned systems. Besides the simplicity of Broyden's update, the method provides a mean to exploit the possible sparsity in the matrix and to derive a suitable preconditioner.

Keywords: Broyden's updates, matrix inverse, inverse factorization, solution of linear algebraic equations, ill-conditioned matrices, preconditioning

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Authors: Benyelles Zakaria, Yousfi Djaafar, Karoui Moussa Sofiane

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Agriculture is fundamental and remains an important objective in the Algerian economy, based on traditional techniques and structures, it generally has a purpose of consumption. Collection of agricultural statistics in Algeria is done using traditional methods, which consists of investigating the use of land through survey and field survey. These statistics suffer from problems such as poor data quality, the long delay between collection of their last final availability and high cost compared to their limited use. The objective of this work is to develop a processing chain for a reliable inventory of agricultural land by trying to develop and implement a new method of extracting information. Indeed, this methodology allowed us to combine data from remote sensing and field data to collect statistics on areas of different land. The contribution of remote sensing in the improvement of agricultural statistics, in terms of area, has been studied in the wilaya of Sidi Bel Abbes. It is in this context that we applied a method for extracting information from satellite images. This method is called the non-negative matrix factorization, which does not consider the pixel as a single entity, but will look for components the pixel itself. The results obtained by the application of the MNF were compared with field data and the results obtained by the method of maximum likelihood. We have seen a rapprochement between the most important results of the FMN and those of field data. We believe that this method of extracting information from satellite data leads to interesting results of different types of land uses.

Keywords: blind source separation, hyper-spectral image, non-negative matrix factorization, remote sensing

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Authors: Alfi Y. Zakiyyah, Hanni Garminia, M. Salman, A. N. Irawati

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In the terminology of the hypergraph, there is a relation with the terminology graph. In the theory of graph, the edges connected two vertices. In otherwise, in hypergraph, the edges can connect more than two vertices. There is representation matrix of a graph such as adjacency matrix, Laplacian matrix, and incidence matrix. The adjacency matrix is symmetry matrix so that all eigenvalues is real. This matrix is a nonnegative matrix. The all diagonal entry from adjacency matrix is zero so that the trace is zero. Another representation matrix of the graph is the Laplacian matrix. Laplacian matrix is symmetry matrix and semidefinite positive so that all eigenvalues are real and non-negative. According to the spectral study in the graph, some that result is generalized to hypergraph. A hypergraph can be represented by a matrix such as adjacency, incidence, and Laplacian matrix. Throughout for this term, we use Laplacian matrix to represent a complete tripartite hypergraph. The aim from this research is to determine second smallest eigenvalues from this matrix and find a relation this eigenvalue with the connectivity of that hypergraph.

Keywords: connectivity, graph, hypergraph, Laplacian matrix

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Authors: Ogundele Lasun Tunde, Ayeku Oluwagbemiga Patrick

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Heavy metals are released into the sediments in aquatic environment from both natural and anthropogenic sources and they are considered as worldwide issue due to their deleterious ecological risks and food chain disruption. In this study, sediments samples were collected at three major sites (Awoye, Abereke and Ayetoro) along Ondo coastal area using VanVeen grab sampler. The concentrations of As, Cd, Cr, Cu, Fe, Mn, Ni, Pb, V and Zn were determined by employing Atomic Absorption Spectroscopy (AAS). The combined concentrations data were subjected to Positive Matrix Factorization (PMF) receptor approach for source identification and apportionment. The probable risks that might be posed by heavy metals in the sediment were estimated by potential and integrated ecological risks indices. Among the measured heavy metals, Fe had the average concentrations of 20.38 ± 2.86, 23.56 ± 4.16 and 25.32 ± 4.83 lg/g at Abereke, Awoye and Ayetoro sites, respectively. The PMF resulted in identification of four sources of heavy metals in the sediments. The resolved sources and their percentage contributions were oil exploration (39%), industrial waste/sludge (35%), detrital process (18%) and Mn-sources (8%). Oil exploration activities and industrial wastes are the major sources that contribute heavy metals into the coastal sediments. The major pollutants that posed ecological risks to the local aquatic ecosystem are As, Pb, Cr and Cd (40 B Ei ≤ 80) classifying the sites as moderate risk. The integrate risks values of Awoye, Abereke and Ayetoro are 231.2, 234.0 and 236.4, respectively suggesting that the study areas had a moderate ecological risk. The study showed the suitability of PMF receptor model for source identification of heavy metals in the sediments. Also, the intensive anthropogenic activities and natural sources could largely discharge heavy metals into the study area, which may increase the heavy metal contents of the sediments and further contribute to the associated ecological risk, thus affecting the local aquatic ecosystem.

Keywords: positive matrix factorization, sediments, heavy metals, sources, ecological risks

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Authors: Yixun Shi

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Many interior point methods for convex programming solve an (n+m)x(n+m)linear system in each iteration. Many implementations solve this system in each iteration by considering an equivalent mXm system (4) as listed in the paper, and thus the job is reduced into solving the system (4). However, the system(4) has to be solved exactly since otherwise the error would be entirely passed onto the last m equations of the original system. Often the Cholesky factorization is computed to obtain the exact solution of (4). One Cholesky factorization is to be done in every iteration, resulting in higher computational costs. In this paper, two iterative methods for solving linear systems using vector division are combined together and embedded into interior point methods. Instead of computing one Cholesky factorization in each iteration, it requires only one Cholesky factorization in the entire procedure, thus significantly reduces the amount of computation needed for solving the problem. Based on that, a hybrid algorithm for solving convex programming problems is proposed.

Keywords: convex programming, interior point method, linear systems, vector division

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Authors: Shih Yu Pan, Pao Chen Hung, Chuan Yao Lin, Charles C.-K. Chou, Yu Chi Lin, Kai Hsien Chi

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This study analyzed 16 atmospheric PAHs species which were controlled by USEPA and IARC. To measure the concentration of PAHs, four rural sampling sites and two urban sampling sites were selected in Central Taiwan during spring and summer. In central Taiwan, the rural sampling stations were located in the downstream of Da-An River, Da-Jang River, Wu River and Chuo-shui River. On the other hand, the urban sampling sites were located in Taichung district and close to the roadside. Ambient air samples of both vapor phase and particle phase of PAHs compounds were collected using high volume sampling trains (Analitica). The sampling media were polyurethane foam (PUF) with XAD2 and quartz fiber filters. Diagnostic ratio, Principal component analysis (PCA), Positive Matrix Factorization (PMF) models were used to evaluate the apportionment of PAHs in the atmosphere and speculate the relative contribution of various emission sources. Because of the high temperature and low wind speed, high PAHs concentration in the atmosphere was observed. The total PAHs concentration, especially in vapor phase, had significant change during summer. During the sampling periods the total PAHs concentration of atmospheric at four rural and two urban sampling sites in spring and summer were 3.70±0.40 ng/m3,3.40±0.63 ng/m3,5.22±1.24 ng/m3,7.23±0.37 ng/m3,7.46±2.36 ng/m3,6.21±0.55 ng/m3　; 15.0± 0.14 ng/m3,18.8±8.05 ng/m3,20.2±8.58 ng/m3,16.1±3.75 ng/m3,29.8±10.4 ng/m3,35.3±11.8 ng/m3, respectively. In order to identify PAHs sources, we used diagnostic ratio to classify the emission sources. The potential sources were diesel combustion and gasoline combustion in spring and summer, respectively. According to the principal component analysis (PCA), the PC1 and PC2 had 23.8%, 20.4% variance and 21.3%, 17.1% variance in spring and summer, respectively. Especially high molecular weight PAHs (BaP, IND, BghiP, Flu, Phe, Flt, Pyr) were dominated in spring when low molecular weight PAHs (AcPy, Ant, Acp, Flu) because of the dominating high temperatures were dominated in the summer. Analysis by using PMF model found the sources of PAHs in spring were stationary sources (34%), vehicle emissions (24%), coal combustion (23%) and petrochemical fuel gas (19%), while in summer the emission sources were petrochemical fuel gas (34%), the natural environment of volatile organic compounds (29%), coal combustion (19%) and stationary sources (18%).

Keywords: PAHs, source identification, diagnostic ratio, principal component analysis, positive matrix factorization

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Authors: Moulana Mohammed

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Topic models are widely used in building clusters of documents for more than a decade, yet problems occurring in choosing optimal number of topics. The main problem is the lack of a stable metric of the quality of topics obtained during the construction of topic models. The authors analyzed from previous works, most of the models used in determining the number of topics are non-parametric and quality of topics determined by using perplexity and coherence measures and concluded that they are not applicable in solving this problem. In this paper, we used the parametric method, which is an extension of the traditional topic model with visual access tendency for visualization of the number of topics (clusters) to complement clustering and to choose optimal number of topics based on results of cluster validity indices. Developed hybrid topic models are demonstrated with different Twitter datasets on various topics in obtaining the optimal number of topics and in measuring the quality of clusters. The experimental results showed that the Visual Non-negative Matrix Factorization (VNMF) topic model performs well in determining the optimal number of topics with interactive visualization and in performance measure of the quality of clusters with validity indices.

Keywords: interactive visualization, visual mon-negative matrix factorization model, optimal number of topics, cluster validity indices, Twitter data clustering

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Authors: Caihong Sun, Xizi Zhang

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Rating prediction is an important problem for recommender systems. The task is to predict the rating for an item that a user would give. Most of the existing algorithms for the task ignore the effect of negative ratings rated by users on items, but the negative ratings have a significant impact on users’ purchasing decisions in practice. In this paper, we present a rating prediction algorithm based on factorization machines that consider the effect of negative ratings inspired by Loss Aversion theory. The aim of this paper is to develop a concave and a convex negative disgust function to evaluate the negative ratings respectively. Experiments are conducted on MovieLens dataset. The experimental results demonstrate the effectiveness of the proposed methods by comparing with other four the state-of-the-art approaches. The negative ratings showed much importance in the accuracy of ratings predictions.

Keywords: factorization machines, feature engineering, negative ratings, recommendation systems

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Authors: Martins Olatunbosun Babatunde, Muhammed Bashir Muazu, Emmanuel Adewale Adedokun

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This paper presents the development of a double-loop trajectory-tracking controller for the ball and plate system (BPS) using the Normalized Right Coprime Factorization (NRCF) scheme.The Linear Algebraic (LA) method is used to design the inner loop required to stabilize the ball, while H-infinity NRCF method, that involved the lead-lag compensator design approach, is used to develop the outer loop that controls the plate. Simulation results show that the plate was stabilized at 0.2989 seconds and the ball was able to settle after 0.9646 seconds, with a trajectory tracking error of 0.0036. This shows that the controller has good adaptability and robustness.

Keywords: ball and plate system, normalized right coprime factorization, linear algebraic method, compensator, controller, tracking.

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Authors: Linda Smail, Zineb Azouz

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Given a Bayesian network relative to a set I of discrete random variables, we are interested in computing the probability distribution P(S) where S is a subset of I. The general idea is to write the expression of P(S) in the form of a product of factors where each factor is easy to compute. More importantly, it will be very useful to give an interpretation of each of the factors in terms of conditional probabilities. This paper considers a semantic interpretation of the factors involved in computing marginal probabilities in Bayesian networks. Establishing such a semantic interpretations is indeed interesting and relevant in the case of large Bayesian networks.

Keywords: Bayesian networks, D-Separation, level two Bayesian networks, factorization of computation

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Authors: Bharat Singh Om Prakash Vyas

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Now a day’s applications deal with High Dimensional Data have tremendously used in the popular areas. To tackle with such kind of data various approached has been developed by researchers in the last few decades. To tackle with such kind of data various approached has been developed by researchers in the last few decades. One of the problems with the NMF approaches, its randomized valued could not provide absolute optimization in limited iteration, but having local optimization. Due to this, we have proposed a new approach that considers the initial values of the decomposition to tackle the issues of computationally expensive. We have devised an algorithm for initializing the values of the decomposed matrix based on the PSO (Particle Swarm Optimization). Through the experimental result, we will show the proposed method converse very fast in comparison to other row rank approximation like simple NMF multiplicative, and ACLS techniques.

Keywords: ALS, NMF, high dimensional data, RMSE

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Authors: Kazuyoshi Mori

Abstract:

In this paper, we consider the parametrization of Anantharam’s model within the framework of the factorization approach. In the parametrization, we investigate the number of required parameters of Anantharam’s model. We consider single-input single-output systems in this paper. By the investigation, we find three cases that are (1) there exist plants which require only one parameter and (2) two parameters, and (3) the number of parameters is at most three.

Keywords: linear systems, parametrization, coprime factorization, number of parameters

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Authors: Ric Joseph R. Murillo, Edna N. Gueco, Dennis I. Merino

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Let F be C or R, where C and R are the set of complex numbers and real numbers, respectively, and n be a natural number. An n-by-n matrix A over the field F is called an α-involutory matrix or an α-involution if there exists an α in the field such that the square of the matrix is equal to αI, where I is the n-by-n identity matrix. If α is a complex number or a nonnegative real number, then an n-by-n matrix A over the field F can be written as a sum of n-by-n α-involutory matrices over the field F if and only if the trace of that matrix is an integral multiple of the square root of α. Meanwhile, if α is a negative real number, then a 2n-by-2n matrix A over R can be written as a sum of 2n-by-2n α-involutory matrices over R if and only the trace of the matrix is zero. Some other properties of α-involutory matrices are also determined

Keywords: α-involutory Matrices, sum of α-involutory Matrices, Trace, Matrix Theory

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Authors: Mojtaba Hakimi-Moghaddam

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Positive realness as the most important property of driving point impedance of passive electrical networks appears in the control systems stability theory in 1960’s. There are three important subsets of positive real (PR) systems are introduced by researchers, that is, loos-less positive real (LLPR) systems, weakly strictly positive real (WSPR) systems and strictly positive real (SPR) systems. In this paper, definitions, properties, lemmas, and theorems related to family of positive real systems are summarized. Properties in both frequency domain and state space representation of system are explained. Also, several illustrative examples are presented.

Keywords: real rational matrix transfer functions, positive realness property, strictly positive realness property, Hermitian form asymptotic property, pole-zero properties

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Authors: Soyon Kim, Edward Kim

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In order to retrieve information from the massive stream of songs in the music industry, music search by title, lyrics, artist, mood, and genre has become more important. Despite the subjectivity and controversy over the definition of music genres across different nations and cultures, automatic genre classification systems that facilitate the process of music categorization have been developed. Manual genre selection by music producers is being provided as statistical data for designing automatic genre classification systems. In this paper, an automatic music genre classification system utilizing non-negative matrix factorization (NMF) is proposed. Short-term characteristics of the music signal can be captured based on the timbre features such as mel-frequency cepstral coefficient (MFCC), decorrelated filter bank (DFB), octave-based spectral contrast (OSC), and octave band sum (OBS). Long-term time-varying characteristics of the music signal can be summarized with (1) the statistical features such as mean, variance, minimum, and maximum of the timbre features and (2) the modulation spectrum features such as spectral flatness measure, spectral crest measure, spectral peak, spectral valley, and spectral contrast of the timbre features. Not only these conventional basic long-term feature vectors, but also NMF based feature vectors are proposed to be used together for genre classification. In the training stage, NMF basis vectors were extracted for each genre class. The NMF features were calculated in the log spectral magnitude domain (NMF-LSM) as well as in the basic feature vector domain (NMF-BFV). For NMF-LSM, an entire full band spectrum was used. However, for NMF-BFV, only low band spectrum was used since high frequency modulation spectrum of the basic feature vectors did not contain important information for genre classification. In the test stage, using the set of pre-trained NMF basis vectors, the genre classification system extracted the NMF weighting values of each genre as the NMF feature vectors. A support vector machine (SVM) was used as a classifier. The GTZAN multi-genre music database was used for training and testing. It is composed of 10 genres and 100 songs for each genre. To increase the reliability of the experiments, 10-fold cross validation was used. For a given input song, an extracted NMF-LSM feature vector was composed of 10 weighting values that corresponded to the classification probabilities for 10 genres. An NMF-BFV feature vector also had a dimensionality of 10. Combined with the basic long-term features such as statistical features and modulation spectrum features, the NMF features provided the increased accuracy with a slight increase in feature dimensionality. The conventional basic features by themselves yielded 84.0% accuracy, but the basic features with NMF-LSM and NMF-BFV provided 85.1% and 84.2% accuracy, respectively. The basic features required dimensionality of 460, but NMF-LSM and NMF-BFV required dimensionalities of 10 and 10, respectively. Combining the basic features, NMF-LSM and NMF-BFV together with the SVM with a radial basis function (RBF) kernel produced the significantly higher classification accuracy of 88.3% with a feature dimensionality of 480.

Keywords: mel-frequency cepstral coefficient (MFCC), music genre classification, non-negative matrix factorization (NMF), support vector machine (SVM)

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Authors: Xiaoqian Cheng, Jon Kleppe, Ole Torsæter

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The properties of rocks have effects on efficiency of surfactant. One objective of this study is to analyze the effects of rock properties (permeability, porosity, initial water saturation) on surfactant spontaneous imbibition at laboratory scale. The other objective is to evaluate existing upscaling methods and establish a modified upscaling method. A core is put in a container that is full of surfactant solution. Assume there is no space between the bottom of the core and the container. The core is modelled as a cuboid matrix with a length of 3.5 cm, a width of 3.5 cm, and a height of 5 cm. The initial matrix, brine and oil properties are set as the properties of Ekofisk Field. The simulation results of matrix permeability show that the oil recovery rate has a strong positive linear relationship with matrix permeability. Higher oil recovery is obtained from the matrix with higher permeability. One existing upscaling method is verified by this model. The study on matrix porosity shows that the relationship between oil recovery rate and matrix porosity is a negative power function. However, the relationship between ultimate oil recovery and matrix porosity is a positive power function. The initial water saturation of matrix has negative linear relationships with ultimate oil recovery and enhanced oil recovery. However, the relationship between oil recovery and initial water saturation is more complicated with the imbibition time because of the transition of dominating force from capillary force to gravity force. Modified upscaling methods are established. The work here could be used as a reference for the surfactant application in fractured reservoirs. And the description of the relationships between properties of matrix and the oil recovery rate and ultimate oil recovery helps to improve upscaling methods.

Keywords: initial water saturation, permeability, porosity, surfactant EOR

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Authors: Elena Barbaro, Elena Gregoris, Rossano Piazza, Boris Mifka, Tatjana Ivošević, Ivo Orlić, Ana Alebić-Juretić, Andrea Gambaro, Daniele Contini

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The aim of the POSEIDON project is to quantify the relative contribution of maritime traffic and harbor activities to atmospheric pollutants concentration in four port-cities of the Adriatic Sea. This study focuses on the harbors of Venice and Rijeka. In order to investigate the main pollution sources, emission inventories were used as input for receptor models: PMF (positive matrix factorization) and PCA (principal components analysis); moreover source identification was also conducted using PAHs diagnostic ratios. The ship traffic impact was quantified: i) on gaseous and particulate PAHs, collected using a new method which consisted in a double simultaneous sampling, in different wind sectors; ii) applying PMF to data of metals, PAHs and ions in PM10; iii) using the vanadium concentration according to the Agrawal methodology.

Keywords: ship traffic, PMF, harbor, POSEIDON

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Authors: M. Hadji, N. Chiker, Y. Hadji, A. Haddad

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In this paper, we report for the first time on the synthesis and characterization of novel MAX phases (Ti3SiC2, Ti2AlC) reinforced Ni-matrix and Ti2AlC reinforced Al-matrix. The stability of MAX phases in Al-matrix and Ni-matrix at a temperature of 985°C has been investigated. All the composites were cold pressed and sintered at a temperature of 985°C for 20min in H2 environment, except (Ni/Ti3SiC2) who was sintered at 1100°C for 1h.Microstructure analysis by scanning electron microscopy and phase analysis by X-Ray diffraction confirmed that there was minimal interfacial reaction between MAX particles and Ni, thus Al/MAX samples shown that MAX phases was totally decomposed at 985°C.The Addition of MAX enhanced the Al-matrix and Ni-matrix.

Keywords: MAX phase, microstructures, composites, hardness, SEM

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Authors: Renata Masarova, Bohuslava Juhasova, Martin Juhas, Zuzana Sutova

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In dynamic system theory a mathematical model is often used to describe their properties. In order to find a transfer matrix of a dynamic system we need to calculate an inverse matrix. The paper contains the fusion of the classical theory and the procedures used in the theory of automated control for calculating the inverse matrix. The final part of the paper models the given problem by the Matlab.

Keywords: dynamic system, transfer matrix, inverse matrix, modeling

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Authors: Kirill Trapezon, Alexandr Trapezon

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A problem is formulated for the natural oscillations of a circular plate of linearly variable thickness on the basis of the symmetry method. The equations of natural frequencies and forms for a plate are obtained, providing that it is rigidly fixed along the inner contour. The first three eigenfrequencies are calculated, and the eigenmodes of the oscillations of the acoustic element are constructed. An algorithm for applying the symmetry method and the factorization method for solving problems in the theory of oscillations for plates of variable thickness is shown. The effectiveness of the approach is demonstrated on the basis of comparison of known results and those obtained in the article. It is shown that the results are more accurate and reliable.

Keywords: vibrations, plate, method of symmetries, differential equation, factorization, approximation

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Authors: Danny Manuel Calvo Velasco, Robert Sanchez Cano

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By using the transference matrix formalism, in this work, it is presented the study of the optical properties of the 1D graded structure, constructed by multiple bi-layers of dielectric and air, considering a redistribution of the material lengths following an arithmetic progression as a function of two parameters. It is presented a factorization for the transference matrices for the graded structure, which allows the interpretation of their optical properties in terms of the properties of simpler structures. It is shown that the graded structure presents new transmission peaks, which can be controlled by the parameter values located in frequencies for which a periodic system has a photonic bandgap. This result is extended to the case of a photonic crystal for which the unitary cell is the proposed graded structure, showing new transmission bands which are due to the multiple new sub-structures present in the system. Also, for the TE polarization, it is observed transmission bands' low frequencies which present low variation of its width and position with the incidence angle. It is expected that these results could guide a route in the design of new photonic devices.

Keywords: graded, material redistribution, photonic system, transference matrix

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Authors: Boris Melnikov, Dmitrii Chaikovskii, Elena Melnikova

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The traveling salesman problem (TSP) is a well-known optimization problem that seeks to find the shortest possible route that visits a set of points and returns to the starting point. In this paper, we apply some heuristics of the TSP for the task of restoring the DNA matrix. This restoration problem is often considered in biocybernetics. For it, we must recover the matrix of distances between DNA sequences if not all the elements of the matrix under consideration are known at the input. We consider the possibility of using this method in the testing of distance calculation algorithms between a pair of DNAs to restore the partially filled matrix.

Keywords: optimization problems, DNA matrix, partially filled matrix, traveling salesman problem, heuristic algorithms

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Authors: Hussaini Doko Ibrahim, Hamilton Cyprian Chinwenyi, Henrietta Nkem Ude

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In this paper, efforts were made to examine and compare the algorithmic iterative solutions of the conjugate gradient method as against other methods such as Gauss-Seidel and Jacobi approaches for solving systems of linear equations of the form Ax=b, where A is a real n×n symmetric and positive definite matrix. We performed algorithmic iterative steps and obtained analytical solutions of a typical 3×3 symmetric and positive definite matrix using the three methods described in this paper (Gauss-Seidel, Jacobi, and conjugate gradient methods), respectively. From the results obtained, we discovered that the conjugate gradient method converges faster to exact solutions in fewer iterative steps than the two other methods, which took many iterations, much time, and kept tending to the exact solutions.

Keywords: conjugate gradient, linear equations, symmetric and positive definite matrix, gauss-seidel, Jacobi, algorithm

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Authors: Kourosh Modarresi

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The Netflix problem has brought the topic of “Recommendation Systems” into the mainstream of computer science, mathematics, and statistics. Though much progress has been made, the available algorithms do not obtain satisfactory results. The success of these algorithms is rarely above 5%. This work is based on the belief that the main challenge is to come up with “scalable personalization” models. This paper uses an adaptive regularization of inverse singular value decomposition (SVD) that applies adaptive penalization on the singular vectors. The results show far better matching for recommender systems when compared to the ones from the state of the art models in the industry.

Keywords: convex optimization, LASSO, regression, recommender systems, singular value decomposition, low rank approximation

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Authors: Jiao Sun, Li Pan, Shijun Liu

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Recommender systems have been widely used in contemporary industry, and plenty of work has been done in this field to help users to identify items of interest. Collaborative Filtering (CF, for short) algorithm is an important technology in recommender systems. However, less work has been done in automobile recommendation system with the sharp increase of the amount of automobiles. What’s more, the computational speed is a major weakness for collaborative filtering technology. Therefore, using MapReduce framework to optimize the CF algorithm is a vital solution to this performance problem. In this paper, we present a recommendation of the users’ comment on industrial automobiles with various properties based on real world industrial datasets of user-automobile comment data collection, and provide recommendation for automobile providers and help them predict users’ comment on automobiles with new-coming property. Firstly, we solve the sparseness of matrix using previous construction of score matrix. Secondly, we solve the data normalization problem by removing dimensional effects from the raw data of automobiles, where different dimensions of automobile properties bring great error to the calculation of CF. Finally, we use the MapReduce framework to optimize the CF algorithm, and the computational speed has been improved times. UV decomposition used in this paper is an often used matrix factorization technology in CF algorithm, without calculating the interpolation weight of neighbors, which will be more convenient in industry.

Keywords: collaborative filtering, recommendation, data normalization, mapreduce

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Authors: Malika Yaici, Kamel Hariche

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In control engineering, systems described by matrix fractions are studied through properties of block roots, also called solvents. These solvents are usually dealt with in a block Vandermonde matrix form. Inverses and determinants of Vandermonde matrices and block Vandermonde matrices are used in solving problems of numerical analysis in many domains but require costly computations. Even though Vandermonde matrices are well known and method to compute inverse and determinants are many and, generally, based on interpolation techniques, methods to compute the inverse and determinant of a block Vandermonde matrix have not been well studied. In this paper, some properties of these matrices and iterative algorithms to compute the determinant and the inverse of a block Vandermonde matrix are given. These methods are deducted from the partitioned matrix inversion and determinant computing methods. Due to their great size, parallelization may be a solution to reduce the computations cost, so a parallelization of these algorithms is proposed and validated by a comparison using algorithmic complexity.

Keywords: block vandermonde matrix, solvents, matrix polynomial, matrix inverse, matrix determinant, parallelization

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Authors: Kazuyoshi Mori

Abstract:

In this paper, we consider the parametrization of the discrete-time systems without the unit-delay element within the framework of the factorization approach. In the parametrization, we investigate the number of required parameters. We consider single-input single-output systems in this paper. By the investigation, we find, on the discrete-time systems without the unit-delay element, three cases that are (1) there exist plants which require only one parameter and (2) two parameters, and (3) the number of parameters is at most three.

Keywords: factorization approach, discrete-time system, parameterization of stabilizing controllers, system without unit-delay

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