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Comparative Study of the Adomian Decomposition Method and Alternating Direction Implicit (ADI) for the Resolution of the Problems of Advection-Diffusion-Reaction

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Journal of Applied Mathematics and Physics 2018年第9期6卷 1937-1950页

作者： André Bitsindou Joseph Bonazebi-Yindoula Gabriel Bissanga Laboratory of Numerical Analysis Computer Science and Applications University Marien NGOUABI Brazzaville Congo

In this paper, we use the Adomian decomposition method (ADM), the finite differences method and the Alternating Direction Implicit method to estimate the advantages and the weakness of the above methods. For it, we make a numerical simulation of the different solutions constructed with these methods and compare the error investigated case.

关键词： Adomian Decomposition Method Finite Differences Method Advection-Diffusion-Reaction Equations

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Acute Genital Peritonitis in Brazzaville, Congo

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Surgical science 2019年第10期10卷 368-376页

作者： Massamba Miabaou Didace Mbongo Jean Alfred Note Madzélé Murielle Motoula Latou Noé Itoua Clautaire Massamba Alphonse Digestive Surgery Department Brazzaville University Hospital Brazzaville Congo Gynecology-Obstetrics Department Brazzaville University Hospital Brazzaville Congo Laboratory of Numerical Analysis Computer Science and Applications (LANIA) Faculty of Sciences and Technology Marien Ngouabi University Brazzaville Congo.

Genital peritonitis is rare in daily surgical practice in Congo-Brazzaville. Clandestine abortions are incriminated. The purpose of the study is to analyze the epidemiological, etiological, diagnostic and therapeutic aspects of genital peritonitis. A retrospective and case series study was realized in departments of Digestive Surgery and Gynecology-Obstetrics of the University Hospital of Brazzaville. The inclusion criteria for the diagnosis of peritonitis were abdominal pain, fever, transit disturbances and signs of peritoneal irritation. The parameters studied were: age, etiological circumstances, anatomical lesions, type of surgical treatment and evolution. During the study period (July 1, 2015-December 31, 2017), 306 patients were admitted to both departments for acute generalized peritonitis. Among them, a genital cause was incriminated in 18 (5.9%) patients. The mean age was 27.6 ± 3.1 years. At the parity and gestational level, 93% of patients had at least two pregnancies, but not more than the second trimester. In addition, 50% of the patients had an induced miscarriage, due to uterine and intestinal lesions. Induced miscarriages accounted for half of etiological circumstances. Physical examination of the abdomen revealed abdominal contracture in 61.1% of cases. Main visceral lesions were uterine perforation (55.5%) followed by rupture of tubo-ovarian abscess (38.9%). The operative follow-up was simple in 83.33% of cases. In conclusion, genital peritonitis remains unfrequented. Median laparotomy has been the main therapeutic approach in our context where emergency laparoscopic surgery is not yet common.

关键词： Peritonitis Abortion Uterine Perforation

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Changes Induced by Physical Activity, Weight Loss and Calorie Restriction in Body Composition, Lipoproteins and Functional Capacity in Obese Congolese Women

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Health 2020年第6期12卷 548-571页

作者： Moulongo Jean Georges André Makosso Vheiye Georges Eouani Max Lévy Eméry Mouanda Richard Le Savant Ndalla Mathias Cyriaque Packa Tchissambou Bernard Massamba Alphonse Laboratory of Sports Biosciences Higher Institute of Physical Education and Sports Marien NGOUABI University Brazzaville Congo Unit of Nutritional Science and Metabolism Higher Institute of Physical Education and Sports Marien NGOUABI University Brazzaville Congo Department of Gynecology & Obstetrics Loandjili Hospital Pointe-Noire (Congo) and Faculty of Health Sciences Marien NGOUABI University Brazzaville Congo Clinical Psychology Research Division Marien NGOUABI University Brazzaville Congo Biomedical Analyses Center Makelekele Brazzaville Congo Laboratory of Numerical Analysis Computer Science and Applications Faculty of Sciences and Technology Marien NGOUABI University Brazzaville Congo

Background. The effects of physical exercises combined with a low-calorie diet on weight loss, body composition, lipoproteins profile, and physical fitness had been well described. However, Central Africa’s studies investigating these kinds of diets and exercise regimens are lacking. Objective. To investigate the effects of adding 14-weeks exercises to a hypocaloric diet on changes in body composition, lipoproteins concentrations, and physical capacities in obese Congolese women. Population and Methods. In total, 34 obese women aged 30 - 39 years (mean age: 33.7 ± 2.4 years) assigned to 14-weeks training program and low energy ketogenic diet. Body composition was assessed using classic methods and impedancemetry. Fasting plasma glucose (FPG) and fasting serum insulin were assessing using enzymatic colorimetric and radioim-munoradiometric methods. HOMA-IR and lipoproteins concentrations were assessed using standardized laboratory methods. VO2peak was measured on a treadmill during a progressive exercise test. Speed, cadence and stride length were measured along the 10-m level walkway. Muscular endurance was measured using the tests of sit-up and inflections-extensions of elbows. All the variables of the study were assessed at the beginning, in the 7-weeks, and in the 14-weeks of training methods. Results. Declines in body weight (16%), percent fat (12.1%), fat weight (26.4%), abdominal fat (34.2%), and waist circumference (10.4%) were found. A significant decrease in FPG (13%), fasting serum insulin (60.9%), HOMA-IR (64.7%), total cholesterol (12.2%), LDL-cholesterol (20.3%), triglycerides (92.8%), and VLDL-triglycerides (17.5%) was shown. In contrast, significant increase in HDL-cholesterol (27.13%) was found. The peak oxygen consumption VO2peak relative to body weight improved more in the 14-weeks training program (13.4%). Obese women exhibited higher values in the 14-weeks training program for speed gait (16.5%), cadence (9.1%), and stride length (15.7%) during no

关键词： Lipoproteins Body Composition Calorie Restriction Physical Exercise Obese Congolese Women

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Evaluating associative classification algorithms for Big Data

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Big Data Analytics 2019年第1期4卷 1-27页

作者： Padillo, Francisco Luna, José María Ventura, Sebastián Department of Computer Science and Numerical Analysis University of Cordoba Cordoba Spain Knowledge Discovery and Intelligent Systems in Biomedicine Laboratory Maimonides Biomedical Research Institute of Cordoba Cordoba Spain Faculty of Computing and Information Technology King Abdulaziz University Jeddah Saudi Arabia

Associative Classification, a combination of two important and different fields (classification and association rule mining), aims at building accurate and interpretable classifiers by means of association rules. A major problem in this field is that existing proposals do not scale well when Big Data are considered. In this regard, the aim of this work is to propose adaptations of well-known associative classification algorithms (CBA and CPAR) by considering different Big Data platforms (Spark and Flink). An experimental study has been performed on 40 datasets (30 classical datasets and 10 Big Data datasets). Classical data have been used to find which algorithms perform better sequentially. Big Data dataset have been used to prove the scalability of Big Data proposals. Results have been analyzed by means of non-parametric tests. Results proved that CBA-Spark and CBA-Flink obtained interpretable classifiers but it was more time consuming than CPAR-Spark or CPAR-Flink. In this study, it was demonstrated that the proposals were able to run on Big Data (file sizes up to 200 GBytes). The analysis of different quality metrics revealed that no statistical difference can be found for these two approaches. Finally, three different metrics (speed-up, scale-up and size-up) have also been analyzed to demonstrate that the proposals scale really well on Big Data. The experimental study has revealed that sequential algorithms cannot be used on large quantities of data and approaches such as CBA-Spark, CBA-Flink, CPAR-Spark or CPAR-Flink are required. CBA has proved to be very useful when the main goal is to obtain highly interpretable results. However, when the runtime has to be minimized CPAR should be used. No statistical difference could be found between the two proposals in terms of quality of the results except for the interpretability of the final classifiers, CBA being statistically better than CPAR.

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Feasibility of Acousto-Electric Tomography

arXiv

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arXiv 2019年

作者： Jensen, Bjørn Kirkeby, Adrian Knudsen, Kim Faculty of Information Technology University of Jyväskylä Finland Department of Numerical Analysis and Scientific Computing Simula Research Laboratory Oslo Norway Department of Applied Mathematics and Computer Science Technical University of Denmark Kgs Lyngby Denmark

In acousto-electric tomography the goal is to reconstruct the electric conductivity in a domain from electrostatic boundary measurements of corresponding currents and voltages, while the domain is penetrated by a time-dependent acoustic wave. In this paper we provide an in-silico model of the entire coupled physics scenario and perform computational experiments. We propose a complete inversion framework for acousto-electric tomography in two steps: First the interior power density is obtained from boundary measurements by solving a linear inverse problem;second the interior conductivity is reconstructed from the power density by solving a non-linear, fairly well-posed problem. We develop a numerical model with realistically chosen parameters inspired by medical imaging. The critical signal strength is analyzed and the omnipresent Johnson-Nyquist noise is estimated. With this setup we perform numerical experiments on synthetic data with noise and demonstrate the feasibility of the method. However, our findings are a mix of positive and negative. We reconstruct features even under severe noise conditions, but we also find that the required Signal-to-Noise ratio yet remains infeasible for practical *** Codes 35R30, 65N21 Copyright © 2019, The Authors. All rights reserved.

关键词： Inverse problems

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Modeling eye gaze velocity trajectories using GANs with spectral loss for enhanced fidelity

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Scientific reports 2025年第1期15卷 19929页

作者： Shailendra Bhandari Pedro Lencastre Rujeena Mathema Alexander Szorkovszky Anis Yazidi Pedro G Lind Department of Computer Science OsloMet - Oslo Metropolitan University P.O. Box 4 St. Olavs plass N-0130 Oslo Norway. shailendra.bhandari@oslomet.no. OsloMet Artificial Intelligence Lab Pilestredet 52 N-0166 Oslo Norway. shailendra.bhandari@oslomet.no. Department of Computer Science OsloMet - Oslo Metropolitan University P.O. Box 4 St. Olavs plass N-0130 Oslo Norway. OsloMet Artificial Intelligence Lab Pilestredet 52 N-0166 Oslo Norway. Simula Research Laboratory Numerical Analysis and Scientific Computing Oslo 0164 Norway. Department of Informatics University of Oslo Oslo Norway. School of Economics Innovation and Technology Kristiania University of Applied Sciences Kirkegata 24-26 N-0153 Oslo Norway.

Accurate modeling of eye gaze dynamics is essential for advancement in human-computer interaction, neurological diagnostics, and cognitive research. Traditional generative models like Markov models often fail to capture the complex temporal dependencies and distributional nuance inherent in eye gaze trajectories data. This study introduces a Generative Adversarial Network (GAN) framework employing Long Short-Term Memory (LSTM) and Convolutional Neural Network (CNN) generators and discriminators to generate high-fidelity synthetic eye gaze velocity trajectories. We conducted a comprehensive evaluation of four GAN architectures: CNN-CNN, LSTM-CNN, CNN-LSTM, and LSTM-LSTM-trained under two conditions: using only adversarial loss ([Formula: see text]) and using a weighted combination of adversarial and spectral losses. Our findings reveal that the LSTM-CNN architecture trained with this new loss function exhibits the closest alignment to the real data distribution, effectively capturing both the distribution tails and the intricate temporal dependencies. The inclusion of spectral regularization significantly enhances the GANs' ability to replicate the spectral characteristics of eye gaze movements, leading to a more stable learning process and improved data fidelity. Comparative analysis with a Hidden Markov Model (HMM) optimized to four hidden states further highlights the advantages of the LSTM-CNN GAN. Statistical metrics show that the HMM-generated data significantly diverges from the real data in terms of mean, standard deviation, skewness, and kurtosis. In contrast, the LSTM-CNN model closely matches the real data across these statistics, affirming its capacity to model the complexity of eye gaze dynamics effectively. These results position the spectrally regularized LSTM-CNN GAN as a robust tool for generating synthetic eye gaze velocity data with high fidelity. Its ability to accurately replicate both the distributional and temporal properties of real data holds

关键词： Eye-gaze trajectories Generative Adversarial Networks Hidden Markov Models Stochastic Processes

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A mixture of experts model for predicting persistent weather patterns

arXiv

引用

arXiv 2019年

作者： Pérez-Ortiz, M. Gutiérrez, P.A. Tino, P. Casanova-Mateo, C. Salcedo-Sanz, S. Computer Laboratory University of Cambridge United Kingdom Dpt. of Computer Science and Numerical Analysis University of Córdoba Spain School of Computer Science University of Birmingham United Kingdom Department of Civil Engineering: Construction Infrastructure and Transport Universidad Politécnica de Madrid Madrid Spain Department of Signal Processing and Communications University of Alcalá Spain

Weather and atmospheric patterns are often persistent. The simplest weather forecasting method is the so-called persistence model, which assumes that the future state of a system will be similar (or equal) to the present state. Machine learning (ML) models are widely used in different weather forecasting applications, but they need to be compared to the persistence model to analyse whether they provide a competitive solution to the problem at hand. In this paper, we devise a new model for predicting low-visibility in airports using the concepts of mixture of experts. Visibility level is coded as two different ordered categorical variables: cloud height and runway visual height. The underlying system in this application is stagnant approximately in 90% of the cases, and standard ML models fail to improve on the performance of the persistence model. Because of this, instead of trying to simply beat the persistence model using ML, we use this persistence as a baseline and learn an ordinal neural network model that refines its results by focusing on learning weather fluctuations. The results show that the proposal outperforms persistence and other ordinal autoregressive models, especially for longer time horizon predictions and for the runway visual height variable. Copyright © 2019, The Authors. All rights reserved.

关键词： Weather forecasting

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Hyperbolic geometrical approach to model reduction

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IFAC-PapersOnLine 2017年第1期50卷 12905-12910页

作者： Soumelidis, Alexandros Bokor, József Schipp, Ferenc Szabó, Zoltán Systems and Control Laboratory Institute for Computer Science and Control Budapest Hungary Institute for Computer Science and Control Hungarian Academy of Sciences MTA-BME Control Engineering Research Group Hungary Department of Numerical Analysis Eötvös Loránd University Budapest Hungary

Model reduction of large scale systems is an actively researched area of modelling and control. The problem is more involved if uncertainties are also present and a computational tractable nominal model is needed for the design. Based on results of the Kolmogorov n-width theory the paper provides useful bounds for the worst case approximation error - both H2and H∞– in terms of the hyperbolic distance related to the sets of uncertain poles. A related model reduction strategy that uses only this a priori pole information is also proposed. The method is illustrated through numerical examples. © 2017

关键词： numerical methods Computation theory Frequency domain analysis Large scale systems Poles Approximation errors Frequency domain identification Geometrical approaches Hyperbolic distances Identification for control Model reduction strategies Modelling and controls Nonparametric methods

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Simulation of seismic responses from the 3D non-linear model of the Bazhenov formation

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IOP Conference Series: Materials science and Engineering 2020年第1期927卷

作者： I S Nikitin V I Golubev A V Ekimenko M B Anosova Department of Mathematical Simulation Institute of Computer Aided Design of RAS 19/18 2-nd Brestskaya str. Moscow 123056 Russia Laboratory of Applied Numerical Geophysics Moscow Institute of Physics and Technology 9 Institutskiy per. Dolgoprudny Moscow Region 141701 Russia Seismic Data Analysis Department Gazprom Neft Science & Technology Centre Moika river embankment 75-79 Saint Petersburg 190000 Russia

The article is devoted to the investigation of seismic responses from probable oil-bearing formations. The three-dimensional geological model of the Bazhenov formation situated at Western Siberia is constructed. It is based on the elastic two-dimensional cross-section with curvilinear boundaries between different layers. For this purpose, logging and seismic data were processed jointly. To describe correctly the internal structure of mudstones the novel continuum model of media with interlayer slippage and delamination was utilized. The grid-characteristic method was used to solve numerically the govern system of the linear elasticity. The non-linearity of the model is incorporated with the appropriate explicit-implicit approximation procedure. For increasing the reliability of obtained synthetic seismograms the presence of the static rock pressure was taken into account. Reasonable computational time was achieved with the help of the parallelization based on the Message Passing Interface (MPI) technology. To analyze the structure of seismic responses wave patterns for the model with different parameters were presented. The influence of fractured layer on registered seismic traces were estimated. The proposed numerical approach may be used for simulation of complex geological objects.

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Laplacian preconditioning of elliptic pdes: Localization of the eigenvalues of the discretized operator

arXiv

引用

arXiv 2018年

作者： Gergelits, Tomáš Mardal, Kent-André Nielsen, Bjørn Fredrik Strakoš, Zdeněk Institute of Computer Sciences Czech Academy of Science Prague Czech Republic Faculty of Mathematics and Physics Charles University Prague Czech Republic Department of Mathematics University of Oslo Oslo0316 Norway Department of Numerical Analysis and Scientific Computing Simula Research Laboratory Lysaker1325 Norway Faculty of Science and Technology Norwegian University of Life Sciences ÅsNO-1432 Norway

In the paper Preconditioning by inverting the Laplacian;an analysis of the eigenvalues. IMA Journal of numerical analysis 29, 1 (2009), 24-42, Nielsen, Hackbusch and Tveito study the operator generated by using the inverse of the Laplacian as preconditioner for second order elliptic PDEs ∇ · (k(x)∇u) = f. They prove that the range of k(x) is contained in the spectrum of the preconditioned operator, provided that k is continuous. Their rigorous analysis only addresses mappings defined on infinite dimensional spaces, but the numerical experiments in the paper suggest that a similar property holds in the discrete case. Motivated by this investigation, we analyze the eigenvalues of the matrix L−1A, where L and A are the stiffness matrices associated with the Laplace operator and general second order elliptic operators, respectively. Without any assumption about the continuity of k(x), we prove the existence of a one-to-one pairing between the eigenvalues of L−1A and the intervals determined by the images under k(x) of the supports of the FE nodal basis functions. As a consequence, we can show that the nodal values of k(x) yield accurate approximations of the eigenvalues of L−1A. Our theoretical results are illuminated by several numerical experiments.65F08, 65F15, 65N12, 35J99 Copyright © 2018, The Authors. All rights reserved.

关键词： Eigenvalues and eigenfunctions

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