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arXiv 2024年

作者： Flock, Rafael Liu, Shuigen Dong, Yiqiu Tong, Xin T. Department of Applied Mathematics and Computer Science Technical University of Denmark Denmark National University of Singapore Singapore

We consider Bayesian inference for image deblurring with total variation (TV) prior. Since the posterior is analytically intractable, we resort to Markov chain Monte Carlo (MCMC) methods. However, since most MCMC methods significantly deteriorate in high dimensions, they are not suitable to handle high resolution imaging problems. In this paper, we show how low-dimensional sampling can still be facilitated by exploiting the sparse conditional structure of the posterior. To this end, we make use of the local structures of the blurring operator and the TV prior by partitioning the image into rectangular blocks and employing a blocked Gibbs sampler with proposals stemming from the Metropolis-Hastings adjusted Langevin Algorithm (MALA). We prove that this MALA-within-Gibbs (MLwG) sampling algorithm has dimension-independent block acceptance rates and dimension-independent convergence rate. In order to apply the MALA proposals, we approximate the TV by a smoothed version, and show that the introduced approximation error is evenly distributed and dimension-independent. Since the posterior is a Gibbs density, we can use the Hammersley-Clifford Theorem to identify the posterior conditionals which only depend locally on the neighboring blocks. We outline computational strategies to evaluate the conditionals, which are the target densities in the Gibbs updates, locally and in parallel. In two numerical experiments, we validate the dimension-independent properties of the MLwG algorithm and demonstrate its superior performance over *** Codes 62F15, 68U10, 60J22 © 2024, CC BY.

关键词： Markov chains

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Improved Gevrey-1 estimates of formal series expansions of center manifolds

arXiv

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arXiv 2024年

作者： Kristiansen, Kristian Uldall Department of Applied Mathematics and Computer Science Technical University of Denmark Kgs. Lyngby2800 Denmark

In this paper, we show that the coefficients n of the formal series expansions ∑∞n=1 nxn ∈ xℂ[[x]] of center manifolds of planar analytic saddle-nodes grow like Γ(n+a) (after rescaling x) as n → ∞. Here the quantity a is the formal analytic invariant associated with the saddle-node (following the work of J. Martinet and J.-P. Ramis). This growth property of n, which is optimal, was recently (2024) described for a restricted class of nonlinearities by the present author in collaboration with P. Szmolyan. This joint work was in turn inspired by the work of Merle, Raphaël, Rodnianski, and Szeftel (2022), which described the growth of the coefficients for a system related to self-similar solutions of the compressible Euler. In the present paper, we combine the previous approaches with a Borel-Laplace approach. Specifically, we adapt the Banach norm of Bonckaert and De Maesschalck (2008) in order to capture the singularity in the complex plane. Finally, we apply the result to a family of Riccati equations and obtain a partial classification of the analytic center manifolds. Copyright © 2024, The Authors. All rights reserved.

关键词： Riccati equations

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Evaluating the spike in the symptomatic proportion of SARS-CoV-2 in China in 2022 with variolation effects:a modeling analysis

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Infectious Disease Modelling 2024年第2期9卷 601-617页

作者： Salihu S.Musa Shi Zhao Ismail Abdulrashid Sania Qureshi Andrés Colubri Daihai He Department of Genomics and Computational Biology University of Massachusetts Chan Medical SchoolWorcesterMA01605USA Department of Applied Mathematics Hong Kong Polytechnic UniversityHong Kong SARChina Department of Mathematics Aliko Dangote University of Science and TechnologyKanoNigeria School of Public Health Tianjin Medical UniversityTianjin300070China School of Finance and Operations Management The University of Tulsa800 South Tucker Dr.TulsaOK74104USA Department of Basic Sciences and Related Studies Mehran University of Engineering and Tech.JamshoroPakistan Department of Computer Science and Mathematics Lebanese American UniversityBeirutLebanon

Despite most COVID-19 infections being asymptomatic,China's Mainland had a high increase in symptomatic cases at the end of *** this study,we examine China's sudden COVID-19 symptomatic surge using a conceptual SIR-based *** model considers the epidemiological characteristics of SARS-CoV-2,particularly variolation,from non-pharmaceutical intervention(facial masking and social distance),demography,and disease mortality in China's *** increase in symptomatic proportions in China may be attributable to(1)higher sensitivity and vulnerability during winter and(2)enhanced viral inhalation due to spikes in SARS-CoV-2 infections(high transmissibility).These two reasons could explain China's high symptomatic proportion of COVID-19 in December *** study,therefore,can serve as a decision-support tool to enhance SARS-CoV-2 prevention and control ***,we highlight that facemask-induced variolation could potentially reduces transmissibility rather than severity in infected ***,further investigation is required to understand the variolation effect on disease severity.

关键词： SARS-CoV-2 Epidemic Epidemiological modeling Reproduction number Variolation

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Dynamic Optimization for Monoclonal Antibody Production

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IFAC-PapersOnLine 2023年第2期56卷 6229-6234页

作者： Morten Wahlgreen Kaysfeld Deepak Kumar Marcus Krogh Nielsen John Bagterp Jørgensen Department of Applied Mathematics and Computer Science Technical University of Denmark DK-2800 Kgs. Lyngby Denmark

This paper presents a dynamic optimization numerical case study for Monoclonal Antibody (mAb) production. The fermentation is conducted in a continuous perfusion reactor. We represent the existing model in terms of a general modeling methodology well-suited for simulation and optimization. The model consists of six ordinary differential equations (ODEs) for the non-constant volume and the five components in the reactor. We extend the model with a glucose inhibition term to make the model feasible for optimization case studies. We formulate an optimization problem in terms of an optimal control problem (OCP) and consider four different setups for optimization. Compared to the base case, the optimal operation of the perfusion reactor increases the mAb yield with 44% when samples are taken from the reactor and with 52% without sampling. Additionally, our results show that multiple optimal feeding trajectories exist and that full glucose utilization can be forced without loss of mAb formation.

关键词： Monoclonal antibody production optimal control process modeling perfusion reactor fermentation

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A Pseudo-Spectral Scheme for Systems of Two-Point Boundary Value Problems with Left and Right Sided Fractional Derivatives and Related Integral Equations

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computer Modeling in Engineering & sciences 2021年第7期128卷 21-41页

作者： I.G.Ameen N.A.Elkot M.A.Zaky A.S.Hendy E.H.Doha Department of Mathematics Faculty of ScienceAl-Azhar UniversityCairoEgypt Department of Mathematics Faculty of ScienceCairo UniversityGiza12613Egypt Department of Applied Mathematics Physics DivisionNational Research CentreDokkiCairo12622Egypt Department of Computational Mathematics and Computer Science Institute of Natural Sciences and MathematicsUral Federal UniversityYekaterinburg620002Russia Department of Mathematics Faculty of ScienceBenha UniversityBenha13511Egypt

We target here to solve numerically a class of nonlinear fractional two-point boundary value problems involving left-and right-sided fractional *** main ingredient of the proposed method is to recast the problem into an equivalent system of weakly singular integral ***,a Legendre-based spectral collocation method is developed for solving the transformed ***,we can make good use of the advantages of the Gauss quadrature *** present the construction and analysis of the collocation *** results can be indirectly applied to solve fractional optimal control problems by considering the corresponding Euler–Lagrange *** numerical examples are given to confirm the convergence analysis and robustness of the scheme.

关键词： Spectral collocation method weakly singular integral equations two-point boundary value problems convergence analysis

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A Novel Perspective on Brain Tumor Classification Using Hybrid Algorithm

A Novel Perspective on Brain Tumor Classification Using Hybr...

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2023 International Conference on computer, Electronics and Electrical Engineering and their Applications, IC2E3 2023

作者： Jayanthi, R. Christinal, A. Hepzibah Hephzibah, R. Shekinah, T. Bajaj, Chandrajit Chandy, D. Abraham Karunya University Department of Mathematics Coimbatore India Loyola - Icam College of Engineering and Technology Department of Computer Science and Engineering Chennai India University of Texas Computational Applied Mathematics Chair in Visualization Austin United States Karunya University Department of Electronics and Communication Engineering Coimbatore India

ISBN: (纸本)9798350338003

Brain tumor classification is a critical task in medical imaging, where the early and accurate detection of brain tumors is crucial for patient treatment and survival. In recent years, Machine Learning techniques have emerged as a promising approach for automated brain tumor classification. In this paper, we investigate the performance of three ML classifiers - Support Vector Machine, Naïve Bayes, and an ensemble of SVM and Naïve Bayes - for the two-class classification of brain tumor data into a tumor and no tumor classes. Our experiments demonstrate that the ensemble of SVM and Naïve Bayes classifier achieved an accuracy of 97% outperforming the other classifiers. These results indicate that our ensemble classifier can be a powerful tool for the accurate and efficient classification of brain tumor data, potentially leading to improved patient outcomes. © 2023 IEEE.

关键词： Tumors

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Oracle complexity in nonsmooth nonconvex optimization

The Journal of Machine Learning Research

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The Journal of Machine Learning Research 2022年第1期23卷 14161-14204页

作者： Guy Kornowski Ohad Shamir Department of Computer Science and Applied Mathematics Weizmann Institute of Science Rehovot Israel

It is well-known that given a smooth, bounded-from-below, and possibly nonconvex function, standard gradient-based methods can find ε-stationary points (with gradient norm less than ε) in O(1/ε2) iterations. However, many important nonconvex optimization problems, such as those associated with training modern neural networks, are inherently not smooth, making these results inapplicable. In this paper, we study nonsmooth nonconvex optimization from an oracle complexity viewpoint, where the algorithm is assumed to be given access only to local information about the function at various points. We provide two main results: First, we consider the problem of getting near ε-stationary points. This is perhaps the most natural relaxation of finding ε-stationary points, which is impossible in the nonsmooth nonconvex case. We prove that this relaxed goal cannot be achieved efficiently, for any distance and ε smaller than some constants. Our second result deals with the possibility of tackling nonsmooth nonconvex optimization by reduction to smooth optimization: Namely, applying smooth optimization methods on a smooth approximation of the objective function. For this approach, we prove under a mild assumption an inherent trade-off between oracle complexity and smoothness: On the one hand, smoothing a nonsmooth nonconvex function can be done very efficiently (e.g., by randomized smoothing), but with dimension-dependent factors in the smoothness parameter, which can strongly affect iteration complexity when plugging into standard smooth optimization methods. On the other hand, these dimension factors can be eliminated with suitable smoothing methods, but only by making the oracle complexity of the smoothing process exponentially large.

关键词： nonconvex nonsmooth optimization optimization theory oracle complexity smoothing

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Fuzzy Rough Choquet Distances for Classification

arXiv

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arXiv 2024年

作者： Theerens, Adnan Cornelis, Chris Computational Web Intelligence Department of Applied Mathematics Computer Science and Statistics Ghent University Ghent Belgium

This paper introduces a novel Choquet distance using fuzzy rough set based measures. The proposed distance measure combines the attribute information received from fuzzy rough set theory with the flexibility of the Choquet integral. This approach is designed to adeptly capture non-linear relationships within the data, acknowledging the interplay of the conditional attributes towards the decision attribute and resulting in a more flexible and accurate distance. We explore its application in the context of machine learning, with a specific emphasis on distance-based classification approaches (e.g. k-nearest neighbours). The paper examines two fuzzy rough set based measures that are based on the positive region. Moreover, we explore two procedures for monotonizing the measures derived from fuzzy rough set theory, making them suitable for use with the Choquet integral, and investigate their differences. © 2024, CC BY-NC-ND.

关键词： Machine learning

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Data Mining and Bioinformatics Approaches to Elucidate Bacterial Communities in the Extreme Environment

Data Mining and Bioinformatics Approaches to Elucidate Bacte...

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2023 International Conference on Informatics, Multimedia, Cyber and Information Systems, ICIMCIS 2023

作者： Trinugroho, Joko Pebrianto Hidayat, Alam Ahmad Nirwantono, Rudi Asadi, Faisal Pardamean, Bens Bina Nusantara University Bioinformatics and Data Science Research Center Jakarta11480 Indonesia Bina Nusantara University School of Computer Science Bioinformatics and Data Science Research Center Mathematics Department Jakarta11480 Indonesia Bina Nusantara University Faculty of Engineering Bioinformatics and Data Science Research Center Biotechnology Department Jakarta11480 Indonesia Bina Nusantara University School of Computer Science Bioinformatics and Data Science Research Center Computer Science Department Jakarta11480 Indonesia Bina Nusantara University Binus Graduate Program Computer Science Computer Science Department Jakarta11480 Indonesia

ISBN: (纸本)9798350307306

Bacteria are microscopic organisms that can be found in many environments. They are abundant and have many roles in our life. Studying bacteria is essential so that we can identify the bacteria that are needed for many industrial applications. However, the main problem is that majority of the bacteria are unculturable, hampering the exploration of bacteria from different environments. Metagenomics approach which employs Next Generation Sequencing technology could help study bacteria by utilizing 16S rRNA marker gene. This study aims to demonstrate data mining and bioinformatics approaches to analyze 16S rRNA sequencing data. The raw sequencing data of 16S rRNA was collected from biological database. Then, the data were trimmed, denoised, and clustered to generate Amplicon Sequence Variants (ASVs). Diversity (alpha and beta) and taxonomic analyses were then conducted to elucidate the bacterial diversity and taxonomic profile of ASVs. The results of this work showed that Shannon and PD indices in China's hot spring were higher than Singapore and the USA. Furthermore, a significant difference was observed in the PD index. The unweighted UniFrac distance also showed there was a significant difference of the bacterial communities between the three locations. In addition, the taxonomic investigation unveiled prevalent bacterial groups in the ecosystem, namely Proteobacteria, Chloroflexi, Cyanobacteria, and Crenarchaeota. The research outcomes have the potential to serve as a foundational resource for subsequent bacterial metagenomic research, particularly the hot spring environment. © 2023 IEEE.

关键词： Bacteria

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Intelligent recognition system for viewpoint variations on gait and speech using CNN-CapsNet

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International Journal of Intelligent Computing and Cybernetics 2022年第3期15卷 363-382页

作者： G.Merlin Linda N.V.S.Sree Rathna Lakshmi N.Senthil Murugan Rajendra Prasad Mahapatra V.Muthukumaran M.Sivaram Department of Computer Science and Engineering SRM Institute of Science and Technology–Vadapalani CampusChennaiIndia Department of Electronics and Communication Engineering Agni College of TechnologyChennaiIndia School of Computer Science and Engineering VIT-AP UniversityAmaravatiIndia Department of Computer Science and Engineering SRM Institute of Science and TechnologyGhaziabadIndia Department of Mathematics School of Applied SciencesREVA UniversityBangaloreIndia Faculty of Information Technology Ton Duc Thang UniversityHo Chi Minh CityVietnam

Purpose-The paper aims to introduce an intelligent recognition system for viewpoint variations of gait and *** proposes a convolutional neural network-based capsule network(CNN-CapsNet)model and outlining the performance of the system in recognition of gait and speech *** proposed intelligent system mainly focuses on relative spatial hierarchies between gait features in the entities of the image due to translational invariances in sub-sampling and speech ***/methodology/approach-This proposed work CNN-CapsNet is mainly used for automatic learning of feature representations based on CNNand used capsule vectors as neurons to encode all the spatial information of an image by adapting equal variances to change in *** proposed study will resolve the discrepancies caused by cofactors and gait recognition between opinions based on a model of ***-This research work provides recognition of signal,biometric-based gait recognition and sound/speech *** evaluations are conducted on three aspects of scenarios,namely fixed-view,cross-view and multi-view *** main parameters for recognition of gait are speed,change in clothes,subjects walking with carrying object and intensity of *** limitations/implications-The proposed CNN-CapsNet has some limitations when considering for detecting the walking targets from surveillance videos considering multimodal fusion approaches using hardware sensor *** can also act as a pre-requisite tool to analyze,identify,detect and verify the malware *** implications-This research work includes for detecting the walking targets from surveillance videos considering multimodal fusion approaches using hardware sensor *** can also act as a pre-requisite tool to analyze,identify,detect and verify the malware ***/value-This proposed research work proves to be performing better for the recognition of gait and speech when

关键词： Intelligent system Gait recognition Convolutional neural network Deep learning Capsule network Viewpoint variations

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