Journal of Computational Mathematics and Data Science最新文献_第5页

Fast sampling from time-integrated bridges using deep learning 使用深度学习从时间集成桥快速采样

Journal of Computational Mathematics and Data Science Pub Date : 2022-12-01 DOI: 10.1016/j.jcmds.2022.100060

Leonardo Perotti , Lech A. Grzelak

{"title":"Fast sampling from time-integrated bridges using deep learning","authors":"Leonardo Perotti , Lech A. Grzelak","doi":"10.1016/j.jcmds.2022.100060","DOIUrl":"10.1016/j.jcmds.2022.100060","url":null,"abstract":"<div><p>We propose a methodology for sampling from time-integrated stochastic bridges, i.e., random variables defined as <span><math><mrow><msubsup><mrow><mo>∫</mo></mrow><mrow><msub><mrow><mi>t</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow><mrow><msub><mrow><mi>t</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></msubsup><mi>f</mi><mrow><mo>(</mo><mi>Y</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>)</mo></mrow><mi>d</mi><mi>t</mi></mrow></math></span> conditional on <span><math><mrow><mi>Y</mi><mrow><mo>(</mo><msub><mrow><mi>t</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>)</mo></mrow><mspace></mspace><mo>=</mo><mspace></mspace><mi>a</mi></mrow></math></span> and <span><math><mrow><mi>Y</mi><mrow><mo>(</mo><msub><mrow><mi>t</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>)</mo></mrow><mspace></mspace><mo>=</mo><mspace></mspace><mi>b</mi></mrow></math></span>, with <span><math><mrow><mi>a</mi><mo>,</mo><mi>b</mi><mo>∈</mo><mi>R</mi></mrow></math></span>. The techniques developed in Grzelak et al. (2019) – the Stochastic Collocation Monte Carlo sampler – and in Liu et al. (2020) – the Seven-League scheme – are applied for this purpose. Notably, the time-integrated bridge distribution is approximated using a polynomial chaos expansion constructed over an appropriate set of stochastic collocation points. In addition, artificial neural networks are employed to learn the collocation points. The result is a robust, data-driven procedure for Monte Carlo sampling from time-integrated conditional processes, which guarantees high accuracy and generates thousands of samples in milliseconds. Applications are also presented, with a focus on finance.</p></div>","PeriodicalId":100768,"journal":{"name":"Journal of Computational Mathematics and Data Science","volume":"5 ","pages":"Article 100060"},"PeriodicalIF":0.0,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2772415822000207/pdfft?md5=305a6ab11208f407d10fd97dc71efcd6&pid=1-s2.0-S2772415822000207-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88032720","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

A treecode algorithm based on tricubic interpolation 一种基于三次插值的三码算法

Journal of Computational Mathematics and Data Science Pub Date : 2022-12-01 DOI: 10.1016/j.jcmds.2022.100068

Henry A. Boateng , Svetlana Tlupova

{"title":"A treecode algorithm based on tricubic interpolation","authors":"Henry A. Boateng , Svetlana Tlupova","doi":"10.1016/j.jcmds.2022.100068","DOIUrl":"10.1016/j.jcmds.2022.100068","url":null,"abstract":"<div><p>Treecode algorithms efficiently approximate N-body interactions in <span><math><mrow><mi>O</mi><mrow><mo>(</mo><mi>N</mi><mo>)</mo></mrow></mrow></math></span> or <span><math><mrow><mi>O</mi><mrow><mo>(</mo><mi>N</mi><mtext>log</mtext><mi>N</mi><mo>)</mo></mrow></mrow></math></span>. In order to treat general 3D kernels, recent developments employ polynomial interpolation to approximate the kernels. The polynomials are a tensor product of 1-dimensional polynomials. Here, we develop an <span><math><mrow><mi>O</mi><mrow><mo>(</mo><mi>N</mi><mtext>log</mtext><mi>N</mi><mo>)</mo></mrow></mrow></math></span> tricubic interpolation based treecode method for 3D kernels. The tricubic interpolation is inherently three-dimensional and as such does not employ a tensor product. The form allows for easy evaluation of the derivatives of the kernel, required in dynamical simulations, which is not the case for the tensor product approach. We develop both a particle-cluster and cluster-particle variants and present results for the Coulomb, screened Coulomb and the real space Ewald kernels. We also present results of an MD simulation of a Lennard-Jones liquid using the tricubic treecode.</p></div>","PeriodicalId":100768,"journal":{"name":"Journal of Computational Mathematics and Data Science","volume":"5 ","pages":"Article 100068"},"PeriodicalIF":0.0,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2772415822000281/pdfft?md5=3c134f39c68f4ef44c46526b17abbfdc&pid=1-s2.0-S2772415822000281-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77535957","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

α-HMM and optimal decoding higher-order structures on sequential data α-HMM和序列数据的最优解码高阶结构

Journal of Computational Mathematics and Data Science Pub Date : 2022-12-01 DOI: 10.1016/j.jcmds.2022.100065

Fereshteh R. Dastjerdi , David A. Robinson , Liming Cai

{"title":"α-HMM and optimal decoding higher-order structures on sequential data","authors":"Fereshteh R. Dastjerdi , David A. Robinson , Liming Cai","doi":"10.1016/j.jcmds.2022.100065","DOIUrl":"10.1016/j.jcmds.2022.100065","url":null,"abstract":"<div><p>Decoding higher-order structure on sequential data is an indispensable task in data science. It requires models to have the capability to characterize interdependencies among hidden events that have generated observable data. However, to be able to decode arbitrary structures, such models would need to cope with the intractability arising from computing context-sensitive relations, likely compromising the quality of answers. To address this important issue, the current paper introduces the <em>arbitrary order hidden Markov model</em> (<span><math><mi>α</mi></math></span>-HMM), an extension of the HMM that permits decoding of the optimal higher-order structure with an assurance of computational tractability. The advantage of the <span><math><mi>α</mi></math></span>-HMMis made possible by an identified principle on how random variables influence each other in a stochastic process. In particular, it is shown that decoding the optimal structure with an <span><math><mi>α</mi></math></span>-HMMcan be computed in <span><math><mrow><mi>O</mi><mrow><mo>(</mo><msup><mrow><mi>n</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>)</mo></mrow></mrow></math></span>-time for any stochastic process of <span><math><mi>n</mi></math></span> random variables. As an application, it is demonstrated the decoding algorithm inspires a simple yet effective algorithm for RNA secondary structure prediction.</p></div>","PeriodicalId":100768,"journal":{"name":"Journal of Computational Mathematics and Data Science","volume":"5 ","pages":"Article 100065"},"PeriodicalIF":0.0,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2772415822000256/pdfft?md5=dbdeefc075425bee6733e90b348391d6&pid=1-s2.0-S2772415822000256-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91428549","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Pipeline to identify dominant features in spatial data 管道识别空间数据中的主导特征

Journal of Computational Mathematics and Data Science Pub Date : 2022-12-01 DOI: 10.1016/j.jcmds.2022.100063

Roman Flury , Reinhard Furrer

引用次数: 0

Combined impacts of Radiation absorption and Chemically reacting on MHD Free Convective Casson fluid flow past an infinite vertical inclined porous plate 辐射吸收和化学反应对MHD自由对流卡森流体通过无限垂直倾斜多孔板的综合影响

Journal of Computational Mathematics and Data Science Pub Date : 2022-12-01 DOI: 10.1016/j.jcmds.2022.100069

B.V. Swarnalathamma , D.M. Praveen Babu , M. Veera Krishna

{"title":"Combined impacts of Radiation absorption and Chemically reacting on MHD Free Convective Casson fluid flow past an infinite vertical inclined porous plate","authors":"B.V. Swarnalathamma , D.M. Praveen Babu , M. Veera Krishna","doi":"10.1016/j.jcmds.2022.100069","DOIUrl":"10.1016/j.jcmds.2022.100069","url":null,"abstract":"<div><p>In the current investigation, it is explored the unsteady MHD free convective Casson fluid movement over a boundless straight up inclined absorbent plate with heat source and/or heat absorption. The established equations are subsequently solved thoroughly by utilize of perturbation method. The velocity, temperature as well as concentration profiles are shown in graphical profiles. The consequences on the stream region for disparate foremost parameter had been investigated. Furthermore the skin friction factor, Nusselt number in addition to Sherwood numbers are found by the disparate foremost parameters as well as revealed in the tabular formats. The velocity reduces by an escalating into the chemical reaction constraint in addition to improved by an enhancement into heat resources parameters. The temperatures fields reduce by an enhancement into the Prandtl number, whereas it enlarges with an augment in temperature absorption parameter. The concentration field is enhances with an escalating into the chemical reaction constraint, while this retards by an enhancing into Schmidt number.</p></div>","PeriodicalId":100768,"journal":{"name":"Journal of Computational Mathematics and Data Science","volume":"5 ","pages":"Article 100069"},"PeriodicalIF":0.0,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2772415822000293/pdfft?md5=c78d420cfd49df7a2f310d9376a4ca8c&pid=1-s2.0-S2772415822000293-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86494631","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 2

A review on the selection criteria for the truncated SVD in Data Science applications 数据科学应用中截断奇异值分解的选择标准综述

Journal of Computational Mathematics and Data Science Pub Date : 2022-12-01 DOI: 10.1016/j.jcmds.2022.100064

Antonella Falini

引用次数: 4

Effects of viscous dissipation and thermal radiation on time dependent incompressible squeezing flow of CuO−Al2O3/water hybrid nanofluid between two parallel plates with variable viscosity 黏性耗散和热辐射对变黏度平行板间CuO−Al2O3/水混合纳米流体不可压缩压缩流动的影响

Journal of Computational Mathematics and Data Science Pub Date : 2022-12-01 DOI: 10.1016/j.jcmds.2022.100062

O.A. Famakinwa, O.K. Koriko, K.S. Adegbie

{"title":"Effects of viscous dissipation and thermal radiation on time dependent incompressible squeezing flow of CuO−Al2O3/water hybrid nanofluid between two parallel plates with variable viscosity","authors":"O.A. Famakinwa, O.K. Koriko, K.S. Adegbie","doi":"10.1016/j.jcmds.2022.100062","DOIUrl":"10.1016/j.jcmds.2022.100062","url":null,"abstract":"<div><p>In view of the dominant properties of hybrid nanofluid such as high thermal and electrical conductivity in addition to enhanced heat transfer rate, efforts had been strengthened by many researchers to upgrade the thermal behavior of the base fluid through different approaches. In this study, viscous dissipation and thermal radiation effects on unsteady incompressible squeezing flow conveying <span><math><mrow><mi>C</mi><mi>u</mi><mi>O</mi><mo>−</mo><mi>A</mi><msub><mrow><mi>l</mi></mrow><mrow><mn>2</mn></mrow></msub><msub><mrow><mi>O</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>/</mo></mrow></math></span>water hybrid nanoparticles between two aligned surfaces with variable viscosity is examined. The fluid model is transformed to ordinary differential equations by incorporating appropriate similarity transformation. The numerical simulation is carried out in MATLAB software package via shooting procedure coupled with <span><math><mrow><mn>4</mn><mi>t</mi><mi>h</mi></mrow></math></span> order Runge–Kutta integration scheme. The limiting case is found to be in accord relative to the preceding reports. The outcomes of the scrutiny are unveiled in tables and graphs. It was revealed that the velocity and temperature augment with increasing viscosity variation and squeezing fluid parameters. Meanwhile, increasing viscous dissipation and thermal radiation parameters decrease the temperature distribution with no significant change in the fluid velocity.</p></div>","PeriodicalId":100768,"journal":{"name":"Journal of Computational Mathematics and Data Science","volume":"5 ","pages":"Article 100062"},"PeriodicalIF":0.0,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2772415822000220/pdfft?md5=9424e5a9e389ee13b5970c55ab05f778&pid=1-s2.0-S2772415822000220-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87594959","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 11

Variably Scaled Persistence Kernels (VSPKs) for persistent homology applications 用于持久同构应用程序的可变缩放持久化内核(vspk)

Journal of Computational Mathematics and Data Science Pub Date : 2022-08-01 DOI: 10.1016/j.jcmds.2022.100050

Stefano De Marchi , Federico Lot , Francesco Marchetti , Davide Poggiali

引用次数: 2

Reducing the Gibbs effect in multimodal medical imaging by the Fake Nodes approach 假淋巴结法减少多模态医学成像中的吉布斯效应

Journal of Computational Mathematics and Data Science Pub Date : 2022-08-01 DOI: 10.1016/j.jcmds.2022.100040

Davide Poggiali , Diego Cecchin , Stefano De Marchi

引用次数: 1

Deep learning, stochastic gradient descent and diffusion maps 深度学习，随机梯度下降和扩散图

Journal of Computational Mathematics and Data Science Pub Date : 2022-08-01 DOI: 10.1016/j.jcmds.2022.100054

Carmina Fjellström, Kaj Nyström

{"title":"Deep learning, stochastic gradient descent and diffusion maps","authors":"Carmina Fjellström, Kaj Nyström","doi":"10.1016/j.jcmds.2022.100054","DOIUrl":"https://doi.org/10.1016/j.jcmds.2022.100054","url":null,"abstract":"<div><p>Stochastic gradient descent (SGD) is widely used in deep learning due to its computational efficiency, but a complete understanding of why SGD performs so well remains a major challenge. It has been observed empirically that most eigenvalues of the Hessian of the loss functions on the loss landscape of over-parametrized deep neural networks are close to zero, while only a small number of eigenvalues are large. Zero eigenvalues indicate zero diffusion along the corresponding directions. This indicates that the process of minima selection mainly happens in the relatively low-dimensional subspace corresponding to the top eigenvalues of the Hessian. Although the parameter space is very high-dimensional, these findings seems to indicate that the SGD dynamics may mainly live on a low-dimensional manifold. In this paper, we pursue a truly data driven approach to the problem of getting a potentially deeper understanding of the high-dimensional parameter surface, and in particular, of the landscape traced out by SGD by analyzing the data generated through SGD, or any other optimizer for that matter, in order to possibly discover (local) low-dimensional representations of the optimization landscape. As our vehicle for the exploration, we use diffusion maps introduced by R. Coifman and coauthors.</p></div>","PeriodicalId":100768,"journal":{"name":"Journal of Computational Mathematics and Data Science","volume":"4 ","pages":"Article 100054"},"PeriodicalIF":0.0,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2772415822000177/pdfft?md5=38c0dff05f24faf5b0990bd6aa9fd984&pid=1-s2.0-S2772415822000177-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"137407104","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0