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Three-dimensional numerical schemes for the segmentation of the psoas muscle in X-ray computed tomography images 在 X 射线计算机断层扫描图像中分割腰肌的三维数值方案
arXiv - CS - Numerical Analysis Pub Date : 2023-12-10 DOI: arxiv-2312.05887
Giulio Paolucci, Isabella Cama, Cristina Campi, Michele Piana
{"title":"Three-dimensional numerical schemes for the segmentation of the psoas muscle in X-ray computed tomography images","authors":"Giulio Paolucci, Isabella Cama, Cristina Campi, Michele Piana","doi":"arxiv-2312.05887","DOIUrl":"https://doi.org/arxiv-2312.05887","url":null,"abstract":"The analysis of the psoas muscle in morphological and functional imaging has\u0000proved to be an accurate approach to assess sarcopenia, i.e. a systemic loss of\u0000skeletal muscle mass and function that may be correlated to multifactorial\u0000etiological aspects. The inclusion of sarcopenia assessment into a radiological\u0000workflow would need the implementation of computational pipelines for image\u0000processing that guarantee segmentation reliability and a significant degree of\u0000automation. The present study utilizes three-dimensional numerical schemes for\u0000psoas segmentation in low-dose X-ray computed tomography images. Specifically,\u0000here we focused on the level set methodology and compared the performances of\u0000two standard approaches, a classical evolution model and a three-dimension\u0000geodesic model, with the performances of an original first-order modification\u0000of this latter one. The results of this analysis show that these gradient-based\u0000schemes guarantee reliability with respect to manual segmentation and that the\u0000first-order scheme requires a computational burden that is significantly\u0000smaller than the one needed by the second-order approach.","PeriodicalId":501061,"journal":{"name":"arXiv - CS - Numerical Analysis","volume":"7 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138574865","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Duality Approach to Regularized Learning Problems in Banach Spaces 巴拿赫空间中正规化学习问题的对偶方法
arXiv - CS - Numerical Analysis Pub Date : 2023-12-10 DOI: arxiv-2312.05734
Raymond Cheng, Rui Wang, Yuesheng Xu
{"title":"A Duality Approach to Regularized Learning Problems in Banach Spaces","authors":"Raymond Cheng, Rui Wang, Yuesheng Xu","doi":"arxiv-2312.05734","DOIUrl":"https://doi.org/arxiv-2312.05734","url":null,"abstract":"Learning methods in Banach spaces are often formulated as regularization\u0000problems which minimize the sum of a data fidelity term in a Banach norm and a\u0000regularization term in another Banach norm. Due to the infinite dimensional\u0000nature of the space, solving such regularization problems is challenging. We\u0000construct a direct sum space based on the Banach spaces for the data fidelity\u0000term and the regularization term, and then recast the objective function as the\u0000norm of a suitable quotient space of the direct sum space. In this way, we\u0000express the original regularized problem as an unregularized problem on the\u0000direct sum space, which is in turn reformulated as a dual optimization problem\u0000in the dual space of the direct sum space. The dual problem is to find the\u0000maximum of a linear function on a convex polytope, which may be solved by\u0000linear programming. A solution of the original problem is then obtained by\u0000using related extremal properties of norming functionals from a solution of the\u0000dual problem. Numerical experiments are included to demonstrate that the\u0000proposed duality approach leads to an implementable numerical method for\u0000solving the regularization learning problems.","PeriodicalId":501061,"journal":{"name":"arXiv - CS - Numerical Analysis","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138574867","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Decay estimates for Cayley transforms and inverses of semigroup generators via the $mathcal{B}$-calculus 通过 $mathcal{B}$ 微积分对半群生成器的 Cayley 变换和倒数进行衰减估计
arXiv - CS - Numerical Analysis Pub Date : 2023-12-09 DOI: arxiv-2312.05692
Masashi Wakaiki
{"title":"Decay estimates for Cayley transforms and inverses of semigroup generators via the $mathcal{B}$-calculus","authors":"Masashi Wakaiki","doi":"arxiv-2312.05692","DOIUrl":"https://doi.org/arxiv-2312.05692","url":null,"abstract":"Let $-A$ be the generator of a bounded $C_0$-semigroup $(e^{-tA})_{t geq 0}$\u0000on a Hilbert space. First we study the long-time asymptotic behavior of the\u0000Cayley transform $V_{omega}(A) := (A-omega I) (A+omega I)^{-1}$ with $omega\u0000>0$. We give a decay estimate for $|V_{omega}(A)^nA^{-1}|$ when\u0000$(e^{-tA})_{t geq 0}$ is polynomially stable. Considering the case where the\u0000parameter $omega$ varies, we estimate $|prod_{k=1}^n\u0000(V_{omega_k}(A))A^{-1}|$ for exponentially stable $C_0$-semigroups\u0000$(e^{-tA})_{t geq 0}$. Next we show that if the generator $-A$ of the bounded\u0000$C_0$-semigroup has a bounded inverse, then $sup_{t geq 0} |e^{-tA^{-1}}\u0000A^{-alpha} | < infty$ for all $alpha >0$. We also present an estimate for\u0000the rate of decay of $|e^{-tA^{-1}} A^{-1} |$, assuming that $(e^{-tA})_{t\u0000geq 0}$ is polynomially stable. To obtain these results, we use operator norm\u0000estimates offered by a functional calculus called the $mathcal{B}$-calculus.","PeriodicalId":501061,"journal":{"name":"arXiv - CS - Numerical Analysis","volume":"21 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138577278","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Spectral Jacobi approximations for Boussinesq systems 布辛斯克系统的雅可比谱近似值
arXiv - CS - Numerical Analysis Pub Date : 2023-12-09 DOI: arxiv-2312.05559
Angel Durán
{"title":"Spectral Jacobi approximations for Boussinesq systems","authors":"Angel Durán","doi":"arxiv-2312.05559","DOIUrl":"https://doi.org/arxiv-2312.05559","url":null,"abstract":"This paper is concerned with the numerical approximation of\u0000initial-boundary-value problems of a three-parameter family of Bona-Smith\u0000systems, derived as a model for the propagation of surface waves under a\u0000physical Boussinesq regime. The work proposed here is focused on the\u0000corresponding problem with Dirichlet boundary conditions and its approximation\u0000in space with spectral methods based on Jacobi polynomials, which are defined\u0000from the orthogonality with respect to some weighted $L^{2}$ inner product.\u0000Well-posedness of the problem on the corresponding weighted Sobolev spaces is\u0000first analyzed and existence and uniqueness of solution, locally in time, are\u0000proved. Then the spectral Galerkin semidiscrete scheme and some detailed\u0000comments on its implementation are introduced. The existence of numerical\u0000solution and error estimates on those weighted Sobolev spaces are established.\u0000Finally, the choice of the time integrator to complete the full discretization\u0000takes care of different stability issues that may be relevant when\u0000approximating the semidiscrete system. Some numerical experiments illustrate\u0000the results.","PeriodicalId":501061,"journal":{"name":"arXiv - CS - Numerical Analysis","volume":"38 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138577128","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Data-Driven Framework for Improving Public EV Charging Infrastructure: Modeling and Forecasting 改善公共电动汽车充电基础设施的数据驱动框架：建模与预测
arXiv - CS - Numerical Analysis Pub Date : 2023-12-08 DOI: arxiv-2312.05333
Nassr Al-Dahabreh, Mohammad Ali Sayed, Khaled Sarieddine, Mohamed Elhattab, Maurice Khabbaz, Ribal Atallah, Chadi Assi
{"title":"A Data-Driven Framework for Improving Public EV Charging Infrastructure: Modeling and Forecasting","authors":"Nassr Al-Dahabreh, Mohammad Ali Sayed, Khaled Sarieddine, Mohamed Elhattab, Maurice Khabbaz, Ribal Atallah, Chadi Assi","doi":"arxiv-2312.05333","DOIUrl":"https://doi.org/arxiv-2312.05333","url":null,"abstract":"This work presents an investigation and assessment framework, which,\u0000supported by realistic data, aims at provisioning operators with in-depth\u0000insights into the consumer-perceived Quality-of-Experience (QoE) at public\u0000Electric Vehicle (EV) charging infrastructures. Motivated by the unprecedented\u0000EV market growth, it is suspected that the existing charging infrastructure\u0000will soon be no longer capable of sustaining the rapidly growing charging\u0000demands; let alone that the currently adopted ad hoc infrastructure expansion\u0000strategies seem to be far from contributing any quality service sustainability\u0000solutions that tangibly reduce (ultimately mitigate) the severity of this\u0000problem. Without suitable QoE metrics, operators, today, face remarkable\u0000difficulty in assessing the performance of EV Charging Stations (EVCSs) in this\u0000regard. This paper aims at filling this gap through the formulation of novel\u0000and original critical QoE performance metrics that provide operators with\u0000visibility into the per-EVCS operational dynamics and allow for the\u0000optimization of these stations' respective utilization. Such metrics shall then\u0000be used as inputs to a Machine Learning model finely tailored and trained using\u0000recent real-world data sets for the purpose of forecasting future long-term\u0000EVCS loads. This will, in turn, allow for making informed optimal EV charging\u0000infrastructure expansions that will be capable of reliably coping with the\u0000rising EV charging demands and maintaining acceptable QoE levels. The model's\u0000accuracy has been tested and extensive simulations are conducted to evaluate\u0000the achieved performance in terms of the above listed metrics and show the\u0000suitability of the recommended infrastructure expansions.","PeriodicalId":501061,"journal":{"name":"arXiv - CS - Numerical Analysis","volume":"10 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138577276","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A novel time-domain direct sampling approach for inverse scattering problems in acoustics 声学反向散射问题的时域直接采样新方法
arXiv - CS - Numerical Analysis Pub Date : 2023-12-07 DOI: arxiv-2312.04241
Yukun Guo, Hongjie Li, Xianchao Wang
{"title":"A novel time-domain direct sampling approach for inverse scattering problems in acoustics","authors":"Yukun Guo, Hongjie Li, Xianchao Wang","doi":"arxiv-2312.04241","DOIUrl":"https://doi.org/arxiv-2312.04241","url":null,"abstract":"This work is concerned with an inverse scattering problem of determining\u0000unknown scatterers from time-dependent acoustic measurements. A novel\u0000time-domain direct sampling method is developed to efficiently determine both\u0000the locations and shapes of inhomogeneous media. In particular, our approach is\u0000very easy to implement since only cheap space-time integrations are involved in\u0000the evaluation of the imaging functionals. Based on the Fourier-Laplace\u0000transform, we establish an inherent connection between the time-domain and\u0000frequency-domain direct sampling method. Moreover, rigorous theoretical\u0000justifications and numerical experiments are provided to verify the validity\u0000and feasibility of the proposed method.","PeriodicalId":501061,"journal":{"name":"arXiv - CS - Numerical Analysis","volume":"20 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138553619","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Reconstruction of dynamical systems from data without time labels 从无时间标签的数据中重建动力系统
arXiv - CS - Numerical Analysis Pub Date : 2023-12-07 DOI: arxiv-2312.04038
Zhijun Zeng, Pipi Hu, Chenglong Bao, Yi Zhu, Zuoqiang Shi
{"title":"Reconstruction of dynamical systems from data without time labels","authors":"Zhijun Zeng, Pipi Hu, Chenglong Bao, Yi Zhu, Zuoqiang Shi","doi":"arxiv-2312.04038","DOIUrl":"https://doi.org/arxiv-2312.04038","url":null,"abstract":"In this paper, we study the method to reconstruct dynamical systems from data\u0000without time labels. Data without time labels appear in many applications, such\u0000as molecular dynamics, single-cell RNA sequencing etc. Reconstruction of\u0000dynamical system from time sequence data has been studied extensively. However,\u0000these methods do not apply if time labels are unknown. Without time labels,\u0000sequence data becomes distribution data. Based on this observation, we propose\u0000to treat the data as samples from a probability distribution and try to\u0000reconstruct the underlying dynamical system by minimizing the distribution\u0000loss, sliced Wasserstein distance more specifically. Extensive experiment\u0000results demonstrate the effectiveness of the proposed method.","PeriodicalId":501061,"journal":{"name":"arXiv - CS - Numerical Analysis","volume":"114 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138553409","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A M|M|m|m Queue System Transient Behavior Study M|M|m|m 队列系统瞬态行为研究
arXiv - CS - Numerical Analysis Pub Date : 2023-12-06 DOI: arxiv-2312.03870
Manuel Alberto M. Ferreira
{"title":"A M|M|m|m Queue System Transient Behavior Study","authors":"Manuel Alberto M. Ferreira","doi":"arxiv-2312.03870","DOIUrl":"https://doi.org/arxiv-2312.03870","url":null,"abstract":"It is a very hard task to compute an exact solution for the differential\u0000equations, with differences, system that allows the determination of the\u0000M|M|m|m system transient probabilities. The respective complexity grows with m.\u0000The computations are extremely fastidious and the length and the fact that the\u0000expressions obtained are often approximate, and not exact, will not allow the\u0000transient probabilities behavior as time functions characterization. To\u0000overcome these problems, in this work it is analyzed how that system can supply\u0000approximate values to the M|M|m|m queue system. It is also presented an\u0000asymptotic method to solve the system that becomes possible in many cases to\u0000obtain simple approximated expressions for those probabilities using the\u0000M|M|Inf transient probabilities, very well-known and very much easier to study.","PeriodicalId":501061,"journal":{"name":"arXiv - CS - Numerical Analysis","volume":"2 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138553484","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Quantum algorithm for linear non-unitary dynamics with near-optimal dependence on all parameters 线性非单元动力学的量子算法，其对所有参数的依赖性接近最优
arXiv - CS - Numerical Analysis Pub Date : 2023-12-06 DOI: arxiv-2312.03916
Dong An, Andrew M. Childs, Lin Lin
{"title":"Quantum algorithm for linear non-unitary dynamics with near-optimal dependence on all parameters","authors":"Dong An, Andrew M. Childs, Lin Lin","doi":"arxiv-2312.03916","DOIUrl":"https://doi.org/arxiv-2312.03916","url":null,"abstract":"We introduce a family of identities that express general linear non-unitary\u0000evolution operators as a linear combination of unitary evolution operators,\u0000each solving a Hamiltonian simulation problem. This formulation can\u0000exponentially enhance the accuracy of the recently introduced linear\u0000combination of Hamiltonian simulation (LCHS) method [An, Liu, and Lin, Physical\u0000Review Letters, 2023]. For the first time, this approach enables quantum\u0000algorithms to solve linear differential equations with both optimal state\u0000preparation cost and near-optimal scaling in matrix queries on all parameters.","PeriodicalId":501061,"journal":{"name":"arXiv - CS - Numerical Analysis","volume":"276 2 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138553615","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Analysis and preconditioning of a probabilistic domain decomposition algorithm for elliptic boundary value problems 椭圆边界值问题概率域分解算法的分析与预处理
arXiv - CS - Numerical Analysis Pub Date : 2023-12-06 DOI: arxiv-2312.03930
Francisco Bernal, Jorge Morón-Vidal
{"title":"Analysis and preconditioning of a probabilistic domain decomposition algorithm for elliptic boundary value problems","authors":"Francisco Bernal, Jorge Morón-Vidal","doi":"arxiv-2312.03930","DOIUrl":"https://doi.org/arxiv-2312.03930","url":null,"abstract":"PDDSparse is a new hybrid parallelisation scheme for solving large-scale\u0000elliptic boundary value problems on supercomputers, which can be described as a\u0000Feynman-Kac formula for domain decomposition. At its core lies a stochastic\u0000linear, sparse system for the solutions on the interfaces, whose entries are\u0000generated via Monte Carlo simulations. Assuming small statistical errors, we\u0000show that the random system matrix ${tilde G}(omega)$ is near a nonsingular\u0000M-matrix $G$, i.e. ${tilde G}(omega)+E=G$ where $||E||/||G||$ is small. Using\u0000nonstandard arguments, we bound $||G^{-1}||$ and the condition number of $G$,\u0000showing that both of them grow moderately with the degrees of freedom of the\u0000discretisation. Moreover, the truncated Neumann series of $G^{-1}$ -- which is\u0000straightforward to calculate -- is the basis for an excellent preconditioner\u0000for ${tilde G}(omega)$. These findings are supported by numerical evidence.","PeriodicalId":501061,"journal":{"name":"arXiv - CS - Numerical Analysis","volume":"114 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138553690","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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