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arXiv 2018年

作者： Chen, Yuxin Gemmer, John A. Silber, Mary Volkening, Alexandria Department of Engineering Sciences and Applied Mathematics Northwestern University Department of Mathematics and Statistics Wake Forest University Committee on Computational and Applied Mathematics Department of Statistics University of Chicago Mathematical Biosciences Institute Ohio State University

We consider a periodically-forced 1-D Langevin equation that possesses two stable periodic solutions in the absence of noise. We ask the question: is there a most likely noise-induced transition path between these periodic solutions that allows us to identify a preferred phase of the forcing when tipping occurs? The quasistatic regime, where the forcing period is long compared to the adiabatic relaxation time, has been well studied;our work instead explores the case when these timescales are comparable. We compute optimal paths using the path integral method incorporating the Onsager-Machlup functional and validate results with Monte Carlo simulations. Results for the preferred tipping phase are compared with the deterministic aspects of the problem. We identify parameter regimes where nullclines, associated with the deterministic problem in a 2-D extended phase space, form passageways through which the optimal paths transit. As the nullclines are independent of the relaxation time and the noise strength, this leads to a robust deterministic predictor of preferred tipping phase in a regime where forcing is neither too fast, nor too slow.68Q25, 60G17, 37J50 Copyright © 2018, The Authors. All rights reserved.

关键词： Relaxation time

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A new energy inversion for parameter identification in saddle point problems with an application to the elasticity imaging inverse problem of predicting tumor location

A new energy inversion for parameter identification in saddl...

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作者： Doyley, M.M. Jadamba, B. Khan, A.A. Sama, M. Winkler, B. School of Engineering and Applied Sciences Department of Biomedical Engineering University of Rochester Rochester NY United States Center for Applied and Computational Mathematics School of Mathematical Sciences Rochester Institute of Technology 80 Lomb Memorial Drive Rochester NY 14623 United States Departamento de Matemática Aplicada Universidad Nacional de Educación A Distancia Madrid Spain

The primary objective of this work is a detailed theoretical and computational study of the elasticity imaging inverse problem for tumor identification within the human body. Apart from this inverse problem's important and interesting application, it also poses noteworthy mathematical challenges since the underlying mathematical model is a system of elasticity involving incompressibility. This gives rise to the "locking" effect and special treatment is necessary for both the direct and inverse problems. To study the inverse problem in an optimization framework, we introduce a general computational scheme for handling parameter identification in saddle point problems along with the introduction and analysis of a new energy output least-squares objective functionals. We also present a treatment of the identification of discontinuous elasticity coefficients using the total variation regularization method. General formulas for the computation of the coefficient-to-solution map and a complete convergence analysis are given for the continuous problem as well as for its discrete analogue. Discrete formulas and implementation issues are discussed in detail and numerical examples for smooth and discontinuous coefficients are given. © 2014 Copyright Taylor & Francis Group, LLC.

关键词： Inverse problems

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Physical origins of entropy production, free energy dissipation, and their mathematical representations

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Physical Review E 2010年第5期81卷 051133-051133页

作者： Hao Ge Hong Qian School of Mathematical Sciences and Centre for Computational Systems Biology Fudan University Shanghai 200433 People’s Republic of China Department of Applied Mathematics University of Washington Seattle Washington 98195 USA

A unifying mathematical theory of nonequilibrium thermodynamics of stochastic systems in terms of master equations is presented. As generalizations of isothermal entropy and free energy, two functions of state play central roles: the Gibbs entropy S and the relative entropy F, which are related via the stationary distribution of the stochastic dynamics. S satisfies the fundamental entropy balance equation dS/dt=ep−hd/T with entropy production rate ep≥0 and heat dissipation rate hd, while dF/dt=−fd≤0. For closed systems that satisfy detailed balance: Tep(t)=fd(t). For open systems, one has Tep(t)=fd(t)+Qhk(t), where the housekeeping heat, Qhk≥0, was first introduced in the phenomenological nonequilibrium steady-state thermodynamics put forward by Oono and Paniconi. Qhk represents the irreversible work done by the surrounding to the system that is kept away from reaching equilibrium. Hence, entropy production ep consists of free energy dissipation associated with spontaneous relaxation (i.e., self-organization), fd, and active energy pumping that sustains the open system Qhk. The amount of excess heat involved in the relaxation Qex=hd−Qhk=fd−T(dS/dt). Two kinds of irreversibility, and the meaning of the arrow of time, emerge. Quasistationary processes, adiabaticity, and maximum principle for entropy are also generalized to nonequilibrium settings.

关键词： Free energy

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The core-merging giant impact in Earth's accretion history and its implications

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Acta Geochimica 2022年第4期41卷 553-567页

作者： You Zhou Yun Liu Christian Reinhardt Hongping Deng International Research Center for Planetary Sciences College of Earth SciencesChengdu University of TechnologyChengdu610059China State Key Laboratory of Ore Deposit Geochemistry Institute of GeochemistryChinese Academy of SciencesGuiyang550081China CAS Center for Excellence in Comparative Planetology HefeiChina Center for Theoretical Astrophysics and Cosmology Institute for Computational ScienceUniversity of ZurichWinterthurerstrasse 1908057ZurichSwitzerland Department of Applied Mathematics and Theoretical Physics Centre for Mathematical SciencesUniversity of CambridgeWilberforce RoadCambridgeCB30WAUK

The Earth’s accretion process is accompanied by a large number of *** is widely accepted that collisions dominate the Earth’s late accretion *** all these collisions,there is a special type of collision called Core-merging giant impact(CMGI),in which much or most the impactor’s core merges directly with the protoEarth’s *** core-merging scenario plays an important role in the Earth’s accretion process and deeply affects the formation of the Earth’s core and ***,because CMGI is a small probability event,it has not been fully *** we use the SPH method to comprehensively study all possible CMGIs in the Earth’s accretion *** find that CMGI only occurs in the initial conditions with small impact angle,small impact velocity and big *** further discuss the implications of *** are confident that CMGI inevitably causes the chemical disequilibrium of the Earth’s core and *** CMGI process also brings many light elements into the Earth’s *** particular,if the Moon-forming giant impact is a CMGI,then CMGI can also explain the abnormal content of HSEs in the Earth’s current mantle.

关键词： Giant impact Core-merging process Disequilibrium of the Earth’s core and mantle

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A HYBRIDIZABLE DISCONTINUOUS GALERKIN METHOD ON UNFITTED MESHES FOR SINGLE-PHASE DARCY FLOW IN FRACTURED POROUS MEDIA

arXiv

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arXiv 2022年

作者： Fu, Guosheng Yang, Yang Department of Applied and Computational Mathematics and Statistics University of Notre Dame United States Department of Mathematical Sciences Michigan Technological University United States

We present a novel hybridizable discontinuous Galerkin (HDG) method on unfitted meshes for single-phase Darcy flow in a fractured porous media. In particular we apply the HDG methodology to the recently introduced reinterpreted discrete fracture model (RDFM) [1] that use Dirac-δ functions to model both conductive and blocking fractures. Due to the use of Dirac-δ function approach for the fractures, our numerical scheme naturally allows for unfitted meshes with respect to the fractures, which is the major novelty of the proposed scheme. Moreover, the scheme is locally mass conservative and is relatively easy to implement comparing with existing work on the subject. In particular, our scheme is a simple modification of an existing regular Darcy flow HDG solver by adding the following two components: (i) locate the co-dimension one fractures in the background mesh and adding the appropriate surface integrals associated with these fractures into the stiffness matrix, (ii) adjust the penalty parameters on cells cut through conductive and blocking fractures (fractured cells). Despite the simplicity of the proposed scheme, it performs extremely well for various benchmark test cases in both two- and three-dimensions. This is the first time that a truly unfitted finite element scheme been applied to complex fractured porous media flow problems in 3D with both blocking and conductive fractures without any restrictions on the meshes. © 2022, CC BY.

关键词： Delta functions

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Robust estimation of rotations from relative measurements by maximum likelihood

Robust estimation of rotations from relative measurements by...

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IEEE Annual Conference on Decision and Control

作者： Nicolas Boumal Amit Singer P.-A. Absil Department of Mathematical Engineering ICTEAM Institute Universite catholique de Louvain Belgium Program in Applied and Computational Mathematics Princeton University NJ USA

ISBN: (纸本)9781467357159

We estimate unknown rotation matrices R_i from a set of measurements of relative rotations R_iR_j~T. Measurements are strongly affected by noise such that a small fraction of them are well concentrated around the true relative rotations while the majority of measurements are outliers bearing little or no information. We propose a maximum likelihood estimator (MLE) that explicitly acknowledges this noise model, yielding a robust estimation algorithm. The MLE is computed via Riemannian trust-region optimization using the Manopt toolbox. Comparisons of the MLE with Cramer-Rao bounds suggest the estimator is asymptotically efficient.

关键词： Maximum likelihood estimation Noise Synchronization Rotation measurement Noise measurement Vectors Optimization

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A hybrid-mixed finite element method for single-phase Darcy flow in fractured porous media

arXiv

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arXiv 2021年

We present a hybrid-mixed finite element method for a novel hybrid-dimensional model of single-phase Darcy flow in a fractured porous media. In this model, the fracture is treated as an (d − 1)-dimensional interface within the d-dimensional fractured porous domain, for d = 2, 3. Two classes of fracture are distinguished based on the permeability magnitude ratio between the fracture and its surrounding medium: when the permeability in the fracture is (significantly) larger than in its surrounding medium, it is considered as a conductive fracture;when the permeability in the fracture is (significantly) smaller than in its surrounding medium, it is considered as a blocking fracture. The conductive fractures are treated using the classical hybrid-dimensional approach of the interface model where pressure is assumed to be continuous across the fracture interfaces, while the blocking fractures are treated using the recent Dirac-δ function approach where normal component of Darcy velocity is assumed to be continuous across the interface. Due to the use of Dirac-δ function approach for the blocking fractures, our numerical scheme allows for nonconforming meshes with respect to the blocking fractures. This is the major novelty of our model and numerical discretization. Moreover, our numerical scheme produces locally conservative velocity approximations and leads to a symmetric positive definite linear system involving pressure degrees of freedom on the mesh skeleton only. The performance of the proposed method is demonstrated by various benchmark test cases in both two- and three-dimensions. Numerical results indicate that the proposed scheme is highly competitive with existing methods in the literature. © 2021, CC0.

关键词： Fracture

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Multi-objective hybrid harmony search-simulated annealing for location-inventory-routing problem in supply chain network design of reverse logistics with CO2 emission 28

Multi-objective hybrid harmony search-simulated annealing fo...

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28th Simposium Kebangsaan Sains Matematik, SKSM 2021

作者： Misni, F. Lee, L.S. Jaini, N.I. Centre for Mathematical Sciences College of Computing and Applied Sciences Universiti Malaysia Pahang Lebuhraya Tun Razak Pahang Kuantan Gambang26300 Malaysia Laboratory of Computational Statistics and Operations Research Institute for Mathematical Research Universiti Putra Malaysia UPM Serdang Selangor43400 Malaysia Department of Mathematics Faculty of Science Universiti Putra Malaysia UPM Serdang Selangor43400 Malaysia

The advancement of supply chain network design in reverse logistics is gaining interest from the industries. In recent years, the multi-objective framework of the problem has been widely studied by researchers. This paper integrates three different levels of decision planning in supply chain network design: location-allocation problem for strategic planning, inventory planning management for tactical planning, and vehicle routing for operational planning. A location-inventory-routing problem based on the economic production quantity model with environmental concerns is considered. This study aims to minimise the total cost of operating facilities, inventory and distance travelled by the vehicles as the first objective while minimising the CO2 emission cost as the second objective. Due to the complexity of the problem, a non-dominated sorting and ranking procedure is applied into a Multi-Objective Hybrid Harmony Search-Simulated Annealing (MOHS-SA) algorithm to find the trade-off between these two objectives. computational experiments on the benchmark instances indicate that the proposed MOHS-SA algorithm can produce well-distributed Pareto-optimal solutions for multi-objective problems. © Published under licence by IOP Publishing Ltd.

关键词： Simulated annealing

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Tangent functional canonical correlation analysis for densities and shapes, with applications to multimodal imaging data

arXiv

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arXiv 2021年

作者： Cho, Min Ho Kurtek, Sebastian Bharath, Karthik Department of Applied and Computational Mathematics and Statistics The University of Notre Dame Department of Statistics The Ohio State University School of Mathematical Sciences The University of Nottingham

It is quite common for functional data arising from imaging data to assume values in infinite-dimensional manifolds. Uncovering associations between two or more such nonlinear functional data extracted from the same object across medical imaging modalities can assist development of personalized treatment strategies. We propose a method for canonical correlation analysis between paired probability densities or shapes of closed planar curves, routinely used in biomedical studies, which combines a convenient linearization and dimension reduction of the data using tangent space coordinates. Leveraging the fact that the corresponding manifolds are submanifolds of unit Hilbert spheres, we describe how finite-dimensional representations of the functional data objects can be easily computed, which then facilitates use of standard multivariate canonical correlation analysis methods. We further construct and visualize canonical variate directions directly on the space of densities or shapes. Utility of the method is demonstrated through numerical simulations and performance on a magnetic resonance imaging dataset of Glioblastoma Multiforme brain tumors. © 2021, CC BY.

关键词： Principal component analysis

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High-order interaction modeling of tumor-microenvironment crosstalk for tumor growth

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Physics of Life Reviews 2025年

作者： Jincan Che Yu Wang Li Feng Claudia Gragnoli Christopher Griffin Rongling Wu Beijing Key Laboratory of Topological Statistics and Applications for Complex Systems Beijing Institute of Mathematical Sciences and Applications Beijing 101408 China Center for Computational Biology School of Grassland Science Beijing Forestry University Beijing 100083 China Department of Public Health Sciences Penn State College of Medicine Hershey PA 17033 USA Department of Medicine Creighton University School of Medicine Omaha NE 68124 USA Molecular Biology Laboratory Bios Biotech Multi-Diagnostic Health Center Rome 00197 Italy Applied Research Laboratory The Pennsylvania State University University Park PA 16802 USA Shanghai Institute for Mathematics and Interdisciplinary Sciences Shanghai 200433 China

Signaling interactions between cancer cells and nonmalignant cells in the tumor microenvironment (TME) are believed to influence tumor progression and drug resistance. However, the genomic machineries mediating such an influence remain elusive, making it difficult to determine therapeutic targets on the tumor and its microenvironment. Here, we argue that a computational model, derived from the integration of evolutionary game theory and ecosystem theory through allometric scaling law, can chart the genomic atlas of high-order interaction networks involving tumor cells, TME, and tumor mass. We assess the application of this model to identify the causal influence of gene-induced tumor-TME crosstalk on tumor growth. The findings demonstrate that cooperation and competition between tumor cells and their infiltrating microenvironment promote or inhibit tumor growth in diverse ways. We identify specific genes that govern this promotion or inhibition, which can be used as genetic targets to alter tumor growth. This model opens up a new avenue to precisely infer the genomic underpinnings of tumor-TME interactions and their impact on tumor progression from any omics data.

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