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Predicting the friction angle of clays using a multi-layer perceptron neural network enhanced by yeo-johnson transformation and coral reefs optimization

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Journal of Rock Mechanics and Geotechnical Engineering 2024年第10期16卷 3982-4003页

作者： Libing Yang Trung Nguyen-Thoi Trung-Tin Tran College of Civil Engineering and Architecture Hunan Institute of Science and TechnologyYueyang414006China Laboratory for Applied and Industrial Mathematics Institute for Computational Science and Artificial IntelligenceVan Lang UniversityHo Chi Minh CityViet Nam Faculty of Mechanical-Electrical and Computer Engineering School of TechnologyVan Lang UniversityHo Chi Minh CityViet Nam Department of Information Technology Greenwich VietnamFPT UniversityDa Nang550000Viet Nam

The accurate prediction of the friction angle of clays is crucial for assessing slope stability in engineering *** study addresses the importance of estimating the friction angle and presents the development of four soft computing models:YJ-FPA-MLPnet,YJ-CRO-MLPnet,YJ-ACOC-MLPnet,and *** of all,the Yeo-Johnson(YJ)transformation technique was used to stabilize the variance of data and make it more suitable for parametric statistical models that assume normality and equal *** technique is expected to improve the accuracy of friction angle prediction *** friction angle prediction models then utilized multi-layer perceptron neural networks(MLPnet)and metaheuristic optimization algorithms to further enhance performance,including flower pollination algorithm(FPA),coral reefs optimization(CRO),ant colony optimization continuous(ACOC),and cuckoo search algorithm(CSA).The prediction models without the YJ technique,***-MLPnet,CRO-MLPnet,ACOC-MLPnet,and CSA-MLPnet,were then compared to those with the YJ technique,***-FPA-MLPnet,YJ-CRO-MLPnet,YJ-ACOC-MLPnet,and *** these,the YJ-CRO-MLPnet model demonstrated superior reliability,achieving an accuracy of up to 83%in predicting the friction angle of clay in practical engineering *** improvement is significant,as it represents an increase from 1.3%to approximately 20%compared to the models that did not utilize the YJ transformation technique.

关键词： Natural hazards Slope stability Friction angle Clay Soft computing models Geotechnical engineering

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Simultaneous Estimation of Many Sparse Networks via Hierarchical Poisson Log-Normal Model

arXiv

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arXiv 2024年

作者： Ge, Changhao Li, Hongzhe Graduate Group of Applied Mathematics and Computational Science University of Pennsylvania United States Department of Biostatistics Epidemiology and Informatics University of Pennsylvania United States

The advancement of single-cell RNA-sequencing (scRNA-seq) technologies allow us to study the individual level cell-type-specific gene expression networks by direct inference of genes’ conditional independence structures. scRNA-seq data facilitates the analysis of gene expression data across different conditions or samples, enabling simultaneous estimation of condition- or sample-specific gene networks. Since the scRNA-seq data are count data with many zeros, existing network inference methods based on Gaussian graphs cannot be applied to such single cell data directly. We propose a hierarchical Poisson Log-Normal model to simultaneously estimate many such networks to effectively incorporate the shared network structures. We develop an efficient simultaneous estimation method that uses the variational EM and alternating direction method of multipliers (ADMM) algorithms, optimized for parallel processing. Simulation studies show this method outperforms traditional methods in network structure recovery and parameter estimation across various network models. We apply the method to two single cell RNA-seq datasets, a yeast single-cell gene expression dataset measured under 11 different environmental conditions, and a single-cell gene expression data from 13 inflammatory bowel disease patients. We demonstrate that simultaneous estimation can uncover a wider range of conditional dependence networks among genes, offering deeper insights into gene expression mechanisms. © 2024, CC BY.

关键词： Expectation maximization algorithm

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Non-Hermitian dynamics of a two-spin system with PT symmetry

arXiv

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arXiv 2022年

作者： Komineas, Stavros Department of Mathematics and Applied Mathematics University of Crete Crete Heraklion70013 Greece Institute of Applied and Computational Mathematics FORTH Crete Heraklion70013 Greece

A system of interacting spins that are under the influence of spin-polarized currents can be described using a complex functional, or a non-Hermitian (NH) Hamiltonian. We study the dynamics of two exchange-coupled spins on the Bloch sphere. In the case of currents leading to PT symmetry, an exceptional point that survives also in the nonlinear system is identified. The nonlinear system is bistable for small currents and it exhibits stable oscillating motion or it can relax to a fixed point. The oscillating motion of the two spins is akin to synchronised spin-torque oscillators. For the full nonlinear system, we derive two conserved quantities that furnish a geometric description of the spin trajectories in phase space and indicate stability of the oscillating motion. Our analytical results provide tools for the description of the dynamics of NH systems that are defined on the Bloch sphere. © 2022, CC BY.

关键词： Dynamics

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A fitted scheme for a Caputo initial-boundary value problem

arXiv

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arXiv 2024年

作者： Gracia, Jose Luis O’Riordan, E. Stynes, M. Department of Applied Mathematics University of Zaragoza Torres Quevedo Building Campus Rio Ebro Zaragoza50018 Spain School of Mathematical Sciences Dublin City University Glasnevin Dublin 9 Ireland Applied and Computational Mathematics Division Beijing Computational Science Research Center Haidian District Beijing100193 China

In this paper we consider an initial-boundary value problem with a Caputo time derivative of order α ∈ (0, 1). The solution typically exhibits a weak singularity near the initial time and this causes a reduction in the orders of convergence of standard schemes. To deal with this singularity, the solution is computed with a fitted difference scheme on a graded mesh. The convergence of this scheme is analysed using a discrete maximum principle and carefully chosen barrier functions. Sharp error estimates are proved, which show an enhancement in the convergence rate compared with the standard L1 approximation on uniform meshes, and also indicate an optimal choice for the mesh grading. This optimal mesh grading is less severe than the optimal grading for the standard L1 scheme. Furthermore, the dependence of the error on the final time forms part of our error estimate. Numerical experiments are presented which corroborate our theoretical results. © 2024, CC BY-NC-ND.

关键词： Grading

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Optimal control, viscosity approximation and Arrhenius Law for the shallow lake problem

arXiv

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arXiv 2024年

作者： Koutsimpela, Angeliki Loulakis, Michail Department of Mathematics University of Augsburg Augsburg86159 Germany School of Applied Mathematical and Physical Sciences National Technical University of Athens Athens15780 Greece Institute of Applied and Computational Mathematics Foundation for Research and Technology Hellas Crete Heraklion70013 Greece

We prove existence of optimal control for the deterministic and stochastic shallow lake problem without any restrictions on the parameter space and we establish a generalization of the Arrhenius Law in the case of noise-dependent potentials, which naturally arise in control theory problems. We also prove a result about convergence of the derivatives in the viscosity approximation of the value function and use this result to derive the Arrhenius Law for the shallow lake *** Codes 93E20, 60H30, 49L25 Copyright © 2024, The Authors. All rights reserved.

关键词： Stochastic systems

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Hydrodynamics of marbling art

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Physical Review Fluids 2024年第11期9卷 110506-110506页

作者： Yue Sun John W. M. Bush Saverio E. Spagnolie Chris H. Rycroft Department of Mathematics University of Wisconsin–Madison Madison Wisconsin 53706 USA John A. Paulson School of Engineering and Applied Sciences Harvard University Cambridge Massachusetts 02138 USA Department of Mathematics Massachusetts Institute of Technology Cambridge Massachusetts 02139 USA Computational Research Division Lawrence Berkeley Laboratory Berkeley California 94720 USA

This paper is associated with a video winner of a 2023 American Physical Society's Division of Fluid Dynamics (DFD) Milton van Dyke Award for work presented at the DFD Gallery of Fluid Motion. The original video i... 详细信息

关键词： Low Reynolds number flows Surface & interfacial phenomena

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Least energy positive solutions for Schrödinger systems with critical exponent in R³: Mixed cooperation and competition

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Journal of Differential Equations 2025年 440卷

作者： Liu, Tianhao Zou, Wenming Institute of Applied Physics and Computational Mathematics Beijing 100088 China Department of Mathematical Sciences Tsinghua University Beijing 100084 China

Consider the following coupled Schrödinger system with Sobolev critical exponent −Δui+λiui=∑j=1dβij|uj|[Formula presented]|ui|[Formula presented]−2ui in Ω,i=1,2,.,d, where d≥2, 2⁎=[Formula presented] is the... 详细信息

Consider the following coupled Schrödinger system with Sobolev critical exponent −Δu_i+λ_iu_i=∑j=1dβ_ij|u_j|^{[Formula presented]}|u_i|^{[Formula presented]−2}u_i in Ω,i=1,2,.,d, where d≥2, 2^⁎=[Formula presented] is the Sobolev critical exponent, β_ii>0 for every i and β_ij=β_ji for i≠j. The domain Ω⊂R^N is either bounded or the whole space, and u_i∈H₀¹(Ω) or u_i∈H¹(R^N) respectively. We are concerned with the mixed cooperative and competitive system, incorporating some of the “Grouping” ideas first introduced by [N. Soave: Calc. Var. Partial Differential Equations. 53 (3) (2015), 689–718.]. The existence of least energy positive solutions for N≥4 has been well-studied by H. Tavares et al. [Calc. Var. Partial Differential Equations. 59, (2020);J. Funct. Anal. 283 (2022)]. In this paper, we will study the existence of solutions for N=3. Different from the high dimensional case N≥4, the dimension N=3 makes the proof more challenging, requiring different analysis. When Ω is bounded, we firstly establish the existence of nonnegative solutions with m (1≤m≤d) nontrivial components. The proof is performed by mathematical induction on the number of appropriate subsystem. Then we obtain the existence of least energy positive solution for the mixed cooperative and competitive case, as well as the existence and classification result of ground state solutions for the purely cooperative case. Besides, we obtain a nonexistence result of fully nontrivial ground state under some further assumptions. When Ω is the whole space and λ₁=⋯=λ_d=0, we obtain some nonexistence results for the mixed cooperative and competitive case. © 2025 Elsevier Inc.

关键词： Cooperative and competitive Schrödinger system Critical exponent Dimension three Least energy positive solutions Variational arguments

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Entropic van der Corput’s Difference Theorem

arXiv

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arXiv 2024年

作者： Gu, Weichen Li, Xiang Department of Mathematics and Statistics University of New Hampshire DurhamNH03824 United States Integrated Applied Mathematics Program University of New Hampshire DurhamNH03824 United States

We prove an entropy version of van der Corput’s difference theorem: the entropy of a sequence is equal to the entropy of its differences. This reveals a potential correspondence between the theory of uniform distribution mod 1 and entropy. As applications, we establish the corresponding entropy versions for several other results on uniform distribution. Copyright © 2024, The Authors. All rights reserved.

关键词： Entropy

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Is a single lethal electric field threshold sufficient to characterize the lesion size in computational modeling of cardiac pulsed-field ablation?

Heart Rhythm O2

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Heart Rhythm O2 2025年第5期6卷 671-677页

作者： Petras, Argyrios Amoros Figueras, Gerard Moreno Weidmann, Zoraida García-Sánchez, Tomás Viladés Medel, David Ivorra, Antoni Guerra, Jose M. Gerardo-Giorda, Luca RICAM–Johann Radon Institute for Computational and Applied Mathematics Linz Austria Department of Cardiology Hospital de la Santa Creu i Sant Pau Universitat Autònoma de Barcelona CIBER CV Barcelona Spain Department of Information and Communication Technologies Universitat Pompeu Fabra Barcelona Spain Institute for Mathematical Methods in Medicine and Data-Based Modelling Johannes Kepler University Linz Austria

Background: Pulsed-field ablation (PFA) is a novel cardiac ablation technology based on irreversible electroporation (IRE). PFA computational models rely on identification of a lethal electric field threshold to predict the IRE area. However, the predicted lesion anisotropy ratios (width over depth) vary extensively among recent studies, and these discrepancies remain a subject of discussion. Objective: This work aims to evaluate the predicted lesion anisotropy ratios using a PFA computational model by applying it to an open-chest in vivo porcine model geometry. Methods: Six domestic swine underwent epicardial PFA applications using a previously described waveform protocol. Animals were killed at least 3 hours after the last ablation, and lesions were assessed using triphenyltetrazolium chloride (TTC) staining. Numeric simulations were performed on a segmented and meshed porcine thoracic computed tomography (CT) scan, mimicking the open-chest experimental setup. Results: The maximum width of all simulated lesions was observed at the epicardial surface. The anisotropy ratios (AR) of the experimental lesions were smaller than the simulated ones (AR experimental vs simulated, 1.0–1.7 vs 2–2.7;Q1–Q3 quartiles). Increasing the peak voltage resulted in larger lesions;however, the computational model clearly underestimated the increase in lesion depth compared with the experimental data. Conclusion: Our computational model shows that a single lethal electric field threshold is insufficient to accurately predict both lesion depth and width in cardiac PFA. Our study suggests that for the given PFA waveforms, a threshold between 270 and 500 V/cm provides satisfactory lesion depth estimations, and a higher threshold between 790 and 1000 V/cm better captures the lesion width. © 2025 Heart Rhythm Society

关键词： Cardiac ablation Computer simulations Electric field threshold Mathematical modeling Pulsed field ablation

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Solving Non Linear Differential Equations by Using A G - Homotopy Analysis Method 2

Solving Non Linear Differential Equations by Using A G - Hom...

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2nd International Conference on Mathematical Modeling and computational Methods in Science and Engineering, ICMMCMSE 2020

作者： Saratha, S.R. Bagyalakshmi, M. Sai Sundara Krishnan, G. Department of Mathematics Kumaraguru College of Technology Tamilnadu Coimbatore India Department of Mathematics PSG College of Technology Tamilnadu Coimbatore India Department of Applied Mathematics and Computational Sciences PSG College of Technology Tamilnadu Coimbatore India

This paper proposes an efficient hybrid analytical method named the Generalized Homotopy Analysis Method (GHAM) for solving nonlinear differential equations. The proposed hybrid method consists of topology based Homotopy Analysis Method (HAM) and Laplace typed integral transform (G-transform). Compared with HAM, GHAM does not require the effort to perform repeated integration and differentiation, when it is applied to solve higher order differential equations. Compared with G-transform, GHAM serves as an effective approach to tackle higher-order nonlinear differential equations. The effectiveness of GHAM is illustrated through the analysis of numerical examples, and the obtained results are graphically depicted. Also, GHAM is effectively utilized to analyze the density of the forest cover incorporating various parameters, which include the seed reproduction, seed deposition, seed establishment rates, old trees due to aging and the coefficients of mortality due to space variables. © Published under licence by IOP Publishing Ltd.

关键词： Mathematical transformations

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