Results 71 to 80 of about 2,473,621 (173)

Spatial modeling of crime dynamics: Patch and reaction–diffusion compartmental systems

Mathematical Methods in the Applied Sciences, Volume 48, Issue 7, Page 7440-7459, 15 May 2025.
We study the dynamics of abstract models for crime evolution. The population is divided into three compartments, taking into account the participation in crime and incarceration. Individuals transit between the three segments, assuming that having more contact with criminally active people increases one's risk of learning and acquiring the same traits;
Julia Calatayud, Marc Jornet, Jorge Mateu   +2 more
wiley   +1 more source

Forward uncertainty quantification in random differential equation systems with delta‐impulsive terms: Theoretical study and applications

Mathematical Methods in the Applied Sciences, Volume 48, Issue 7, Page 7609-7629, 15 May 2025.
This contribution aims at studying a general class of random differential equations with Dirac‐delta impulse terms at a finite number of time instants. Our approach directly addresses calculating the so‐called first probability density function, from which all the relevant statistical information about the solution, a stochastic process, can be ...
Vicente J. Bevia, Juan C. Cortés, Rafael J. Villanueva   +2 more
wiley   +1 more source

Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations

Communications on Pure and Applied Mathematics, Volume 78, Issue 5, Page 995-1041, May 2025.
Abstract The randomly pivoted Cholesky algorithm (RPCholesky) computes a factorized rank‐k$k$ approximation of an N×N$N \times N$ positive‐semidefinite (psd) matrix. RPCholesky requires only (k+1)N$(k + 1)N$ entry evaluations and O(k2N)$\mathcal {O}(k^2 N)$ additional arithmetic operations, and it can be implemented with just a few lines of code.
Yifan Chen, Ethan N. Epperly, Joel A. Tropp, Robert J. Webber   +3 more
wiley   +1 more source

Numerical Analysis of HiPPO-LegS ODE for Deep State Space Models [PDF]

arXiv
In deep learning, the recently introduced state space models utilize HiPPO (High-order Polynomial Projection Operators) memory units to approximate continuous-time trajectories of input functions using ordinary differential equations (ODEs), and these techniques have shown empirical success in capturing long-range dependencies in long input sequences ...
arxiv  

Scattering for a particle interacting with a Bose gas [PDF]

arXiv, 2019
We study the asymptotic behavior of solutions to an ODE - Schr\"{o}dinger type system that models the interaction of a particle with a Bose gas. We show that the particle has a ballistic trajectory asymptotically, and that the wave function describing the Bose gas converges to a soliton in $L^{\infty}.$
arxiv  

Mean‐field limit of non‐exchangeable systems

Communications on Pure and Applied Mathematics, Volume 78, Issue 4, Page 651-741, April 2025.
Abstract This paper deals with the derivation of the mean‐field limit for multi‐agent systems on a large class of sparse graphs. More specifically, the case of non‐exchangeable multi‐agent systems consisting of non‐identical agents is addressed. The analysis does not only involve PDEs and stochastic analysis but also graph theory through a new concept ...
Pierre‐Emmanuel Jabin, David Poyato, Juan Soler   +2 more
wiley   +1 more source

On the stability of Runge–Kutta methods for arbitrarily large systems of ODEs

Communications on Pure and Applied Mathematics, Volume 78, Issue 4, Page 821-855, April 2025.
Abstract We prove that Runge–Kutta (RK) methods for numerical integration of arbitrarily large systems of Ordinary Differential Equations are linearly stable. Standard stability arguments—based on spectral analysis, resolvent condition or strong stability, fail to secure the stability of RK methods for arbitrarily large systems.
Eitan Tadmor
wiley   +1 more source

Influence of Joule Heating and Nonlinear Thermal Radiation on the Electrical Conductivity of Second‐Grade Hybrid Nanofluid Flow Over a Stretching Cylinder

Engineering Reports, Volume 7, Issue 4, April 2025.
The present study investigates heat and mass transfer of electrically conducting second‐grade hybrid nanofluid flow over a stretching cylinder in the presence of nonuniform heat sources and nonlinear thermal radiation. The application of such hybrid nanofluid in second‐grade fluid flow can significantly enhance thermal conductivity and heat transfer ...
Eshetu Haile Gorfie, Asfaw Tsegaye Moltot, Gurju Awgichew Zergaw, Hunegnaw Dessie   +3 more
wiley   +1 more source

A Geometric Interpretation for the Algebraic Properties of Second‐Order Ordinary Differential Equations

Mathematical Methods in the Applied Sciences, Volume 48, Issue 6, Page 6912-6917, April 2025.
ABSTRACT Nowadays, a substantial portion of investigations concerning the symmetry analysis of differential equations predominantly adhere to a framework comprising the following key procedures: (i) the derivation of symmetries, (ii) the determination of an optimal system, (iii) the utilization of these symmetries to construct invariants or ...
A. Paliathanasis, S. Moyo, P. G. L. Leach   +2 more
wiley   +1 more source

Comparing Scientific Machine Learning With Population Pharmacokinetic and Classical Machine Learning Approaches for Prediction of Drug Concentrations

CPT: Pharmacometrics &Systems Pharmacology, Volume 14, Issue 4, Page 759-769, April 2025.
ABSTRACT A variety of classical machine learning (ML) approaches has been developed over the past decade aiming to individualize drug dosages based on measured plasma concentrations. However, the interpretability of these models is challenging as they do not incorporate information on pharmacokinetic (PK) drug disposition.
Diego Valderrama, Olga Teplytska, Luca Marie Koltermann, Elena Trunz, Eduard Schmulenson, Achim Fritsch, Ulrich Jaehde, Holger Fröhlich   +7 more
wiley   +1 more source