An N-dimensional nonlinear Fokker-Planck equation is investigated here by considering the time dependence of the coefficients, where drift-controlled and source terms are present. We exhibit the exact solution based on the generalized Gaussian function related to the Tsallis statistics. Furthermore, we show that a rich class of diffusive processes, including normal and anomalous ones, can be obtained by changing the time dependence of the coefficients.
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http://dx.doi.org/10.1103/PhysRevE.65.052101 | DOI Listing |
Neural Netw
February 2025
the School of Automation, Nanjing University of Science and Technology, Nanjing, PR China. Electronic address:
In this paper, a new static pinning intermittent control based on resource awareness triggering is proposed. A multi-layer control technique is used to synchronize the coupled neural network. First, a hierarchical network structure including pinned and interaction layers is induced using each pinning strategy.
View Article and Find Full Text PDFMath Biosci Eng
July 2023
Marian Smoluchowski Institute of Physics, Jagiellonian University, 31-348 Cracow, Poland.
In positron emission tomography (PET) studies, convolutional neural networks (CNNs) may be applied directly to the reconstructed distribution of radioactive tracers injected into the patient's body, as a pattern recognition tool. Nonetheless, unprocessed PET coincidence data exist in tabular format. This paper develops the transformation of tabular data into n-dimensional matrices, as a preparation stage for classification based on CNNs.
View Article and Find Full Text PDFBull Math Biol
January 2023
Department of Mathematics, University College London, London, WC1H 0AY, UK.
Pattern formation has been extensively studied in the context of evolving (time-dependent) domains in recent years, with domain growth implicated in ameliorating problems of pattern robustness and selection, in addition to more realistic modelling in developmental biology. Most work to date has considered prescribed domains evolving as given functions of time, but not the scenario of concentration-dependent dynamics, which is also highly relevant in a developmental setting. Here, we study such concentration-dependent domain evolution for reaction-diffusion systems to elucidate fundamental aspects of these more complex models.
View Article and Find Full Text PDFNeural Netw
January 2023
Dipartimento di Scienze del Sistema Nervoso e del Comportamento, Università di Pavia, Via Agostino Bassi, 21, Pavia, 27100, Italy; Gruppo Nazionale per la Fisica Matematica, INDAM, Italy; Istituto Nazionale di Fisica Nucleare, sezione di Milano, INFN, Italy. Electronic address:
We proposed in a previous work a geometric framework to study a deep neural network, seen as sequence of maps between manifolds, employing singular Riemannian geometry. In this paper, we present an application of this framework, proposing a way to build the class of equivalence of an input point: such class is defined as the set of the points on the input manifold mapped to the same output by the neural network. In other words, we build the preimage of a point in the output manifold in the input space.
View Article and Find Full Text PDFMath Biosci Eng
May 2022
School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou 730070, China.
This study examines an optimal harvesting problem for a periodic n-dimensional food chain model that is dependent on size structure in a polluted environment. This is closely related to the protection of biodiversity, as well as the development and utilization of renewable resources. The model contains state variables representing the density of the ith population, the concentration of toxicants in the ith population, and the concentration of toxicants in the environment.
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