September 28, 2023

p-adic Cellular Neural Networks

In this article we introduce the p-adic cellular neural networks which are mathematical generalizations of the classical cellular neural networks (CNNs) introduced by Chua and Yang. The new networks have infinitely many cells which are organized hierarchically in rooted trees, and, they have infinitely many hidden layers. Intuitively, the p-adic CNNs occur as limits of large hierarchical discrete CNNs. More precisely, the new networks can be very well approximated by hierarchical discrete CNNs. Mathematically speaking, each of the new networks is modeled by one integro-differential equation depending on several p-adic spatial variables and the time. We study the Cauchy problem associated to these integro-differential equations and also provide numerical methods for solving them.

About the speaker

Mr. Baboucarr Dibba is a PhD candidate at the University of Texas Rio Grande Valley. He grew up in Kanifing South, which is a town in the Gambia, and lies immediately west of the capital city of Banjul. His academic journey began at Nusrat Senior Secondary School and his interests veered him towards earning an Automotive Engineering diploma at Gambia Technical Training Institute (GTTI). Following a series of health challenges, and inspired by the scant local mathematical expertise in Gambia, Mr. Dibba pivoted career directions, earning a Bachelors of Science with Honors in Mathematics from the University of The Gambia. This spurred his advanced studies in Mathematical Engineering and Industrial Mathematics at the universities of L'Aquila and Silesia in Italy and Poland, respectively, broadening his intellectual horizons through a thesis on Quantum Control of Qubits and Qutrits. 

As a Ph.D. candidate at the University of Texas Rio Grande Valley, USA, in Mathematics and Statistics with Interdisciplinary Applications, Mr. Dibba's numerical ardor fuels his exploration into neural networks, partial differential equations (PDEs), and statistical methods. This enriched scholarly voyage, peppered with research and teaching engagements, has sharpened his acumen, bolstering his resolve to excel in mathematical modeling. Throughout Mr. Dibba's journey is an echo of unwavering dedication to enhancing Gambia's mathematical domain, of which encapsulates the essence of his enduring academic expedition.