Academic Articles & Research Papers

Conceptual Mathematics

In the last 60 years, the use of the notion of category has led to a remarkable unification and simplification of mathematics. Conceptual Mathematics introduces this tool for the learning, development, and use of mathematics, to beginning s...

On practical ℎ-observer design for nonlinear non-autonomous dynamical systems with disturbances

In this paper, a particular form of practical ℎ-observers for piecewise continuous Lipschitz, one-sided piecewise continuous Lipschitz systems and quasi-one-sided piecewise continuous Lipschitz systems is extended to nonlinear non-autonomou...

Existence results and Ulam-Hyers stability for a sequential deformable fractional initial value problem

Abstract In this study, we establish existence and Ulam-Hyers results for nonlinear sequential fractional differential equations involving the deformable derivative. We employ the Banach contraction principle and Krasnoselskii’s theorem to ...

Dynamical Systems in Neuroscience

Explains the relationship of electrophysiology, nonlinear dynamics, and the computational properties of neurons, with each concept presented in terms of both neuroscience and mathematics and illustrated using geometrical intuition. In order...

Benchmarking spiking neurons for linear quadratic regulator control of multi-linked pole on a cart: from single neuron to ensemble

The emerging field of neuromorphic computing for edge control applications poses the need to quantitatively estimate and limit the number of spiking neurons, to reduce network complexity and optimize the number of neurons per core and hence...

A NEURAL NETWORK PRIMER

Neural networks are composed of basic units somewhat analogous to neurons. These units are linked to each other by connections whose strength is modifiable as a result of a learning process or algorithm. Each of these units integrates indep...

Neural networks for system identification

Two approaches are presented for utilization of neural networks in identification of dynamical systems. In the first approach, a Hopfield network is used to implement a least-squares estimation for time-varying and time-invariant systems. T...

Immunology for physicists

The immune system is a complex system of cells and molecules that can provide us with a basic defense against pathogenic organisms. Like the nervous system, the immune system performs pattern recognition tasks, learns, and retains a memory ...

Understanding the role of autoencoders for stiff dynamical systems using information theory

Using information theory, this study provides insights into how the construction of latent space of autoencoder (AE) using deep neural network (DNN) training finds a smooth (non-stiff) low-dimensional manifold in the stiff dynamical system....

Topological Data Analysis: Foundations, Algorithms, and Emerging Applications

Topological data analysis (TDA) has evolved into a flexible and robust paradigm for obtaining qualitative, geometry-inspired insights from high-dimensional, noisy, and complex data. Grounded in algebraic topology, geometry, statistics, and ...

A Proposal on Machine Learning via Dynamical Systems

Physics-Informed Machine Learning

Data-driven discovery is revolutionizing how we model, predict, and control complex systems. Now with Python and MATLAB®, this textbook trains mathematical scientists and engineers for the next generation of scientific discovery by offering...

Attractor reconstruction by machine learning

A machine-learning approach called "reservoir computing" has been used successfully for short-term prediction and attractor reconstruction of chaotic dynamical systems from time series data. We present a theoretical framework that describes...