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We introduce and study a fractional version of the Skellam process of order $k$ by time-changing it with an independent inverse stable subordinator. We call it the fractional Skellam process of order $k$ (FSPoK). An integral representation…
The vertical motion of a tokamak plasma is analytically modelled during its non-linear phase by a free-moving current-carrying rod inductively coupled to a set of fixed conducting wires or a cylindrical conducting shell. The solutions…
Finding an embedding space for a linear approximation of a nonlinear dynamical system enables efficient system identification and control synthesis. The Koopman operator theory lays the foundation for identifying the nonlinear-to-linear…
In this paper we propose a tensor-based nonlinear model for high-order data classification. The advantages of the proposed scheme are that (i) it significantly reduces the number of weight parameters, and hence of required training samples,…
A novel conformal mapping based Fractional Order (FO) methodology is developed in this paper for tuning existing classical (Integer Order) Proportional Integral Derivative (PID) controllers especially for sluggish and oscillatory second…
The present study proposes a new Orthogonal Floating Search framework for structure selection of nonlinear systems by adapting the existing floating search algorithms for feature selection. The proposed framework integrates the concept of…
We consider a conflict-controlled dynamical system described by a nonlinear ordinary fractional differential equation with the Caputo derivative of an order $\alpha \in (0, 1).$ Basing on the finite-difference Gr\"{u}nwald-Letnikov…
Recent advances in scientific machine learning have shed light on the modeling of pattern-forming systems. However, simulations of real patterns still incur significant computational costs, which could be alleviated by leveraging large…
This paper presents a novel episodic method to learn a robot's nonlinear dynamics model and an increasingly optimal control sequence for a set of tasks. The method is based on the {\em Koopman operator} approach to nonlinear dynamical…
Recent research in deep learning (DL) has investigated the use of the Fast Fourier Transform (FFT) to accelerate the computations involved in Convolutional Neural Networks (CNNs) by replacing spatial convolution with element-wise…
Designing effective neural networks requires tuning architectural elements. This study integrates fractional calculus into neural networks by introducing fractional order derivatives (FDO) as tunable parameters in activation functions,…
Diffractive neural network (DNN), which can perform machine learning tasks based on the light propagation and diffraction, has recently emerged as a promising optical computing paradigm due to its high parallel processing speed and low…
Our work addresses the problem of predicting the highest priority functional group present in an organic molecule. Functional Groups are groups of bound atoms that determine the physical and chemical properties of organic molecules. In the…
This paper introduces an operator-based neural network, the mirror-padded Fourier neural operator (MFNO), designed to learn the dynamics of stochastic systems. MFNO extends the standard Fourier neural operator (FNO) by incorporating mirror…
This article describes an approximation technique based on fractional order Bernstein wavelets for the numerical simulations of fractional oscillation equations under variable order, and the fractional order Bernstein wavelets are derived…
The use of variational method in functional integral approach is discussed for fermion and boson systems with Coulomb interaction. The formal general expression of thermodynamic potential is obtained by Feynman path integral technique and…
In this paper, a weighted proportional fair (PF) scheduling method is proposed in the context of non-orthogonal multiple access (NOMA) with successive interference cancellation (SIC) at the receiver side. The new scheme introduces weights…
Dynamical system models such as Recurrent Neural Networks (RNNs) have become increasingly popular as hypothesis-generating tools in scientific research. Evaluating the dynamics in such networks is key to understanding their learned…
We propose a new network architecture, the Fractal Pyramid Networks (PFNs) for pixel-wise prediction tasks as an alternative to the widely used encoder-decoder structure. In the encoder-decoder structure, the input is processed by an…
The invariant distribution, which is characterized by the stationary Fokker-Planck equation, is an important object in the study of randomly perturbed dynamical systems. Traditional numerical methods for computing the invariant distribution…