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Many state-of-the-art computer vision architectures leverage U-Net for its adaptability and efficient feature extraction. However, the multi-resolution convolutional design often leads to significant computational demands, limiting…
One of the outstanding problems in complexity science and dynamical system theory is understanding the dynamic behavior of high-dimensional networked systems and their susceptibility to transitions to undesired states. Because of varied…
A numerical study of the radiation in coupled bent waveguides is presented. Such arrangements of curved waveguides in reduced radiation-loss configurations can be used to enhance the quality factor of integrated micro-resonators. 3D full…
In this article we discuss the numerical analysis for the finite difference scheme of the one-dimensional nonlinear wave equations with dynamic boundary conditions. From the viewpoint of the discrete variational derivative method we propose…
A theoretical study of photonic bands for one-dimensional (1D) lattices embedded in planar waveguides with strong refractive index contrast is presented. The approach relies on expanding the electromagnetic field on the basis of guided…
It is well known that the water-wave problem with weak surface tension has small-amplitude line solitary-wave solutions which to leading order are described by the nonlinear Schr\"odinger equation. The present paper contains an existence…
In this paper, we study the nonlinear dispersive waves including the rarefaction and dispersive shock waves in the discrete modified KdV equation through the numerical simulations of the dispersive Riemann problems. In particular, we…
In this work, we present two numerical methods to approximate solutions of systems of dissipative sine-Gordon equations that arise in the study of one-dimensional, semi-infinite arrays of Josephson junctions coupled through superconducting…
We study quantum transport properties of finite periodic quasi-one-dimensional waveguides whose classical dynamics is diffusive. The system we consider is a scattering configuration, composed of a finite periodic chain of $L$ identical…
This paper develops new theory and algorithms for 1D general mode decompositions. First, we introduce the 1D synchrosqueezed wave packet transform and prove that it is able to estimate the instantaneous information of well-separated modes…
This work focuses on the length correction due to radiation effect of a duct discontinuity or at the surface of a perforated plate in the linear acoustic domain and at large wavelengths. Two results are obtained from the comparison of…
Dimensionality reduction of ECG signals is considered within the framework of sparse representation. The approach constructs the signal model by selecting elementary components from a redundant dictionary via a greedy strategy. The proposed…
This work presents an overview of several nonlinear reduction strategies for data compression from various research fields, and a comparison of their performance when applied to problems characterized by diffusion and/or advection terms. We…
We study the transmission of light through a system consisting of an arbitrary number $N$ of microtoroidal resonators coupled to a one-dimensional (1D) waveguide. The transmission $T$ through such a system and its full-width at half-maximum…
The quasi-one-dimensional rhombic array of the waveguides is considered. System of equations describing coupled waves in the waveguide in the linear limit is solved exactly. The electric field distribution was found both for the…
The electrodynamic features of the multiband model are examined using the transverse equation of motion approach in order to give the explanation of several long-standing problems. It turns out that the exact summation of the most singular…
A (d+1)-dimensional dispersionless PDE is said to be integrable if its n-component hydrodynamic reductions are locally parametrized by (d-1)n arbitrary functions of one variable. Given a PDE which does not pass the integrability test, the…
A $\Gamma$-convergence analysis is used to perform a 3D-2D dimension reduction of variational problems with linear growth. The adopted scaling gives rise to a nonlinear membrane model which, because of the presence of higher order external…
Dimensionality reduction is an effective method for learning high-dimensional data, which can provide better understanding of decision boundaries in human-readable low-dimensional subspace. Linear methods, such as principal component…
Solving compressible flows containing discontinuities remains a major challenge for numerical methods especially on unstructured grids. Thus in this work, we make contributions to shock capturing schemes on unstructured grids with aim of…