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Many computer vision problems can be formulated as binary quadratic programs (BQPs). Two classic relaxation methods are widely used for solving BQPs, namely, spectral methods and semidefinite programming (SDP), each with their own…
A spectral decomposition method is used to obtain solutions to a class of nonlinear differential equations. We extend this approach to the analysis of the fractional form of these equations and demonstrate the method by applying it to the…
This article introduces a flexible and adaptive nonparametric method for estimating the association between multiple covariates and power spectra of multiple time series. The proposed approach uses a Bayesian sum of trees model to capture…
In this paper we first study partial regularity of weak solutions to the initial boundary value problem for the system $-\mbox{div}\left[(I+\mathbf{m}\otimes \mathbf{m})\nabla p\right]=S(x),\ \ \partial_t\mathbf{m}-D^2\Delta…
The impedance probe is a measurement device to measure plasma parameter like electron density. It consists of one electrode connected to a network analyzer via a coaxial cable and is immersed into a plasma. A bias potential superposed with…
Conventional finite-difference schemes for solving partial differential equations are based on approximating derivatives by finite-differences. In this work, an alternative theory is proposed which view finite-difference schemes as…
We propose a novel decomposition framework for the distributed optimization of Difference Convex (DC)-type nonseparable sum-utility functions subject to coupling convex constraints. A major contribution of the paper is to develop for the…
We find an explicit form of weak solutions to a Riemann problem for a degenerate semilinear parabolic equation with piecewise constant diffusion coefficient. It is demonstrated that the phase transition lines (free boundaries) correspond to…
In this paper, we present numerical procedures to compute solutions of partial differential equations posed on fractals. In particular, we consider the strong form of the equation using standard graph Laplacian matrices and also weak forms…
In this paper, the Discontinuous Cell Method (DCM) is formulated with the objective of simulating cohesive fracture propagation and fragmentation in homogeneous solids without issues relevant to excessive mesh deformation typical of…
Computing the rate-distortion function for continuous sources is commonly regarded as a standard continuous optimization problem. When numerically addressing this problem, a typical approach involves discretizing the source space and…
We proposed a novel dense line spectrum super-resolution algorithm, the DMRA, that leverages dynamical multi-resolution of atoms technique to address the limitation of traditional compressed sensing methods when handling dense point-source…
The EMI (Extracellular-Membrane-Intracellular) model describes electrical activity in excitable tissue, where the extracellular and intracellular spaces and cellular membrane are explicitly represented. The model couples a system of partial…
Symmetry principles play an important role in geometry, and physics, allowing for the reduction of complicated systems to simpler, more comprehensible models that preserve the system's features of interest. Biological systems are often…
The interaction between excitation and inhibition is crucial for brain computation. To understand synaptic mechanisms underlying brain function, it is important to separate excitatory and inhibitory inputs to a target neuron. In the…
A classic approach for solving differential equations with neural networks builds upon neural forms, which employ the differential equation with a discretisation of the solution domain. Making use of neural forms for time-dependent…
The paper concerns the multiscale modeling of a myelinated axon. Taking into account the microstructure with alternating myelinated parts and nodes Ranvier, we derive a nonlinear cable equation describing the potential propagation along the…
Partial discharge (PD) is a common indication of faults in power systems, such as generators, and cables. These PD can eventually result in costly repairs and substantial power outages. PD detection traditionally relies on hand-crafted…
Within recent years, considerable progress has been made regarding high-performance solvers for Partial Differential Equations (PDEs), yielding potential gains in efficiency compared to industry standard tools. However, the latter largely…
An alternative to the fully implicit or monolithic methods used for the solution of the coupling of fluid flow and deformation in porous media is a sequential approach in which the fully coupled system is broken into subproblems (flow and…