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Charged point defects in materials are widely studied using Density Functional Theory (DFT) packages with periodic boundary conditions. The formation energy and defect level computed from these simulations need to be corrected to remove the…
We first review the convolution fast-Fourier-transform (CFFT) approach for the numerical solution of backward stochastic differential equations (BSDEs) introduced in (Hyndman and Oyono Ngou, 2017). We then propose a method for improving the…
It is observed that the Cauchy integral formula (CIF) can be used to represent holomorphic functions of diagonalizable operators on a finite domain. This forms the theoretical foundation for applying various operators in the form of a…
We show via counterexamples that relative entropy between the solution of a Markovian master equation and the steady state is not a convex function of time. We thus let down a curtain on a possible formulation of a principle of…
Window decoding, first proposed to reduce decoding complexity for real-time decoding, is an essential component to realize scalable, universal-fault tolerant computation. Prior work has focused on improving throughput through…
Verification of C++ programs has seen considerable progress in several areas, but not for programs that use these languages' mathematical libraries. The reason is that all libraries in widespread use come with no guarantees about the…
We revisit the computation of the phase space factors (PSF) involved in the positron decay and electron capture (EC) processes for a large number of nuclei of experimental interest. To obtain the electron/positron wave functions needed in…
Full Waveform Inversion (FWI) is a powerful technique for estimating high-resolution subsurface velocity models by minimizing the discrepancy between modeled and observed seismic data. However, the oscillatory nature of seismic waveforms…
An efficient procedure for error-value calculations based on fast discrete Fourier transforms (DFT) in conjunction with Berlekamp-Massey-Sakata algorithm for a class of affine variety codes is proposed. Our procedure is achieved by…
We present an explicit multiscale algorithm for solving differential equations for problems with high-frequency modes that can be averaged over by separating and scaling the fast and slow dynamics within a single equation. We introduce a…
A microscopic description of nuclear fission represents one of the most challenging problems in nuclear theory. While phenomenological coordinates, such as multipole moments, have often been employed to describe fission, it is not obvious…
Iterative processing is widely adopted nowadays in modern wireless receivers for advanced channel codes like turbo and LDPC codes. Extension of this principle with an additional iterative feedback loop to the demapping function has proven…
Recent progress in robust statistical learning has mainly tackled convex problems, like mean estimation or linear regression, with non-convex challenges receiving less attention. Phase retrieval exemplifies such a non-convex problem,…
In this work, we present a new technique for the decomposition of multivariate data, which we call Multivariate Fast Iterative Filtering (MvFIF) algorithm. We study its properties, proving rigorously that it converges in finite time when…
In this paper, we consider the computation of charged moments of the reduced density matrix of two disjoint intervals in the $1+1$ dimensional free compactified boson conformal field theory (CFT) by studying the four-point function of the…
Neutral atom quantum computers hold promise for scaling up to hundreds of thousands or more qubits, but their progress is constrained by slow qubit readout. Parallel measurement of qubit arrays currently takes milliseconds, much longer than…
Variational time discretization schemes are getting of increasing importance for the accurate numerical approximation of transient phenomena. The applicability and value of mixed finite element methods (MFEM) in space for simulating…
Integral representations are considered of solutions of the inhomogeneous Airy differential equation $w''-z w=\pm1/\pi$. The solutions of these equations are also known as Scorer functions. Certain functional relations for these functions…
The mean shift (MS) algorithm seeks a mode of the kernel density estimate (KDE). This study presents a convergence guarantee of the mode estimate sequence generated by the MS algorithm and an evaluation of the convergence rate, under fairly…
Storage systems have a strong need for substantially improving their error correction capabilities, especially for long-term storage where the accumulating errors can exceed the decoding threshold of error-correcting codes (ECCs). In this…