Related papers: Cancellations for Circle-valued Morse Functions vi…
A deep-learning-aided successive-cancellation list (DL-SCL) decoding algorithm for polar codes is introduced with deep-learning-aided successive-cancellation (DL-SC) decoding being a specific case of it. The DL-SCL decoder works by allowing…
We study transformations between discrete Morse functions on a finite simplicial complex via birth-death transitions--elementary chain maps between discrete Morse complexes that either create or cancel pairs of critical simplices. We prove…
We give exact formulae for a wide family of complexity measures that capture the organization of hidden nonlinear processes. The spectral decomposition of operator-valued functions leads to closed-form expressions involving the full…
We present the results of a National Science Foundation (NSF) Project Scoping Workshop, the purpose of which was to assess the current status of calculations for the nuclear matrix elements governing neutrinoless double-beta decay and…
This paper provides a unified framework connecting dynamical systems with tools from topological data analysis and geometric topology and inspires new interactions among dynamical systems, topology, and nonlinear analysis. To this end, we…
Forman introduced discrete Morse theory as a tool for studying CW complexes by essentially collapsing them onto smaller, simpler-to-understand complexes of critical cells in [Fo]. Chari reformulated discrete Morse theory for regular cell…
The "spectral correlation function" analysis we introduce in this paper is a new tool for analyzing spectral-line data cubes. Our initial tests, carried out on a suite of observed and simulated data cubes, indicate that the spectral…
We consider the flows generated by generic gradients of Morse maps of a closed connected manifold $M$ to a circle. To each such flow we associate an invariant counting the closed orbits of the flow. Each closed orbit is counted with the…
We perform a statistical study of permanent changes in longitudinal fields associated with solar flares by tracking magnetic features. The YAFTA feature tracking algorithm is applied to GONG++ one-minute magnetograms for 77 X-class and…
The spectral form factor (SFF) is a powerful diagnostic of random matrix behavior in quantum many-body systems. We introduce a family of random circuit ensembles whose SFFs can be computed \textit{exactly}. These ensembles describe the…
This work is concerned with variational analysis of so-called spectral functions and spectral sets of matrices that only depend on eigenvalues of the matrix. Based on our previous work [H. T. B\`ui, M. N. B\`ui, and C. Clason, Convex…
The flux reconstruction (FR) approach offers a flexible framework for describing a range of high-order numerical schemes; including nodal discontinuous Galerkin and spectral difference schemes. This is accomplished through the use of…
We present an alternative analysis of the $^{113}$Cd $\beta$-decay electron energy spectrum in terms of spectral moments $\mu_n$, corresponding to the averaged values of $n^{\rm th}$ powers of the $\beta$ particle energy. The zeroth moment…
Using high spatial and temporal data from the \emph{Solar Dynamics Observatory} (\emph{SDO}) and the \emph{Interface Region Imaging Spectrograph} (\emph{IRIS}), several observational signatures of magnetic reconnection in the course of…
Monotone chain polar codes generalize classical polar codes to multivariate settings, offering a flexible approach for achieving the entire admissible rate region in the distributed lossless coding problem. However, this flexibility also…
Frequencies of magnetic patch processes on supergranule boundary, namely flux emergence, splitting, merging, and cancellation, are investigated through an automatic detection. We use a set of line of sight magnetograms taken by the Solar…
A Krylov subspace recycling method for the efficient evaluation of a sequence of matrix functions acting on a set of vectors is developed. The method improves over the recycling methods presented in [Burke et al., arXiv:2209.14163, 2022] in…
A simple analytical relation of form {\alpha} = 2 {\kappa} -1 between the magnetic energy spectral exponent {\alpha} of the turbulent magnetic field in the solar photosphere and its magnetic flux cancellation exponent {\kappa}, valid under…
We present an algorithm which produces a decomposition of a regular cellular complex with a discrete Morse function analogous to the Morse-Smale decomposition of a smooth manifold with respect to a smooth Morse function. The advantage of…
Regenerated (FRF curves), synthesis of (FRF) curves there are two main requirement in the form of response model, The first being that of regenerating "Theoretical" curve for the frequency response function actually measured and analysis…