Related papers: A Spectral Sequence for a Graded Linear Map
Recent advances in operator learning theory have improved our knowledge about learning maps between infinite dimensional spaces. However, for large-scale engineering problems such as concurrent multiscale simulation for mechanical…
Much recent work has addressed the solution of a family of partial differential equations by computing the inverse operator map between the input and solution space. Toward this end, we incorporate function-valued reproducing kernel Hilbert…
Recent advancements in quantum computing and quantum-inspired algorithms have sparked renewed interest in binary optimization. These hardware and software innovations promise to revolutionize solution times for complex problems. In this…
A systematic framework is presented for the construction of hierarchies of soliton equations. This is realised by considering scalar linear integral equations and their representations in terms of infinite matrices, which give rise to all…
This work connects two mathematical fields - computational complexity and interval linear algebra. It introduces the basic topics of interval linear algebra - regularity and singularity, full column rank, solving a linear system, deciding…
In HEP experiments the description of the trajectory of a charged particle is obtained from a fit to measurements in tracking detectors. The parametrization of the trajectory has to account for bending in the magnetic field, energy loss and…
Complex networks or graphs are ubiquitous in sciences and engineering: biological networks, brain networks, transportation networks, social networks, and the World Wide Web, to name a few. Spectral graph theory provides a set of useful…
We construct spherical vector bases that are bandlimited and spatially concentrated, or, alternatively, spacelimited and spectrally concentrated, suitable for the analysis and representation of real-valued vector fields on the surface of…
Tracy and Widom showed that fundamentally important kernels in random matrix theory arise from differential equations with rational coefficients. More generally, this paper considers symmetric Hamiltonian systems abd determines the…
We study homotopy theory of the category of spectral sequences with respect to the class of weak equivalences given by maps which are quasi-isomorphisms on a fixed page. We introduce the category of extended spectral sequences and show that…
We introduce a new spectral sequence called the p-chain spectral sequence which converges to the (co-)homology of a contravariant C-space with coefficients in a covariant C-spectrum for a small category C. It is different from the…
In this work, a kernel-based surrogate for integrating Hamiltonian dynamics that is symplectic by construction and tailored to large prediction horizons is proposed. The method learns a scalar potential whose gradient enters a…
Optical two-dimensional (2D) coherent spectroscopy excels in studying coupling and dynamics in complex systems. The dynamical information can be learned from lineshape analysis to extract the corresponding linewidth. However, it is usually…
A sequence $\{\delta_n^{(k)}\}$ associated to a Bochner differential operator is introduced as an effective tool to study this kind of operators. Some properties of this sequence are proven and used to deduce that a particular operator…
Persistent homology is constrained to purely topological persistence while multiscale graphs account only for geometric information. This work introduces persistent spectral theory to create a unified low-dimensional multiscale paradigm for…
Genomic signal processing has been used successfully in bioinformatics to analyze biomolecular sequences and gain varied insights into DNA structure, gene organization, protein binding, sequence evolution, etc. But challenges remain in…
The aim of the paper is to investigate the solutions of special inhomogeneous linear functional equations by using spectral analysis in a translation invariant closed linear subspace of additive/multiadditive functions containing the…
We describe a seriation algorithm for ranking a set of items given pairwise comparisons between these items. Intuitively, the algorithm assigns similar rankings to items that compare similarly with all others. It does so by constructing a…
We first prove a one-to-one correspondence between finding Hamiltonian cycles in a cubic planar graphs and finding trees with specific properties in dual graphs. Using this information, we construct an exact algorithm for finding…
Through the theory of Lie bi-algebroids and generalized complex structures, one could define a cohomology theory naturally associated to a holomorphic Poisson structure. It is known that it is the hypercohomology of a bi-complex such that…