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This work is concerned with the computation of the action of a matrix function f(A), such as the matrix exponential or the matrix square root, on a vector b. For a general matrix A, this can be done by computing the compression of A onto a suitable Krylov ...
A novel surrogate model based on the Grassmannian diffusion maps (GDMaps) and utilizing geometric harmonics (GH) is developed for predicting the response of complex physical phenomena. The method utilizes GDMaps to obtain a low-dimensional representation o ...
The development of fluorescence-based molecular imaging has revolutionized cell biology allowing the visualization of specific biomolecules at the microscopic and, more recently, at the nanoscopic scale while in their relevant biological contexts. Nonethel ...
The computation of the matrix exponential is a ubiquitous operation in numerical mathematics, and for a general, unstructured n×n matrix it can be computed in O(n3) operations. An interesting problem arises if the input matrix is a Toeplitz matrix, for exa ...
We prove exponential convergence to equilibrium for the Fredrickson-Andersen one-spin facilitated model on bounded degree graphs satisfying a subexponential, but larger than polynomial, growth condition. This was a classical conjecture related to non-attra ...
Small relative perturbations to the entries of an essentially nonnegative matrix introduce small relative errors to entries of its exponential. It is thus desirable to compute the exponential with high componentwise relative accuracy. Taylor series approxi ...
Leptogenesis with heavy neutrino flavours is discussed within a density matrix formalism. We write the density matrix equation, describing the generation of the matter-antimatter asymmetry, for an arbitrary choice of the right-handed (RH) neutrino masses. ...
A medical student learning to perform a laparoscopic procedure or a recently paralyzed user of a powered wheelchair must learn to operate machinery via interfaces that translate their actions into commands for an external device. Since the user’s actions a ...
We study the problem of computing the matrix exponential of a block triangular matrix in a peculiar way: Block column by block column, from left to right. The need for such an evaluation scheme arises naturally in the context of option pricing in polynomia ...
The family of natural evolution strategies (NES) offers a principled approach to real-valued evolutionary optimization by following the natural gradient of the expected fitness. Like the well-known CMA-ES, the most competitive algorithm in the field, NES c ...
