Current dynamical overlap fermion hybrid Monte Carlo simulations encounter large fermionic forces when there is mixing between near zero-eigenvectors of the kernel operator. This leads to low acceptance rates when there is a large density of near zero eigenvectors. I present a method where these large forces are eliminated and the large action jumps seen when two eigenvectors approach zero are ...

In this article, nondegeneracy of singular vector tuples, Z-eigenvectors and eigenvectors tensors is studied, which have found many applications in diverse areas. The main results are: (i) each (Z-)eigenvector/singular tuple a generic tensor nondegenerate, (ii) nonzero Z-eigenvector/singular an orthogonally decomposable nondegenerate.

We exploit the Laplace-Beltrami operator to represent shapes which in turn is used for designing a shape based transfer function for volume rendering. Laplace-Beltrami spectral measures are isometry invariant and are one of the most powerful ways to represent shape, also called “Shape-DNA”. Isosurfaces are extracted from the volume data and the Laplace-Beltrami operator is applied on these extr...

We exploit the Laplace-Beltrami (LB) operator to represent shapes, which in turn is used to visualize certain standard datasets specifically for biomedical applications. LB spectral measures are isometry invariant and are one of the most powerful ways to represent shape, also called “Shape-DNA”. We define a shape signature by finding the eigenvalues and eigenvectors of the LB matrix for the giv...

This paper presents and analyzes a new algorithm for computing eigenvectors of symmetric tridiagonal matrices factored as LDLt, with D diagonal and L unit bidiagonal. If an eigenpair is well behaved in a certain sense with respect to the factorization, the algorithm is shown to compute an approximate eigenvector which is accurate to working precision. As a consequence, all the eigenvectors comp...

We show the existence of discrete sets of Raman sidebands which self-consistently establish a Raman coherence and propagate without change in amplitude and relative phase. Equivalently, there exist periodic femtosecond-time-scale, temporal pulse shapes which propagate without change in shape.

This paper introduces a framework for solving time-autonomous nonlinear infinite horizon optimal control problems, under the assumption that all minimizers satisfy Pontryagin’s necessary optimality conditions. In detail, we use methods from field of symplectic geometry to analyze eigenvalues Koopman operator lifts differential equation into suitably defined dimensional space. has advantage spec...

We hypothesize that coordinated functional activity within discrete neural circuits induces morphological organization and plasticity within those circuits. Identifying regions of morphological covariation that are independent of morphological covariation in other regions therefore may therefore allow us to identify discrete neural systems within the brain. Comparing the magnitude of these vari...

Two definitions of the problem of graph drawing are considered, and an analytical solution is provided for each of them. The solutions obtained make use of the eigenvectors of the Laplacian matrix of a related structure. The procedures give good results for symmetrical graphs, and they have already been used for drawing fullerene molecules in the literature. The analysis characterizes precisely...

The map which takes a square matrix to its tropical eigenvalue-eigenvector pair is piecewise linear. We determine the cones of linearity of this map. They are simplicial but they do not form a fan. Motivated by statistical ranking, we also study the restriction of that cone decomposition to the subspace of skew-symmetric matrices.