We map the Eigen model of biological evolution [Naturwissenschaften 58, 465 (1971)] into a quantum spin model with non-Hermitian Hamiltonian. Based on such a connection, we derive exact relaxation periods for the Eigen model to approach static energy landscape from various initial conditions. We also study a simple case of dynamic fitness function.

Let $$\phi $$ be an even Hecke–Maass cusp form on $${{\text {SL}}}_2({\mathbb {Z}})$$ whose L-function does not vanish at the center of functional equation. In this article, we obtain exact formula average triple products , f and $${\bar{f}}$$ where runs over orthonormal basis $$H_k$$ Hecke eigen elliptic forms a fixed weight $$k\geqslant 4$$ . As application, prove quantitative non-vanishing r...

A generalized Cohen-Grossberg neural network with both ordinary and neutral type discrete time varying delays is considered here. Behaved functions are not required to be differentiable. Sufficient conditions are presented for the uniqueness of periodic solution. By using Lyapunov stability theory and Linear Matrix Inequality (LMI) technique sufficient conditions are derived to ascertain the gl...

Previous investigations have shown that one mechanism of irregular vocal fold vibration may be a desynchronization of two or more vibratory modes of the vocal fold tissues. In the current investigation, mechanisms of irregular vibration were further examined using a self-oscillating, physical model of vocal fold vibration, a hemi-model methodology, and high-speed, stereoscopic, digital imaging....

Abstract: We investigate the dynamics of a current-biased Josephson junction quantum bit or “qubit” coupled to an LC resonator. The Hamiltonian of this superconductor-based system is developed and the energies and eigen-functions of the entangled states are studied by Harmonic approximation. Since such a superconducting junction behaves as a two-level artificial atom coupled to a harmonic oscil...

A Bayesian approach to analyze the modes of variation in a set of curves is suggested. It is based on a generative model thus allowing for noisy and sparse observations of curves. A Demmler-Reinsch(-type) basis is used to enforce smoothness of the latent (‘eigen’-)functions. Inference, including estimation, error assessment and model choice, particularly the choice of the number of eigenfunctio...

We consider α scale spaces, a parameterized class (α ∈ (0, 1]) of scale space representations beyond the well-established Gaussian scale space, which are generated by the α-th power of the minus Laplace operator on a bounded domain using the Neumann boundary condition. The Neumann boundary condition ensures that there is no grey-value flux through the boundary. Thereby no artificial grey-values...

The RcppEigen package provides access from R (R Core Team 2015a) to the Eigen (Guennebaud, Jacob et al. 2012) C++ template library for numerical linear algebra. Rcpp (Eddelbuettel et al. 2017; Eddelbuettel 2013) classes and specializations of the C++ templated functions as and wrap from Rcpp provide the “glue” for passing objects from R to C++ and back. Several introductory examples are present...