Herein, we present a novel Hamiltonian replica exchange protocol for classical molecular dynamics simulations of protein folding/unfolding. The scheme starts from the analysis of the energy-networks responsible for the stabilization of the folded conformation, by means of the energy-decomposition approach. In this framework, the compact energetic map of the native state is generated by a prelim...

We study a 4-fold symmetric kicked-oscillator map with sawtooth kick function. For the values of the kick amplitude λ = 2 cos(2πp/q) with rational p/q, the dynamics is known to be pseudochaotic, with no stochastic web of non-zero Lebesgue measure. We show that this system can be represented as a piecewise affine map of the unit square —the so-called local map— driving a lattice map. We develop ...

Let H(d) be the space of complex hermitian matrices of size d×d and let H+(d) ⊂ H(d) be the cone of positive semidefinite matrices. A linear operator Φ : H(d1) → H(d2) is said to be positive if Φ[H+(d1)] ⊂ H+(d2). The concurrence C(Φ; ·) of a positive operator Φ : H(d1) → H(d2) is a real-valued function on the cone H+(d1), defined as the largest convex function which coincides with 2 q σ d2 2 (...

Let (Mn,g) be a closed Riemannian manifold of dimension n?3. Assume [g] is conformal class for which the Conformal Laplacian Lg has at least two negative eigenvalues. We show existence (generalized) metric that maximizes second eigenvalue over all metrics (the first maximized by Yamabe metric). also maximal defines either nodal solution equation, or harmonic map to sphere. Moreover, we construc...

given four complex matrices a, b, c and d where a 2 cnn and d 2 cmm andlet the matrix(a bc d)be a normal matrix and assume that  is a given complex number that is not eigenvalue of matrix a. we present a method to calculate the distance norm (with respect to 2-norm) from d to the set of matrices x 2 cmm such that,  be a multiple eigenvalue of matrix(a bc x). we also nd the nearest matrix ...

Introduction 2 1. Preliminaries 6 1.1. Algebraic modular forms 6 1.2. Modular forms over C 9 1.3. p-adic modular forms 11 1.4. Elliptic curves with complex multiplication 12 1.5. Values of modular forms at CM points 14 2. Generalised Heegner cycles 15 2.1. Kuga-Sato varieties 15 2.2. The variety Xr and its cohomology 18 2.3. Definition of the cycles 19 2.4. Relation with Heegner cycles and L-se...

Existing measures of bipartite nonclassical correlations that are typically characterized by nonvanishing nonlocalizable information under the zero-way CLOCC protocol are expensive in the computational cost. We define and evaluate economical measures on the basis of a new class of maps, eigenvalue-preserving-but-not-completelyeigenvalue-preserving (EnCE) maps. The class is in analogy to the cla...

We define a class of “algebraic” random matrices. These are random matrices for which the Stieltjes transform of the limiting eigenvalue distribution function is algebraic, i.e., it satisfies a (bivariate) polynomial equation. The Wigner and Wishart matrices whose limiting eigenvalue distributions are given by the semi-circle law and the Marčenko-Pastur law are special cases. Algebraicity of a ...

1. Wigner Matrices 2 2. Wigner’s Semicircle Law 4 3. Markov’s Inequality and Convergence of Expectation 6 4. First Proof of Wigner’s Semicircle Law 7 4.1. Convergence of matrix moments in Expectation 7 4.2. Convergence of Matrix Moments in Probability 12 4.3. Weak Convergence 15 5. Removing Moment Assumptions 17 6. Largest Eigenvalue 21 7. The Stiletjes Transform 31 8. The Stieltjes Transform a...