We derive exact results for correlations in the displacement fields $\{ \delta \vec{r} \} \equiv \{ r_{\mu = x,y} \}$ near-crystalline athermal systems two dimensions. analyze produced by different types of microscopic disorder, and show that disorder at scale gives rise to long-range with a dependence on system size $L$ given $\langle r_{\mu} r_{\nu} \rangle \sim c_{\mu \nu}(r/L,\theta)$. In a...

Let Cg be a smooth projective irreducible curve over C of genus g ≥ 1 and let {p1, p2, . . . , ps} be a set of distinct points on Cg. We fix a nonnegative integer l and denote by Mg(p, λ) the moduli space of parabolic semistable vector bundles of rank r with trivial determinant and fixed parabolic structure of type λ = (λ1, λ2, . . . , λs) at p = (p1, p2, . . . , ps), where each weight λi is in...

This letter is an attempt to carry out a first-principle computation in M-theory using the point of view that the eleven-dimensional membrane gives the fundamental degrees of freedom of M-theory. Our aim is to derive the exact BPS R couplings in M-theory compactified on a torus T from the toroidal BPS membrane, by pursuing the analogy with the one-loop string theory computation. We exhibit an S...

The density matrix rho(r,r(')) of a spherically symmetric system can be expanded as a Fourier-Legendre series of Legendre polynomials P(l)(cos theta=rr(')rr(')). Application is here made to harmonically trapped electron pairs (i.e., Moshinsky's and Hooke's atoms), for which exact wavefunctions are known, and to the helium atom, using a near-exact wavefunction. In the present approach, generic c...

BACKGROUND Cerebrospinal fluid (CSF) biomarkers and quantitative EEG show particular patterns of change in Alzheimer's disease (AD) and reflect neuropathologic processes and cerebral function, respectively. The changes precede cognitive decline and should be visible already in preclinical stages. We therefore aimed to investigate their relationship in cognitively healthy individuals. METHOD T...

The hydrostatic equilibrium is a prominent topic in fluid dynamics and astrophysics. Understanding the stability of perturbations near Boussinesq systems helps gain insight into certain weather phenomena. 2D system focused here anisotropic involves only horizontal dissipation thermal diffusion. Due to lack vertical dissipation, precise large-time behavior problem difficult. When spatial domain ...

We investigated the development of the brain's functional connectivity throughout the life span (ages 5 through 71 years) by measuring EEG activity in a large population-based sample. Connectivity was established with Synchronization Likelihood. Relative randomness of the connectivity patterns was established with Watts and Strogatz' (1998) graph parameters C (local clustering) and L (global pa...

We introduce a general method, based on a mapping onto quantum mechanics, for investigating the large-T limit of the distribution P(r,T) of the nonlinear functional r[V]=(1/T)integral(T)(0)dT' V[X(T')], where V(X) is an arbitrary function of the stationary Gaussian Markov process X(T). For T-->infinity at fixed r we obtain P(r,T) approximately exp[-theta(r)T], where theta(r) is a large-deviatio...