We propose the notion of {\it resistance of a graph} as an accompanying notion of the structure entropy to measure the force of the graph to resist cascading failure of strategic virus attacks. We show that for any connected network $G$, the resistance of $G$ is $\mathcal{R}(G)=\mathcal{H}^1(G)-\mathcal{H}^2(G)$, where $\mathcal{H}^1(G)$ and $\mathcal{H}^2(G)$ are the one- and two-dimensional s...

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...

This paper extends joint work with R. Friedman to show that the closure of the locus of intermediate Jacobians of smooth cubic threefolds, in the moduli space of principally polarized abelian varieties (ppavs) of dimension five, is an irreducible component of the locus of ppavs whose theta divisor has a point of multiplicity three or more. This paper also gives a sharp bound on the multiplicity...

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...

It is explained how the Mordell integral ∫ R e −2πzx cosh(πx) dx unifies the mock theta functions, partial (or false) theta functions, and some of Zagier’s quantum modular forms. As an application, we exploit the connections between q-hypergeometric series and mock and partial theta functions to obtain finite evaluations of the Mordell integral for rational choices of τ and z. 1. The Mordell In...

Hindered convection of macromolecules in gels was studied by measuring the sieving coefficient (theta) of narrow fractions of Ficoll (Stokes-Einstein radius, r(s) = 2.7-5.9 nm) in agarose and agarose-dextran membranes, along with the Darcy permeability (kappa). To provide a wide range of kappa, varying amounts of dextran (volume fractions < or = 0.011) were covalently attached to agarose gels w...

We find identities between theta constants with rational characteristics evaluated at period matrix of R, a cyclic 3 sheeted cover of the sphere with 3k branch points λ1...λ3k. These identities follow from Thomae formula [BR]. This formula expresses powers of theta constants as polynomials in λ1...λ3k. We apply the representation of the symmetric group to find relations between the polynomials ...

Quantitative electroencephalographic (QEEG) changes relating to dissociative experiences have only rarely been demonstrated, and dissociative states were not quantified in those studies. The aim of this study was to explore concurrent associations between quantified dissociative states and QEEG spectral parameters, in particular theta activity, in psychiatric patients. Fifty psychiatric patient...

We describe a method for co-estimating r = C/mu (where C is the per-site recombination rate and mu is the per-site neutral mutation rate) and Theta = 4N(e)mu (where N(e) is the effective population size) from a population sample of molecular data. The technique is Metropolis-Hastings sampling: we explore a large number of possible reconstructions of the recombinant genealogy, weighting accordin...