The inference of population recombination (rho), population mutation (Theta), and adaptive selection is of great interest in microbial population genetics. These parameters can be efficiently estimated using explicit statistical frameworks (evolutionary models) that describe their effect on gene sequences. Within this framework, we estimated rho and Theta using a coalescent approach, and adapti...

A polynomial ideal I ⊆ R[x] is THk-exact if every linear polynomial that is non-negative over VR(I), the real variety of I , is a sum of squares of polynomials of degree at most k modulo I . Lovász recognized that a graph is perfect if and only if the vanishing ideal of the characteristic vectors of its stable sets is TH1-exact, and asked for a characterization of ideals which are TH1-exact. We...

The medial septum (MS) plays an essential role in rhythmogenesis in the hippocampus (HIPP); theta-rhythmic bursts of MS neurons are believed to drive theta oscillations in rats' HIPP. The MS theta pacemaker hypothesis has solid foundation but the MS-hippocampal interactions during different behavioral states are poorly understood. The MS and the HIPP have reciprocal connections and it is not cl...

We obtain some Bailey pairs associated with indefinite quadratic forms the $\beta_n$ connected to a finite sum. A new general identity is given, which provides identities for $q$-hypergeometric series, including mock theta functions.

In Ramanujan’s final letter to Hardy, he wrote of a strange new class of infinite series he called “mock theta functions”. It turns out all of Ramanujan’s mock theta functions are essentially specializations of a so-called universal mock theta function g3(z, q) of Gordon–McIntosh. Here we show that g3 arises naturally from the reciprocal of the classical Jacobi triple product—and is intimately ...

We construct maps from moduli spaces of vector bundles on a Riemann surface X to opers on X, using nonabelian theta functions. Opers are generalizations of projective structures, and can be considered as differential operators, kernel functions or special bundles with connection. The matrix opers (analogues of opers for matrix differential operators) combine the structures of flat vector bundle...

In Ramanujan’s final letter to Hardy, he wrote of a strange new class of infinite series he called “mock theta functions”. It turns out all of Ramanujan’s mock theta functions are essentially specializations of a so-called universal mock theta function g3(z, q) of Gordon–McIntosh. Here we show that g3 arises naturally from the reciprocal of the classical Jacobi triple product—and is intimately ...

We construct natural maps (the Klein and Wirtinger maps) from moduli spaces of vector bundles on an algebraic curve X to affine spaces, as quotients of the nonabelian theta linear series. We prove a finiteness result for these maps over generalized Kummer varieties (moduli of torus bundles), leading us to conjecture that the maps are finite in general. The conjecture provides canonical explicit...

Objectives: To find out which Quantitative EEG (QEEG) parameters could best distinguish patients with Parkinson's disease (PD) with and without Mild Cognitive Impairment from healthy individuals and to find an optimal method for feature selection. Background: Certain QEEG parameters have been seen to be associated with dementia in Parkinson's and Alzheimer's disease. Studies have also shown som...