We show that the probability, P0(l), that the height of a fluctuating (d+1)-dimensional interface in its steady state stays above its initial value up to a distance l, along any linear cut in the d-dimensional space, decays as P0(l) approximately l(theta). Here straight theta is a "spatial" persistence exponent, and takes different values, straight theta(s) or straight theta(0), depending on ho...

The theta map sends code polynomials into the ring of Siegel modular forms of even weights. Explicit description of the image is known for g ≤ 3 and the surjectivity of the theta map follows. Instead it is known that this map is not surjective for g ≥ 5. In this paper we discuss the possibility of an embedding between the associated projective varieties. We prove that this is not possible for g...

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...

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...

Five key topics have been reverberating in hippocampal-entorhinal cortex (EC) research over the past five decades: episodic and semantic memory, path integration ("dead reckoning") and landmark ("map") navigation, and theta oscillation. We suggest that the systematic relations between single cell discharge and the activity of neuronal ensembles reflected in local field theta oscillations provid...

Given a finite alphabet $\mathbb{A}$ and primitive substitution $\theta:\mathbb{A}\to\mathbb{A}^\lambda$ (of constant length $\lambda$), let $(X_\theta,S)$ denote the corresponding dynamical system, where $X_{\theta}$ is closure of orbit via left shift $S$ fixed point natural extension $\theta$ to self-map $\mathbb{A}^{\mathbb{Z}}$. The main result paper that all continuous observables in are o...

Autosomal dominant hypophosphatemic rickets (ADHR) is an inherited disorder of isolated renal phosphate wasting, the pathogenesis of which is unknown. We performed a genome-wide linkage study in a large kindred to determine the chromosome location of the ADHR gene. Two-point LOD scores indicate that the gene is linked to the markers D12S314 [Z(theta) = 3.15 at theta = 0.0], vWf [Z(theta) = 5.32...

In the present article, we study conjecture of Sharifi on surjectivity map $\varpi_{\theta}$. Here $\theta$ is a primitive even Dirichlet character conductor $Np$, which exceptional in sense Ohta. After localizing at prime ideal $\mathfrak{p}$ Iwasawa algebra related to trivial zero Kubota\textendash Leopoldt $p$-adic $L$-function $L_p(s,\theta^{-1}\omega^2)$, compute image $\varpi_{\theta,\mat...