We introduce and study a transfer map between ideals of the universal enveloping algebras of two members of a reductive dual pair of Lie algebras. Its definition is motivated by the approach to the real Howe duality through the theory of Capelli identities. We prove that this map provides a lower bound on the annihilators of theta lifts of representations with a fixed annihilator ideal. We also...

Abstract. In this article we study the inverse of the period map for the family F of complex algebraic curves of genus 6 equipped with an automorphism of order 5. This is a family with 2 parameters, and is fibred over a certain type of Del Pezzo surace. The period satisfies the hypergeometric differential equation for Appell’s F1( 3 5 , 3 5 , 2 5 , 6 5 ) of two variables after a certain normali...

The theta rhythm is one of the largest and most sinusoidal activity patterns in the brain. Here I survey progress in the field of theta rhythms research. I present arguments supporting the hypothesis that theta rhythms emerge owing to intrinsic cellular properties yet can be entrained by several theta oscillators throughout the brain. I review behavioral correlates of theta rhythms and consider...

The anterior thalamic nuclei are assumed to support episodic memory with anterior thalamic dysfunction a core feature of diencephalic amnesia. To date, the electrophysiological characterization of this region in behaving rodents has been restricted to the anterodorsal nucleus. Here we compared single-unit spikes with population activity in the anteroventral nucleus (AV) of freely moving rats du...

Intracellular recordings were made in the dorsal hippocampal formation of urethane-anesthetized rats as the local field activity spontaneously cycled between a synchronous condition termed theta and an asynchronous condition termed LIA. All cells reported in this study were labeled with Neurobiotin and classified as theta-related or non-theta-related according to the system of Colom and Bland [...

A regular slow wave theta rhythm can be recorded in the medial entorhinal cortex (MEC) of freely moving rats during voluntary behaviors and paradoxical sleep. Electrode penetrations normal to the cortical layers proceeding from the deeper to the more superficial layers reveal a continuous theta rhythm in layers IV-III (deep MEC theta rhythm) with an amplitude maximum in layer III, a null betwee...

Abstract We show that there are one-loop IR singularities arising from UV/IR mixing in noncommutative SU(N) Yang–Mills theory defined by means of the $$\theta $$ θ -exact Seiberg–Witten map. This is spite fact no ordinary U(1) gauge fields and this at variance with U(N) case, where two-point part effective ac...

Let e⊂ R be a finite union of disjoint closed intervals. In the study of orthogonal polynomials on the real line with measures whose essential support is e, a fundamental role is played by the isospectral torus. In this paper, we use a covering map formalism to define and study this isospectral torus. Our goal is to make a coherent presentation of properties and bounds for this special class as...

Measures of the local phase of potential fields can be a useful aid to their interpretation. There are several variations in use, such as the tilt angle, tilt derivative and the Theta map. This paper compares the results of these filters, and introduces some new phase-based filters which show improved performance as edge detectors in different ways. The filters are demonstrated on synthetic gra...

According to Mukai, any prime Fano threefold X of genus 7 is a linear section of the spinor tenfold in the projectivized half-spinor space of Spin(10). The orthogonal linear section of the spinor tenfold is a canonical genus-7 curve Γ, and the intermediate Jacobian J(X) is isomorphic to the Jacobian of Γ. It is proven that, for a generic X , the Abel-Jacobi map of the family of elliptic sextics...