This book is a modern introduction to the theory of abelian varieties and theta functions.Here the Fourier transform techniques play a central role, appearing in several different contexts. In transcendental theory, the usual Fourier transform plays a major role in the representation theory of the Heisenberg group, the main building block for the theory of theta functions. Also, the Fourier tra...

Using urethane-anesthetized rats, 18 simultaneously recorded septohippocampal cell pairs (36 individual cells), each classified as theta-related according to the criteria of, were studied during four spontaneously occurring hippocampal field conditions: (1) large amplitude irregular activity (LIA) only; (2) the transition from LIA to theta; (3) theta only; and (4) the transition from theta to L...

A Kummer variety is obtained as the quotient of an abelian variety by the automorphism (−1) acting on it. Kummer varieties can be seen as a higher dimensional generalisation of the xcoordinate representation of a point of an elliptic curve given by its Weierstrass model. Although there is no group law on the set of points of a Kummer variety, the multiplication of a point by a scalar still make...

Young CK. Behavioral significance of hippocampal theta oscillations: looking elsewhere to find the right answers. J Neurophysiol 106: 497– 499, 2011. First published May 11, 2010; doi:10.1152/jn.00358.2011.— The function of hippocampal theta oscillations has been subjected to constant speculation. Dynamic coupling of theta field potentials and spiking activity between the hippocampus and extra-...

The main goal of this paper is to introduce and study a new class of function via the notions of $e$-$theta$-open sets and $e$-$theta$-closure operator which are defined by Özkoç and Aslım [10] called weakly $eR$-open functions and $e$-$theta$-open functions. Moreover, we investigate not only some of their basic properties but also their relationships with other types of already existing topolo...

Let $(X, \tau)$ and $(Y, \sigma)$ be topological spaces in which no separation axioms are assumed, unless explicitly stated if $\mathcal{I}$ is an ideal on $X$.Given a multifunction $F\colon (X, \tau)\rightarrow (Y, \sigma)$, $\alpha,\beta$ operators \tau)$, $\theta,\delta$ proper $X$. We introduce study upper lower $(\alpha, \beta,\theta,\delta,\mathcal{I})$-continuous multifunctions.A said to...

An essential requirement for hippocampal circuits to function in episodic memory is the ability to rapidly disambiguate and store incoming sensory information. This "pattern separation" function has been classically associated to the dentate gyrus, where spatial learning is accompanied by rapid and persistent modifications of place-cell representation. How these rapid modifications are implemen...

INTRODUCTION A fundamental question in phantom perception is determining whether the brain creates a network that represents the sound intensity of the auditory phantom as measured by tinnitus matching (in dB), or whether the phantom perception is actually only a representation of the subjectively perceived loudness. METHODS In tinnitus patients, tinnitus loudness was tested in two ways, by a...

We study the spanning properties of Theta-Theta graphs. Similar in spirit with the Yao-Yao graphs, Theta-Theta graphs partition the space around each vertex into a set of k cones, for some fixed integer k > 1, and select at most one edge per cone. The difference is in the way edges are selected. Yao-Yao graphs select an edge of minimum length, whereas Theta-Theta graphs select an edge of minimu...