Hippocampal theta rhythm arises from a combination of recently described intrinsic theta oscillators and inputs from multiple brain areas. Interneurons expressing the markers parvalbumin (PV) and somatostatin (SOM) are leading candidates to participate in intrinsic rhythm generation and principal cell (PC) coordination in distal CA1 and subiculum. We tested their involvement by optogenetically ...

A topographical relationship exists between the hippocampus-entorhinal cortex and the neocortex. However, it is not known how these anatomical connections are utilized during information exchange and behavior. We recorded theta oscillations along the entire extent of the septotemporal axis of the hippocampal CA1 pyramidal layer. While the frequency of theta oscillation remained same along the e...

Inspired by a question of Lovász, we introduce a hierarchy of nested semidefinite relaxations of the convex hull of real solutions to an arbitrary polynomial ideal, called theta bodies of the ideal. For the stable set problem in a graph, the first theta body in this hierarchy is exactly Lovász’s theta body of the graph. We prove that theta bodies are, up to closure, a version of Lasserre’s rela...

The generation of EEG theta rhythms in the mammalian limbic cortex is a prime example of rhythmic activity that involves central mechanisms of oscillations and synchrony. In 1985 for the first time we demonstrated that bath perfusion of the hippocampal formation slices with cholinergic agonists resulted in theta-like oscillations. Since this initial demonstration of the in vitro theta activity,...

Inspired by a question of Lovász, we introduce a hierarchy of nested semidefinite relaxations of the convex hull of real solutions to an arbitrary polynomial ideal, called theta bodies of the ideal. For the stable set problem in a graph, the first theta body in this hierarchy is exactly Lovász’s theta body of the graph. We prove that theta bodies are, up to closure, a version of Lasserre’s rela...

Let $(X, \omega)$ be a compact Kahler manifold of complex dimension n and $\theta$ smooth closed real $(1,1)$-form on $X$ such that its cohomology class $\{ \theta \}\in H^{1,1}(X, \mathbb{R})$ is pseudoeffective. $\varphi$ $\theta$-psh function, let $f$ continuous function with bounded distributional laplacian respect to $\omega$ $\varphi \leq f. $ Then the non-pluripolar measure $\theta_\va...

In the paper‎, ‎some new existence theorems of maximal elements for‎ ‎$mathscr{F}_{C,theta}$-mappings and $mathscr{F}_{C,theta}$-majorized mappings are established‎. ‎As applications, ‎some new existence theorems of equilibrium points for‎ ‎one-person games‎, ‎qualitative games and generalized games are obtained‎. ‎Our results unify and generalize most known results‎ ‎in recent literature‎.

In this paper we study the relation between module amenability of $theta$-Lau product $A×_theta B$ and that of Banach algebras $A, B$. We also discuss module biprojectivity of $A×theta B$. As a consequent we will see that for an inverse semigroup $S$, $l^1(S)×_theta l^1(S)$ is module amenable if and only if $S$ is amenable.

It is well known that classical theta series which are attached to positive definite rational quadratic forms yield elliptic modular forms, and linear combinations of theta series attached to lattices in a fixed genus can yield both cusp forms and Eisenstein series whose weight is one-half the rank of the quadratic form. In contrast, generalized theta series—those augmented with a spherical har...

The isoforms of the highly conserved and ubiquitously expressed 14-3-3 family of proteins function primarily as adapters that modulate interactions between components of various cellular signaling and cell cycle regulatory pathways. Low levels of 14-3-3 isoforms appear to be expressed in most tissues, but specific isoforms or combinations have been shown to be overexpressed in a cell-specific m...