Pituitary Adenylate Cyclase-Activating Polypeptide Orchestrates Neuronal Regulation Of The Astrocytic Glutamate-Releasing Mechanism System x\u3csub\u3ec\u3c/sub\u3e\u3csup\u3e−\u3c/sup\u3e

Glutamate signaling is achieved by an elaborate network involving neurons and astrocytes. Hence, it is critical to better understand how neurons and astrocytes interact to coordinate the cellular regulation of glutamate signaling. In these studies, we used rat cortical cell cultures to examine whether neurons or releasable neuronal factors were capable of regulating system xc-(Sxc), a glutamate-releasing mechanism that is expressed primarily by astrocytes and has been shown to regulate synaptic transmission. We found that astrocytes cultured with neurons or exposed to neuronal-conditioned media displayed significantly higher levels of Sxc activity. Next, we demonstrated that the pituitary adenylate cyclase-activating polypeptide (PACAP) may be a neuronal factor capable of regulating astrocytes. In support, we found that PACAP expression was restricted to neurons, and that PACAP receptors were expressed in astro-cytes. Interestingly, blockade of PACAP receptors in cultures comprised of astrocytes and neurons significantly decreased Sxc activity to the level observed in purified astrocytes, whereas application of PACAP to purified astrocytes increased Sxc activity to the level observed in cultures comprised of neurons and astrocytes. Collectively, these data reveal that neurons coordinate the actions of glutamate-related mechanisms expressed by astrocytes, such as Sxc, a process that likely involves PACAP

Examples of k-iterated spreading models

It is shown that for every $k\in\mathbb{N}$ and every spreading sequence $\{e_n\}_{n\in\mathbb{N}}$ that generates a uniformly convex Banach space $E$, there exists a uniformly convex Banach space $X_{k+1}$ admitting $\{e_n\}_{n\in\mathbb{N}}$ as a $k+1$-iterated spreading model, but not as a $k$-iterated one.Comment: 16 pages, no figure

Almost-Euclidean subspaces of ℓ1N\ell_1^N via tensor products: a simple approach to randomness reduction

It has been known since 1970's that the N-dimensional $\ell_1$-space contains nearly Euclidean subspaces whose dimension is $\Omega(N)$. However, proofs of existence of such subspaces were probabilistic, hence non-constructive, which made the results not-quite-suitable for subsequently discovered applications to high-dimensional nearest neighbor search, error-correcting codes over the reals, compressive sensing and other computational problems. In this paper we present a "low-tech" scheme which, for any $a > 0$, allows to exhibit nearly Euclidean $\Omega(N)$-dimensional subspaces of $\ell_1^N$ while using only $N^a$ random bits. Our results extend and complement (particularly) recent work by Guruswami-Lee-Wigderson. Characteristic features of our approach include (1) simplicity (we use only tensor products) and (2) yielding "almost Euclidean" subspaces with arbitrarily small distortions.Comment: 11 pages; title change, abstract and references added, other minor change

Isomorphic properties of Intersection bodies

We study isomorphic properties of two generalizations of intersection bodies, the class of k-intersection bodies and the class of generalized k-intersection bodies. We also show that the Banach-Mazur distance of the k-intersection body of a convex body, when it exists and it is convex, with the Euclidean ball, is bounded by a constant depending only on k, generalizing a well-known result of Hensley and Borell. We conclude by giving some volumetric estimates for k-intersection bodies

Examples of asymptotically \ell_^1 Banach spaces

Two examples of asymptotic $\ell_{1}$ Banach spaces are given. The first, $X_{u}$, has an unconditional basis and is arbitrarily distortable. The second, $X$, does not contain any unconditional basic sequence. Both are spaces of the type of Tsirelson. We thus answer a question raised by W.T.Gowers

Stability of chemical reaction fronts in solids:Analytical and numerical approaches

Localized chemical reactions in deformable solids are considered. A chemical transformation is accompanied by the transformation strain and emerging mechanical stresses, which affect the kinetics of the chemical reaction front to the reaction arrest. A chemo-mechanical coupling via the chemical affinity tensor is used, in which the stresses affect the reaction rate. The emphasis is made on the stability of the propagating reaction front in the vicinity of the blocked state. There are two major novel contributions. First, it is shown that for a planar reaction front, the diffusion of the gaseous-type reactant does not influence the stability of the reaction front – the stability is governed only by the mechanical properties of solid reactants and stresses induced by the transformation strain and the external loading, which corresponds to the mathematically analogous phase transition problem. Second, the comparison of two computational approaches to model the reaction front propagation is performed – the standard finite-element method with a remeshing technique to resolve the moving interface is compared to the cut-finite-element-based approach, which allows the interface to cut through the elements and to move independently of the finite-element mesh. For stability problems considered in the present paper, the previously-developed implementation of the cut-element approach has been extended with the additional post-processing procedure that obtains more accurate stresses and strains, relying on the fact that the structured grid is used in the implementation. The approaches are compared using a range of chemo-mechanical problems with stable and unstable reaction fronts.</p

The Compact Approximation Property does not imply the Approximation Property

It is shown how to construct, given a Banach space which does not have the approximation property, another Banach space which does not have the approximation property but which does have the compact approximation property