In vivo characterization of hippocampal electrophysiological processes in the heterozygous Pten knockout model of autism

While cognitive deficits have been described in the heterozygous Pten (+/-) KO mouse model of autism, little work has been done to demonstrate how corresponding in vitro physiological alterations in this model may underpin these cognitive deficits in vivo. As Pten KO (+/-) is known to alter electrophysiological characteristics of neurons in vitro, this study measures the in vivo electrophysiological characteristics of CA1 interneurons, pyramidal cells, and place cells which may underlie the spatial cognitive deficits seen in the model. Four transgenic conditional heterozygous Pten+/loxPloxP;Gfap-cre mice (HetPten) and four homozygous Pten littermate control mice were used in this study. This transgene drives cre expression and excision of the Pten gene in hippocampal granule cells of the dentate gyrus, and neurons in CA2 and CA1, but not astrocytes. In vivo local field potentials and single cell recordings were made in CA1 of each mouse during an open field foraging task in two distinct arenas. HetPten mice were found to have increased interneuron and pyramidal cell firing rates. In addition, place cells demonstrated abnormal properties including increased out-of-field firing rates, an increased number of fields, and trends towards larger field sizes that were less stable in comparison to controls. HetPten mice had slower CA1 fast gamma oscillations and more variable speed/theta oscillation correlations. Behaviorally, there were weak trends towards decreased motor output compared to controls. These data suggest that the electrophysiological alterations due to Pten KO (+/-) in mouse hippocampal neurons lead to hyperactivation of CA1 interneurons, pyramidal cells, and place cells

Strongly non embeddable metric spaces

Enflo constructed a countable metric space that may not be uniformly embedded into any metric space of positive generalized roundness. Dranishnikov, Gong, Lafforgue and Yu modified Enflo's example to construct a locally finite metric space that may not be coarsely embedded into any Hilbert space. In this paper we meld these two examples into one simpler construction. The outcome is a locally finite metric space $(\mathfrak{Z}, \zeta)$ which is strongly non embeddable in the sense that it may not be embedded uniformly or coarsely into any metric space of non zero generalized roundness. Moreover, we show that both types of embedding may be obstructed by a common recursive principle. It follows from our construction that any metric space which is Lipschitz universal for all locally finite metric spaces may not be embedded uniformly or coarsely into any metric space of non zero generalized roundness. Our construction is then adapted to show that the group $\mathbb{Z}_\omega=\bigoplus_{\aleph_0}\mathbb{Z}$ admits a Cayley graph which may not be coarsely embedded into any metric space of non zero generalized roundness. Finally, for each $p \geq 0$ and each locally finite metric space $(Z,d)$, we prove the existence of a Lipschitz injection $f : Z \to \ell_{p}$.Comment: 10 page

A direct proof that ℓ∞(3)\ell_\infty^{(3)} has generalized roundness zero

Metric spaces of generalized roundness zero have interesting non-embedding properties. For instance, we note that no metric space of generalized roundness zero is isometric to any metric subspace of any $L_{p}$-space for which $0 < p \leq 2$. Lennard, Tonge and Weston gave an indirect proof that $\ell_{\infty}^{(3)}$ has generalized roundness zero by appealing to highly non-trivial isometric embedding theorems of Bretagnolle Dacunha-Castelle and Krivine, and Misiewicz. In this paper we give a direct proof that $\ell_{\infty}^{(3)}$ has generalized roundness zero. This provides insight into the combinatorial geometry of $\ell_{\infty}^{(3)}$ that causes the generalized roundness inequalities to fail. We complete the paper by noting a characterization of real quasi-normed spaces of generalized roundness zero.Comment: The first version of this paper had the title "The generalized roundness of $\ell_\infty^{(3)}$ revisited". This version includes some minor modifications of the text and corrections to several typographic error

Experiential Education on the Edge: SETI Activities for the College Classroom

In a sophomore-level, interdisciplinary honors class, we introduced students to the Search for Extraterrestrial Intelligence through assigned readings, student presentations, classroom discussions, and multiple experiential activities. In this paper, we present four of these novel experiential activities. In the first, students suddenly find themselves trying to make contact with an unknown person who is simultaneously trying to contact them. The second is a course-long role-playing exercise patterned after a &quot;first contact&quot; simulation held annually at the CONTACT: Culture of the Imagination conferences. The third and fourth are parts of a unique final exam where students must respond as a group to two surreal encounters, one being a &quot;2001&quot;-style monolith that shows up, as in the film, entirely without warning or instructions. For the final, we also developed an assessment rubric appropriate for this kind of open-ended test. We conclude by discussing recommendations for implementing similar experiential education activities, both specifically and in spirit, in other classes. Outlin

Enhanced negative type for finite metric trees

Finite metric trees are known to have strict 1-negative type. In this paper we introduce a new family of inequalities that quantify the extent of the "strictness" of the 1-negative type inequalities for finite metric trees. These inequalities of "enhanced 1-negative type" are sufficiently strong to imply that any given finite metric tree must have strict p-negative type for all values of p in an open interval that contains the number 1. Moreover, these open intervals can be characterized purely in terms of the unordered distribution of edge weights that determine the path metric on the particular tree, and are therefore largely independent of the tree's internal geometry. From these calculations we are able to extract a new non linear technique for improving lower bounds on the maximal p-negative type of certain finite metric spaces. Some pathological examples are also considered in order to stress certain technical points.Comment: 35 pages, no figures. This is the final version of this paper sans diagrams. Please note the corrected statement of Theorem 4.16 (and hence inequality (1)). A scaling factor was omitted in Version #