A NWB-based dataset and processing pipeline of human single-neuron activity during a declarative memory task

A challenge for data sharing in systems neuroscience is the multitude of different data formats used. Neurodata Without Borders: Neurophysiology 2.0 (NWB:N) has emerged as a standardized data format for the storage of cellular-level data together with meta-data, stimulus information, and behavior. A key next step to facilitate NWB:N adoption is to provide easy to use processing pipelines to import/export data from/to NWB:N. Here, we present a NWB-formatted dataset of 1863 single neurons recorded from the medial temporal lobes of 59 human subjects undergoing intracranial monitoring while they performed a recognition memory task. We provide code to analyze and export/import stimuli, behavior, and electrophysiological recordings to/from NWB in both MATLAB and Python. The data files are NWB:N compliant, which affords interoperability between programming languages and operating systems. This combined data and code release is a case study for how to utilize NWB:N for human single-neuron recordings and enables easy re-use of this hard-to-obtain data for both teaching and research on the mechanisms of human memory

Metric trees of generalized roundness one

Every finite metric tree has generalized roundness strictly greater than one. On the other hand, some countable metric trees have generalized roundness precisely one. The purpose of this paper is to identify some large classes of countable metric trees that have generalized roundness precisely one. At the outset we consider spherically symmetric trees endowed with the usual combinatorial metric (SSTs). Using a simple geometric argument we show how to determine decent upper bounds on the generalized roundness of finite SSTs that depend only on the downward degree sequence of the tree in question. By considering limits it follows that if the downward degree sequence $(d_{0}, d_{1}, d_{2}...)$ of a SST $(T,\rho)$ satisfies $|\{j \, | \, d_{j} > 1 \}| = \aleph_{0}$, then $(T,\rho)$ has generalized roundness one. Included among the trees that satisfy this condition are all complete $n$-ary trees of depth $\infty$ ($n \geq 2$), all $k$-regular trees ($k \geq 3$) and inductive limits of Cantor trees. The remainder of the paper deals with two classes of countable metric trees of generalized roundness one whose members are not, in general, spherically symmetric. The first such class of trees are merely required to spread out at a sufficient rate (with a restriction on the number of leaves) and the second such class of trees resemble infinite combs.Comment: 14 pages, 2 figures, 2 table

Maximal surface group representations in isometry groups of classical Hermitian symmetric spaces

Higgs bundles and non-abelian Hodge theory provide holomorphic methods with which to study the moduli spaces of surface group representations in a reductive Lie group G. In this paper we survey the case in which G is the isometry group of a classical Hermitian symmetric space of non-compact type. Using Morse theory on the moduli spaces of Higgs bundles, we compute the number of connected components of the moduli space of representations with maximal Toledo invariant.Comment: v2: added due credits to the work of Burger, Iozzi and Wienhard. v3: corrected count of connected components for G=SU(p,q) (p \neq q); added due credits to the work of Xia and Markman-Xia; minor corrections and clarifications. 31 page

Topological wave functions and heat equations

It is generally known that the holomorphic anomaly equations in topological string theory reflect the quantum mechanical nature of the topological string partition function. We present two new results which make this assertion more precise: (i) we give a new, purely holomorphic version of the holomorphic anomaly equations, clarifying their relation to the heat equation satisfied by the Jacobi theta series; (ii) in cases where the moduli space is a Hermitian symmetric tube domain $G/K$, we show that the general solution of the anomaly equations is a matrix element \IP{\Psi | g | \Omega} of the Schr\"odinger-Weil representation of a Heisenberg extension of $G$, between an arbitrary state $\bra{\Psi}$ and a particular vacuum state $\ket{\Omega}$. Based on these results, we speculate on the existence of a one-parameter generalization of the usual topological amplitude, which in symmetric cases transforms in the smallest unitary representation of the duality group $G'$ in three dimensions, and on its relations to hypermultiplet couplings, nonabelian Donaldson-Thomas theory and black hole degeneracies.Comment: 50 pages; v2: small typos fixed, references added; v3: cosmetic changes, published version; v4: typos fixed, small clarification adde

Decomposition of the tensor product of two Hilbert modules

Given a pair of positive real numbers $\alpha, \beta$ and a sesqui-analytic function $K$ on a bounded domain $\Omega \subset \mathbb C^m$, in this paper, we investigate the properties of the sesqui-analytic function $\mathbb K^{(\alpha, \beta)}:= K^{\alpha+\beta}\big(\partial_i\bar{\partial}_j\log K\big )_{i,j=1}^ m,$ taking values in $m\times m$ matrices. One of the key findings is that $\mathbb K^{(\alpha, \beta)}$ is non-negative definite whenever $K^\alpha$ and $K^\beta$ are non-negative definite. In this case, a realization of the Hilbert module determined by the kernel $\mathbb K^{(\alpha,\beta)}$ is obtained. Let $\mathcal M_i$, $i=1,2,$ be two Hilbert modules over the polynomial ring $\mathbb C[z_1, \ldots, z_m]$. Then $\mathbb C[z_1, \ldots, z_{2m}]$ acts naturally on the tensor product $\mathcal M_1\otimes \mathcal M_2$. The restriction of this action to the polynomial ring $\mathbb C[z_1, \ldots, z_m]$ obtained using the restriction map $p \mapsto p_{|\Delta}$ leads to a natural decomposition of the tensor product $\mathcal M_1\otimes \mathcal M_2$, which is investigated. Two of the initial pieces in this decomposition are identified

Temporal Dissociation between Myeloperoxidase (MPO)-Modified LDL and MPO Elevations during Chronic Sleep Restriction and Recovery in Healthy Young Men

OBJECTIVES: Many studies have evaluated the ways in which sleep disturbances may influence inflammation and the possible links of this effect to cardiovascular risk. Our objective was to investigate the effects of chronic sleep restriction and recovery on several blood cardiovascular biomarkers. METHODS AND RESULTS: Nine healthy male non-smokers, aged 22-29 years, were admitted to the Sleep Laboratory for 11 days and nights under continuous electroencephalogram polysomnography. The study consisted of three baseline nights of 8 hours sleep (from 11 pm to 7 am), five sleep-restricted nights, during which sleep was allowed only between 1 am and 6 am, and three recovery nights of 8 hours sleep (11 pm to 7 am). Myeloperoxidase-modified low-density lipoprotein levels increased during the sleep-restricted period indicating an oxidative stress. A significant increase in the quantity of slow-wave sleep was measured during the first recovery night. After this first recovery night, insulin-like growth factor-1 levels increased and myeloperoxidase concentration peaked. CONCLUSIONS: We observed for the first time that sleep restriction and the recovery process are associated with differential changes in blood biomarkers of cardiovascular disease

VarGoats project: a dataset of 1159 whole-genome sequences to dissect Capra hircus global diversity

Background: Since their domestication 10,500 years ago, goat populations with distinctive genetic backgrounds have adapted to a broad variety of environments and breeding conditions. The VarGoats project is an international 1000-genome resequencing program designed to understand the consequences of domestication and breeding on the genetic diversity of domestic goats and to elucidate how speciation and hybridization have modeled the genomes of a set of species representative of the genus Capra. Findings: A dataset comprising 652 sequenced goats and 507 public goat sequences, including 35 animals representing eight wild species, has been collected worldwide. We identified 74,274,427 single nucleotide polymorphisms (SNPs) and 13,607,850 insertion-deletions (InDels) by aligning these sequences to the latest version of the goat reference genome (ARS1). A Neighbor-joining tree based on Reynolds genetic distances showed that goats from Africa, Asia and Europe tend to group into independent clusters. Because goat breeds from Oceania and Caribbean (Creole) all derive from imported animals, they are distributed along the tree according to their ancestral geographic origin. Conclusions: We report on an unprecedented international effort to characterize the genome-wide diversity of domestic goats. This large range of sequenced individuals represents a unique opportunity to ascertain how the demographic and selection processes associated with post-domestication history have shaped the diversity of this species. Data generated for the project will also be extremely useful to identify deleterious mutations and polymorphisms with causal effects on complex traits, and thus will contribute to new knowledge that could be used in genomic prediction and genome-wide association studies

Notes on Stein-Sahi representations and some problems of non L2L^2 harmonic analysis

We discuss one natural class of kernels on pseudo-Riemannian symmetric spaces.Comment: 40p

Meromorphic tensor equivalence for Yangians and quantum loop algebras

Let ${\mathfrak g}$ be a complex semisimple Lie algebra, and $Y_h({\mathfrak g})$, $U_q(L{\mathfrak g})$ the corresponding Yangian and quantum loop algebra, with deformation parameters related by $q=\exp(\pi i h)$. When $h$ is not a rational number, we constructed in arXiv:1310.7318 a faithful functor $\Gamma$ from the category of finite-dimensional representations of $Y_h ({\mathfrak g})$ to those of $U_q(L{\mathfrak g})$. The functor $\Gamma$ is governed by the additive difference equations defined by the commuting fields of the Yangian, and restricts to an equivalence on a subcategory of $Y_h({\mathfrak g})$ defined by choosing a branch of the logarithm. In this paper, we construct a tensor structure on $\Gamma$ and show that, if $|q|\neq 1$, it yields an equivalence of meromorphic braided tensor categories, when $Y_h({\mathfrak g})$ and $U_q(L{\mathfrak g})$ are endowed with the deformed Drinfeld coproducts and the commutative part of the universal $R$-matrix. This proves in particular the Kohno-Drinfeld theorem for the abelian $q$KZ equations defined by $Y_h({\mathfrak g})$. The tensor structure arises from the abelian $q$KZ equations defined by a appropriate regularisation of the commutative $R$-matrix of $Y_h({\mathfrak g})$.Comment: Title changed, details added. 67 pages, 1 figure. Final version, to appear in Publ. Math IHE