Repetitive concussive and subconcussive injury in a human tau mouse model results in chronic cognitive dysfunction and disruption of white matter tracts, but not tau pathology

Due to the unmet need for a means to study chronic traumatic encephalopathy (CTE) in vivo, there have been numerous efforts to develop an animal model of this progressive tauopathy. However, there is currently no consensus in the field on an injury model that consistently reproduces the neuropathological and behavioral features of CTE. We have implemented a repetitive Closed-Head Impact Model of Engineered Rotational Acceleration (CHIMERA) injury paradigm in human transgenic (hTau) mice. Animals were subjected to daily subconcussive or concussive injuries for 20 days and tested acutely, 3 months, and 12 months post-injury for deficits in social behavior, anxiety, spatial learning and memory, and depressive behavior. Animals also were assessed for chronic tau pathology, astrogliosis, and white matter degeneration. Repetitive concussive injury caused acute deficits in Morris water maze performance, including reduced swimming speed and increased distance to the platform during visible and hidden platform phases that persisted during the subacute and chronic time-points following injury. We found evidence of white matter disruption in animals injured with subconcussive and concussive injuries, with the most severe disruption occurring in the repetitive concussive injury group. Severity of white matter disruption in the corpus callosum was moderately correlated with swimming speed, while white matter disruption in the fimbria showed weak but significant correlation with worse performance during probe trial. There was no evidence of tau pathology or astrogliosis in sham or injured animals. In summary, we show that repetitive brain injury produces persistent behavioral abnormalities as late as 1 year post-injury that may be related to chronic white matter disruption, although the relationship with CTE remains to be determined

Wigner transform and pseudodifferential operators on symmetric spaces of non-compact type

We obtain a general expression for a Wigner transform (Wigner function) on symmetric spaces of non-compact type and study the Weyl calculus of pseudodifferential operators on them

A Hierarchical Array of Integrable Models

Motivated by Harish-Chandra theory, we construct, starting from a simple CDD\--pole $S$\--matrix, a hierarchy of new $S$\--matrices involving ever ``higher'' (in the sense of Barnes) gamma functions.These new $S$\--matrices correspond to scattering of excitations in ever more complex integrable models.From each of these models, new ones are obtained either by ``$q$\--deformation'', or by considering the Selberg-type Euler products of which they represent the ``infinite place''. A hierarchic array of integrable models is thus obtained. A remarkable diagonal link in this array is established.Though many entries in this array correspond to familiar integrable models, the array also leads to new models. In setting up this array we were led to new results on the $q$\--gamma function and on the $q$\--deformed Bloch\--Wigner function.Comment: 18 pages, EFI-92-2

Counting and effective rigidity in algebra and geometry

The purpose of this article is to produce effective versions of some rigidity results in algebra and geometry. On the geometric side, we focus on the spectrum of primitive geodesic lengths (resp., complex lengths) for arithmetic hyperbolic 2-manifolds (resp., 3-manifolds). By work of Reid, this spectrum determines the commensurability class of the 2-manifold (resp., 3-manifold). We establish effective versions of these rigidity results by ensuring that, for two incommensurable arithmetic manifolds of bounded volume, the length sets (resp., the complex length sets) must disagree for a length that can be explicitly bounded as a function of volume. We also prove an effective version of a similar rigidity result established by the second author with Reid on a surface analog of the length spectrum for hyperbolic 3-manifolds. These effective results have corresponding algebraic analogs involving maximal subfields and quaternion subalgebras of quaternion algebras. To prove these effective rigidity results, we establish results on the asymptotic behavior of certain algebraic and geometric counting functions which are of independent interest.Comment: v.2, 39 pages. To appear in Invent. Mat

Gauge Field Theory Coherent States (GCS) : II. Peakedness Properties

In this article we apply the methods outlined in the previous paper of this series to the particular set of states obtained by choosing the complexifier to be a Laplace operator for each edge of a graph. The corresponding coherent state transform was introduced by Hall for one edge and generalized by Ashtekar, Lewandowski, Marolf, Mour\~ao and Thiemann to arbitrary, finite, piecewise analytic graphs. However, both of these works were incomplete with respect to the following two issues : (a) The focus was on the unitarity of the transform and left the properties of the corresponding coherent states themselves untouched. (b) While these states depend in some sense on complexified connections, it remained unclear what the complexification was in terms of the coordinates of the underlying real phase space. In this paper we resolve these issues, in particular, we prove that this family of states satisfies all the usual properties : i) Peakedness in the configuration, momentum and phase space (or Bargmann-Segal) representation, ii) Saturation of the unquenched Heisenberg uncertainty bound. iii) (Over)completeness. These states therefore comprise a candidate family for the semi-classical analysis of canonical quantum gravity and quantum gauge theory coupled to quantum gravity, enable error-controlled approximations and set a new starting point for {\it numerical canonical quantum general relativity and gauge theory}. The text is supplemented by an appendix which contains extensive graphics in order to give a feeling for the so far unknown peakedness properties of the states constructed.Comment: 70 pages, LATEX, 29 figure

Gauge Field Theory Coherent States (GCS) : I. General Properties

In this article we outline a rather general construction of diffeomorphism covariant coherent states for quantum gauge theories. By this we mean states $\psi_{(A,E)}$, labelled by a point (A,E) in the classical phase space, consisting of canonically conjugate pairs of connections A and electric fields E respectively, such that (a) they are eigenstates of a corresponding annihilation operator which is a generalization of A-iE smeared in a suitable way, (b) normal ordered polynomials of generalized annihilation and creation operators have the correct expectation value, (c) they saturate the Heisenberg uncertainty bound for the fluctuations of $\hat{A},\hat{E}$ and (d) they do not use any background structure for their definition, that is, they are diffeomorphism covariant. This is the first paper in a series of articles entitled ``Gauge Field Theory Coherent States (GCS)'' which aim at connecting non-perturbative quantum general relativity with the low energy physics of the standard model. In particular, coherent states enable us for the first time to take into account quantum metrics which are excited {\it everywhere} in an asymptotically flat spacetime manifold. The formalism introduced in this paper is immediately applicable also to lattice gauge theory in the presence of a (Minkowski) background structure on a possibly {\it infinite lattice}.Comment: 40 pages, LATEX, no figure

Time separation as a hidden variable to the Copenhagen school of quantum mechanics

The Bohr radius is a space-like separation between the proton and electron in the hydrogen atom. According to the Copenhagen school of quantum mechanics, the proton is sitting in the absolute Lorentz frame. If this hydrogen atom is observed from a different Lorentz frame, there is a time-like separation linearly mixed with the Bohr radius. Indeed, the time-separation is one of the essential variables in high-energy hadronic physics where the hadron is a bound state of the quarks, while thoroughly hidden in the present form of quantum mechanics. It will be concluded that this variable is hidden in Feynman's rest of the universe. It is noted first that Feynman's Lorentz-invariant differential equation for the bound-state quarks has a set of solutions which describe all essential features of hadronic physics. These solutions explicitly depend on the time separation between the quarks. This set also forms the mathematical basis for two-mode squeezed states in quantum optics, where both photons are observable, but one of them can be treated a variable hidden in the rest of the universe. The physics of this two-mode state can then be translated into the time-separation variable in the quark model. As in the case of the un-observed photon, the hidden time-separation variable manifests itself as an increase in entropy and uncertainty.Comment: LaTex 10 pages with 5 figure. Invited paper presented at the Conference on Advances in Quantum Theory (Vaxjo, Sweden, June 2010), to be published in one of the AIP Conference Proceedings serie

Transition Densities and Traces for Invariant Feller Processes on Compact Symmetric Spaces

We find necessary and sufficient conditions for a finite K–bi–invariant measure on a compact Gelfand pair (G, K) to have a square–integrable density. For convolution semigroups, this is equivalent to having a continuous density in positive time. When (G, K) is a compact Riemannian symmetric pair, we study the induced transition density for G–invariant Feller processes on the symmetric space X = G/K. These are obtained as projections of K–bi–invariant L´evy processes on G, whose laws form a convolution semigroup. We obtain a Fourier series expansion for the density, in terms of spherical functions, where the spectrum is described by Gangolli’s L´evy–Khintchine formula. The density of returns to any given point on X is given by the trace of the transition semigroup, and for subordinated Brownian motion, we can calculate the short time asymptotics of this quantity using recent work of Ba˜nuelos and Baudoin. In the case of the sphere, there is an interesting connection with the Funk–Hecke theorem

Maternal characteristics associated with the dietary intake of nitrates, nitrites, and nitrosamines in women of child-bearing age: a cross-sectional study

<p>Abstract</p> <p>Background</p> <p>Multiple <it>N</it>-nitroso compounds have been observed in animal studies to be both mutagenic and teratogenic. Human exposure to <it>N</it>-nitroso compounds and their precursors, nitrates and nitrites, can occur through exogenous sources, such as diet, drinking water, occupation, or environmental exposures, and through endogenous exposures resulting from the formation of <it>N</it>-nitroso compounds in the body. Very little information is available on intake of nitrates, nitrites, and nitrosamines and factors related to increased consumption of these compounds.</p> <p>Methods</p> <p>Using survey and dietary intake information from control women (with deliveries of live births without major congenital malformations during 1997-2004) who participated in the National Birth Defects Prevention Study (NBDPS), we examined the relation between various maternal characteristics and intake of nitrates, nitrites, and nitrosamines from dietary sources. Estimated intake of these compounds was obtained from the Willet Food Frequency Questionnaire as adapted for the NBDPS. Multinomial logistic regression models were used to estimate odds ratios and 95% confidence intervals for the consumption of these compounds by self-reported race/ethnicity and other maternal characteristics.</p> <p>Results</p> <p>Median intake per day for nitrates, nitrites, total nitrites (nitrites + 5% nitrates), and nitrosamines was estimated at 40.48 mg, 1.53 mg, 3.69 mg, and 0.472 μg respectively. With the lowest quartile of intake as the referent category and controlling for daily caloric intake, factors predicting intake of these compounds included maternal race/ethnicity, education, body mass index, household income, area of residence, folate intake, and percent of daily calories from dietary fat. Non-Hispanic White participants were less likely to consume nitrates, nitrites, and total nitrites per day, but more likely to consume dietary nitrosamines than other participants that participated in the NBDPS. Primary food sources of these compounds also varied by maternal race/ethnicity.</p> <p>Conclusions</p> <p>Results of this study indicate that intake of nitrates, nitrites, and nitrosamines vary considerably by race/ethnicity, education, body mass index, and other characteristics. Further research is needed regarding how consumption of foods high in nitrosamines and <it>N</it>-nitroso precursors might relate to risk of adverse pregnancy outcomes and chronic diseases.</p