Microtubule (MT) associated protein tau is abnormally hyperphosphorylated and aggregated into paired helical filaments (PHFs), which manifest as neurofibrillary tangles (NFTs) in the brains of individuals with Alzheimer's disease (AD) and related tauopathies. Hyperphosphorylation and truncation of tau have been linked to the progression of the disease. However, the nature of phosphorylation and...

We revisit Smith’s frame of curvelets and discretize it making use of the USFFT as developed by Dutt and Roklin, and Beylkin. In the discretization, we directly approximate the underlying dyadic parabolic decomposition, its (rotational) symmetry, and approximate all the necessary decay estimates in phase space with arbitrary accuracy. Numerically, our transform is unitary. Moreover, if we apply...

Let $F$ be a non-Archimedean locally compact field‎. ‎Let $sigma$ and $tau$ be finite-dimensional representations of the Weil-Deligne group of $F$‎. ‎We give strong upper and lower bounds for the Artin and Swan exponents of $sigmaotimestau$ in terms of those of $sigma$ and $tau$‎. ‎We give a different lower bound in terms of $sigmaotimeschecksigma$ and $tauotimeschecktau$‎. ‎Using the Langlands...

Alzheimer's disease (AD) and a subset of frontotemporal dementia termed FTLD-Tau are characterized by a massive, yet incompletely characterized and understood redistribution of Tau. To establish a framework for understanding this pathology, we used the genome-editing tool TALEN and generated Tau-mEOS2 knock-in mice to determine the mobility and subcellular localization of endogenous Tau in hipp...

In this paper, we introduce the notion of super finitely separating functions which gives a characterization of RB-domains. Then we prove that FS-domains and RB-domains are equivalent in some special cases by the following three claims: a dcpo is an RB-domain if and only if there exists an approximate identity for it consisting of super finitely separating functions; a consistent join-semilatti...

We consider in dimension four weakly convergent sequences of approximate biharmonic maps into sphere with bi-tension fields bounded in L for some p > 1. We prove an energy identity that accounts for the loss of Hessian energies by the sum of Hessian energies over finitely many nontrivial biharmonic maps on R.

Let X and A be sets and α : X → A a map between them. We call a map μ : X ×X ×X → A an approximate Mal’tsev operation with approximation α, if it satisfies μ(x, y, y) = α(x) = μ(y, y, x) for all x, y ∈ X. Note that if A = X and the approximation α is an identity map, then μ becomes an ordinary Mal’tsev operation. We prove the following two characterization theorems: a category X is a Mal’tsev c...

Time resolved photometry of the long-period intermediate polar V1062 Tau confirmed the presence of the previously reported orbital and spin periods, and revealed the presence of a third one, corresponding to the beat of the two. While the orbital periodicity was present throughout our data, only one of the shorter periods was detectable at any given time. On a time-scale of ∼90 days, the short-...

(Cell 142, 320–332; July 23, 2010) As a result of an error during figure preparation, the model in Figure 6D was omitted. Additionally, in Figure S1B, Tau-pSer399 was incorrectly typed. This has been corrected to Tau-pSer396 both in the figure and in the text. Corrected versions of both figures are shown below. These errors in no way affect the conclusions of the paper, and the authors apologiz...