Let $X$ be a Banach space of $dim X > 2$ and $B(X)$ be the space of bounded linear operators on X. If $L : B(X)to B(X)$ be a Lie higher derivation on $B(X)$, then there exists an additive higher derivation $D$ and a linear map $tau : B(X)to FI$ vanishing at commutators $[A, B]$ for all $A, Bin B(X)$ such that $L = D + tau$.

‎we determine the‎ ‎form of polynomially bounded solutions to the loewner differential ‎equation that is satisfied by univalent subordination chains of the‎ ‎form $f(z,t)=e^{int_0^t a(tau){rm d}tau}z+cdots$‎, ‎where‎ ‎$a:[0,infty]rightarrow l(mathbb{c}^n,mathbb{c}^n)$ is a locally‎ ‎lebesgue integrable mapping and satisfying the condition‎ ‎$$sup_{sgeq0}int_0^inftyleft|expleft{int_s^t‎ ‎[a(tau)...

Although tau is a cytoplasmic protein, it is also found in brain extracellular fluids, e.g., CSF. Recent findings suggest that aggregated tau can be transferred between cells and extracellular tau aggregates might mediate spread of tau pathology. Despite these data, details of whether tau is normally released into the brain interstitial fluid (ISF), its concentration in ISF in relation to CSF, ...

Neurodegenerative tauopathies characterized by hyperphosphorylated tau include frontotemporal dementia and Parkinsonism linked to chromosome 17 (FTDP-17) and Alzheimer's disease (AD). Reducing tau levels improves cognitive function in mouse models of AD and FTDP-17, but the mechanisms regulating the turnover of pathogenic tau are unknown. We found that tau is acetylated and that tau acetylation...

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...

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...

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...