We give a simple formula for the essential dimension of a finite pseudoreflection group at a prime p and determine the absolute essential dimension for most irreducible pseudo-reflection groups. We also study the “poor man’s essential dimension” of an arbitrary finite group, an intermediate notion between the absolute essential dimension and the essential dimension at a prime p.

Neuronal microtubules (MTs) are essential for neurite extension, axonal guidance, and communication between the cell body and neuronal processes. Dynamic properties of individual MTs and the architecture of the MT array are regulated by MT-associated proteins (MAPs). One member of the MAP family, tau, has received particular attention since hyperphosphorylation of tau has been linked to the for...

The structure, dynamic behavior, and spatial organization of microtubules are regulated by microtubule-associated proteins. An important microtubule-associated protein is the protein Tau, because its microtubule interaction is impaired in the course of Alzheimer's disease and several other neurodegenerative diseases. Here, we show that Tau binds to microtubules by using small groups of evolutio...

Prion-like propagation of tau aggregation might underlie the stereotyped progression of neurodegenerative tauopathies. True prions stably maintain unique conformations ("strains") in vivo that link structure to patterns of pathology. We now find that tau meets this criterion. Stably expressed tau repeat domain indefinitely propagates distinct amyloid conformations in a clonal fashion in culture...

We analyze the compatibility of hypothesis third-family quark-lepton unification at TeV scale with electroweak precision data, lepton flavor universality tests, and high-$p_T$ constraints. work within framework UV complete non-universal 4321 gauge model, which is matched one loop to Standard Model Effective Field Theory. For consistency, all observables are also computed effective field theory....

Conflicting evidence supports a role for tau as an essential neuronal cytoskeletal protein or as a redundant protein whose function can be fulfilled by other microtubule-associated proteins. To investigate the function of tau in axonogenesis, we created tau deficient mice by disrupting the TAU gene. The engineered mice do not express the tau protein, appear physically normal and are able to rep...

Tau is an intrinsically disordered protein (IDP) implicated in Alzheimer's disease. Recently, tau proteins were discovered to be able to catalyze self-acetylation, which may promote its pathological aggregation. Understanding the paradox of tau's random-like conformations, aggregation propensity, and enzymatic activity are challenging questions. We characterized the atomic structures of two tru...

Abstract A number of measurements in decays induced by the semileptonic $b\to s$ and c$ transitions hint towards a possible role new physics both sectors.
 Motivated these anomalies, we investigate lepton flavor violating $B\to K^*_2 (1430)\mu^{\pm}\tau^{\mp}$ decays. We calculate two-fold angular distribution K^*_2\ell_1\ell_2$ decay presence vector, axial-vector, scalar pseudo-scalar ...