520 research outputs found
The twisted forms of a semisimple group over an fq-curve
Let C be a smooth, projective and geometrically connected curve defined over a finite field Fq . Given a semisimple C −S-group scheme G where S is a finite set of closed points of C, we describe the set of (OS-classes of) twisted forms of G in terms of geometric invariants of its fundamental group F (G)
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Different Amyloid-β Self-Assemblies Have Distinct Effects on Intracellular Tau Aggregation.
Alzheimer's disease (AD) pathology is characterized by the aggregation of beta-amyloid (Aβ) and tau in the form of amyloid plaques and neurofibrillary tangles in the brain. It has been found that a synergistic relationship between these two proteins may contribute to their roles in disease progression. However, how Aβ and tau interact has not been fully characterized. Here, we analyze how tau seeding or aggregation is influenced by different Aβ self-assemblies (fibrils and oligomers). Our cellular assays utilizing tau biosensor cells show that transduction of Aβ oligomers into the cells greatly enhances seeded tau aggregation in a concentration-dependent manner. In contrast, transduced Aβ fibrils slightly reduce tau seeding while untransduced Aβ fibrils promote it. We also observe that the transduction of α-synuclein fibrils, another amyloid protein, has no effect on tau seeding. The enhancement of tau seeding by Aβ oligomers was confirmed using tau fibril seeds derived from both recombinant tau and PS19 mouse brain extracts containing human tau. Our findings highlight the importance of considering the specific form and cellular location of Aβ self-assembly when studying the relationship between Aβ and tau in future AD therapeutic development
On the genera of semisimple groups defined over an integral domain of a global function field
Let be the global function field of rational functions
over a smooth and projective curve defined over a finite field
. The ring of regular functions on where
is any finite set of closed points on is a Dedekind domain
of . For a semisimple -group with a smooth
fundamental group , we aim to describe both the set of genera of
and its principal genus (the latter if is isotropic at ) in terms of abelian groups
depending on and only. This leads to a
necessary and sufficient condition for the Hasse local-global principle to hold
for certain . We also use it to express the Tamagawa number
of a semisimple -group by the Euler Poincar\'e invariant. This
facilitates the computation of for twisted -groups.Comment: 18 page
On the flat cohomology of binary norm forms
Let be an order of index in the maximal order of a
quadratic number field . Let
be the orthogonal -group of the
associated norm form . We describe the structure of the pointed set
, which classifies
quadratic forms isomorphic (properly or improperly) to in the flat
topology. Gauss classified quadratic forms of fundamental discriminant and
showed that the composition of any binary -form of discriminant
with itself belongs to the principal genus. Using cohomological
language, we extend these results to forms of certain non-fundamental
discriminants.Comment: 24 pages, submitted. Comments are welcom
Theory of interacting electrons on the honeycomb lattice
The low-energy theory of electrons interacting via repulsive short-range
interactions on graphene's honeycomb lattice at half filling is presented. The
exact symmetry of the Lagrangian with local quartic terms for the Dirac field
dictated by the lattice is D_2 x U_c(1) x (time reversal), where D_2 is the
dihedral group, and U_c(1) is a subgroup of the SU_c(2) "chiral" group of the
non-interacting Lagrangian, that represents translations in Dirac language. The
Lagrangian describing spinless particles respecting this symmetry is
parameterized by six independent coupling constants. We show how first imposing
the rotational, then Lorentz, and finally chiral symmetry to the quartic terms,
in conjunction with the Fierz transformations, eventually reduces the set of
couplings to just two, in the "maximally symmetric" local interacting theory.
We identify the two critical points in such a Lorentz and chirally symmetric
theory as describing metal-insulator transitions into the states with either
time-reversal or chiral symmetry being broken. In the site-localized limit of
the interacting Hamiltonian the low-energy theory describes the continuous
transitions into the insulator with either a finite Haldane's (circulating
currents) or Semenoff's (staggered density) masses, both in the universality
class of the Gross-Neveu model. The picture of the metal-insulator transition
on a honeycomb lattice emerges at which the residue of the quasiparticle pole
at the metallic and the mass-gap in the insulating phase both vanish
continuously as the critical point is approached. We argue that the Fermi
velocity is non-critical as a consequence of the dynamical exponent being fixed
to unity by the emergent Lorentz invariance. Effects of long-range interaction
and the critical behavior of specific heat and conductivity are discussed.Comment: 16 revtex pages, 4 figures; typos corrected, new and updated
references; published versio
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