4,437 research outputs found
Local unitary invariants for multipartite quantum systems
A method is presented to obtain local unitary invariants for multipartite
quantum systems consisting of fermions or distinguishable particles. The
invariants are organized into infinite families, in particular, the
generalization to higher dimensional single particle Hilbert spaces is
straightforward. Many well-known invariants and their generalizations are also
included.Comment: 13 page
Two generalizations of the PRV conjecture
Let G be a complex connected reductive group. The PRV conjecture, which was
proved independently by S. Kumar and O. Mathieu in 1989, gives explicit
irreducible submodules of the tensor product of two irreducible G-modules. This
paper has three aims. First, we simplify the proof of the PRV conjecture, then
we generalize it to other branching problems. Finally, we find other
irreducible components of the tensor product of two irreducible G-modules that
appear for "the same reason" as the PRV ones
Stringy K-theory and the Chern character
For a finite group G acting on a smooth projective variety X, we construct
two new G-equivariant rings: first the stringy K-theory of X, and second the
stringy cohomology of X. For a smooth Deligne-Mumford stack Y we also construct
a new ring called the full orbifold K-theory of Y. For a global quotient
Y=[X/G], the ring of G-invariants of the stringy K-theory of X is a subalgebra
of the full orbifold K-theory of the the stack Y and is linearly isomorphic to
the ``orbifold K-theory'' of Adem-Ruan (and hence Atiyah-Segal), but carries a
different, ``quantum,'' product, which respects the natural group grading. We
prove there is a ring isomorphism, the stringy Chern character, from stringy
K-theory to stringy cohomology, and a ring homomorphism from full orbifold
K-theory to Chen-Ruan orbifold cohomology. These Chern characters satisfy
Grothendieck-Riemann-Roch for etale maps.
We prove that stringy cohomology is isomorphic to Fantechi and Goettsche's
construction. Since our constructions do not use complex curves, stable maps,
admissible covers, or moduli spaces, our results simplify the definitions of
Fantechi-Goettsche's ring, of Chen-Ruan's orbifold cohomology, and of
Abramovich-Graber-Vistoli's orbifold Chow.
We conclude by showing that a K-theoretic version of Ruan's Hyper-Kaehler
Resolution Conjecture holds for symmetric products.
Our results hold both in the algebro-geometric category and in the
topological category for equivariant almost complex manifolds.Comment: Exposition improved and additional details provided. To appear in
Inventiones Mathematica
Rhode Island’s Health Equity Zones: Addressing Local Problems with Local Solutions
The Rhode Island Department of Health (RIDOH) describes the strategies and infrastructure it has developed to fund its placed-based initiatives to address the social determinants of health to eliminate health disparities. Using a data driven and community-led approach, RIDOH funded 10 local collaboratives, each with its own, geographically-defined “Health Equity Zone,” or “HEZ,” and, to support the collaboratives, created a new “Health Equity Institute,” a “HEZ Team” of 9 seasoned project managers, and direct lines of communications between these assets and the Office of the Director of Health
Classification of double flag varieties of complexity 0 and 1
A classification of double flag varieties of complexity 0 and 1 is obtained.
An application of this problem to decomposing tensor products of irreducible
representations of semisimple Lie groups is considered
Grothendieck groups and a categorification of additive invariants
A topologically-invariant and additive homology class is mostly not a natural
transformation as it is. In this paper we discuss turning such a homology class
into a natural transformation; i.e., a "categorification" of it. In a general
categorical set-up we introduce a generalized relative Grothendieck group from
a cospan of functors of categories and also consider a categorification of
additive invariants on objects. As an example, we obtain a general theory of
characteristic homology classes of singular varieties.Comment: 27 pages, to appear in International J. Mathematic
Hyperinsulinism-hyperammonaemia syndrome: novel mutations in the GLUD1 gene and genotype-phenotype correlations
Background: Activating mutations in the GLUD1 gene (which encodes for the intra-mitochondrial enzyme glutamate dehydrogenase, GDH) cause the hyperinsulinism–hyperammonaemia (HI/HA) syndrome. Patients present with HA and leucine-sensitive hypoglycaemia. GDH is regulated by another intra-mitochondrial enzyme sirtuin 4 (SIRT4). Sirt4 knockout mice demonstrate activation of GDH with increased amino acid-stimulated insulin secretion.
Objectives: To study the genotype–phenotype correlations in patients with GLUD1 mutations. To report the phenotype and functional analysis of a novel mutation (P436L) in the GLUD1 gene associated with the absence of HA.
Patients and methods: Twenty patients with HI from 16 families had mutational analysis of the GLUD1 gene in view of HA (n=19) or leucine sensitivity (n=1). Patients negative for a GLUD1 mutation had sequence analysis of the SIRT4 gene. Functional analysis of the novel P436L GLUD1 mutation was performed.
Results: Heterozygous missense mutations were detected in 15 patients with HI/HA, 2 of which are novel (N410D and D451V). In addition, a patient with a normal serum ammonia concentration (21 µmol/l) was heterozygous for a novel missense mutation P436L. Functional analysis of this mutation confirms that it is associated with a loss of GTP inhibition. Seizure disorder was common (43%) in our cohort of patients with a GLUD1 mutation. No mutations in the SIRT4 gene were identified.
Conclusion: Patients with HI due to mutations in the GLUD1 gene may have normal serum ammonia concentrations. Hence, GLUD1 mutational analysis may be indicated in patients with leucine sensitivity; even in the absence of HA. A high frequency of epilepsy (43%) was observed in our patients with GLUD1 mutations
Heisenberg antiferromagnet on the square lattice for S>=1
Theoretical predictions of a semiclassical method - the pure-quantum
self-consistent harmonic approximation - for the correlation length and
staggered susceptibility of the Heisenberg antiferromagnet on the square
lattice (2DQHAF) agree very well with recent quantum Monte Carlo data for S=1,
as well as with experimental data for the S=5/2 compounds Rb2MnF4 and KFeF4.
The theory is parameter-free and can be used to estimate the exchange coupling:
for KFeF4 we find J=2.33 +- 0.33 meV, matching with previous determinations. On
this basis, the adequacy of the quantum nonlinear sigma model approach in
describing the 2DQHAF when S>=1 is discussed.Comment: 4 pages RevTeX file with 5 figures included by psfi
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