Trace as an alternative decategorification functor

Categorification is a process of lifting structures to a higher categorical level. The original structure can then be recovered by means of the so-called "decategorification" functor. Algebras are typically categorified to additive categories with additional structure and decategorification is usually given by the (split) Grothendieck group. In this expository article we study an alternative decategorification functor given by the trace or the zeroth Hochschild--Mitchell homology. We show that this form of decategorification endows any 2-representation of the categorified quantum sl(n) with an action of the current algebra U(sl(n)[t]) on its center.Comment: 47 pages with tikz figures. arXiv admin note: text overlap with arXiv:1405.5920 by other author

One-Year Risk of Stroke after Transient Ischemic Attack or Minor Stroke

BACKGROUND Previous studies conducted between 1997 and 2003 estimated that the risk of stroke or an acute coronary syndrome was 12 to 20% during the first 3 months after a transient ischemic attack (TIA) or minor stroke. The TIAregistry.org project was designed to describe the contemporary profile, etiologic factors, and outcomes in patients with a TIA or minor ischemic stroke who receive care in health systems that now offer urgent evaluation by stroke specialists. METHODS We recruited patients who had had a TIA or minor stroke within the previous 7 days. Sites were selected if they had systems dedicated to urgent evaluation of patients with TIA. We estimated the 1-year risk of stroke and of the composite outcome of stroke, an acute coronary syndrome, or death from cardiovascular causes. We also examined the association of the ABCD2 score for the risk of stroke (range, 0 [lowest risk] to 7 [highest risk]), findings on brain imaging, and cause of TIA or minor stroke with the risk of recurrent stroke over a period of 1 year. RESULTS From 2009 through 2011, we enrolled 4789 patients at 61 sites in 21 countries. A total of 78.4% of the patients were evaluated by stroke specialists within 24 hours after symptom onset. A total of 33.4% of the patients had an acute brain infarction, 23.2% had at least one extracranial or intracranial stenosis of 50% or more, and 10.4% had atrial fibrillation. The Kaplan–Meier estimate of the 1-year event rate of the composite cardiovascular outcome was 6.2% (95% confidence interval, 5.5 to 7.0). Kaplan–Meier estimates of the stroke rate at days 2, 7, 30, 90, and 365 were 1.5%, 2.1%, 2.8%, 3.7%, and 5.1%, respectively. In multivariable analyses, multiple infarctions on brain imaging, large-artery atherosclerosis, and an ABCD2 score of 6 or 7 were each associated with more than a doubling of the risk of stroke. CONCLUSIONS We observed a lower risk of cardiovascular events after TIA than previously reported. The ABCD2 score, findings on brain imaging, and status with respect to large-artery atherosclerosis helped stratify the risk of recurrent stroke within 1 year after a TIA or minor stroke. (Funded by Sanofi and Bristol-Myers Squibb.)Supported by an unrestricted grant from Sanofi and Bristol-Myers Squibb

Computational Vaccinology: An Important Strategy to Discover New Potential S. mansoni Vaccine Candidates

The flatworm Schistosoma mansoni is a blood fluke parasite that causes schistosomiasis, a debilitating disease that occurs throughout the developing world. Current schistosomiasis control strategies are mainly based on chemotherapy, but many researchers believe that the best long-term strategy to control schistosomiasis is through immunization with an antischistosomiasis vaccine combined with drug treatment. Several papers on Schistosoma mansoni vaccine and drug development have been published in the past few years, representing an important field of study. The advent of technologies that allow large-scale studies of genes and proteins had a remarkable impact on the screening of new and potential vaccine candidates in schistosomiasis. In this postgenomic scenario, bioinformatic technologies have emerged as important tools to mine transcriptomic, genomic, and proteomic databases. These new perspectives are leading to a new round of rational vaccine development. Herein, we discuss different strategies to identify potential S. mansoni vaccine candidates using computational vaccinology

Classical BV theories on manifolds with boundary

In this paper we extend the classical BV framework to gauge theories on spacetime manifolds with boundary. In particular, we connect the BV construction in the bulk with the BFV construction on the boundary and we develop its extension to strata of higher codimension in the case of manifolds with corners. We present several examples including electrodynamics, Yang-Mills theory and topological field theories coming from the AKSZ construction, in particular, the Chern-Simons theory, the $BF$ theory, and the Poisson sigma model. This paper is the first step towards developing the perturbative quantization of such theories on manifolds with boundary in a way consistent with gluing.Comment: The second version has many typos corrected, references added. Some typos are probably still there, in particular, signs in examples. In the third version more typoes are corrected and the exposition is slightly change

Peaks in the Hartle-Hawking Wave Function from Sums over Topologies

Recent developments in ``Einstein Dehn filling'' allow the construction of infinitely many Einstein manifolds that have different topologies but are geometrically close to each other. Using these results, we show that for many spatial topologies, the Hartle-Hawking wave function for a spacetime with a negative cosmological constant develops sharp peaks at certain calculable geometries. The peaks we find are all centered on spatial metrics of constant negative curvature, suggesting a new mechanism for obtaining local homogeneity in quantum cosmology.Comment: 16 pages,LaTeX, no figures; v2: some changes coming from revision of a math reference: wave function peaks sharp but not infinite; v3: added paragraph in intro on interpretation of wave functio

Chern-Simons States at Genus One

We present a rigorous analysis of the Schr\"{o}dinger picture quantization for the $SU(2)$ Chern-Simons theory on 3-manifold torus$\times$line, with insertions of Wilson lines. The quantum states, defined as gauge covariant holomorphic functionals of smooth $su(2)$-connections on the torus, are expressed by degree $2k$ theta-functions satisfying additional conditions. The conditions are obtained by splitting the space of semistable $su(2)$-connections into nine submanifolds and by analyzing the behavior of states at four codimension $1$ strata. We construct the Knizhnik-Zamolodchikov-Bernard connection allowing to compare the states for different complex structures of the torus and different positions of the Wilson lines. By letting two Wilson lines come together, we prove a recursion relation for the dimensions of the spaces of states which, together with the (unproven) absence of states for spins\s>{_1\over^2}level implies the Verlinde dimension formula.Comment: 33 pages, IHES/P

Entropy vs. Action in the (2+1)-Dimensional Hartle-Hawking Wave Function

In most attempts to compute the Hartle-Hawking ``wave function of the universe'' in Euclidean quantum gravity, two important approximations are made: the path integral is evaluated in a saddle point approximation, and only the leading (least action) extremum is taken into account. In (2+1)-dimensional gravity with a negative cosmological constant, the second assumption is shown to lead to incorrect results: although the leading extremum gives the most important single contribution to the path integral, topologically inequivalent instantons with larger actions occur in great enough numbers to predominate. One can thus say that in 2+1 dimensions --- and possibly in 3+1 dimensions as well --- entropy dominates action in the gravitational path integral.Comment: 17 page

Quantum Gravity and the Algebra of Tangles

In Rovelli and Smolin's loop representation of nonperturbative quantum gravity in 4 dimensions, there is a space of solutions to the Hamiltonian constraint having as a basis isotopy classes of links in R^3. The physically correct inner product on this space of states is not yet known, or in other words, the *-algebra structure of the algebra of observables has not been determined. In order to approach this problem, we consider a larger space H of solutions of the Hamiltonian constraint, which has as a basis isotopy classes of tangles. A certain algebra T, the ``tangle algebra,'' acts as operators on H. The ``empty state'', corresponding to the class of the empty tangle, is conjectured to be a cyclic vector for T. We construct simpler representations of T as quotients of H by the skein relations for the HOMFLY polynomial, and calculate a *-algebra structure for T using these representations. We use this to determine the inner product of certain states of quantum gravity associated to the Jones polynomial (or more precisely, Kauffman bracket).Comment: 16 pages (with major corrections