43 research outputs found
Natural Exact Covering Systems and the Reversion of the Möbius Series
We prove that the number of natural exact covering systems of cardinality k is equal to the coefficient of xkin the reversion of the power series âkâ„1ÎŒ(k) xk, where Ό(k) is the usual number-theoretic Möbius function. Using this result, we deduce an asymptotic expression for the number of such systems
ABCD of Beta Ensembles and Topological Strings
We study beta-ensembles with Bn, Cn, and Dn eigenvalue measure and their
relation with refined topological strings. Our results generalize the familiar
connections between local topological strings and matrix models leading to An
measure, and illustrate that all those classical eigenvalue ensembles, and
their topological string counterparts, are related one to another via various
deformations and specializations, quantum shifts and discrete quotients. We
review the solution of the Gaussian models via Macdonald identities, and
interpret them as conifold theories. The interpolation between the various
models is plainly apparent in this case. For general polynomial potential, we
calculate the partition function in the multi-cut phase in a perturbative
fashion, beyond tree-level in the large-N limit. The relation to refined
topological string orientifolds on the corresponding local geometry is
discussed along the way.Comment: 33 pages, 1 figur
Integrability properties of Hurwitz partition functions. II. Multiplication of cut-and-join operators and WDVV equations
Correlators in topological theories are given by the values of a linear form
on the products of operators from a commutative associative algebra (CAA). As a
corollary, partition functions of topological theory always satisfy the
generalized WDVV equations. We consider the Hurwitz partition functions,
associated in this way with the CAA of cut-and-join operators. The ordinary
Hurwitz numbers for a given number of sheets in the covering provide trivial
(sums of exponentials) solutions to the WDVV equations, with finite number of
time-variables. The generalized Hurwitz numbers from arXiv:0904.4227 provide a
non-trivial solution with infinite number of times. The simplest solution of
this type is associated with a subring, generated by the dilatation operators
tr X(d/dX).Comment: 24 page
On products of long cycles: short cycle dependence and separation probabilities
We present various results on multiplying cycles in the symmetric group. One result is a generalisation
of the following theorem of Boccara (1980): the number of ways of writing an odd permutation
in the symmetric group on n symbols as a product of an n-cycle and an (n - 1)-cycle is independent of
the permutation chosen. We give a number of different approaches of our generalisation. One partial proof
uses an inductive method which we also apply to other problems. In particular, we give a formula for the
distribution of the number of cycles over all products of cycles of fixed lengths. Another application is related
to the recent notion of separation probabilities for permutations introduced by Bernardi, Du, Morales
and Stanley (2014)
Supersymmetric QCD corrections to and the Bernstein-Tkachov method of loop integration
The discovery of charged Higgs bosons is of particular importance, since
their existence is predicted by supersymmetry and they are absent in the
Standard Model (SM). If the charged Higgs bosons are too heavy to be produced
in pairs at future linear colliders, single production associated with a top
and a bottom quark is enhanced in parts of the parameter space. We present the
next-to-leading-order calculation in supersymmetric QCD within the minimal
supersymmetric SM (MSSM), completing a previous calculation of the SM-QCD
corrections. In addition to the usual approach to perform the loop integration
analytically, we apply a numerical approach based on the Bernstein-Tkachov
theorem. In this framework, we avoid some of the generic problems connected
with the analytical method.Comment: 14 pages, 6 figures, accepted for publication in Phys. Rev.
The Changing Landscape for Stroke\ua0Prevention in AF: Findings From the GLORIA-AF Registry Phase 2
Background GLORIA-AF (Global Registry on Long-Term Oral Antithrombotic Treatment in Patients with Atrial Fibrillation) is a prospective, global registry program describing antithrombotic treatment patterns in patients with newly diagnosed nonvalvular atrial fibrillation at risk of stroke. Phase 2 began when dabigatran, the first non\u2013vitamin K antagonist oral anticoagulant (NOAC), became available. Objectives This study sought to describe phase 2 baseline data and compare these with the pre-NOAC era collected during phase 1. Methods During phase 2, 15,641 consenting patients were enrolled (November 2011 to December 2014); 15,092 were eligible. This pre-specified cross-sectional analysis describes eligible patients\u2019 baseline characteristics. Atrial fibrillation disease characteristics, medical outcomes, and concomitant diseases and medications were collected. Data were analyzed using descriptive statistics. Results Of the total patients, 45.5% were female; median age was 71 (interquartile range: 64, 78) years. Patients were from Europe (47.1%), North America (22.5%), Asia (20.3%), Latin America (6.0%), and the Middle East/Africa (4.0%). Most had high stroke risk (CHA2DS2-VASc [Congestive heart failure, Hypertension, Age 6575 years, Diabetes mellitus, previous Stroke, Vascular disease, Age 65 to 74 years, Sex category] score 652; 86.1%); 13.9% had moderate risk (CHA2DS2-VASc = 1). Overall, 79.9% received oral anticoagulants, of whom 47.6% received NOAC and 32.3% vitamin K antagonists (VKA); 12.1% received antiplatelet agents; 7.8% received no antithrombotic treatment. For comparison, the proportion of phase 1 patients (of N = 1,063 all eligible) prescribed VKA was 32.8%, acetylsalicylic acid 41.7%, and no therapy 20.2%. In Europe in phase 2, treatment with NOAC was more common than VKA (52.3% and 37.8%, respectively); 6.0% of patients received antiplatelet treatment; and 3.8% received no antithrombotic treatment. In North America, 52.1%, 26.2%, and 14.0% of patients received NOAC, VKA, and antiplatelet drugs, respectively; 7.5% received no antithrombotic treatment. NOAC use was less common in Asia (27.7%), where 27.5% of patients received VKA, 25.0% antiplatelet drugs, and 19.8% no antithrombotic treatment. Conclusions The baseline data from GLORIA-AF phase 2 demonstrate that in newly diagnosed nonvalvular atrial fibrillation patients, NOAC have been highly adopted into practice, becoming more frequently prescribed than VKA in Europe and North America. Worldwide, however, a large proportion of patients remain undertreated, particularly in Asia and North America. (Global Registry on Long-Term Oral Antithrombotic Treatment in Patients With Atrial Fibrillation [GLORIA-AF]; NCT01468701
Enumerating branched orientable surface coverings over a non-orientable surface
The isomorphism classes of several types of graph coverings of a graph have been enumerated by many authors [M. Hofmeister, Graph covering projections arising from finite vector space over finite fields, Discrete Math. 143 (1995) 87-97; S. Hong, J.H. Kwak, J. Lee, Regular graph coverings whose covering transformation groups have the isomorphism extention property, Discrete Math. 148 (1996) 85-105; J.H. Kwak, J.H. Chun, J.Lee, Enumeration of regular graph coverings having finite abelian covering transformation groups, SIAM J. Discrete Math. 11 (1998) 273-285; J.H. Kwak, J. Lee, Isomorphism classes of graph bundles, Canad. J. Math. XLII (1990) 747-761; J.H. Kwak, J. Lee, Enumeration of connected graph coverings, J. Graph Theory 23 (1996) 105-109]. Recently, Kwak et at [Balanced regular coverings of a signed graph and regular branched orientable surface coverings over a non-orientable surface, Discrete Math. 275 (2004) 177-193] enumerated the isomorphism classes of balanced regular coverings of a signed graph, as a continuation of an enumeration work done by Archdeacon et al [Bipartite covering graphs, Discrete Math. 214 (2000) 51-63] the isomorphism classes of branched orientable regular surface coverings of a non-orientable surface having a finite abelian covering transformation group. In this paper, we enumerate the isomorphism classes of connected balanced (regular or irregular) coverings of a signed graph and those of unbranched orientable coverings of a non-orientable surface, as an answer of the question raised by Liskovets [Reductive enumeration under mutually orthogonal group actions, Acta-Appl.Math. 52 (1998) 91-120]. As a consequence of these two results, we also enumerate the isomorphism classes of branched orientable surface coverings of a non-orientable surface. (c) 2005 Elsevier B.V. All rights reserved.X112sciescopu