Toda Equations and Piecewise Polynomiality for Mixed Double Hurwitz Numbers

This article introduces mixed double Hurwitz numbers, which interpolate combinatorially between the classical double Hurwitz numbers studied by Okounkov and the monotone double Hurwitz numbers introduced recently by Goulden, Guay-Paquet and Novak. Generalizing a result of Okounkov, we prove that a certain generating series for the mixed double Hurwitz numbers solves the 2-Toda hierarchy of partial differential equations. We also prove that the mixed double Hurwitz numbers are piecewise polynomial, thereby generalizing a result of Goulden, Jackson and Vakil

Polynomiality of monotone Hurwitz numbers in higher genera

Hurwitz numbers count branched covers of the Riemann sphere with specified ramification, or equivalently, transitive permutation factorizations in the symmetric group with specified cycle types. Monotone Hurwitz numbers count a restricted subset of these branched covers, related to the expansion of complete symmetric functions in the Jucys-Murphy elements, and have arisen in recent work on the the asymptotic expansion of the Harish-Chandra-Itzykson-Zuber integral. In previous work we gave an explicit formula for monotone Hurwitz numbers in genus zero. In this paper we consider monotone Hurwitz numbers in higher genera, and prove a number of results that are reminiscent of those for classical Hurwitz numbers. These include an explicit formula for monotone Hurwitz numbers in genus one, and an explicit form for the generating function in arbitrary positive genus. From the form of the generating function we are able to prove that monotone Hurwitz numbers exhibit a polynomiality that is reminiscent of that for the classical Hurwitz numbers, i.e., up to a specified combinatorial factor, the monotone Hurwitz number in genus g with ramification specified by a given partition is a polynomial indexed by g in the parts of the partition.Comment: 23 page

Monotone Hurwitz numbers and the HCIZ integral

In this article, we prove that the complex convergence of the HCIZ free energy is equivalent to the non-vanishing of the HCIZ integral in a neighbourhood of $z=0$. Our approach is based on a combinatorial model for the Maclaurin coefficients of the HCIZ integral together with classical complex-analytic techniques.Comment: 13 page

Monotone Hurwitz numbers in genus zero

Hurwitz numbers count branched covers of the Riemann sphere with specified ramification data, or equivalently, transitive permutation factorizations in the symmetric group with specified cycle types. Monotone Hurwitz numbers count a restricted subset of the branched covers counted by the Hurwitz numbers, and have arisen in recent work on the the asymptotic expansion of the Harish-Chandra-Itzykson-Zuber integral. In this paper we begin a detailed study of monotone Hurwitz numbers. We prove two results that are reminiscent of those for classical Hurwitz numbers. The first is the monotone join-cut equation, a partial differential equation with initial conditions that characterizes the generating function for monotone Hurwitz numbers in arbitrary genus. The second is our main result, in which we give an explicit formula for monotone Hurwitz numbers in genus zero.Comment: 22 pages, submitted to the Canadian Journal of Mathematic

Viscous photons in relativistic heavy ion collisions

Theoretical studies of the production of real thermal photons in relativistic heavy ion collisions at the Relativistic Heavy Ion Collider (RHIC) are performed. The space-time evolution of the colliding system is modelled using MUSIC, a 3+1D relativistic hydrodynamic simulation, using both its ideal and viscous versions. The inclusive spectrum and its azimuthal angular anisotropy are studied separately, and the relative contributions of the different photon sources are highlighted. It is shown that the photon v2 coefficient is especially sensitive to the details of the microscopic dynamics like the equation of state, the ratio of shear viscosity over entropy density, eta/s, and to the morphology of the initial state.Comment: 15 pages, 12 figures. References updated and discussion adde

Problems of Educational Processes Development and Labor Market Needs Analysis in Russia

This article is dedicated to the analysis of the problems of the educational process development and its relation to the labor market. Main problems caused by inconsistency of the education system and labor market needs were revealed. The study of the educational expectations and needs of graduates and students (using questionnaires) was made herein. Labor market analysis wad done to show the main negative and positive aspects of its development. Market industry forecast trends and the education market tendency for the next few years were built to reveal disproportion of the industry needs and educational system outcomes

Linked Data and Linked Open Data Projects for Libraries, Archives and Museums: Constructing Pathways to Information Discovery and Cultural Heritage Sector Collaboration

This paper examines current Cultural Heritage-based Linked data and linked open data projects developed by Libraries, Archives and Museums (LAMs). The following research questions are explored: R1: Are there similarities and/or differences between libraries, archives and museums in how their linked data and linked open data projects, approaches and strategies are being implemented? R2: What specific linked data and linked open data tools and tactics are being employed, and are there key variations between libraries, archives and museums? The linked data/linked open data landscape has advanced since Tim Berners-Lee (et al.) introduced the concept of the Semantic Web, but challenges for LAMs remain as they work with their collections’ data to create new web-based projects. Fundamental to these efforts is the creation, linking, and publishing of good quality metadata that will allow LAM collections to be discovered, accessed, and disseminated through viable methods. Trends across LAM sectors for linked data and linked open data projects include: global communication and collaborative research, use of wiki-based technologies, and efforts to improve sustainability. Application concepts from the Digital Curation Centre’s Curation Lifecycle Model and Adrian Brown’s Digital Preservation Maturity Model may help guide LAMs toward greater sustainability of linked data and linked open data collections’ projects. Keywords

Range Expansion by Moose into Coastal Temperate Rainforests of British Columbia, Canada

Ranges of species are dynamic and respond to long-term climate change and contemporary effects such as habitat modification. We report here that moose (Alces alces) have recently colonized coastal temperate rainforests of British Columbia, Canada. Contrary to recent publications, field observations of moose and their sign, combined with their occurrence in wolf (Canis lupus) faeces, suggest that moose are now widespread on the coastal mainland and occur on least three islands. Traditional ecological knowledge (information accumulated by aboriginal peoples about their environment) suggests that colonization occurred during the mid 1900s, concomitant with logging of major watersheds that bisect the Coast Mountain Range. Range expansion by moose may have ecological consequences such as alteration of predator– prey dynamics and transmission of disease to native deer (Odocoileus hemionus)