Enumeration of chord diagrams on many intervals and their non-orientable analogs

Two types of connected chord diagrams with chord endpoints lying in a collection of ordered and oriented real segments are considered here: the real segments may contain additional bivalent vertices in one model but not in the other. In the former case, we record in a generating function the number of fatgraph boundary cycles containing a fixed number of bivalent vertices while in the latter, we instead record the number of boundary cycles of each fixed length. Second order, non-linear, algebraic partial differential equations are derived which are satisfied by these generating functions in each case giving efficient enumerative schemes. Moreover, these generating functions provide multi-parameter families of solutions to the KP hierarchy. For each model, there is furthermore a non-orientable analog, and each such model likewise has its own associated differential equation. The enumerative problems we solve are interpreted in terms of certain polygon gluings. As specific applications, we discuss models of several interacting RNA molecules. We also study a matrix integral which computes numbers of chord diagrams in both orientable and non-orientable cases in the model with bivalent vertices, and the large-N limit is computed using techniques of free probability.Comment: 23 pages, 7 figures; revised and extended versio

Kleinian groups and the complex of curves

We examine the internal geometry of a Kleinian surface group and its relations to the asymptotic geometry of its ends, using the combinatorial structure of the complex of curves on the surface. Our main results give necessary conditions for the Kleinian group to have `bounded geometry' (lower bounds on injectivity radius) in terms of a sequence of coefficients (subsurface projections) computed using the ending invariants of the group and the complex of curves. These results are directly analogous to those obtained in the case of punctured-torus surface groups. In that setting the ending invariants are points in the closed unit disk and the coefficients are closely related to classical continued-fraction coefficients. The estimates obtained play an essential role in the solution of Thurston's ending lamination conjecture in that case.Comment: 32 pages. Published copy, also available at http://www.maths.warwick.ac.uk/gt/GTVol4/paper3.abs.htm

Loop operators and S-duality from curves on Riemann surfaces

We study Wilson-'t Hooft loop operators in a class of N=2 superconformal field theories recently introduced by Gaiotto. In the case that the gauge group is a product of SU(2) groups, we classify all possible loop operators in terms of their electric and magnetic charges subject to the Dirac quantization condition. We then show that this precisely matches Dehn's classification of homotopy classes of non-self-intersecting curves on an associated Riemann surface--the same surface which characterizes the gauge theory. Our analysis provides an explicit prediction for the action of S-duality on loop operators in these theories which we check against the known duality transformation in several examples.Comment: 41 page

Perturbative Chern-Simons Theory From The Penner Model

We show explicitly that the perturbative SU(N) Chern-Simons theory arises naturally from two Penner models, with opposite coupling constants. As a result computations in the perturbative Chern-Simons theory are carried out using the Penner model, and it turns out to be simpler and transparent. It is also shown that the connected correlators of the puncture operator in the Penner model, are related to the connected correlators of the operator that gives the Wilson loop operator in the conjugacy class.Comment: 7 Pages, Published Versio

Crustal failure during binary inspiral

We present the first fully relativistic calculations of the crustal strain induced in a neutron star by a binary companion at the late stages of inspiral, employing realistic equations of state for the fluid core and the solid crust. We show that while the deep crust is likely to fail only shortly before coalescence, there is a large variation in elastic strain, with the outermost layers failing relatively early on in the inspiral. We discuss the significance of the results for both electromagnetic and gravitational-wave astronomy.Comment: 5 pages, 3 eps figure

From Matrices to Strings and Back

We discuss an explicit construction of a string dual for the Gaussian matrix model. Starting from the matrix model and employing Strebel differential techniques we deduce hints about the structure of the dual string. Next, following these hints a worldheet theory is constructed. The correlators in this string theory are assumed to localize on a finite set of points in the moduli space of Riemann surfaces. To each such point one associates a Feynman diagram contributing to the correlator in the dual matrix model, and thus recasts the worldsheet expression as a sum over Feynman diagrams.Comment: 27 pages, 3 figure

Properties of Bulk In-Pt Intermetallic Compounds in Methanol Steam Reforming

Catalytic properties of In-Pt intermetallic compounds in methanol steam reforming have been investigated. In2Pt has been proven to be mandatory for a high activity and selectivity. Only small amounts of In2O3 have been found to be beneficial for catalytic performance. Heterogeneous catalysts are often complex materials containing different compounds. While this can lead to highly beneficial interfaces, it is difficult to identify the role of single components. In methanol steam reforming (MSR), the interplay between intermetallic compounds, supporting oxides and redox reactions leads to highly active and CO2-selective materials. Herein, the intrinsic catalytic properties of unsupported In3Pt2, In2Pt, and In7Pt3 as model systems for Pt/In2O3-based catalytic materials in MSR are addressed. In2Pt was identified as the essential compound responsible for the reported excellent CO2-selectivity of 99.5 % at 300 °C in supported systems, showing a CO2-selectivity above 99 % even at 400 °C. Additionally, the partial oxidation of In7Pt3 revealed that too much In2O3 is detrimental for the catalytic properties. The study highlights the crucial role of intermetallic In−Pt compounds in Pt/In2O3 materials with excellent CO2-selectivity

Language of Existential Experience of a Person in the Digital Age

The article presents the problem of the existential feasible in the digital. The relevance of the problem is gaining weight in the so-called digital age, when the objectives in the human world are represented by technology and the technological. The following questions from the 20th century are becoming relevant again: the relationship between a person and technology; the future of a person and technology; the human / existential in the context of multiplying technology. In the 21st century, the digital can be seen as a cluster of external objectivity in the everyday life. The article raises questions about how the talk about the existential dimension in the digital age is possible; whether there are grounds of speaking about the dynamics of human existential conditions in the process of intensification of everything that is called digital today; and if yes, then in what format and with what language. Given these questions, we understand the digital as a special topos of human existence, a space of manifestation, “highlighting” the existential, which can be comprehended and conceptualized. In the digital age the human being remains, same as his/her existentials. In the markup of the digital, both the individual and the existentials are subject to serious transformation. This is illustrated by digital subjects, digital twins, digital traces/prints, which have an effect on the individual and his/her existential filling. From this we deduce the idea of digital anthropology as a new research field

Reining in Punitive Discipline: Recent Trends in Exclusionary School Discipline Disparities

Concerns around disparities in suspensions and expulsions from schools in the United States have resulted in a concerted effort to reduce the use of exclusionary school discipline. In this article, the authors describe trends in the use of exclusionary discipline in Indiana and Oregon, two U.S. states with different school discipline policy climates. The findings point to a substantial decline in the use of suspensions and other forms of exclusionary discipline in both states. The authors further find that racial and socioeconomic disparities have recently narrowed in both states, though Black students and students who were identified as economically disadvantaged remain likely to be disproportionately exposed to exclusionary discipline. These trends, and their timing, illustrate the broad-based change in disciplinary norms that has occurred in the U.S. over the past decade

Tidal deformations of neutron stars: The role of stratification and elasticity

We discuss the response of neutron stars to the tidal interaction in a compact binary system, as encoded in the Love number associated with the induced deformation. This problem is of interest for gravitational-wave astronomy as there may be a detectable imprint on the signal from the late stages of binary coalescence. Previous work has focussed on simple barotropic neutron star models, providing an understanding of the role of the stellar compactness and overall density profile. We add realism to the discussion by developing the framework required to model stars with varying composition and an elastic crust. These effects are not expected to be significant for the next generation of detectors but it is nevertheless useful to be able to quantify them. Our results show that (perhaps surprisingly) internal stratification has no impact whatsoever on the Love number. We also show that crust elasticity provides a (predictably) small correction to existing models.Comment: 16 pages, RevTeX, 3 eps figure