Models of discretized moduli spaces, cohomological field theories, and Gaussian means

We prove combinatorially the explicit relation between genus filtrated $s$-loop means of the Gaussian matrix model and terms of the genus expansion of the Kontsevich--Penner matrix model (KPMM). The latter is the generating function for volumes of discretized (open) moduli spaces $M_{g,s}^{\mathrm{disc}}$ given by $N_{g,s}(P_1,\dots,P_s)$ for $(P_1,\dots,P_s)\in{\mathbb Z}_+^s$. This generating function therefore enjoys the topological recursion, and we prove that it is simultaneously the generating function for ancestor invariants of a cohomological field theory thus enjoying the Givental decomposition. We use another Givental-type decomposition obtained for this model by the second authors in 1995 in terms of special times related to the discretisation of moduli spaces thus representing its asymptotic expansion terms (and therefore those of the Gaussian means) as finite sums over graphs weighted by lower-order monomials in times thus giving another proof of (quasi)polynomiality of the discrete volumes. As an application, we find the coefficients in the first subleading order for ${\mathcal M}_{g,1}$ in two ways: using the refined Harer--Zagier recursion and by exploiting the above Givental-type transformation. We put forward the conjecture that the above graph expansions can be used for probing the reduction structure of the Delgne--Mumford compactification $\overline{\mathcal M}_{g,s}$ of moduli spaces of punctured Riemann surfaces.Comment: 36 pages in LaTex, 6 LaTex figure

Counting lattice points in compactified moduli spaces of curves

We define and count lattice points in the moduli space of stable genus g curves with n labeled points. This extends a construction of the second author for the uncompactified moduli space. The enumeration produces polynomials with top degree coefficients tautological intersection numbers on the compactified moduli space and constant term the orbifold Euler characteristic of the compactified moduli space. We also prove a recursive formula which can be used to effectively calculate these polynomials.Comment: 21 pages, corrected Theorem

Untersuchung der elektrischen und dielektrischen Eigenschaften von Kohlenstoffnanomembrane und ihre Anwendung in Kohlenstoffnanokondensatoren

Penner P. Untersuchung der elektrischen und dielektrischen Eigenschaften von Kohlenstoffnanomembrane und ihre Anwendung in Kohlenstoffnanokondensatoren. Bielefeld: Universität Bielefeld; 2018

Diet Of Peary Caribou, Banks Island, N.W.T.

The results of analyses of rumen contents from 101 Peary caribou (Rangifer tarandus pearyi J. A. Allen 1902) collected on Banks Island are presented. Peary caribou on Banks Island were found to be versatile, broad spectrum grazers specializing on upland monocots, to ingest few lichens, and to exhibit significant seasonal and/or regional differences in diet

Topological recursion for Gaussian means and cohomological field theories

We introduce explicit relations between genus-filtrated s-loop means of the Gaussian matrix model and terms of the genus expansion of the Kontsevich–Penner matrix model (KPMM), which is the generating function for volumes of discretized (open) moduli spaces M_(g,s)^(disc) (discrete volumes). Using these relations, we express Gaussian means in all orders of the genus expansion as polynomials in special times weighted by ancestor invariants of an underlying cohomological field theory. We translate the topological recursion of the Gaussian model into recurrence relations for the coefficients of this expansion, which allows proving that they are integers and positive. We find the coefficients in the first subleading order for M_(g,1) for all g in three ways: using the refined Harer–Zagier recursion, using the Givental-type decomposition of the KPMM, and counting diagrams explicitly

Efficient electron-induced removal of oxalate ions and formation of copper nanoparticles from copper(II) oxalate precursor layers

Rueckriem K, Grotheer S, Vieker H, et al. Efficient electron-induced removal of oxalate ions and formation of copper nanoparticles from copper(II) oxalate precursor layers. BEILSTEIN JOURNAL OF NANOTECHNOLOGY. 2016;7:852-861.Copper(II) oxalate grown on carboxy-terminated self-assembled monolayers (SAM) using a step-by-step approach was used as precursor for the electron-induced synthesis of surface-supported copper nanoparticles. The precursor material was deposited by dipping the surfaces alternately in ethanolic solutions of copper(II) acetate and oxalic acid with intermediate thorough rinsing steps. The deposition of copper(II) oxalate and the efficient electron-induced removal of the oxalate ions was monitored by reflection absorption infrared spectroscopy (RAIRS). Helium ion microscopy (HIM) reveals the formation of spherical nanoparticles with well-defined size and X-ray photoelectron spectroscopy (XPS) confirms their metallic nature. Continued irradiation after depletion of oxalate does not lead to further particle growth giving evidence that nanoparticle formation is primarily controlled by the available amount of precursor

Compassion motivations: Distinguishing submissive compassion from genuine compassion and its association with shame, submissive behavior, depression, anxiety and stress

Abstract Recent research has suggested that being compassionate and helpful to others is linked to well-being. However, people can pursue compassionate motives for different reasons, one of which may be to be liked or valued. Evolutionary theory suggests this form of helping may be related to submissive appeasing behavior and therefore could be negatively associated with well-being. To explore this possibility we developed a new scale called the submissive compassion scale and compared it to other established submissive and shame-based scales, along with measures of depression, anxiety and stress in a group of 192 students. As predicted, a submissive form of compassion (being caring in order to be liked) was associated with submissive behavior, shame-based caring, ego-goals and depression, anxiety, and stress. In contrast, compassionate goals and compassion for others were not. As research on compassion develops, new ways of understanding the complex and mixed motivations that can lie behind compassion are required. The desire to be helpful, kind, and compassionate, when it arises from fears of rejection and desires for acceptance, needs to be explored.N/

Matrix models as solvable glass models

We present a family of solvable models of interacting particles in high dimensionalities without quenched disorder. We show that the models have a glassy regime with aging effects. The interaction is controlled by a parameter $p$. For $p=2$ we obtain matrix models and for $p>2$ `tensor' models. We concentrate on the cases $p=2$ which we study analytically and numerically.Comment: 10 pages + 2 figures, Univ.Roma I, 1038/94, ROM2F/94/2

Painlevé monodromy manifolds, decorated character varieties and cluster algebras

In this paper we introduce the concept of decorated character variety for the Riemann surfaces arising in the theory of the Painlevé differential equations. Since all Painlevé differential equations (apart from the sixth one) exhibit Stokes phenomenon, it is natural to consider Riemann spheres with holes and bordered cusps on such holes. The decorated character is defined as complexification of the bordered cusped Teichm ̈uller spaceintroduced in [8]. We show that the decorated character variety of a Riemann sphere withs holes and n >1 cusps is a Poisson manifold of dimension 3s+ 2n−6 and we explicitly compute the Poisson brackets which are naturally of cluster type. We also show how to obtain the confluence procedure of the Painlevé differential equations in geometric terms