Physicists working in two-dimensional quantum gravity invented a new method of map enumeration based on computation of Gaussian integrals over the space of Hermitian matrices. This paper explains the basic facts of the method and provides an accessible introduction to the subject. Keywords-Maps, Imbedded graphs, Enumerative combinatorics, Matrix integrals, Quantum field theory, String theory.

In this paper, we introduce a method to construct ambient isotopy invariants for smooth imbeddings of closed surfaces into 4-space by using hyperbolic splittings of the imbedded surfaces and an arbitrary given isotopy or regular isotopy invariant of classical knots and links in 3-space. Using this construction, adopting the Kauffman bracket polynomial as an example, we produce some invariants.

A discrete analogue of the holomorphic map z γ is studied. It is given by Schramm's circle pattern with the combinatorics of the square grid. It is shown that the corresponding circle patterns are imbedded and described by special separatrix solutions of discrete Painlevé equations. Global properties of these solutions, as well as of the discrete z γ , are established.

This report discusses a mathematical software package DKLAG5 which consists of a suite of FORTRAN subroutines for the numerical solution of systems of functional di erential equations with state dependent delays. The package implements continuously imbedded Runge{ Kutta methods which are based on C polynomial interpolants. These interpolants are exploited by the software to handle the necessary...

Let Θ be a smooth compact oriented manifold without boundary, imbedded in a euclidean space E, and let γ be a smooth map of Θ into a Riemannian manifold Λ. An unknown state θ ∈ Θ is observed via X = θ + ǫξ where ǫ > 0 is a small parameter and ξ is a white Gaussian noise. For a given smooth prior λ on Θ and smooth estimators g(X) of the map γ we derive a second-order asymptotic expansion for the...

1. Muscle can be prepared in the form of a dry powder in which myosin exists in a state similar to that in intact muscle. As in intact muscle, myosin in powdered muscle is soluble and can be caused to rapidly coagulate. 2. Restoring to powdered muscle the quantity of water previously removed causes coagulation of myosin. The rate of coagulation is considerably slower at 0 degrees than at 20 deg...

The present study is a part of a broader multisited field study on involvement of relatives in Danish psychiatry. The article aims to elucidate which political classifications of normality and mental illness that are displayed in two health political campaigns regarding anti-stigmatization and social inclusion and how such classifications co-constitute the subjectivity of individuals suffering ...

Abstract. Let Θ be a smooth compact oriented manifold without boundary, imbedded in a euclidean space E, and let γ be a smooth map of Θ into a Riemannian manifold Λ. An unknown state θ ∈ Θ is observed via X = θ + ǫξ where ǫ > 0 is a small parameter and ξ is a white Gaussian noise. For a given smooth prior λ on Θ and smooth estimators g(X) of the map γ we have derived a second-order asymptotic e...