The Specification and Influence of Asset Markets

This paper is a chapter in the forthcoming Handbook of International Economics. It surveys the literature on the specification of models of asset markets and the implications of differences in specification for the macroeconomic adjustment process. Builders of portfolio balance models have generally employed "postulated" asset demand functions, rather than deriving these directly from micro foundations. The first major sec-tion of the paper lays out a postulated general specification of asset markets and summarizes the fundamental short-run results of portfolio balance models using a very basic specification of asset markets. Then,rudimentary specifications of a balance of payments equation and goods market equilibrium conditions are supplied, so that the dynamic distribution effects of the trade account under static and rational expectations with both fixed goods prices and flexible goods prices can be analyzed.The second major section of the paper surveys and analyzes microfoundation models of asset demands using stochastic calculus. The microeconomic theory of asset demands implies some but not all of the properties of the basic specification of postulated asset demands at the macrolevel. Since the conclusions of macroeconomic analysis depend crucially on the form of asset demand functions, it is important to continue to explore the implications of micro foundations for macro specification.

Spectral Action for Robertson-Walker metrics

We use the Euler-Maclaurin formula and the Feynman-Kac formula to extend our previous method of computation of the spectral action based on the Poisson summation formula. We show how to compute directly the spectral action for the general case of Robertson-Walker metrics. We check the terms of the expansion up to a_6 against the known universal formulas of Gilkey and compute the expansion up to a_{10} using our direct method

Further functional determinants

Functional determinants for the scalar Laplacian on spherical caps and slices, flat balls, shells and generalised cylinders are evaluated in two, three and four dimensions using conformal techniques. Both Dirichlet and Robin boundary conditions are allowed for. Some effects of non-smooth boundaries are discussed; in particular the 3-hemiball and the 3-hemishell are considered. The edge and vertex contributions to the $C_{3/2}$ coefficient are examined.Comment: 25 p,JyTex,5 figs. on request

Asymptotics of relative heat traces and determinants on open surfaces of finite area

The goal of this paper is to prove that on surfaces with asymptotically cusp ends the relative determinant of pairs of Laplace operators is well defined. We consider a surface with cusps (M,g) and a metric h on the surface that is a conformal transformation of the initial metric g. We prove the existence of the relative determinant of the pair $(\Delta_{h},\Delta_{g})$ under suitable conditions on the conformal factor. The core of the paper is the proof of the existence of an asymptotic expansion of the relative heat trace for small times. We find the decay of the conformal factor at infinity for which this asymptotic expansion exists and the relative determinant is defined. Following the paper by B. Osgood, R. Phillips and P. Sarnak about extremal of determinants on compact surfaces, we prove Polyakov's formula for the relative determinant and discuss the extremal problem inside a conformal class. We discuss necessary conditions for the existence of a maximizer.Comment: This is the final version of the article before it gets published. 51 page

Wood Creek Tidal Marsh Enhancement Project Benthic Macroinvertebrate Monitoring Report 2019

The focus of this report was to monitor benthic macroinvertebrate communities on the Freshwater Farms Reserve, which underwent two phases of restoration as part of the Wood Creek Tidal Marsh Enhancement Project in 2009-2010 and 2016-2018. Objectives for the restoration activities were to increase winter rearing refugia habitat for several threatened/endangered fish species such as the tidewater goby (Eucyclogobius newberryi), Coho salmon (Oncorhynchus kisutch) and steelhead trout (Oncorhynchus mykiss). The goals of this project were to (1) sample and identify BMIs along a salinity gradient in Wood Creek; (2) assess water quality; and (3) report general trajectory of community composition over time. Results show that the abundance of benthic macroinvertebrates increased dramatically in Wood Creek in 2019 for all sampled sites when compared to previous years of monitoring data. Three taxa accounted for over 99% of the overall composition at each of the sample sites. Increased abundance of benthic macroinvertebrates may provide additional nutritional support for fish present in Wood Creek and Freshwater Creek. Overall, Freshwater Farms Reserve’s post-restoration ecological trajectory seems to be improving in relation to the goals of supporting fish refugia for threatened/endangered species

Thermodynamics, Euclidean Gravity and Kaluza-Klein Reduction

The aim of this paper is to find out a correspondence between one-loop effective action $W_E$ defined by means of path integral in Euclidean gravity and the free energy $F$ obtained by summation over the modes. The analysis is given for quantum fields on stationary space-times of a general form. For such problems a convenient procedure of a "Wick rotation" from Euclidean to Lorentzian theory becomes quite non-trivial implying transition from one real section of a complexified space-time manifold to another. We formulate conditions under which $F$ and $W_E$ can be connected and establish an explicit relation of these functionals. Our results are based on the Kaluza-Klein method which enables one to reduce the problem on a stationary space-time to equivalent problem on a static space-time in the presence of a gauge connection. As a by-product, we discover relation between the asymptotic heat-kernel coefficients of elliptic operators on a $D$ dimensional stationary space-times and the heat-kernel coefficients of a $D-1$ dimensional elliptic operators with an Abelian gauge connection.Comment: latex file, 22 page

Boundary dynamics and multiple reflection expansion for Robin boundary conditions

In the presence of a boundary interaction, Neumann boundary conditions should be modified to contain a function S of the boundary fields: (\nabla_N +S)\phi =0. Information on quantum boundary dynamics is then encoded in the $S$-dependent part of the effective action. In the present paper we extend the multiple reflection expansion method to the Robin boundary conditions mentioned above, and calculate the heat kernel and the effective action (i) for constant S, (ii) to the order S^2 with an arbitrary number of tangential derivatives. Some applications to symmetry breaking effects, tachyon condensation and brane world are briefly discussed.Comment: latex, 22 pages, no figure

Noncommutative geometry and lower dimensional volumes in Riemannian geometry

In this paper we explain how to define "lower dimensional'' volumes of any compact Riemannian manifold as the integrals of local Riemannian invariants. For instance we give sense to the area and the length of such a manifold in any dimension. Our reasoning is motivated by an idea of Connes and involves in an essential way noncommutative geometry and the analysis of Dirac operators on spin manifolds. However, the ultimate definitions of the lower dimensional volumes don't involve noncommutative geometry or spin structures at all.Comment: 12 page