Equilibrium Existence and Approximation for Incomplete Market Models with Substantial Heterogeneity

This paper contains an analysis of incomplete market models with finitely but arbitrarily many heterogeneous agents. We discuss the mathematical foundation for equilibrium conditions which leads to two findings. First, we establish existence of equilibria for small and large risks. Second, we develop a simple but general solution technique which handles many state and choice variables for each agent and thus an extremely high-dimensional state space. The method is based on perturbations around a point at which the solution is known. The novel idea is to exploit the symmetry of the problem to overcome the curse of dimensionality. We use the analysis to demonstrate the impact of heterogeneity on macroeconomic quantities and the pricing of risk. Furthermore, we set our technique apart from the standard method used in the literature

Scattering and absorption of ultracold atoms by nanotubes

We investigate theoretically how cold atoms, including Bose-Einstein condensates, are scattered from, or absorbed by nanotubes with a view to analysing recent experiments. In particular we consider the role of potential strength, quantum reflection, atomic interactions and tube vibrations on atom loss rates. Lifshitz theory calculations deliver a significantly stronger scattering potential than that found in experiment and we discuss possible reasons for this. We find that the scattering potential for dielectric tubes can be calculated to a good approximation using a modified pairwise summation approach, which is efficient and easily extendable to arbitrary geometries. Quantum reflection of atoms from a nanotube may become a significant factor at low temperatures, especially for non-metallic tubes. Interatomic interactions are shown to increase the rate at which atoms are lost to the nanotube and lead to non-trivial dynamics. Thermal nanotube vibrations do not significantly increase loss rates or reduce condensate fractions, but lower frequency oscillations can dramatically heat the cloud.Comment: 7 pages, 4 figure

Detecting periodicity in experimental data using linear modeling techniques

Fourier spectral estimates and, to a lesser extent, the autocorrelation function are the primary tools to detect periodicities in experimental data in the physical and biological sciences. We propose a new method which is more reliable than traditional techniques, and is able to make clear identification of periodic behavior when traditional techniques do not. This technique is based on an information theoretic reduction of linear (autoregressive) models so that only the essential features of an autoregressive model are retained. These models we call reduced autoregressive models (RARM). The essential features of reduced autoregressive models include any periodicity present in the data. We provide theoretical and numerical evidence from both experimental and artificial data, to demonstrate that this technique will reliably detect periodicities if and only if they are present in the data. There are strong information theoretic arguments to support the statement that RARM detects periodicities if they are present. Surrogate data techniques are used to ensure the converse. Furthermore, our calculations demonstrate that RARM is more robust, more accurate, and more sensitive, than traditional spectral techniques.Comment: 10 pages (revtex) and 6 figures. To appear in Phys Rev E. Modified styl

Difference score correlations in relationship research: A conceptual primer

The practice of computing correlations between “difference” or “discrepancy” scores and an outcome variable is common in many areas of social science. Relationship researchers most commonly use difference scores to index the (dis)similarity of members of two-person relationships. Using an intuitive, graphical approach—and avoiding formulas and pointing fingers—we illustrate problems with using difference score correlations in relationship research, suggest ways to ensure that difference score correlations are maximally informative, and briefly review alternatives to difference score correlations in studying similarity, accuracy, and related constructs.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/73008/1/j.1475-6811.1999.tb00206.x.pd

Group Formation Among Peer-to-Peer Agents: Learning Group Characteristics

This paper examines the decentralized formation of groups within a peer-to-peer multi-agent system. More specifically, it frames group formation as a clustering problem, and examines how to determine cluster characteristics such as area and density in the absence of information about the entire data set, such as the number of points, the number of clusters, or the maximum distance between points, that are available to centralized clustering algorithms. We develop a method in which agents individually search for other agents with similar characteristics in a peer-to-peer manner. These agents group into small centrally controlled clusters which learn cluster parameters by examining and improving their internal composition over time. We show through simulation that this method allows us to find clusters of a wide variety of sizes without adjusting agent parameters

Analytic Treatment of Positronium Spin Splittings in Light-Front QED

We study the QED bound-state problem in a light-front hamiltonian approach. Starting with a bare cutoff QED Hamiltonian, $H_{_{B}}$, with matrix elements between free states of drastically different energies removed, we perform a similarity transformation that removes the matrix elements between free states with energy differences between the bare cutoff, $\Lambda$, and effective cutoff, \lam (\lam < \Lam). This generates effective interactions in the renormalized Hamiltonian, $H_{_{R}}$. These effective interactions are derived to order $\alpha$ in this work, with $\alpha \ll 1$. $H_{_{R}}$ is renormalized by requiring it to satisfy coupling coherence. A nonrelativistic limit of the theory is taken, and the resulting Hamiltonian is studied using bound-state perturbation theory (BSPT). The effective cutoff, \lam^2, is fixed, and the limit, 0 \longleftarrow m^2 \alpha^2\ll \lam^2 \ll m^2 \alpha \longrightarrow \infty, is taken. This upper bound on \lam^2 places the effects of low-energy (energy transfer below \lam) emission in the effective interactions in the $| e {\overline e} >$ sector. This lower bound on \lam^2 insures that the nonperturbative scale of interest is not removed by the similarity transformation. As an explicit example of the general formalism introduced, we show that the Hamiltonian renormalized to $O(\alpha)$ reproduces the exact spectrum of spin splittings, with degeneracies dictated by rotational symmetry, for the ground state through $O(\alpha^4)$. The entire calculation is performed analytically, and gives the well known singlet-triplet ground state spin splitting of positronium, $7/6 \alpha^2 Ryd$. We discuss remaining corrections other than the spin splittings and how they can be treated in calculating the spectrum with higher precision.Comment: 46 pages, latex, 3 Postscript figures included, section on remaining corrections added, title changed, error in older version corrected, cutoff placed in a windo

The Effects Of Students Predispositions Toward Communication, Learning Styles, And Sex On Academic Achievement

Females are more apprehensive when talking in class, but more nonverbally immediate, and prefer a collaborative learning style.  Males prefer independent and avoidant learning styles, and report learning less than females

Influence of composite particle formation on the performance and economics of grit removal

Grit is routinely removed at the headworks of municipal wastewater treatment works to limit its onerous impact on downstream processes. Grit separation technologies are normally based on sedimentation of a homogeneous material (usually sand). However, in practice inorganic grit particles are likely to be combined with organic matter, such as fats oils and grease (FOG), producing a composite particle whose settling properties vary with the inorganic/organic content. A study of the impact of particle composition on its sedimentation has been conducted encompassing theoretical description (for particle settling in transitional flow), practical measurement and economic analysis. Practical measurement included sedimentation tests of homogeneous and composite particles along with characterisation of accumulated granular material sampled from actual municipal wastewater treatment works. The economic assessment was based on data from full-scale installations in the UK and US pertaining to remedial measures undertaken as a result of grit impacts, primarily accumulation in vessels and channels and damage of mechanical equipment through abrasion. Practical tests revealed coating of the sand grains with a FOG analogue (candlewax) to generate composite particles containing 45% wax by weight. The coated particles were then 30% less dense, 22% larger and 14% less settleable, on average, than the uncoated particles. Samples of accumulated grit taken from anaerobic digesters and aeration lanes from a full-scale plant indicated a FOG content (43%) similar to that of the waxed particles in the bench-scale tests, thus leading to a similar grain retardation of 14% assuming the FOG to be entirely associated with the grit. An assessment of the impact of the consequential breakthrough of grit particles due to buoyancy generated by composite particle formation indicated a $1.1 increase in operating costs per megalitre (ML) wastewater

Sum Rules for Multi-Photon Spectroscopy of Ions in Finite Symmetry

Models describing one- and two-photon transitions for ions in crystalline environments are unified and extended to the case of parity-allowed and parity- forbidden p-photon transitions. The number of independent parameters for characterizing the polarization dependence is shown to depend on an ensemble of properties and rules which combine symmetry considerations and physical models.Comment: 16 pages, Tex fil