A comparative analysis of graphical interaction and logistic regression modelling: self-care and coping with a chronic illness in later life

Quantitative research especially in the social, but also in the biological sciences has been limited by the availability and applicability of analytic techniques that elaborate interactions among behaviours, treatment effects, and mediating variables. This gap has been filled by a newly developed statistical technique, known as graphical interaction modelling. The merit of graphical models for analyzing highly structured data is explored in this paper by an empirical study on coping with a chronic condition as a function of interrelationships between three sets of factors. These include background factors, illness context factors and four self--care practices. Based on a graphical chain model, the direct and indirect dependencies are revealed and discussed in comparison to the results obtained from a simple logistic regression model ignoring possible interaction effects. Both techniques are introduced from a more tutorial point of view instead of going far into technical details

Continuum Derrida Approach to Drift and Diffusivity in Random Media

By means of rather general arguments, based on an approach due to Derrida that makes use of samples of finite size, we analyse the effective diffusivity and drift tensors in certain types of random medium in which the motion of the particles is controlled by molecular diffusion and a local flow field with known statistical properties. The power of the Derrida method is that it uses the equilibrium probability distribution, that exists for each {\em finite} sample, to compute asymptotic behaviour at large times in the {\em infinite} medium. In certain cases, where this equilibrium situation is associated with a vanishing microcurrent, our results demonstrate the equality of the renormalization processes for the effective drift and diffusivity tensors. This establishes, for those cases, a Ward identity previously verified only to two-loop order in perturbation theory in certain models. The technique can be applied also to media in which the diffusivity exhibits spatial fluctuations. We derive a simple relationship between the effective diffusivity in this case and that for an associated gradient drift problem that provides an interesting constraint on previously conjectured results.Comment: 18 pages, Latex, DAMTP-96-8

Aquatic Resources Management of the Colorado River Ecosystem

The Colorado River system has often been referred to as the most regulated river system in the world. The Colorado River Basin serves millions of people through agricultural, energy, municipal and industrial uses, fish and wildlife activities, and recreation. The symposium was conceived and organized to allow researchers, private industry, consultants, water users, regulatory agencies, and concerned citizens the opportunity to express needs, desires, and concerns about the vast resources of the Colorado River. We found that there were a diverse number of problems confronting the individuals who are involved in the management of this important ecosystem. A variety of broad topics have been presented which include: water policy and major diversions; energy impacts; oil shale development--resources and impacts; Lake Mead and the other major reservoirs in the system; the ecology and management of the watershed and the riparian habitat in the system; fisheries; salinity problems; sedimentation; eutrophication; flow depletion; and water augmentation. This timely symposium brought together many individuals, representing a variety of disciplines, to discuss and transfer information appropriate to the needs of the Colorado River Basin. The results of this symposium, which have been compiled herein, are an attempt to examine current and projected effects of water and land management within the Colorado River Basin and to provide a basis for determining what can be done to better manage the resources within the total context of activities affecting the Colorado River Ecosystem

Predicted Limnology of the Proposed Ridges Basin Reservoir

A limnological evaluation was conducted for the offstream Ridges Basin Reservoir proposed by the Bureau of Reclamation in southwest Colorado. The study required the determination of existing water quality in the source river and use of the information to predict the algal standing crop, hypolimnetic oxygen deficity, Secchi disk transparency, and retention of metals in the proposed reservoir. A water quality study was conducted between May 1977 and August 1978. Samplse were collected from the Animas River, which will provide the inflow to the proposed reservoir, and from the La Plata River, which will receive discharge from the reservoir. Samples were analyzed for 49 water quality constituents. The data were used to evaluate the quality of water in both rivers with respect to the proposed Colorado Water Quatiy Standards for raw ater supply, agricultural use, and the protection of the aquatic biota. A phophorus loading model was evaluated and used to predict the summer standing crop of chlorophyl

On the distribution of estimators of diffusion constants for Brownian motion

We discuss the distribution of various estimators for extracting the diffusion constant of single Brownian trajectories obtained by fitting the squared displacement of the trajectory. The analysis of the problem can be framed in terms of quadratic functionals of Brownian motion that correspond to the Euclidean path integral for simple Harmonic oscillators with time dependent frequencies. Explicit analytical results are given for the distribution of the diffusion constant estimator in a number of cases and our results are confirmed by numerical simulations.Comment: 14 pages, 5 figure

Extreme Value Statistics of Eigenvalues of Gaussian Random Matrices

We compute exact asymptotic results for the probability of the occurrence of large deviations of the largest (smallest) eigenvalue of random matrices belonging to the Gaussian orthogonal, unitary and symplectic ensembles. In particular, we show that the probability that all the eigenvalues of an (NxN) random matrix are positive (negative) decreases for large N as ~\exp[-\beta \theta(0) N^2] where the Dyson index \beta characterizes the ensemble and the exponent \theta(0)=(\ln 3)/4=0.274653... is universal. We compute the probability that the eigenvalues lie in the interval [\zeta_1,\zeta_2] which allows us to calculate the joint probability distribution of the minimum and the maximum eigenvalue. As a byproduct, we also obtain exactly the average density of states in Gaussian ensembles whose eigenvalues are restricted to lie in the interval [\zeta_1,\zeta_2], thus generalizing the celebrated Wigner semi-circle law to these restricted ensembles. It is found that the density of states generically exhibits an inverse square-root singularity at the location of the barriers. These results are confirmed by numerical simulations.Comment: 17 pages Revtex, 5 .eps figures include

Overscreening in 1D lattice Coulomb gas model of ionic liquids

Overscreening in the charge distribution of ionic liquids at electrified interfaces is shown to proceed from purely electrostatic and steric interactions in an exactly soluble one dimensional lattice Coulomb gas model. Being not a mean-field effect, our results suggest that even in higher dimensional systems the overscreening could be accounted for by a more accurate treatment of the basic lattice Coulomb gas model, that goes beyond the mean field level of approximation, without any additional interactions.Comment: 4 pages 5 .eps figure

Steady State Behavior of Mechanically Perturbed Spin Glasses and Ferromagnets

A zero temperature dynamics of Ising spin glasses and ferromagnets on random graphs of finite connectivity is considered, like granular media these systems have an extensive entropy of metastable states. We consider the problem of what energy a randomly prepared spin system falls to before becoming stuck in a metastable state. We then introduce a tapping mechanism, analogous to that of real experiments on granular media, this tapping, corresponding to flipping simultaneously any spin with probability $p$, leads to stationary regime with a steady state energy $E(p)$. We explicitly solve this problem for the one dimensional ferromagnet and $\pm J$ spin glass and carry out extensive numerical simulations for spin systems of higher connectivity. The link with the density of metastable states at fixed energy and the idea of Edwards that one may construct a thermodynamics with a flat measure over metastable states is discussed. In addition our simulations on the ferromagnetic systems reveal a novel first order transition, whereas the usual thermodynamic transition on these graphs is second order.Comment: 11 pages, 7 figure

Equilibrium solutions of the shallow water equations

A statistical method for calculating equilibrium solutions of the shallow water equations, a model of essentially 2-d fluid flow with a free surface, is described. The model contains a competing acoustic turbulent {\it direct} energy cascade, and a 2-d turbulent {\it inverse} energy cascade. It is shown, nonetheless that, just as in the corresponding theory of the inviscid Euler equation, the infinite number of conserved quantities constrain the flow sufficiently to produce nontrivial large-scale vortex structures which are solutions to a set of explicitly derived coupled nonlinear partial differential equations.Comment: 4 pages, no figures. Submitted to Physical Review Letter