Return times, recurrence densities and entropy for actions of some discrete amenable groups

Results of Wyner and Ziv and of Ornstein and Weiss show that if one observes the first k outputs of a finite-valued ergodic process, then the waiting time until this block appears again is almost surely asymptotic to $2^{hk}$, where $h$ is the entropy of the process. We examine this phenomenon when the allowed return times are restricted to some subset of times, and generalize the results to processes parameterized by other discrete amenable groups. We also obtain a uniform density version of the waiting time results: For a process on $s$ symbols, within a given realization, the density of the initial $k$-block within larger $n$-blocks approaches $2^{-hk}$, uniformly in $n>s^k$, as $k$ tends to infinity. Again, similar results hold for processes with other indexing groups.Comment: To appear in Journal d'Analyse Mathematiqu

Towards a unification of HRT and SCOZA

The Hierarchical Reference Theory (HRT) and the Self-Consistent Ornstein-Zernike Approximation (SCOZA) are two liquid state theories that both furnish a largely satisfactory description of the critical region as well as phase separation and the equation of state in general. Furthermore, there are a number of similarities that suggest the possibility of a unification of both theories. As a first step towards this goal we consider the problem of combining the lowest order gamma expansion result for the incorporation of a Fourier component of the interaction with the requirement of consistency between internal and free energies, leaving aside the compressibility relation. For simplicity we restrict ourselves to a simplified lattice gas that is expected to display the same qualitative behavior as more elaborate models. It turns out that the analytically tractable Mean Spherical Approximation is a solution to this problem, as are several of its generalizations. Analysis of the characteristic equations shows the potential for a practical scheme and yields necessary conditions any closure to the Ornstein Zernike relation must fulfill for the consistency problem to be well posed and to have a unique differentiable solution. These criteria are expected to remain valid for more general discrete and continuous systems, even if consistency with the compressibility route is also enforced where possible explicit solutions will require numerical evaluations.Comment: Minor changes in accordance with referee comment

Market forces and airline safety: an empirical reevaluation

The recent publicity with regard to commercial airline accidents and near accidents has sparked new debate over the issue of safety in the industry under deregulation, with the main issue being the unregulated market\u27s ability to impose significant penalties for poor safety attitudes. This study shows that although there are large movements in the price of airline stocks subsequent to accidents, the market imposed costs do not provide a direct motivation for enhanced safety performance. Instead, the market\u27s reaction to airline accidents is based on the nature of airline stocks as short term investment tools. It is necessary, therefore, to continue to carefully evaluate the role of government in the promotion of airline safety in a deregulated environment. One cannot assert, without qualification, that free market forces, in and of themselves, will provide individual firms with the impetus to provide the socially optimal level of safety performance

Improving the Teaching Evaluation Process: A Report from the Classroom

[Excerpt] Students’ evaluations of instructors’ teaching may be one of many longstanding approaches to improving instruction which has lost its utility as a diagnostic tool and has become a quantitative device used to determine merit pay and tenure. Comments such as “Instructor has great legs” or “You should lose weight” or “Buy a new tie,” while occasionally amusing, suggest that the students themselves take the process of feedback lightly. Instructors who view student responses as critical to their future salary and promotion opportunities may take a tactical stance and pander to student wishes: if the material is too complex, make it simpler; if the assignments are too long, make them shorter; if the grade distribution is too discriminating, adjust it. Perhaps more distressing is the good teacher who will not tinker or innovate for fear that changing the course will result in lower student evaluations. Across the country the process of evaluating instruction has moved from an activity centered on providing helpful feedback and suggestions for improvement into a means of making comparisons across faculty in an effort to link salary and promotion decisions to seemingly objective data

The Socialization of Children’s Memory: Linking Maternal Conversational Style to the Development of Children’s Autobiographical and Deliberate Memory Skills

Data from a large-scale, longitudinal research study with an ethnically and socioeconomically diverse sample were utilized to explore linkages between maternal elaborative conversational style and the development of children’s autobiographical and deliberate memory. Assessments were made when the children were 3, 5, and 6 years of age, and the results reveal concurrent and longitudinal linkages between maternal conversational style in a mother-child reminiscing task and children’s autobiographical memory performance. Maternal conversational style while reminiscing was also significantly related to children’s strategic behaviors and recall in two deliberate memory tasks, both concurrently and longitudinally. Results from this examination replicate and extend what is known about the linkages between maternal conversational style, children’s abilities to talk about previous experiences, and children’s deliberate memory skills as they transition from the preschool to early elementary school years

Thermodynamic and dynamic anomalies for a three dimensional isotropic core-softened potential

Using molecular dynamics simulations and integral equations (Rogers-Young, Percus-Yevick and hypernetted chain closures) we investigate the thermodynamic of particles interacting with continuous core-softened intermolecular potential. Dynamic properties are also analyzed by the simulations. We show that, for a chosen shape of the potential, the density, at constant pressure, has a maximum for a certain temperature. The line of temperatures of maximum density (TMD) was determined in the pressure-temperature phase diagram. Similarly the diffusion constant at a constant temperature, $D$, has a maximum at a density $\rho_{max}$ and a minimum at a density $\rho_{min}<\rho_{max}$. In the pressure-temperature phase-diagram the line of extrema in diffusivity is outside of TMD line. Although in this interparticle potential lacks directionality, this is the same behavior observed in SPC/E water.Comment: 16 page

Classification of minimal actions of a compact Kac algebra with amenable dual

We show the uniqueness of minimal actions of a compact Kac algebra with amenable dual on the AFD factor of type II$_1$. This particularly implies the uniqueness of minimal actions of a compact group. Our main tools are a Rohlin type theorem, the 2-cohomology vanishing theorem, and the Evans-Kishimoto type intertwining argument.Comment: 68 pages, Introduction rewritten; minor correction

Caregiving over time: The impact of the behavioral and psychological symptoms of dementia on caregiver depression

This dissertation was motivated by the growth in the number of elderly with dementia in the United States and worldwide, and the consequent need to assist caregivers who face the chronic stress and consequent negative outcomes of caring for dementia patients for increasingly longer periods of time. While behavioral and psychological symptoms of dementia (BPSD) are routinely cited as important predictors of negative caregiving outcomes, they consist of a wide variety of patient behaviors (e.g., depression, physical aggression and paranoid delusions). This dissertation aimed to further elucidate the BPSD-caregiver relationship by determining if and why individual components of BPSD impacted caregiver depression, how these relationships change over time, and how the timing of behaviors across the disease course affect the caregiver. First, via a systematic literature review we found that despite the significant amount of research conducted examining BPSD and caregiving, the literature focused on the aggregate effect of symptoms rather than on the effect of individual symptoms. Existing studies categorized BPSD based on how they clinically manifest in the patient, rather than from the perspective of how they may differentially impact the caregiver. Second, we tested the differential impact of four symptom clusters derived based on their likely impact on the caregiver (accusatory/aggressive symptoms, non-threatening psychotic symptoms, depressive symptoms, and difficult behaviors) on caregiver depression. All clusters exerted similar effect sizes on caregiver depression, with patient depressive symptoms exerting the strongest and most consistently stable relationship with caregiver depression. The patient depression-caregiver depression relationship was mediated by both perceived burden to caregivers and impact of symptoms on the patient. Finally, we did not find evidence that the presence of individual BPSD early in the disease course impacted subsequent caregiver depressive symptoms. When examining change patterns over time, we found that most caregivers had stable trajectories of depressive symptoms, with a smaller subset showing more evidence for wear-and-tear over time. Given that there may be a differential effect of individual symptoms on caregivers, research in this field should continue to study the effects of individual BPSD symptoms rather than the cumulative effects of a range of behaviors and should also consider how symptoms may negatively impact caregivers by evoking empathy in addition to increasing burden for the patient. Future work should continue to utilize a longitudinal perspective on caregiving to better characterize the relationship between individual BPSD and caregiver outcomes and to understand varied outcome trajectories. The continued focus on understanding how, why and when BPSD are most detrimental to caregivers can help target and improve patient treatment and caregiver intervention efforts

Orbit equivalence rigidity for ergodic actions of the mapping class group

We establish orbit equivalence rigidity for any ergodic, essentially free and measure-preserving action on a standard Borel space with a finite positive measure of the mapping class group for a compact orientable surface with higher complexity. We prove similar rigidity results for a finite direct product of mapping class groups as well.Comment: 11 pages, title changed, a part of contents remove

Liquid Transport Due to Light Scattering

Using experiments and theory, we show that light scattering by inhomogeneities in the index of refraction of a fluid can drive a large-scale flow. The experiment uses a near-critical, phase-separated liquid, which experiences large fluctuations in its index of refraction. A laser beam traversing the liquid produces a large-scale deformation of the interface and can cause a liquid jet to form. We demonstrate that the deformation is produced by a scattering-induced flow by obtaining good agreements between the measured deformations and those calculated assuming this mechanism.Comment: 4 pages, 5 figures, submitted to Physical Review Letters v2: Edited based on comments from referee