Index k saddles and dividing surfaces in phase space, with applications to isomerization dynamics

In this paper we continue our studies of the phase space geometry and dynamics associated with index k saddles (k > 1) of the potential energy surface. Using normal form theory, we give an explicit formula for a "dividing surface" in phase space, i.e. a co-dimension one surface (within the energy shell) through which all trajectories that "cross" the region of the index k saddle must pass. With a generic non-resonance assumption, the normal form provides k (approximate) integrals that describe the saddle dynamics in a neighborhood of the index k saddle. These integrals provide a symbolic description of all trajectories that pass through a neighborhood of the saddle. We give a parametrization of the dividing surface which is used as the basis for a numerical method to sample the dividing surface. Our techniques are applied to isomerization dynamics on a potential energy surface having 4 minima; two symmetry related pairs of minima are connected by low energy index one saddles, with the pairs themselves connected via higher energy index one saddles and an index two saddle at the origin. We compute and sample the dividing surface and show that our approach enables us to distinguish between concerted crossing ("hilltop crossing") isomerizing trajectories and those trajectories that are not concerted crossing (potentially sequentially isomerizing trajectories). We then consider the effect of additional "bath modes" on the dynamics, which is a four degree-of-freedom system. For this system we show that the normal form and dividing surface can be realized and sampled and that, using the approximate integrals of motion and our symbolic description of trajectories, we are able to choose initial conditions corresponding to concerted crossing isomerizing trajectories and (potentially) sequentially isomerizing trajectories.Comment: 49 pages, 12 figure

Of Junk Food and Junk Science

The popular press has triumphantly announced that the cause of the obesity epidemic is “junk food.†After a moment’s reflection, however, it seems likely that the true causal structure of the obesity epidemic can be neither single-equation nor univariate. Therefore, while the hypothesis that “junk food†is the cause of obesity has little a priori plausibility, these articles in the popular press present a testable hypothesis that, in spite of some measurement impossibilities, is tested here. While one can always argue about p values etc., it is safe to say that the results show no evidence to indicate support for a causal link. The second section of the paper explains this result and suggests a rudimentary structural model of obesity that begins to address the issues of specification error, simultaneity, etc., that plague much of the obesity research. This model shows that because of the dynamic nature of weight status, there is no necessary reason to expect to find a statistical relation between a person’s observed weight and the amount he or she is currently eating or exercising. Therefore, studies which regress weight, obesity, or the probability of obesity on eating and exercise patterns have serious specification error. Further development of structural econometric models of obesity may lead to consistent estimates of the partial effects of exogenous variables on obesity levels. We conclude with a discussion of the implications for policy development and industry.obesity, junk food, Granger-causality, Research Methods/ Statistical Methods, Teaching/Communication/Extension/Profession, Q10, Q16,

School District Consolidation And Its Academic And Financial Effects

School district consolidation is a contentious policy debated and implemented in states across the nation. Though consolidation occurred rapidly throughout the 20th century, with the number of districts falling from over 120,000 to approximately 13,000, and several states and communities continue to mandate or incentivize it, little is known about the effects of the policy on student learning or the efficient use of the public’s resources. The purpose of this dissertation is to describe recent school district consolidation in the United States and estimate the effects of one mandatory consolidation policy on student and financial outcomes. Using national and state administrative records and media reports of mergers, I counted the number of consolidations between 2000 and 2015 and examined the characteristics of affected districts. I found that one of every nine districts was part of a consolidation during this period. Most of the mergers melded a very low-enrollment rural district into a much larger neighbor, but some consolidations paired multiple high-enrollment urban districts. Consolidating districts were above-average spenders but generally carried little debt. To examine the efficiency effects of consolidation, I studied student and spending outcomes of a 2004 Arkansas law that established minimum district enrollments. From a differences-in-differences analysis, I found that graduation rates were negatively affected by consolidation while the effect on spending was negligible. Some administrative expense savings, specifically targeted by the legislation, were realized through a reduction in the number of central office personnel, but increases in transportation spending offset half of the small savings. These findings suggest that efficiency improvements should not be expected to automatically follow from school district consolidation. The results of the descriptive analysis, in conjunction with the many mandatory consolidation proposals under consideration in states across the nation, highlight the need for an acceleration of research into the effects of school district consolidation on community resources and student learning and life outcomes

Pennsylvania School Tax Burden

PA Act 35 was signed into law on June 1, 2016. The act amended the state public school code, including the creation of a school funding formula. In this policy brief, Pennsylvania School Tax Burden, Gregory Collins examines how the new formula directs state basic education funding, how it is allocated to local school districts based on need, its ability to pay, and the local school tax effort. Pennsylvania School Tax Burden examines the claim that differences exist in local school tax burdens across Pennsylvania\u27s 500 districts

All tarred with the same Brush

The ongoing situation in Afghanistan highlights the deadly implications that the convergence of security and development can create. The article argues that prior to the current focus on the securitydevelopment nexus, the convergence was first evidenced by the creation of human security. The article reviews the power relationships involved in the processes that have affected understandings of security and development in the process of the creation of human security. By investigating how the securitisation process operates with regards to human security, the ongoing convergence of security and development will be made evident. The implications for humanitarian workers in Afghanistan will be used to highlight that a clearer delineation is needed between security and development, both in discourse and in practice

Multiple Transition States and Roaming in Ion-Molecule Reactions: a Phase Space Perspective

We provide a dynamical interpretation of the recently identified `roaming' mechanism for molecular dissociation reactions in terms of geometrical structures in phase space. These are NHIMs (Normally Hyperbolic Invariant Manifolds) and their stable/unstable manifolds that define transition states for ion-molecule association or dissociation reactions. The associated dividing surfaces rigorously define a roaming region of phase space, in which both reactive and nonreactive trajectories can be trapped for arbitrarily long times.Comment: 20 pages, 6 figure

Recrutamento, emprego, retenção e escassez de professores minoritários

This study examines and compares the recruitment, employment, and retention of minority and nonminority school teachers over the quarter century from the late 1980s to 2013. Our objective is to empirically ground the ongoing debate regarding minority teacher shortages and changes in the minority teaching force. The data we analyze are from the National Center for Education Statistics’ nationally representative Schools and Staffing Survey (SASS) and its longitudinal supplement, the Teacher Follow-up Survey (TFS). Our data analyses document the persistence of a gap between the percentage of minority students and the percentage of minority teachers in the US. But the data also show that this gap is not due to a failure to recruit new minority teachers. In the two decades since the late 1980s, the number of minority teachers almost doubled, outpacing growth in both the number of White teachers and the number of minority students. Minority teachers are also overwhelmingly employed in public schools serving high-poverty, high-minority and urban communities. Hence, the data suggest that widespread efforts over the past several decades to recruit more minority teachers and employ them in disadvantaged schools have been very successful. But, these efforts have also been undermined because minority teachers have significantly higher turnover than White teachers and this is strongly tied to poor working conditions in their schools.El presente estudio analizar y comparar el reclutamiento, el empleo y la retención de los profesores minoritarios y los escolares nonminority a partir de finales de los años 1980 a 2013. Analizamos los datos de las Schools and Staffing Survey (SASS) y su suplemento longitudinal, el Teacher Follow-up Survey (TFS). Nuestros análisis documentan la persistencia de una brecha entre el porcentaje de alumnos y el porcentaje de profesores en los Estados Unidos. Los datos también muestran que esta laguna no se debe a la falta de reclutamiento de nuevos profesores minoritarios. Desde el final de los años 80, el número de profesores minoritarios casi se ha duplicado, superando el número de profesores blancos y el número de otros alumnos. Los profesores minoritarios también son empleados en escuelas públicas que atienden a comunidades de alta pobreza, minorías y urbanas. Así, los datos sugieren que los esfuerzos para reclutar más profesores minoritarios y emplearlos en escuelas carentes tuvieron mucho éxito. Estos esfuerzos también se vieron perjudicados porque tienen una rotación significativamente mayor que los profesores y esta situación está fuertemente ligada a condiciones de trabajo precarias en sus escuelas.O presente estudo analisar e comparar o recrutamento, emprego e retenção de professores minoritários e escolares nonminority partir do final dos anos 1980 a 2013. Analisamos os dados da Schools and Staffing Survey (SASS) e seu suplemento longitudinal, o Teacher Follow-up Survey (TFS). Nossas análises documentam a persistência de uma lacuna entre o percentual de alunos e o percentual de professores nos EUA. Os dados também mostram que essa lacuna não se deve à falta de recrutamento de novos professores minoritários. Desde o final dos anos 80, o número de professores minoritários quase duplicou, superando o número de professores brancos e o número de outros alunos. Professores minoritários também são empregados em escolas públicas que atendem comunidades de alta pobreza, minorias e urbanas. Assim, os dados sugerem que os esforços para recrutar mais professores minoritários e empregá-los em escolas carentes tiveram muito sucesso. Esses esforços também foram prejudicados porque eles têm uma rotatividade significativamente maior do que os professores e essa situação está fortemente ligada a condições de trabalho precárias em suas escolas

Attitudes toward Death Anxiety and Dying Among Respiratory Therapy Students: A Pilot Study

Objective: To evaluate relative and absolute reliability and repeatability in assessing median nerve mobility at the level of the wrist and distal upper arm of the right upper extremity during wrist extension. Methods: Six healthy participants participated in the study. Median nerve mobility was captured three times at both sites using Sonocyte Turbo by two sonologists for a total of 72 video clips (36 for each site and 18 by each sonologist). Longitudinal movement was measured using Motion Tracking Analysis Program (MTAP) by the two assessors who were rehabilitation medicine residents. After one month, the assessors remeasured the longitudinal excursion of the median nerve of the previous video clips. Results: There was moderate agreement between the two sonologists of the median nerve mobility at the level of the distal upper arm and the wrist respectively. There was a moderate to almost perfect agreement between the two assessors’ readings in the mobility of the nerve at level of the distal upper arm and wrist for the first and second readings. Repeatability testing showed that there was variable agreement at the level of the distal upper arm and at the wrist. Conclusion: MTAP using fast template tracking with an adaptive template is a reliable tool that can be employed in the accurate assessment of median nerve mobility at the distal upper arm and wrist