Autoresonance in a Dissipative System

We study the autoresonant solution of Duffing's equation in the presence of dissipation. This solution is proved to be an attracting set. We evaluate the maximal amplitude of the autoresonant solution and the time of transition from autoresonant growth of the amplitude to the mode of fast oscillations. Analytical results are illustrated by numerical simulations.Comment: 22 pages, 3 figure

Statistical Inference in a Directed Network Model with Covariates

Networks are often characterized by node heterogeneity for which nodes exhibit different degrees of interaction and link homophily for which nodes sharing common features tend to associate with each other. In this paper, we propose a new directed network model to capture the former via node-specific parametrization and the latter by incorporating covariates. In particular, this model quantifies the extent of heterogeneity in terms of outgoingness and incomingness of each node by different parameters, thus allowing the number of heterogeneity parameters to be twice the number of nodes. We study the maximum likelihood estimation of the model and establish the uniform consistency and asymptotic normality of the resulting estimators. Numerical studies demonstrate our theoretical findings and a data analysis confirms the usefulness of our model.Comment: 29 pages. minor revisio

Quasi-linear Stokes phenomenon for the Painlev\'e first equation

Using the Riemann-Hilbert approach, the $\Psi$-function corresponding to the solution of the first Painleve equation, $y_{xx}=6y^2+x$, with the asymptotic behavior $y\sim\pm\sqrt{-x/6}$ as $|x|\to\infty$ is constructed. The exponentially small jump in the dominant solution and the coefficient asymptotics in the power-like expansion to the latter are found.Comment: version accepted for publicatio

Aging Puerto Ricans’ Experiences of Depression Treatment: A New Ethnographic Exploration

PurposeTo examine aging Puerto Ricans’ experiences with and perceptions of depression treatment.Methodology/approachIn-depth analysis of eight exemplary cases from ethnographic interviews with a subsample of 16 aging Puerto Ricans in the Boston area who are part of the Boston Puerto Rican Health Study.FindingsThe results show that respondents were resistant to accepting pharmacological treatment for their depression, and they often characterized antidepressants as “dope.” Moreover, they claimed that in addition to their health problems, social stressors such as financial strain, lack of jobs, housing problems, and social isolation are triggering or contributing to their depression. Because of this, they express reluctance in accepting clinical treatment only, and suggest that broader social issues and other health needs ought to be addressed as part of an effective treatment. For many, pharmacological treatment is acceptable only in the more severe forms of depression.Research limitations/implicationsThese results have important implications for improving the quality of depression treatment and reducing health disparities for mainland Puerto Ricans.Originality/value of chapterEven though recent studies continue to show a high frequency of depression among Puerto Ricans, issues of treatment quality are still understudied and ethnographic accounts are especially lacking. Our study offers an exploratory investigation of this unresolved research issue

Maxwell Model of Traffic Flows

We investigate traffic flows using the kinetic Boltzmann equations with a Maxwell collision integral. This approach allows analytical determination of the transient behavior and the size distributions. The relaxation of the car and cluster velocity distributions towards steady state is characterized by a wide range of velocity dependent relaxation scales, $R^{1/2}<\tau(v)<R$, with $R$ the ratio of the passing and the collision rates. Furthermore, these relaxation time scales decrease with the velocity, with the smallest scale corresponding to the decay of the overall density. The steady state cluster size distribution follows an unusual scaling form $P_m \sim ^{-4} \Psi(m/< m>^2)$. This distribution is primarily algebraic, $P_m\sim m^{-3/2}$, for $m\ll ^2$, and is exponential otherwise.Comment: revtex, 10 page

Kindling the Fire: Fueling Preservice Science Teachers\u27 Interest to Teach in High-Needs Schools

This study applies psychological models of interest and motivation (i.e., a model of interest‐development and self‐determination theory) to the experiences of six preservice science Noyce scholars who participated in a teacher preparation program. The National Science Foundation\u27s Noyce grant aims to incentivize mathematics and science majors to teach in high‐needs school districts. Through this interview study, we sought to understand how Noyce scholars\u27 pre‐existing interests and their experiences in the Noyce program interact to develop individual commitments to teach in high‐needs school settings. Case studies reveal that scholars had no prior experiences in high‐needs schools, abstract ideas about teachers, students, and resources in these contexts, and varying degrees of initial connectedness to teaching in high‐needs school settings. Scholars found that site visits to diverse high‐needs schools (i.e., rural and urban) triggered their interest to teach in similar contexts. Preservice science teachers\u27 emerging interest and level of commitment to teaching in high‐needs schools following the teacher preparation program was dependent upon context‐specific mastery experiences and autonomy within their long‐term clinical field experience. This study offers implications for teacher educators who are recruiting and preparing students to teach in high‐needs school contexts

The abundances of constituents of Titan's atmosphere from the GCMS instrument on the Huygens probe

Saturn's largest moon, Titan, remains an enigma, explored only by remote sensing from Earth, and by the Voyager and Cassini spacecraft. The most puzzling aspects include the origin of the molecular nitrogen and methane in its atmosphere, and the mechanism(s) by which methane is maintained in the face of rapid destruction by photolysis. The Huygens probe, launched from the Cassini spacecraft, has made the first direct observations of the satellite's surface and lower atmosphere. Here we report direct atmospheric measurements from the Gas Chromatograph Mass Spectrometer (GCMS), including altitude profiles of the constituents, isotopic ratios and trace species ( including organic compounds). The primary constituents were confirmed to be nitrogen and methane. Noble gases other than argon were not detected. The argon includes primordial Ar-36, and the radiogenic isotope Ar-40, providing an important constraint on the outgassing history of Titan. Trace organic species, including cyanogen and ethane, were found in surface measurements.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/62703/1/nature04122.pd

A meeting report: cross-cultural comparability of questionnaire measures in large-scale international surveys

The value of cross-country comparisons is at the heart of large-scale international surveys. Yet the validity of such comparisons is often challenged, particularly in the case of latent traits whose estimates are based on self-reported answers to a small number of questionnaire items. Many believe self-reports to be unreliable and not comparable, and indeed, formal statistical procedures very often reject the assumption that the questions are understood and answered in the same way in different countries (measurement invariance). A methodological conference on the comparability of questionnaire scales was hosted by the OECD on 8 and 9 November 2018. This meeting report summarises the discussions held at the conference about measurement invariance testing and instrument design. The report first provides a brief introduction to the measurement models and the accompanying invariance analyses typically used in the industry of large-scale international surveys and points to the main limitations of these current standard approaches. It then presents classical and novel ways to deal with imperfect comparability of measurements when scaling and reporting on continuous traits and on categorical latent variables. It finally discusses the extent to which item design can improve the cross-country comparability of the measured constructs (e.g. by adopting innovative item formats such as anchoring vignettes and situational judgement test items). It concludes with some general considerations for survey design and reporting on invariance analyses and survey results

An Information Theory Approach to Hypothesis Testing in Criminological Research

Background: This research demonstrates how the Akaike information criterion (AIC) can be an alternative to null hypothesis significance testing in selecting best fitting models. It presents an example to illustrate how AIC can be used in this way. Methods: Using data from Milwaukee, Wisconsin, we test models of place-based predictor variables on street robbery and commercial robbery. We build models to balance explanatory power and parsimony. Measures include the presence of different kinds of businesses, together with selected age groups and social disadvantage. Results: Models including place-based measures of land use emerged as the best models among the set of tested models. These were superior to models that included measures of age and socioeconomic status. The best models for commercial and street robbery include three measures of ordinary businesses, liquor stores, and spatial lag. Conclusions: Models based on information theory offer a useful alternative to significance testing when a strong theoretical framework guides the selection of model sets. Theoretically relevant ‘ordinary businesses’ have a greater influence on robbery than socioeconomic variables and most measures of discretionary businesses