A Lower Bound on the Mixing Time of Uniformly Ergodic Markov Chains in Terms of the Spectral Radius

We give a bound on the mixing time of a uniformly ergodic, reversible Markov chain in terms of the spectral radius of the transition operator. This bound has been established previously in finite state spaces, and is widely believed to hold in general state spaces, but a proof has not been provided to our knowledge

Elementary Teachers’ Ideologies On The Experience Of A Mixed-Race Student

With bi/multi-racial students existing within a nebulous racial categorization that has been historically defined to support an economic agenda, creating a positive self-identity for students in this group can be challenging. This article examined those challenges by exploring the reflections of elementary level teachers’ classroom practices and perceptions of the collective elementary educational experience of one bi-racial student in a southeastern U.S. public school

The Secondary School Writing Center: A Place to Build Confident, Competent Writers

The three of us led an International Writing Centers Association-sponsored allday workshop on secondary school writing centers at the NCTE Convention. Writing centers at all levels follow the theoretical background of Bruffee, Murray, Elbow, and North, to name a few. They are not remedial facilities, as some schools would like them to be, or ESL facilities to improve basic writing in English. No, a secondary school writing center is primarily a place where we work with all students, regardless of their innate talent, to build their confidence and competency as writers. Whether we are talking about students who need to fine-tune excellent papers or students who need to discover what they really want to say, a writing center can be a safe harbor within the sometimes stormy seas of the school day. We can think of no better way to reform writing instruction.University Writing Cente

Conditions for rapid mixing of parallel and simulated tempering on multimodal distributions

We give conditions under which a Markov chain constructed via parallel or simulated tempering is guaranteed to be rapidly mixing, which are applicable to a wide range of multimodal distributions arising in Bayesian statistical inference and statistical mechanics. We provide lower bounds on the spectral gaps of parallel and simulated tempering. These bounds imply a single set of sufficient conditions for rapid mixing of both techniques. A direct consequence of our results is rapid mixing of parallel and simulated tempering for several normal mixture models, and for the mean-field Ising model.Comment: Published in at http://dx.doi.org/10.1214/08-AAP555 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

The Habitable Zone Gallery

The Habitable Zone Gallery (www.hzgallery.org) is a new service to the exoplanet community which provides Habitable Zone (HZ) information for each of the exoplanetary systems with known planetary orbital parameters. The service includes a sortable table with information on the percentage of orbital phase spent within the HZ, planetary effective temperatures, and other basic planetary properties. In addition to the table, we also plot the period and eccentricity of the planets with respect to their time spent in the HZ. The service includes a gallery of known systems which plot the orbits and the location of the HZ with respect to those orbits. Also provided are animations which aid in orbit visualization and provide the changing effective temperature for those planets in eccentric orbits. Here we describe the science motivation, the under-lying calculations, and the structure of the web site.Comment: 6 pages, 3 figures, accepted for publication in PAS

Confirmatory factor analysis and invariance testing between Blacks and Whites of the Multidimensional Health Locus of Control scale.

The factor structure of the Multidimensional Health Locus of Control scale remains in question. Additionally, research on health belief differences between Black and White respondents suggests that the Multidimensional Health Locus of Control scale may not be invariant. We reviewed the literature regarding the latent variable structure of the Multidimensional Health Locus of Control scale, used confirmatory factor analysis to confirm the three-factor structure of the Multidimensional Health Locus of Control, and analyzed between-group differences in the Multidimensional Health Locus of Control structure and means across Black and White respondents. Our results indicate differences in means and structure, indicating more research is needed to inform decisions regarding whether and how to deploy the Multidimensional Health Locus of Control appropriately

Expanding Opportunity Structures: Parental Investments in Education, Migration, and Extrinsic Risk Reduction among Indo-Fijians

Parental investment strategies are contingent on parental capacities and ecology. Parental embodied capital may be important in aspiration construction and investments in children’s human capital, which is especially important in urban environments where skills are directly tied to wage income. For Indo-Fijians, rural ecology strongly limits opportunities. Here this limitation is conceptualized as extrinsic risk and immune to reduction through enhanced parental investment. Urban migration is interpreted as a risk reduction strategy, given an expanded urban opportunity structure (lower extrinsic risk). Qualitative and quantitative data from 678 Indo-Fijian children suggest that, contingent on parental capacities, parents migrate in response to their perceptions of decreased opportunities that manifest as high levels of extrinsic risk in rural environments. Parental investment in quality and quantity corresponds to parental perceptions of extrinsic risk, which in turn correspond to migration status, indicating that parental strategies do respond to perceived limits on investment payoffs