Optimal fits of diffusion constants from single-time data points of Brownian trajectories

Experimental methods based on single particle tracking (SPT) are being increasingly employed in the physical and biological sciences, where nanoscale objects are visualized with high temporal and spatial resolution. SPT can probe interactions between a particle and its environment but the price to be paid is the absence of ensemble averaging and a consequent lack of statistics. Here we address the benchmark question of how to accurately extract the diffusion constant of one single Brownian trajectory. We analyze a class of estimators based on weighted functionals of the square displacement. For a certain choice of the weight function these functionals provide the true ensemble averaged diffusion coefficient, with a precision that increases with the trajectory resolution.

The evolution of man: a popular exposition of the principal points of human ontogney phylogeny / From the German of Ernst Haeckel.

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The evolution of man: a popular exposition of the principal points of human ontogeny and phylogeny. From the German of Ernst Haeckel.

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The evolution of man: a popular exposition of the principal points of human ontogeny and phylogeny. From the German of Ernst Haeckel.

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The oxygen and carbon dioxide compensation points of C3 plants: possible role in regulating atmospheric oxygen.

The O2 and CO2 compensation points (O2 and CO2) of plants in a closed system depend on the ratio of CO2 and O2 concentrations in air and in the chloroplast and the specificities of ribulose bisphosphate carboxylase/oxygenase (Rubisco). The photosynthetic O2 is defined as the atmospheric O2 level, with a given CO2 level and temperature, at which net O2 exchange is zero. In experiments with C3 plants, the O2 with 220 ppm CO2 is 23% O2; O2 increases to 27% with 350 ppm CO2 and to 35% O2 with 700 ppm CO2. At O2 levels below the O2, CO2 uptake and reduction are accompanied by net O2 evolution. At O2 levels above the O2, net O2 uptake occurs with a reduced rate of CO2 fixation, more carbohydrates are oxidized by photorespiration to products of the C2 oxidative photosynthetic carbon cycle, and plants senesce prematurely. The CO2 increases from 50 ppm CO2 with 21% O2 to 220 ppm with 100% O2. At a low CO2/high O2 ratio that inhibits the carboxylase activity of Rubisco, much malate accumulates, which suggests that the oxygen-insensitive phosphoenolpyruvate carboxylase becomes a significant component of the lower CO2 fixation rate. Because of low global levels of CO2 and a Rubisco specificity that favors the carboxylase activity, relatively rapid changes in the atmospheric CO2 level should control the permissive O2 that could lead to slow changes in the immense O2 pool.

Comprehensive Validation Of A Measure Of Student School Engagement: A Pilot Study Of Middle School Students

Although it may sound reasonable that American education continues to be more effective at sending high school students to college, in a study conducted in 2009, The Council of the Great City Schools states that "slightly more than half of entering ninth grade students arrive performing below grade level in reading and math, while one in five entering ninth grade students is more than two years behind grade level...[and] 25% received support in the form of remedial literacy instruction or interventions" (Council of the Great City Schools, 2009). Students are distracted with technology (Lei & Zhao, 2005), family (Xu & Corno, 2003), medical illnesses (Nielson, 2009), learning disabilities and perhaps the most detrimental to academic success, the very lack of interest in school (Ruch, 1963). In a Johns Hopkins research study, Building a Graduation Nation - Colorado (Balfanz, 2008), warning signs were apparent years before the student dropped out of high school. The ninth grade was often referenced as a critical point that indicated success or failure to graduate high school. The research conducted by Johns Hopkins illustrates the problem: students who become disengaged from school have a much greater chance of dropping out of high school and not graduating. The first purpose of this study was to compare different measurement models of the Student School Engagement (SSE) using Factor Analysis to verify model fit with student engagement. The second purpose was to determine the extent to which the SSE instrument measures student school engagement by investigating convergent validity (via the SSE and Appleton, Christenson, Kim and Reschly's instrument and Fredricks, Blumenfeld, Friedel and Paris's instrument), discriminant validity (via Huebner's Student Life Satisfaction Survey) and criterion-related validity (via the sub-latent variables of Aspirations, Belonging and Productivity and student outcome measures such as achievement, attendance and discipline). Discriminant validity was established between the SSE and the Appleton, Christenson, Kim and Reschly's model and Fredricks, Blumenfeld, Friedel and Paris's (2005) Student Engagement Instruments (SEI). When confirming discriminant validity, the SSE's correlations were weak and statistically not significant, thus establishing discriminant validity with the SLSS. Criterion-related validity was established through structural equation modeling when the SSE was found to be a significant predictor of student outcome measures when both risk score and CSAP scores were used. The third purpose of this study was to assess the factorial invariance of the SSE instrument across gender to ensure the instrument is measuring the intended construct across different groups. Conclusively, configural, weak and metric invariances were established for the SSE as a non-significant change in chi-square indicating that all parameters including the error variances were invariant across groups of gender. Engagement is not a clearly defined psychological construct; it requires more research in order to fully comprehend its complexity. Hopefully, with parental and teacher involvement and a sense of community, student engagement can be nurtured to result in a meaningful attachment to school and academic success.

Psychometric Investigation of the Check-In, Check-Out Fidelity of Implementation Measure

Suspension and expulsion are utilized frequently and disproportionality in schools in the United States. Many schools utilize Positive Behavioral Interventions and Supports (PBIS), a tiered framework to prevent problem behavior and reduce the use of discipline practices (Sugai et al., 2000). Check-In, Check-Out (CICO) is a targeted group behavioral intervention that is utilized within this framework in schools to prevent severe problem behavior in students that are beginning to exhibit externalizing and/or internalizing behavioral needs; thus, preventing the use of exclusionary discipline practices (Crone et al., 2010; Hawken & Horner, 2003). As the use of CICO in schools continues to grow, so too does the need for an instrument measuring its fidelity of implementation. The purpose of this study was to investigate the reliability and validity of the Check-In, Check-Out Fidelity of Implementation Measure (Crone et al., 2010), an instrument created to measure the fidelity of implementation of CICO intervention. This study assessed the psychometric properties of the instrument utilizing an archival data set collected by the statewide PBIS initiative in a western state in the U.S. The results demonstrated promising content validity, construct validity, internal consistency, and interrater reliability. A unidimensional structure was determined to be the best structure for the instrument based on parsimony and the strong results obtained from the item loadings, internal consistency, and interrater reliability. Implications for use and future research are discussed.