Variants of geometric RSK, geometric PNG and the multipoint distribution of the log-gamma polymer

We show that the reformulation of the geometric Robinson-Schensted-Knuth (gRSK) correspondence via local moves, introduced in \cite{OSZ14} can be extended to cases where the input matrix is replaced by more general polygonal, Young-diagram-like, arrays of the form \polygon. We also show that a rearrangement of the sequence of the local moves gives rise to a geometric version of the polynuclear growth model (PNG). These reformulations are used to obtain integral formulae for the Laplace transform of the joint distribution of the point-to-point partition functions of the log-gamma polymer at different space-time points. In the case of two points at equal time $N$ and space at distance of order $N^{2/3}$, we show formally that the joint law of the partition functions, scaled by $N^{1/3}$, converges to the two-point function of the Airy processComment: 44 pages. Proposition 3.4 and Theorem 3.5 are now stated in a more general form and some more minor changes are made (most of them following suggestions by a referee). To appear at IMR

Daily 5 Implementation to Improve ELL Students’ Performances

This paper focuses on an action research project that integrated the Daily 5 literacy framework into a fourth-grade classroom in a small rural town in Kansas. The study aimed to enhance the literacy skills of English Language Learners (ELL) using the Daily 5 method, which includes five key activities: Read to Self, Work on Writing, Read to Someone, Listen to Reading, and Word Work. The research involved a six-week intervention and used student performance data, including daily assignment scores and oral reading fluency, to assess the impact of this framework on ELL students. The findings indicated significant improvements in students\u27 literacy skills, suggesting the effectiveness of the Daily 5 in this context. Discussion, reflection and implications for further studies were included

A CASE STUDY OF PEER ASSESSMENT IN A MOOC-BASED COMPOSITION COURSE: STUDENTS’ PERCEPTIONS, PEERS’ GRADING SCORES VERSUS INSTRUCTORS’ GRADING SCORES, AND PEERS’ COMMENTARY VERSUS INSTRUCTORS’ COMMENTARY

Although the use of peer assessment in MOOCs is common, there has been little empirical research about peer assessment in MOOCs, especially composition MOOCs. This study aimed to address issues in peer assessment in a MOOC-based composition course, in particular student perceptions, peer-grading scores versus instructor-grading scores, and peer commentary versus instructor commentary. The findings provided evidence that peer assessment was well received by the majority of student participants from their perspective as both peer evaluators of other students’ papers and as students being evaluated by their peers. However, many student participants also expressed negative feelings about certain aspects of peer assessment, for example peers’ lack of qualifications, peers’ negative and critical comments, and unfairness of peer grading. Statistical analysis of grades given by student peers and instructors revealed a consistency among grades given by peers but a low consistency between grades given by peers and those given by instructors, with the peer grades tending to be higher than those assigned by instructors. In addition, analysis of peer and instructor commentary revealed that peers’ commentary differed from instructors’ on specific categories of writing issues (idea development, organization, or sentence-level). For instance, on average peers focused a greater percentage of their comments (70%) on sentence-level issues than did instructors (64.7%), though both groups devoted more comments to sentence-level issues than to the two other issue categories. Peers’ commentary also differed from instructors’ in the approaches their comments took to communicating the writing issue (through explanation, question, or correction). For example, in commenting on sentence-level errors, on average 85% of peers’ comments included a correction as compared to 96% of instructors’ comments including that approach. In every comment category (idea development, organization, sentence-level), peers used a lower percentage of explanation—at least 10% lower—than did instructors. Overall, findings and conclusions of the study have limitations due to (1) the small size of composition MOOC studied and small sample size of graded papers used for the analysis, (2) the lack of research and scarcity of document archives on issues the study discussed, (3) the lack of examination of factors (i.e. level of education, cultural background, and English language proficiency) that might affect student participants’ perception of peer assessment, and (4) the lack of analysis of head notes, end notes, and length of comments. However, the study has made certain contributions to the existing literature, especially student perception of peer assessment in the composition MOOC in this study. Analysis of the grades given by peers and instructors in the study provides evidence-based information about whether online peer assessment should be used in MOOCs, especially composition MOOCs and what factors might affect the applicability and consistency of peer grading in MOOCs. In addition, analysis of the data provides insights into types of comments students in a composition MOOC made as compared to those instructors made. The findings of the study as a whole can inform the design of future research on peer assessment in composition MOOCs and indicate questions designers of peer assessment training and practice in such MOOCs could find helpful to consider

Localization in log-gamma polymers with boundaries

Consider the directed polymer in one space dimension in log-gamma environment with boundary conditions, introduced by Sepp{\"a}l{\"a}inen. In the equilibrium case, we prove that the end point of the polymer converges in law as the length increases, to a density proportional to the exponent of a zero-mean random walk. This holds without space normalization, and the mass concentrates in a neighborhood of the minimum of this random walk. We have analogous results out of equilibrium as well as for the middle point of the polymer with both ends fixed. The existence and the identification of the limit relies on the analysis of a random walk seen from its infimum.Comment: 33 pages, 3 figure

Multilevel determinants of children's health outcomes

Background: Children’s health, particularly in the early years, forms the basis of future health and development and plays a significant role in predicting individual life and opportunities. Thus, studies which enhance the understanding of the determinants of children’s health status are needed. Previous research on children’s health had focused on the family’s and infant’s characteristics and ignored the potential impact of macro-level influences. The objectives of this thesis were (i) to examine the independent effects of neighbourhood factors on childhood health outcomes, (ii) to explore neighbourhood moderating effects on the associations between some individual risk factors and childhood health outcomes, and (iii) to quantify the contribution of neighbourhood factors to childhood health outcomes.Method: The study population included 9,888 children born to women residing in Saskatoon during three years, 1992-1994. The data used in this study were extracted from three sources. The information related to birth outcomes and the mother’s characteristics was extracted from the birth registration files maintained by Saskatchewan’s Vital Statistics Branch. The health services utilization information was generated from Saskatchewan Health’s computerized administrative databases. The information related to the neighbourhood characteristics was obtained from Statistics Canada’s 1991 Census, from local sources such as the Planning Department of the City, and two specialized neighbourhood surveys. Six domains of neighbourhood were examined in this study: socio-economic disadvantage, social interaction, physical condition, population density, local programs and services, and unhealthy lifestyle norm. This study was divided into two focused topics corresponding to two children’s health outcomes: low birth weight (LBW) and children’s hospitalizations (both incidence and length of stay). Multilevel modelling was employed to examine the independent/moderating impacts of neighbourhood characteristics on these children’s health outcomes. GIS mapping was used to visualize the associations between neighbourhood characteristics and children’s health outcomes.Findings of focused topic 1: There was a significant variation across Saskatoon neighbourhoods in the distribution of LBW rate. This significant variation was attributed to both the characteristics of individuals living within the neighbourhoods as well as the characteristics of the neighbourhood of residence. Neighbourhood variables were both independent risk factors for LBW and moderators for the association between maternal characteristics and LBW. Specifically, a greater level of socio-economic disadvantage, a lower level of program availability and accessibility within the neighbourhoods were associated with a higher risk of LBW. A significant interaction between neighbourhood social interaction and single parent status was found. The risk of single parent status on LBW was mitigated by a greater level of social interaction within neighbourhoods. With individual level variables held constant, three neighbourhood variables predicted LBW, together contributing to a change in LBW rate of 7.0%.Findings of focused topic 2: This focused topic employed a longitudinal/multilevel design to examine the effects of socio-economic status at multiple levels on children’s hospitalization. The key findings of this focused topic are the following: (i) There was a gradient association between the number of adverse birth outcomes and childhood hospitalization; (ii) There was a significant interaction between family income and adverse birth outcomes (i.e., the effect of adverse birth outcomes on childhood hospitalization was heightened among those children living in low income families); (iii) Neighbourhood characteristics, specifically neighbourhood socio-economic disadvantage, neighbourhood physical condition, and neighbourhood population density had independent effects on childhood hospitalization over and above the effect of family income; (iv) With individual level variables held constant, three neighbourhood variables (i.e., neighbourhood socio-economic disadvantage, physical condition and population density) together accounted for a variation of 40% in the incidence rate of hospitalization, and two neighbourhood variables (i.e., neighbourhood socio-economic disadvantage and physical condition) together accounted for a change in the length of stay per hospitalization from 2.88 days to 5.18 days across neighbourhoods.Conclusion: Both individual and neighbourhood characteristics determined childhood health outcomes examined. Neighbourhood factors acted as independent risk factors as well as moderators on the association between individual risk factors and health outcomes. The contribution of neighbourhood factors to children’s health outcomes was quite substantial. The findings suggest that future interventions aimed at improving children’s health status in Saskatoon may be enhanced by targeting both high risk individuals and high risk neighbourhoods. The geographical variations in children’s health outcomes reported in this study are modifiable; they can be altered through public policy and urban planning, and through the efforts of families and children

Public Investment Management of Higher Education in Vietnam : Current Issues and Policy Recommendations

Purpose: The aim of the paper is to provide a comprehensive insight on public investment management practices in higher education and experiences of developed countries, to analyse the current approaches to public investment management in Vietnam and to propose applicablepolicy recommendations.Design/methodology/approach: Case study based on literature of public investment in higher education and analysis of legal documents, reports and data regarding Vietnam’s current practices in the field.Findings: Public investment management practices of Vietnam still follow the traditional approach, which has shown various weaknesses and drawbacks in terms of efficiency, lack of unification, and incapability of higher education institutions to seek for autonomy and alternative operational resources.Research and practical limitations/implications: Lack of quantitative data and survey tools to enhance the practical implementation of the study.Originality/value: This paper can become a reference resource for policy makers in terms of promoting reforms in the public investment system for higher education in the future.Paper type: Case study

Limitations of cyclic pile load tests by kentledge system in soft clay soil

The paper describes the inadequacies of cycled head-down load tests on two barrettes and one bored pile installed in soft clay soil region in Binh Thanh district, and district 7, Ho Chi Minh City, Vietnam, respectively. The soil profile of these sites consisted of layers of organic soft clay and silt from 22.5 m to 28.6 m depth on compact silty sand or semi-stiff to stiff clays to about 60 m depth and followed by dense to very dense sand. The cross-section area of two barrettes located on the Tan Cang complex area was 2,800 mm by 800 mm, which were constructed using the bucket drill technique with bentonite slurry into 65 m depth.  The bored pile of the Lakeside project in district 7 having a pile diameter was 1200 mm and 80 m depth. All instrumented piles were attached from ten to eleven strain gages levels along the pile shaft to record the deformation data during the load tests. The strain data analysis shows that the shaft frictions of pile portions located in the soft clay soil regions were increased dramatically, and the base resistances were smaller expected by the setting-up of Kentledge and the cyclic loading tests

Exact Mode Shapes of T-shaped and Overhang-shaped Microcantilevers

Resonance frequencies and mode shapes of microcantilevers are of important interest in micro-mechanical systems for enhancing the functionality and applicable range of the cantilevers in vibration transducing, energy harvesting, and highly sensitive measurement. In this study, using the Euler-Bernoulli theory for beam, we figured out the exact mode shapes of cantilevers of varying widths such as the overhang- or T-shaped cantilevers. The obtained mode shapes have been shown to significantly deviate from the approximate forms of a rectangular cantilever that are commonly used in mechanics and physics. They were then used to figure out the resonance frequencies of the cantilever. The analytical solutions have been confirmed by using the finite element method simulations with very low deviation. This study suggested a method for correctly obtaining the resonance frequency of microcantilevers with complicated dimensions, such as the doubly clamped cantilever with the undercut, with the overhangs at the clamped positions, or with an attached mass in the middle