Critical frontier of the Potts and percolation models in triangular-type and kagome-type lattices I: Closed-form expressions

We consider the Potts model and the related bond, site, and mixed site-bond percolation problems on triangular-type and kagome-type lattices, and derive closed-form expressions for the critical frontier. For triangular-type lattices the critical frontier is known, usually derived from a duality consideration in conjunction with the assumption of a unique transition. Our analysis, however, is rigorous and based on an established result without the need of a uniqueness assumption, thus firmly establishing all derived results. For kagome-type lattices the exact critical frontier is not known. We derive a closed-form expression for the Potts critical frontier by making use of a homogeneity assumption. The closed-form expression is new, and we apply it to a host of problems including site, bond, and mixed site-bond percolation on various lattices. It yields exact thresholds for site percolation on kagome, martini, and other lattices, and is highly accurate numerically in other applications when compared to numerical determination.Comment: 22 pages, 13 figure

Vertex Models and Random Labyrinths: Phase Diagrams for Ice-type Vertex Models

We propose a simple geometric recipe for constructing phase diagrams for a general class of vertex models obeying the ice rule. The disordered phase maps onto the intersecting loop model which is interesting in its own right and is related to several other statistical mechanical models. This mapping is also useful in understanding some ordered phases of these vertex models as they correspond to the polymer loop models with cross-links in their vulcanised phase.Comment: 8 pages, 6 figure

The development of long-term retention in children : differentiating amnesia and hypermnesia

Although there is a considerable amount of knowledge about how children acquire information, very little is known about how they retain information in memory. Both acquisition and retention are important in cognition and both must be understood to have a more complete picture of cognitive development. Some of the factors responsible for the absence of research in children's long-term retention, as well as the methodological and analytical refinements necessary for studying children's long-term retention, are discussed. A mathematical model of long-term retention, one that partitions forgetting and relearning into storage and retrieval components, is described and applied to an experiment in which grade 2 and 5 children's retention of 3-item clusters was examined. The clusters varied in semantic relatedness (related or unrelated) and in presentation modality (pictures or words) and retention was examined across 2 sessions over different retention intervals (at 2 and 16 days or 16 and 30 days after acquisition). Both forgetting and relearning were observed at retention with changes in performance being due to alterations in both the availability of information in storage and the retrievability of that information. The most prominent developmental difference was found in forgetting, not relearning, with younger children forgetting more than the older children. Interestingly, regardless of age, storage failure was greater than retrieval failure. The results of this study were interpreted in the context of the recently developed trace-integrity theory of long-term retention in which both the storage and retrieval aspects of forgetting and relearning are combined into a single unified framework

ジェネリックスキルテストを使用した言語学習能力評価の実行可能性：2018 年度多摩大学共同研究プロジェクト報告

This report explains the preliminary findings of a longitudinal study that uses statistical analyses of PROG scores and TOEIC scores to determine if the PROG might be an indicator of language learning ability. PROG scores for Literacy and Competency from 2018 for a group of university freshmen were correlated with English grades, TOEIC scores and changes in TOEIC scores over time. Additional correlations were calculated for sub-groups such as TOEIC range and gender. The preliminary findings indicate weak correlations between PROG scores and TOEIC scores. Similarly, there are weak to moderate correlations between PROG scores and final grades in English classes. More importantly, the correlation coefficients are statistically significant at less than .05 p value and less than .01 p value. Although more data analysis is necessary, the results indicate that generic skills tests can provide language educators with valuable information for both language course design and student placement into language course levels.本稿では、PROG が言語学習能力の指標であるかどうかを判断するために行ったPROG スコアとTOEIC スコアの統計分析を使用した縦断的研究の予備調査結果を報告する。2018 年の大学の新入生のグループが受験したPROG のリテラシーとコンピテンシーのスコアが、英語の成績、TOEIC スコア、及び時間経過に伴うTOEICスコアの変化と相関しているかを分析した。さらに、TOEIC スコアの分布や性別などの下位グループについても相関関係を調べた。予備調査の結果は、PROG スコアとTOEIC スコアの間に弱い相関があることを示している。同様に、PROG スコアと英語クラスの成績との間には弱から中程度の相関がみられた。より重要なことに、相関係数は .05ｐ値未満および .01ｐ値未満で、統計的に有意である。より多くのデータの分析が必要であるが、本研究は、ジェネリックスキルテストが語学コースの設計とコース受講者のプレースメントに役立ち、語学教育の担当者に貴重な情報を提供できる可能性を示している

On the generalized continuity equation

A generalized continuity equation extending the ordinary continuity equation has been found using quanternions. It is shown to be compatible with Dirac, Schrodinger, Klein-Gordon and diffusion equations. This generalized equation is Lorentz invariant. The transport properties of electrons are found to be governed by Schrodinger-like equation and not by the diffusion equation.Comment: 9 Latex pages, no figure

BCL-2 family protein expression and platinum drug resistance in ovarian carcinoma

The expression of the BCL-2 family proteins, BCL-2, BAX, BCLXLand BAK have been determined in a panel of 12 human ovarian carcinoma cell lines encompassing a wide range in sensitivity to cisplatin. Whereas BAX, BCLXLand BAK levels did not correlate with sensitivity, there was a statistically significant inverse correlation (r = –0.81;P = 0.002) between growth inhibition by cisplatin and BCL-2 levels. In sublines possessing acquired resistance to various platinum-based drugs or across a panel of human ovarian carcinoma xenografts, there was no consistent pattern of BCL-2 expression. Two relatively sensitive lines (A2780 and CH1) have been stably transfected with bcl-2 and bclXLrespectively and two relatively resistant lines (A2780cisR and SKOV-3) stably transfected with bax. Overexpression of BCL-2 in A2780 cells led to resistance to cisplatin compared to the vector control when assayed at 48 h post-drug incubation but a significant increase in sensitivity at 96 h. Relative rates of apoptosis at 48- and 96-h post-cisplatin exposure mirrored the growth inhibition. There was no significant difference in sensitivity of the pair of lines by clonogenic assay. No significant changes in chemosensitivity to a variety of DNA-damaging or tubulin-interactive agents were observed in the remaining transfected lines. Taken together, these results suggest that, in human ovarian carcinoma cells, high BCL-2 levels (either naturally occurring or through gene transfection) confers a trend towards sensitivity not resistance to platinum drugs. © 2000 Cancer Research Campaig