The social organization of mathematics classrooms and English language learners’ opportunities to participate

In this paper, I discuss the significance of classroom organization in English Language Learners’ (ELLs) opportunities to participate in mathematics classrooms through a review of relevant contemporary literature. In particular, I will focus on the following areas of classroom organization: language organization, instructional organization, and discourse organization. By highlighting the relationship between classroom organization and English language learners’ opportunities to participate in the mathematics classroom, I will provide insight into when and under which contexts ELLs are acknowledged (or not) with their existing resources

Are SRI Funds More Resilient towards the Global Financial Crisis?

This paper compares the resilience of Socially Responsible Investment (SRI) funds with that of conventional funds towards the global financial crisis by using an event study methodology. Taking the bankruptcy of Lehman Brothers as the particular event, we estimated the average cumulative abnormal returns of both SRI funds and conventional funds. Our results show that SRI funds are more resilient to such a shock. Similar results are obtained by an estimation with a market model that accounts for ARCH effects.SRI, Event study, Financial crisis

Schwarzschild radius from Monte Carlo calculation of the Wilson loop in supersymmetric matrix quantum mechanics

In the string/gauge duality it is important to understand how the space-time geometry is encoded in gauge theory observables. We address this issue in the case of the D0-brane system at finite temperature T. Based on the duality, the temporal Wilson loop operator W in gauge theory is expected to contain the information of the Schwarzschild radius R_{Sch} of the dual black hole geometry as log = R_{Sch} / (2 pi alpha' T). This translates to the power-law behavior log = 1.89 (T/lambda^{1/3})^{-3/5}, where lambda is the 't Hooft coupling constant. We calculate the Wilson loop on the gauge theory side in the strongly coupled regime by performing Monte Carlo simulation of supersymmetric matrix quantum mechanics with 16 supercharges. The results reproduce the expected power-law behavior up to a constant shift, which is explainable as alpha' corrections on the gravity side.Comment: REVTeX4, 4 pages, 1 figur

Early Years Students’ Relationships with Mathematics

Early years mathematics experiences have been shown to be a significant predictor for students’ school readiness and future mathematics achievement. Previous research also indicates an important connection between emotion and mathematics learning. How do students in early years education in Alberta describe their emotional relationship with mathematics? This article documents the findings of our research focusing on Kindergarten to Grade 2 students. Our analysis showed that many students in the early years, including those at the Kindergarten level, recognized what is considered to be mathematics but mainly associated mathematics with number and numerical operations. The majority of these students reported positive relationships with mathematics, though some described negative relationships with school mathematics learning.Les expériences préscolaires avec les mathématiques se sont avérées être des prédicteurs importants de la maturité scolaire des jeunes enfants et de leur rendement en mathématiques à l’avenir. La recherche a également révélé un lien important entre les émotions et l’apprentissage des mathématiques. Comment les jeunes Albertains décrivent-ils leur relation émotionnelle avec les mathématiques? Cet article explique les résultats d’une recherche portant sur des élèves de la maternelle à la 2e année. Notre analyse démontre que plusieurs jeunes élèves, y compris ceux de la maternelle, ont reconnu ce qui est considéré comme étant les mathématiques, mais que pour eux, les mathématiques sont surtout liés aux chiffres et aux opérations numériques. Alors que la plupart de ces élèves ont indiqué qu’ils avaient un rapport positif avec les mathématiques, certains ont décrit des liens négatifs par rapport à l’apprentissage des mathématiques à l’école.

Selective Inference for Changepoint detection by Recurrent Neural Network

In this study, we investigate the quantification of the statistical reliability of detected change points (CPs) in time series using a Recurrent Neural Network (RNN). Thanks to its flexibility, RNN holds the potential to effectively identify CPs in time series characterized by complex dynamics. However, there is an increased risk of erroneously detecting random noise fluctuations as CPs. The primary goal of this study is to rigorously control the risk of false detections by providing theoretically valid p-values to the CPs detected by RNN. To achieve this, we introduce a novel method based on the framework of Selective Inference (SI). SI enables valid inferences by conditioning on the event of hypothesis selection, thus mitigating selection bias. In this study, we apply SI framework to RNN-based CP detection, where characterizing the complex process of RNN selecting CPs is our main technical challenge. We demonstrate the validity and effectiveness of the proposed method through artificial and real data experiments.Comment: 41pages, 16figure

Bounded P-values in Parametric Programming-based Selective Inference

Selective inference (SI) has been actively studied as a promising framework for statistical hypothesis testing for data-driven hypotheses. The basic idea of SI is to make inferences conditional on an event that a hypothesis is selected. In order to perform SI, this event must be characterized in a traceable form. When selection event is too difficult to characterize, additional conditions are introduced for tractability. This additional conditions often causes the loss of power, and this issue is referred to as over-conditioning. Parametric programming-based SI (PP-based SI) has been proposed as one way to address the over-conditioning issue. The main problem of PP-based SI is its high computational cost due to the need to exhaustively explore the data space. In this study, we introduce a procedure to reduce the computational cost while guaranteeing the desired precision, by proposing a method to compute the upper and lower bounds of p-values. We also proposed three types of search strategies that efficiently improve these bounds. We demonstrate the effectiveness of the proposed method in hypothesis testing problems for feature selection in linear models and attention region identification in deep neural networks.Comment: 47pages, 14figure

Statistical Test for Attention Map in Vision Transformer

The Vision Transformer (ViT) demonstrates exceptional performance in various computer vision tasks. Attention is crucial for ViT to capture complex wide-ranging relationships among image patches, allowing the model to weigh the importance of image patches and aiding our understanding of the decision-making process. However, when utilizing the attention of ViT as evidence in high-stakes decision-making tasks such as medical diagnostics, a challenge arises due to the potential of attention mechanisms erroneously focusing on irrelevant regions. In this study, we propose a statistical test for ViT's attentions, enabling us to use the attentions as reliable quantitative evidence indicators for ViT's decision-making with a rigorously controlled error rate. Using the framework called selective inference, we quantify the statistical significance of attentions in the form of p-values, which enables the theoretically grounded quantification of the false positive detection probability of attentions. We demonstrate the validity and the effectiveness of the proposed method through numerical experiments and applications to brain image diagnoses.Comment: 42pages, 17figure

Structural and dynamic behavior of lithium iron polysulfide Li₈FeS₅ during charge–discharge cycling

Lithium sulfide (Li₂S) is one of the promising positive electrode materials for next-generation rechargeable lithium batteries. To improve the electrochemical performance of electronically resistive Li₂S, a Fe-doped Li₂S-based positive electrode material (Li₈FeS₅) has been recently designed and found to exhibit excellent discharge capacity close to 800 mAh g⁻¹. In the present study, we investigate the structural and dynamic behavior of Li₈FeS₅ during charge–discharge cycling. In Li₈FeS₅, Fe ions are incorporated into the Li₂S framework structure. The Li₂S-based structure is found to transform to an amorphous phase during the charge process. The delithiation-induced amorphization is associated with the formation of S-S polysulfide bonds, indicating charge compensation by S ions. The crystalline to non-crystalline structural transformation is reversible, but Li ions are extracted from the material via a two-phase reaction, although they are inserted via a single-phase process. These results indicate that the delithiation/lithiation mechanism is neither a topotactic extraction/insertion nor a conversion-type reaction. Moreover, the activation energies for Li ion diffusion in the pristine, delithiated, and lithiated materials are estimated to be in the 0.30–0.37 eV range, which corresponds to the energy barriers for local hopping of Li ions along the Li sublattice in the Li₂S framework