Une nouvelle condition d'independance pour le theoreme de la limite centrale

We prove a central limit theorem with aassumptions which are many weak than classical condition

Central limit theorem by polynomial dependence coefficients

AbstractWe study the asymptotic behaviour of normalized sums of n random variables ∑n = n−12(X1 + X2 + … + Xn). We obtain a necessary and sufficient condition in order that the moments of ∑n converge to the moments of a normal distribution. This condition is expressed by means of polynomial dependence coefficients ϱj1,j2, … ,jn. Then, one can obtain central limit theorems with minimal assumptions

A study of summative teacher performance evaluation instruments

This study made a critical analysis of summative teacher performance evaluation instruments used nationally in public school systems. The investigation involved identifying in the literature the types of instruments used, the types of rating scales and response modes used, and the merits of the comment section that may be found on the evaluation document. The following purposes provided the framework for the investigation: (1) To determine the degree to which school systems were using summative teacher performance evaluation instruments. (2) To determine the current status of teacher performance evaluation instruments used nationally by ascertaining: (a) the kinds of instruments being used, and (b) the types of criterion found on the instruments. (3) To compare summative teacher performance evaluation instruments by district size and purpose for which the district has said the instrument is used;The findings support the following conclusions: (a) little difference was noted regarding the summative teacher performance evaluation instrument as it relates to the purposes for which districts have said they use the instrument, (b) the category/rating scale evaluation instrument is used most frequently by districts, (c) districts have identified growth as the major purpose for which teachers are evaluated, (d) evaluation instruments usually have criteria that are embedded rather than in a discrete position, and (e) the verbal rating scale is used with a high degree of frequency by the school districts studied

Optimizing Tensor Contraction Paths: A Greedy Algorithm Approach With Improved Cost Functions

Finding efficient tensor contraction paths is essential for a wide range of problems, including model counting, quantum circuits, graph problems, and language models. There exist several approaches to find efficient paths, such as the greedy and random greedy algorithm by Optimized Einsum (opt_einsum), and the greedy algorithm and hypergraph partitioning approach employed in cotengra. However, these algorithms require a lot of computational time and resources to find efficient contraction paths. In this paper, we introduce a novel approach based on the greedy algorithm by opt_einsum that computes efficient contraction paths in less time. Moreover, with our approach, we are even able to compute paths for large problems where modern algorithms fail