Search results for: Max Rothschild

Authors: Rachida Ouysse

Abstract:

This paper proposes a constrained principal components (CnPC) estimator for efficient estimation of large-dimensional factor models when errors are cross sectionally correlated and the number of cross-sections (N) may be larger than the number of observations (T). Although principal components (PC) method is consistent for any path of the panel dimensions, it is inefficient as the errors are treated to be homoskedastic and uncorrelated. The new CnPC exploits the assumption of bounded cross-sectional dependence, which defines Chamberlain and Rothschild’s (1983) approximate factor structure, as an explicit constraint and solves a constrained PC problem. The CnPC method is computationally equivalent to the PC method applied to a regularized form of the data covariance matrix. Unlike maximum likelihood type methods, the CnPC method does not require inverting a large covariance matrix and thus is valid for panels with N ≥ T. The paper derives a convergence rate and an asymptotic normality result for the CnPC estimators of the common factors. We provide feasible estimators and show in a simulation study that they are more accurate than the PC estimator, especially for panels with N larger than T, and the generalized PC type estimators, especially for panels with N almost as large as T.

Keywords: high dimensionality, unknown factors, principal components, cross-sectional correlation, shrinkage regression, regularization, pseudo-out-of-sample forecasting

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Authors: Ahmed Elbeltagy, Francesca Bertolini, Damarius Fleming, Angelica Van Goor, Chris Ashwell, Carl Schmidt, Donald Kugonza, Susan Lamont, Max Rothschild

Abstract:

The major factor in shaping genomic variation of the African indigenous rural chicken is likely natural selection drives the development genetic footprints in the chicken genomes. To investigate such a hypothesis of a selection footprint, a total of 292 birds were randomly sampled from three indigenous ecotypes from East Africa (Uganda, Rwanda) and North Africa (Egypt) and two registered Egyptian breeds (Fayoumi and Dandarawi), and from the synthetic Kuroiler breed. Samples were genotyped using the Affymetrix 600K Axiom® Array. A total of 526,652 SNPs were utilized in the downstream analysis after quality control measures. The intra-population runs of homozygosity (ROH) that were consensuses in > 50% of individuals of an ecotype or > 75% of a breed were studied. To identify inter-population differentiation due to genetic structure, FST was calculated for North- vs. East- African populations in addition to population-pairwise combinations for overlapping windows (500Kb with an overlap of 250Kb). A total of 28,563 ROH were determined and were classified into three length categories. ROH and Fst detected sweeps were identified on several autosomes. Several genes in these regions are likely to be related to adaptation to local environmental stresses that include high altitude, diseases resistance, poor nutrition, oxidative and heat stresses and were linked to gene ontology terms (GO) related to immune response, oxygen consumption and heme binding, carbohydrate metabolism, oxidation-reduction, and behavior. Results indicated a possible effect of natural selection forces on shaping genomic structure for adaptation to local environmental stresses.

Keywords: African Chicken, runs of homozygosity, FST, selection footprints

Procedia PDF Downloads 292

Authors: J. Shamash

Abstract:

The high-school curriculum in algebra deals mainly with the solution of different types of equations. However, modern algebra has a completely different viewpoint and is concerned with algebraic structures and operations. A question then arises: What might be the relevance and contribution of an abstract algebra course for developing expertise and mathematical perspective in secondary school mathematics instruction? This is the focus of this paper. The course Algebra: From Equations to Structures is a carefully designed abstract algebra course for Israeli secondary school mathematics teachers. The course provides an introduction to algebraic structures and modern abstract algebra, and links abstract algebra to the high-school curriculum in algebra. It follows the historical attempts of mathematicians to solve polynomial equations of higher degrees, attempts which resulted in the development of group theory and field theory by Galois and Abel. In other words, algebraic structures grew out of a need to solve certain problems, and proved to be a much more fruitful way of viewing them. This theorems in both group theory and field theory. Along the historical ‘journey’, many other major results in algebra in the past 150 years are introduced, and recent directions that current research in algebra is taking are highlighted. This course is part of a unique master’s program – the Rothschild-Weizmann Program – offered by the Weizmann Institute of Science, especially designed for practicing Israeli secondary school teachers. A major component of the program comprises mathematical studies tailored for the students at the program. The rationale and structure of the course Algebra: From Equations to Structures are described, and its relevance to teaching school algebra is examined by analyzing three kinds of data sources. The first are position papers written by the participating teachers regarding the relevance of advanced mathematics studies to expertise in classroom instruction. The second data source are didactic materials designed by the participating teachers in which they connected the mathematics learned in the mathematics courses to the school curriculum and teaching. The third date source are final projects carried out by the teachers based on material learned in the course.

Keywords: abstract algebra , linking abstract algebra and school mathematics, school algebra, secondary school mathematics, teacher professional development

Procedia PDF Downloads 122