Fixed points for actions of Aut(Fn) on CAT(0) spaces

For n greater or equal 4 we discuss questions concerning global fixed points for isometric actions of Aut(Fn), the automorphism group of a free group of rank n, on complete CAT(0) spaces. We prove that whenever Aut(Fn) acts by isometries on complete d-dimensional CAT(0) space with d is less than 2 times the integer function of n over 4 and minus 1, then it must fix a point. This property has implications for irreducible representations of Aut(Fn), which are also presented here. For SAut(Fn), the unique subgroup of index two in Aut(Fn), we obtain similar results

The GPU vs Phi Debate: Risk Analytics Using Many-Core Computing

The risk of reinsurance portfolios covering globally occurring natural catastrophes, such as earthquakes and hurricanes, is quantified by employing simulations. These simulations are computationally intensive and require large amounts of data to be processed. The use of many-core hardware accelerators, such as the Intel Xeon Phi and the NVIDIA Graphics Processing Unit (GPU), are desirable for achieving high-performance risk analytics. In this paper, we set out to investigate how accelerators can be employed in risk analytics, focusing on developing parallel algorithms for Aggregate Risk Analysis, a simulation which computes the Probable Maximum Loss of a portfolio taking both primary and secondary uncertainties into account. The key result is that both hardware accelerators are useful in different contexts; without taking data transfer times into account the Phi had lowest execution times when used independently and the GPU along with a host in a hybrid platform yielded best performance.Comment: A modified version of this article is accepted to the Computers and Electrical Engineering Journal under the title - "The Hardware Accelerator Debate: A Financial Risk Case Study Using Many-Core Computing"; Blesson Varghese, "The Hardware Accelerator Debate: A Financial Risk Case Study Using Many-Core Computing," Computers and Electrical Engineering, 201

An integrated teaching model to develop english proficiency of ESL management students

The gap between receptive and productive English language skills is perceived to be unusually large among ESL students in the culturally segregated states of India. While the students’ listening and reading comprehension skills strengthen with class lectures and reading assignments, their speaking and writing skills remain underdeveloped. The purpose of this study is to create an integrated teaching model to improve the English proficiency of management students in order to make them more employable. The model combines two models of curriculum design with two models of teaching methodology. Using the basic ESP model of curriculum design, the other models are incorporated into it to achieve three objectives, to reduce the unusually wide gap between receptive and productive language skills, to gain proficiency in business communication tasks and to improve identified language deficiencies. The model is applied to a sample of ESL management students. The business communication tasks required at the corporate level as well as the language deficiencies of the respondents are assessed and are used to create the course design. Their motivation and attitude levels are measured. Learner-centered assessment techniques and learning styles are analysed in order to incorporate these into the teaching learning process. Along with the teaching methodology suggested in the model, these inputs provide the entire framework for an intervention that aims to achieve the stated objectives

On positivity of the Kadison constant and noncommutative Bloch theory

In an earlier paper, we established a natural connection between the Baum-Connes conjecture and noncommutative Bloch theory, viz. the spectral theory of projectively periodic elliptic operators on covering spaces. We elaborate on this connection here and provide significant evidence for a fundamental conjecture in noncommutative Bloch theory on the non-existence of Cantor set type spectrum. This is accomplished by establishing an explicit lower bound for the Kadison constant of twisted group C*-algebras in a large number of cases, whenever the multiplier is rational.Comment: Latex2e, 16 pages, final version, to appear in a special issue of Tohoku Math. J. (in press