Circle bundles over 4-manifolds

Every 1-connected topological 4-manifold M admits a $S^{1}$-covering by #_{r-1}S^{2}\times S^{3}, where $r=$rankH^{2}(M;\QTR{Bbb}{Z}).Comment: 6 pages to appear in Archiv der Mat

Constrained portfolio-consumption strategies with uncertain parameters and borrowing costs

This paper studies the properties of the optimal portfolio-consumption strategies in a {finite horizon} robust utility maximization framework with different borrowing and lending rates. In particular, we allow for constraints on both investment and consumption strategies, and model uncertainty on both drift and volatility. With the help of explicit solutions, we quantify the impacts of uncertain market parameters, portfolio-consumption constraints and borrowing costs on the optimal strategies and their time monotone properties.Comment: 35 pages, 8 tables, 1 figur

Refinements of Miller's Algorithm over Weierstrass Curves Revisited

In 1986 Victor Miller described an algorithm for computing the Weil pairing in his unpublished manuscript. This algorithm has then become the core of all pairing-based cryptosystems. Many improvements of the algorithm have been presented. Most of them involve a choice of elliptic curves of a \emph{special} forms to exploit a possible twist during Tate pairing computation. Other improvements involve a reduction of the number of iterations in the Miller's algorithm. For the generic case, Blake, Murty and Xu proposed three refinements to Miller's algorithm over Weierstrass curves. Though their refinements which only reduce the total number of vertical lines in Miller's algorithm, did not give an efficient computation as other optimizations, but they can be applied for computing \emph{both} of Weil and Tate pairings on \emph{all} pairing-friendly elliptic curves. In this paper we extend the Blake-Murty-Xu's method and show how to perform an elimination of all vertical lines in Miller's algorithm during Weil/Tate pairings computation on \emph{general} elliptic curves. Experimental results show that our algorithm is faster about 25% in comparison with the original Miller's algorithm.Comment: 17 page

A Workload-Specific Memory Capacity Configuration Approach for In-Memory Data Analytic Platforms

We propose WSMC, a workload-specific memory capacity configuration approach for the Spark workloads, which guides users on the memory capacity configuration with the accurate prediction of the workload's memory requirement under various input data size and parameter settings.First, WSMC classifies the in-memory computing workloads into four categories according to the workloads' Data Expansion Ratio. Second, WSMC establishes a memory requirement prediction model with the consideration of the input data size, the shuffle data size, the parallelism of the workloads and the data block size. Finally, for each workload category, WSMC calculates the shuffle data size in the prediction model in a workload-specific way. For the ad-hoc workload, WSMC can profile its Data Expansion Ratio with small-sized input data and decide the category that the workload falls into. Users can then determine the accurate configuration in accordance with the corresponding memory requirement prediction.Through the comprehensive evaluations with SparkBench workloads, we found that, contrasting with the default configuration, configuration with the guide of WSMC can save over 40% memory capacity with the workload performance slight degradation (only 5%), and compared to the proper configuration found out manually, the configuration with the guide of WSMC leads to only 7% increase in the memory waste with the workload's performance slight improvement (about 1%