11,175 research outputs found
Circle bundles over 4-manifolds
Every 1-connected topological 4-manifold M admits a -covering by
#_{r-1}S^{2}\times S^{3}, where 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in his unpublished manuscript.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%
Lyapunov exponents of partially hyperbolic volume-preserving maps with 2-dimensional center bundle
We consider the set of partially hyperbolic symplectic diffeomorphisms which
are accessible, have 2-dimensional center bundle and satisfy some pinching and
bunching conditions. In this set, we prove that the non-uniformly hyperbolic
maps are open and there exists a open and dense subset of
continuity points for the center Lyapunov exponents. We also generalize these
results to volume-preserving systems.Comment: Final version. Published online on Annales de l'Institut Henri
Poincar\'e, Analyse non lin\'eair
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