618 research outputs found
Homotopy types of complements of 2-arrangements in R^4
We study the homotopy types of complements of arrangements of n transverse
planes in R^4, obtaining a complete classification for n <= 6, and lower bounds
for the number of homotopy types in general. Furthermore, we show that the
homotopy type of a 2-arrangement in R^4 is not determined by the cohomology
ring, thereby answering a question of Ziegler. The invariants that we use are
derived from the characteristic varieties of the complement. The nature of
these varieties illustrates the difference between real and complex
arrangements.Comment: LaTeX2e, 25 pages with 5 figures. Revised version, to appear in
Topolog
Cohomology rings and nilpotent quotients of real and complex arrangements
For an arrangement with complement X and fundamental group G, we relate the
truncated cohomology ring, H^{<=2}(X), to the second nilpotent quotient, G/G_3.
We define invariants of G/G_3 by counting normal subgroups of a fixed prime
index p, according to their abelianization. We show how to compute this
distribution from the resonance varieties of the Orlik-Solomon algebra mod p.
As an application, we establish the cohomology classification of 2-arrangements
of n<=6 planes in R^4.Comment: LaTeX2e, 22 pages, to appear in Singularities and Arrangements,
Sapporo-Tokyo 1998, Advanced Studies in Pure Mathematic
Characteristic varieties of graph manifolds and quasi-projectivity of fundamental groups of algebraic links
The present paper studies the structure of characteristic varieties of
fundamental groups of graph manifolds. As a consequence, a simple proof of
Papadima's question is provided on the characterization of algebraic links that
have quasi-projective fundamental groups. The type of quasi-projective
obstructions used here are in the spirit of Papadima's original work.Comment: 22 pages, 6 figures, to appear in European Journal of Mathematic
Cu codoping control over magnetic precipitate formation in ZnCoO nanowires
Using electrodeposition, we have grown nanowires of ZnCoO with Cu codoping
concentrations varying from 4-10 at.%, controlled only by the deposition
potential. We demonstrate control over magnetic Co oxide nano-precipitate
formation in the nanowires via the Cu concentration. The different magnetic
behavior of the Co oxide nano-precipitates indicates the potential of ZnCoO for
magnetic sensor applications.Comment: 5 pages, 5 figure
Timely-Throughput Optimal Coded Computing over Cloud Networks
In modern distributed computing systems, unpredictable and unreliable
infrastructures result in high variability of computing resources. Meanwhile,
there is significantly increasing demand for timely and event-driven services
with deadline constraints. Motivated by measurements over Amazon EC2 clusters,
we consider a two-state Markov model for variability of computing speed in
cloud networks. In this model, each worker can be either in a good state or a
bad state in terms of the computation speed, and the transition between these
states is modeled as a Markov chain which is unknown to the scheduler. We then
consider a Coded Computing framework, in which the data is possibly encoded and
stored at the worker nodes in order to provide robustness against nodes that
may be in a bad state. With timely computation requests submitted to the system
with computation deadlines, our goal is to design the optimal computation-load
allocation scheme and the optimal data encoding scheme that maximize the timely
computation throughput (i.e, the average number of computation tasks that are
accomplished before their deadline). Our main result is the development of a
dynamic computation strategy called Lagrange Estimate-and Allocate (LEA)
strategy, which achieves the optimal timely computation throughput. It is shown
that compared to the static allocation strategy, LEA increases the timely
computation throughput by 1.4X - 17.5X in various scenarios via simulations and
by 1.27X - 6.5X in experiments over Amazon EC2 clustersComment: to appear in MobiHoc 201
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