24,171 research outputs found
Safe Schedulability of Bounded-Rate Multi-Mode Systems
Bounded-rate multi-mode systems (BMMS) are hybrid systems that can switch
freely among a finite set of modes, and whose dynamics is specified by a finite
number of real-valued variables with mode-dependent rates that can vary within
given bounded sets. The schedulability problem for BMMS is defined as an
infinite-round game between two players---the scheduler and the
environment---where in each round the scheduler proposes a time and a mode
while the environment chooses an allowable rate for that mode, and the state of
the system changes linearly in the direction of the rate vector. The goal of
the scheduler is to keep the state of the system within a pre-specified safe
set using a non-Zeno schedule, while the goal of the environment is the
opposite. Green scheduling under uncertainty is a paradigmatic example of BMMS
where a winning strategy of the scheduler corresponds to a robust
energy-optimal policy. We present an algorithm to decide whether the scheduler
has a winning strategy from an arbitrary starting state, and give an algorithm
to compute such a winning strategy, if it exists. We show that the
schedulability problem for BMMS is co-NP complete in general, but for two
variables it is in PTIME. We also study the discrete schedulability problem
where the environment has only finitely many choices of rate vectors in each
mode and the scheduler can make decisions only at multiples of a given clock
period, and show it to be EXPTIME-complete.Comment: Technical report for a paper presented at HSCC 201
Semistability and Hilbert-Kunz multiplicities for curves
We study Hilbert-Kunz multiplicity of non-singular curves in positive
characteristic. We analyse the relationship between the Frobenius semistability
of the kernel sheaf associated with the curve and its ample line bundle, and
the HK multiplicity. This leads to a lower bound, achieved iff the kernel sheaf
is Frobenius semistable, and otherwise to formulas for the HK multiplicity in
terms of parameters measuring the failure of Frobenius semistability. As a
byproduct, an explicit example of a vector bundle on a curve is given whose
-th iterated Frobenius pullback is not semistable, while its -th such
pullback is semistable, where is arbitrary.Comment: Latex2e, 12 pages, final version, revised as per the referee's
suggestions, to appear in Journal of Algebr
The Legal Needs of Local Media Reform Organizations: Report of a National Survey
This report summarizes a nationwide survey of media reform groups to gauge their needs for pro bono legal assistance. Conclusions are that local media democracy groups need legal help on multiple issues, ranging from municipal broadband to cable franchising to low-power radio
- …