18,172 research outputs found
Confluence Reduction for Probabilistic Systems (extended version)
This paper presents a novel technique for state space reduction of probabilistic specifications, based on a newly developed notion of confluence for probabilistic automata. We prove that this reduction preserves branching probabilistic bisimulation and can be applied on-the-fly. To support the technique, we introduce a method for detecting confluent transitions in the context of a probabilistic process algebra with data, facilitated by an earlier defined linear format. A case study demonstrates that significant reductions can be obtained
Confluence reduction for Markov automata
Markov automata are a novel formalism for specifying systems exhibiting nondeterminism, probabilistic choices and Markovian rates. Recently, the process algebra MAPA was introduced to efficiently model such systems. As always, the state space explosion threatens the analysability of the models generated by such specifications. We therefore introduce confluence reduction for Markov automata, a powerful reduction technique to keep these models small. We define the notion of confluence directly on Markov automata, and discuss how to syntactically detect confluence on the MAPA language as well. That way, Markov automata generated by MAPA specifications can be reduced on-the-fly while preserving divergence-sensitive branching bisimulation. Three case studies demonstrate the significance of our approach, with reductions in analysis time up to an order of magnitude
Analytical solutions for a two-level system driven by a class of chirped pulses
We present analytical solutions for the problem of a two-level atom driven by
a class of chirped pulses. The solutions are given in terms of Heun functions.
Using appropriate chirping parameters an enhancement of four-orders of
magnitudes in the population transfer is obtained.Comment: 5 pages, 5 figure
On the accuracy of solving confluent Prony systems
In this paper we consider several nonlinear systems of algebraic equations
which can be called "Prony-type". These systems arise in various reconstruction
problems in several branches of theoretical and applied mathematics, such as
frequency estimation and nonlinear Fourier inversion. Consequently, the
question of stability of solution with respect to errors in the right-hand side
becomes critical for the success of any particular application. We investigate
the question of "maximal possible accuracy" of solving Prony-type systems,
putting stress on the "local" behavior which approximates situations with low
absolute measurement error. The accuracy estimates are formulated in very
simple geometric terms, shedding some light on the structure of the problem.
Numerical tests suggest that "global" solution techniques such as Prony's
algorithm and ESPRIT method are suboptimal when compared to this theoretical
"best local" behavior
Reachability Analysis of Communicating Pushdown Systems
The reachability analysis of recursive programs that communicate
asynchronously over reliable FIFO channels calls for restrictions to ensure
decidability. Our first result characterizes communication topologies with a
decidable reachability problem restricted to eager runs (i.e., runs where
messages are either received immediately after being sent, or never received).
The problem is EXPTIME-complete in the decidable case. The second result is a
doubly exponential time algorithm for bounded context analysis in this setting,
together with a matching lower bound. Both results extend and improve previous
work from La Torre et al
Cannabinoid signalling in TNF-alpha induced IL-8 release
Original article can be found at: http://www.sciencedirect.com/science/journal/00142999 Copyright Elsevier B.V. DOI : 10.1016/j.ejphar.2006.04.015Peer reviewe
Root system chip-firing II: Central-firing
Jim Propp recently proposed a labeled version of chip-firing on a line and
conjectured that this process is confluent from some initial configurations.
This was proved by Hopkins-McConville-Propp. We reinterpret Propp's labeled
chip-firing moves in terms of root systems: a "central-firing" move consists of
replacing a weight by for any positive root
that is orthogonal to . We show that central-firing is always
confluent from any initial weight after modding out by the Weyl group, giving a
generalization of unlabeled chip-firing on a line to other types. For
simply-laced root systems we describe this unlabeled chip-firing as a number
game on the Dynkin diagram. We also offer a conjectural classification of when
central-firing is confluent from the origin or a fundamental weight.Comment: 30 pages, 6 figures, 1 table; v2, v3: minor revision
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