22,421 research outputs found
Compositional Performance Modelling with the TIPPtool
Stochastic process algebras have been proposed as compositional specification formalisms for performance models. In this paper, we describe a tool which aims at realising all beneficial aspects of compositional performance modelling, the TIPPtool. It incorporates methods for compositional specification as well as solution, based on state-of-the-art techniques, and wrapped in a user-friendly graphical front end. Apart from highlighting the general benefits of the tool, we also discuss some lessons learned during development and application of the TIPPtool. A non-trivial model of a real life communication system serves as a case study to illustrate benefits and limitations
The Stochastic Representation of Hamiltonian Dynamics and The Quantization of Time
Here it is shown that the unitary dynamics of a quantum object may be
obtained as the conditional expectation of a counting process of object-clock
interactions. Such a stochastic process arises from the quantization of the
clock, and this is derived naturally from the matrix-algebra representation of
the nilpotent Newton-Leibniz time differential [Belavkin]. It is observed that
this condition expectation is a rigorous formulation of the Feynman Path
Integral.Comment: 21 page
Density of the set of probability measures with the martingale representation property
Let be a multi-dimensional random variable. We show that the set of
probability measures such that the -martingale
has the Martingale Representation Property (MRP) is either empty or dense in
-norm. The proof is based on a related result involving
analytic fields of terminal conditions and probability
measures over an open set . Namely, we show that
the set of points such that does not
have the MRP, either coincides with or has Lebesgue measure zero. Our study
is motivated by the problem of endogenous completeness in financial economics.Comment: 24 pages, forthcoming in Annals of Probabilit
Model checking probabilistic and stochastic extensions of the pi-calculus
We present an implementation of model checking for probabilistic and stochastic extensions of the pi-calculus, a process algebra which supports modelling of concurrency and mobility. Formal verification techniques for such extensions have clear applications in several domains, including mobile ad-hoc network protocols, probabilistic security protocols and biological pathways. Despite this, no implementation of automated verification exists. Building upon the pi-calculus model checker MMC, we first show an automated procedure for constructing the underlying semantic model of a probabilistic or stochastic pi-calculus process. This can then be verified using existing probabilistic model checkers such as PRISM. Secondly, we demonstrate how for processes of a specific structure a more efficient, compositional approach is applicable, which uses our extension of MMC on each parallel component of the system and then translates the results into a high-level modular description for the PRISM tool. The feasibility of our techniques is demonstrated through a number of case studies from the pi-calculus literature
Multifractals, Mumford curves, and Eternal Inflation
We relate the Eternal Symmetree model of Harlow, Shenker, Stanford, and
Susskind to constructions of stochastic processes arising from quantum
statistical mechanical systems on Cuntz--Krieger algebras. We extend the
eternal inflation model from the Bruhat--Tits tree to quotients by p-adic
Schottky groups, again using quantum statistical mechanics on graph algebras.Comment: 19 pages, LaTeX, 4 pdf figure
Process Calculi Abstractions for Biology
Several approaches have been proposed to model biological systems by means of the formal techniques and tools available in computer science. To mention just a few of them, some representations are inspired by Petri Nets theory, and some other by stochastic processes. A most recent approach consists in interpreting the living entities as terms of process calculi where the behavior of the represented systems can be inferred by applying syntax-driven rules. A comprehensive picture of the state of the art of the process calculi approach to biological modeling is still missing. This paper goes in the direction of providing such a picture by presenting a comparative survey of the process calculi that have been used and proposed to describe the behavior of living entities. This is the preliminary version of a paper that was published in Algorithmic Bioprocesses. The original publication is available at http://www.springer.com/computer/foundations/book/978-3-540-88868-
Quantum theory without Hilbert spaces
Quantum theory does not only predict probabilities, but also relative phases
for any experiment, that involves measurements of an ensemble of systems at
different moments of time. We argue, that any operational formulation of
quantum theory needs an algebra of observables and an object that incorporates
the information about relative phases and probabilities. The latter is the
(de)coherence functional, introduced by the consistent histories approach to
quantum theory. The acceptance of relative phases as a primitive ingredient of
any quantum theory, liberates us from the need to use a Hilbert space and
non-commutative observables. It is shown, that quantum phenomena are adequately
described by a theory of relative phases and non-additive probabilities on the
classical phase space. The only difference lies on the type of observables that
correspond to sharp measurements. This class of theories does not suffer from
the consequences of Bell's theorem (it is not a theory of Kolmogorov
probabilities) and Kochen- Specker's theorem (it has distributive "logic"). We
discuss its predictability properties, the meaning of the classical limit and
attempt to see if it can be experimentally distinguished from standard quantum
theory. Our construction is operational and statistical, in the spirit of
Kopenhagen, but makes plausible the existence of a realist, geometric theory
for individual quantum systems.Comment: 32 pages, Latex, 4 figures. Small changes in the revised version,
comments and references added; essentially the version to appear in Found.
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