4,991 research outputs found
A new twist for the simulation of hybrid systems using the true jump method
The use of stochastic models, in effect piecewise deterministic Markov
processes (PDMP), has become increasingly popular especially for the modeling
of chemical reactions and cell biophysics. Yet, exact simulation methods, for
the simulation of these models in evolving environments, are limited by the
need to find the next jumping time at each recursion of the algorithm. Here, we
report on a new general method to find this jumping time for the True Jump
Method. It is based on an expression in terms of ordinary differential
equations for which efficient numerical methods are available. As such, our new
result makes it possible to study numerically stochastic models for which
analytical formulas are not available thereby providing a way to approximate
the state distribution for example. We conclude that the wide use of event
detection schemes for the simulation of PDMPs should be strongly reconsidered.
The only relevant remaining question being the efficiency of our method
compared to the Fictitious Jump Method, question which is strongly case
dependent
A Way Out of the Quantum Trap
We review Event Enhanced Quantum Theory (EEQT). In Section 1 we address the
question "Is Quantum Theory the Last Word". In particular we respond to some of
recent challenging staments of H.P. Stapp. We also discuss a possible future of
the quantum paradigm - see also Section 5. In Section 2 we give a short sketch
of EEQT. Examples are given in Section 3. Section 3.3 discusses a completely
new phenomenon - chaos and fractal-like phenomena caused by a simultaneous
"measurement" of several non-commuting observables (we include picture of
Barnsley's IFS on unit sphere of a Hilbert space). In Section 4 we answer
"Frequently Asked Questions" concerning EEQT.Comment: Replacement. Corrected affiliation. Latex, one .jpg figure. To appear
in Proc. Conf. Relativistic Quantum Measurements, Napoli 1998, Ed. F.
Petruccion
Statistical estimation of jump rates for a specific class of Piecewise Deterministic Markov Processes
We consider the class of Piecewise Deterministic Markov Processes (PDMP),
whose state space is , that possess an increasing deterministic
motion and that shrink deterministically when they jump. Well known examples
for this class of processes are Transmission Control Protocol (TCP) window size
process and the processes modeling the size of a "marked" {\it Escherichia
coli} cell. Having observed the PDMP until its th jump, we construct a
nonparametric estimator of the jump rate . Our main result is that for
a compact subset of , if is in the H{\''{o}}lder
space , the squared-loss error of the estimator
is asymptotically close to the rate of . Simulations illustrate
the behavior of our estimator
Event-Enhanced Quantum Theory And Piecewise Deterministic Dynamics
The standard formalism of quantum theory is enhanced and definite meaning is
given to the concepts of experiment, measurement and event. Within this
approach one obtains a uniquely defined piecewise deterministic algorithm
generating quantum jumps, classical events and histories of single quantum
objects. The wave-function Monte Carlo method of Quantum Optics is generalized
and promoted to the level of a fundamental process generating all the real
events in Nature. The already worked out applications include SQUID-tank model
and generalized cloud chamber model with GRW spontaneous localization as a
particular case. Differences between the present approach and quantum
measurement theories based on environment induced master equations are
stressed. Questions: what is classical, what is time, and what are observers
are addressed. Possible applications of the new approach are suggested, among
them connection between the stochastic commutative geometry and
Connes'noncommutative formulation of the Standard Model, as well as potential
applications to the theory and practice of quantum computers.Comment: 10 pages, twocolumn, REVTE
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