1,487 research outputs found
On Deadlockability, Liveness and Reversibility in Subclasses of Weighted Petri Nets
International audienceLiveness, (non-)deadlockability and reversibility are behavioral properties of Petri nets that are fundamental for many real-world systems. Such properties are often required to be mono-tonic, meaning preserved upon any increase of the marking. However, their checking is intractable in general and their monotonicity is not always satisfied. To simplify the analysis of these features, structural approaches have been fruitfully exploited in particular subclasses of Petri nets, deriving the behavior from the underlying graph and the initial marking only, often in polynomial time. In this paper, we further develop these efficient structural methods to analyze deadlockability, live-ness, reversibility and their monotonicity in weighted Petri nets. We focus on the join-free subclass, which forbids synchronizations, and on the homogeneous asymmetric-choice subclass, which allows conflicts and synchronizations in a restricted fashion. For the join-free nets, we provide several structural conditions for checking liveness, (non-)deadlock-ability, reversibility and their monotonicity. Some of these methods operate in polynomial time. Furthermore , in this class, we show that liveness, non-deadlockability and reversibility, taken together or separately, are not always monotonic, even under the assumptions of structural boundedness and structural liveness. These facts delineate more sharply the frontier between monotonicity and non-monotonicity of the behavior in weighted Petri nets, present already in the join-free subclass. In addition, we use part of this new material to correct a flaw in the proof of a previous characterization of monotonic liveness and boundedness for homogeneous asymmetric-choice nets, published in 2004 and left unnoticed
Transition manifolds of complex metastable systems: Theory and data-driven computation of effective dynamics
We consider complex dynamical systems showing metastable behavior but no
local separation of fast and slow time scales. The article raises the question
of whether such systems exhibit a low-dimensional manifold supporting its
effective dynamics. For answering this question, we aim at finding nonlinear
coordinates, called reaction coordinates, such that the projection of the
dynamics onto these coordinates preserves the dominant time scales of the
dynamics. We show that, based on a specific reducibility property, the
existence of good low-dimensional reaction coordinates preserving the dominant
time scales is guaranteed. Based on this theoretical framework, we develop and
test a novel numerical approach for computing good reaction coordinates. The
proposed algorithmic approach is fully local and thus not prone to the curse of
dimension with respect to the state space of the dynamics. Hence, it is a
promising method for data-based model reduction of complex dynamical systems
such as molecular dynamics
Orbital measures in non-equilibrium statistical mechanics: the Onsager relations
We assume that the properties of nonequilibrium stationary states of systems
of particles can be expressed in terms of weighted orbital measures, i.e.
through periodic orbit expansions. This allows us to derive the Onsager
relations for systems of particles subject to a Gaussian thermostat, under
the assumption that the entropy production rate is equal to the phase space
contraction rate. Moreover, this also allows us to prove that the relevant
transport coefficients are not negative. In the appendix we give an argument
for the proper way of treating grazing collisions, a source of possible
singularities in the dynamics.Comment: LaTeX, 14 pages, 1 TeX figure in the tex
Optimal Monte Carlo Updating
Based on Peskun's theorem it is shown that optimal transition matrices in
Markov chain Monte Carlo should have zero diagonal elements except for the
diagonal element corresponding to the largest weight. We will compare the
statistical efficiency of this sampler to existing algorithms, such as
heat-bath updating and the Metropolis algorithm. We provide numerical results
for the Potts model as an application in classical physics. As an application
in quantum physics we consider the spin 3/2 XY model and the Bose-Hubbard model
which have been simulated by the directed loop algorithm in the stochastic
series expansion framework.Comment: 6 pages, 5 figures, replaced with published versio
Conditioned stochastic particle systems and integrable quantum spin systems
We consider from a microscopic perspective large deviation properties of
several stochastic interacting particle systems, using their mapping to
integrable quantum spin systems. A brief review of recent work is given and
several new results are presented: (i) For the general disordered symmectric
exclusion process (SEP) on some finite lattice conditioned on no jumps into
some absorbing sublattice and with initial Bernoulli product measure with
density we prove that the probability of no absorption event
up to microscopic time can be expressed in terms of the generating function
for the particle number of a SEP with particle injection and empty initial
lattice. Specifically, for the symmetric simple exclusion process on conditioned on no jumps into the origin we obtain the explicit first and
second order expansion in of and also to first order in
the optimal microscopic density profile under this conditioning. For the
disordered ASEP on the finite torus conditioned on a very large current we show
that the effective dynamics that optimally realizes this rare event does not
depend on the disorder, except for the time scale. For annihilating and
coalescing random walkers we obtain the generating function of the number of
annihilated particles up to time , which turns out to exhibit some universal
features.Comment: 25 page
Entropy, time irreversibility and Schroedinger equation in a primarily discrete space-time
In this paper we show that the existence of a primarily discrete space-time
may be a fruitful assumption from which we may develop a new approach of
statistical thermodynamics in pre-relativistic conditions. The discreetness of
space-time structure is determined by a condition that mimics the Heisenberg
uncertainty relations and the motion in this space-time model is chosen as
simple as possible. From these two assumptions we define a path-entropy that
measures the number of closed paths associated with a given energy of the
system preparation. This entropy has a dynamical character and depends on the
time interval on which we count the paths. We show that it exists an
like-equilibrium condition for which the path-entropy corresponds exactly to
the usual thermodynamic entropy and, more generally, the usual statistical
thermodynamics is reobtained. This result derived without using the Gibbs
ensemble method shows that the standard thermodynamics is consistent with a
motion that is time-irreversible at a microscopic level. From this change of
paradigm it becomes easy to derive a . A comparison with the
traditional Boltzmann approach is presented. We also show how our approach can
be implemented in order to describe reversible processes. By considering a
process defined simultaneously by initial and final conditions a well defined
stochastic process is introduced and we are able to derive a Schroedinger
equation, an example of time reversible equation.Comment: latex versio
Innovation Behaviour At Farm Level – Selection And Identification
Using a squential logit model and a mixed-effects logistic regression approach this empirical study investigates factors for the adoption of automatic milking technology (AMS) at the farm level accounting for problems of sequential sample selection and behaviour identification. The results suggest the importance of the farmer’s risk perception, significant effects of peer-group behaviour, and a positive impact of previous innovation experiences.Technology Adoption, Mixed-Effects Regression, Risk, Agricultural and Food Policy, Farm Management, Land Economics/Use,
Innovation behaviour at farm level: Selection and identification
Using a squential logit model and a mixed-effects logistic regression approach this empirical study investigates factors for the adoption of automatic milking technology (AMS) at the farm level accounting for problems of sequential sample selection and behaviour identification. The results suggest the importance of the farmer’s risk perception, significant effects of peer-group behaviour, and a positive impact of previous innovation experiences.squential logit model, automatic milking technology (AMS), Livestock Production/Industries, Research Methods/ Statistical Methods, Risk and Uncertainty,
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