Related papers: Deficiency Zero Petri Nets and Product Form
Stochastic chemical processes are described by the chemical master equation satisfying the law of mass-action. We first ask whether the dual master equation, which has the same steady state as the chemical master equation, but with inverted…
In this paper we show that the dynamics of a class of kinetic compartmental models with bounded capacities, monotone reaction rates and a strongly connected interconnection structure is persistent. The result is based on the chemical…
A natural condition on the structure of the underlying chemical reaction network, namely weak reversibility, is shown to guarantee the existence of an equilibrium (steady state) in each positive stoichiometric compatibility class for the…
The dynamics of network formation are generally very complex, making the study of distributions over the space of networks often intractable. Under a condition called conservativeness, I show that the stationary distribution of a network…
We study a two-species partially asymmetric exclusion process where the left boundary is permeable for the `slower' species but the right boundary is not. We find a matrix product solution for the stationary state, and the exact stationary…
Queueing networks are notoriously difficult to analyze sans both Markovian and stationarity assumptions. Much of the theoretical contribution towards performance analysis of time-inhomogeneous single class queueing networks has focused on…
It is well known that stochastically modeled reaction networks that are complex balanced admit a stationary distribution that is a product of Poisson distributions. In this paper, we consider the following related question: supposing that…
Stochastic Petri nets are commonly used for modeling distributed systems in order to study their performance and dependability. This paper proposes a realization of stochastic Petri nets in SystemC for modeling large embedded control…
We define the concept of an `open' Markov process, a continuous-time Markov chain equipped with specified boundary states through which probability can flow in and out of the system. External couplings which fix the probabilities of…
A compositional Petri net-based semantics is given to a simple language allowing pointer manipulation and parallelism. The model is then applied to give a notion of validity to the judgements made by concurrent separation logic that…
In this work, we analyse Petri nets where places are allowed to have a negative number of tokens. For each net we build its correspondent category of executions, which is compact closed, and prove that this procedure is functorial. We…
Given a dynamical system with polynomial right-hand side, can it be generated by a reaction network that possesses certain properties? This question is important because some network properties may guarantee specific dynamical properties,…
To what extent do the characteristic features of a chemical reaction network reflect its purpose and function? In general, one argues that correlations between specific features and specific functions are key to understanding a complex…
We consider here the morphogenesis (pattern formation) problem for some genetic network models. First, we show that any given spatio-temporal pattern can be generated by a genetic network involving a sufficiently large number of genes.…
A key problem in the study and design of complex systems is the apparent disconnection between the microscopic and the macroscopic. It is not straightforward to identify the local interactions that give rise to an observed global…
Consider a setting where $N$ players, partitioned into $K$ observable types, form a directed network. Agents' preferences over the form of the network consist of an arbitrary network benefit function (e.g., agents may have preferences over…
In the setting of stochastic dynamical systems that eventually go extinct, the quasi-stationary distributions are useful to understand the long-term behavior of a system before evanescence. For a broad class of applicable continuous-time…
We formalise a general concept of distributed systems as sequential components interacting asynchronously. We define a corresponding class of Petri nets, called LSGA nets, and precisely characterise those system specifications which can be…
We introduce a new threshold model of social networks, in which the nodes influenced by their neighbours can adopt one out of several alternatives. We characterize social networks for which adoption of a product by the whole network is…
In many scenarios, networks emerge endogenously as cognitive agents establish links in order to exchange information. Network formation has been widely studied in economics, but only on the basis of simplistic models that assume that the…