We introduce a natural language interface for building stochastic π calculus models of biological systems. In this language, complex constructs describing biochemical events are built from basic primitives of association, dissociation and transformation. This language thus allows us to model biochemical systems modularly by describing their dynamics in a narrative-style language, while making a...

A critical aspect in the modeling of biological systems is the description view point. On the one hand, the Stochastic π-calculus formalism provides an intuitive and compact representation from an internal perspective. On the other hand, other proposed languages such as Hybrid Automata and Stochastic Concurrent Constraint Programming introduce in the system description an external control and p...

Stochastic calculus methods are used to estimate the instantaneous frequency of a signal. The frequency is modeled as a polynomial in time. It is assumed that the phase has a Brownian-motion component. Using stochastic calculus, one is able to develop a stochastic differential equation that relates the observations to instantaneous frequency. Pseudo-maximum likelihood estimates are obtained thr...

Stochastic calculus is famous for providing the foundations for modern mathematical finance and is also used extensively in a large number of other areas of applied probability. The introductory text by Øksendal [3] strikes an excellent balance between theory and accessibility. Here we give a very brief review of the underlying concepts. A central notion for stochastic calculus is that of a (co...

The operating point of a node is an interesting concept from large deviations theory which defines the asymptotic buffer occupancy distribution at the node. The effective bandwidth function evolved out of large deviations theory, establishes the crucial connection between the node operating point and the theory of statistical network calculus. This paper uses the concepts of effective bandwidth...

For a given stochastic process X, its segment Xt at time t represents the “slice” of each path of X over a fixed time-interval [t−r, t], where r is the length of the “memory” of the process. Segment processes are important in the study of stochastic systems with memory (stochastic functional differential equations, SFDEs). The main objective of this paper is to study non-linear transforms of se...

We develop a process calculus – the nanoκ calculus – for modeling, analyzing and predicting the properties of molecular devices. The nanoκ calculus is equipped with a simple stochastic model, that we use to model and simulate the behaviour of a molecular shuttle, a basic nano device currently used for building more complex systems.

The physicist R. Feynman advanced an idea of forming an abstract operator calculus for a finite number of noncommuting operators by attaching time indices to the operators. In joint work with G.W. Johnson, time-ordering measures are introduced to serve as weights for various functional calculi, such as the Weyl functional calculus (equal weights), the Kohn-Nirenberg or ordered functional calcul...