The Attributed Pi Calculus with Priorities

International audienceWe present the attributed $\pi$-calculus for modeling concurrent systems with interaction constraints depending on the values of attributes of processes. The $\pi$-calculus serves as a constraint language underlying the $\pi$-calculus. Interaction constraints subsume priorities, by which to express global aspects of populations. We present a nondeterministic and a stochastic semantics for the attributed $\pi$-calculus. We show how to encode the $\pi$-calculus with priorities and polyadic synchronization $\pi$@ and thus dynamic compartments, as well as the stochastic $\pi$-calculus with concurrent objects spico. We illustrate the usefulness of the attributed $\pi$-calculus for modeling biological systems at two particular examples: Euglena’s spatial movement in phototaxis, and cooperative protein binding in gene regulation of bacteriophage lambda. Furthermore, population-based model is supported beside individual-based modeling. A stochastic simulation algorithm for the attributed $\pi$-calculus is derived from its stochastic semantics. We have implemented a simulator and present experimental results, that confirm the practical relevance of our approach

A Stochastic Pi Calculus for Concurrent Objects

International audienceWe present SpiCO, a new modeling and simulation language for system biology, based on the stochastic pi-calculus. SpiCO supports higher level modeling via multi-profile concurrent objects with static inheritance. We present a semantics for SpiCO in terms of continuous time Markov chains, and show how to compile SpiCO back into the biochemical stochastic pi-calculus while preserving semantics

A foundation for higher-order concurrent constraint programming

We present the gamma-calculus, a computational calculus for higher-order concurrent programming. The calculus can elegantly express higher-order functions (both eager and lazy) and concurrent objects with encapsulated state and multiple inheritance. The primitives of the gamma-calculus are logic variables, names, procedural abstraction, and cells. Cells provide a notion of state that is fully compatible with concurrency and constraints. Although it does not have a dedicated communication primitive, the gamma-calculus can elegantly express one-to-many and many-to-one communication. There is an interesting relationship between the gamma-calculus and the pi-calculus: The gamma-calculus is subsumed by a calculus obtained by extending the asynchronous and polyadic pi-calculus with logic variables. The gamma-calculus can be extended with primitives providing for constraint-based problem solving in the style of logic programming. A such extended gamma-calculus has the remarkable property that it combines first-order constraints with higher-order programming

A Stochastic Pi Calculus for Concurrent Objects

International audienceWe present SpiCO, a new modeling and simulation language for system biology, based on the stochastic pi-calculus. SpiCO supports higher level modeling via multi-profile concurrent objects with static inheritance. We present a semantics for SpiCO in terms of continuous time Markov chains, and show how to compile SpiCO back into the biochemical stochastic pi-calculus while preserving semantics

Picturing classical and quantum Bayesian inference

We introduce a graphical framework for Bayesian inference that is sufficiently general to accommodate not just the standard case but also recent proposals for a theory of quantum Bayesian inference wherein one considers density operators rather than probability distributions as representative of degrees of belief. The diagrammatic framework is stated in the graphical language of symmetric monoidal categories and of compact structures and Frobenius structures therein, in which Bayesian inversion boils down to transposition with respect to an appropriate compact structure. We characterize classical Bayesian inference in terms of a graphical property and demonstrate that our approach eliminates some purely conventional elements that appear in common representations thereof, such as whether degrees of belief are represented by probabilities or entropic quantities. We also introduce a quantum-like calculus wherein the Frobenius structure is noncommutative and show that it can accommodate Leifer's calculus of `conditional density operators'. The notion of conditional independence is also generalized to our graphical setting and we make some preliminary connections to the theory of Bayesian networks. Finally, we demonstrate how to construct a graphical Bayesian calculus within any dagger compact category.Comment: 38 pages, lots of picture

Comparing the orthogonal and homotopy functor calculi

Goodwillie's homotopy functor calculus constructs a Taylor tower of approximations to F, often a functor from spaces to spaces. Weiss's orthogonal calculus provides a Taylor tower for functors from vector spaces to spaces. In particular, there is a Weiss tower associated to the functor which sends a vector space V to F evaluated at the one-point compactification of V. In this paper, we give a comparison of these two towers and show that when F is analytic the towers agree up to weak equivalence. We include two main applications, one of which gives as a corollary the convergence of the Weiss Taylor tower of BO. We also lift the homotopy level tower comparison to a commutative diagram of Quillen functors, relating model categories for Goodwillie calculus and model categories for the orthogonal calculus.Comment: 28 pages, sequel to Capturing Goodwillie's Derivative, arXiv:1406.042

The probability of non-confluent systems

We show how to provide a structure of probability space to the set of execution traces on a non-confluent abstract rewrite system, by defining a variant of a Lebesgue measure on the space of traces. Then, we show how to use this probability space to transform a non-deterministic calculus into a probabilistic one. We use as example Lambda+, a recently introduced calculus defined through type isomorphisms.Comment: In Proceedings DCM 2013, arXiv:1403.768