ADAM: Analysis of Discrete Models of Biological Systems Using Computer Algebra

Background: Many biological systems are modeled qualitatively with discrete models, such as probabilistic Boolean networks, logical models, Petri nets, and agent-based models, with the goal to gain a better understanding of the system. The computational complexity to analyze the complete dynamics of these models grows exponentially in the number of variables, which impedes working with complex models. Although there exist sophisticated algorithms to determine the dynamics of discrete models, their implementations usually require labor-intensive formatting of the model formulation, and they are oftentimes not accessible to users without programming skills. Efficient analysis methods are needed that are accessible to modelers and easy to use. Method: By converting discrete models into algebraic models, tools from computational algebra can be used to analyze their dynamics. Specifically, we propose a method to identify attractors of a discrete model that is equivalent to solving a system of polynomial equations, a long-studied problem in computer algebra. Results: A method for efficiently identifying attractors, and the web-based tool Analysis of Dynamic Algebraic Models (ADAM), which provides this and other analysis methods for discrete models. ADAM converts several discrete model types automatically into polynomial dynamical systems and analyzes their dynamics using tools from computer algebra. Based on extensive experimentation with both discrete models arising in systems biology and randomly generated networks, we found that the algebraic algorithms presented in this manuscript are fast for systems with the structure maintained by most biological systems, namely sparseness, i.e., while the number of nodes in a biological network may be quite large, each node is affected only by a small number of other nodes, and robustness, i.e., small number of attractors

Connectivity in Sub-Poisson Networks

We consider a class of point processes (pp), which we call {\em sub-Poisson}; these are pp that can be directionally-convexly ($dcx$) dominated by some Poisson pp. The $dcx$ order has already been shown useful in comparing various point process characteristics, including Ripley's and correlation functions as well as shot-noise fields generated by pp, indicating in particular that smaller in the $dcx$ order processes exhibit more regularity (less clustering, less voids) in the repartition of their points. Using these results, in this paper we study the impact of the $dcx$ ordering of pp on the properties of two continuum percolation models, which have been proposed in the literature to address macroscopic connectivity properties of large wireless networks. As the first main result of this paper, we extend the classical result on the existence of phase transition in the percolation of the Gilbert's graph (called also the Boolean model), generated by a homogeneous Poisson pp, to the class of homogeneous sub-Poisson pp. We also extend a recent result of the same nature for the SINR graph, to sub-Poisson pp. Finally, as examples we show that the so-called perturbed lattices are sub-Poisson. More generally, perturbed lattices provide some spectrum of models that ranges from periodic grids, usually considered in cellular network context, to Poisson ad-hoc networks, and to various more clustered pp including some doubly stochastic Poisson ones.Comment: 8 pages, 10 figures, to appear in Proc. of Allerton 2010. For an extended version see http://hal.inria.fr/inria-00497707 version

Mathematical approaches to differentiation and gene regulation

We consider some mathematical issues raised by the modelling of gene networks. The expression of genes is governed by a complex set of regulations, which is often described symbolically by interaction graphs. Once such a graph has been established, there remains the difficult task to decide which dynamical properties of the gene network can be inferred from it, in the absence of precise quantitative data about their regulation. In this paper we discuss a rule proposed by R.Thomas according to which the possibility for the network to have several stationary states implies the existence of a positive circuit in the corresponding interaction graph. We prove that, when properly formulated in rigorous terms, this rule becomes a theorem valid for several different types of formal models of gene networks. This result is already known for models of differential or boolean type. We show here that a stronger version of it holds in the differential setup when the decay of protein concentrations is taken into account. This allows us to verify also the validity of Thomas' rule in the context of piecewise-linear models and the corresponding discrete models. We discuss open problems as well.Comment: To appear in Notes Comptes-Rendus Acad. Sc. Paris, Biologi

Several types of types in programming languages

Types are an important part of any modern programming language, but we often forget that the concept of type we understand nowadays is not the same it was perceived in the sixties. Moreover, we conflate the concept of "type" in programming languages with the concept of the same name in mathematical logic, an identification that is only the result of the convergence of two different paths, which started apart with different aims. The paper will present several remarks (some historical, some of more conceptual character) on the subject, as a basis for a further investigation. The thesis we will argue is that there are three different characters at play in programming languages, all of them now called types: the technical concept used in language design to guide implementation; the general abstraction mechanism used as a modelling tool; the classifying tool inherited from mathematical logic. We will suggest three possible dates ad quem for their presence in the programming language literature, suggesting that the emergence of the concept of type in computer science is relatively independent from the logical tradition, until the Curry-Howard isomorphism will make an explicit bridge between them.Comment: History and Philosophy of Computing, HAPOC 2015. To appear in LNC

Analytical investigation of the dynamics of tethered constellations in earth orbit

This Quarterly Report on Tethering in Earth Orbit deals with three topics: (1) Investigation of the propagation of longitudinal and transverse waves along the upper tether. Specifically, the upper tether is modeled as three massive platforms connected by two perfectly elastic continua (tether segments). The tether attachment point to the station is assumed to vibrate both longitudinally and transversely at a given frequency. Longitudinal and transverse waves propagate along the tethers affecting the acceleration levels at the elevator and at the upper platform. The displacement and acceleration frequency-response functions at the elevator and at the upper platform are computed for both longitudinal and transverse waves. An analysis to optimize the damping time of the longitudinal dampers is also carried out in order to select optimal parameters. The analytical evaluation of the performance of tuned vs. detuned longitudinal dampers is also part of this analysis. (2) The use of the Shuttle primary Reaction Control System (RCS) thrusters for blowing away a recoiling broken tether is discussed. A microcomputer system was set up to support this operation. (3) Most of the effort in the tether plasma physics study was devoted to software development. A particle simulation code has been integrated into the Macintosh II computer system and will be utilized for studying the physics of hollow cathodes