In recent years, great efforts have been made to analyze biological systems to understand the long-run behaviors. As a well-established formalism for modelling real-life biological systems, Boolean networks (BNs) allow their representation and analysis using formal reasoning and tools. Most biological systems are robust-they can withstand the loss of links and cope with external environmental perturbations. Hence, the BNs used to model such systems are necessarily large and dense, and yet modular. However, existing analysis methods only work well on networks of moderate size. Thus, there is a great need for efficient methods that can handle large-scale BNs and for doing so it is inevitable to exploit both the structural and dynamic properties of the networks. In this paper, we propose a method towards the optimal decomposition of BNs to balance the relation between the structure and dynamics of a network. We show that our method can greatly improve the existing decomposition-based attractor detection by analyzing a number of large real-life biological networks.

We study the problem of computing a minimal subset of nodes of a given asynchronous Boolean network that need to be perturbed in a single-step to drive its dynamics from an initial state to a target steady state (or attractor), which we call the source-target control of Boolean networks. Due to the phenomenon of state-space explosion, a simple global approach that performs computations on the entire network may not scale well for large networks. We believe that efficient algorithms for such networks must exploit the structure of the networks together with their dynamics. Taking this view, we derive a decomposition-based solution to the minimal source-target control problem which can be significantly faster than the existing approaches on large networks. We then show that the solution can be further optimized if we take into account appropriate information about the source state. We apply our solutions to both real-life biological networks and randomly generated networks, demonstrating the efficiency and efficacy of our approach.

MOTIVATION: The control of Boolean networks has traditionally focussed on strategies where the perturbations are applied to the nodes of the network for an extended period of time. In this work, we study if and how a Boolean network can be controlled by perturbing a minimal set of nodes for a single-step and letting the system evolve afterwards according to its original dynamics. More precisely, given a Boolean network (BN), we compute a minimal subset Cmin of the nodes such that BN can be driven from any initial state in an attractor to another 'desired' attractor by perturbing some or all of the nodes of Cmin for a single-step. Such kind of control is attractive for biological systems because they are less time consuming than the traditional strategies for control while also being financially more viable. However, due to the phenomenon of state-space explosion, computing such a minimal subset is computationally inefficient and an approach that deals with the entire network in one-go, does not scale well for large networks. RESULTS: We develop a 'divide-and-conquer' approach by decomposing the network into smaller partitions, computing the minimal control on the projection of the attractors to these partitions and then composing the results to obtain Cmin for the whole network. We implement our method and test it on various real-life biological networks to demonstrate its applicability and efficiency. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Cellular reprogramming, a technique that opens huge opportunities in modern and regenerative medicine, heavily relies on identifying key genes to perturb. Most of the existing computational methods for controlling which attractor (steady state) the cell will reach focus on finding mutations to apply to the initial state. However, it has been shown, and is proved in this article, that waiting between perturbations so that the update dynamics of the system prepares the ground, allows for new reprogramming strategies. To identify such sequential perturbations, we consider a qualitative model of regulatory networks, and rely on Binary Decision Diagrams to model their dynamics and the putative perturbations. Our method establishes a set identification of sequential perturbations, whether permanent (mutations) or only temporary, to achieve the existential or inevitable reachability of an arbitrary state of the system. We apply an implementation for temporary perturbations on models from the literature, illustrating that we are able to derive sequential perturbations to achieve trans-differentiation.

International audience

We study the relative efficiencies of the random and systematic approaches to automated software testing. Using a simple but realistic set of assumptions, we propose a general model for software testing and define sampling strategies for random (R) and systematic (S0) testing, where each sampling is associated with a sampling cost: 1 and c units of time, respectively. The two most important goals of software testing are: (i) achieving in minimal time a given degree of confidence x in a program's correctness and (ii) discovering a maximal number of errors within a given time bound n̂. For both (i) and (ii), we show that there exists a bound on c beyond which R performs better than S0on the average. Moreover for (i), this bound depends asymptotically only on x. We also show that the efficiency of R can be fitted to the exponential curve. Using these results we design a hybrid strategy H that starts with R and switches to S0when S0is expected to discover more errors per unit time. In our experiments we find that H performs similarly or better than the most efficient of both and that S0may need to be significantly faster than our bounds suggest to retain efficiency over R.

The aim of automated program testing is to gain confidence about a program's correctness by sampling its input space. The sampling process can be either systematic or random. For every systematic testing technique the sampling is informed by the analysis of some program artefacts, like the specification, the source code (e.g., to achieve coverage), or even faulty versions of the program (e.g., mutation testing). This analysis incurs some cost. In contrast, random testing is unsystematic and does not sustain any analysis cost. In this paper, we investigate the theoretical efficiency of systematic versus random testing. First, we mathematically model the most effective systematic testing technique S_0 in which every sampled test input strictly increases the "degree of confidence" and is subject to the analysis cost c. Note that the efficiency of S_0 depends on c. Specifically, if we increase c, we also increase the time it takes S_0 to establish the same degree of confidence. So, there exists a maximum analysis cost beyond which R is generally more efficient than S_0. Given that we require the confidence that the program works correctly for x% of its input, we prove an upper bound on c of S_0, beyond which R is more efficient on the average. We also show that this bound depends asymptotically only on x. For instance, let R take 10ms time to sample one test input; to establish that the program works correctly for 90% of its input, S_0 must take less than 41ms to sample one test input. Otherwise, R is expected to establish the 90%-degree of confidence earlier. We prove similar bounds on the cost if the software tester is interested in revealing as many errors as possible in a given time span.

We study repeated normal form games where the number of players is large and suggest that it is useful to consider a neighbourhood structure on the players. The structure is given by a graph G whose nodes are players and edges denote visibility. The neighbourhoods are maximal cliques in G. The game proceeds in rounds where in each round the players of every clique X of G play a strategic form game among each other. A player at a node v strategises based on what she can observe, i.e., the strategies and the outcomes in the previous round of the players at vertices adjacent to v. Based on this, the player may switch strategies in the same neighbourhood, or migrate to another neighbourhood. Player types, giving the rationale for such switching, are specified in a simple modal logic.

We suggest that extending Muller games with preference ordering for players is a natural way to reason about unbounded duration games. In this context, we look at the standard solution concept of Nash equilibrium for non-zero sum games. We show that Nash equilibria always exists for such generalised Muller games on finite graphs and present a procedure to compute an equilibrium strategy profile. We also give a procedure to compute a subgame perfect equilibrium when it exists in such games.

We study games in which the choices available to players are not fixed, and may change during the course of play. Specifically, we consider a model in which players may switch strategies, and a global (social) decision may remove some choices, based on the strategies being adopted by players. We propose a logical formalism in which such choices are specified, and a model of bounded memory strategies in which the eventual implications of such choices can be computed, and present preliminary results.