No abstract

In this article we study the minimum number κ of additional automata that a Boolean automata network (BAN) associated with a given blocksequential update schedule needs in order to simulate a given BAN with a parallel update schedule. We introduce a graph that we call NECC graph built from the BAN and the update schedule. We show the relation between κ and the chromatic number of the NECC graph. Thanks to this NECC graph, we bound κ in the worst case between n/2 and 2n/3 + 2 (n being the size of the BAN simulated) and we conjecture that this number equals n/2. We support this conjecture with two results: the clique number of a NECC graph is always less than or equal to n/2 and, for the subclass of bijective BANs, κ is always less than or equal to n/2 + 1.

A Boolean network (BN) with n components is a discrete dynamical system described by the successive iterations of a function f : {0, 1} n → {0, 1} n. This model finds applications in biology, where fixed points play a central role. For example, in genetic regulations, they correspond to cell phenotypes. In this context, experiments reveal the existence of positive or negative influences among components: component i has a positive (resp. negative) influence on component j meaning that j tends to mimic (resp. negate) i. The digraph of influences is called signed interaction digraph (SID), and one SID may correspond to a large number of BNs (which is, in average, doubly exponential according to n). The present work opens a new perspective on the well-established study of fixed points in BNs. When biologists discover the SID of a BN they do not know, they may ask: given that SID, can it correspond to a BN having at least/at most k fixed points? Depending on the input, we prove that these problems are in P or complete for NP, NP NP , NP #P or NEXPTIME. In particular, we prove that it is NP-complete (resp. NEXPTIME-complete) to decide if a given SID can correspond to a BN having at least two fixed points (resp. no fixed point).

On Twitter, social capitalists use dedicated hashtags and mutual subscriptions to each other in order to gain followers and to be retweeted. Their methods are successful enough to make them appear as influent users. Indeed, applications dedicated to the influence measurement such as Klout and Kred give high scores to most of these users. Meanwhile, their high number of retweets and followers are not due to the relevance of the content they tweet, but to their social capitalism techniques. In order to be able to detect these users, we train a classifier using a dataset of social capitalists and regular users. We then implement this classifier in a web application that we call DDP. DDP allows users to test whether a Twitter account is a social capitalist or not and to visualize the data we use to make the prediction. DDP allows administrator to crawl data from a lot of users automatically. Furthermore, administrators can manually label Twitter accounts as social capitalists or regular users to add them into the dataset. Finally, administrators can train new classifiers in order to take into account the new Twitter accounts added to the dataset, and thus making evolve the classifier with these new recently collected data. The web application is thus a way to collect data, make evolve the knowledge about social capitalists and to keep detecting them efficiently.