Dynamic network models describe many important scientific processes, from cell biology and epidemiology to sociology and finance. Estimating dynamic networks from noisy time series data is a difficult task since the number of components involved in the system is very large. As a result, the number of parameters to be estimated is typically larger than the number of observations. However, a characteristic of many real life networks is that they are sparse. For example, the molecular structure of genes make interactions with other components a highly-structured and, therefore, a sparse process. Until now, the literature has focused on static networks, which lack specific temporal interpretations.

We propose a flexible collection of ANOVA-like dynamic network models, where the user can select specific time dynamics, known presence or absence of links, and a particular autoregressive structure. We use undirected graphical models with block equality constraints on the parameters. This reduces the number of parameters, increases the accuracy of the estimates and makes interpretation of the results more relevant. We illustrate the flexibility of the method on both synthetic and real data.

We aim at characterizing viability, invariance and some reachability properties of controlled piecewise deterministic Markov processes (PDMPs). Using analytical methods from the theory of viscosity solutions, we establish criteria for viability and invariance in terms of the first order normal cone. We also investigate reachability of arbitrary open sets. The method is based on viscosity techniques and duality for some associated linearized problem. The theoretical results are applied to general On/Off systems, Cook’s model for haploinsufficiency, and a stochastic model for bacteriophage λ.

No other concepts have shaken so deeply the bases of engineering like those of positiveand negative feedback. They have played a most prominent role in engineering since the beginningof the previous century. The birth certificate of positive feedback can be traced back to a pair ofpatents by Edwin H. Armstrong in 1914 and 1922, whereas that of negative feedback is alreadylost in time. We present in this paper a short review on the feedback's origins in the fields ofengineering and biology. Besides, we compare the main feedback's ideas in control theory andsystem biology in order to get a better understanding of the lactose and tryptophan operons' regulatorysystems (control systems). It is obvious that we need to know the genome of an organismin order to understand how it works, but that is only half of the puzzle, for we also need to knowhow the underlying genetic regulatory systems work in order to get a complete picture of the cell'sdynamics.