Statistical properties of two-color randomly reinforced urn design targeting fixed allocations

This paper deals with the statistical properties of a response adaptive design, described in terms of a two colors urn model, targeting prespecified asymptotic allocations. Results on the rate of divergence of number of patients assigned to each treatment are proved as well as on the asymptotic behavior of the urn composition. Suitable statistics are introduced and studied to test the hypothesis on treatments’ difference

Interacting Innovation processes: case studies from Reddit and Gutenberg

The existing literature about innovation processes focuses on a single process at a time and proposes models and tools in order to characterize how novelties arise, diffuse and initiate further novelties inside the considered process. However, it is doubtless important to understand if and how different innovation processes influence each other. In this work, we introduce an extremely general model for a collection of innovation processes in order to model and analyze the interaction among them. We provide theoretical results, analytically proven, and we show how the proposed model fits the behaviors observed in some real data sets (from Reddit and Gutenberg). It is worth mentioning that the given applications are only examples of the potentialities of the proposed model and related results: due to its abstractness and generality, it can be applied to many interacting innovation processes.Comment: 6 figure

Interacting Reinforced Stochastic Processes: Statistical Inference based on the Weighted Empirical Means

This work deals with a system of interacting reinforced stochastic processes, where each process X-j = (X-n,X-j )(n), is located at a vertex j of a finite weighted directed graph, and it can be interpreted as the sequence of "actions" adopted by an agent j of the network. The interaction among the dynamics of these processes depends on the weighted adjacency matrix W associated to the underlying graph: indeed, the probability that an agent j chooses a certain action depends on its personal "inclination" Z(n,j) and on the inclinations Z(n,h), with h not equal j, of the other agents according to the entries of W. The best known example of reinforced stochastic process is the Polya urn. The present paper focuses on the weighted empirical means N-n,N-j = Sigma(n)(k)(=1) q(n,k) X-k,X- j, since, for example, the current experience is more important than the past one in reinforced learning. Their almost sure synchronization and some central limit theorems in the sense of stable convergence are proven. The new approach with weighted means highlights the key points in proving some recent results for the personal inclinations Z(j) = (Z(n,j))(n) and for the empirical means (X) over bar (j) = (Sigma(n)(k)(=1) X-k,X- j/n)(n) given in recent papers (e.g. Aletti, Crimaldi and Ghiglietti (2019), Ann. Appl. Probab. 27 (2017) 3787-3844, Crimaldi et al. Stochastic Process. Appl. 129 (2019) 70-101). In fact, with a more sophisticated decomposition of the considered processes, we can understand how the different convergence rates of the involved stochastic processes combine. From an application point of view, we provide confidence intervals for the common limit inclination of the agents and a test statistics to make inference on the matrix W, based on the weighted empirical means. In particular, we answer a research question posed in Aletti, Crimaldi and Ghiglietti (2019)

Lab-on-Chip for testing myelotoxic effect of drugs and chemicals

In the last 20 years, one of the main goals in the drug discovery field has been the development of reliable in vitro models. In particular, in 2006 the European Centre for the Validation of Alternative Methods has approved the colony-forming unit granulocytes–macrophages test, which is the first and currently unique test applied to evaluate the myelotoxicity of xenobiotics in vitro. The present work aimed at miniaturizing this in vitro assay by developing and validating a Lab-on-Chip platform consisting of a high number of bioreactor chambers with screening capabilities in a high-throughput regime