Andrea Ghiglietti

LRRK2 mutations in Parkinson's disease: Confirmation of a gender effect in the Italian population

Background The relative risk of developing idiopathic PD is 1.5 times greater in men than in women, but an increased female prevalence in LRRK2-carriers has been described in the Ashkenazi Jewish population. We report an update about the frequency of major LRRK2 mutations in a large series of consecutive patients with Parkinsons disease (PD), including extensive characterization of clinical features. In particular, we investigated gender-related differences in motor and non-motor symptoms in the LRRK2 population. Methods 2976 unrelated consecutive Italian patients with degenerative Parkinsonism were screened for mutations on exon 41 (G2019S, I2020T) and a subgroup of 1190 patients for mutations on exon 31 (R1441C/G/H). Demographic and clinical features were compared between LRRK2-carriers and non-carriers, and between male and female LRRK2 mutation carriers. Results LRRK2 mutations were identified in 40 of 2523 PD patients (1.6%) and not in other primary parkinsonian syndromes. No major clinical differences were found between LRRK2-carriers and non-carriers. We found a novel I2020L missense variant, predicted to be pathogenic. Female gender was more common amongst carriers than non-carriers (57% vs. 40%; p = 0.01), without any gender-related difference in clinical features. Family history of PD was more common in women in the whole PD group, regardless of their LRRK2 status. Conclusions PD patients with LRRK2 mutations are more likely to be women, suggesting a stronger genetic load compared to idiopathic PD. Further studies are needed to elucidate whether there is a different effect of gender on the balance between genetic and environmental factors in the pathogenesis of PD.

Synchronization of reinforced stochastic processes with a network-based interaction

Randomly evolving systems composed by elements which interact among each other have always been of great interest in several scientific fields. This work deals with the synchronization phenomenon, that could be roughly defined as the tendency of different components to adopt a common behavior. We continue the study of a model of interacting stochastic processes with reinforcement, that recently has been introduced in Crimaldi et al. (2016, arXiv:1602.06217). Generally speaking, by reinforcement we mean any mechanism for which the probability that a given event occurs has an increasing dependence on the number of times that events of the same type occurred in the past. The particularity of systems of such stochastic processes is that synchronization is induced along time by the reinforcement mechanism itself and does not require a large-scale limit. We focus on the relationship between the topology of the network of the interactions and the long-time synchronization phenomenon. After proving the almost sure synchronization, we provide some CLTs in the sense of stable convergence that establish the convergence rates and the asymptotic distributions for both convergence to the common limit and synchronization. The obtained results lead to the construction of asymptotic confidence intervals for the limit random variable and of statistical tests to make inference on the topology of the network given the observation of the reinforced stochastic processes positioned at the vertices.

Central limit theorem for an adaptive randomly reinforced urn model

The generalized P\`olya urn (GPU) models and their variants have been investigated in several disciplines. However, typical assumptions made with respect to the GPU do not include urn models with diagonal replacement matrix, which arise in several applications, specifically in clinical trials. To facilitate mathematical analyses of models in these applications, we introduce an adaptive randomly reinforced urn model that uses accruing statistical information to adaptively skew the urn proportion toward specific targets. We study several probabilistic aspects that are important in implementing the urn model in practice. Specifically, we establish the law of large numbers and a central limit theorem for the number of sampled balls. To establish these results, we develop new techniques involving last exit times and crossing time analyses of the proportion of balls in the urn. To obtain precise estimates in these techniques, we establish results on the harmonic moments of the total number of balls in the urn. Finally, we describe our main results in the context an application to response-adaptive randomization in clinical trials. Our simulation experiments in this context demonstrate the ease and scope of our model.

Interacting generalized Friedman's urn systems

We consider systems of interacting Generalized Friedman’s Urns (GFUs) having irreducible mean replacement matrices. The interaction is modeled through the probability to sample the colors from each urn, that is defined as convex combination of the urn proportions in the system. From the weights of these combinations we individuate subsystems of urns evolving with different behaviors. We provide a complete description of the asymptotic properties of urn proportions in each subsystem by establishing limiting proportions, convergence rates and Central Limit Theorems. The main proofs are based on a detailed eigenanalysis and stochastic approximation techniques.

BarCamp: Technology Foresight and Statistics for the Future

Barcamp is quite a new event for the scientific and technological community. In full generality, it is an “unconference”, a meeting where everyone can contribute, presenting a topic and generating a discussion. In this paper, we propose the BarCamp as an innovative way of producing and communicating statistical knowledge, and we describe the experiment held at Politecnico di Milano, entitled “Technology Foresight and Statistics for the Future”.

Dynamics of an adaptive randomly reinforced urn

Adaptive randomly reinforced urn (ARRU) is a two-color urn model where the updating process is defined by a sequence of non-negative random vectors

Nonparametric covariate-adjusted response-adaptive design based on a functional urn model

\{(D_{1,n}, D_{2,n});n\geq1\}

Asymptotic Properties of an Adaptive Randomly Reinforced Urn Model

and randomly evolving thresholds which utilize accruing statistical information for the updates. Let

Randomly Reinforced Urn Designs Whose Allocation Proportions Converge to Arbitrary Prespecified Values

m_1=E[D_{1,n}]

Randomly reinforced urn designs with prespecified allocations

and