First--order continuous models of opinion formation

We study certain nonlinear continuous models of opinion formation derived from a kinetic description involving exchange of opinion between individual agents. These models imply that the only possible final opinions are the extremal ones, and are similar to models of pure drift in magnetization. Both analytical and numerical methods allow to recover the final distribution of opinion between the two extremal ones.Comment: 17 pages, 4 figure

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

In this paper we propose a general class of covariate-adjusted response-adaptive (CARA) designs based on a new functional urn model. We prove strong consistency concerning the functional urn proportion and the proportion of subjects assigned to the treatment groups, in the whole study and for each covariate profile, allowing the distribution of the responses conditioned on covariates to be estimated nonparametrically. In addition, we establish joint central limit theorems for the above quantities and the sufficient statistics of features of interest, which allow to construct procedures to make inference on the conditional response distributions. These results are then applied to typical situations concerning Gaussian and binary responses

Interacting Generalized Pólya Urn Systems

We consider a system of interacting Generalized P\'olya Urns (GPUs) 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

A K-means clustering algorithm for multivariate big data with correlated components

Common clustering algorithms require multiple scans of all the data to achieve convergence, and this is prohibitive when large databases, with millions of data, must be processed. Some algorithms to extend the popular K-means method to the analysis of big data are present in literature since the publication of (Bradley et al, Scaling clustering algorithms to large databases, 1998) but they assume that the random vectors which are processed and grouped have uncorrelated components. Unfortunately this is not the case in many practical situations. We here propose an extension of the algorithm of Bradley, Fayyad and Reina to the processing of massive multivariate data, having correlated components

A clustering algorithm for multivariate big data with correlated components=Un algoritmo di clustering per big data multivariati con componenti correlate

I comuni algoritmi di clustering richiedono di esaminare piu volte tutti i ` dati per raggiungere la convergenza, e cio risulta proibitivo quando devono essere ` analizzati database enormi, con milioni di dati. In letteratura sono presenti fin dal 1998 [1] alcuni algoritmi che estendono il popolare metodo K-medie all\u2019analisi di big data, ma essi assumono che i vettori aleatori che vengono analizzati e raggruppati abbiano componenti non correlate. Purtroppo tale condizione non e soddisfat- ` ta in molti casi pratici. Qui proponiamo un\u2019estensione dell\u2019algoritmo di Bradley, Fayyad e Reina all\u2019analisi di grandi moli di dati multivariati, con componenti correlate fra loro.Common clustering algorithms require multiple scans of all the data to achieve convergence, and this is prohibitive when large databases, with millions of data, must be processed. Some algorithms to extend the popular K-means method to the analysis of big data are present in literature since 1998, but they assume that the random vectors which are processed and grouped have uncorrelated components. Unfortunately this is not the case in many practical situations. We here propose an extension of the algorithm of Bradley, Fayyad and Reina to the processing of massive multivariate data, having correlated components

Farmland Use Transitions After the CAP Greening: a Preliminary Analysis Using Markov Chains Approach

This paper represents a preliminary attempt to evaluate ex-post impact of the CAP greening payment on farmland use changes, testing by a Markov Chain approach whether farmland use transitions dynamics changed after the introduction of this new policy instrument. Unlike previous contributions, relying on ex-ante simulations, this analysis is based on the actual behaviour of farmers over the period immediately after the last CAP reform. Such ex-post assessment was based on real georeferenced data on farmland allocation, collected in the Lombardy Region, in Northern Italy, over the period 2011-2016. As the current CAP has recently entered in force (in 2015), the present analysis covers the \ufb01rst two years of implementation of the new rules along with the previous four years. Results are in line with previous ex-ante simulations in the same region, detecting a deep discontinuity for those farmland uses characterised by monoculture before the introduction of the greening. They show a signi\ufb01cant discontinuity of farmland use transitions in the reference area after the introduction of greening rules, pointing to a decrease in maize monoculture, in favour of other cereals and legume crops like soybean and alfalfa. Unlike some critical opinions that see current greening rules as a \u201clow pro\ufb01le\u201d compromise, the present analysis points to a strong e\ufb00ect of such rules on regions with high-intensity agriculture

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 {(D1,n, D2,n); n 65 1} and randomly evolving thresholds which utilize accruing statistical information for the updates. Let m1 = E[D1,n] and m2 = E[D2,n]. In this paper we undertake a detailed study of the dynamics of the ARRU model. First, for the case m1 6= m2, we establish L1 bounds on the increments of the urn proportion, i.e. the proportion of ball colors in the urn, at fixed and increasing times under very weak assumptions on the random threshold sequences. As a consequence, we deduce weak consistency of the evolving urn proportions. Second, under slightly stronger conditions, we establish the strong consistency of the urn proportions for all finite values of m1 and m2. Specifically we show that when m1 = m2, the proportion converges to a non-degenerate random variable. Third, we establish the asymptotic distribution, after appropriate centering and scaling, for the proportion of sampled ball colors and urn proportions for the case m1 = m2. In the process, we resolve the issue concerning the asymptotic distribution of the proportion of sampled ball colors for a randomly reinforced urn (RRU). To address the technical issues, we establish results on the harmonic moments of the total number of balls in the urn at different times under very weak conditions, which is of independent interest

The Experts Method for the prediction of periodic multivariate time series of high dimension = Il Metodo degli Esperti per la previsione di serie temporali multivariate e periodiche, di dimensione elevata

In questo lavoro viene proposto un metodo, detto Metodo degli Esperti, per predire l\u2019evoluzione di un insieme multivariato e di grosse dimensioni di serie temporali. Il metodo e basato sulla definizione di un insieme di \u201desperti\u201d, ovvero \ub4 di porzioni, di un training set delle serie temporali considerate, che approssimano al meglio i dati che precedono quelli che devono essere previsti. Viene utilizzata una opportuna combinazione di decomposizioni ai valori singolari per filtrare il rumore, e fornire previsioni robuste. Il vantaggio di questo metodo, rispetto ai classici metodi di analisi di serie temporali multivariate, e che esso pu \ub4 o essere applicato \ub4 anche quando l\u2019ordine con cui le serie sono registrate nelle colonne del dataset, viene scambiato di tanto in tanto.We propose a method, called Experts Method, to predict the evolution of a high dimensional multivariate set of time series. The method is based on the definition of a set of \u201dexperts\u201d, which are portions of a training set of the considered time series which best fit the data immediately preceding those to be predicted. A suitable combination of Singular Value Decompositions is used to filter out the noise, and provide robust predictions. The advantage of this method, if compared with classical multivariate time series analysis, is that it can be applied also when the time series column order is reshuffled, from time to time, in the collected dataset

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 $X^j=(X_n,j)_n$ is located at a vertex $j$ of a finite weighted direct 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 $h\neq j$, 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 characterizes the asymptotic behavior of the weighted empirical means $N_n,j=\sum_k=1^n q_n,k X_k,j$, proving their almost sure synchronization and some central limit theorems in the sense of stable convergence. By means of a more sophisticated decomposition of the considered processes adopted here, these findings complete and improve some asymptotic results for the personal inclinations $Z^j=(Z_n,j)_n$ and for the empirical means \overlineX^j=(\sum_k=1^n X_k,j/n)_n given in recent papers (e.g. [arXiv:1705.02126, Bernoulli, Forth.]; [arXiv:1607.08514, Ann. Appl. Probab., 27(6):3787-3844, 2017]; [arXiv:1602.06217, Stochastic Process. Appl., 129(1):70-101, 2019]). Our work is motivated by the aim to understand how the different rates of convergence of the involved stochastic processes combine and, from an applicative point of view, by the construction of confidence intervals for the common limit inclination of the agents and of 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 [arXiv:1705.02126, Bernoulli, Forth.

Fast wide-volume functional imaging of engineered in vitro brain tissues

The need for in vitro models that mimic the human brain to replace animal testing and allow high-throughput screening has driven scientists to develop new tools that reproduce tissue-like features on a chip. Three-dimensional (3D) in vitro cultures are emerging as an unmatched platform that preserves the complexity of cell-to-cell connections within a tissue, improves cell survival, and boosts neuronal differentiation. In this context, new and flexible imaging approaches are required to monitor the functional states of 3D networks. Herein, we propose an experimental model based on 3D neuronal networks in an alginate hydrogel, a tunable wide-volume imaging approach, and an efficient denoising algorithm to resolve, down to single cell resolution, the 3D activity of hundreds of neurons expressing the calcium sensor GCaMP6s. Furthermore, we implemented a 3D co-culture system mimicking the contiguous interfaces of distinct brain tissues such as the cortical-hippocampal interface. The analysis of the network activity of single and layered neuronal co-cultures revealed cell-type-specific activities and an organization of neuronal subpopulations that changed in the two culture configurations. Overall, our experimental platform represents a simple, powerful and cost-effective platform for developing and monitoring living 3D layered brain tissue on chip structures with high resolution and high throughput