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We prove a result on the existence and uniqueness of the solution of a new feature-preserving nonlinear nonlocal diffusion equation for signal denoising for the one-dimensional case. The partial differential equation is based on a novel diffusivity coefficient that uses a nonlocal automatically detected parameter related to the local bounded variation and the local oscillating pattern of the noisy input signal.

The problem of detecting a major change point in a stochastic process is often of interest in applications, in particular when the effects of modifications of some external variables, on the process itself, must be identified. We here propose a modification of the classical Pearson $$\chi ^2$$ test to detect the presence of such major change point in the transition probabilities of an inhomogeneous discrete time Markov Chain, taking values in a finite space. The test can be applied also in presence of big identically distributed samples of the Markov Chain under study, which might not be necessarily independent. The test is based on the maximum likelihood estimate of the size of the ’right’ experimental unit, i.e. the units that must be aggregated to filter out the small scale variability of the transition probabilities. We here apply our test both to simulated data and to a real dataset, to study the impact, on farmland uses, of the new Common Agricultural Policy, which entered into force in EU in 2015.

Networks and graphs offer a suitable and powerful framework for studying the spread of infection in human and animal populations. In the case of a heterogeneous population, the social contact network has a pivotal role in the analysis of directly transmitted infectious diseases. The literature presents several works where network-based models encompass realistic features (such as contacts networks or host–pathogen biological data), but analytical results are nonetheless scarce. As a significant example, in this paper, we develop a multi-group version of the epidemiological SEIR population-based model. Each group can represent a social subpopulation with the same habits or a group of geographically localized people. We consider also heterogeneity in the weighting of contacts between two groups. As a simple application, we propose a simple control algorithm in which we optimize the connection weights in order to minimize the combination between an economic cost and a social cost. Some numerical simulations are also provided.

In this paper we introduce and study a new feature-preserving nonlinear nonlocal diffusion equation for denoising signals. The proposed partial differential equation is based on a novel diffusivity coefficient that uses a nonlocal automatically detected parameter related to the local bounded variation and the local oscillating pattern of the noisy input signal. We provide a mathematical analysis of the existence of the solution in the two dimensional case, but easily extensible to the one-dimensional model. Finally, we show some numerical experiments, which demonstrate the effectiveness of the new approach.

One major challenge in neuroscience is the identification of interrelations between signals reflecting neural activity and how information processing occurs in the neural circuits. At the cellular and molecular level, mechanisms of signal transduction have been studied intensively and a better knowledge and understanding of some basic processes of information handling by neurons has been achieved. In contrast, little is known about the organization and function of complex neuronal networks. Experimental methods are now available to simultaneously monitor electrical activity of a large number of neurons in real time. Then, the qualitative and quantitative analysis of the spiking activity of individual neurons is a very valuable tool for the study of the dynamics and architecture of the neural networks. Such activity is not due to the sole intrinsic properties of the individual neural cells but it is mostly the consequence of the direct influence of other neurons. The deduction of the effective connectivity between neurons, whose experimental spike trains are observed, is of crucial importance in neuroscience: first for the correct interpretation of the electro-physiological activity of the involved neurons and neural networks, and, for correctly relating the electrophysiological activity to the functional tasks accomplished by the network. In this work, we propose a novel method for the identification of connectivity of neural networks using recorded voltages. Our approach is based on the assumption that the network has a topology with sparse connections. After a brief description of our method, we will report the performances and compare it to the cross-correlation computed on the spike trains, which represents a gold standard method in the field.

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 first 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 significant 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 “low profile” compromise, the present analysis points to a strong effect of such rules on regions with high-intensity agriculture.

Taylor&rsquo, s law quantifies the scaling properties of the fluctuations of the number of innovations occurring in open systems. Urn-based modeling schemes have already proven to be effective in modeling this complex behaviour. Here, we present analytical estimations of Taylor&rsquo, s law exponents in such models, by leveraging on their representation in terms of triangular urn models. We also highlight the correspondence of these models with Poisson&ndash, Dirichlet processes and demonstrate how a non-trivial Taylor&rsquo, s law exponent is a kind of universal feature in systems related to human activities. We base this result on the analysis of four collections of data generated by human activity: (i) written language (from a Gutenberg corpus), (ii) an online music website (Last.fm), (iii) Twitter hashtags, (iv) an online collaborative tagging system (Del.icio.us). While Taylor&rsquo, s law observed in the last two datasets agrees with the plain model predictions, we need to introduce a generalization to fully characterize the behaviour of the first two datasets, where temporal correlations are possibly more relevant. We suggest that Taylor&rsquo, s law is a fundamental complement to Zipf&rsquo, s and Heaps&rsquo, laws in unveiling the complex dynamical processes underlying the evolution of systems featuring innovation.

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 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 $h\neq j$, of the other agents according to the entries of $W$. The best known example of reinforced stochastic process is the Pólya urn. ¶ The present paper focuses on the weighted empirical means $N_{n,j}=\sum_{k=1}^{n}q_{n,k}X_{k,j}$, 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 $\overline{X}^{j}=(\sum_{k=1}^{n}X_{k,j}/n)_{n}$ 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).

We present new properties for the Fractional Poisson process and the Fractional\ud Poisson field on the plane. A martingale characterization for Fractional Poisson\ud processes is given. We extend this result to Fractional Poisson fields, obtaining some\ud other characterizations. The fractional differential equations are studied. We consider\ud a more general Mixed-Fractional Poisson process and show that this process is the\ud stochastic solution of a system of fractional differential-difference equations. Finally,\ud we give some simulations of the Fractional Poisson field on the plane.

In this paper, we face the problem of simulating discrete random variables with general and varying distributions in a scalable framework, where fully parallelizable operations should be preferred. The new paradigm is inspired by the context of discrete choice models. Compared to classical algorithms, we add parallelized randomness, and we leave the final simulation of the random variable to a single associative operation. We characterize the set of algorithms that work in this way, and those algorithms that may have an additive or multiplicative local noise. As a consequence, we could define a natural way to solve some popular simulation problems., Comment: The first sections of the paper have been almost completely rewritten. A deep revision of the English has been made

In this study we investigated the performance of a computational pipeline for protein identification and label free quantification (LFQ) of LC–MS/MS data sets from experimental animal tissue samples, as well as the impact of its specific peptide search combinatorial approach. The full pipeline workflow was composed of peptide search engine adapters based on different identification algorithms, in the frame of the open‐source OpenMS software running within the KNIME analytics platform. Two different in silico tryptic digestion, database‐search assisted approaches (X!Tandem and MS‐GF+), de novo peptide sequencing based on Novor and consensus library search (SpectraST), were tested for the processing of LC‐MS/MS raw data files obtained from proteomic LC‐MS experiments done on proteolytic extracts from mouse ex vivo liver samples. The results from proteomic LFQ were compared to those based on the application of the two software tools MaxQuant and Proteome Discoverer for protein inference and label‐free data analysis in shotgun proteomics. Data are available via ProteomeXchange with identifier PXD025097.

Twitter is among the most used online platforms for the political communications, due to the concision of its messages (which is particularly suitable for political slogans) and the quick diffusion of messages. Especially when the argument stimulate the emotionality of users, the content on Twitter is shared with extreme speed and thus studying the tweet sentiment if of utmost importance to predict the evolution of the discussions and the register of the relative narratives. In this article, we present a model able to reproduce the dynamics of the sentiments of tweets related to specific topics and periods and to provide a prediction of the sentiment of the future posts based on the observed past. The model is a recent variant of the P\'olya urn, introduced and studied in arXiv:1906.10951 and arXiv:2010.06373, which is characterized by a "local" reinforcement, i.e. a reinforcement mechanism mainly based on the most recent observations, and by a random persistent fluctuation of the predictive mean. In particular, this latter feature is capable of capturing the trend fluctuations in the sentiment curve. While the proposed model is extremely general and may be also employed in other contexts, it has been tested on several Twitter data sets and demonstrated greater performances compared to the standard P\'olya urn model. Moreover, the different performances on different data sets highlight different emotional sensitivities respect to a public event., Comment: 19 pages, 12 figures

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.

Observations which are realizations from some continuous process are frequent in sciences, engineering, economics, and other fields. We consider linear models, with possible random effects, where the responses are random functions in a suitable Sobolev space. The processes cannot be observed directly. With smoothing procedures from the original data, both the response curves and their derivatives can be reconstructed, even separately. From both these samples of functions, just one sample of representatives is obtained to estimate the vector of functional parameters. A simulation study shows the benefits of this approach over the common method of using information either on curves or derivatives. The main theoretical result is a strong functional version of the Gauss-Markov theorem. This ensures that the proposed functional estimator is more efficient than the best linear unbiased estimator based only on curves or derivatives., the best information from the two samples of functions and derivatives: a strong version of the Gauss-Markov theorem. Relaxed an hidden hypothesis on linear independence of the Riesz representation of the Karhunen-Loeve base

This paper develops a new mathematical-statistical approach to analyze a class of Flajolet-Martin algorithms (FMa), and provides analytical confidence intervals for the number F0 of distinct elements in a stream, based on Chernoff bounds. The class of FMa has reached a significant popularity in bigdata stream learning, and the attention of the literature has mainly been based on algorithmic aspects, basically complexity optimality, while the statistical analysis of these class of algorithms has been often faced heuristically. The analysis provided here shows deep connections with mathematical special functions and with extreme value theory. The latter connection may help in explaining heuristic considerations, while the first opens many numerical issues, faced at the end of the present paper. Finally, the algorithms are tested on an anonymized real data stream and MonteCarlo simulations are provided to support our analytical choice in this context., accepted version

In this paper we study periodical stochastic processes, and we define the conditions that are needed by a model to be a good noise model on the circumference. The classes of processes that fit the required conditions are studied together with their expansion in random Fourier series in order to provide results about their path regularity. Finally, we discuss a simple and flexible parametric model with prescribed regularity that is used in applications, and we prove the asymptotic properties of the maximum likelihood estimates of model parameters., 24pp, final version; the final publication is available at http://www.ism.ac.jp/editsec/aism/

This paper studies the effect of agri-environmental measures (AEMs) in improving greener farming practices. We focus on the quantification of the effectiveness of AEMs implemented in the Rural Development Programme of the Lombardy Region, during the 2007–2013 programming period. Our work attempts to address the well-known potential failures of these kinds of policy instruments – such as adverse selection effects – by relying on an innovative matching procedure, the coarsened exact matching (CEM). This methodology presents a number of interesting properties that are worth considering in policy-evaluation analyses. Our empirical analysis focuses on three AEM schemes protecting and enhancing the environment, Crops diversification, Grassland maintenance and Organic farming. Overall, our results suggest that AEMs were apparently effective in improving the farms’ environmental performances. However, our preliminary cost-benefit analysis highlights that the costs of implementing this policy, when compared to the additional results obtained, tend to be quite large.

Background The training of midwives is critical in order to acquire the professional skills necessary in the support of breastfeeding. The use of tools that demonstrate student competency in the field of midwifery is fundamental. Objectives The aim for this study was to translate and apply a questionnaire to an Italian cohort of students – determining their self-efficacy and establishing the validity of the tool collectively. Design This study was a descriptive cross-sectional study. Setting The study was conducted at a large university in northern Italy. Participants Seventy-six female students from the Midwifery Degree Course. Methods The questionnaire translated into Italian was administered to students participating in a Midwifery Degree Course. Rasch analysis was applied using ConQuest software, version 4. Results Seventy-six questionnaires were collected. Fifty-six questionnaires have modal value 3 of the Likert response scale (It's easy for me to do it), 17 have a mode of 4 (It's very easy for me to do it), 3 of 2 (It's difficult for me to do it) and no questionnaire of 1 (It's very difficult for me to do it). A questionnaire identified the perception of self-efficacy of midwifery students in assisting breastfeeding mothers. Conclusion The results of this research demonstrate that students of midwifery consider themselves competent when assisting breast feeding mothers.

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 $\{(D_{1,n}, D_{2,n});n\geq1\}$ and randomly evolving thresholds which utilize accruing statistical information for the updates. Let $m_1=E[D_{1,n}]$ and $m_2=E[D_{2,n}]$. Motivated by applications, in this paper we undertake a detailed study of the dynamics of the ARRU model. First, for the case $m_1 \neq m_2$, we establish $L_1$ bounds on the increments of the urn proportion at fixed and increasing times under very weak assumptions on the random threshold sequence. 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 $m_1$ and $m_2$. Specifically, we show that when $m_1=m_2$ the proportion converges to a non-degenerate random variable. Third, we establish the asymptotic distribution, after appropriate centering and scaling, of the proportion of sampled balls in the case $m_1=m_2$. In the process, we settle the issue of asymptotic distribution of the number of sampled balls 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., Comment: arXiv admin note: text overlap with arXiv:1502.06130

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.

This work deals with systems 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 evolving 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 elements of $W$. ¶ Asymptotic results for the stochastic processes of the personal inclinations $Z^{j}=(Z_{n,j})_{n}$ have been subject of studies in recent papers (e.g., Aletti, Crimaldi and Ghiglietti [Ann. Appl. Probab. 27 (2017) 3787–3844], Crimaldi et al. [Synchronization and functional central limit theorems for interacting reinforced random walks (2019)]); while the asymptotic behavior of quantities based on the stochastic processes $X^{j}$ of the actions has never been studied yet. In this paper, we fill this gap by characterizing the asymptotic behavior of the empirical means $N_{n,j}=\sum_{k=1}^{n}X_{k,j}/n$, proving their almost sure synchronization and some central limit theorems in the sense of stable convergence. Moreover, we discuss some statistical applications of these convergence results concerning confidence intervals for the random limit toward which all the processes of the system almost surely converge and tools to make inference on the matrix $W$.