Introduction Practicing physical activity (PA) on a regular basis is an important support for people with type 1 diabetes (T1D). However, exercise may induce in them hypoglycaemic events during or after it. One major consequence of this is that, to limit this risk, many people with T1D tend to avoid performing PA. The availability of modern continuous glucose-monitoring (CGM) devices is potentially a great asset for reducing the chances of hypoglycaemia (HP) due to PA. Several algorithms have already been proposed to predict HP in subjects with T1D. However, not many of them are specifically focused on HP induced by exercise. Among those, many involve a large number of covariates making the applicability more difficult, and none uses CGM values available during the training session. Objectives We study the problem of predicting hypoglycaemia events in subjects with T1D during PA. The final aim is to produce algorithms enabling a person with T1D to perform a planned PA session without experiencing HP. Method One of the two algorithms we developed uses the CGM data in an initial part of a PA session. A parametric model is fitted to the data and then used to predict a possible HP during the remaining part of the session. Our second algorithm uses the CGM value at the start of a session. It also relies on statistical information about the average rate of decrease of the aforementioned model, as derived from a previously measured CGM data during PA. Then, the algorithm estimates the probability of HP during the planned PA session. Both algorithms have a very simple structure and therefore are of wide applicability. Results The application of the two algorithms to a very large dataset shows their very good ability to predict HP during PA in people with T1D.

Objectives: Cardiovascular diseases (CVDs) represent a major risk for people with type 1 diabetes (T1D). Our aim here is to develop a new methodology that overcomes some of the problems and limitations of existing risk calculators. First, they are rarely tailored to people with T1D and, in general, they do not deal with missing values for any risk factor. Moreover, they do not take into account information on risk factors dependencies, which is often available from medical experts. Method: This study introduces a Bayesian Belief Network (BBN) model to quantify CVD risk in individuals with T1D. The developed methodology is applied to a large T1D dataset and its performances are assessed. A simulation study is also carried out to quantify the parameter estimation properties. Results: The performances of individual risk estimation, as measured by the area under the ROC curve and by the C-index, are about 0.75 for both real and simulated data with comparable sample sizes. Conclusions: We observe a good predictive ability of the proposed methodology with accurate parameter estimation. The BBN approach takes into account causal relationships between variables, providing a comprehensive description of the system. This makes it possible to derive useful tools for optimising intervention.

Future occurrence of a disease can be highly influenced by some specific risk factors. This work presents a comprehensive approach to quantify the event probability as a function of each separate risk factor by means of a parametric model. The proposed methodology is mainly described and applied here in the case of a linear model, but the non-linear case is also addressed. To improve estimation accuracy, three distinct methods are developed and their results are integrated. One of them is Bayesian, based on a non-informative prior. Each of the other two, uses aggregation of sample elements based on their factor values, which is optimized by means of a different specific criterion. For one of these two, optimization is performed by Simulated Annealing. The methodology presented is applicable across various diseases but here we quantify the risk for cardiovascular diseases in subjects with type 1 diabetes. The results obtained combining the three different methods show accurate estimates of cardiovascular risk variation rates for the factors considered. Furthermore, the detection of a biological activation phenomenon for one of the factors is also illustrated. To quantify the performances of the proposed methodology and to compare them with those from a known method used for this type of models, a large simulation study is done, whose results are illustrated here.

Background: The high contagiousness and rapid spreading of the coronavirus disease 2019 (COVID-19) has caused a high number of critical to severe life-threatening cases, which required urgent hospital admission and treatment in intensive care units (ICUs). The pandemic has been a tough test for all European national health systems and their capability to provide an adequate reaction. Methods: The present work aims to reveal correlations between parameters such as COVID-19 incidence, ICU bed occupancy, ICU excess area, and mortality in Italian regions. Public data for the period of March 1 to July 16, 2020, were analyzed using several mathematical and statistical methods. Results: The analysis defined two separate groups of Italian regions. The examined variables considered within these groups were interlinked and dependent on each other. The regions of the two groups shared the same kind of fitted model (linear) explaining mortality as a function of cumulative incidence, but with higher value of the constant in one group, so characterized by a high intrinsic "strength" of the pandemic, certainly playing a major role in the generation of a large number of severe and life-threatening cases. These results are confirmed at European level. Other factors may condition mortality and be linked to incidence, such as ICU saturation and excess. Conclusions: These quantitative results could be a very helpful tool to set up preventive measures and optimize biomedical interventions before the pandemic, in its recurrent waves, could overcome the reaction capacity of any public health system.

(1) Background: A better understanding of COVID-19 dynamics in terms of interactions among individuals would be of paramount importance to increase the effectiveness of containment measures. Despite this, the research lacks spatiotemporal statistical and mathematical analysis based on large datasets. We describe a novel methodology to extract useful spatiotemporal information from COVID-19 pandemic data. (2) Methods: We perform specific analyses based on mathematical and statistical tools, like mathematical morphology, hierarchical clustering, parametric data modeling and non-parametric statistics. These analyses are here applied to the large dataset consisting of about 19,000 COVID-19 patients in the Veneto region (Italy) during the entire Italian national lockdown. (3) Results: We estimate the COVID-19 cumulative incidence spatial distribution, significantly reducing image noise. We identify four clusters of connected provinces based on the temporal evolution of the incidence. Surprisingly, while one cluster consists of three neighboring provinces, another one contains two provinces more than 210 km apart by highway. The survival function of the local spatial incidence values is modeled here by a tapered Pareto model, also used in other applied fields like seismology and economy in connection to networks. Model's parameters could be relevant to describe quantitatively the epidemic. (4) Conclusion: The proposed methodology can be applied to a general situation, potentially helping to adopt strategic decisions such as the restriction of mobility and gatherings.

SARS-CoV-2 is highly contagious, rapidly turned into a pandemic, and is causing a relevant number of critical to severe life-threatening COVID-19 patients. However, robust statistical studies of a large cohort of patients, potentially useful to implement a vaccination campaign, are rare. We analyzed public data of about 19,000 patients for the period 28 February to 15 May 2020 by several mathematical methods. Precisely, we describe the COVID-19 evolution of a number of variables that include age, gender, patient's care location, and comorbidities. It prompts consideration of special preventive and therapeutic measures for subjects more prone to developing life-threatening conditions while affording quantitative parameters for predicting the effects of an outburst of the pandemic on public health structures and facilities adopted in response. We propose a mathematical way to use these results as a powerful tool to face the pandemic and implement a mass vaccination campaign. This is done by means of priority criteria based on the influence of the considered variables on the probability of both death and infection.

We report on the Covid-19 epidemic in Italy in relation to the extraordinary measures implemented by the Italian Government between the 24th of February and the 12th of March. We analysed the Covid-19 cumulative incidence (CI) using data from the 1st to the 31st of March. We estimated that in Lombardy, the worst hit region in Italy, the observed Covid-19 CI diverged towards values lower than the ones expected in the absence of government measures approximately 7-10 days after the measures implementation. The Covid-19 CI growth rate peaked in Lombardy the 22nd of March and in other regions between the 24th and the 27th of March. The CI growth rate peaked in 87 out of 107 Italian provinces on average 13.6 days after the measures implementation. We projected that the CI growth rate in Lombardy should substantially slow by mid-May 2020. Other regions should follow a similar pattern. Our projections assume that the government measures will remain in place during this period. The evolution of the epidemic in different Italian regions suggests that the earlier the measures were taken in relation to the stage of the epidemic, the lower the total cumulative incidence achieved during this epidemic wave. Our analyses suggest that the government measures slowed and eventually reduced the Covid-19 CI growth where the epidemic had already reached high levels by mid-March (Lombardy, Emilia-Romagna and Veneto) and prevented the rise of the epidemic in regions of central and southern Italy where the epidemic was at an earlier stage in mid-March to reach the high levels already present in northern regions. As several governments indicate that their aim is to "push down" the epidemic curve, the evolution of the epidemic in Italy supports the WHO recommendation that strict containment measures should be introduced as early as possible in the epidemic curve.

The crack density within a fault's damage zone is thought to vary as seismic rupture is approached, as well as in the postseismic period. Moreover, external stress loads, seasonal or tidal, may also change the crack density in rocks, and all such processes can leave detectable signatures on seismic attenuation. Here we show that attenuation time histories from the San Andreas Fault at Parkfield are affected by seasonal loading cycles, as well as by 1.5-3-year periodic variations of creep rates, consistent with Turner et al. (2015, https://biblioproxy.cnr.it:2481/10.1002/2015JB011998), who documented a broad spectral peak, between 1.5 and 4 years, of the spectra calculated over the activity of repeating earthquakes, and over InSAR time series. After the Parkfield main shock, we see a clear modulation between seismic attenuation correlated to tidal forces. Opposite attenuation trends are seen on the two sides of the fault up to the M6.5 2003 San Simeon earthquake, when attenuation changed discontinuously, in the same directions of the relative trends. Attenuation increased steadily of over one year on the SW side of the San Andreas Fault, until the San Simeon earthquake, whereas it decreased steadily on the NE side of the San Andreas Fault, roughly for the six months prior to the event. Random fluctuations are observed up to the 2004 M6 Parkfield main shock, when rebounds in opposite directions are observed, in which attenuation decreased on the SW side, and increased on the NE side.

During the seismic cycle, in nature and as well as in lab samples, the crack density of rocks varies substantially, as stressed rocks approach a critical state and eventually fail (Vasseur et al, 2017; Nur, 1972; Gupta, 1973) . At Earth scales, small periodical stress variations such as seasonal loading/unloading and tides (Johnson_etal_2017) are constantly being superimposed on the tectonic loading stress of crustal rocks, inducing periodic changes in crack porosity, pore-fluid pressure, and saturation, that should leave a signature on crustal attenuation. However, results from seismic techniques applied thus far have been too noisy, or lacked sufficient resolution, to yield meaningful measurements. Here we use a new technique that shows that seismic attenuation on the creeping section of the San Andreas Fault (SAF) at Parkfield is modulated by recognizable periodicities mostly due to tides, as well as to longer period fluctuations in creep rates (between 1.5 and 3-4 years) that have been previously observed (Nadeau sensitive to periodic stress perturbations well below 100 Pa, more than one order of magnitude smaller than the largest of all periodic stress fluctuations, due to water/snow loading/unloading (Johnson earthquake, we observe changes in anelastic attenuation on both sides of the SAF. and McEvilly, 2004; Turner et al., 2015) . Our analysis is et al., 2017) . Before and after the 2004 M6 Parkfield main Frequency-dependent precursors with opposite signs are seen on the two sides of the fault, reflecting the fact that prior to the earthquake, the Pacific side of the SAF was under decreasing compressional stress, whereas the North-American side of the fault was experiencing increasing compression. Coseismic and post-seismic stress relaxation cause anomalies of opposite signs on the two sides of the SAF at Parkfield, opposite to the pre-seismic ones. Due to rock damage, pre-2008 fluctuations show enhanced sensitivity to seasonal stresses and solid tides (Gao eta., 2000) , with amplitudes modulated by decreasing slip rate through healing. Post-2008 fluctuations indicate close-to-fault medium healing.

During the last 20 years, three seismic sequences affected the Apenninic belt (central Italy): Colfiorito (1997-98), L'Aquila (2009) and Amatrice Visso-Norcia Campotosto (2016-17). They lasted for a long time, with a series of moderate-to-large earthquakes distributed over 40-60 km long Apenninic-trending segments. Their closeness in space and time suggested to study their aftershock sequences to highlight similarities and differences. Aftershock space migration and the distribution of aftershock inter-arrival time were studied. Mathematical Morphology and nonparametric statistics were applied to reduce the effect of spatial noise. Parametric analysis in time domain and spectral analysis were performed. Two different types of aftershock sequences were found. The L'Aquila sequence presented a continuous and periodic temporal variation (period ? 120 days) of aftershock activity centre along the sequence axis, while the other two sequences showed a piecewise continuous pattern and a shorter duration. We also found two different types of temporal evolution of the mean radial distance between the aftershock ipocentres and the one of a reference event corresponding to the start of a large and fast increase of daily energy release. One type was well described by a simple exponential model, while a power-law model was more appropriate for the other one. Furthermore, in the first case, the aftershock inter-arrival time were very well fitted by an exponential model, while noticeable deviations were present in the other case. A possible explanation was provided in terms of the local geological and hydrogeological properties, which depend on the region location w.r.t. the Ancona-Anzio tectonic lineament.

We propose a new iterative procedure to find the best time for re-initialization of meta-heuristic algorithms to solve combinatorial optimization problems. The sequence of algorithm executions with different random inizializations evolves at each iteration by either adding new independent executions or extending all existing ones up to the current maximum execution time. This is done on the basis of a criterion that uses a surrogate of the algorithm failure probability, where the optimal solution is replaced by the best so far one. Therefore, the new procedure can be applied in practice. We prove that, with probability one, the maximum time of current executions of the proposed procedure approaches, as the number of iterations diverges, the optimal value minimizing the expected time to find the solution. We apply the new procedure to several Traveling Salesman Problem instances with hundreds or thousands of cities, whose solution is known, and to some instances of a pseudo-Boolean problem. As base algorithm, we use different versions of an Ant Colony Optimization algorithm or a Genetic Algorithm. We compare the results from the proposed procedure with those from the base algorithm. This comparison shows that the failure probability estimated values of the new procedure are several orders of magnitude lower than those of the base algorithm for equal computation cost.

We propose a version of the pure temporal epidemic type aftershock sequences (ETAS) model: the ETAS model with correlated magnitudes. As for the standard case, we assume the Gutenberg-Richter law to be the probability density for the magnitudes of the background events. Instead, the magnitude of the triggered shocks is assumed to be probabilistically dependent on that of the relative mother events. This probabilistic dependence is motivated by some recent works in the literature and by the results of a statistical analysis made on some seismic catalogs [Spassiani and Sebastiani, J. Geophys. Res. 121, 903 (2016)10.1002/2015JB012398]. On the basis of the experimental evidences obtained in the latter paper for the real catalogs, we theoretically derive the probability density function for the magnitudes of the triggered shocks proposed in Spassiani and Sebastiani and there used for the analysis of two simulated catalogs. To this aim, we impose a fundamental condition: averaging over all the magnitudes of the mother events, we must obtain again the Gutenberg-Richter law. This ensures the validity of this law at any event's generation when ignoring past seismicity. The ETAS model with correlated magnitudes is then theoretically analyzed here. In particular, we use the tool of the probability generating function and the Palm theory, in order to derive an approximation of the probability of zero events in a small time interval and to interpret the results in terms of the interevent time between consecutive shocks, the latter being a very useful random variable in the assessment of seismic hazard.

The distribution of the magnitudes of seismic events is generally assumed to be independent on past seismicity. However, by considering events in causal relation, for example, mother-daughter, it seems natural to assume that the magnitude of a daughter event is conditionally dependent on one of the corresponding mother events. In order to find experimental evidence supporting this hypothesis, we analyze different catalogs, both real and simulated, in two different ways. From each catalog, we obtain the law of the magnitude of the triggered events by kernel density. The results obtained show that the distribution density of the magnitude of the triggered events varies with the magnitude of their corresponding mother events. As the intuition suggests, an increase of the magnitude of the mother events induces an increase of the probability of having high values of the magnitude of the triggered events. In addition, we see a statistically significant increasing linear dependence of the magnitude means.

In this paper, we study two earthquakes: the April 6th 2009 earthquake of L'Aquila in the re-gion of Abruzzo (Italy) and the 1997 Colfiorito earthquake in the regions of Umbria and Marche (Italy). The data sets of these two earthquakes were analysed in both time and space domains. For time domain we used statistical methods and models both parametric and non-parametric. Concerning the space domain, we used Mathe-matical Morphology filters. The time domain analysis provides evidence of a possible corre-lation between seismic activities and the tides of the crust of the Earth. The results obtained show evidence that the daily number of earthquakes of the sequences proceeding and following the April 6th 2009 earthquake of L'Aquila and that of the sequence following the 1997 Colfiorito earth-quake have a periodic component of occurrence with period of about 7 days. It seems that the maxima of this component occur at a position of the Moon with respect to the Earth and the Sun corresponding to approximately 3 days before the four main Moon phases. The space domain analysis indicates that the foreshock activity in both earthquakes is clustered and concentrated. Furthermore, in each of the two earthquakes the clusters are located at about 3 kilometers from the epicentre of the main shock.

Design/methodology/approach - The method relies on alternation of identification of the active genes using a mixture model and clustering of the samples based on Ward hierarchical clustering. The initial-point of the procedure is obtained by means of a ?2 test. The method attempts to locally minimize the sum of the within cluster sample variances under a suitable Gaussian assumption on the distribution of data. Findings - This paper illustrates the proposed methodology and its success by means of results from both simulated and real cDNA microarray data. The comparison of the results with those from a related known method demonstrates the superiority of the proposed approach. Research limitations/implications - Only empirical evidence of algorithm convergence is provided. Theoretical proof of algorithm convergence is an open issue. Practical implications - The proposed methodology can be applied to perform cDNA microarray data analysis. Originality/value - This paper provides a contribution to the development of successful statistical methods for cDNA microarray data analysis.

In Fricke-agarose gels, an accurate determination of the spatial dose distribution is hindered by the diffusion of ferric ions. In this work, a model was developed to describe the diffusion process within gel samples of finite length and, thus, permit the reconstruction of the initial spatial distribution of the ferric ions. The temporal evolution of the ion concentration as a function of the initial concentration is derived by solving Fick's second law of diffusion in two dimensions with boundary reflections. The model was applied to magnetic resonance imaging data acquired at high spatial resolution (0.3 mm) and was found to describe accurately the observed diffusion effects.