Claudio Giberti

We prime-encode the natural numbers via recursive factorisation, iterated to the exponents, generating a corpus of planar rooted trees equivalently represented as Dyck words. This forms a deterministic text endowed with internal rules. Statistical analysis of the corpus reveals that the dictionary and the entropy grow sublinearly, compression shows non-monotonic trend, and the rank-frequency curves assume a stable parabolic form deviating from Zipf's law. Correlation analysis using mean-squared displacement reveals a transition from normal diffusion to superdiffusion in the associated walk. These findings characterise the tree-encoded sequence as a statistically structured text with long-range correlations grounded in its generative arithmetic law, providing an empirical basis for subsequent theoretical and learnability

Background: The study aimed to compare the prognostic importance of the heart rate (HR) and QT—corrected (QTc) according to Fridericia, Framingham, and Bazett with respect to all-cause mortality in a large non-selected population. Methods: The analysis of digital electrocardiograms archived from 2008 to 2022 in the metropolitan area of Modena, Italy, was carried out. The population under study was divided into three groups based on age, and survival analysis was performed. Results: 131,627 patients were enrolled and, during the follow-up (mean 1641.4 days), all-cause mortality was 8.9%. Both HR and QTc were associated with mortality. All-cause mortality significantly increased with HR values greater than 81 BPM and QTc values greater than 440 msec in young subjects and 455 msec in old subjects (values of the 75th percentiles/optimal operating point). A Cox analysis confirmed the better prognostic value of Bazett’s QTc and HR in the whole population and in the three age-groups. Conclusion: Bazett’s method performed better than the others, but, unexpectedly, the HR had the same or an even better correlation with all-cause mortality. Since the HR is simple and readily available, its evaluation should be improved. However, QTC and HR values are difficult to define, causing many confounding factors, and further population studies are required.

Background: the study aimed at comparing the prognostic importance of Heart Rate (HR) and of QT corrected (QTc) according to Fridericia, Framingham and Bazett methods, in a large non-selected population. Methods: the analysis of digital Electrocardiograms archived from 2008 to 2022 in the metropolitan area of Modena, Italy, was made. The population under study was divided into three age-groups and survival analysis was performed. Results: 131.627 patients were enrolled and during the follow-up (mean 1641.4 days), all-cause mortality was 8.9%. Both HR and QTc were associated with mortality. All-cause mortality significantly increased from HR values greater than 81 BPM and from QTc values greater than 440 msec in young subjects and 455 msec in old subjects (values of the 75th percentiles/optimal operating point). Cox analysis confirmed the better prognostic value of Bazett’s QTc and of HR in the whole population and in the three age-groups. Conclusion: Bazett’s method performed better than other methods but unexpectedly HR had the same or a better correlation with all-cause mortality. Since HR is simple and readily available, its evaluation should be improved. However, reference values for QTc and for HR are difficult to define causing many confounding factors and further population-study are required.

Uphill diffusions constitute an intriguing phenomenon reported in a series of numerical simulations and experiments in which particles move from lower to higher density regions, at variance with the basic tenets of transport theory. In this paper we review several examples of uphill diffusions that appear in quite different frameworks. We highlight the role of the coupling with external reservoirs in the onset of particle currents with the ‘wrong’ sign, and also put forward a statistical mechanical explanation of the phenomenon for stochastic multi-species systems as well as for single-species models undergoing a phase transition.

Background: Previous studies have evaluated average electrocardiographic (ECG) values in healthy subjects or specific subpopulations. However, none have evaluated ECG average values in not selected populations, so we examined ECG changes with respect to age and sex in a large primary population. Methods: From digitized ECG stored from 2008 to 2021 in the Modena province, 130,471 patients were enrolled. Heart rate, P, QRS and T wave axis, P, QRS and T wave duration, PR interval, QTc, and frontal QRS-T angle were evaluated. Results: All ECG parameters showed a dependence on age, but only some of them with a straight-line correlation: QRS axis (p < 0.001, R² = 0.991, r = 0.996), PR interval (p < 0.001, R² = 0.978, r = 0.989), QTc (p < 0.001, R² = 0.935, r = 0.967), and, in over 51.5 years old, QRS-T angle (p < 0.001, R² = 0.979, r = 0.956). Differences between females and males and in different clinical settings were observed. Conclusions: ECG changes with ageing are explainable by intrinsic modifications of the heart and thorax and with the appearance of cardiovascular diseases and comorbidities. Age-related reference values were computed and applicable in clinical practice. Significant deviations from mean values and from Z-scores should be investigated.

Designing an order picking system can be very complex, as several interrelated control variables are involved. We address the sizing of the storage capacity of the picking bay, the crew of pickers, and the AGV fleet, which are the most important variables from a tactical viewpoint in a parts-to-pickers system. Although order picking is a widely explored topic in the literature, no analytical model that can simultaneously deal with these variables is currently available. To bridge this gap, we introduce a queue model for Markovian processes, which enables us to jointly optimise the aforementioned control variables. A discrete-event simulation is then used to validate our model, and we then test our proposal with real data under different operative scenarios, with the aim of assessing the usefulness of the proposal in real settings.

We consider spin models on complex networks frequently used to model social and technological systems. We study the annealed ferromagnetic Ising model for random networks with either independent edges (Erdős-Rényi) or prescribed degree distributions (configuration model). Contrary to many physical models, the annealed setting is poorly understood and behaves quite differently than the quenched system. In annealed networks with a fluctuating number of edges, the Ising model changes the degree distribution, an aspect previously ignored. For random networks with Poissonian degrees, this gives rise to three distinct annealed critical temperatures depending on the precise model choice, only one of which reproduces the quenched one. In particular, two of these annealed critical temperatures are finite even when the quenched one is infinite because then the annealed graph creates a giant component for all sufficiently small temperatures. We see that the critical exponents in the configuration model with deterministic degrees are the same as the quenched ones, which are the mean-field exponents if the degree distribution has finite fourth moment and power-law-dependent critical exponents otherwise. Remarkably, the annealing for the configuration model with random independent and identically distributed degrees washes away the universality class with power-law critical exponents.

In this paper, we study the annealed ferromagnetic Ising model on the configuration model. In an annealed system, we take the average on both sides of the ratio {defining the Boltzmann-Gibbs measure of the Ising model}. In the configuration model, the degrees are specified. Remarkably, when the degrees are deterministic, the critical value of the annealed Ising model is the same as that for the quenched Ising model. For independent and identically distributed (i.i.d.) degrees, instead, the annealed critical value is strictly smaller than that of the quenched Ising model. This identifies the degree structure of the underlying graph as the main driver for the critical value. Furthermore, in both contexts (deterministic or random degrees), we provide the variational expression for the annealed pressure. Interestingly, our rigorous results establish that only part of the heuristic conjectures in the physics literature were correct.