Riboli, A, Nardi, F, Osti, M, Cefis, Tesoro, G, and Mazzoni, S. Training load, official match locomotor demand, their association in top-class soccer players during a full competitive season. J Strength Cond Res 39(2): 249-259, 2025-To examine training load demands of season to evaluate association. Twenty-five competing UEFA international competitions were included. The was divided into 2 different categories: matches (M2) or 3 (M3) 8 days. Starters nonstarters classified. Total distance...

We consider a class of weakly interacting particle systems mean-field type. The interactions between the particles are encoded in graph sequence, i.e., two if and only they connected underlying graph. establish Law Large Numbers for empirical measure system that holds whenever sequence is convergent sense limits theory, to graphon. limit shown be solution non-linear Fokker-Planck equation weighted by (possibly random) graphon limit. In contrast with existing literature, our analysis focuses...

Metastability is a physical phenomenon ubiquitous in first order phase transitions. A fruitful mathematical way to approach this the study of rare transitions Markov chains. For Metropolis chains associated with Statistical Mechanics systems, has been described an elegant terms energy landscape Hamiltonian system. In paper, we provide similar description general setup. Beside their theoretical content, believe that our results are useful tool metastability for non--Metropolis systems such as...

We study the hitting times of Markov processes to target set $G$, starting from a reference configuration $x_0$ or its basin attraction. The can correspond bottom (meta)stable well, while $G$ could be either saddle (exit) points further configurations. Three types results are reported: (1) A general theory is developed, based on path-wise approach metastability, which has three important attributes. First, it in that does not assume reversibility process, focus only rare events and...

We consider the hard-core model with Metropolis transition probabilities on finite grid graphs and investigate asymptotic behavior of first hitting time between its two maximum-occupancy configurations in low-temperature regime. In particular, we show how order-of-magnitude this depends sizes boundary conditions by means a novel combinatorial method. Our analysis also proves exponentiality scaled yields mixing process limit as side-result. order to derive these results, extended...

We consider the Ising model on hexagonal lattice evolving according to Metropolis dynamics. study its metastable behavior in limit of vanishing temperature when system is immersed a small external magnetic field. determine asymptotic properties transition time from stable state up multiplicative factor and mixing spectral gap Markov process. give geometrical description critical configurations show how not only their size but shape varies depending thermodynamical parameters. Finally we...

We consider the ferromagnetic q-state Potts model on a finite grid with non-zero external field and periodic boundary conditions. The system evolves according to Glauber-type dynamics described by Metropolis algorithm, we focus low temperature asymptotic regime. analyze case of negative magnetic field. In this scenario, there are q − 1 stable configurations unique metastable state. describe behavior first hitting time from state set states as β → ∞ in probability, expectation, distribution....

Abstract This article highlights and evaluates the role of CEPI its contribution to global equitable access COVID-19 vaccines through established partnerships for vaccine development. The adds understanding how when such can work public health, especially under emergency citations.

We consider the ferromagnetic q-state Potts model on a finite grid graph with non-zero external field and periodic boundary conditions. The system evolves according to Glauber-type dynamics described by Metropolis algorithm, we focus low temperature asymptotic regime. analyze case of positive magnetic associated one spin value. In this energy landscape there is stable configuration q−1 metastable states. study behavior first hitting time from any state as β→∞ in probability, expectation,...

We study the asymptotic hitting time $\tau^{(n)}$ of a family Markov processes $X^{(n)}$ to target set $G^{(n)}$ when process starts from "trap" defined by very general properties. give an explicit description law conditioned stay within trap, and this we deduce exponential distribution $\tau^{(n)}$. Our approach is broad—it does not require reversibility, $G$ need be rare event traps limit on $n$ can nature—and leads bounds deviations exponentially. provide two nontrivial examples which our...

COVID-19 exposed major gaps in global, regional, state, and local responses to public health emergencies. In preparation for the WHA Special Session consider benefits of developing an international instrument on pandemic preparedness, O’Neill Institute partnership with Foundation National Institutes Health convened 30 world’s leading authorities global law, financing, biomedical science, implementation, emergency response along leaders from prominent organizations. This meeting was followed...

The problem of competitive nucleation in the framework probabilistic cellular automata is studied from dynamical point view. dependence metastability scenario on self-interaction discussed. An intermediate metastable phase, made two flip-flopping chessboard configurations, shows up depending ratio between magnetic field and self-interaction. A behavior similar to one stochastic Blume-Capel model with Glauber dynamics found.

This is the first in a series of three papers which we study two-dimensional lattice gas consisting two types particles subject to Kawasaki dynamics atlow temperature large finite box with an open boundary. Each pair particlesoccupying neighboring sites has negative binding energy provided their aredifferent, while each particle positive activation that depends onits type. There no between same type.At boundary are created and annihilated way thatrepresents presence infinite reservoir. We...