We have studied a model of a complex fluid consisting of particles interacting through a hard-core and short-range attractive potential of both Yukawa and square-well form. Using a hybrid method, including a self-consistent and quite accurate approximation for the liquid integral equation in the case of the Yukawa fluid, perturbation theory to evaluate the crystal free energies, and mode-coupling theory of the glass transition, we determine both the equilibrium phase diagram of the system and the lines of equilibrium between the supercooled fluid and the glass phases. For these potentials, we study the phase diagrams for different values of the potential range, the ratio of the range of the interaction to the diameter of the repulsive core being the main control parameter. Our arguments are relevant to a variety of systems, from dense colloidal systems with depletion forces, through particle gels, nanoparticle aggregation, and globular protein crystallization.

Objective This study reviewed the current state of machine learning (ML) research for the prediction of sports-related injuries. It aimed to chart the various approaches used and assess their efficacy, considering factors such as data heterogeneity, model specificity and contextual factors when developing predictive models. Design Scoping review. Data sources PubMed, EMBASE, SportDiscus and IEEEXplore. Results In total, 1241 studies were identified, 58 full texts were screened, and 38 relevant studies were reviewed and charted. Football (soccer) was the most commonly investigated sport. Area under the curve (AUC) was the most common means of model evaluation; it was reported in 71% of studies. In 60% of studies, tree-based solutions provided the highest statistical predictive performance. Random Forest and Extreme Gradient Boosting (XGBoost) were found to provide the highest performance for injury risk prediction. Logistic regression outperformed ML methods in 4 out of 12 studies. Three studies reported model performance of AUC>0.9, yet the clinical relevance is questionable. Conclusions A variety of different ML models have been applied to the prediction of sports-related injuries. While several studies report strong predictive performance, their clinical utility can be limited, with wide prediction windows or broad definitions of injury. The efficacy of ML is hampered by small datasets and numerous methodological heterogeneities (cohort sizes, definition of injury and dependent variables), which were common across the reviewed studies.

K-core percolation is an extension of the concept of classical percolation and is particularly relevant to understanding the resilience of complex networks under random damage. A new analytical formalism has been recently proposed to deal with heterogeneous k-cores, where each vertex is assigned a local threshold ki. In this Letter we identify a binary mixture of heterogeneous k-cores which exhibits a tricritical point. We investigate the new scaling scenario and calculate the relevant critical exponents, by analytical and computational methods, for Erd\ifmmode \mbox{\H{o}}\else \H{o}\fi{}s-R\'enyi networks and 2D square lattices.

We introduce an order parameter for dynamical arrest. Dynamically available volume (unoccupied space that is available to the motion of particles) is expressed as holes for the simple lattice models we study. Near the arrest transition the system is dilute in holes, so we expand dynamical quantities in a series of hole density. Unlike the situation when presented in particle density, all cases of simple models that we examine have a quadratic dependence of the diffusion constant on hole density. This observation implies that in certain regimes ideal dynamical arrest transitions may possess a hitherto unnoticed degree of universality.