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Association football (commonly known as football or soccer) in the modern era places a greater emphasis on collaborating and working together as a team instead of relying solely on individual skills to strategize winning performances. The low-scoring and unpredictable nature of association football makes evaluating team performances challenging. Space creation and space utilization have been discussed in the football world lately. Existing literature evaluates this with on and off-ball runs by players for deceiving defenders to create open spaces. However, the contribution of these team ball movements’ enhanced randomness or chaotic nature to winning performances has yet to be explored. This work proposes a novel entropy-based time-series performance evaluation metric, EDRan, for quantifying this enhanced random nature by analyzing the spatial distribution of game events at regular intervals. Additionally, an unexplored cumulative ball possession matrix is used to quantify randomness. The correlation between the match winner and spatial event distribution randomness at regular intervals was analyzed. The significance of the proposed metric was demonstrated using a generalized linear model (GLM), which achieved an average accuracy of 80% for match-winning performance classification. The GLM p-values and coefficients revealed statistically significant relationships between the extracted temporal features and match-winning performances. Findings further revealed dispersed, highly random event distribution by winning teams during the early phases of the game, implying attacking behavior, followed by a compact, cautious playing style toward the end, suggesting that the game’s first-half performances are more pivotal. Despite the unpredictability of actual scores in association football, the proposed approach effectively captured the differences in performances between stronger and weaker teams with temporal relationships, highlighting its significance as a time-series metric for performance evaluation.

The high cost associated with high-fidelity computational fluid dynamics (CFD) is one of the main challenges that inhibit the design and optimisation of new fluid-flow systems. In this study, we explore the feasibility of a physics-informed deep learning approach to predict turbulence evolution and mixing without requiring a classical CFD solver. The deep learning architecture was inspired by integrating U-Net with inception modules for capturing the multi-scale nature of turbulent flows. In addition, a physics-constrained loss function was designed to enforce the mass and pressure conservation of the predicted solution. After trained, the optimised model was validated in the large eddy simulation (LES) of a forced turbulent mixing layer at two distinct Reynolds numbers ( $\mathrm {Re} =3000$ and 30000). The results demonstrate that the proposed approach achieves a promising solution accuracy and extrapolation ability with a significant reduction in computing time when compared to those obtained using a classical LES flow solver. The success in developing such a physics-informed deep learning approach not only justifies the potential of ML-based surrogate solvers for fast prototyping and design of generic fluid-flow systems but also highlights the key challenges arising from data-driven surrogate solver development for turbulence modelling.

A simple-form scalar differential equation with delay and nonlinear negative periodic feedback is considered. The existence of several types of slowly oscillating periodic solutions is shown with the same and double periods of the feedback coefficient. The periodic solutions are built explicitly in the case with piecewise constant nonlinearities involved. The periodic dynamics are shown to persist under small perturbations of the equation, which make it smooth. The theoretical results are verified through extensive numerical simulations.

Solar pores are ideal magnetic structures for wave propagation and transport of energy radially outwards across the upper layers of the solar atmosphere. We aim to model the excitation and propagation of magnetohydrodynamic waves in a pore with a light bridge modeled as two interacting magnetic flux tubes separated by a thin, weaker-field layer. We solve the three-dimensional magnetohydrodynamic equations numerically and calculate the circulation as a measure of net torsional motion. We find that the interaction between flux tubes results in the natural excitation of propagating torsional Alfvén waves but find no torsional waves in the model with a single flux tube. The torsional Alfvén waves propagate with wave speeds matching the local Alfvén speed where wave amplitude peaks.

This study investigated the mechanisms of vorticity generation and the role of vortex tubes in plasma heating and energy transport. Vortex tubes were identified using the instantaneous vorticity deviation technique in the MURaM data set of a simulated solar plage region of the solar photosphere. Within 3D kinetic vortex tubes, the misalignment of the magnetic pressure and the inverse of the density gradient, rather than baroclinic effects, primarily drive vorticity within the tubes. During their lifetime, vortices become less dense as the Lorentz force pushes plasma outwards against pressure gradients. In the simulated upper photosphere, the Lorentz force contributes to adiabatic cooling and heating by expanding or compressing the plasma around the vortex tubes. In turn, vortex motion affects the magnetic field, enhancing current generation and intensifying the Lorentz force, which may further increase adiabatic cooling and heating. Moreover, our results confirm that vortices can significantly boost viscous and ohmic heating on intergranular scales in the photosphere. They generate more magnetic than kinetic energy, with energy transport by Poynting flux notably nonuniform and dominant at the vortex boundaries. This creates energy circulation in which the net upwards Poynting flux can enhance chromospheric plasma heating and support chromospheric temperatures.

We present a novel mathematical model of two adversarial forces in the vicinity of a non-combatant population in order to explore the impact of each force pursuing specific decision-making strategies. Each force has the opportunity to draw support by enabling the decision-making initiative of the population, in tension with maintaining tactical and organisational effectiveness over their adversary. Each dynamic model component of force, population and decision-making, is defined by the archetypal Lanchester, Lotka-Volterra and Kuramoto-Sakaguchi models, with feedback between each component adding heterogeneity. Developing a scheme where cultural factors determine decision-making strategies for each force, this work highlights the parametric and topological factors that influence favourable results in a non-linear system where physical outcomes are highly dependent on the non-physical and cognitive nature of each force's intended strategy.

An emerging body of work has revealed alterations in structural (SC) and functional (FC) brain connectivity following mild TBI (mTBI), with mixed findings. However, these studies seldom integrate complimentary neuroimaging modalities within a unified framework. Multilayer network analysis is an emerging technique to uncover how white matter organization enables functional communication. Using our novel graph metric (SC-FC Bandwidth), we quantified the information capacity of synchronous brain regions in 53 mild TBI patients (46 females; age mean = 40.2 years (y), σ = 16.7 (y), range: 18–79 (y). Diffusion MRI and resting state fMRI were administered at the acute and chronic post-injury intervals. Moreover, participants completed a cognitive task to measure processing speed (30 Seconds and Counting Task; 30-SACT). Processing speed was significantly increased at the chronic, relative to the acute post-injury intervals (p =

BackgroundSleep disorders, such as insomnia, have been associated with extended periods of inactive, sedentary behaviour. Many factors contribute to insomnia, including stress, irregular sleep patterns, mental health issues, inadequate sleeping schedules, diseases, neurological disorders and prescription medications.ObjectivesIdentification of the patterns of sedentary time and its duration in adults with acute insomnia and healthy controls to determine the statistically significant sedentary bouts; comparison of the sedentary behaviour patterns in acute insomnia adults with healthy controls.MethodsWe investigate the daytime actigraphy data and identify temporal patterns of inactivity among adults with acute insomnia and healthy adults. Seven days of actigraphy data were utilised to calculate sedentary time and bouts of variable duration based on a threshold of activity counts (ResultsWe found that individuals with acute insomnia accumulate a significant amount of their sedentary time in medium (6-30 minutes and 31-60 minutes) and longer (more than 60 minutes) duration bouts in comparison to healthy adults. Furthermore, a low p value for total sedentary time (2.54 ⋅ 10-4) association with acute insomnia supports the finding that acute insomnia individuals are significantly more engaged in sedentary activities compared to healthy controls. Also, as shown by the weekend vs weekday analysis, the physical and sedentary activity patterns of acute insomnia adults demonstrate higher variability during the weekdays in comparison to the weekend.ConclusionThe results of the present study demonstrate that adults with acute insomnia spend more time in low-intensity daily physical activities compared to healthy adults.

Background: The human brain is a complex network that seamlessly manifests behaviour and cognition. This network comprises neurons that directly, or indirectly mediate communication between brain regions. Here, we show how multilayer/multiplex network analysis provides a suitable framework to uncover the throughput of structural connectivity (SC) to mediate information transfer—giving rise to functional connectivity (FC). Method: We implemented a novel method to reconcile SC and FC using diffusion and resting-state functional MRI connectivity data from 484 subjects (272 females, 212 males; age = 29.15 ± 3.47) from the Human Connectome Project. First, we counted the number of direct and indirect structural paths that mediate FC. FC nodes with indirect SC paths were then weighted according to their least restrictive SC path. We refer to this as SC-FC Bandwidth. We then mapped paths with the highest SC-FC Bandwidth across 7 canonical resting-state networks. Findings: We found that most pairs of FC nodes were connected by SC paths of length two and three (SC paths of length >5 were virtually non-existent). Direct SC-FC connections accounted for only 10% of all SC-FC connections. The majority of FC nodes without a direct SC path were mediated by a proportion of two (44%) or three SC path lengths (39%). Only a small proportion of FC nodes were mediated by SC path lengths of four (5%). We found high-bandwidth direct SC-FC connections show dense intra- and sparse inter-network connectivity, with a bilateral, anteroposterior distribution. High bandwidth SC-FC triangles have a right superomedial distribution within the somatomotor network. High-bandwidth SC-FC quads have a superoposterior distribution within the default mode network. Conclusion: Our method allows the measurement of indirect SC-FC using undirected, weighted graphs derived from multimodal MRI data in order to map the location and throughput of SC to mediate FC. An extension of this work may be to explore how SC-FC Bandwidth changes over time, relates to cognition/behavior, and if this measure reflects a marker of neurological injury or psychiatric disorders.

Team sports can be viewed as dynamical systems unfolding in time and thus require tools and approaches congruent to the analysis of dynamical systems. The analysis of the pattern-forming dynamics of player interactions can uncover the clues to underlying tactical behaviour. This study aims to propose quantitative measures of a team's performance derived only using player interactions. Concretely, we segment the data into events ending with a goal attempt, that is, “$Shot$”. Using the acquired sequences of events, we develop a coarse-grain activity model representing a player-to-player interaction network. We derive measures based on information theory and total interaction activity, to demonstrate an association with an attempt to score. In addition, we developed a novel machine learning approach to predict the likelihood of a team making an attempt to score during a segment of the match. Our developed prediction models showed an overall accuracy of 75.2% in predicting the correct segmental outcome from 13 matches in our dataset. The overall predicted winner of a match correlated with the true match outcome in 66.6% of the matches that ended in a result. Furthermore, the algorithm was evaluated on the largest available open collection of soccer logs. The algorithm showed an accuracy of 0.84 in the classification of the 42, 860 segments from 1, 941 matches and correctly predicted the match outcome in 81.9% of matches that ended in a result. The proposed measures of performance offer an insight into the underlying performance characteristics.

The aim of this paper is to investigate the cardiorespiratory synchronization in athletes subjected to extreme physical stress combined with a cognitive stress tasks. ECG and respiration were measured in 14 athletes before and after the Ironman competition. Stroop test was applied between the measurements before and after the Ironman competition to induce cognitive stress. Synchrogram and empirical mode decomposition analysis were used for the first time to investigate the effects of physical stress, induced by the Ironman competition, on the phase synchronization of the cardiac and respiratory systems of Ironman athletes before and after the competition. A cognitive stress task (Stroop test) was performed both pre- and post-Ironman event in order to prevent the athletes from cognitively controlling their breathing rates. Our analysis showed that cardiorespiratory synchronization increased post-Ironman race compared to pre-Ironman. The results suggest that the amount of stress the athletes are recovering from post-competition is greater than the effects of the Stroop test. This indicates that the recovery phase after the competition is more important for restoring and maintaining homeostasis, which could be another reason for stronger synchronization.

Existing physiological control fatigue models propose that there may be a regulator in the central nervous system which modulates our daily physical activity. Within limits, this regulator ensures physical activity is completed without physiological system failure through interactive communications between the peripheral systems and the central systems. The ability of the central nervous system to regulate exercise is vital to optimise sport performance when severe intensity exercise might be required for prolonged or frequent periods. Based on mathematical models, this investigation explores the complex relationship between some of the mechanisms controlling physical activity and behaviour. In order to analyse the system control mechanisms, heart rate, volume of oxygen consumption and power output were measured for a well-trained male cyclist. Using power spectrum analysis, fractal analysis and continuous wavelet transforms, we show that the system control mechanisms regulating physiological systems, have distinct complexity. Moreover, the potential central controller uses specific frequency bands simultaneously to control and communicate with the various physiological systems. We show that pacing trials are regulated by different physiological systems.