Background Freezing of gait (FoG) is a disabling manifestation of Parkinson's disease (PD). Most gait studies in FoG rely on spatiotemporal parameters or discrete kinematic peaks, which may underestimate multi-joint deviations across the gait cycle. The Gait Profile Score (GPS) and Gait Variable Score (GVS) were introduced as composite indices to provide a more comprehensive and accessible evaluation. This study aimed to use GPS and GVS to detect gait differences between individuals with and without FoG (nFoG) and to assess the modulatory effects of levodopa (L-DOPA) medication. Methods Twenty-two individuals with PD (11 FoG) and 18 age-matched healthy controls were recruited. Kinematic data were collected during self-selected walking speed. PD participants were evaluated in both ON and OFF medication. GPS and GVS values were normalized using control data. A Linear Mixed-Effects Models (LMM) with Bonferroni correction was used to assess differences between groups (FoG and nFoG) and medication states (ON and OFF). Findings A significant group-by-medication interaction was observed for pelvic tilt and rotation, and ankle dorsiflexion, with FoG individuals exhibiting higher values in the OFF state. FoG group exhibited significantly higher GPS and GVS values mainly in the sagittal plane, compared with the nFoG group. L-DOPA medication was associated with reduced pelvic tilt, hip adduction, hip flexion, and ankle dorsiflexion. Interpretation GPS and GVS offer a concise description of FoG-related gait impairment, capturing distributed multi-joint deviations not evident from spatiotemporal parameters alone. The limited dopaminergic responsiveness of these indices highlights the contribution of non-dopaminergic mechanisms. These indices may serve as rapid, reliable tools for clinical and research applications in gait assessment.
Landfill gas (LFG) is a renewable yet highly diluted fuel whose variable composition and operation at elevated pressures pose significant challenges for stable and efficient combustion. In this work, the laminar burning velocity (LBV) and Markstein length of realistic CH4-CO2-N2 mixtures were investigated experimentally and numerically at 298 K, at pressures up to 5 bar, and for equivalence ratios ranging from 0.6 to 1.3, with special focus on the lean region where new burners concepts are expected operate and where data is quite scarce. Two surrogate fuels containing 65% and 55% CH4 were formulated while maintaining a constant CO2:N2 ratio to isolate the effect of total dilution. Experimental LBVs were determined using the outwardly propagating spherical flame method and compared with detailed chemical-kinetic mechanisms. Among the mechanisms evaluated, Konnov Mech 0.6 provided the best agreement with experimental data at 1 bar. The results show that increasing pressure and dilution both significantly reduce the LBV; however, they act through distinct mechanisms. Dilution primarily suppresses flame propagation through thermal effects, reducing adiabatic flame temperature and overall reaction rates, whereas pressure enhances competition between chain-branching and termination reactions, leading to reduced radical concentrations. Sensitivity and pathway analyses identified the reaction H + O2 -><- O + OH as the dominant promoting step controlling flame propagation under all conditions. The Markstein length was found to increase from lean to rich mixtures and to decrease with increasing pressure, indicating enhanced flame instability at elevated pressures. The present study provides new high-pressure experimental data and a detailed mechanistic interpretation of LFG combustion, contributing to improved modeling and the design of energy systems operating with low-calorific-value fuels.
The status of classical high-luminosity long gamma-ray bursts (GRBs) as candidate sources of ultra-high-energy cosmic rays (UHECRs) and high-energy neutrinos has changed substantially since 2019, and it has changed on three fronts more or less simultaneously. We restrict attention to that population throughout; the low-luminosity and hidden populations, on which the recent constraints bear far more weakly, are discussed only where recent results bear on them. A very-high-energy (VHE, E greater than or similar to 100 GeV) class of GRBs has been established by H.E.S.S., MAGIC, and LHAASO, culminating in GRB 221009A, for which the onset of the TeV afterglow was resolved and photons up to similar to 13 TeV were recorded. IceCube has converted the absence of GRB neutrinos into quantitative bounds, both through stacked searches over thousands of bursts and through burst-specific limits on GRB 221009A. The Pierre Auger Observatory and the Telescope Array have consolidated a mass composition that grows heavier above the ankle, with a narrowing X (max) dispersion, and Auger has reported evidence, at the similar to 4 sigma level, for an intermediate-scale anisotropy towards the Centaurus region, compatible with several nearby galaxy catalogues including starbursts. This focus review covers these developments and the constraints they place on one another, rather than the GRB field as a whole. These constraints apply to physically distinct regions: the TeV photons are afterglow emission from the external forward shock, whereas the neutrino limits and the Fermi-LAT cascade bound constrain the prompt dissipation zone, and the site of nuclear acceleration and escape is a model assumption in both cases. We therefore map each constraint onto its zone before combining anything. Within a single zone the compactness that governs photomeson production also governs photodisintegration and internal gamma gamma opacity, so transparency, neutrino faintness and nuclear survival are not independent; across zones no such implication holds without a model linking the prompt and afterglow flows. What the recent measurements do show is a convergence: analyses of different zones, by different methods, favour the same corner of parameter space, namely large radii and high bulk Lorentz factors, with the prompt-zone limits additionally requiring low baryonic loading. We summarize the resulting picture, which applies to co-spatial one-zone models of classical long GRBs and leaves multi-zone, reverse-shock, low-luminosity, and choked-jet configurations largely untested, together with the systematic uncertainties that currently limit it and the observations with CTAO, IceCube-Gen2, KM3NeT, GRAND, and AugerPrime that would test it.
In this paper, we perform a classification of Lie point symmetries of a (3+1)-dimensional model describing tumour cells, extracellular matrix (ECM), and matrix-degrading enzymes (MDEs). From the symmetries, we were able to find new exact solutions for the model. One of the solutions we found has haptotaxis effect. We explore these solutions, analysing the invasion of tumour cells, the evolution of the ECM degradation by MDEs and the diffusion of the MDEs. We also obtain three conserved currents and from them we explore the time variation of certain biological quantities.
We propose a unified algebraic framework for classification performance evaluation covering binary, multiclass, multilabel, ordinal, hierarchical, cost-sensitive and soft-label settings. Actual and predicted labels are represented as binary indicator matrices, and three aggregation operators (global, column-wise, and row-wise) correspond exactly to micro, macro/weighted, and exemplar averaging. Any binary measure expressed in terms of the four confusion-matrix counts extends to all these settings by substituting an operator, with no measure-specific derivation. We show that the structural properties governing which identities hold for an extension are themselves derivable from the binary formula. Micro-averaging equals denominator-weighted macro-averaging precisely for the class of aggregation-decomposable (linear-fractional) measures, which we characterise algebraically and show by counterexample to be a strict class. For soft ground truth, we prove from the t-norm axioms alone that the product t-norm is the unique choice whose confusion counts preserve marginal memberships. In multiclass settings, micro-precision, micro-recall and micro-F1 collapse identically onto accuracy. Furthermore, binary skew-invariance transfers unconditionally to multilabel aggregation, but only partially to multiclass problems. For measures with a linear numerator and a prediction-independent denominator, the optimal decision threshold is the share of the numerator’s total weight that favours a negative prediction. Consequently, standard training targets the measure exactly when positive and negative predictions carry equal weight; outside this class (including precision and the F-measures), no such closed form exists. Under one-hot multiclass encoding, a measure fails to attain its theoretical minimum whenever its value with zero true positives still depends on true negatives, establishing non-trivial performance floors even for completely incorrect classifiers; for example, a classifier wrong on every example still achieves a label accuracy of 0.8 on a ten-class problem.
