Individual variation adaptive correction: Thermal error prediction for motorized spindles with limited measurement points of the same model

This article discusses a single-prey and single-predator model by incorporating two behavioral mechanisms, namely group defense in prey modeled through a Holling type IV response function and cooperative hunting in predators represented by a predation rate dependent on predator density. Through system analysis, three critical points were obtained, namely the total extinction point, the predator extinction point, and the interior point that describes the coexistence of both species. The total extinction point is always unstable, while the other two critical points are conditionally stable depending on the predator attack rate parameter. Numerical simulations in the form of phase portraits were obtained by varying the parameters related to the predator attack rate. The simulation results show double stability (bistability) when α = 3, where the system can lead to predator extinction or stable coexistence depending on the initial population conditions. Furthermore, numerical continuation was performed to track changes in equilibrium point stability. The results show a Hopf bifurcation at α = 0.4595, marked by a change in the stability of the interior point, a limit point bifurcation (saddle-node) at α = 0.0478 due to the merging of two interior equilibrium points, and a transcritical bifurcation at α = 3.0505, which shows an exchange of stability between equilibrium points.

The Pharmacy First Scheme, introduced on 31 January 2024 as part of NHS England's Primary Care Recovery Plan, allows community pharmacies to treat seven common minor ailments. Pharmacy First aimed to ease pressures on primary care and improve accessibility as over 80% of people live within 20-minute walking distance of a community pharmacy. This study aimed to evaluate the effect of Pharmacy First on General Practice appointments, particularly within a 2-week or same-day target, and how this varies regionally, by deprivation and urbanity. This retrospective descriptive and interrupted time-series analyses used Stata to analyse an open NHS Digital dataset of appointments (January 2022 - November 2024). Deprivation and urbanity measures are derived from the 2022 Health Foundation report. Key measures included time from booking to appointment, and healthcare professional type. The results found a significant pre-intervention increase in appointments with limited significant post-intervention trends. Statistically significant decreases occurred in same-day GP appointments in both the most and least deprived 20% of Integrated Care Boards (ICBs) and the least urban 20%. The data showed strong seasonal variation, peaking in autumn, and falling in summer. Limited post-intervention data points and pronounced seasonality limit certainty on Pharmacy First's early impact. These results align with NHS Wales Choose Pharmacy interim reports, perhaps indicating that consistently high appointment demand means available appointments remain filled. Future research could explore appointment reasons and patient demographics. Decreases in same-day GP appointment numbers for less urban areas and the most and least deprived areas could be a focus for promotion.

Molecular marker-based source apportionment of PM2.5-Associated organic compounds in a transboundary-influenced urbanized receptor region.

The coefficient of determination is a popular goodness-of-fit measure in linear regression analysis. Despite its widespread popularity in applied statistics, the statistical inference of the coefficient of determination is very limited. The paper aims to fill the gap by developing exact unbiased statistical hypothesis testing and a short confidence interval on the log scale. Power functions and p-values for testing the double-sided statistical hypotheses are presented. A novel estimator for the coefficient of determination, called the maximum concentration estimator on the log scale, is introduced as the limit point of the shrinking short confidence interval as the confidence level approaches zero. Our theoretical derivations are accompanied by the respective algorithms, which are readily available for implementation in computer languages. Exact optimal statistical inference for the coefficient of determination is illustrated by a cancer research example. The R codes are readily available in the Supplemental Material file.

Learning a single shared model across multiple tasks is a long-standing goal in machine learning, traditionally addressed through Multi-Task Learning (MTL) or Serial Continual Learning (SCL). However, MTL assumes fixed task availability, limiting adaptability to new tasks, while SCL suffers from delayed response due to its strictly sequential learning protocol. This paper studies the novel paradigm of Parallel Continual Learning (PCL) in dynamic multi-task scenarios, where a diverse set of tasks is encountered at different time points. PCL inherits the challenges of both MTL and SCL, namely, task conflict and catastrophic forgetting, compounded by the dynamic and asynchronous arrival of tasks. To address these challenges, we propose Elastic Multi-Gradient Descent (EMGD), which formulates PCL as a dynamic multi-objective optimization problem. EMGD introduces task-specific elastic factors to guide gradient updates toward Pareto-optimal directions, ensuring balanced learning across tasks. Additionally, we develop a gradient-guided memory editing mechanism that aligns rehearsal data with the optimized descent direction, mitigating memory-induced interference. Theoretical analysis shows that accumulation points of the EMGD update rule are Pareto critical under the proposed formulation, and extensive experiments on image classification benchmarks demonstrate that EMGD significantly outperforms existing methods, including state-of-the-art PCL, MTL, and SCL approaches.

The fractional Poisson process and other limit point processes for rare events in infinite ergodic theory

In the present paper, we assess the dynamical response of a network under small perturbations that do not modify the network topology by means of a centrality index, called Icentr (see section 3.1 and Mussone et al. (2022) for its definition). In its design, this centrality index accepts weights on both nodes and edges, and so it can be iteratively applied, so to simulate a discrete linear dynamical system. It is associated to a suitable matrix M , that depends only on the topology of the network and on the edge weights. We prove that the dynamical system converges, independent of the network, and compute the limit point. We apply it to a dataset of 34 underground transportation networks from cities throughout the world and investigate the convergence type of a single network and of a single node. We show that the nodes of the network tend to cluster according to their convergence type and that the convergence rate of a single network is exponential in the number of iterations. Furthermore, we show that the ratio | λ 2 / λ 1 | where λ 1 ≥ | λ 2 | are the two largest module eigenvalues of M , is suitable to compare the dynamical behavior of different networks.

Assessment of potential toxic elements accumulation and consumption risk in fishery resources of the southeast Mediterranean Sea.

In this paper, we investigate rough I - γ τ -statistical convergence of order α in neutrosophic normed spaces and establish several fundamental structural properties of the associated limit sets. We first show that the family { L j } j ≥ 0 of rough statistical limit sets is monotone with respect to the roughness parameter j , and each L j is convex under mild monotonicity assumptions on the neutrosophic components. For j = 0 , rough convergence reduces to the classical I - γ τ -statistical convergence of order α , ensuring that the limit set is a singleton. We further demonstrate that the rough limit set is always neutrosophically closed and neutrosophically convex, highlighting its stability under both topological and geometric operations. A characterization of strong I - s t γ τ α -boundedness is obtained via the non-emptiness of the rough limit set. In addition, we introduce the notion of I j − s t γ τ α -cluster points and prove that every rough limit point is a cluster point, while the cluster set remains neutrosophically closed. Finally, we show that this convergence framework unifies several classical notions of statistical and ideal convergences as particular cases.

This paper considers the problem of minimizing a differentiable function with locally Lipschitz continuous gradient on the algebraic variety of real matrices of upper-bounded rank. This problem is known to enable the formulation of various machine learning or signal processing tasks such as dimensionality reduction, collaborative filtering, and signal recovery. Several definitions of stationarity exist for this nonconvex problem. Among them, Bouligand stationarity is the strongest necessary condition for local optimality. This paper proposes two first-order methods that generate a sequence in the variety whose accumulation points are Bouligand stationary. The first method combines the well-known projected projected-gradient descent map with a rank reduction mechanism. The second method is a hybrid of projected gradient descent and projected projected-gradient descent. Both methods stand out in the field of low-rank optimization methods when considering their convergence properties, their streamlined design, their typical computational cost per iteration, and their empirically observed numerical performance. The theoretical framework used to analyze the proposed methods is of independent interest. Funding: This work was supported by the Fonds de la Recherche Scientifique–FNRS and the Fonds Wetenschappelijk Onderzoek–Vlaanderen [EOS Project 30468160], by the Fonds de la Recherche Scientifique–FNRS [Grant T.0001.23], by G-Statistics from the European Research Council under the European Union’s Horizon 2020 research and innovation program [Grant 786854], and by the French government through the 3IA Côte d’Azur Investments [Grant ANR-23-IACL-0001] managed by the National Research Agency. K. A. Gallivan was partially supported by the U.S. National Science Foundation [Grant CIBR 1934157]. This work was done in part when K. A. Gallivan was visiting UCLouvain, supported by the “Professeurs et chercheurs visiteurs” budget of the Science and Technology Sector.

Fine particulate matter (PM)-induced pollution is one of the major causes of indoor air quality deterioration. Passive air purification technologies offer advantages of structural simplicity and low energy consumption, yet their spatiotemporal mass transfer characteristics remain poorly understood. This study presents a theoretical and experimental investigation of PM spatiotemporal mass transfer under the sink effect induced by an electro-convective passive air purifier. The apparent mass transfer coefficient (Dapp) and PM concentration prediction models based on Fick’s second law were established, and then the space-and-time-dependent mass transfer coefficient (Dst) was determined by using the Boltzmann–Matano method. The results revealed that the absolute values of Dst quantified local migration intensity, while its sign provided directional information unattainable from conventional averaged parameters. The logarithmic values of Dapp showed a consistent logarithmic relationship with distance at fixed time windows, and the validated prediction model maintained errors within ±15%, enabling accurate reconstruction of full-field concentration distributions from limited measurement points. The complementary nature of these two coefficients offers a comprehensive evaluation framework. This work advances both the theoretical understanding and practical application of passive air purification technology, offering new tools for indoor PM exposure control and purifier performance optimization.

Highlights A novel non-discrete topology is defined on the unit group using conjugate pairs as basic open sets, where every open set is also closed (clopen). Highlights A novel non-discrete topology is defined on the unit group using conjugate pairs as basic open sets, where every open set is also closed (clopen). The function mapping to is continuous, open, and closed, establishing a strong topological link between the unit group and quadratic residues. The quotient space , under the equivalence , is homeomorphic to the discrete space of quadratic residues . The topology is disconnected and fails the separation axiom, whereas the discrete topology on satisfies stronger separation properties such as . Key topological operators (interior, closure, boundary, limit points) are explicitly characterized for arbitrary subsets of , revealing how structure depends on conjugate-pair symmetryfunction mapping to is continuous, open, and closed, establishing a strong topological link between the unit group and quadratic residues. The quotient space , under the equivalence , is homeomorphic to the discrete space of quadratic residues . The topology is disconnected and fails the separation axiom, whereas the discrete topology on satisfies stronger separation properties such as . Key topological operators (interior, closure, boundary, limit points) are explicitly characterized for arbitrary subsets of , revealing how structure depends on conjugate-pair symmetry This paper introduces a finite topological space on the group of units modulo a prime , defined by its basis of conjugate residue pairs for all units . We investigate the fundamental topological concepts such as point-set topology, separation axioms, and characterise the structure and behaviour of this topology. Additionally, we examine a function from to the topology of quadratic residues , mapping each unit to its square modulo . We analyse the continuity, openness of , and explore its implications for separation properties. Furthermore, we define a quotient topology on based on the equivalence relation if and only if, showing that the resulting quotient space is homeomorphic to .

Snap-through dynamics between the two potential wells of bistable oscillators are exhibited over a wide frequency range which narrows with decreasing harmonic excitation amplitudes until disappearing at a critical forcing level. However, for efficient conversion from vibrational to electrical energy in harvesting applications, the bistable oscillator must retain its favorable broadband cross-well response while the input excitation is minimized. To maintain effectiveness at low forcing levels, an actuation approach is proposed where external perturbations are used to extend the oscillator’s cross-well bandwidths by switching from co-existing low to high energy attractors. By utilizing Macro Fiber Composites (MFC) in a [ 0 MFC / 90 MFC ] T bistable piezoelectric laminate, the application of rectangular voltage pulse signals are cycled through different response phases to continuously alter the basins of attraction until the desired cross-well orbit is sustained at each frequency. The pulse magnitude is where the system exhibits limit point behavior and the resulting snap through actuation mechanism brings consistency between perturbation trials. A multi degree of freedom electromechanical model that captures the stable shapes and cross-well dynamics and finite element analysis in Abaqus/Standard demonstrate the efficacy of the perturbation method. The model is then employed to significantly increase the bandwidths inducing cross-well oscillations.

Cryptosporidium parvum is an apicomplexan parasite and an important pathogen of mammals and humans, which can be infected by zoonotic transmission or directly by human-to-human contact. This parasite attacks the small intestine, and the main symptom is a watery diarrhea that can be particularly severe in newborns and deadly in immunodeficient subjects. Rhomboids are ubiquitous proteases embedded in cell membranes that act by cleaving other membrane proteins in or near their transmembrane domains. Apicomplexan rhomboids play an important role in approaching and invading the host cell. This study analyzed the phylogenetic origin, the structural motifs, and the subcellular localization of C. parvum rhomboids. Altogether, C. parvum possesses three rhomboids, namely, CpRom1, CpRom2, and CpRom3. The similarity search in Cryptosporidium genus revealed that C. parvum and other "intestinal" species lack a PARL-like rhomboid whereas this type of mitochondrial rhomboid was present in "gastric" species like Cryptosporidium muris and Cryptosporidium andersoni. At the genome level, this was revealed by a precise excision of the PARL-like gene in intestinal species whereas the rest of chromosomal synteny was well conserved among the Cryptosporidium species. The analysis of the structural domains revealed that C. parvum rhomboids can be classified as mixed secretases, and the comparison with orthologs from Toxoplasma gondii and Plasmodium falciparum showed that C. parvum rhomboids can be distinguished in two separate clusters based on similarities at the level of the catalytic sites. The three rhomboids were expressed simultaneously in the invasive stage of sporozoite, but each of them had a different spatial distribution. Indeed, CpRom1 had a dual localization: this rhomboid was internal at the apical complex, and it was also accumulated at the posterior pole of the sporozoite. Otherwise, CpRom2 was prevalently contained in the apical complex, and a point of accumulation was on the surface of the apical end. Differently from CpRom1 and CpRom2, CpRom3 is distributed along the entire surface of sporozoites. Finally, we listed 10 membrane proteins as candidate substrates for the C. parvum rhomboids based on the similarities with some proven substrates of apicomplexan rhomboids and the copresence in subcellular structures with the three rhomboids.

Ship hull stress reconstruction with limited sensors: A time-domain coupled modal superposition method and parametric layout optimization

Abstract This paper reports the first investigation of magnetic island-associated beta-induced Alfvén eigenmodes (m-BAEs) in spherical torus, based on the EXL-50U device. Experimentally, a magnetic island with toroidal/poloidal mode numbers m/n = +3/-1 is found to drive a pair of m-BAEs at ~ 20 kHz. This m-BAE pair propagates in opposite directions, shares the same mode numbers as the island, and exhibits a frequency difference exactly equal to twice the island’s rotation frequency. Under static magnetic conditions, only one m-BAE can be observed, which displays a standing-wave structure with m/n = ±3/±1. The standing-wave nodes of the toroidal and poloidal magnetic perturbation from m-BAE, δBθ,m-BAE and δBφ,m-BAE, are locked near the O-point and X-point of the island. The frequency of the m-BAE (fm-BAE) shows a significant positive linear correlation with the magnetic island width (wisland), and the mode disappears when wisland becomes either too large or too small. Additionally, fm-BAE is also found to be proportional to the Alfvén velocity, consistent with the fundamental characteristics of Alfvén eigenmodes. In short, the experiments on EXL-50U have systematically brought together the m-BAE features that were previously observed in isolation on different tokamaks. This demonstrates that these features are universal, even in spherical torus. Simulation and calculation of the continuum accumulation point frequency (fcap) is also given in the paper, confirming that experimental fm-BAE falls within the BAE gap at the q = 3 rational surface, and the modes disappear no matter when fm-BAE > fcap. Based on the findings above, the paper further proposes a possible excitation mechanism for m-BAE.

Rapid urbanization in developing countries has intensified solid waste generation and compromised municipal waste management infrastructure, creating conditions favorable to mosquito proliferation. This cross-sectional quantitative study assessed the impact of solid waste management practices on mosquito larval density in selected urban communities. A total of 150 households were systematically sampled and 30 waste accumulation points were surveyed using the standard dipping method. Open dumping was the most prevalent disposal method (40%), and discarded tires recorded the highest mean larval density (22.7 ± 5.1 larvae/dip). A strong positive correlation was observed between waste accumulation and larval density (r = 0.68, p = 0.001). Multiple linear regression revealed that open dumping (β = 0.61), collection frequency (β = −0.47), and covered container use (β = −0.39) collectively explained 52% of larval density variation (R² = 0.52, F = 18.6, p < 0.001). Stegomyia indices in open-dumping zones exceeded WHO emergency outbreak thresholds. These findings confirm that poor solid waste management significantly drives mosquito breeding and underscore the urgent need for strengthened municipal collection infrastructure, covered container promotion, and anti-dumping enforcement as integrated vector management strategies.

Inflammation is the body’s way of responding to infection, and one needs to develop effective strategies to control it. In this work, bifurcation analysis and multiobjective nonlinear model predictive control are performed on an inflammatory immune response model. Bifurcation analysis is a powerful mathematical tool for studying the nonlinear dynamics of any process. Several factors must be considered, and multiple objectives must be met simultaneously. The MATLAB program MATCONT was used to perform the bifurcation analysis. The MNLMPC calculations were performed using the optimization language PYOMO in conjunction with the state-of-the-art global optimization solvers IPOPT and BARON. The bifurcation analysis revealed the existence of limit and branch points. The MNLMC converged on the Utopia solution (best possible). The limit and branch points (which cause multiple steady-state solutions from a singular point) are very beneficial because they enable the Multiobjective nonlinear model predictive control calculations to converge to the Utopia point (the best possible solution) in the model.

Abstract The codegree Turán density of a ‐graph is the smallest such that every ‐graph with contains a copy of . In this work, we show that for every , there is a ‐uniform hypergraph with . The initial preprint of this work leads to significant subsequent research on accumulation points of variants of the Turán density.