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Research on social‐ecological systems (SES) has highlighted their complex and adaptive character and pointed to the importance of recognizing their intertwined nature. Yet, we often base our analysis and governance of SES on static and independent objects, such as actors and resources which are not well suited to address complexity and intertwinedness. This bias, which is largely implicit, has its roots in substance ontologies that have influenced most of contemporary science. This paper argues that it is useful to critically reflect on this ontological grounding and develop SES research from a process ontological perspective. Key insights are that process ontological concepts such as process, event and possibility space are able to overcome the dichotomy between the social and the ecological and allow for a conceptualization of continuous change (dynamism) that enhances our understanding of SES as truly intertwined and complex systems. This will enable SES researchers to conceptualize problems as well as corresponding solutions in novel ways which will ultimately support the development of novel governance approaches, from rethinking the aims of policies from managing people towards managing relations between and among people and the natural system. To fully tap the potential which comes with a change in worldview towards a process ontology, changing research approaches and ways of ing are required. Résumé La recherche sur les systèmes socio‐écologiques (SSE) a mis en évidence leur caractère complexe et adaptatif et a souligné l'importance de reconnaître l'enchevêtrement du social et de l’écologique. Pourtant, nos analyses et nos modes de gouvernance se basent souvent sur l'existence d'objets statiques et indépendants, tels que des acteurs ou des ressources qui, soit ne permettent pas d'expliquer/communiquer le caractère complexe de ces systèmes, soit ignorent leur nature enchevêtrée. Ce biais, largement implicite, trouve ses racines dans les ontologies de la substance qui ont influencé la plupart des sciences contemporaines. Cet article propose de réfléchir de manière critique sur les fondements ontologiques des SSE et de s'inspirer d'ontologies qui considèrent les relations et processus comme fondamentaux pour développer des recherches sur les SSE, tenant compte de leur caractère complexe, adaptatif et enchevêtré. Des concepts tels que processus, événements et espace de possibilité permettent de dépasser la dichotomie nature/société et de conceptualiser le changement continu (dynamisme) de telle sorte que notre compréhension des SSE se trouve améliorée. Cette nouvelle perspective permettra de repenser les problèmes des SSE et, par conséquent, de développer de nouvelles approches de gouvernance visant à gérer les relations entre les personnes tout aussi bien qu'entre les personnes et leur environnement. Pour exploiter pleinement le potentiel d'une ontologie des processus, il est nécessaire de modifier nos approches de recherche et nos méthodes d'ion. A free Plain Language Summary can be found within the Supporting Information of this article. A free Plain Language Summary can be found within the Supporting Information of this article.

The aim of this paper is to provide new characterizations for polynomial dichotomies of discrete nonautonomous systems on the half-line. First, we establish equivalent structures for the ranges of projections for a polynomial dichotomy with respect to a sequence of norms. Next, we establish the connections between polynomial dichotomies and other dichotomic behaviors. We obtain for the first time a characterization of polynomial dichotomy with respect to a sequence of norms in terms of ordinary dichotomy and exponential dichotomy of suitable systems with respect to well-chosen sequences of norms. The results are obtained in the most general case, without any additional assumptions regarding the coefficients of the underlying systems.

Abstract Elite athletic competitions have separate male and female events due to men's physical advantages in strength, speed, and endurance so that a protected female category with objective entry criteria is required. Prior to puberty, there is no sex difference in circulating testosterone concentrations or athletic performance, but from puberty onward a clear sex difference in athletic performance emerges as circulating testosterone concentrations rise in men because testes produce 30 times more testosterone than before puberty with circulating testosterone exceeding 15-fold that of women at any age. There is a wide sex difference in circulating testosterone concentrations and a reproducible dose-response relationship between circulating testosterone and muscle mass and strength as well as circulating hemoglobin in both men and women. These dichotomies largely account for the sex differences in muscle mass and strength and circulating hemoglobin levels that result in at least an 8% to 12% ergogenic advantage in men. Suppression of elevated circulating testosterone of hyperandrogenic athletes results in negative effects on performance, which are reversed when suppression ceases. Based on the nonoverlapping, bimodal distribution of circulating testosterone concentration (measured by liquid chromatography-mass spectrometry)-and making an allowance for women with mild hyperandrogenism, notably women with polycystic ovary syndrome (who are overrepresented in elite athletics)-the appropriate eligibility criterion for female athletic events should be a circulating testosterone of <5.0 nmol/L. This would include all women other than those with untreated hyperandrogenic disorders of sexual development and noncompliant male-to-female transgender as well as testosterone-treated female-to-male transgender or androgen dopers.

The brake system requires careful attention for continuous monitoring as a vital module. This study specifically focuses on monitoring the hydraulic brake system using vibration signals through experimentation. Vibration signals from the brake pad assembly of commercial vehicles were captured under both good and defective conditions. Relevant histograms and wavelet features were extracted from these signals. The selected features were then categorized using Nested dichotomy family classifiers. The accuracy of all the algorithms during categorization was evaluated. Among the algorithms tested, the class-balanced nested dichotomy algorithm with a wavelet filter achieved a maximum accuracy of 99.45%. This indicates a highly effective method for accurately categorizing the brake system based on vibration signals. By implementing such a monitoring system, the reliability of the hydraulic brake system can be ensured, which is crucial for the safe and efficient operation of commercial vehicles in the market.

In this paper we investigate a diffusive logistic model with a free boundary in one space dimension. We aim to use the dynamics of such a problem to describe the spreading of a new or invasive species, with the free boundary representing the expanding front. We prove a spreading-vanishing dichotomy for this model, namely the species either successfully spreads to all the new environment and stabilizes at a positive equilibrium state, or it fails to establish and dies out in the long run. Sharp criteria for spreading and vanishing are given. Moreover, we show that when spreading occurs, for large time, the expanding front moves at a constant speed. This spreading speed is uniquely determined by an elliptic problem induced from the original model. [PUBLICATION ABSTRACT]

Fire refugia are landscape elements that remain unburned or minimally affected by fire, thereby supporting postfire ecosystem function, biodiversity, and resilience to disturbances. Although fire refugia have been studied across continents, scales, and affected taxa, they have not been characterized systematically over space and time, which is crucial for understanding their role in facilitating resilience in the context of global change. We identify four dichotomies that delineate an overarching conceptual framework of fire refugia: unburned versus lower severity, species-specific versus landscape-process characteristics, predictable versus stochastic, and ephemeral versus persistent. We outline the principal concepts underlying the ecological function of fire refugia and describe both the role of fire refugia and uncertainties regarding their persistence under global change. An improved understanding of fire refugia is crucial to conservation given the role that humans play in shaping disturbance regimes across landscapes.

Among Zeno paradoxes the most known are Dichotomy, Achilles, Arrow, and Stadium. These argumentations state that movement is impossible since it is not thinkable. According to the ascendant form of dichotomy, a mobile cannot touch its destination since it always must to reach the half of the distance. The solutions of Diogenes, Aristotle and mathematical analysis are not satisfactory. Finally, the difference between rest and movement can be only conventionally established.

Perceptual manifolds arise when a neural population responds to an ensemble of sensory signals associated with different physical features (e.g., orientation, pose, scale, location, and intensity) of the same perceptual object. Object recognition and discrimination require classifying the manifolds in a manner that is insensitive to variability within a manifold. How neuronal systems give rise to invariant object classification and recognition is a fundamental problem in brain theory as well as in machine learning. Here, we study the ability of a readout network to classify objects from their perceptual manifold representations. We develop a statistical mechanical theory for the linear classification of manifolds with arbitrary geometry, revealing a remarkable relation to the mathematics of conic decomposition. We show how special anchor points on the manifolds can be used to define novel geometrical measures of radius and dimension, which can explain the classification capacity for manifolds of various geometries. The general theory is demonstrated on a number of representative manifolds, includingℓ2ellipsoids prototypical of strictly convex manifolds,ℓ1balls representing polytopes with finite samples, and ring manifolds exhibiting nonconvex continuous structures that arise from modulating a continuous degree of freedom. The effects of label sparsity on the classification capacity of general manifolds are elucidated, displaying a universal scaling relation between label sparsity and the manifold radius. Theoretical predictions are corroborated by numerical simulations using recently developed algorithms to compute maximum margin solutions for manifold dichotomies. Our theory and its extensions provide a powerful and rich framework for applying statistical mechanics of linear classification to data arising from perceptual neuronal responses as well as to artificial deep networks trained for object recognition tasks.

Answering an open question affirmatively it is shown that every ergodic invariant measure of a mean equicontinuous (i.e. mean-L-stable) system has discrete spectrum. Dichotomy results related to mean equicontinuity and mean sensitivity are obtained when a dynamical system is transitive or minimal. Localizing the notion of mean equicontinuity, notions of almost mean equicontinuity and almost Banach mean equicontinuity are introduced. It turns out that a system with the former property may have positive entropy and meanwhile a system with the latter property must have zero entropy.

The spins of ten stellar black holes have been measured using the continuum-fitting method. These black holes are located in two distinct classes of X-ray binary systems, one that is persistently X-ray bright and another that is transient. Both the persistent and transient black holes remain for long periods in a state where their spectra are dominated by a thermal accretion disk component. The spin of a black hole of known mass and distance can be measured by fitting this thermal continuum spectrum to the thin-disk model of Novikov and Thorne; the key fit parameter is the radius of the inner edge of the black hole’s accretion disk. Strong observational and theoretical evidence links the inner-disk radius to the radius of the innermost stable circular orbit, which is trivially related to the dimensionless spin parameter a ∗ of the black hole (| a ∗ |<1). The ten spins that have so far been measured by this continuum-fitting method range widely from a ∗ ≈0 to a ∗ >0.95. The robustness of the method is demonstrated by the dozens or hundreds of independent and consistent measurements of spin that have been obtained for several black holes, and through careful consideration of many sources of systematic error. Among the results discussed is a dichotomy between the transient and persistent black holes; the latter have higher spins and larger masses. Also discussed is recently discovered evidence in the transient sources for a correlation between the power of ballistic jets and black hole spin.