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\"Drawing on research from around the world, this atlas gives shape and meaning to statistics, making it an indispensable resource for understanding global inequalities and an inspiration for social and political action. Inequality underlies many of the challenges facing the world today, and The Atlas of Global Inequalities considers the issue in all its dimensions. Organized in thematic parts, it maps not only the global distribution of income and wealth, but also inequalities in social and political rights and freedoms. It describes how inadequate health services, unsafe water, and barriers to education hinder people's ability to live their lives to the full; assesses poor transport, energy, and digital communication infrastructures and their effect on economic development; and highlights the dangers of unclean and unhealthy indoor and outdoor environments. Through world, regional, and country maps, and innovative and intriguing graphics, the authors unravel the complexity of inequality, revealing differences between countries as well as illustrating inequalities within them. Topics include: the discrimination suffered by children with a disability; the impact of inefficient and dangerous household fuels on the daily lives and long-term health of those who rely on them; the unequal opportunities available to women; and the reasons for families' descent into, and reemergence from, poverty.\"--Publisher description.

Let X , Y be two real normed spaces with dimension X ≥ 2 and f : X → Y ( f ≠ 0 ) be a map which preserves equality of phase-distance with f ( 0 ) = 0 , i.e., { ∥ f ( x ) + f ( y ) ∥ , ∥ f ( x ) − f ( y ) ∥ } = { ρ ( ∥ x + y ∥ ) , ρ ( ∥ x − y ∥ ) } , ∀ x , y ∈ X , for some function ρ : [ 0 , ∞ ) → [ 0 , ∞ ) . In this paper, we prove that if f is surjective or Y is strictly convex, then f is phase equivalent to a linear map. More precisely, f = λ σ ⋅ T , where λ is a non-zero real number, σ : X → { − 1 , 1 } is a phase function and T : X → Y is a linear isometry. Counter example for the case when dimension X = 1 is also presented.

Travel time to cities in 2015 is quantified in a high-resolution global map that will be useful for socio-economic policy design and conservation research. The roads to equality Resources that sustain human wellbeing, such as education, jobs and health services, are distributed unequally, with higher concentrations in dense urban areas. Increasing access to such opportunities and services is a key factor in the advancement of fair and sustainable development. Integrating multiple large data sources for road and city geography, Daniel Weiss and colleagues have created a high-resolution global map that quantifies travel time to cities in the year 2015. This map provides a detailed view of the heterogeneity in accessibility to cities around the world, serving not just as a potential indicator for development but also as an input for future models in areas such as conservation biology. The economic and man-made resources that sustain human wellbeing are not distributed evenly across the world, but are instead heavily concentrated in cities. Poor access to opportunities and services offered by urban centres (a function of distance, transport infrastructure, and the spatial distribution of cities) is a major barrier to improved livelihoods and overall development. Advancing accessibility worldwide underpins the equity agenda of ‘leaving no one behind’ established by the Sustainable Development Goals of the United Nations 1 . This has renewed international efforts to accurately measure accessibility and generate a metric that can inform the design and implementation of development policies. The only previous attempt to reliably map accessibility worldwide, which was published nearly a decade ago 2 , predated the baseline for the Sustainable Development Goals and excluded the recent expansion in infrastructure networks, particularly in lower-resource settings. In parallel, new data sources provided by Open Street Map and Google now capture transportation networks with unprecedented detail and precision. Here we develop and validate a map that quantifies travel time to cities for 2015 at a spatial resolution of approximately one by one kilometre by integrating ten global-scale surfaces that characterize factors affecting human movement rates and 13,840 high-density urban centres within an established geospatial-modelling framework. Our results highlight disparities in accessibility relative to wealth as 50.9% of individuals living in low-income settings (concentrated in sub-Saharan Africa) reside within an hour of a city compared to 90.7% of individuals in high-income settings. By further triangulating this map against socioeconomic datasets, we demonstrate how access to urban centres stratifies the economic, educational, and health status of humanity.

Given a surface M and a fixed conformal class c one defines _k(M,c) to be the supremum of the k -th nontrivial Laplacian eigenvalue over all metrics gın c of unit volume. It has been observed by Nadirashvili that the metrics achieving _k(M,c) are closely related to harmonic maps to spheres. In the present paper, we identify _1(M,c) and _2(M,c) with min-max quantities associated to the energy functional for sphere-valued maps. As an application, we obtain several new eigenvalue bounds, including a sharp isoperimetric inequality for the first two Steklov eigenvalues. This characterization also yields an alternative proof of the existence of maximal metrics realizing _1(M,c) , _2(M,c) , and moreover allows us to obtain a regularity theorem for maximal Radon measures satisfying a natural compactness condition.

Population and public health are in the midst of an artificial intelligence revolution capable of radically altering existing models of care delivery and practice. Just as AI seeks to mirror human cognition through its data-driven analytics, it can also reflect the biases present in our collective conscience. In this Viewpoint, we use past and counterfactual examples to illustrate the sequelae of unmitigated bias in healthcare artificial intelligence. Past examples indicate that if the benefits of emerging AI technologies are to be realized, consensus around the regulation of algorithmic bias at the policy level is needed to ensure their ethical integration into the health system. This paper puts forth regulatory strategies for uprooting bias in healthcare AI that can inform ongoing efforts to establish a framework for federal oversight. We highlight three overarching oversight principles in bias mitigation that maps to each phase of the algorithm life cycle.

In this manuscript we use novel types of soft operators to define new approaches of soft maps in the frame of supra soft topologies (or SSTSs), namely supra soft somewhere dens continuous (or SS-sd-continuous), SS-sd-open and SS-sd-closed maps. With the help of SS-closure (interior) operators and SS-sd-closure (interior) operators we succeed to introduce many equivalent conditions and several important properties to these notions. To name a few: We prove that there is an one to one between the SS-sd-open and SS-sd-closed maps under a bijective soft map, supported by counterexample to confirm the necessity of the bijectivity condition. Furthermore, we present the concept of SS-sd-separated sets with intersected characterizations, as a prelude to studying the connectedness in a supra soft topological space (or SSTS). Moreover, we show that, there is no priori relationship between supra soft-sd-connectedness in an SSTS and its parametric supra topological spaces in general, supported by concrete counterexamples. Finally, we prove that the image of an SS-sd-connected set under an SS-sd-irresolute map is an SS-sd-connected.

It is shown that the colored isomorphism class of a unital, simple, $\\mathcal {Z}$ -stable, separable amenable C $^*$ -algebra satisfying the universal coefficient theorem is determined by its tracial simplex.

The goal of this note is to show that in the case of ‘transversal intersections’ the ‘true local terms’ appearing in the Lefschetz trace formula are equal to the ‘naive local terms’. To prove the result, we extend the strategy used in our previous work, where the case of contracting correspondences is treated. Our new ingredients are the observation of Verdier that specialization of an étale sheaf to the normal cone is monodromic and the assertion that local terms are ‘constant in families’. As an application, we get a generalization of the Deligne–Lusztig trace formula.

The Gender Equality Index allows analyzing and measuring the progress of gender equality in the EU and, therefore, the relation between men and women in different domains, such as Health, Work or Money. Even though the European Institute for Gender Equality has created some visualizations that are useful to look at the data, this website does not manage to make graphs that allow for observing the spatiotemporal variable. This article enhances the understanding of the index with spatiotemporal visualizations, such as cartograms, heatmaps and choropleth maps, and some strategies focusing on analyzing the evolution of the countries over the years in an open-access environment. The results show how the application created may be used as an addition to the EIGE website.

In this paper we continue presenting new types of soft operators for supra soft topological spaces (or SSTSs). Specifically, we investigate more interesting properties and relationships between the supra soft somewhere dense interior (or SS-sd-interior) operator, the SS-sd-closure operator, the SS-sd-cluster operator, and the SS-sd-boundary operator. We prove that the SS-sd-interior operator, SS-sd-boundary operator, and SS-sd-exterior operator form a partition for the absolute soft set. Furthermore, we apply the notion of SS-sd-sets to soft continuity. In addition, we use the SS-sd-interior operator and the SS-sd-closure operator to provide equivalent conditions and many characterizations for SS-sd-continuous, SS-sd-irresolute, SS-sd-open, SS-sd-closed, and SS-sd-homeomorphism maps. Examples include the following: The soft mapping is an SS-sd-homeomorphism if, and only if it is both SS-sd-continuous and an SS-sd-closed if, and only if, the soft mapping in addition to its inverse is SS-sd-continuous. Moreover, a bijective soft mapping is SS-sd-open if, and only if, it is SS-sd-closed. Furthermore, we provide many examples and counterexamples to show our results, which are extensions of previous studies. A diagram summarizing our results is also introduced.