9,065 research outputs found

    ON INTERVAL UNCERTAINTIES OF CARDINAL NUMBERS OF SUBSETS OF FINITE SPACES WITH TOPOLOGIES WEAKER THAN T 1

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    In the work using interval mathematics, we develop knowledge for cardinal numbers from the viewpoint of uncertainty analysis. In the finite non-T 1 topological spaces, the inclusion-exclusion formula provide interval estimations for the closure and interior of given sets. This paper introduces a novel approach that combines combinatorial and point-set topology, which leads to a number of results. Among these is the cardinality estimation for the intersection of two open sets that cover a hyperconnected topo-logical space

    A discussion on the origin of quantum probabilities

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    We study the origin of quantum probabilities as arising from non-boolean propositional-operational structures. We apply the method developed by Cox to non distributive lattices and develop an alternative formulation of non-Kolmogorvian probability measures for quantum mechanics. By generalizing the method presented in previous works, we outline a general framework for the deduction of probabilities in general propositional structures represented by lattices (including the non-distributive case).Comment: Improved versio

    Finitely dependent coloring

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    We prove that proper coloring distinguishes between block-factors and finitely dependent stationary processes. A stochastic process is finitely dependent if variables at sufficiently well-separated locations are independent; it is a block-factor if it can be expressed as an equivariant finite-range function of independent variables. The problem of finding non-block-factor finitely dependent processes dates back to 1965. The first published example appeared in 1993, and we provide arguably the first natural examples. More precisely, Schramm proved in 2008 that no stationary 1-dependent 3-coloring of the integers exists, and conjectured that no stationary k-dependent q-coloring exists for any k and q. We disprove this by constructing a 1-dependent 4-coloring and a 2-dependent 3-coloring, thus resolving the question for all k and q. Our construction is canonical and natural, yet very different from all previous schemes. In its pure form it yields precisely the two finitely dependent colorings mentioned above, and no others. The processes provide unexpected connections between extremal cases of the Lovasz local lemma and descent and peak sets of random permutations. Neither coloring can be expressed as a block-factor, nor as a function of a finite-state Markov chain; indeed, no stationary finitely dependent coloring can be so expressed. We deduce extensions involving d dimensions and shifts of finite type; in fact, any non-degenerate shift of finite type also distinguishes between block-factors and finitely dependent processes

    Leaving no-one behind? Informal economies, economic inclusion, and Islamic extremism in Nigeria

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    This article examines how the Post-2015 commitment to economic inclusion affects informal economic actors in developing countries. It highlights the selective dynamics of inclusive market models which generate new processes of exclusion in which the most vulnerable continue to be left behind. The case of Nigeria reveals how inclusive market initiatives reinforce parallel processes of informalization, poverty and Islamic extremism in the north of the country. Fieldwork in northern Nigeria shows that inclusive initiatives are intensifying competitive struggles within the informal economy in which stronger actors are crowding out poorer, less educated and migrant actors, exacerbating disaffection and vulnerability to radicalization

    Leave No One Behind: Infrastructure and Inclusion

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    This review outlines ways in which different groups of people might be unintentionally excluded if their needs and livelihoods are not taken into account in infrastructure projects. The Sustainable Development Goals (SDGs) and the concept of ‘leave no one behind’ capture the desire to ensure people are not excluded as citizens in their society. Some of the SDGs that illustrate factors to be addressed to prevent social exclusion and leave no one behind include: (1) No poverty, (2) Good health and well-being, (5) Gender equality, (10) Reduced inequalities and (11) Sustainable cities and communities

    COVID-19: A turning point to further sanitation justice?

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    Sanitation has received increased attention during the COVID-19 pandemic, but the heterogeneity of infrastructures, investments, practices and needs that exist on the ground, have often been overlooked. Consequently, the intersecting inequalities shaping how COVID-19 and sanitation interact remain unaddressed. This paper suggests it is possible to move beyond ‘deficit narratives’, and to support pathways towards just sanitation for all women and men, girls and boys during and beyond the pandemic. Tracking down past, ongoing and projected sanitary arrangements, exploring the political economy of both grid and off-grid investments and promises, and paying attention to the diversity of needs and practices from an intersectional perspective that considers, among other things, class, gender, age, ethnicity and ability, are three directions to do so. Together, these three directions can account for how illness or health, poverty or prosperity, suffering or well-being, stigma or respect are generated for different people who are dependent on, or who are providing, sanitation services. COVID-19 marks a turning point to critically reframe how we talk and act upon just sanitation and to challenge long-term inequalities
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