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This study develops a Connectivity Utility Model that can be used to assess the connectivity of an airport, a train station, a city or a region in multi-modal transport networks involving multiple quality dimensions of transport s...
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This study develops a Connectivity Utility Model that can be used to assess the connectivity of an airport, a train station, a city or a region in multi-modal transport networks involving multiple quality dimensions of transport services. This new connectivity measure considers both direct connections, and single- and multi-modal indirect connections. A novel feature of our model is the use of various radiation functions that not only help aggregate the overall connectivity of different transport modes' terminals in a city, but also capture their contribution to neighbouring cities' connectivity. This makes it possible to assess a region's or a country's overall transport connectivity. The methodology of this model is illustrated using the 2016 Chinese air and rail schedule data. The high concentration in transport services at large cities suggests that there exists a certain degree of inertia in the overall geography of China's transport infrastructure.
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For a connected graph G of order at least two, a connected outer connected geodetic set S of G is called a minimal connected outer connected geodetic set if no proper subset of S is a connected outer connected geodetic set of G. T...
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For a connected graph G of order at least two, a connected outer connected geodetic set S of G is called a minimal connected outer connected geodetic set if no proper subset of S is a connected outer connected geodetic set of G. The upper connected outer connected geodetic number cg(co)(+) (G) of G is the maximum cardinality of a minimal connected outer connected geodetic set of G. We determine bounds for it and certain general properties satisfied by this parameter are studied. It is shown that, for any two integers a, b with 3 <= a <= b, there exists a connected graph G with cg(co) (G) = a and cg(co)(+) (G) = b, where cg(co) (G) is the connected outer connected geodetic number of a graph. Also, another parameter forcing connected outer connected geodetic number f(cog)(G) of a graph G is introduced and several interesting results on this parameter are studied.
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This lecture comprises two parts. Firstly, after a formal definition of segmentation as the largest partition of the space according to a criterion a and a function /, the notion of a morphological connection is reminded. It is us...
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This lecture comprises two parts. Firstly, after a formal definition of segmentation as the largest partition of the space according to a criterion a and a function /, the notion of a morphological connection is reminded. It is used as an input to a central theorem of the paper (Theorem 7), that identifies segmentation with some classes of connections. Just as connections, the segmentations can then be regrouped by suprema and infima. The generality of the theorem makes it valid for all functions from any space to any other one. Two propositions make precise the AND and OR combinations of connective criteria. The segmentation classes turn out to be independent of their location in the measuring held, assuming that a convenient neighbourhood is experimentally accessible. The second part studies the notion of a connected operator, in a more restricted framework than previously. It provides segmentations with more flexibility, and allows us to make them depend- on parameters. Hierarchies of connected filters are built, whose the partitions increase when going up in the pyramid, and where the various levels are structured as semi-groups.
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The traditional vulnerability parameter connectivity is the minimum number of nodes needed to be removed to disconnect a network. Likewise, edge connectivity is the minimum number of edges needed to be removed to disconnect. A dis...
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The traditional vulnerability parameter connectivity is the minimum number of nodes needed to be removed to disconnect a network. Likewise, edge connectivity is the minimum number of edges needed to be removed to disconnect. A disconnected network may still be viable if it contains a sufficiently large component. Component order connectivity and component order edge connectivity are the minimum number of nodes, respectively edges needed to be removed so that all components of the resulting network have order less than some preassigned threshold value. In this paper we survey some results of the component order connectivity models.
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We study the connection between the Goodwillie tower of the identity and the lower central series of the loop group on connected spaces. We define homotopy n–nilpotent groups as homotopy algebras over certain simplicial algebraic...
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We study the connection between the Goodwillie tower of the identity and the lower central series of the loop group on connected spaces. We define homotopy n–nilpotent groups as homotopy algebras over certain simplicial algebraic theories. This notion interpolates between infinite loop spaces and loop spaces, but backwards. We study the relation to ordinary nilpotent groups. We prove that n–excisive functors of the form ΩF factor over the category of homotopy n –nilpotent groups.
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Vertex connectivity and edge connectivity are two important parameters in interconnection networks. Even though they reflect the fault tolerance correctly, they undervalue the resilience of large networks. By the concept of condit...
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Vertex connectivity and edge connectivity are two important parameters in interconnection networks. Even though they reflect the fault tolerance correctly, they undervalue the resilience of large networks. By the concept of conditional connectivity and super-connectivity, the concept of restricted vertex connectivity and restricted edge connectivity of graphs was proposed by Esfahanian [A.H. Esfahanian, Generalized measures of fault tolerance with application to N-cube networks, IEEE Transactions on Computers 38 (1989) 1586–1591]. Such measures take the resilience of large networks into consideration. In this paper, we propose three families of interconnection networks and discuss their restricted vertex connectivity and restricted edge connectivity. In particular, the hypercubes, twisted-cubes, crossed-cubes, mobius cubes, star graphs, pancake graphs, recursive circulant graphs, and k-ary n-cubes are special cases of these families.
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We study connected sum at infinity on smooth, open manifolds. This operation requires a choice of proper ray in each manifold summand. In favorable circumstances, the connected sum at infinity operation is independent of ray choic...
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We study connected sum at infinity on smooth, open manifolds. This operation requires a choice of proper ray in each manifold summand. In favorable circumstances, the connected sum at infinity operation is independent of ray choices. For each m≥ 3, we construct an infinite family of pairs of m-mani folds on which the connected sum at infinity operation yields distinct manifolds for certain ray choices. We use cohomology algebras at infinity to distinguish these manifolds.
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In basic homological algebra, projective, injective and flat modules play an important and fundamental role. In this paper, we discuss some properties of Gorenstein projective, injective and flat modules and Study some connections...
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In basic homological algebra, projective, injective and flat modules play an important and fundamental role. In this paper, we discuss some properties of Gorenstein projective, injective and flat modules and Study some connections between Gorenstein injective and Gorenstein flat modules. We also investigate some connections between Gorenstein projective, injective and flat modules under change of rings.
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The object of the paper is to study some recurrent properties of Generalized Semi-SymmetricConnection on a Riemannian manifold. Some interesting results of a Riemannian Manifold admitting GeneralizedSemi-Symmetric Connection are investigated.
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While the concept of connectivity has gained popularity in fields like hydrology and ecology, little agreement exists on its definition, which hinders its use in both scientific and legal contexts. In contrast, neuroscientists hav...
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While the concept of connectivity has gained popularity in fields like hydrology and ecology, little agreement exists on its definition, which hinders its use in both scientific and legal contexts. In contrast, neuroscientists have developed not only strong conceptualizations of connectivity but also tools to quantify it: a clear distinction is made between structural connectivity, which is determined from brain anatomy; functional connectivity, which is estimated based on statistical dependencies between neuronal electric timeseries; and effective connectivity, which infers causal relations from the same timeseries based on the assumption that "true" interactions occur with a certain time delay. The motivation of this review arose from the hypothesis that connectivity related statistical techniques, which are applied to timeseries of electrical currents measured by placing electrodes on the scalp of the human brain, could also apply to high-frequency hydrological timeseries acquired to characterize catchment response to precipitation. Here we bring together existing conceptualizations of structural, functional and effective connectivity in hydrology and ecology and compare them with those used in brain neuroscience. We then summarize the most important brain connectivity measures and their associated mathematical frameworks before evaluating the potential of those measures to help advance our understanding of hydrologic connectivity properties-in terms of the frequency, magnitude, timing, duration and rate of water movement linking two disparate locations. Lastly, we present a short case study where a selection of brain connectivity measures is applied to 35 groundwater and streamflow timeseries from a Swiss catchment to infer subsurface flow-driven hydrologic connectivity. Our literature review combined with our short case study suggest that an ensemble of functional and effective connectivity measures should be used and constrained not only by structural connecti
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