Continuous Average Straightness in Spatial Graphs

The Straightness is a measure designed to characterize a pair of vertices in a spatial graph. It is defined as the ratio of the Euclidean distance to the graph distance between these vertices. It is often used as an average, for instance to describe the accessibility of a single vertex relatively to all the other vertices in the graph, or even to summarize the graph as a whole. In some cases, one needs to process the Straightness between not only vertices, but also any other points constituting the graph of interest. Suppose for instance that our graph represents a road network and we do not want to limit ourselves to crossroad-to-crossroad itineraries, but allow any street number to be a starting point or destination. In this situation, the standard approach consists in: 1) discretizing the graph edges, 2) processing the vertex-to-vertex Straightness considering the additional vertices resulting from this discretization, and 3) performing the appropriate average on the obtained values. However, this discrete approximation can be computationally expensive on large graphs, and its precision has not been clearly assessed. In this article, we adopt a continuous approach to average the Straightness over the edges of spatial graphs. This allows us to derive 5 distinct measures able to characterize precisely the accessibility of the whole graph, as well as individual vertices and edges. Our method is generic and could be applied to other measures designed for spatial graphs. We perform an experimental evaluation of our continuous average Straightness measures, and show how they behave differently from the traditional vertex-to-vertex ones. Moreover, we also study their discrete approximations, and show that our approach is globally less demanding in terms of both processing time and memory usage. Our R source code is publicly available under an open source license

The Network Analysis of Urban Streets: A Primal Approach

The network metaphor in the analysis of urban and territorial cases has a long tradition especially in transportation/land-use planning and economic geography. More recently, urban design has brought its contribution by means of the "space syntax" methodology. All these approaches, though under different terms like accessibility, proximity, integration,connectivity, cost or effort, focus on the idea that some places (or streets) are more important than others because they are more central. The study of centrality in complex systems,however, originated in other scientific areas, namely in structural sociology, well before its use in urban studies; moreover, as a structural property of the system, centrality has never been extensively investigated metrically in geographic networks as it has been topologically in a wide range of other relational networks like social, biological or technological. After two previous works on some structural properties of the dual and primal graph representations of urban street networks (Porta et al. cond-mat/0411241; Crucitti et al. physics/0504163), in this paper we provide an in-depth investigation of centrality in the primal approach as compared to the dual one, with a special focus on potentials for urban design.Comment: 19 page, 4 figures. Paper related to the paper "The Network Analysis of Urban Streets: A Dual Approach" cond-mat/041124

Street centrality and land use intensity in Baton Rouge, Louisiana

This paper examines the relationship between street centrality and land use intensity in Baton Rouge, Louisiana. Street centrality is calibrated in terms of a node's closeness, betweenness and straightness on the road network. Land use intensity is measured by population (residential) and employment (business) densities in census tracts, respectively and combined. Two CIS-based methods are used to transform data sets of centrality (at network nodes) and densities (in census tracts) to one unit for correlation analysis. The kernel density estimation (KDE) converts both measures to raster pixels, and the floating catchment area (FCA) method computes average centrality values around census tracts. Results indicate that population and employment densities are highly correlated with street centrality values. Among the three centrality indices, closeness exhibits the highest correlation with land use densities, straightness the next and betweenness the last. This confirms that street centrality captures location advantage in a city and plays a crucial role in shaping the intraurban variation of land use intensity. (C) 2010 Elsevier Ltd. All rights reserved

Correlating densities of centrality and activities in cities : the cases of Bologna (IT) and Barcelona (ES)

This paper examines the relationship between street centrality and densities of commercial and service activities in cities. The aim is to verify whether a correlation exists and whether some 'secondary' activities, i.e. those scarcely specialized oriented to the general public and ordinary daily life, are more linked to street centrality than others. The metropolitan area of Barcelona (Spain) is investigated, and results are compared with those found in a previous work on the city of Bologna (Italy). Street centrality is calibrated in a multiple centrality assessment (MCA) model composed of multiple measures such as closeness, betweenness and straightness. Kernel density estimation (KDE) is used to transform data sets of centrality and activities to one scale unit for correlation analysis between them. Results indicate that retail and service activities in both Bologna and Barcelona tend to concentrate in areas with better centralities, and that secondary activities exhibit a higher correlation

The influence of oxygen fronts and mesoscale eddies on the foraging patterns and space-use of blue and mako sharks

As populações de predadores pelágicos de topo têm vindo a decrescer drasticamente nas últimas décadas, sendo a sobrepesca considerada a principal responsável por estes declínios. As repercussões destes decréscimos são especialmente graves para as populações de tubarões, uma vez que, dado o seu lento ciclo de vida, estas espécies apresentam uma maior dificuldade em restabelecer os seus números após períodos de pesca intensiva. Além disso, dada a sua posição de topo na cadeia trófica, a remoção de tubarões dos ecossistemas gera efeitos em cascata nos níveis tróficos inferiores, tendo consequências graves e imprevisíveis para todo o ecossistema. Os tubarões azul (Prionace glauca) e anequim (Isurus oxyrinchus) são as duas espécies de tubarões pelágicos mais pescadas no Oceano Atlântico, constituindo, em conjunto, mais de 95% de todos os tubarões pelágicos capturados anualmente neste oceano e estando, respetivamente, classificadas como “quase ameaçada” e “em perigo” pelo IUCN. No entanto, continuam a existir graves problemas ao nível da regulamentação, monitorização e reporte da pesca destas duas espécies, tendo apenas no ano passado (2020) sido estabelecida uma quota máxima para a captura de tubarão azul no Oceano Atlântico, enquanto o tubarão anequim continua sem qualquer quota a restringir a sua captura. A determinação de áreas prioritárias para a conservação de predadores pelágicos de topo é complicada pela extrema mobilidade destes animais e a consequente dificuldade em identificar zonas de agregação devido à falta de dados fiáveis, uma vez que os estudos destas espécies estão historicamente restringidos a dados inerentes às pescas, sendo, por isso, extremamente enviesados. Porém, o advento da tecnologia de telemetria de satélite tem permitido descrever novos comportamentos, bem como uma melhor compreensão da real distribuição espacial e utilização de habitat, horizontal e vertical, destes predadores. Neste sentido, estudos anteriores utilizando dados de esforço de pesca e/ou telemetria de satélite têm sugerido a atração de uma grande variedade de predadores de topo por fenómenos dinâmicos de média dimensão, tais como frentes térmicas e vórtices oceânicos, que estará relacionada com movimentos de procura de alimento. Neste estudo, os movimentos de procura de alimento de 34 tubarões azuis e 24 tubarões anequins foram analisados relativamente à presença de frentes de oxigénio dissolvido (OD), que até agora não tinham sido consideradas na literatura. Para tal, estes tubarões foram capturados em 5 localizações diferentes do Oceano Atlântico Norte (Açores, Cabo Verde, ao largo de Nova Iorque e a sudoeste de Portugal e Inglaterra) e marcados com transmissores de satélite SPOT, que são fixados à barabatana dorsal e permitem seguir os seus movimentos horizontais com elevada precisão. Todas as variáveis ambientais foram extraídas da plataforma CMEMS’s (Copernicus Marine Environment Monitoring Service) Ocean Products, que disponibiliza dados oceanográficos diários e mensais recolhidos através de uma combinação de medições de satélites e de boias à superfície e a meia água. Para identificar a presença de frentes, foram calculados os gradientes máximos de OD (e temperatura) entre células adjacentes. Os resultados aqui apresentados sugerem que frentes de OD podem representar extensas zonas de alimentação para estas duas espécies, sendo esta relação particularmente evidente para os tubarões azuis. Dois tipos de frentes de OD foram identificadas como atrativas para estas espécies: frentes conjuntas de temperatura e OD, forte, persistente e verticalmente estruturadas, onde a grande produtividade existente cria importantes áreas de alimentação que, por sua vez, atraem predadores de níveis tróficos subsequentemente mais elevados; e frentes exclusivas de OD, associadas a zonas hipóxicas, onde a compressão de presas nas águas superficiais, mais oxigenadas, da coluna de água aumenta a probabilidade de encontro entre predador e presa. No entanto, apesar de ambas as espécies terem revelado afinidade para com estes fenómenos, diferenças importantes foram constatadas. Os tubarões azuis demonstraram uma maior relação com as frentes de OD que os tubarões anequins, enquanto o contrário se verificou em relação às frentes de temperatura, resultados que se coadunam com as diferentes estratégias metabólicas apresentadas pelas duas espécies. Presumivelmente, dada a menor taxa metabólica associada a uma estratégia ectotérmica, os tubarões azuis terão uma maior tolerância a diminuições momentâneas de oxigénio, explorando, por isso, zonas de frentes exclusivas de OD quando possível, tal como acontece nas zonas de oxigénio mínimo (ZOMs). Por outro lado, os tubarões anequins, dada a sua capacidade em manter uma temperatura corporal mais ou menos constante – endotermia - combinada com uma maior necessidade de oxigénio, tenderão a favorecer zonas de fortes gradientes térmicos. Este estudo reforça ainda a importância dos vórtices oceânicos para a alimentação de predadores pelágicos em águas oligotróficas, tendo os tubarões anequins revelado uma clara preferência por vórtices ciclónicos (VCs). Por outro lado, os tubarões azuis demonstraram uma utilização mais equilibrada de VCs e vórtices anticiclónicos (VACs), corroborando parcialmente estudos anteriores que sugerem uma relação entre procura de alimento por parte de predadores de topo e VACs, apesar de estes, há muito, serem considerados apenas como “desertos biológicos”. Os resultados aqui apresentados sugerem que a integração de frentes de OD em modelos utilizados para identificação e gestão de áreas prioritárias de conservação destas duas espécies poderá melhorar significativamente os seus resultados. Além disso, a adoção de medidas de gestão de stocks em tempo real, de acordo com a informação inferida destes modelos, tal como é feito, na Austrália, com o Atum Rabilho do Sul (Thunnus maccoyii), uma espécie ameaçada e com uma quota limite estabelecida, poderá melhorar significativamente a gestão e conservação destas espécies, sendo o mesmo, possivelmente, aplicável ao caso de outros predadores pelágicos de topo. Finalmente, este estudo realça a importância da telemetria de satélite para a aquisição de informação relativa aos padrões ecológicos de movimentação a larga escala de grandes predadores marinhos. Acresce que a análise destes movimentos em conjunto com dados oceanográficos permite inferir com maior confiança quanto à importância de determinadas áreas e fenómenos para estas e outras espécies, possibilitando assim, decisões mais informadas no que respeita à gestão de stocks e proteção de habitats de extrema importância ecológica e económica. Pois apenas melhorando o conhecimento que temos sobre os hábitos destas espécies podemos almejar impedir uma total perda da biodiversidade e uma completa disrupção dos ecossistemas marinhos.Pelagic top predator populations worldwide have suffered sharp decreases in abundance over the last decades, with overfishing being the main cause of such declines. Blue (Prionace glauca) and mako sharks (Isurus oxyrinchus) are the two most caught pelagic shark species in the Atlantic Ocean, being classified, respectively, as “near-threatened” and “endangered” by the IUCN red list. However, their catches remain highly unregulated, unmonitored, and unreported. Identification of priority areas for pelagic top predators’ conservation is hampered by the high mobility of these animals and the consequent difficulty in determining aggregation areas, yet mesoscale dynamic features such as thermal fronts and eddies have been suggested to attract a variety of large apex predators while foraging. In this study, the foraging movements of 34 blue and 24 mako sharks, satellite-tagged across 5 different locations in the North Atlantic Ocean, were analysed in relation to dissolved oxygen (DO) fronts, which until now had not been considered. The results presented here suggest that DO fronts might represent extensive foraging areas for these two species, but particularly for blue sharks. Two different DO front types were noticed to attract these species: strong, persistent, and vertically structured thermal-oxygen fronts, where high productivity creates important foraging opportunities; and oxygen-only fronts associated with hypoxic areas where the compression of prey in the more oxygenated surface waters results in higher predator-prey encounters. This study also reinforces the importance of eddies for pelagic predators foraging in oligotrophic waters. In addition, mako sharks revealed a clear preference for cyclonic eddies (CEs) while blue sharks showed a more balanced usage of CEs and anticyclonic eddies. These results strongly suggest the integration of DO fronts in conservation and management modelling, as they can substantially improve the identification of priority conservation areas for these two sharks and, possibly, many other pelagic top predators

CrowdCam: Instantaneous Navigation of Crowd Images Using Angled Graph

We present a near real-time algorithm for interactively exploring a collectively captured moment without explicit 3D reconstruction. Our system favors immediacy and local coherency to global consistency. It is common to represent photos as vertices of a weighted graph, where edge weights measure similarity or distance between pairs of photos. We introduce Angled Graphs as a new data structure to organize collections of photos in a way that enables the construction of visually smooth paths. Weighted angled graphs extend weighted graphs with angles and angle weights which penalize turning along paths. As a result, locally straight paths can be computed by specifying a photo and a direction. The weighted angled graphs of photos used in this paper can be regarded as the result of discretizing the Riemannian geometry of the high dimensional manifold of all possible photos. Ultimately, our system enables everyday people to take advantage of each others' perspectives in order to create on-the-spot spatiotemporal visual experiences similar to the popular bullet-time sequence. We believe that this type of application will greatly enhance shared human experiences spanning from events as personal as parents watching their children's football game to highly publicized red carpet galas.Swiss National Science FoundationEuropean Commission (ERC grant #210806 4DVideo, 7th Framework Programme (FP7/2007- 2013)

Cellular buckling in I-section struts

An analytical model that describes the interactive buckling of a thin-walled I-section strut under pure compression based on variational principles is presented. A formulation combining the Rayleigh--Ritz method and continuous displacement functions is used to derive a system of differential and integral equilibrium equations for the structural component. Numerical continuation reveals progressive cellular buckling (or snaking) arising from the nonlinear interaction between the weakly stable global buckling mode and the strongly stable local buckling mode. The resulting behaviour is highly unstable and when the model is extended to include geometric imperfections it compares excellently with some recently published experiments.Comment: 23 pages, 12 figures. Submitted for special issue of Thin-Walled Structure

Characterization of complex networks: A survey of measurements

Each complex network (or class of networks) presents specific topological features which characterize its connectivity and highly influence the dynamics of processes executed on the network. The analysis, discrimination, and synthesis of complex networks therefore rely on the use of measurements capable of expressing the most relevant topological features. This article presents a survey of such measurements. It includes general considerations about complex network characterization, a brief review of the principal models, and the presentation of the main existing measurements. Important related issues covered in this work comprise the representation of the evolution of complex networks in terms of trajectories in several measurement spaces, the analysis of the correlations between some of the most traditional measurements, perturbation analysis, as well as the use of multivariate statistics for feature selection and network classification. Depending on the network and the analysis task one has in mind, a specific set of features may be chosen. It is hoped that the present survey will help the proper application and interpretation of measurements.Comment: A working manuscript with 78 pages, 32 figures. Suggestions of measurements for inclusion are welcomed by the author

Mathematics and Morphogenesis of the City: A Geometrical Approach

Cities are living organisms. They are out of equilibrium, open systems that never stop developing and sometimes die. The local geography can be compared to a shell constraining its development. In brief, a city's current layout is a step in a running morphogenesis process. Thus cities display a huge diversity of shapes and none of traditional models from random graphs, complex networks theory or stochastic geometry takes into account geometrical, functional and dynamical aspects of a city in the same framework. We present here a global mathematical model dedicated to cities that permits describing, manipulating and explaining cities' overall shape and layout of their street systems. This street-based framework conciliates the topological and geometrical sides of the problem. From the static analysis of several French towns (topology of first and second order, anisotropy, streets scaling) we make the hypothesis that the development of a city follows a logic of division / extension of space. We propose a dynamical model that mimics this logic and which from simple general rules and a few parameters succeeds in generating a large diversity of cities and in reproducing the general features the static analysis has pointed out.Comment: 13 pages, 13 figure

Integrating reinforcement learning, equilibrium points and minimum variance to understand the development of reaching: a computational model

Despite the huge literature on reaching behaviour we still lack a clear idea about the motor control processes underlying its development in infants. This article contributes to overcome this gap by proposing a computational model based on three key hypotheses: (a) trial-anderror learning processes drive the progressive development of reaching; (b) the control of the movements based on equilibrium points allows the model to quickly find the initial approximate solution to the problem of gaining contact with the target objects; (c) the request of precision of the end-movement in the presence of muscular noise drives the progressive refinement of the reaching behaviour. The tests of the model, based on a two degrees of freedom simulated dynamical arm, show that it is capable of reproducing a large number of empirical findings, most deriving from longitudinal studies with children: the developmental trajectory of several dynamical and kinematic variables of reaching movements, the time evolution of submovements composing reaching, the progressive development of a bell-shaped speed profile, and the evolution of the management of redundant degrees of freedom. The model also produces testable predictions on several of these phenomena. Most of these empirical data have never been investigated by previous computational models and, more importantly, have never been accounted for by a unique model. In this respect, the analysis of the model functioning reveals that all these results are ultimately explained, sometimes in unexpected ways, by the same developmental trajectory emerging from the interplay of the three mentioned hypotheses: the model first quickly learns to perform coarse movements that assure a contact of the hand with the target (an achievement with great adaptive value), and then slowly refines the detailed control of the dynamical aspects of movement to increase accuracy