centrality measures

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A Comparison of Centrality Measures for Graph-Based Keyphrase Extraction

A Comparison of Centrality Measures for Graph-Based Keyphrase Extraction

The concept of centrality in a graph has been extensively studied in the field of social network analysis and many different measures were pro- posed, see (Opsahl et al., 2010) for a review. Sur- prisingly, very few attempts have been made to ap- ply such measures to keyphrase extraction. (Lit- vak et al., 2011) is one of them, where degree cen- trality is used to select keyphrases. However, they evaluate their method indirectly through a summa- rization task, and to our knowledge there are no published experiments using other centrality mea- sures for keyphrase extraction. In this study, we conduct a systematic evaluation of the most well- known centrality measures applied to the task of keyphrase extraction on three standard evaluation datasets of different languages and domains 1 .
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Centrality measures for evacuation: Finding agile evacuation routes

Centrality measures for evacuation: Finding agile evacuation routes

If we imagine crowd flowing between nodes in the network and always taking the shortest possible geodesic path, then betweenness centrality measures the fraction of that crowd that will flow through i on its way to wherever it is going. Even though this measure might be relevant to application scenarios where all arcs have the same cost (travel time), the issues with the usage of betweenness centrality in evacuation are related with the definition of distance and the origin- destination pairs. In particular, we are concerned with the shortest evacuation time and not the shortest geodesic distance. Moreover, we are not interested in all origin destination pairs, but only in a limited subset of evacuees’ origins O and safe exits D. In the following, we deal with these two issues.
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Local and consistent centrality measures in parameterized networks

Local and consistent centrality measures in parameterized networks

While there is a very large literature in mathematical sociology on centrality mea- sures (see e.g. Borgatti and Everett, 2006; Bonacich and Loyd, 2001; Wasserman and Faust, 1994), little is known about the foundation of centrality measures from a behavioral viewpoint. 2 Ballester et al. (2006) were the first to provide a microfoun- dation for the Katz-Bonacich centrality. They show that, if the utility of each agent is linear-quadratic, then, under some condition, the unique Nash equilibrium in pure strategies of a game where n agents embedded in a network simultaneously choose their effort level is such that the equilibrium effort is equal to the Katz-Bonacich centrality of each agent. This result is true for any possible connected network of n agents. In other words, Nash is Katz-Bonacich and the position of each agent in a network fully explains her behavior in terms of effort level.
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Quasi-stationary distributions as centrality measures of reducible graphs

Quasi-stationary distributions as centrality measures of reducible graphs

highlights the sites with stru ture as in Figure 2 but at the same time the relative ranking of the other sites provided by the standard PageRank with c = 0.85 is preserved. T o illustrate this fa t, we give in T able 3 rankings of some sites under dierent entrality measures. Even though the absolute value of ranking is hanging, the relative ranking among these sites is the same for all

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From Graph Centrality to Data Depth

From Graph Centrality to Data Depth

theory, in particular the study of the Laplacian ( Belkin and Niyogi , 2008 ; Chung , 1997 ; Gin´ e and Koltchinskii , 2006 ; Singer , 2006 ). Our Contribution. Inspired by this movement, we draw a bridge between notions of depth for point clouds and notions of centrality for nodes in a graph. In a nutshell, we consider a multivariate analysis setting where the data consist of a set of points in the Euclidean space. The bridge is, as usual, a neighborhood graph built on this point set, which effectively enables the use of centrality measures, whose large sample limit we examine in a standard asymptotic framework where the number of points increases, while the connectivity radius remains fixed or converges to zero slowly enough. In so doing, we draw a correspondence between some well-known measures of centrality and depth, while some notions of centrality are found to lead to new notions of depth.
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Control Centrality and Hierarchical Structure in Complex Networks

Control Centrality and Hierarchical Structure in Complex Networks

The efficiency of the random upstream attack is even comparable to targeted attacks (see Fig. 3). Since the former requires only the knowledge of the network’s local structure rather than any knowledge of the nodes’ centrality measures or any other global information (i.e. the structure of the A matrix) while the latter rely heavily on them, this finding indicates the advantage of the random upstream attack. The fact that those targeted attacks do not always show significant superiority over the random attacks is intriguing and would be explored in future work. Notice that for the intra-organization network all attack strategies fail in the sense that d is either positive or very close to zero (Fig. 3a). This is due to the fact this network is so dense (with mean degree SkT&58) that we have C c (i)~C c (j)~N for almost all the edges (i?j).
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Social networks: Prestige, centrality, and influence (Invited paper)

Social networks: Prestige, centrality, and influence (Invited paper)

control. Despite this fact, all centrality measures should have some features in common, e.g., they should rank highest the most central node. As concluded in [19] all the three measures of network centrality agree in assigning the maxi- mum centrality score to the star, and the minimum centrality score to a cycle and complete networks. Between these extremes, the three measures of network centrality may differ significantly in their rankings of networks. In a given ap- plication, one centrality measure or a combination of some measures might be more appropriate than another measure or a combination of measures.
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Contextual centrality: going beyond network structure

Contextual centrality: going beyond network structure

This formulation generalizes diffusion centrality and inherits its nice properties in nesting existing reachability-based centrality measures. Moreover, it is easier to compute than Eq. ( 3 ), with this scoring function, we now formally propose contextual centrality. The computational complexity of the algorithm to score according to Eq. ( 3 ) is O(NMT), where M is the aver- age degree, and T is the lengths of the paths that have been inspected. Note that the computational complexity of the formulation (5) is O(NMT). We repeat the operation of multiplying a vector of length N with a sparse matrix, which has an average of M entries per row for T times. This significantly reduces the run time.
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Measures minimizing regularized dispersion

Measures minimizing regularized dispersion

Abstract We consider a continuous extension of a regularized version of the minimax, or dis- persion, criterion widely used in space-filling design for computer experiments and quasi-Monte Carlo methods. We show that the criterion is convex for a certain range of the regularization parameter (depending on space dimension) and give a necessary and sufficient condition char- acterizing the optimal distribution of design points. Using results from potential theory, we investigate properties of optimal measures. The example of design in the unit ball is considered in details and some analytic results are presented. Using recent results and algorithms from ex- perimental design theory, we show how to construct optimal measures numerically. They are often close to the uniform measure but do not coincide with it. The results suggest that designs minimizing the regularized dispersion for suitable values of the regularization parameter should have good space-filling properties. An algorithm is proposed for the construction of n-point designs.
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Kernels on Graphs as Proximity Measures

Kernels on Graphs as Proximity Measures

Data and Link Analysis. Cambridge University Press. 25. Horn, R.A. and Johnson, C.R., 2013. Matrix Analysis (2nd Edition). Cambridge University Press. 26. Ivashkin,V. and Chebotarev P., 2017. Do logarithmic proximity measures outper- form plain ones in graph clustering? In V.A. Kalyagin et al., eds. Models, Algo- rithms, and Technologies for Network Analysis, Proceedings in Mathematics & Statistics, Vol. 197, Springer, In press.

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Viewing Risk Measures as information

Viewing Risk Measures as information

4 Conclusion and Future Directions We have shown ambiguity among situations of rising and falling probability in loss distributions when one, two, and three risk measures are reported. Thus, we suggest that banks be required to submit five risk measures to regulatory bodies, specifically a 95%-VaR, 99%-VaR, 95%-ES, and 99%-ES, and a Maximum Loss, where this is possible. We have demonstrated that the reporting of five risk measures can theoretically lead to an infinite family of possibilities for the actual loss distribution, but we have also conceded that such loss distributions are unlikely to occur. Thus, we feel that banking regulations would be much safer if such regulations require the reporting of five different risk measures.
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International Conference “Melville’s Measures”

International Conference “Melville’s Measures”

Through a structuralist, Foucauldian and neo-materialist prism, Edouard Marsoin (Université de Paris) offered a reading of several of Melville’s works focusing on d[r]

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COMPENSATION MEASURES IN BULGARIA

COMPENSATION MEASURES IN BULGARIA

East part of Bulgaria) which represents a major migratory route for endangered species of birds was constructed a wind power generation field, as well as other projects without adequate assessments of their environmental effects A reasoned opinion on this matter was sent in June 2012 to Bulgaria. The Governmenthas undertaken significant efforts to restrict the damage and prevent further developments but however failed to comply with a key requirement of the EU Habitats Directive, which obliges Member States to take appropriate measures to avoid the deterioration of habitats and disturbance of species for which the Nature 2000 sites have been designated, and compensate for any damage that occurs. The main critics of the Commission were that the Bulgarian government has permitted the constructions of the above wind turbines without approving any mitigation and/or compensation measures.
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Loss-Based Risk Measures

Loss-Based Risk Measures

ρ(X) = max{− min(X(ω 1 ), 0), ..., − min(X(ω n ), 0)} (10) where ω 1 , ..., ω n are the stress scenarios. Naturally, the clearinghouse only consider the losses of the portfolio when computing the margin: as a result, such margin re- quirements may be viewed as a loss-based risk measure. This example satisfies all the properties of Definition 1: it is a loss-based risk measure. This is the main idea behind the SPAN method used by the Chicago Merchantile Exchange (CME). Inter- estingly, the SPAN method was considered as an initial motivation for the definition of coherent risk measures in Artzner et al. (1999). Yet it is easy to check that (10) is loss-dependent and therefore not cash-additive, so is not a coherent risk measure. Example 3 (Expected tail-loss) This popular risk measure is defined as
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Multiperiodic multifractal martingale measures

Multiperiodic multifractal martingale measures

Unité de recherche INRIA Rocquencourt Domaine de Voluceau - Rocquencourt - BP 105 - 78153 Le Chesnay Cedex France Unité de recherche INRIA Lorraine : LORIA, Technopôle de Nancy-Brabois -[r]

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Viewing Risk Measures as information

Viewing Risk Measures as information

We will start by using both the 95%-VaR and the 95%-ES. Again we are left with a problem. In Figure 5 we see that the loss distribution X 1 is uniform, while X 2 has rising probabilities as losses grow, and X 3 is the most standard looking probability tail. It is discouraging that the two most frequently used measures do not distinguish among these three situations. Each of the dis- tributions has a 95%-VaR of 0 and each of them has an 95%-ES of 10. With such different loss characteristics sharing the same VaR and ES, it is astounding that these are the only two measures mentioned in the Basel 3 document. We are encouraged, though, because here the Maximum Loss
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Comonotonic Measures of Multivariate Risks

Comonotonic Measures of Multivariate Risks

convexity and strong coherence have the same representation as in [14], which we discuss further below. The work is organized as follows. The first section motivates a new notion called strong coherence which is shown to be intimately related to existing risk measures axioms, yet appears to be a more natural axiom. The second section shows how the concept of comono- tonic regular risk measures can be extended to the case of multivariate risks, by introducing a proper generalization of the notion of comonotonicity and giving a representation theo- rem. The third section discusses in depth the relation with Optimal Transportation Theory, and shows important examples of actual computations.
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Stability of Curvature Measures

Stability of Curvature Measures

Figure 4: The mean (left) and gaussian (right) curvatures of a point cloud P sampling the union of a solid cube and a solid torus. The colors vary from green (minimum value of the curvature) to red (maximum value of the curvature) passing through blue. The curvature measures are computed using our approach for a fixed offset value of α = 0.1 (the diameter of the point cloud being equal to 2). A curvature value is assigned to each data point p by integration of a Lipschitz function with support contained in a ball of center p and radius 0.3. These values are then used to color the faces of the boundary of the α-shape of P .
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Multiple measures of socio-economic position and psychosocial health: proximal and distal measures.

Multiple measures of socio-economic position and psychosocial health: proximal and distal measures.

well; for example the combined fit for men and women is: χ 2 = 514.96, d.f. = 22, MSEA = 0.047, CFI = 0.995. This is because they are equivalent models, 38 the difference being that Models II and III provide alternative ways of looking at the data. As is clear from Figure 1, Model II treats the three measures of SEP as being situated at the same point in temporal space. It allowed us to examine the direct effects of each measure of social position on psychosocial health. In men, the direct effect is significant for education and occupation but not for income. The negative coefficient (Table 2) for education indicates that a low score of education (implying higher education) is associated with a high score on psychosocial health (implying poorer health). The positive direct effect of occupation on psychosocial health implies that higher score on occupation (implying lower position) is associated with high score on psychosocial health (implying poorer health). The results obtained here (for both
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Comonotonic measures of multivariate risks

Comonotonic measures of multivariate risks

KEY WORDS: regular risk measures, coherent risk measures, comonotonicity, maximal correlation, optimal transportation, strongly coherent risk measures. 1. INTRODUCTION The notion of coherent risk measure was proposed by Artzner et al. (1999) as a set of axioms to be verified by a real-valued measure of the riskiness of an exposure. In addition to monotonicity, positive homogeneity and translation invariance, the proposed coherency axioms include subadditivity, which is loosely associated with hedging. Given this interpretation, it is natural to require the risk measure to be additive on the subsets of risky exposures that are comonotonic, as this situation corresponds to the worse- case scenario for the correlation of the risks. In Kusuoka (2001), Kusuoka showed the remarkable result that law invariant coherent risk measures that are also comonotonic additive are defined by the integral of the quantile function with respect to a positive
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