Testing Spatial Autocorrelation in Weighted Networks : the Modes Permutation Test

In a weighted spatial network, as specified by an exchange matrix, the variances of the spatial values are inversely proportional to the size of the regions. Spatial values are no more exchangeable under independence, thus weakening the rationale for ordinary permutation and bootstrap tests of spatial autocorrelation. We propose an alternative permutation test for spatial autocorrelation, based upon exchangeable spatial modes, constructed as linear orthogonal combinations of spatial values. The coefficients obtain as eigenvectors of the standardised exchange matrix appearing in spectral clustering, and generalise to the weighted case the concept of spatial filtering for connectivity matrices. Also, two proposals aimed at transforming an acessibility matrix into a exchange matrix with with a priori fixed margins are presented. Two examples (inter-regional migratory flows and binary adjacency networks) illustrate the formalism, rooted in the theory of spectral decomposition for reversible Markov chains.

Cabo Verde: um desafio teórico-paradigmático ou um caso Singular?

Fruto de uma experiência de pesquisa em curso, este pequeno ensaio incide sobre a análise do Estado cabo-verdiano no contexto do «paradigma» hegemónico de catalogação (hierárquica) dos Estados na esfera internacional, que vem progressivamente se revelando como sendo uma abordagem inadequada, principalmente no que diz respeito à catalogação de determinados Estados como sendo «frágeis», «falhados» ou «colapsados». Essa análise permitiu a constatação de que Cabo Verde se apresenta com uma dupla «vantagem»: por um lado, constitui uma prova empírico/conceptual da inadequação do referido «paradigma» e simultaneamente surge, a nosso ver, como um caso excepcional de relativo sucesso que se enquadra numa abordagem normativa inovadora.

A singular function and its relation with the number systems involved in its definition

Minkowski's ?(x) function can be seen as the confrontation of two number systems: regular continued fractions and the alternated dyadic system. This way of looking at it permits us to prove that its derivative, as it also happens for many other non-decreasing singular functions from [0,1] to [0,1], when it exists can only attain two values: zero and infinity. It is also proved that if the average of the partial quotients in the continued fraction expansion of x is greater than k* =5.31972, and ?'(x) exists then ?'(x)=0. In the same way, if the same average is less than k**=2 log2(F), where F is the golden ratio, then ?'(x)=infinity. Finally some results are presented concerning metric properties of continued fraction and alternated dyadic expansions.

Riesz-Nágy singular functions revisited

In 1952 F. Riesz and Sz.Nágy published an example of a monotonic continuous function whose derivative is zero almost everywhere, that is to say, a singular function. Besides, the function was strictly increasing. Their example was built as the limit of a sequence of deformations of the identity function. As an easy consequence of the definition, the derivative, when it existed and was finite, was found to be zero. In this paper we revisit the Riesz-N´agy family of functions and we relate it to a system for real numberrepresentation which we call (t, t-1) expansions. With the help of these real number expansions we generalize the family. The singularity of the functions is proved through some metrical properties of the expansions used in their definition which also allows us to give a more precise way of determining when the derivative is 0 or infinity.

Sobriété volontaire : en quête de nouveaux modes de vie

Textes d'Aurélien Boutaud, Jean-Claude Galey, Sylvia Generoso, Susana Jourdan, Jacques Mirenowicz, René Nouailhat, Sylvain Piron, Cécile Renouard, Yvan Rytz et Marie-Christine Zélem.

Un punto de interés geológico singular : La Pedralta (Girona, Catalunya)

Descripció del bloc granític basculant, conegut amb el nom de 'Pedralta', situat entre els termes municipals de Santa Cristina d'Aro i Sant Feliu arrel de la seva caiguda per causes naturals, el 10 de desembre de 1996

Journal des dames et des modes

1819/02/15 (N9,A23).

Journal des dames et des modes

1822/07/25 (N41,A26).

Journal des dames et des modes

1819/02/10 (N8,A23).

Journal des dames et des modes

1819/07/20 (N40,A23).

Journal des dames et des modes

1821/08/20 (N46,A25).

Journal des dames et des modes

1820/05/15 (N27,A24).

Journal des dames et des modes

1822/02/15 (N9,A26).