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.

The brain uses single-trial multisensory memories to discriminate without awareness.

Multisensory experiences enhance perceptions and facilitate memory retrieval processes, even when only unisensory information is available for accessing such memories. Using fMRI, we identified human brain regions involved in discriminating visual stimuli according to past multisensory vs. unisensory experiences. Subjects performed a completely orthogonal task, discriminating repeated from initial image presentations intermixed within a continuous recognition task. Half of initial presentations were multisensory, and all repetitions were exclusively visual. Despite only single-trial exposures to initial image presentations, accuracy in indicating image repetitions was significantly improved by past auditory-visual multisensory experiences over images only encountered visually. Similarly, regions within the lateral-occipital complex-areas typically associated with visual object recognition processes-were more active to visual stimuli with multisensory than unisensory pasts. Additional differential responses were observed in the anterior cingulate and frontal cortices. Multisensory experiences are registered by the brain even when of no immediate behavioral relevance and can be used to categorize memories. These data reveal the functional efficacy of multisensory processing.

On the sources of business cycles in the G-7

This paper examines sources of cyclical movements in output, inflation and the term structure of interest rates. It employs a novel identification approach which uses the sign of the cross correlation function in response to shocks to catalog orthogonal disturbances. We find that demand shocks are the dominant source output, inflation and term structure fluctuations in six of the G-7 countries. Within the class of demand disturbances, nominal shocks are dominant, but their importance declined after 1982. Furthermore, there are no significant differences in the proportion of term structure variability explained by different structural sources at different horizons.

A estação arqueológica de Salamansa (ilha de São Vicente, República de Cabo Verde)

Apresentam‑se os principais resultados obtidos nas duas missões arqueológicas patrocinadas pelo Centro Português de Actividades Subaquáticas (CPAS) à ilha de São Vicente (República de Cabo Verde), em 1998 e em 2005. Em 1998, confirmou‑se o efectivo interesse arqueológico do sítio, localizado sobre o mar, em local abrigado da vasta baía de Salamansa, situada na parte setentrional da ilha, tendo‑se registado a respectiva extensão e estratigrafia e procedido à colheita de amostras para datação. Embora os resultados dessa campanha tivessem sido publicados, indicando estação de carácter habitacional, revelada pela notável acumulação de conchas, acompanhada de abundantes fragmentos de cerâmicas manuais, de produção africana, mantinha‑se indefinida a sua verdadeira natureza. Impunha‑se, assim, proceder à escavação integral da área que ainda subsistia da estação — sujeita de forma contínua a forte erosão marinha — bem como à colheita de novos materiais para datação, de forma a confirmar as conclusões preliminares anteriormente obtidas, objectivos que se concretizaram em 2005. Deste modo, foi possível concluir que, contrariando a hipótese, de início considerada, de poder corresponder a um testemunho da ocupação da ilha em época anterior à chegada dos Portugueses — hipótese que já as primeiras datas de radiocarbono contradiziam — se trata de um sítio onde uma unidade habitacional construída por muros de pedra seca, de planta ortogonal, revela inspiração europeia, aliás sublinhada pelos materiais exumados, onde estão representados produtos com tal origem, como cachimbos de caulino, vidros, faianças portuguesas, e projécteis de armas de fogo, a par de objectos oriundos do Extremo Oriente, num quadro dominado pelas produções cerâmicas africanas. Esta situação evidencia um estabelecimento cuja ocupação se centrou no século XVII, conforme indicam os materiais recolhidos e os resultados das datações obtidas, francamente aberto aos contactos de longa distância, apesar do isolamento do local escolhido. Os restos faunísticos recolhidos, com a presença deburro e de boi, sugerem um estacionamento sedentário, sendo a alimentação assegurada essencialmente pela captura de tartarugas, pela pesca e pela recolecção de moluscos marinhos (especialmente grandes lapas) e complementada pelo consumo de cabra, que poderia ser doméstica ou caçada, dado o estado selvagem a que retornou ali esta espécie. na última parte do trabalho, discutem‑se as diversas hipóteses susceptíveis de explicar esta estação — desde um entreposto comercial relacionado com a exploração agro‑pecuária da ilha de Santo Antão, passando por pequeno estabelecimento especializado de apoio à navegação, com a produção de carne salgada de tartaruga, até ter constituído refúgio relacionado com a intensa pirataria vigente à época no arquipélago, tendo presente os elementos históricos conhecidos, que, aliás, indicam que o início da ocupação permanente de São Vicente só se produziu a partir da segunda década do século XIX. Seja como for, a forte componente cultural africana revelada pelo espólio destes primeiros ocupantes da ilha expressa‑se também pelos rituais que terão envolvido o abandono do estabelecimento, com o enterramento de dois vasos emborcados sob o chão da habitação explorada, e a deposição de uma pequena taça, nas mesmas circunstâncias, junto à parede da mesma, do lado externo.

Speculative dynamics in the term structure of interest rates

When long maturity bonds are traded frequently and traders have non-nestedinformation sets, speculative behavior in the sense of Harrison and Kreps (1978) arises.Using a term structure model displaying such speculative behavior, this paper proposesa conceptually and observationally distinct new mechanism generating time varying predictableexcess returns. It is demonstrated that (i) dispersion of expectations about futureshort rates is sufficient for individual traders to systematically predict excess returns and(ii) the new term structure dynamics driven by speculative trade is orthogonal to publicinformation in real time, but (iii) can nevertheless be quantified using only publicly availableyield data. The model is estimated using monthly data on US short to medium termTreasuries from 1964 to 2007 and it provides a good fit of the data. Speculative dynamicsare found to be quantitatively important, potentially accounting for a substantial fractionof the variation of bond yields and appears to be more important at long maturities.

Biplots of fuzzy coded data

A biplot, which is the multivariate generalization of the two-variable scatterplot, can be used to visualize the results of many multivariate techniques, especially those that are based on the singular value decomposition. We consider data sets consisting of continuous-scale measurements, their fuzzy coding and the biplots that visualize them, using a fuzzy version of multiple correspondence analysis. Of special interest is the way quality of fit of the biplot is measured, since it is well-known that regular (i.e., crisp) multiple correspondence analysis seriously under-estimates this measure. We show how the results of fuzzy multiple correspondence analysis can be defuzzified to obtain estimated values of the original data, and prove that this implies an orthogonal decomposition of variance. This permits a measure of fit to be calculated in the familiar form of a percentage of explained variance, which is directly comparable to the corresponding fit measure used in principal component analysis of the original data. The approach is motivated initially by its application to a simulated data set, showing how the fuzzy approach can lead to diagnosing nonlinear relationships, and finally it is applied to a real set of meteorological data.

Computing congruences of modular forms and Galois representations modulo prime powers

This article starts a computational study of congruences of modular forms and modular Galoisrepresentations modulo prime powers. Algorithms are described that compute the maximum integermodulo which two monic coprime integral polynomials have a root in common in a sensethat is defined. These techniques are applied to the study of congruences of modular forms andmodular Galois representations modulo prime powers. Finally, some computational results withimplications on the (non-)liftability of modular forms modulo prime powers and possible generalisationsof level raising are presented.

On the robustness of least-squares Monte Carlo (LSM) for pricing American derivatives

This paper analyses the robustness of Least-Squares Monte Carlo, a techniquerecently proposed by Longstaff and Schwartz (2001) for pricing Americanoptions. This method is based on least-squares regressions in which theexplanatory variables are certain polynomial functions. We analyze theimpact of different basis functions on option prices. Numerical resultsfor American put options provide evidence that a) this approach is veryrobust to the choice of different alternative polynomials and b) few basisfunctions are required. However, these conclusions are not reached whenanalyzing more complex derivatives.

Macaulay style formulas for sparse resultants

We present formulas for computing the resultant of sparse polyno- mials as a quotient of two determinants, the denominator being a minor of the numerator. These formulas extend the original formulation given by Macaulay for homogeneous polynomials.

Galois representations, embedding problems and modular forms

To an odd irreducible 2-dimensional complex linear representation of the absolute Galois group of the field Q of rational numbers, a modular form of weight 1 is associated (modulo Artin's conjecture on the L-series of the representation in the icosahedral case). In addition, linear liftings of 2-dimensional projective Galois representations are related to solutions of certain Galois embedding problems. In this paper we present some recent results on the existence of liftings of projective representations and on the explicit resolution of embedding problems associated to orthogonal Galois representations, and explain how these results can be used to construct modular forms.

Three-dimensional magnetic resonance myocardial motion tracking from a single image plane.

Three-dimensional imaging for the quantification of myocardial motion is a key step in the evaluation of cardiac disease. A tagged magnetic resonance imaging method that automatically tracks myocardial displacement in three dimensions is presented. Unlike other techniques, this method tracks both in-plane and through-plane motion from a single image plane without affecting the duration of image acquisition. A small z-encoding gradient is subsequently added to the refocusing lobe of the slice-selection gradient pulse in a slice following CSPAMM acquisition. An opposite polarity z-encoding gradient is added to the orthogonal tag direction. The additional z-gradients encode the instantaneous through plane position of the slice. The vertical and horizontal tags are used to resolve in-plane motion, while the added z-gradients is used to resolve through-plane motion. Postprocessing automatically decodes the acquired data and tracks the three-dimensional displacement of every material point within the image plane for each cine frame. Experiments include both a phantom and in vivo human validation. These studies demonstrate that the simultaneous extraction of both in-plane and through-plane displacements and pathlines from tagged images is achievable. This capability should open up new avenues for the automatic quantification of cardiac motion and strain for scientific and clinical purposes.

Das römische Theater von Avenches/Aventicum : Architektur, Baugeschichte, kulturhistorische Aspekte

Résumée Le théâtre romain d'Aventicum s'inscrit entre la petite ville moderne d'Avenches et le village de Donatyre, au pied d'une colline en pente douce délimitant au sud-est la plaine de la Broye. Il se situe à l'ouest des quartiers urbains antiques, construits selon un plan orthogonal, et s'intègre à une zone comptant divers temples et édifices publics. Dès l'hiver 1889/1890, l'Association Pro Aventico nouvellement fondée lança les premières fouilles archéologiques. Jusqu'en 1914, on dégagea les parties originales de la maçonnerie tout en assurant la restauration de l'édifice. En 1926/1927 et de 1939 à 1942 auront lieu d'autres fouilles de grande envergure, accompagnées de mesures de conservation. En 2001, la Fondation Pro Aventico lança un projet visant à étudier l'histoire de la construction ainsi que l'architecture du monument, alors connues en partie seulement. Sur la base de vestiges attestant la présence d'édifices antérieurs au théâtre, on définira pour la construction de ce dernier un terminus post quem entre 100 et 120 ap. J.-C. Comme l'indique l'étude du plan au sol, ce projet nécessita une importante planification. L'édifice lui-même se constitue d'une zone en demi-cercle réservée au public, dont les substructions indiquent qu'elle était partiellement isolée des autres. La cavea, subdivisée en trois secteurs concentriques, se termine par le bâtiment des halles et par les aditus; on relèvera que les rangées supérieures réservées aux spectateurs s'étendaient sans doute au-delà des halles et jusqu'à la façade. Les aditus permettaient d'accéder à la zone de l'orchestra et de la scène, dominée par une plate-forme de plan rectangulaire et bordée d'une proédrie. On disposait de deux voies d'accès différentes: l'une à l'avant, par les arcades des halles, et l'une à l'arrière, pratiquée dans le mur en demi-cercle; apparemment, on ne pouvait pénétrer que dans la partie centrale de ce dernier. On ne parvient à restituer que partiellement les voies de circulation dans les substructions de la cavea, en raison de leur piètre état de conservation. On a par contre pu repérer le deambulatorium, à la périphérie, ainsi que cinq vomitoria sur la première praecinctio et six vomitoria sur la seconde praecinctio. On peut admettre, sans toutefois disposer d'arguments à toute épreuve, que la troisième rangée, en haut, était accessible par des cages d'escaliers conduisant à la summa cavea. Ces hypothèses, fondées essentiellement sur le plan au sol de l'édifice et touchant aux voies de circulation, sont corroborées par une restitution des gradins des parties en élévation, aujourd'hui disparus. Quelques éléments architecturaux fournissent des arguments décisifs pour cette restitution, comme par exemple un bloc de gradin qui permet de conclure à un pendage de la cavea de 26.5°. On peut par ailleurs démontrer que le module architectural défini sur la base du plan au sol fut également appliqué lors de la planification de l'élévation. Grâce à des fragments de corniche, à deux chapiteaux de pilastre ornés de feuilles d'acanthe, à une base de pilastre engagée in situ dans la maçonnerie restaurée, et en tenant compte du module architectural, on peut proposer une reconstitution approximative de la composition de la façade de l'enceinte en demi-cercle. Si les structures architecturales révèlent que le théâtre fut planifié et édifié selon un seul et unique concept, on observe cependant quelques transformations et modifications au cours du temps. D'une part, on décèle en divers endroits des traces de réparation et de consolidation, visant sans doute à stabiliser un bâtiment ayant visiblement subi des dégâts. Par ailleurs, on a également entrepris des modifications structurelles ou fonctionnelles, comme l'édification ultérieure du postscaenium le long du mur de scène extérieur. Dans un contexte identique, on relèvera également deux murs flanquant les basiliques, qu'on suppose être en relation avec l'agrandissement du complexe architectural du temple du Cigognier et du théâtre, augmenté des deux temples édifiés au milieu du 2e s. ap. J.-C. au lieu-dit Au Lavoëx. L'excavation, au cours du dernier tiers du IIIe siècle ap. J.-C., d'un fossé de près de 6 m de large pour 1.5 m de profondeur tout autour de l'édifice fit du théâtre un véritable lieu fortifié. Au-dessus du fossé, on a pu relever une séquence stratigraphique témoignant d'une activité d'habitation à proximité du théâtre pour la période allant du IVe au VIIe siècle ap. J.-C. Il s'agit de l'un des rares cas où l'on peut, à Avenches, évoquer la présence d'un habitat de la période du Haut Moyen Age.

A numerical characterization of hypersurface singularities

In this note we give a numerical characterization of hypersurface singularities in terms of the normalized Hilbert-Samuel coefficients, and we interpret this result from the point of view of rigid polynomials.