Extended generalised variances, with applications

We consider a measure ψk of dispersion which extends the notion of Wilk’s generalised variance for a d-dimensional distribution, and is based on the mean squared volume of simplices of dimension k≤d formed by k+1 independent copies. We show how ψk can be expressed in terms of the eigenvalues of the covariance matrix of the distribution, also when a n-point sample is used for its estimation, and prove its concavity when raised at a suitable power. Some properties of dispersion-maximising distributions are derived, including a necessary and sufficient condition for optimality. Finally, we show how this measure of dispersion can be used for the design of optimal experiments, with equivalence to A and D-optimal design for k=1 and k=d, respectively. Simple illustrative examples are presented

Commercial sponge fishing in Libya: Historical records, present status and perspectives

Natural bath sponges (genera Spongia and Hippospongia, Porifera, Demospongiae) have been harvested for millennia to be used as aids to beauty and body tools, in traditional and modem medicine as well as in painting. Recently, a series of severe epidemics have affected Mediterranean commercial sponges fostering the overexploitation of remaining fishing grounds. Furthermore, Mediterranean bath sponges attain the highest prices compared to Caribbean or Indo-Pacific ones but little or no correct information on origin is transferred to the final buyer. A complex network of re-selling activities and the lack of labelling make it almost impossible to track the pathway of sponge trade. Some of the finest Mediterranean natural bath sponges come from Libya. Nevertheless, little information on Libyan sponge banks and trade have been available mostly given the former international ban. Under an Italian-Libyan joint-project it was possible to assess the past and present situation of sponge fishing in Libya, roughly covering a period of 150 years. After rather low production in years 1860-1879, average crop exceeded 40 t/year between 1880 and 1929. The peak was recorded in years 1920-1929 (almost 70 t/year on average). Today Libyan sponge fishery and trade are mostly confined to the eastern area of the country. Less than 10 t/year are currently harvested. According to a preliminary SCUBA diving survey along the Libyan coasts, sponges belonging to the order Dictyoceratida appear to be the most conspicuous sessile invertebrates in the investigated areas. Here, sponges belonging to the genera Ircinia and Sarcotragus (commonly defined "wild sponges" with no commercial value) appear to be more abundant than those belonging to the genera Spongia and Hippospongia. Sustainable approaches to the exploitation of this valuable natural resource such as sponge farming are proposed and discussed. (c) 2007 Elsevier B.V. All rights reserved

Sponges architecture by colour: new insights into the fibres morphogenesis, skeletal spatial layout and morpho-anatomical traits of a marine horny sponge species (Porifera)

This paper focuses on the skeletal architecture and morphotraits of the Mediterranean horny sponge Sarcotragus spinosulus (Demospongiae, Keratosa, Dictyoceratida, Irciniidae). This special endoskeletal system consists of a dense, variably complex connective architecture, which extends throughout the entire sponge body and is embedded in an abundant jelly-like extracellular matrix (ECM). To investigate the topographic arrangement and micro-morphotraits of these connective structures in detail and by colour, also during morphogenetic processes, histology techniques using light microscopy are essential. New information is provided on the coordinated morphogenetic processes that characterize the growth and assembly of collagenic prototype structures in the matrix of fibrous skeletal elements and drive skeleton remodelling. Our results also highlight some novelties and some remarkable peculiarities of fibrous, filamentous and fibrillar components at the levels of both composition and structure. The morphofunctional significance of skeletal architecture is suggested in the background of the anatomical complexity of S. spinosulus

HO-1 induction in cancer progression: A matter of cell adaptation

The upregulation of heme oxygenase-1 (HO-1) is one of the most important mechanisms of cell adaptation to stress. Indeed, the redox sensitive transcription factor Nrf2 is the pivotal regulator of HO-1 induction. Through the antioxidant, antiapoptotic, and antinflammatory properties of its metabolic products, HO-1 plays a key role in healthy cells in maintaining redox homeostasis and in preventing carcinogenesis. Nevertheless, several lines of evidence have highlighted the role of HO-1 in cancer progression and its expression correlates with tumor growth, aggressiveness, metastatic and angiogenetic potential, resistance to therapy, tumor escape, and poor prognosis, even though a tumor-and tissue-specific activity has been observed. In this review, we summarize the current literature regarding the pro-tumorigenic role of HO-1 dependent tumor progression as a promising target in anticancer strategy

Simplicial variances, potentials and Mahalanobis distances

The average squared volume of simplices formed by k independent copies from the sameprobability measure µ on Rddefines an integral measure of dispersion k(µ), which is aconcave functional of µ after suitable normalization. When k = 1 it corresponds to tr(Σµ)and when k = d we obtain the usual generalized variance det(Σµ), with Σµthe covariancematrix of µ. The dispersion k(µ) generates a notion of simplicial potential at any x ∈ Rd,dependent on µ. We show that this simplicial potential is a quadratic convex function ofx, with minimum value at the mean aµfor µ, and that the potential at aµdefines a centralmeasure of scatter similar to k(µ), thereby generalizing results by Wilks (1960) andvan der Vaart (1965) for the generalized variance. Simplicial potentials define generalizedMahalanobis distances, expressed as weighted sums of such distances in every k-margin,and we show that the matrix involved in the generalized distance is a particular generalizedinverse of Σµ, constructed from its characteristic polynomial, when k = rank(Σµ). Finally,we show how simplicial potentials can be used to define simplicial distances between twodistributions, depending on their means and covariances, with interesting features whenthe distributions are close to singularit