Quantifying rock fabrics: a test of autocorrelation of the spatial distribution of cristals

A novel test of spatial independence of the distribution of crystals or phases in rocksbased on compositional statistics is introduced. It improves and generalizes the commonjoins-count statistics known from map analysis in geographic information systems.Assigning phases independently to objects in RD is modelled by a single-trial multinomialrandom function Z(x), where the probabilities of phases add to one and areexplicitly modelled as compositions in the K-part simplex SK. Thus, apparent inconsistenciesof the tests based on the conventional joins{count statistics and their possiblycontradictory interpretations are avoided. In practical applications we assume that theprobabilities of phases do not depend on the location but are identical everywhere inthe domain of de nition. Thus, the model involves the sum of r independent identicalmultinomial distributed 1-trial random variables which is an r-trial multinomialdistributed random variable. The probabilities of the distribution of the r counts canbe considered as a composition in the Q-part simplex SQ. They span the so calledHardy-Weinberg manifold H that is proved to be a K-1-affine subspace of SQ. This isa generalisation of the well-known Hardy-Weinberg law of genetics. If the assignmentof phases accounts for some kind of spatial dependence, then the r-trial probabilitiesdo not remain on H. This suggests the use of the Aitchison distance between observedprobabilities to H to test dependence. Moreover, when there is a spatial uctuation ofthe multinomial probabilities, the observed r-trial probabilities move on H. This shiftcan be used as to check for these uctuations. A practical procedure and an algorithmto perform the test have been developed. Some cases applied to simulated and realdata are presented.Key words: Spatial distribution of crystals in rocks, spatial distribution of phases,joins-count statistics, multinomial distribution, Hardy-Weinberg law, Hardy-Weinbergmanifold, Aitchison geometry

Biodiversity and global change in Mediterranean benthic communities: perspectives over large spatial and long temporal scales

Many terrestrial and marine systems are experiencing accelerating decline due to the effects of global change. This situation has raised concern about the consequences of biodiversity losses for ecosystem function, ecosystem service provision, and human well-being. Coastal marine habitats are a main focus of attention because they harbour a high biological diversity, are among the most productive systems of the world and present high anthropogenic interaction levels. The accelerating degradation of many terrestrial and marine systems highlights the urgent need to evaluate the consequence of biodiversity loss. Because marine biodiversity is a dynamic entity and this study was interested global change impacts, this study focused on benthic biodiversity trends over large spatial and long temporal scales. The main aim of this project was to investigate the current extent of biodiversity of the high diverse benthic coralligenous community in the Mediterranean Sea, detect its changes, and predict its future changes over broad spatial and long temporal scales. These marine communities are characterized by structural species with low growth rates and long life spans; therefore they are considered particularly sensitive to disturbances. For this purpose, this project analyzed permanent photographic plots over time at four locations in the NW Mediterranean Sea. The spatial scale of this study provided information on the level of species similarity between these locations, thus offering a solid background on the amount of large scale variability in coralligenous communities; whereas the temporal scale was fundamental to determine the natural variability in order to discriminate between changes observed due to natural factors and those related to the impact of disturbances (e.g. mass mortality events related to positive thermal temperatures, extreme catastrophic events). This study directly addressed the challenging task of analyzing quantitative biodiversity data of these high diverse marine benthic communities. Overall, the scientific knowledge gained with this research project will improve our understanding in the function of marine ecosystems and their trajectories related to global change.

Transmit diversity vs. spatial multiplexing in modern MIMO systems

A contemporary perspective on the tradeoff between transmit antenna diversity andspatial multiplexing is provided. It is argued that, in the context of most modern wirelesssystems and for the operating points of interest, transmission techniques that utilizeall available spatial degrees of freedom for multiplexing outperform techniques that explicitlysacrifice spatial multiplexing for diversity. In the context of such systems, therefore,there essentially is no decision to be made between transmit antenna diversity and spatialmultiplexing in MIMO communication. Reaching this conclusion, however, requires thatthe channel and some key system features be adequately modeled and that suitable performancemetrics be adopted; failure to do so may bring about starkly different conclusions. Asa specific example, this contrast is illustrated using the 3GPP Long-Term Evolution systemdesign.