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

Public and student awareness science: recreational science as a catalyst

When discussing the traditional and new missions of higher education (1996 Report to UNESCO of the International Commission on Education for the 21st Century) Jacques Delors stated that "Excessive attraction to social sciences has broken equilibrium of available graduates for workforce, thus causing doubts of graduates and employers on the quality of knowledge provided by higher education". Likewise, when discussing the progress of science and technology, the 1998 UNESCO World Conference on Higher Education concluded that "Another challenge concerts the latest advancements of Science, the sine qua non of sustainable development"; and that “with Information Technology, the unavoidable invasion of virtual reality has increased the distance between industrial and developing countries". Recreational Science has a long tradition all over the Educational World; it aims to show the basic aspects of Science, aims to entertain, and aims to induce thinking. Until a few years ago, this field of knowledge consisted of a few books, a few kits and other classical (yet innovative) ways to popularize the knowledge of Nature and the laws governing it. In Spain, the interest for recreational science has increased in the last years. First, new recreational books are being published and found in bookstores. Second the number of Science-related museums and exhibits is increasing. And third, new television shows are produced and new short science-based, superficial sketches are found in variety programs. However, actual programs in Spanish television dealing seriously with Science are scarce. Recreational Science, especially that related to physical phenomena like light or motion, is generally found at Science Museums because special equipment is required. On the contrary, Science related mathematics, quizzes and puzzles use to gather into books, e.g. the extensive collections by Martin Gardner. However, lately Science podcasts have entered the field of science communication. Not only traditional science journals and television channels are providing audio and video podcasts, but new websites deal exclusively with science podcasts, in particular on Recreational Science. In this communication we discuss the above mentioned trends and show our experience in the last two years in participating at Science Fairs and university-sponsored events to attract students to science and technology careers. We show a combination of real examples (e.g., mathemagic), imagination, use of information technology, and use of social networks. We present as well an experience on designing a computational, interactive tool to promote chemistry among high school, prospective students using computers ("Dancing with Bionanomolecules"). Like the concepts related to Web 2.0, it has been already proposed that a new framework for communication of science is emerging, i.e., Science Communication 2.0, where people and institutions develop new innovative ways to explain science topics to diverse publics – and where Recreational Science is likely to play a leading role

“El Mediterráneo en el diálogo Norte-Sur”: III Curso Internacional de Defensa. Jaca (Huesca), 19-23 de septiembre de 1995

Del 19 al 23 de setembre de 1995 es va celebrar a Jaca (Osca) el III Curs Internacional de Defensa, amb el títol específic “ El Mediterrani en el Diàleg Nord Sud”, organitzat per la Càtedra Miguel de Cervantes de l’Acadèmia General Militar i la Universitat de Saragossa. Els objectius assenyalats pels organitzadors es van centrar a potenciar l’intercanvi d’opinions entre especialistes i representants de les institucions sobre aspectes polítics, socials, econòmics i de defensa que afecten l’espai geopolític de les dues riberes del Mediterrani, i a analitzar els mecanismes de cooperació que actuen a l’àrea i la política de la Unió Europea a la zona

Estimation of electronic coupling in π -stacked donor-bridge-acceptor systems: correction of the two-state model

Comparison of donor-acceptor electronic couplings calculated within two-state and three-state models suggests that the two-state treatment can provide unreliable estimates of Vda because of neglecting the multistate effects. We show that in most cases accurate values of the electronic coupling in a π stack, where donor and acceptor are separated by a bridging unit, can be obtained as Ṽ da = (E2 - E1) μ12 Rda + (2 E3 - E1 - E2) 2 μ13 μ23 Rda2, where E1, E2, and E3 are adiabatic energies of the ground, charge-transfer, and bridge states, respectively, μij is the transition dipole moments between the states i and j, and Rda is the distance between the planes of donor and acceptor. In this expression based on the generalized Mulliken-Hush approach, the first term corresponds to the coupling derived within a two-state model, whereas the second term is the superexchange correction accounting for the bridge effect. The formula is extended to bridges consisting of several subunits. The influence of the donor-acceptor energy mismatch on the excess charge distribution, adiabatic dipole and transition moments, and electronic couplings is examined. A diagnostic is developed to determine whether the two-state approach can be applied. Based on numerical results, we showed that the superexchange correction considerably improves estimates of the donor-acceptor coupling derived within a two-state approach. In most cases when the two-state scheme fails, the formula gives reliable results which are in good agreement (within 5%) with the data of the three-state generalized Mulliken-Hush model