When zero doesn't mean it and other geomathematical mischief

There is almost not a case in exploration geology, where the studied data doesn’t includes below detection limits and/or zero values, and since most of the geological data responds to lognormal distributions, these “zero data” represent a mathematical challenge for the interpretation. We need to start by recognizing that there are zero values in geology. For example the amount of quartz in a foyaite (nepheline syenite) is zero, since quartz cannot co-exists with nepheline. Another common essential zero is a North azimuth, however we can always change that zero for the value of 360°. These are known as “Essential zeros”, but what can we do with “Rounded zeros” that are the result of below the detection limit of the equipment? Amalgamation, e.g. adding Na2O and K2O, as total alkalis is a solution, but sometimes we need to differentiate between a sodic and a potassic alteration. Pre-classification into groups requires a good knowledge of the distribution of the data and the geochemical characteristics of the groups which is not always available. Considering the zero values equal to the limit of detection of the used equipment will generate spurious distributions, especially in ternary diagrams. Same situation will occur if we replace the zero values by a small amount using non-parametric or parametric techniques (imputation). The method that we are proposing takes into consideration the well known relationships between some elements. For example, in copper porphyry deposits, there is always a good direct correlation between the copper values and the molybdenum ones, but while copper will always be above the limit of detection, many of the molybdenum values will be “rounded zeros”. So, we will take the lower quartile of the real molybdenum values and establish a regression equation with copper, and then we will estimate the “rounded” zero values of molybdenum by their corresponding copper values. The method could be applied to any type of data, provided we establish first their correlation dependency. One of the main advantages of this method is that we do not obtain a fixed value for the “rounded zeros”, but one that depends on the value of the other variable. Key words: compositional data analysis, treatment of zeros, essential zeros, rounded zeros, correlation dependency

Mixing compositions and other scales

Theory of compositional data analysis is often focused on the composition only. However in practical applications we often treat a composition together with covariables with some other scale. This contribution systematically gathers and develop statistical tools for this situation. For instance, for the graphical display of the dependence of a composition with a categorical variable, a colored set of ternary diagrams might be a good idea for a first look at the data, but it will fast hide important aspects if the composition has many parts, or it takes extreme values. On the other hand colored scatterplots of ilr components could not be very instructive for the analyst, if the conventional, black-box ilr is used. Thinking on terms of the Euclidean structure of the simplex, we suggest to set up appropriate projections, which on one side show the compositional geometry and on the other side are still comprehensible by a non-expert analyst, readable for all locations and scales of the data. This is e.g. done by defining special balance displays with carefully- selected axes. Following this idea, we need to systematically ask how to display, explore, describe, and test the relation to complementary or explanatory data of categorical, real, ratio or again compositional scales. This contribution shows that it is sufficient to use some basic concepts and very few advanced tools from multivariate statistics (principal covariances, multivariate linear models, trellis or parallel plots, etc.) to build appropriate procedures for all these combinations of scales. This has some fundamental implications in their software implementation, and how might they be taught to analysts not already experts in multivariate analysis

Enhancing learning beyond the classroom: blogging and other social networking tools

Blogging has become one of the key ingredients of the so-called socials networks. This phenomenon has indeed invaded the world of education. Connections between people, comments on each other posts, and assessment of innovation are usually interesting characteristics of blogs related to students and scholars. Blogs have become a kind of new form of authority, bringing about (divergent) discussions which lead to creation of knowledge. The use of blogs as an innovative, educational tool is not at all new. However, their use in universities is not very widespread yet. Blogging for personal affairs is rather commonplace, but blogging for professional affairs – teaching, research and service, is scarce, despite the availability of ready-to-use, free tools. Unfortunately, Information Society has not reached yet enough some universities: not only are (student) blogs scarcely used as an educational tool, but it is quite rare to find a blog written by University professors. The Institute of Computational Chemistry of the University of Girona and the Department of Chemistry of the Universitat Autònoma de Barcelona has joined forces to create “InnoCiència”, a new Group on Digital Science Communitation. This group, formed by ca. ten researchers, has promoted the use of blogs, twitters. wikis and other tools of Web 2.0 in activities in Catalonia concerning the dissemination of Science, like Science Week, Open Day or Researchers’ Night. Likewise, its members promote use of social networking tools in chemistry- and communication-related courses. This communication explains the outcome of social-network experiences with teaching undergraduate students and organizing research communication events. We provide live, hands-on examples and interactive ground to show how blogs and twitters can be used to enhance the yield of teaching and research. Impact of blogging and other social networking tools on the outcome of the learning process is very depending on the target audience and the environmental conditions. A few examples are provided and some proposals to use these techniques efficiently to help students are hinted

Participle Preposing and Other Related Phenomena in Old Spanish and Old Catalan

El participi i altres fenòmens relacionats en el Castellà i el Català antic