Applied mathematical problem solving, modelling, applications, and links to other subjects

The paper will consist of three parts. In part I we shall present some background considerations which are necessary as a basis for what follows. We shall try to clarify some basic concepts and notions, and we shall collect the most important arguments (and related goals) in favour of problem solving, modelling and applications to other subjects in mathematics instruction. In the main part II we shall review the present state, recent trends, and prospective lines of development, both in empirical or theoretical research and in the practice of mathematics instruction and mathematics education, concerning (applied) problem solving, modelling, applications and relations to other subjects. In particular, we shall identify and discuss four major trends: a widened spectrum of arguments, an increased globality, an increased unification, and an extended use of computers. In the final part III we shall comment upon some important issues and problems related to our topic.

Translation Invariance in Object Recognition, and Its Relation to Other Visual Transformations

Human object recognition is generally considered to tolerate changes of the stimulus position in the visual field. A number of recent studies, however, have cast doubt on the completeness of translation invariance. In a new series of experiments we tried to investigate whether positional specificity of short-term memory is a general property of visual perception. We tested same/different discrimination of computer graphics models that were displayed at the same or at different locations of the visual field, and found complete translation invariance, regardless of the similarity of the animals and irrespective of direction and size of the displacement (Exp. 1 and 2). Decisions were strongly biased towards same decisions if stimuli appeared at a constant location, while after translation subjects displayed a tendency towards different decisions. Even if the spatial order of animal limbs was randomized ("scrambled animals"), no deteriorating effect of shifts in the field of view could be detected (Exp. 3). However, if the influence of single features was reduced (Exp. 4 and 5) small but significant effects of translation could be obtained. Under conditions that do not reveal an influence of translation, rotation in depth strongly interferes with recognition (Exp. 6). Changes of stimulus size did not reduce performance (Exp. 7). Tolerance to these object transformations seems to rely on different brain mechanisms, with translation and scale invariance being achieved in principle, while rotation invariance is not.

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

Otras clases de Mates ... other Maths lessons.

Resumen basado en la publicación

Do parents and children know each other? : a study about agreement on personality within families. '??Se conocen bien los padres y los hijos? : un estudio sobre el grado de acuerdo en personalidad dentro de las familias'

Resumen tomado de la publicaci??n. Resumen tambi??n en ingl??s

Reading Other File Formats.doc (A1)

Notes on how to get from Excel, Access and Textfiles into SPSS. Used in Research Skills for Biomedical Science

How to Share Word and Other Documents Using Adobe Connect

This 3-minute video shows how you can share documents during an Adobe Connect meeting - for example showing a Word document or Excel spreadsheet to the other participants.

INFO2009 Privacy DPA and other legislation.

Slides related to data protection act, plus guidance on identifying other resources covering the area of privacy

The Webcat and other library resources

This presentation was used early in semester 1 2010-11 to introduce History first year student to the library catalogue (Webcat) and a range of other library resources

IT and other training in the always connected era

Abstract Google and YouTube are quickly becoming the training resource of choice for the IT literate, especially in relation to computer based applications. Many businesses are addressing this training issue in a number of ways, some more successful than others. Find out what the IT services at the university are doing to adapt to this change and contribute to the discussion on how the approach could be improved. Before the talk you could have a look at the following; * One service that has been licenced is Lynda http://go.soton.ac.uk/lynda or lynda.com (note you have to enter www.southampton.ac.uk as the organisation if you don’t log in through the go.soton link) * The IT training team publish a portfolio of systems and courses at http://www.southampton.ac.uk/isolutions/computing/training/portfolio/index.php. * More and more internal systems are being supported through online guides such as http://go.soton.ac.uk/bgsg

Lupus nephritis in colombians: Contrasts and comparisons with other populations

Lupus nephritis (LN) is one of the most serious complications of systemic lupus erythematosus (SLE) since it is the major predictor of poor prognosis. The purpose of this study was to examine the clinical and immunological characteristics associated with LN development during the course of SLE in Colombians. Therefore, patients with SLE followed at five different referral centers in Medellin, Bogota, and Cali were included in this cross-sectional and multicenter study. Factors influencing LN were assessed by conditional logistic regression analysis, adjusting by gender, age at onset, duration of disease, and city of origin. The entire sample population included 467 patients, of whom 51% presented with LN. The presence of anti-dsDNA antibodies (adjusted odds ratio (AOR), 2.06; 95% confidence interval (CI), 1.16–3.65), pleuritis (AOR, 3.82; 95% CI, 1.38–10.54), and hypertension (AOR, 2.63; 95% CI, 1.23–5.62) were positively associated with LN, whereas the presence of anti-La antibodies was a protective factor against LN development (AOR, 0.4; 95% CI, 0.19–0.85). A review of literature on LN in different populations is made. The identified clinical- and laboratory-associated factors would assist earlier diagnosis and guide decisions on therapeutic interventions on this critical and frequent complication of SLE.

Economic integration. an overview of basic economic theory and other related issues

Este documento presenta una visión amplia de la Teoría de Integración Económica desde el punto de vista de la teoría de unión aduanera. Se argumenta que dicha teoría carece de integración y que los recientes desarrollos en el tema no parecen resolver esta falla. A pesar de esto, se sugiere que los desarrollos teóricos surgidos a partir del trabajo seminal de Viner y posteriormente desarrollados por otros teóricos, son aún útiles como herramienta de investigación empírica en el tema.