A didactic sequence of elementary geometric optics Informed by history and philosophy of science

The concepts and instruments required for the teaching and learning of geometric optics are introduced in the didactic processwithout a proper didactic transposition. This claim is secured by the ample evidence of both wide- and deep-rooted alternative concepts on the topic. Didactic transposition is a theory that comes from a reflection on the teaching and learning process in mathematics but has been used in other disciplinary fields. It will be used in this work in order to clear up the main obstacles in the teachinglearning process of geometric optics. We proceed to argue that since Newton’s approach to optics, in his Book I of Opticks, is independent of the corpuscular or undulatory nature of light, it is the most suitable for a constructivist learning environment. However, Newton’s theory must be subject to a proper didactic transposition to help overcome the referred alternative concepts. Then is described our didactic transposition in order to create knowledge to be taught using a dialogical process between students’ previous knowledge, history of optics and the desired outcomes on geometrical optics in an elementary pre-service teacher training course. Finally, we use the scheme-facet structure of knowledge both to analyse and discuss our results as well as to illuminate shortcomings that must be addressed in our next stage of the inquiry.

Genetic structure of Triatoma venosa (Hemiptera: Reduviidae): molecular and morphometric evidence

Triatoma venosa presents a restricted geographical distribution in America and is considered as a secondary vector of Chagas disease in Colombia and Ecuador. A total of 120 adult insects were collected in domestic and peridomestic habitats in an endemic area of the department of Boyacá, Colombia, in order to determine their genetic structure through morphometric and molecular techniques. The head and wings of each specimen were used for the analyses of size, shape, and sexual dimorphism. A significant sexual dimorphism was found, although no differences in size among the studied groups were detected. Differences were found in the analyzed structures except for male heads. DNA was extracted from the legs in order to carry out the internal transcriber space-2 (ITS-2) amplification and the randon amplified polymorphic DNA (RAPD) analyses. Length polymorphisms were not detected in the ITS-2. Fst and Nm values were estimated (0.047 and 3.4, respectively). The high genetic flow found among the insects captured in the domicile and peridomiciliary environment does not permit a genetic differentiation, thus establishing the peridomicile as an important place for epidemiological surveillance.

Where do these bugs come from? Phenotypic structure ofTriatoma infestans populations after control interventions in the Argentine Chaco

House re-invasion by native triatomines after insecticide-based control campaigns represents a major threat for Chagas disease vector control. We conducted a longitudinal intervention study in a rural section (Area III, 407 houses) of Pampa del Indio, northeastern Argentina, and used wing geometric morphometry to compare pre-spray and post-spray (re-infestant bugs) Triatoma infestanspopulations. The community-wide spraying with pyrethroids reduced the prevalence of house infestation by T. infestans from 31.9% to < 1% during a four-year follow-up, unlike our previous studies in the neighbouring Area I. Two groups of bug collection sites differing in wing shape variables before interventions (including 221 adults from 11 domiciles) were used as a reference for assigning 44 post-spray adults. Wing shape variables from post-spray, high-density bug colonies and pre-spray groups were significantly different, suggesting that re-infestant insects had an external origin. Insects from one house differed strongly in wing shape variables from all other specimens. A further comparison between insects from both areas supported the existence of independent re-infestation processes within the same district. These results point to local heterogeneities in house re-infestation dynamics and emphasise the need to expand the geographic coverage of vector surveillance and control operations to the affected region.

Induced aggregation operators in decision making with the Dempster-Shafer belief structure

We study the induced aggregation operators. The analysis begins with a revision of some basic concepts such as the induced ordered weighted averaging (IOWA) operator and the induced ordered weighted geometric (IOWG) operator. We then analyze the problem of decision making with Dempster-Shafer theory of evidence. We suggest the use of induced aggregation operators in decision making with Dempster-Shafer theory. We focus on the aggregation step and examine some of its main properties, including the distinction between descending and ascending orders and different families of induced operators. Finally, we present an illustrative example in which the results obtained using different types of aggregation operators can be seen.

Induced aggregation operators in decision making with the Dempster-Shafer belief structure

We study the induced aggregation operators. The analysis begins with a revision of some basic concepts such as the induced ordered weighted averaging (IOWA) operator and the induced ordered weighted geometric (IOWG) operator. We then analyze the problem of decision making with Dempster-Shafer theory of evidence. We suggest the use of induced aggregation operators in decision making with Dempster-Shafer theory. We focus on the aggregation step and examine some of its main properties, including the distinction between descending and ascending orders and different families of induced operators. Finally, we present an illustrative example in which the results obtained using different types of aggregation operators can be seen.

Surface structure and stability of PdZn and PtZn alloys: Density-functional slab model studies

Geometric parameters of binary (1:1) PdZn and PtZn alloys with CuAu-L10 structure were calculated with a density functional method. Based on the total energies, the alloys are predicted to feature equal formation energies. Calculated surface energies of PdZn and PtZn alloys show that (111) and (100) surfaces exposing stoichiometric layers are more stable than (001) and (110) surfaces comprising alternating Pd (Pt) and Zn layers. The surface energy values of alloys lie between the surface energies of the individual components, but they differ from their composition weighted averages. Compared with the pure metals, the valence d-band widths and the Pd or Pt partial densities of states at the Fermi level are dramatically reduced in PdZn and PtZn alloys. The local valence d-band density of states of Pd and Pt in the alloys resemble that of metallic Cu, suggesting that a similar catalytic performance of these systems can be related to this similarity in the local electronic structures.

Automatic Structure Generation using Genetic Programming and Fractal Geometry

Three dimensional model design is a well-known and studied field, with numerous real-world applications. However, the manual construction of these models can often be time-consuming to the average user, despite the advantages o ffered through computational advances. This thesis presents an approach to the design of 3D structures using evolutionary computation and L-systems, which involves the automated production of such designs using a strict set of fitness functions. These functions focus on the geometric properties of the models produced, as well as their quantifiable aesthetic value - a topic which has not been widely investigated with respect to 3D models. New extensions to existing aesthetic measures are discussed and implemented in the presented system in order to produce designs which are visually pleasing. The system itself facilitates the construction of models requiring minimal user initialization and no user-based feedback throughout the evolutionary cycle. The genetic programming evolved models are shown to satisfy multiple criteria, conveying a relationship between their assigned aesthetic value and their perceived aesthetic value. Exploration into the applicability and e ffectiveness of a multi-objective approach to the problem is also presented, with a focus on both performance and visual results. Although subjective, these results o er insight into future applications and study in the fi eld of computational aesthetics and automated structure design.

Surface structure and stability of PdZn and PtZn alloys: Density-functional slab model studies

Geometric parameters of binary (1:1) PdZn and PtZn alloys with CuAu-L10 structure were calculated with a density functional method. Based on the total energies, the alloys are predicted to feature equal formation energies. Calculated surface energies of PdZn and PtZn alloys show that (111) and (100) surfaces exposing stoichiometric layers are more stable than (001) and (110) surfaces comprising alternating Pd (Pt) and Zn layers. The surface energy values of alloys lie between the surface energies of the individual components, but they differ from their composition weighted averages. Compared with the pure metals, the valence d-band widths and the Pd or Pt partial densities of states at the Fermi level are dramatically reduced in PdZn and PtZn alloys. The local valence d-band density of states of Pd and Pt in the alloys resemble that of metallic Cu, suggesting that a similar catalytic performance of these systems can be related to this similarity in the local electronic structures.

Geometric and Algebraic Aspects of 3D Affine and Projective Structures from Perspective 2D Views

We investigate the differences --- conceptually and algorithmically --- between affine and projective frameworks for the tasks of visual recognition and reconstruction from perspective views. It is shown that an affine invariant exists between any view and a fixed view chosen as a reference view. This implies that for tasks for which a reference view can be chosen, such as in alignment schemes for visual recognition, projective invariants are not really necessary. We then use the affine invariant to derive new algebraic connections between perspective views. It is shown that three perspective views of an object are connected by certain algebraic functions of image coordinates alone (no structure or camera geometry needs to be involved).

The interplay between geometry, electronic structure, and reactivity of Cu-Ni bimetallic (111) surfaces

The mutual influence of surface geometry (e.g. lattice parameters, morphology) and electronic structure is discussed for Cu-Ni bimetallic (111) surfaces. It is found that on flat surfaces the electronic d-states of the adlayer experience very little influence from the substrate electronic structure which is due to their large separation in binding energies and the close match of Cu and Ni lattice constants. Using carbon monoxide and benzene as probe molecules, it is found that in most cases the reactivity of Cu or Ni adlayers is very similar to the corresponding (111) single crystal surfaces. Exceptions are the adsorption of CO on submonolayers of Cu on Ni(111) and the dissociation of benzene on Ni/Cu(111) which is very different from Ni(111). These differences are related to geometric factors influencing the adsorption on these surfaces.

On the use of geometric moments to examine the continuum of sudden stratospheric warmings

The polar winter stratospheric vortex is a coherent structure that undergoes different types of deformation that can be revealed by the geometric invariant moments. Three moments are used—the aspect ratio, the centroid latitude, and the area of the vortex based on stratospheric data from the 40-yr ECMWF Re-Analysis (ERA-40) project—to study sudden stratospheric warmings. Hierarchical clustering combined with data image visualization techniques is used as well. Using the gap statistic, three optimal clusters are obtained based on the three geometric moments considered here. The 850-K potential vorticity field, as well as the vertical profiles of polar temperature and zonal wind, provides evidence that the clusters represent, respectively, the undisturbed (U), displaced (D), and split (S) states of the polar vortex. This systematic method for identifying and characterizing the state of the polar vortex using objective methods is useful as a tool for analyzing observations and as a test for climate models to simulate the observations. The method correctly identifies all previously identified major warmings and also identifies significant minor warmings where the atmosphere is substantially disturbed but does not quite meet the criteria to qualify as a major stratospheric warming.

A detailed single chain model for molten poly(tetrafluoroethylene) from a novel structure refinement technique on neutron scattering data

We present a new methodology that couples neutron diffraction experiments over a wide Q range with single chain modelling in order to explore, in a quantitative manner, the intrachain organization of non-crystalline polymers. The technique is based on the assignment of parameters describing the chemical, geometric and conformational characteristics of the polymeric chain, and on the variation of these parameters to minimize the difference between the predicted and experimental diffraction patterns. The method is successfully applied to the study of molten poly(tetrafluoroethylene) at two different temperatures, and provides unambiguous information on the configuration of the chain and its degree of flexibility. From analysis of the experimental data a model is derived with CC and CF bond lengths of 1.58 and 1.36 Å, respectively, a backbone valence angle of 110° and a torsional angle distribution which is characterized by four isometric states, namely a split trans state at ± 18°, giving rise to a helical chain conformation, and two gauche states at ± 112°. The probability of trans conformers is 0.86 at T = 350°C, which decreases slightly to 0.84 at T = 400°C. Correspondingly, the chain segments are characterized by long all-trans sequences with random changes in sign, rather anisotropic in nature, which give rise to a rather stiff chain. We compare the results of this quantitative analysis of the experimental scattering data with the theoretical predictions of both force fields and molecular orbital conformation energy calculations.

A spatio-temporal structure-based approach to drought characterisation

Drought characterisation is an intrinsically spatio-temporal problem. A limitation of previous approaches to characterisation is that they discard much of the spatio-temporal information by reducing events to a lower-order subspace. To address this, an explicit 3-dimensional (longitude, latitude, time) structure-based method is described in which drought events are defined by a spatially and temporarily coherent set of points displaying standardised precipitation below a given threshold. Geometric methods can then be used to measure similarity between individual drought structures. Groupings of these similarities provide an alternative to traditional methods for extracting recurrent space-time signals from geophysical data. The explicit consideration of structure encourages the construction of summary statistics which relate to the event geometry. Example measures considered are the event volume, centroid, and aspect ratio. The utility of a 3-dimensional approach is demonstrated by application to the analysis of European droughts (15 °W to 35°E, and 35 °N to 70°N) for the period 1901–2006. Large-scale structure is found to be abundant with 75 events identified lasting for more than 3 months and spanning at least 0.5 × 106 km2. Near-complete dissimilarity is seen between the individual drought structures, and little or no regularity is found in the time evolution of even the most spatially similar drought events. The spatial distribution of the event centroids and the time evolution of the geographic cross-sectional areas strongly suggest that large area, sustained droughts result from the combination of multiple small area (∼106 km2) short duration (∼3 months) events. The small events are not found to occur independently in space. This leads to the hypothesis that local water feedbacks play an important role in the aggregation process.

Towards the computer-aided diagnosis of dementia based on the geometric and network connectivity of structural MRI data

We present an intuitive geometric approach for analysing the structure and fragility of T1-weighted structural MRI scans of human brains. Apart from computing characteristics like the surface area and volume of regions of the brain that consist of highly active voxels, we also employ Network Theory in order to test how close these regions are to breaking apart. This analysis is used in an attempt to automatically classify subjects into three categories: Alzheimer’s disease, mild cognitive impairment and healthy controls, for the CADDementia Challenge.

Modelling spectral reflectance of open cork oak woodland: a simulation analysis of the effects of vegetation structure and background

This study analyses the influence of vegetation structure (i.e. leaf area index and canopy cover) and seasonal background changes on moderate-resolution imaging spectrometer (MODIS)-simulated reflectance data in open woodland. Approximately monthly spectral reflectance and transmittance field measurements (May 2011 to October 2013) of cork oak tree leaves (Quercus suber) and of the herbaceous understorey were recorded in the region of Ribatejo, Portugal. The geometric-optical and radiative transfer (GORT) model was used to simulate MODIS response (red, near-infrared) and to calculate vegetation indices, investigating their response to changes in the structure of the overstorey vegetation and to seasonal changes in the understorey using scenarios corresponding to contrasting phenological status (dry season vs. wet season). The performance of normalized difference vegetation index (NDVI), soil-adjusted vegetation index (SAVI), and enhanced vegetation index (EVI) is discussed. Results showed that SAVI and EVI were very sensitive to the emergence of background vegetation in the wet season compared to NDVI and that shading effects lead to an opposing trend in the vegetation indices. The information provided by this research can be useful to improve our understanding of the temporal dynamic of vegetation, monitored by vegetation indices.