Magnification factors for the GTM algorithm

The Generative Topographic Mapping (GTM) algorithm of Bishop et al. (1997) has been introduced as a principled alternative to the Self-Organizing Map (SOM). As well as avoiding a number of deficiencies in the SOM, the GTM algorithm has the key property that the smoothness properties of the model are decoupled from the reference vectors, and are described by a continuous mapping from a lower-dimensional latent space into the data space. Magnification factors, which are approximated by the difference between code-book vectors in SOMs, can therefore be evaluated for the GTM model as continuous functions of the latent variables using the techniques of differential geometry. They play an important role in data visualization by highlighting the boundaries between data clusters, and are illustrated here for both a toy data set, and a problem involving the identification of crab species from morphological data.

Magnification factors for the SOM and GTM algorithms

Magnification factors specify the extent to which the area of a small patch of the latent (or `feature') space of a topographic mapping is magnified on projection to the data space, and are of considerable interest in both neuro-biological and data analysis contexts. Previous attempts to consider magnification factors for the self-organizing map (SOM) algorithm have been hindered because the mapping is only defined at discrete points (given by the reference vectors). In this paper we consider the batch version of SOM, for which a continuous mapping can be defined, as well as the Generative Topographic Mapping (GTM) algorithm of Bishop et al. (1997) which has been introduced as a probabilistic formulation of the SOM. We show how the techniques of differential geometry can be used to determine magnification factors as continuous functions of the latent space coordinates. The results are illustrated here using a problem involving the identification of crab species from morphological data.

Organisation rétinotopique des structures visuelles révélée par imagerie optique cérébrale chez le rat normal

Mémoire numérisé par la Division de la gestion de documents et des archives de l'Université de Montréal

Spatial scaling in human peripheral vision

The observation that performance in many visual tasks can be made independent of eccentricity by increasing the size of peripheral stimuli according to the cortical magnification factor has dominated studies of peripheral vision for many years. However, it has become evident that the cortical magnification factor cannot be successfully applied to all tasks. To find out why, several tasks were studied using spatial scaling, a method which requires no pre-determined scaling factors (such as those predicted from cortical magnification) to magnify the stimulus at any eccentricity. Instead, thresholds are measured at the fovea and in the periphery using a series of stimuli, all of which are simply magnified versions of one another. Analysis of the data obtained in this way reveals the value of the parameter E2, the eccentricity at which foveal stimulus size must double in order to maintain performance equivalent to that at the fovea. The tasks investigated include hyperacuities (vernier acuity, bisection acuity, spatial interval discrimination, referenced displacement detection, and orientation discrimination), unreferenced instantaneous and gradual movement, flicker sensitivity, and face discrimination. In all cases tasks obeyed the principle of spatial scaling since performance in the periphery could be equated to that at the fovea by appropriate magnification. However, E2 values found for different spatial tasks varied over a 200-fold range. In spatial tasks (e.g. bisection acuity and spatial interval discrimination) E2 values were low, reaching about 0.075 deg, whereas in movement tasks the values could be as high as 16 deg. Using a method of spatial scaling it has been possible to equate foveal and peripheral perfonnance in many diverse visual tasks. The rate at which peripheral stimulus size had to be increased as a function of eccentricity was dependent upon the stimulus conditions and the task itself. Possible reasons for these findings are discussed.

Peripheral vision and pattern recognition : a review

We summarize the various strands of research on peripheral vision and relate them to theories of form perception. After a historical overview, we describe quantifications of the cortical magnification hypothesis, including an extension of Schwartz's cortical mapping function. The merits of this concept are considered across a wide range of psychophysical tasks, followed by a discussion of its limitations and the need for non-spatial scaling. We also review the eccentricity dependence of other low-level functions including reaction time, temporal resolution, and spatial summation, as well as perimetric methods. A central topic is then the recognition of characters in peripheral vision, both at low and high levels of contrast, and the impact of surrounding contours known as crowding. We demonstrate how Bouma's law, specifying the critical distance for the onset of crowding, can be stated in terms of the retinocortical mapping. The recognition of more complex stimuli, like textures, faces, and scenes, reveals a substantial impact of mid-level vision and cognitive factors. We further consider eccentricity-dependent limitations of learning, both at the level of perceptual learning and pattern category learning. Generic limitations of extrafoveal vision are observed for the latter in categorization tasks involving multiple stimulus classes. Finally, models of peripheral form vision are discussed. We report that peripheral vision is limited with regard to pattern categorization by a distinctly lower representational complexity and processing speed. Taken together, the limitations of cognitive processing in peripheral vision appear to be as significant as those imposed on low-level functions and by way of crowding.

Peripheral vision and pattern recognition:a review

We summarize the various strands of research on peripheral vision and relate them to theories of form perception. After a historical overview, we describe quantifications of the cortical magnification hypothesis, including an extension of Schwartz's cortical mapping function. The merits of this concept are considered across a wide range of psychophysical tasks, followed by a discussion of its limitations and the need for non-spatial scaling. We also review the eccentricity dependence of other low-level functions including reaction time, temporal resolution, and spatial summation, as well as perimetric methods. A central topic is then the recognition of characters in peripheral vision, both at low and high levels of contrast, and the impact of surrounding contours known as crowding. We demonstrate how Bouma's law, specifying the critical distance for the onset of crowding, can be stated in terms of the retinocortical mapping. The recognition of more complex stimuli, like textures, faces, and scenes, reveals a substantial impact of mid-level vision and cognitive factors. We further consider eccentricity-dependent limitations of learning, both at the level of perceptual learning and pattern category learning. Generic limitations of extrafoveal vision are observed for the latter in categorization tasks involving multiple stimulus classes. Finally, models of peripheral form vision are discussed. We report that peripheral vision is limited with regard to pattern categorization by a distinctly lower representational complexity and processing speed. Taken together, the limitations of cognitive processing in peripheral vision appear to be as significant as those imposed on low-level functions and by way of crowding.

Caracterización y ajuste del factor de magnificación para radiología digital de cadera

Introducción. Las imágenes obtenidas mediante rayos X, determinan una conducta clínica en ortopedia y son analizadas por parte del cirujano en el momento previo a realizar un acto quirúrgico. El planeamiento pre quirúrgico basado en radiografías de cadera, permite predecir el tamaño de los componentes protésicos a utilizar en un reemplazo de cadera. Con el advenimiento de las radiografías digitales, existe la falsa percepción de que estas tienen corregido el factor de magnificación. La corrección de dicho factor requiere un protocolo de calibración de imágenes, aún no implementado en la Fundación Santa Fe de Bogotá (FSFB). Como consecuencia, las radiografías de cadera actualmente resultan magnificadas. Materiales y métodos. Fueron seleccionados 73 pacientes con reemplazo articular total de la cadera intervenidos en la FSFB. Para cada paciente, se estableció la dimensión de la cabeza protésica en la radiografía de cadera obtenida mediante el sistema de radiología digital (PACS-IMPAX) y su tamaño fue comparado con el de la cabeza femoral implantada. Resultados. La concordancia entre los dos observadores al medir la dimensión radiológica de los componentes protésicos fue excelente y el coeficiente de magnificación promedio de 1.2 (20%). Este será introducido al PACS-IMPAX para ajustar el tamaño definitivo de la radiografía. Conclusión. El ajuste del PACS-IMPAX permite obtener radiografías en las cuales se refleja con mayor precisión el tamaño de los segmentos anatómicos y de los componentes protésicos.

Rod bipolar cells in the retina of the capuchin monkey (Cebus apella): Characterization and distribution

Rod bipolar cells in Cebus apella monkey retina were identified by an antibody against the alpha isoform of protein kinase C (PKC alpha). which has been shown to selectively identify rod bipolars in two other primates and various mammals. Vertical sections were used to confirm the identity of these cells by their characteristic morphology of dendrites and axons. Their topographic distribution was assessed in horizontal sections; counts taken along the dorsal, ventral, nasal, and temporal quadrants. The density of rod bipolar cells increased from 500 to 2900 cells/mm(2) at 1 mm from the fovea to reach a peak of 10,000-12,000 cellss/mm(2) at 4 mm, approximately 5 deg of eccentricity, and then gradually decreased toward retinal periphery to values of 5000 cells/mm(2) or less. Rod to rod bipolar density ratio remained between 10 and 20 across most of the retinal extension. The number of rod bipolar cells per retina was 6,360,000 +/- 387,433 (mean +/- S.D., n = 6). The anti-PKC alpha antibody has shown to be a good marker of rod bipolar cells of Cebus, and the cell distribution is similar to that described for other primates. In spite of the difference in the central retina, the density variation of rod bipolar cells in the Cebus and Macaca as well as the convergence from rod to rod bipolar cells are Generally similar, suggesting that both retinae stabilize similar sensitivity (as measured by rod density) and convergence.

Non linear response of planar asymmetric systems

The seismic behaviour of one-storey asymmetric structures has been studied since 1970s by a number of researches studies which identified the coupled nature of the translational-to-torsional response of those class of systems leading to severe displacement magnifications at the perimeter frames and therefore to significant increase of local peak seismic demand to the structural elements with respect to those of equivalent not-eccentric systems (Kan and Chopra 1987). These studies identified the fundamental parameters (such as the fundamental period TL normalized eccentricity e and the torsional-to-lateral frequency ratio Ωϑ) governing the torsional behavior of in-plan asymmetric structures and trends of behavior. It has been clearly recognized that asymmetric structures characterized by Ωϑ >1, referred to as torsionally-stiff systems, behave quite different form structures with Ωϑ <1, referred to as torsionally-flexible systems. Previous research works by some of the authors proposed a simple closed-form estimation of the maximum torsional response of one-storey elastic systems (Trombetti et al. 2005 and Palermo et al. 2010) leading to the so called “Alpha-method” for the evaluation of the displacement magnification factors at the corner sides. The present paper provides an upgrade of the “Alpha Method” removing the assumption of linear elastic response of the system. The main objective is to evaluate how the excursion of the structural elements in the inelastic field (due to the reaching of yield strength) affects the displacement demand of one-storey in-plan asymmetric structures. The system proposed by Chopra and Goel in 2007, which is claimed to be able to capture the main features of the non-linear response of in-plan asymmetric system, is used to perform a large parametric analysis varying all the fundamental parameters of the system, including the inelastic demand by varying the force reduction factor from 2 to 5. Magnification factors for different force reduction factor are proposed and comparisons with the results obtained from linear analysis are provided.

La risposta torsionale non lineare di strutture asimmetriche in pianta

Il lavoro principale di questa tesi è stato quello di fornire gli spettri di particolari coefficienti, detti Magnification Factors, da utilizzare in associazione con gli spettri degli spostamenti già forniti dalla normativa quando si ha a che fare con strutture eccentriche a 3 gradi di libertà per ricavare una prima stima di alcuni punti notevoli di tali strutture (spostamenti longitudinali del centro di massa, del lato flessibile e del lato rigido). In particolare tali Magnification Factors, che dipendono esclusivamente da parametri fisici della struttura (i.e. Ωθ, ξ, e, TL, R), vanno moltiplicati per il valore di spostamento spettrale ricavato dalla normativa entrando nello spettro degli spostamenti con il periodo longitudinale disaccoppiato (TL) della struttura. Il risultato di questo prodotto è lo spostamento longitudinale del punto notevole della struttura eccentrica cui ogni Magnification Factors si riferisce. Gli spettri dei Magnification Factors sono stati ricavati attraverso l’integrazione diretta dell’equazione del moto del sistema dinamico ad 1 piano a 3 gradi di libertà.

Callosal connections of primary visual cortex predict the spatial spreading of binocular rivalry across the visual hemifields

In binocular rivalry, presentation of different images to the separate eyes leads to conscious perception alternating between the two possible interpretations every few seconds. During perceptual transitions, a stimulus emerging into dominance can spread in a wave-like manner across the visual field. These traveling waves of rivalry dominance have been successfully related to the cortical magnification properties and functional activity of early visual areas, including the primary visual cortex (V1). Curiously however, these traveling waves undergo a delay when passing from one hemifield to another. In the current study, we used diffusion tensor imaging (DTI) to investigate whether the strength of interhemispheric connections between the left and right visual cortex might be related to the delay of traveling waves across hemifields. We measured the delay in traveling wave times (ΔTWT) in 19 participants and repeated this test 6 weeks later to evaluate the reliability of our behavioral measures. We found large interindividual variability but also good test-retest reliability for individual measures of ΔTWT. Using DTI in connection with fiber tractography, we identified parts of the corpus callosum connecting functionally defined visual areas V1-V3. We found that individual differences in ΔTWT was reliably predicted by the diffusion properties of transcallosal fibers connecting left and right V1, but observed no such effect for neighboring transcallosal visual fibers connecting V2 and V3. Our results demonstrate that the anatomical characteristics of topographically specific transcallosal connections predict the individual delay of interhemispheric traveling waves, providing further evidence that V1 is an important site for neural processes underlying binocular rivalry.

Visual acuity of dentists under simulated clinical conditions

OBJECTIVES This study examined the near visual acuity of dentists in relation to age and magnification under simulated clinical conditions. MATERIALS AND METHODS Miniaturized visual tests were performed in posterior teeth of a dental phantom head in a simulated clinical setting (dental chair, operating lamp, dental mirror). The visual acuity of 40 dentists was measured under the following conditions: (1) natural visual acuity, distance of 300 mm; (2) natural visual acuity, free choice of distance; (3) Galilean loupes, magnification of ×2.5; (4) Keplerian loupes, ×4.3; (5) operating microscope, ×4, integrated light; (6) operating microscope, ×6.4, integrated light. RESULTS The visual acuity varied widely between individuals and was significantly lower in the group ≥40 years of age (p < 0.001). Significant differences were found between all tested conditions (p < 0.01). Furthermore, a correlation between visual acuity and age was found for all conditions. The performance with the microscope was better than with loupes even with comparable magnification factors. Some dentists had a better visual acuity without optical aids than others with Galilean loupes. CONCLUSIONS Near visual acuity under simulated clinical conditions varies widely between individuals and decreases throughout life. Visual deficiencies can be compensated for with optical aids. CLINICAL RELEVANCE Newly developed miniaturized vision tests have allowed, in a clinically relevant way, to evaluate the influence of magnification and age on the near visual acuity of dentists.

Isotopic signatures and mercury content of arctic char and their prey, and water chemistry of 18 arctic Canadian lakes

Concentrations of mercury (Hg) have increased slowly in landlocked Arctic char over a 10- to 15-year period in the Arctic. Fluxes of Hg to sediments also show increases in most Arctic lakes. Correlation of Hg with trophic level (TL) was used to investigate and compare biomagnification of Hg in food webs from lakes in the Canadian Arctic sampled from 2002 to 2007. Concentrations of Hg (total Hg and methylmercury [MeHg]) in food webs were compared across longitudinal and latitudinal gradients in relation to d13C and d15N in periphyton, zooplankton, benthic invertebrates, and Arctic char of varying size-classes. Trophic magnification factors (TMFs) were calculated for the food web in each lake and related to available physical and chemical characteristics of the lakes. The relative content of MeHg increased with trophic level from 4.3 to 12.2% in periphyton, 41 to 79% in zooplankton, 59 to 72% in insects, and 74 to 100% in juvenile and adult char. The d13C signatures of adult char indicated coupling with benthic invertebrates. Cannibalism among char lengthened the food chain. Biomagnification was confirmed in all 18 lakes, with TMFs ranging from 3.5 ± 1.1 to 64.3 ± 0.8. Results indicate that TMFs and food chain length (FCL) are key factors in explaining interlake variability in biomagnification of [Hg] among different lakes.

Persistent organic pollutants, d13C and d15N in zooplankton, fish and bird species in Kongsfjorden according to season

Seasonality in biomagnification of persistent organic pollutants (POPs; polychlorinated biphenyls, chlorinated pesticides, and brominated flame retardants) in Arctic marine pelagic food webs was investigated in Kongsfjorden, Svalbard, Norway. Trophic magnification factors (TMFs; average factor change in concentration between two trophic levels) were used to measure food web biomagnification in biota in May, July, and October 2007. Pelagic zooplankton (seven species), fish (five species), and seabirds (two species) were included in the study. For most POP compounds, highest TMFs were found in July and lowest were in May. Seasonally changing TMFs were a result of seasonally changing POP concentrations and the d15N-derived trophic positions of the species included in the food web. These seasonal differences in TMFs were independent of inclusion/exclusion of organisms based on physiology (i.e., warm- versus cold-blooded organisms) in the food web. The higher TMFs in July, when the food web consisted of a higher degree of boreal species, suggest that future warming of the Arctic and increased invasion by boreal species can result in increased food web magnification. Knowledge of the seasonal variation in POP biomagnification is a prerequisite for understanding changes in POP biomagnification caused by climate change.

Data visualization during the early stages of drug discovery

Multidimensional compound optimization is a new paradigm in the drug discovery process, yielding efficiencies during early stages and reducing attrition in the later stages of drug development. The success of this strategy relies heavily on understanding this multidimensional data and extracting useful information from it. This paper demonstrates how principled visualization algorithms can be used to understand and explore a large data set created in the early stages of drug discovery. The experiments presented are performed on a real-world data set comprising biological activity data and some whole-molecular physicochemical properties. Data visualization is a popular way of presenting complex data in a simpler form. We have applied powerful principled visualization methods, such as generative topographic mapping (GTM) and hierarchical GTM (HGTM), to help the domain experts (screening scientists, chemists, biologists, etc.) understand and draw meaningful decisions. We also benchmark these principled methods against relatively better known visualization approaches, principal component analysis (PCA), Sammon's mapping, and self-organizing maps (SOMs), to demonstrate their enhanced power to help the user visualize the large multidimensional data sets one has to deal with during the early stages of the drug discovery process. The results reported clearly show that the GTM and HGTM algorithms allow the user to cluster active compounds for different targets and understand them better than the benchmarks. An interactive software tool supporting these visualization algorithms was provided to the domain experts. The tool facilitates the domain experts by exploration of the projection obtained from the visualization algorithms providing facilities such as parallel coordinate plots, magnification factors, directional curvatures, and integration with industry standard software. © 2006 American Chemical Society.