Parts, places, and perspectives : a theory of spatial relations based an mereotopology and convexity

This thesis suggests to carry on the philosophical work begun in Casati's and Varzi's seminal book Parts and Places, by extending their general reflections on the basic formal structure of spatial representation beyond mereotopology and absolute location to the question of perspectives and perspective-dependent spatial relations. We show how, on the basis of a conceptual analysis of such notions as perspective and direction, a mereotopological theory with convexity can express perspectival spatial relations in a strictly qualitative framework. We start by introducing a particular mereotopological theory, AKGEMT, and argue that it constitutes an adequate core for a theory of spatial relations. Two features of AKGEMT are of particular importance: AKGEMT is an extensional mereotopology, implying that sameness of proper parts is a sufficient and necessary condition for identity, and it allows for (lower- dimensional) boundary elements in its domain of quantification. We then discuss an extension of AKGEMT, AKGEMTS, which results from the addition of a binary segment operator whose interpretation is that of a straight line segment between mereotopological points. Based on existing axiom systems in standard point-set topology, we propose an axiomatic characterisation of the segment operator and show that it is strong enough to sustain complex properties of a convexity predicate and a convex hull operator. We compare our segment-based characterisation of the convex hull to Cohn et al.'s axioms for the convex hull operator, arguing that our notion of convexity is significantly stronger. The discussion of AKGEMTS defines the background theory of spatial representation on which the developments in the second part of this thesis are built. The second part deals with perspectival spatial relations in two-dimensional space, i.e., such relations as those expressed by 'in front of, 'behind', 'to the left/right of, etc., and develops a qualitative formalism for perspectival relations within the framework of AKGEMTS. Two main claims are defended in part 2: That perspectival relations in two-dimensional space are four- place relations of the kind R(x, y, z, w), to be read as x is i?-related to y as z looks at w; and that these four-place structures can be satisfactorily expressed within the qualitative theory AKGEMTS. To defend these two claims, we start by arguing for a unified account of perspectival relations, thus rejecting the traditional distinction between 'relative' and 'intrinsic' perspectival relations. We present a formal theory of perspectival relations in the framework of AKGEMTS, deploying the idea that perspectival relations in two-dimensional space are four-place relations, having a locational and a perspectival part and show how this four-place structure leads to a unified framework of perspectival relations. Finally, we present a philosophical motivation to the idea that perspectival relations are four-place, cashing out the thesis that perspectives are vectorial properties and argue that vectorial properties are relations between spatial entities. Using Fine's notion of "qua objects" for an analysis of points of view, we show at last how our four-place approach to perspectival relations compares to more traditional understandings.

Application of compositional data analysis to geochemical data of marine sediments

In an earlier investigation (Burger et al., 2000) five sediment cores near the RodriguesTriple Junction in the Indian Ocean were studied applying classical statistical methods(fuzzy c-means clustering, linear mixing model, principal component analysis) for theextraction of endmembers and evaluating the spatial and temporal variation ofgeochemical signals. Three main factors of sedimentation were expected by the marinegeologists: a volcano-genetic, a hydro-hydrothermal and an ultra-basic factor. Thedisplay of fuzzy membership values and/or factor scores versus depth providedconsistent results for two factors only; the ultra-basic component could not beidentified. The reason for this may be that only traditional statistical methods wereapplied, i.e. the untransformed components were used and the cosine-theta coefficient assimilarity measure.During the last decade considerable progress in compositional data analysis was madeand many case studies were published using new tools for exploratory analysis of thesedata. Therefore it makes sense to check if the application of suitable data transformations,reduction of the D-part simplex to two or three factors and visualinterpretation of the factor scores would lead to a revision of earlier results and toanswers to open questions . In this paper we follow the lines of a paper of R. Tolosana-Delgado et al. (2005) starting with a problem-oriented interpretation of the biplotscattergram, extracting compositional factors, ilr-transformation of the components andvisualization of the factor scores in a spatial context: The compositional factors will beplotted versus depth (time) of the core samples in order to facilitate the identification ofthe expected sources of the sedimentary process.Kew words: compositional data analysis, biplot, deep sea sediments

Cluster recognition in spatial-temporal sequences: The case of forest fires

Forest fire sequences can be modelled as a stochastic point process where events are characterized by their spatial locations and occurrence in time. Cluster analysis permits the detection of the space/time pattern distribution of forest fires. These analyses are useful to assist fire-managers in identifying risk areas, implementing preventive measures and conducting strategies for an efficient distribution of the firefighting resources. This paper aims to identify hot spots in forest fire sequences by means of the space-time scan statistics permutation model (STSSP) and a geographical information system (GIS) for data and results visualization. The scan statistical methodology uses a scanning window, which moves across space and time, detecting local excesses of events in specific areas over a certain period of time. Finally, the statistical significance of each cluster is evaluated through Monte Carlo hypothesis testing. The case study is the forest fires registered by the Forest Service in Canton Ticino (Switzerland) from 1969 to 2008. This dataset consists of geo-referenced single events including the location of the ignition points and additional information. The data were aggregated into three sub-periods (considering important preventive legal dispositions) and two main ignition-causes (lightning and anthropogenic causes). Results revealed that forest fire events in Ticino are mainly clustered in the southern region where most of the population is settled. Our analysis uncovered local hot spots arising from extemporaneous arson activities. Results regarding the naturally-caused fires (lightning fires) disclosed two clusters detected in the northern mountainous area.

Aggravation of chronic stress effects on hippocampal neurogenesis and spatial memory in LPA₁ receptor knockout mice.

BACKGROUND The lysophosphatidic acid LPA₁ receptor regulates plasticity and neurogenesis in the adult hippocampus. Here, we studied whether absence of the LPA₁ receptor modulated the detrimental effects of chronic stress on hippocampal neurogenesis and spatial memory. METHODOLOGY/PRINCIPAL FINDINGS Male LPA₁-null (NULL) and wild-type (WT) mice were assigned to control or chronic stress conditions (21 days of restraint, 3 h/day). Immunohistochemistry for bromodeoxyuridine and endogenous markers was performed to examine hippocampal cell proliferation, survival, number and maturation of young neurons, hippocampal structure and apoptosis in the hippocampus. Corticosterone levels were measured in another a separate cohort of mice. Finally, the hole-board test assessed spatial reference and working memory. Under control conditions, NULL mice showed reduced cell proliferation, a defective population of young neurons, reduced hippocampal volume and moderate spatial memory deficits. However, the primary result is that chronic stress impaired hippocampal neurogenesis in NULLs more severely than in WT mice in terms of cell proliferation; apoptosis; the number and maturation of young neurons; and both the volume and neuronal density in the granular zone. Only stressed NULLs presented hypocortisolemia. Moreover, a dramatic deficit in spatial reference memory consolidation was observed in chronically stressed NULL mice, which was in contrast to the minor effect observed in stressed WT mice. CONCLUSIONS/SIGNIFICANCE These results reveal that the absence of the LPA₁ receptor aggravates the chronic stress-induced impairment to hippocampal neurogenesis and its dependent functions. Thus, modulation of the LPA₁ receptor pathway may be of interest with respect to the treatment of stress-induced hippocampal pathology.

Analysis of Centrosome duplication in "Caenorhabditis elegans" : the role of "sas" genes

Abstract: The centrosome is the major microtubule organizing center (MTOC) of most animal cells. As such, it is essential for a number of processes, including polarized secretion or bipolar spindle assembly. Hence, centrosome number needs to be controlled precisely in coordination with DNA replication. Cells early in the cell cycle contain one centrosome that duplicates during S-phase to give rise to two centrosomes that organize a bipolar spindle during mitosis. A failure in this process is likely to engage the spindle assembly checkpoint and threaten genome stability. Despite its importance for normal and uncontrolled proliferation the mechanisms underlying centrosome duplication are still unclear. The Caenorhabditis elegans embryo is well suited to study the mechanisms of centrosome duplication. It allows for the analysis of cellular processes with high temporal and spatial resolution. Gene identification and inactivation techniques are very powerful and a wide set of mutant and transgenic strains facilitates analysis. My thesis project consisted of characterizing three sas-genes: sas-4, sas-5 and sas-¬6. Embryos lacking these genes fail to form a bipolar spindle, hence their name (spindle assembly). I established that sas-4(RNAi) and sas-6(RNAi) embryos do not form daughter centrioles and thus do not duplicate their centrosomes. Furthermore, I showed that both proteins localize to the cytoplasm and are strikingly enriched at centrioles throughout the cell cycle. By performing fluorescent recovery after photobleaching (FRAP) experiments and differentially labeling centrioles, I established that both proteins are recruited to centrioles once per cell cycle when daughter centrioles form. In contrast, SAS-5, PLK-1 and SPD-2 shuttle permanently between the cytoplasm and centrioles. By showing that SAS-5 and SAS-6 interact in vivo, I established a functional relationship between the proteins. Testing the putative human homologue of SAS-6 (HsSAS-6) and a distant relative of SAS-4 (CPAP), I was able to show that these proteins are required for centrosome duplication in human cells. In addition I found that overexpression of GFP¬HsSAS-6 leads to formation of extra centrosomes. In conclusion, we identified and gained important insights into proteins required for centrosome duplication in C. elegans and in human cells. Thus, our work contributes to further elucidate an important step of cell division in normal and malignant tissues. Eventually, this may allow for the development of novel diagnostic or therapeutic reagents to treat cancer patients. Résumé: Le centrosome est le principal centre organisateur des microtubules dans les cellules animales. De ce fait, il est essentiel pour un certain nombre de processus, comme l'adressage polarisé ou la mise en place d'un fuseau bipolaire. Le nombre de centrosome doit être contrôlé de façon précise et en coordination avec la réplication de l'ADN. Au début du cycle cellulaire, les cellules n'ont qu'un seul centrosome qui se duplique au cours de la phase S pour donner naissance à deux centrosomes qui forment le fuseau bipolaire pendant la mitose. Des défauts dans ce processus déclencheront probablement le "checkpoint" d'assemblage du fuseau et menaceront la stabilité du génome. Malgré leurs importances pour la prolifération normale ou incontrôlée des cellules, les mécanismes gouvernant la duplication des centrosomes restent obscures. L'embryon de Caenorhabditis elegans est bien adapté pour étudier les mécanismes de duplication des centrosomes. Il permet l'analyse des processus cellulaires avec une haute résolution spatiale et temporelle. L'identification des gènes et les techniques d'inactivation sont très puissantes et de larges collections de mutants et de lignées transgéniques facilitent les analyses. Mon projet de thèse a consisté à caractérisé trois gènes: sas-4, sas-5 et sas-6. Les embryons ne possédant pas ces gènes ne forment pas de fuseaux bipolaires, d'où leur nom (spindle assembly). J'ai établi que les embryons sas-4(RNAi) et sas-6(RNAi) ne forment pas de centrioles fils, et donc ne dupliquent pas leur centrosome. De plus, j'ai montré que les deux protéines sont localisées dans le cytoplasme et sont étonnamment enrichies aux centrioles tout le long du cycle cellulaire. En réalisant des expériences de FRAP (fluorscence recovery after photobleaching) et en marquant différentiellement les centrioles, j'ai établi que ces deux protéines sont recrutées une fois par cycle cellulaire aux centrioles, au moment de la duplication. Au contraire, SAS-5, PLK-1 et SPD-2 oscillent en permanence entre le cytoplasme et les centrioles. En montrant que SAS-5 et SAS-6 interagissent in vivo, j'ai établi une relation fonctionnelle entre les deux protéines. En testant les homologues humains putatifs de SAS-6 (HsSAS-6) et de SAS-4 (CPAP), j'ai été capable de montrer que ces protéines étaient aussi requises pour la duplication des centrosomes dans les cellules humaines. De plus, j'ai montré que la surexpression de GFP-HsSAS-6 entrainait la formation de centrosomes surnuméraires. En conclusion, nous avons identifié et progressé dans la compréhension de protéines requises pour la duplication des centrosomes chez C. elegans et dans les cellules humaines. Ainsi, notre travail contribue à mieux élucider une étape importante du la division cellulaire dans les cellules normales et malignes. A terme, ceci devrait aider au développement de nouveaux diagnostics ou de traitements thérapeuthiques pour soigner les malades du cancer.

Measuring and Explaining the Increase of Travel Distance : A Multilevel Analysis Using Repeated Cross Sectional Travel Surveys

We want to shed some light on the development of person mobility by analysing the repeated cross-sectional data of the four National Travel Surveys (NTS) that were conducted in Germany since the mid seventies. The above mentioned driving forces operate on different levels of the system that generates the spatial behaviour we observe: Travel demand is derived from the needs and desires of individuals to participate in spatially separated activities. Individuals organise their lives in an interactive process within the context they live in, using given infrastructure. Essential determinants of their demand are the individual's socio-demographic characteristics, but also the opportunities and constraints defined by the household and the environment are relevant for the behaviour which ultimately can be realised. In order to fully capture the context which determines individual behaviour, the (nested) hierarchy of persons within households within spatial settings has to be considered. The data we will use for our analysis contains information on these three levels. With the analysis of this micro-data we attempt to improve our understanding of the afore subsumed macro developments. In addition we will investigate the prediction power of a few classic sociodemographic variables for the daily travel distance of individuals in the four NTS data sets, with a focus on the evolution of this predictive power. The additional task to correctly measure distances travelled by means of the NTS is threatened by the fact that although these surveys measure the same variables, different sampling designs and data collection procedures were used. So the aim of the analysis is also to detect variables whose control corrects for the known measurement error, as a prerequisite to apply appropriate models in order to better understand the development of individual travel behaviour in a multilevel context. This task is complicated by the fact that variables that inform on survey procedures and outcomes are only provided with the data set for 2002 (see Infas and DIW Berlin, 2003).

JULIDE: a software tool for 3D reconstruction and statistical analysis of autoradiographic mouse brain sections.

In this article we introduce JULIDE, a software toolkit developed to perform the 3D reconstruction, intensity normalization, volume standardization by 3D image registration and voxel-wise statistical analysis of autoradiographs of mouse brain sections. This software tool has been developed in the open-source ITK software framework and is freely available under a GPL license. The article presents the complete image processing chain from raw data acquisition to 3D statistical group analysis. Results of the group comparison in the context of a study on spatial learning are shown as an illustration of the data that can be obtained with this tool.

Monitoring procedures in environmental geochemistry and compositional data analysis theory

First discussion on compositional data analysis is attributable to Karl Pearson, in 1897. However, notwithstanding the recent developments on algebraic structure of the simplex, more than twenty years after Aitchison’s idea of log-transformations of closed data, scientific literature is again full of statistical treatments of this type of data by using traditional methodologies. This is particularly true in environmental geochemistry where besides the problem of the closure, the spatial structure (dependence) of the data have to be considered. In this work we propose the use of log-contrast values, obtained by asimplicial principal component analysis, as LQGLFDWRUV of given environmental conditions. The investigation of the log-constrast frequency distributions allows pointing out the statistical laws able togenerate the values and to govern their variability. The changes, if compared, for example, with the mean values of the random variables assumed as models, or other reference parameters, allow definingmonitors to be used to assess the extent of possible environmental contamination. Case study on running and ground waters from Chiavenna Valley (Northern Italy) by using Na+, K+, Ca2+, Mg2+, HCO3-, SO4 2- and Cl- concentrations will be illustrated

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

Genetic structure of a linear population of Beta vulgaris ssp maritima (sea beet) revealed by isozyme and RFLP analysis

Knowledge of the genetic structure of plant populations is necessary for the understanding of the dynamics of major ecological processes. It also has applications in conservation biology and risk assessment for genetically modified crops. This paper reports the genetic structure of a linear population of sea beet, Beta vulgaris ssp. maritima (the wild relative of sugar beet), on Furzey Island, Poole Harbour. The relative spatial positions of the plants were accurately mapped and the plants were scored for variation at isozyme and RFLP loci. Structure was analysed by repeated subdivision of the population to find the average size of a randomly mating group. Estimates of F-ST between randomly mating units were then made, and gave patterns consistent with the structure of the population being determined largely by founder effects. The implications of these results for the monitoring of transgene spread in wild sea beet populations are discussed.

Emotionally negative stimuli can overcome attentional deficits in patients with visuo-spatial hemineglect.

Left unilateral spatial neglect resulting from right brain damage is characterized by loss of awareness for stimuli in the contralesional side of space, despite intact visual pathways. We examined using fMRI whether patients with neglect are more likely to consciously detect in the neglected hemifield, emotionally negative complex scenes rather than visually similar neutral pictures and if so, what neural mechanisms mediate this effect. Photographs of emotional and neutral scenes taken from the IAPS were presented in a divided visual field paradigm. As expected, the detection rate for emotional stimuli presented in the neglected field was higher than for neutral ones. Successful detection of emotional scenes as opposed to neutral stimuli in the left visual field (LVF) produced activations in the parahippocampal and anterior cingulate areas in the right hemisphere. Detection of emotional stimuli presented in the intact right visual field (RVF) activated a distributed network of structures in the left hemisphere, including anterior and posterior cingulate cortex, insula, as well as visual striate and extrastriate areas. LVF-RVF contrasts for emotional stimuli revealed activations in right and left attention related prefrontal areas whereas RVF-LVF comparison showed activations in the posterior cingulate and extrastriate visual cortex in the left hemisphere. An additional analysis contrasting detected vs. undetected emotional LVF stimuli showed involvement of left anterior cingulate, right frontal and extrastriate areas. We hypothesize that beneficial role of emotion in overcoming neglect is achieved by activation of frontal and limbic lobe networks, which provide a privileged access of emotional stimuli to attention by top-down modulation of processing in the higher-order extrastriate visual areas. Our results point to the importance of top-down regulatory role of the frontal attentional systems, which might enhance visual activations and lead to greater salience of emotional stimuli for perceptual awareness.

Bilinear models for spatio-temporal point distribution analysis: application to extrapolation of left ventricular, biventricular and whole heart cardiac dynamics

In this work we describe the usage of bilinear statistical models as a means of factoring the shape variability into two components attributed to inter-subject variation and to the intrinsic dynamics of the human heart. We show that it is feasible to reconstruct the shape of the heart at discrete points in the cardiac cycle. Provided we are given a small number of shape instances representing the same heart atdifferent points in the same cycle, we can use the bilinearmodel to establish this. Using a temporal and a spatial alignment step in the preprocessing of the shapes, around half of the reconstruction errors were on the order of the axial image resolution of 2 mm, and over 90% was within 3.5 mm. From this, weconclude that the dynamics were indeed separated from theinter-subject variability in our dataset.

Asymmetry of Functional Connectivity in Schizophrenia at Different Spatial Scales

Introduction: The interhemispheric asymmetries that originate from connectivity-related structuring of the cerebral cortex are compromised in schizophrenia (SZ). Recently, we have revealed the whole-head topography of EEG synchronization in SZ (Jalili et al. 2007; Knyazeva et al. 2008). Here we extended the analysis to assess the abnormality in the asymmetry of synchronization, which is further motivated by the evidence that the interhemispheric asymmetries suspected to be abnormal in SZ originate from the connectivity-related structuring of the cortex. Methods: Thirteen right-handed SZ patients and thirteen matched controls, participated in this study and the multichannel (128) EEGs were recorded for 3-5 minutes at rest. Then, Laplacian EEG (LEEG) were calculated using a 2-D spline. The LEEGs were analysis through calculating the power spectral density using Welch's average periodogram method. Furthermore, using a state-space based multivariate synchronization measure, S-estimator, we analyzed the correlate of the functional cortico-cortical connectivity in SZ patients compared to the controls. The values of S-estimator were obtained at three different special scales: first-order neighbors for each sensor location, second-order neighbors, and the whole hemisphere. The synchronization measures based on LEEG of alpha and beta bands were applied and tuned to various spatial scales including local, intraregional, and long-distance levels. To assess the between-group differences, we used a permutation version of Hotelling's T2 test. For correlation analysis, Spearman Rank Correlation was calculated. Results: Compared to the controls, who had rightward asymmetry at a local level (LEEG power), rightward anterior and leftward posterior asymmetries at an intraregional level (first- and second-order S-estimator), and rightward global asymmetry (hemispheric S-estimator), SZ patients showed generally attenuated asymmetry, the effect being strongest for intraregional synchronization. This deviation in asymmetry across the anterior-to-posterior axis is consistent with the cerebral form of the so-called Yakovlevian or anticlockwise cerebral torque. Moreover, the negative occipital and positive frontal asymmetry values suggest higher regional synchronization among the left occipital and the right frontal locations relative to their symmetrical counterparts. Correlation analysis linked the posterior intraregional and hemispheric abnormalities to the negative SZ symptoms, whereas the asymmetry of LEEG power appeared to be weakly coupled to clinical ratings. The posterior intraregional abnormalities of asymmetry were shown to increase with the duration of the disease. The tentative links between these findings and gross anatomical asymmetries, including the cerebral torque and gyrification pattern in normal subjects and SZ patients, are discussed. Conclusions: Overall, our findings reveal the abnormalities in the synchronization asymmetry in SZ patients and heavy involvement of the right hemisphere in these abnormalities. These results indicate that anomalous asymmetry of cortico-cortical connections in schizophrenia is amenable to electrophysiological analysis.

Wavelet analysis residual kriging vs. neural network residual kriging

This paper deals with the problem of spatial data mapping. A new method based on wavelet interpolation and geostatistical prediction (kriging) is proposed. The method - wavelet analysis residual kriging (WARK) - is developed in order to assess the problems rising for highly variable data in presence of spatial trends. In these cases stationary prediction models have very limited application. Wavelet analysis is used to model large-scale structures and kriging of the remaining residuals focuses on small-scale peculiarities. WARK is able to model spatial pattern which features multiscale structure. In the present work WARK is applied to the rainfall data and the results of validation are compared with the ones obtained from neural network residual kriging (NNRK). NNRK is also a residual-based method, which uses artificial neural network to model large-scale non-linear trends. The comparison of the results demonstrates the high quality performance of WARK in predicting hot spots, reproducing global statistical characteristics of the distribution and spatial correlation structure.

Morphometric shape analysis using learning vector quantization neural networks - an example distinguishing two microtine vole species

Closely related species may be very difficult to distinguish morphologically, yet sometimes morphology is the only reasonable possibility for taxonomic classification. Here we present learning-vector-quantization artificial neural networks as a powerful tool to classify specimens on the basis of geometric morphometric shape measurements. As an example, we trained a neural network to distinguish between field and root voles from Procrustes transformed landmark coordinates on the dorsal side of the skull, which is so similar in these two species that the human eye cannot make this distinction. Properly trained neural networks misclassified only 3% of specimens. Therefore, we conclude that the capacity of learning vector quantization neural networks to analyse spatial coordinates is a powerful tool among the range of pattern recognition procedures that is available to employ the information content of geometric morphometrics.