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.

Machine learning for spatial environmental data. Theory, applications and software

The book presents the state of the art in machine learning algorithms (artificial neural networks of different architectures, support vector machines, etc.) as applied to the classification and mapping of spatially distributed environmental data. Basic geostatistical algorithms are presented as well. New trends in machine learning and their application to spatial data are given, and real case studies based on environmental and pollution data are carried out. The book provides a CD-ROM with the Machine Learning Office software, including sample sets of data, that will allow both students and researchers to put the concepts rapidly to practice.

Unpacking the cognitive map: the parallel map theory of hippocampal function

In the parallel map theory, the hippocampus encodes space with 2 mapping systems. The bearing map is constructed primarily in the dentate gyrus from directional cues such as stimulus gradients. The sketch map is constructed within the hippocampus proper from positional cues. The integrated map emerges when data from the bearing and sketch maps are combined. Because the component maps work in parallel, the impairment of one can reveal residual learning by the other. Such parallel function may explain paradoxes of spatial learning, such as learning after partial hippocampal lesions, taxonomic and sex differences in spatial learning, and the function of hippocampal neurogenesis. By integrating evidence from physiology to phylogeny, the parallel map theory offers a unified explanation for hippocampal function.

Testing Spatial Autocorrelation in Weighted Networks : the Modes Permutation Test

In a weighted spatial network, as specified by an exchange matrix, the variances of the spatial values are inversely proportional to the size of the regions. Spatial values are no more exchangeable under independence, thus weakening the rationale for ordinary permutation and bootstrap tests of spatial autocorrelation. We propose an alternative permutation test for spatial autocorrelation, based upon exchangeable spatial modes, constructed as linear orthogonal combinations of spatial values. The coefficients obtain as eigenvectors of the standardised exchange matrix appearing in spectral clustering, and generalise to the weighted case the concept of spatial filtering for connectivity matrices. Also, two proposals aimed at transforming an acessibility matrix into a exchange matrix with with a priori fixed margins are presented. Two examples (inter-regional migratory flows and binary adjacency networks) illustrate the formalism, rooted in the theory of spectral decomposition for reversible Markov chains.

Testing Spatial Autocorrelation in Weighted Networks : the Modes Permutation Test

In a weighted spatial network, as specified by an exchange matrix, the variances of the spatial values are inversely proportional to the size of the regions. Spatial values are no more exchangeable under independence, thus weakening the rationale for ordinary permutation and bootstrap tests of spatial autocorrelation. We propose an alternative permutation test for spatial autocorrelation, based upon exchangeable spatial modes, constructed as linear orthogonal combinations of spatial values. The coefficients obtain as eigenvectors of the standardised exchange matrix appearing in spectral clustering, and generalise to the weighted case the concept of spatial filtering for connectivity matrices. Also, two proposals aimed at transforming an acessibility matrix into a exchange matrix with with a priori fixed margins are presented. Two examples (inter-regional migratory flows and binary adjacency networks) illustrate the formalism, rooted in the theory of spectral decomposition for reversible Markov chains.

The Implied Book and the Narrative Text. On a Blind Spot in Narratological Theory - from a Media Studies Perspective

The article is concerned with the formal definition of a largely unnoticed factor in narrative structure. Based on the assumptions that (1) the semantics of a written text depend, among other factors, directly on its visual alignment in space, that (2) the formal structure of a text has to meet that of its spatial presentation and that (3) these assumptions hold true also for narrative texts (which, however, in modern times typically conceal their spatial dimensions by a low-key linear layout), it is argued that, how ever low-key, the expected material shape of a given narrative determines the configuration of its plot by its author. The ,implied book' thus denotes an author's historically assumable, not necessarily conscious idea of how his text, which is still in the process of creation, will be dimensionally presented and under these circumstances visually absorbed. Assuming that an author's knowledge of this later (potentially) substantiated material form influences the composition, the implied book is to be understood as a text-genetically determined, structuring moment of the text. Historically reconstructed, it thus serves the methodical analysis of structural characteristics of a completed text.

Dissociation between components of spatial memory in rats after recovery from the effects of retrohippocampal lesions

A series of 4 experiments examined the performance of rats with retrohippocampal lesions on a spatial water-maze task. The animals were trained to find and escape onto a hidden platform after swimming in a large pool of opaque water. The platform was invisible and could not be located using olfactory cues. Successful escape performance required the rats to develop strategies of approaching the correct location with reference solely to distal extramaze cues. The lesions encompassed the entire rostro-caudal extent of the lateral and medial entorhinal cortex, and included parts of the pre- and para-subiculum, angular bundle and subiculum. Groups ECR 1 and 2 sustained only partial damage of the subiculum, while Group ECR+S sustained extensive damage. These groups were compared with sham-lesion and unoperated control groups. In Expt 1A, a profound deficit in spatial localisation was found in groups ECR 1 and ECR+S, the rats receiving all training postoperatively. In Expt 1B, these two groups showed hyperactivity in an open-field. In Expt 2, extensive preoperative training caused a transitory saving in performance of the spatial task by group ECR 2, but comparisons with the groups of Expt 1A revealed no sustained improvement, except on one measure of performance in a post-training transfer test. All rats were then given (Expt 3) training on a cueing procedure using a visible platform. The spatial deficit disappeared but, on returning to the normal hidden platform procedure, it reappeared. Nevertheless, a final transfer test, during which the platform was removed from the apparatus, revealed a dissociation between two independent measures of performance: the rats with ECR lesions failed to search for the hidden platform but repeatedly crossed its correct location accurately during traverses of the entire pool. This partial recovery of performance was not (Expt 4) associated with any ability to discriminate between two locations in the pool. The apparently selective recovery of aspects of spatial memory is discussed in relation to O'Keefe and Nadel's (1978) spatial mapping theory of hippocampal function. We propose a modification of the theory in terms of a dissociation between procedural and declarative subcomponents of spatial memory. The declarative component is a flexible access system in which information is stored in a form independent of action. It is permanently lost after the lesion. The procedural component is "unmasked" by the retrohippocampal lesion giving rise to the partial recovery of spatial localisation performance.

Extension of ultrasound Fourier slice Imaging theory to sectorial acquisition

Ultrasound image reconstruction from the echoes received by an ultrasound probe after the transmission of diverging waves is an active area of research because of its capacity to insonify at ultra-high frame rate with large regions of interest using small phased arrays as the ones used in echocardiography. Current state-of-the-art techniques are based on the emission of diverging waves and the use of delay and sum strategies applied on the received signals to reconstruct the desired image (DW/DAS). Recently, we have introduced the concept of Ultrasound Fourier Slice Imaging (UFSI) theory for the reconstruction of ultrafast imaging for linear acquisition. In this study, we extend this theory to sectorial acquisition thanks to the introduction of an explicit and invertible spatial transform. Starting from a diverging wave, we show that the direct use of UFSI theory along with the application of the proposed spatial transform allows reconstructing the insonified medium in the conventional Cartesian space. Simulations and experiments reveal the capacity of this new approach in obtaining competitive quality of ultrafast imaging when compared with the current reference method.

Olfactory traces and spatial learning in rats.

We conducted an experiment to assess the use of olfactory traces for spatial orientation in an open environment in rats, Rattus norvegicus. We trained rats to locate a food source at a fixed location from different starting points, in the presence or absence of visual information. A single food source was hidden in an array of 19 petri dishes regularly arranged in an open-field arena. Rats were trained to locate the food source either in white light (with full access to distant visuospatial information) or in darkness (without any visual information). In both cases, the goal was in a fixed location relative to the spatial frame of reference. The results of this experiment revealed that the presence of noncontrolled olfactory traces coherent with the spatial frame of reference enables rats to locate a unique position as accurately in darkness as with full access to visuospatial information. We hypothesize that the olfactory traces complement the use of other orientation mechanisms, such as path integration or the reliance on visuospatial information. This experiment demonstrates that rats can rely on olfactory traces for accurate orientation, and raises questions about the establishment of such traces in the absence of any other orientation mechanism. Copyright 1998 The Association for the Study of Animal Behaviour.

Modularity of auditory spatial representations

Abstract : Auditory spatial functions are of crucial importance in everyday life. Determining the origin of sound sources in space plays a key role in a variety of tasks including orientation of attention, disentangling of complex acoustic patterns reaching our ears in noisy environments. Following brain damage, auditory spatial processing can be disrupted, resulting in severe handicaps. Complaints of patients with sound localization deficits include the inability to locate their crying child or being over-loaded by sounds in crowded public places. Yet, the brain bears a large capacity for reorganization following damage and/or learning. This phenomenon is referred as plasticity and is believed to underlie post-lesional functional recovery as well as learning-induced improvement. The aim of this thesis was to investigate the organization and plasticity of different aspects of auditory spatial functions. Overall, we report the outcomes of three studies: In the study entitled "Learning-induced plasticity in auditory spatial representations" (Spierer et al., 2007b), we focused on the neurophysiological and behavioral changes induced by auditory spatial training in healthy subjects. We found that relatively brief auditory spatial discrimination training improves performance and modifies the cortical representation of the trained sound locations, suggesting that cortical auditory representations of space are dynamic and subject to rapid reorganization. In the same study, we tested the generalization and persistence of training effects over time, as these are two determining factors in the development of neurorehabilitative intervention. In "The path to success in auditory spatial discrimination" (Spierer et al., 2007c), we investigated the neurophysiological correlates of successful spatial discrimination and contribute to the modeling of the anatomo-functional organization of auditory spatial processing in healthy subjects. We showed that discrimination accuracy depends on superior temporal plane (STP) activity in response to the first sound of a pair of stimuli. Our data support a model wherein refinement of spatial representations occurs within the STP and that interactions with parietal structures allow for transformations into coordinate frames that are required for higher-order computations including absolute localization of sound sources. In "Extinction of auditory stimuli in hemineglect: space versus ear" (Spierer et al., 2007a), we investigated auditory attentional deficits in brain-damaged patients. This work provides insight into the auditory neglect syndrome and its relation with neglect symptoms within the visual modality. Apart from contributing to a basic understanding of the cortical mechanisms underlying auditory spatial functions, the outcomes of the studies also contribute to develop neurorehabilitation strategies, which are currently being tested in clinical populations.

High-resolution spatial mapping of changes in the neurochemical profile after focal ischemia in mice.

After ischemic stroke, the ischemic damage to brain tissue evolves over time and with an uneven spatial distribution. Early irreversible changes occur in the ischemic core, whereas, in the penumbra, which receives more collateral blood flow, the damage is more mild and delayed. A better characterization of the penumbra, irreversibly damaged and healthy tissues is needed to understand the mechanisms involved in tissue death. MRSI is a powerful tool for this task if the scan time can be decreased whilst maintaining high sensitivity. Therefore, we made improvements to a (1) H MRSI protocol to study middle cerebral artery occlusion in mice. The spatial distribution of changes in the neurochemical profile was investigated, with an effective spatial resolution of 1.4 μL, applying the protocol on a 14.1-T magnet. The acquired maps included the difficult-to-separate glutamate and glutamine resonances and, to our knowledge, the first mapping of metabolites γ-aminobutyric acid and glutathione in vivo, within a metabolite measurement time of 45 min. The maps were in excellent agreement with findings from single-voxel spectroscopy and offer spatial information at a scan time acceptable for most animal models. The metabolites measured differed with respect to the temporal evolution of their concentrations and the localization of these changes. Specifically, lactate and N-acetylaspartate concentration changes largely overlapped with the T(2) -hyperintense region visualized with MRI, whereas changes in cholines and glutathione affected the entire middle cerebral artery territory. Glutamine maps showed elevated levels in the ischemic striatum until 8 h after reperfusion, and until 24 h in cortical tissue, indicating differences in excitotoxic effects and secondary energy failure in these tissue types. Copyright © 2011 John Wiley & Sons, Ltd.

Perinatal choline supplementation reveals a dissociation between two types of spatial strategies.

Choline supplementation improving memory functions in rodents is assumed to increase the synthesis and release of acetylcholine in the brain. We have found that a combined pre- and postnatal supplementation results in long-lasting facilitation of spatial memory in juvenile rats when training was conducted in presence of a local salient cue. The present work was aimed at analysing the effects of peri- and postnatal choline supplementation on spatial abilities of naive adult rats. Rats given a perinatal choline supplementation were trained in various cued procedures of the Morris navigation task when aged 5 months. The treatment had a specific effect of reducing the escape latency of the rats when the platform was at a fixed position in space and surrounded by a suspended cue. This effect was associated with an increased spatial bias when the cue and platform were removed. In this condition, the control rats showed impaired spatial discrimination following the removal of the target cue, most likely due to an overshadowing of the distant environmental cues. This impairment was not observed in the treated rats. Further training with the suspended cue at unpredictable places in the pool revealed longer escape latencies in the control than in the treated rats suggesting that this procedure induced a selective perturbation of the normal but not of the treated rats. A special probe trial with the cue at an irrelevant position and no escape platform revealed a significant bias of the control rats toward the cue and of the treated rats toward the uncued spatial escape position. This behavioural dissociation suggests that a salient cue associated with the target induces an alternative "non spatial" guidance strategy in normal rats, with the risk of overshadowing of the more distant spatial cues. In this condition, the choline supplementation facilities a spatial reliance on the cue, that is an overall facilitation of learning a set of spatial relations between several visual cues. As a consequence, the improved escape in presence of the cue is associated with a stronger memory of the spatial position following disappearance of the cue. This and previous observations suggest that a specific spatial attention process relies on the buffering of highly salient visual cues.to facilitate integration of their relative position in the environment.

Auditory spatial deficits following hemispheric lesions : dissociation of explicit and implicit processing

Les déficits auditifs spatiaux se produisent fréquemment après une lésion hémisphérique ; un précédent case report suggérait que la capacité explicite à reconnaître des positions sonores, comme dans la localisation des sons, peut être atteinte alors que l'utilisation implicite d'indices sonores pour la reconnaissance d'objets sonores dans un environnement bruyant reste préservée. En testant systématiquement des patients avec lésion hémisphérique inaugurale, nous avons montré que (1) l'utilisation explicite et/ou implicite des indices sonores peut être perturbée ; (2) la dissociation entre l'atteinte de l'utilisation explicite des indices sonores versus une préservation de l'utilisation implicite de ces indices est assez fréquente ; et (3) différents types de déficits dans la localisation des sons peuvent être associés avec une utilisation implicite préservée de ces indices sonores. Conceptuellement, la dissociation entre l'utilisation explicite et implicite de ces indices sonores peut illustrer la dichotomie des deux voies du système auditif. Nos résultats parlent en faveur d'une évaluation systématique des fonctions auditives spatiales dans un contexte clinique, surtout quand l'adaptation à un environnement sonore est en jeu. De plus, des études systématiques sont nécessaires afin de mettre en lien les troubles de l'utilisation explicite versus implicite de ces indices sonores avec les difficultés à effectuer les activités de la vie quotidienne, afin d'élaborer des stratégies de réhabilitation appropriées et afin de s'assurer jusqu'à quel point l'utilisation explicite et implicite des indices spatiaux peut être rééduquée à la suite d'un dommage cérébral.

Is sociality driven by the costs of dispersal or the benefits of philopatry? A role for kin-discrimination mechanisms.

The role of ecological constraints in promoting sociality is currently much debated. Using a direct-fitness approach, we show this role to depend on the kin-discrimination mechanisms underlying social interactions. Altruism cannot evolve under spatially based discrimination, unless ecological constraints prevent complete dispersal. Increasing constraints enhances both the proportion of philopatric (and thereby altruistic) individuals and the level of altruistic investments conceded in pairwise interactions. Familiarity-based discrimination, by contrast, allows philopatry and altruism to evolve at significant levels even in the absence of ecological constraints. Increasing constraints further enhances the proportion of philopatric (and thereby altruistic) individuals but not the level of altruism conceded. Ecological constraints are thus more likely to affect social evolution in species in which restricted cognitive abilities, large group size, and/or limited period of associative learning force investments to be made on the basis of spatial cues.