Spatio-temporal reasoning is the area of automated reasoning about space and time and is important in the field of robotics. It is desirable for an autonomous robot to have the ability to reason about both time and space. ST0 is a logic that allows for such reasoning by, among other things, defining a formalism used to describe the relationship between spatial regions and a calculus that allows for deducing further information regarding such spatial relations. An extension of ST0 is ST1 that can be used to describe the relationship between spatial entities across time-points (inter-temporal relations) while ST0 is constrained to doing so within a single time-point. This allows for a better ability of expressing how spatial entities change over time. A major obstacle in using ST1 in practise however, is the fact that any observations made regarding spatial relations between regions is constrained to the time-point in which the observation was made, so we are unable to observe inter-temporal relations. Further complicating things is the fact that deducing such inter-temporal relations is not possible without a frame of reference. This thesis examines one method of overcoming these problems by considering the concept of rigid regions which are assumed to always be unchanging and using them as the frame of reference, or as landmarks. The effectiveness of this method is studied by conducting experiments where a comparison is made between various landmark ratios with respect to the total number of regions under consideration. Results show that when a high degree of intra-temporal relations are fully or partially known, increasing the number of landmark regions will reduce the percentage of inter-temporal relations to be completely unknown. Despite this, very few inter-temporal relations can be fully determined even with a high ratio of landmark regions.

No description available.

Stroke is a major cause of disability and death worldwide. Although different clinical studies and trials used Magnetic Resonance Imaging (MRI) to examine patterns of change in different imaging modalities (eg: perfusion and diffusion), we still lack a clear and definite answer to the question: “How does an acute ischemic stroke lesion grow?” The inability to distinguish viable and dead tissue in abnormal MR regions in stroke patients weakens the evidence accumulated to answer this question, and relying on static snapshots of patient scans to fill in the spatio-temporal gaps by “thinking/guessing” make it even harder to tackle. Different opposing observations undermine our understanding of ischemic stroke evolution, especially at the acute stage: viable tissue transiting into dead tissue may be clear and intuitive, however, “visibly” dead tissue restoring to full recovery is still unclear. In this thesis, we search for potential answers to these raised questions from a novel dynamic modelling perspective that would fill in some of the missing gaps in the mechanisms of stroke evolution. We divided our thesis into five parts. In the first part, we give a clinical and imaging background on stroke and state the objectives of this thesis. In the second part, we summarize and review the literature in stroke and medical imaging. We specifically spot gaps in the literature mainly related to medical image analysis methods applied to acute-subacute ischemic stroke. We emphasize studies that progressed the field and point out what major problems remain. Noticeably, we have discovered that macroscopic (imaging-based) dynamic models that simulate how stroke lesion evolves in space and time were completely overlooked: an untapped potential that may alter and hone our understanding of stroke evolution. Progress in the dynamic simulation of stroke was absent –if not inexistent. In the third part, we answer this new call and apply a novel current-based dynamic model âpreviously applied to compare the evolution of facial characteristics between Chimpanzees and Bonobos [Durrleman 2010] – to ischemic stroke. This sets a robust numerical framework and provides us with mathematical tools to fill in the missing gaps between MR acquisition time points and estimate a four-dimensional evolution scenario of perfusion and diffusion lesion surfaces. We then detect two characteristics of patterns of abnormal tissue boundary change: spatial, describing the direction of change –outward as tissue boundary expands or inward as it contracts–; and kinetic, describing the intensity (norm) of the speed of contracting and expanding ischemic regions. Then, we compare intra- and inter-patients estimated patterns of change in diffusion and perfusion data. Nevertheless, topology change limits this approach: it cannot handle shapes with different parts that vary in number over time (eg: fragmented stroke lesions, especially in diffusion scans, which are common). In the fourth part, we suggest a new mathematical dynamic model to increase rigor in the imaging-based dynamic modeling field as a whole by overcoming the topology-change hurdle. Metamorphosis. It morphs one source image into a target one [Trouvé 2005]. In this manuscript, we extend it into dealing with more than two time-indexed images. We propose a novel extension of image-to-image metamorphosis into longitudinal metamorphosis for estimating an evolution scenario of both scattered and solitary ischemic lesions visible on serial MR. It is worth noting that the spatio-temporal metamorphosis we developed is a generic model that can be used to examine intensity and shape changes in time-series imaging and study different brain diseases or disorders. In the fifth part, we discuss our main findings and investigate future directions to explore to sharpen our understanding of ischemia evolution patterns.

Human cognition involves dynamic neural activities in distributed brain areas. For studying such neural mechanisms, magnetoencephalography (MEG) and electroencephalography (EEG) are two important techniques, as they non-invasively detect neural activities with a high temporal resolution. Recordings by MEG/EEG sensors can be approximated as a linear transformation of the neural activities in the brain space (i.e., the source space). However, we only have a limited number sensors compared with the many possible locations in the brain space; therefore it is challenging to estimate the source neural activities from the sensor recordings, in that we need to solve the underdetermined inverse problem of the linear transformation. Moreover, estimating source activities is typically an intermediate step, whereas the ultimate goal is to understand what information is coded and how information flows in the brain. This requires further statistical analysis of source activities. For example, to study what information is coded in different brain regions and temporal stages, we often regress neural activities on some external covariates; to study dynamic interactions between brain regions, we often quantify the statistical dependence among the activities in those regions through “connectivity” analysis. Traditionally, these analyses are done in two steps: Step 1, solve the linear problem under some regularization or prior assumptions, (e.g., each source location being independent); Step 2, do the regression or connectivity analysis. However, biases induced in the regularization in Step 1 can not be adapted in Step 2 and thus may yield inaccurate regression or connectivity results. To tackle this issue, we present novel one-step methods of regression or connectivity analysis in the source space, where we explicitly modeled the dependence of source activities on the external covariates (in the regression analysis) or the cross-region dependence (in the connectivity analysis), jointly with the source-to-sensor linear transformation. In simulations, we observed better performance by our models than by commonly used two-step approaches, when our model assumptions are reasonably satisfied. Besides the methodological contribution, we also applied our methods in a real MEG/EEG experiment, studying the spatio-temporal neural dynamics in the visual cortex. The human visual cortex is hypothesized to have a hierarchical organization, where low-level regions extract low-level features such as local edges, and high-level regions extract semantic features such as object categories. However, details about the spatio-temporal dynamics are less understood. Here, using both the two-step and our one-step regression models in the source space, we correlated neural responses to naturalistic scene images with the low-level and high-level features extracted from a well-trained convolutional neural network. Additionally, we also studied the interaction between regions along the hierarchy using the two-step and our one-step connectivity models. The results from the two-step and the one-step methods were generally consistent; however, the one-step methods demonstrated some intriguing advantages in the regression analysis, and slightly different patterns in the connectivity analysis. In the consistent results, we not only observed an early-to-late shift from low-level to high-level features, which support feedforward information flow along the hierarchy, but also some novel evidence indicating non-feedforward information flow (e.g., topdown feedback). These results can help us better understand the neural computation in the visual cortex. Finally, we compared the empirical sensitivity between MEG and EEG in this experiment, in detecting dependence between neural responses and visual features. Our results show that the less costly EEG was able to achieve comparable sensitivity with that in MEG when the number of observations was about twice of that in MEG. These results can help researchers empirically choose between MEG and EEG when planning their experiments with limited budgets.

Computational models of complex biological systems can provide a better understanding of how living systems function but need to be validated before they are employed for real-life (e.g. clinical) applications. One of the most frequently employed in silico approaches for validating such models is model checking. Traditional model checking approaches are limited to uniscale non-spatial computational models because they do not explicitly distinguish between different scales, and do not take properties of (emergent) spatial structures (e.g. density of multicellular population) into account. This thesis defines a novel multiscale multidimensional spatio-temporal meta model checking methodology which enables validating multiscale (spatial) computational models of biological systems relative to how both numeric (e.g. concentrations) and spatial system properties are expected to change over time and across multiple scales. The methodology has two important advantages. First it supports computational models encoded using various high-level modelling formalisms because it is defined relative to time series data and not the models used to produce them. Secondly the methodology is generic because it can be automatically reconfigured according to case study specific types of spatial structures and properties using the meta model checking approach. In addition the methodology could be employed for multiple domains of science, but we illustrate its applicability here only against biological case studies. To automate the computational model validation process, the approach was implemented in software tools, which are made freely available online. Their efficacy is illustrated against two uniscale and four multiscale quantitative computational models encoding phase variation in bacterial colonies and the chemotactic aggregation of cells, respectively the rat cardiovascular system dynamics, the uterine contractions of labour, the Xenopus laevis cell cycle and the acute inflammation of the gut and lung. This novel model checking approach will enable the efficient construction of reliable multiscale computational models of complex systems.

Mon travail porte sur la construction de générateurs aléatoires de conditions de vent en Bretagne. Ces modèles permettent de simuler artificiellement des conditions météorologiques réalistes et sont couramment utilisés pour la gestion des risques liés aux aléas climatiques. Ils sont construits sur la base de données historiques dans le but de produire des simulations cohérentes avec le climat actuel mais peuvent intégrer des scénarios de changement climatique. Les séquences simulées permettent de pallier le manque de données réelles et sont utilisées en entrée de modèles économiques ou écologiques. / This work is aimed at constructing stochastic weather generators. These models enable to simulate artificially weather data that have statistical properties consistent with observed meteorology and climate. Outputs of these models are generally used in impact studies in agriculture or in ecology.

Pocket Switched Networks (PSNs) offer a means of infrastructureless inter-human communication by utilising Delay and Disruption Tolerant Networking (DTN) technology. However, creating PSNs involves solving challenges which were not encountered in the Deep Space Internet for which DTN technology was originally intended.End-to-end communication over multiple hops in PSNs is a product of short range opportunistic wireless communication between personal mobile wireless devices carried by humans. Opportunistic data delivery in PSNs is far less predictable than in the Deep Space Internet because human movement patterns are harder to predict than the orbital motion of satellites. Furthermore, PSNs require some scheme for efficient neighbour discovery in order to save energy and because mobile devices in PSNs may be unaware of when their next encounter will take place.This thesis offers novel solutions for neighbour discovery and opportunistic data delivery in PSNs that make practical use of dynamic inter-human encounter patterns.The first contribution is a novel neighbour discovery algorithm for PSNs called PISTONS which relies on a new inter-probe time calculation (IPC) and the bursty encounter patterns of humans to set the time between neighbour discovery scans. The IPC equations and PISTONS also give participants the ability to easily specify their required level of connectivity and energy saving with a single variable.This thesis also contains novel distributed spatio-temporal clustering and opportunistic data delivery algorithms for PSNs which can be used to deliver data over multiple hops. The spatio-temporal clustering algorimths are also used to analyse the social networks and transient groups which are formed when humans interact.

Epileptic seizures are characterised by an onset of abnormal brain activity that evolves in space and time, which ultimately returns to normal background activity. For different types of seizures, the abnormal activity can be vastly different both in duration, electrographic morphology and spatial extent. Mechanistic understanding of the different seizure dynamics (spatially, as well as temporally) is crucial for the advancement and improvement of clinical treatment. To gain a deeper mechanistic insight into different seizure dynamics, mathematical models of brain processes were developed in this thesis. These models are used to explain electrographic seizure dynamics in their temporal, as well as their spatio-temporal evolution. Our studies show that the temporal evolution of seizure dynamics can be understood in terms of prototypic waveforms, which in turn can be represented in terms of three neural population processes. Such a minimal framework lends itself to a detailed phase space analysis, which elucidates seizure waveforms and seizure transitions as topological properties of the phase space. Based on the phase space considerations we show how during spike-wave seizures, single-pulse stimuli can have more complex effects than previously thought. In terms of the spatio-temporal dynamics of seizures, mechanisms for focal seizure onset and propagation are investigated in a model cortical sheet of coupled, discretised columns. The coupling followed nearest-neighbour, as well as realistic mesoscopic cortical connectivities. Different possible causes (e.g. spatial heterogeneities) of seizure generation, as well as different seizure spreading patterns (via different networks) have been investigated. We conclude that focal seizure onset can be due to global (e.g. whole-brain level) causes, global conditions & local triggers, and local (e.g. cortical column level) causes. Clinically relevant predictions from this work include the suggestion of a specific stimulation protocol in spike-wave seizures that incorporates phase space information; and the suggestion of using microscopic cortical incisions to disrupt the integrity of abnormal cortical tissue in order to prevent focal seizure onset. In conclusion, multi-scale computational modelling of seizure dynamics is proposed as an important tool to link theoretical understanding, experimental results, and patient-specific clinical data.

La matrice de transmission permet de décrire les effets produit par un milieu multi-diffusant sur une onde monochromatique incidente. L'objectif des travaux présentés dans cette thèse est de développer le concept de matrice de transmission d'un milieu multi-diffusant au cas plus général d'une onde polychromatique impulsionnelle ultra-brève. Dans ce manuscrit nous présentons et mesurons la matrice de transmission multi-spectrale d'un milieu complexe. Cette nouvelle matrice nous donne l'information fondamentale sur le couplage spatio-temporel et spatio-spectral que le milieu engendre au passage d'une onde ultra-brève. Elle permet aussi de contrôler une source monochromatique et polychromatique, après avoir traversé un milieu complexe, de manière déterministe. Nous exploitons ainsi cette connaissance du milieu pour compenser les distorsions du champs en focalisant, façonnant et contrôlant spatialement, spectralement et temporellement un laser ultra-bref grâce à la seule mesure d'une matrice de transmission multi-spectrale. Cette méthode ouvre les portes de plusieurs applications d'imagerie à travers des milieux complexes, ainsi que pour l'interaction lumière-matière en milieux diffusants. / The transmission matrix allows to describe the effects generated by a multiple scattering medium on an incident monochromatic wave. The aim of the work presented in this dissertation is to develop the concept of transmission matrix of a multiple scattering medium to the more general case of a polychromatic ultra-fast pulsed light. In this dissertation we present and measure the multi-spectral transmission matrix of a complex medium. This new matrix describes the spatio-temporal coupling and the spatio-spectral coupling induced by the medium on a polycrhomatic illumination passing through it. The measurement of the multi-spectral transmission matrix allows us to control a monochromatic as well as a polychromatic source, after being scattered by the medium, in a deterministic way. We exploit this knowledge about the medium to compensate the distortions of the optical field by focusing, shaping and controlling spatially, spectrally and temporally an ultra-fast laser, thanks to the knowledge of the multi-spectral transmission matrix. This method paves the way towards many applications in the domain of imaging and light-matter interaction of light through complex media.

Philosophiae Doctor - PhD / This research investigated the application of recurrent neural networks (RNNs) for recognition of facial expressions based on facial action coding system (FACS). Support vector machines (SVMs) were used to validate the results obtained by RNNs. In this approach, instead of recognizing whole facial expressions, the focus was on the recognition of action units (AUs) that are defined in FACS. Recurrent neural networks are capable of gaining knowledge from temporal data while SVMs, which are time invariant, are known to be very good classifiers. Thus, the research consists of four important components: comparison of the use of image sequences against single static images, benchmarking feature selection and network optimization approaches, study of inter-AU correlations by implementing multiple output RNNs, and study of difference images as an approach for performance improvement. In the comparative studies, image sequences were classified using a combination of Gabor filters and RNNs, while single static images were classified using Gabor filters and SVMs. Sets of 11 FACS AUs were classified by both approaches, where a single RNN/SVM classifier was used for classifying each AU. Results indicated that classifying FACS AUs using image sequences yielded better results than using static images. The average recognition rate (RR) and false alarm rate (FAR) using image sequences was 82.75% and 7.61%, respectively, while the classification using single static images yielded a RR and FAR of 79.47% and 9.22%, respectively. The better performance by the use of image sequences can be at- tributed to RNNs ability, as stated above, to extract knowledge from time-series data. Subsequent research then investigated benchmarking dimensionality reduction, feature selection and network optimization techniques, in order to improve the performance provided by the use of image sequences. Results showed that an optimized network, using weight decay, gave best RR and FAR of 85.38% and 6.24%, respectively. The next study was of the inter-AU correlations existing in the Cohn-Kanade database and their effect on classification models. To accomplish this, a model was developed for the classification of a set of AUs by a single multiple output RNN. Results indicated that high inter-AU correlations do in fact aid classification models to gain more knowledge and, thus, perform better. However, this was limited to AUs that start and reach apex at almost the same time. This suggests the need for availability of a larger database of AUs, which could provide both individual and AU combinations for further investigation. The final part of this research investigated use of difference images to track the motion of image pixels. Difference images provide both noise and feature reduction, an aspect that was studied. Results showed that the use of difference image sequences provided the best results, with RR and FAR of 87.95% and 3.45%, respectively, which is shown to be significant when compared to use of normal image sequences classified using RNNs. In conclusion, the research demonstrates that use of RNNs for classification of image sequences is a new and improved paradigm for facial expression recognition.