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Yes / Background: Human vision is vital in determining our interaction with the outside world. In this study we characterize our ability to judge changes in the direction of motion of objects-a common task which can allow us either to intercept moving objects, or else avoid them if they pose a threat. Methodology/Principal Findings: Observers were presented with objects which moved across a computer monitor on a linear path until the midline, at which point they changed their direction of motion, and observers were required to judge the direction of change. In keeping with the variety of objects we encounter in the real world, we varied characteristics of the moving stimuli such as velocity, extent of motion path and the object size. Furthermore, we compared performance for moving objects with the ability of observers to detect a deviation in a line which formed the static trace of the motion path, since it has been suggested that a form of static memory trace may form the basis for these types of judgment. The static line judgments were well described by a 'scale invariant' model in which any two stimuli which possess the same two-dimensional geometry (length/width) result in the same level of performance. Performance for the moving objects was entirely different. Irrespective of the path length, object size or velocity of motion, path deviation thresholds depended simply upon the duration of the motion path in seconds. Conclusions/Significance: Human vision has long been known to integrate information across space in order to solve spatial tasks such as judgment of orientation or position. Here we demonstrate an intriguing mechanism which integrates direction information across time in order to optimize the judgment of path deviation for moving objects. / Wellcome Trust, Leverhulme Trust, NIH

Image features play important roles in a wide range of computer vision applications, such as image registration, 3D reconstruction, object detection and video understanding. These image features include edges, contours, corners, regions, lines, curves, interest points, etc. However, the research is fragmented in these areas, especially when it comes to line and curve detection. In this thesis, we aim to discover, integrate, evaluate and summarize past research as well as our contributions in the area of image features. This thesis provides a comprehensive framework of concept, evaluation, implementation, and applications for image features. Firstly, this thesis proposes a novel concept of interest curves. Interest curves is a concept derived and extended from interest points. Interest curves are significant lines and arcs in an image that are repeatable under various image transformations. Interest curves bring clear guidelines and structures for future curve and line detection algorithms and related applications. Secondly, this thesis presents an evaluation framework for detecting and describing interest curves. The evaluation framework provides a new paradigm for comparing the performance of state-of-the-art line and curve detectors under image perturbations and transformations. Thirdly, this thesis proposes an interest curve detector (Distinctive Curves, DICU), which unifies the detection of edges, corners, lines and curves. DICU represents our state-of-the-art contribution in the areas concerning the detection of edges, corners, curves and lines. Our research efforts cover the most important attributes required by these features with respect to robustness and efficiency. Interest curves preserve richer geometric information than interest points. This advantage gives new ways of solving computer vision problems. We propose a simple description method for curve matching applications. We have found that our proposed interest curve descriptor outperforms all state-of-the-art interest point descriptors (SIFT, SURF, BRISK, ORB, FREAK). Furthermore, in our research we design a novel object detection algorithm that only utilizes DICU geometries without using local feature appearance. We organize image objects as curve chains and to detect an object, we search this curve chain in the target image using dynamic programming. The curve chain matching is scale and rotation-invariant as well as robust to image deformations. These properties have given us the possibility of resolving the rotation-variance problem in object detection applications. In our face detection experiments, the curve chain matching method proves to be scale and rotation-invariant and very computational efficient. / Bilddetaljer har en viktig roll i ett stort antal applikationer för datorseende, t.ex., bildregistrering, 3D-rekonstruktion, objektdetektering och videoförståelse. Dessa bilddetaljer inkluderar kanter, konturer, hörn, regioner, linjer, kurvor, intressepunkter, etc. Forskningen inom dessa områden är splittrad, särskilt för detektering av linjer och kurvor. I denna avhandling, strävar vi efter att hitta, integrera, utvärdera och sammanfatta tidigare forskning tillsammans med vår egen forskning inom området för bildegenskaper. Denna avhandling presenterar ett ramverk för begrepp, utvärdering, utförande och applikationer för bilddetaljer. För det första föreslår denna avhandling ett nytt koncept för intressekurvor. Intressekurvor är ett begrepp som härrör från intressepunkter och det är viktiga linjer och bågar i bilden som är repeterbara oberoende av olika bildtransformationer. Intressekurvor ger en tydlig vägledning och struktur för framtida algoritmer och relaterade tillämpningar för kurv- och linjedetektering. För det andra, presenterar denna avhandling en utvärderingsram för detektorer och beskrivningar av intressekurvor. Utvärderingsramverket utgör en ny paradigm för att jämföra resultatet för de bästa möjliga teknikerna för linje- och kurvdetektorer vid bildstörningar och bildtransformationer. För det tredje presenterar denna avhandling en detektor för intressekurvor (Distinctive curves, DICU), som förenar detektering av kanter, hörn, linjer och kurvor. DICU representerar vårt främsta bidrag inom området detektering av kanter, hörn, kurvor och linjer. Våra forskningsinsatser täcker de viktigaste attribut som krävs av dessa funktioner med avseende på robusthet och effektivitet. Intressekurvor innehåller en rikare geometrisk information än intressepunkter. Denna fördel öppnar för nya sätt att lösa problem för datorseende. Vi föreslår en enkel beskrivningsmetod för kurvmatchningsapplikationer och den föreslagna deskriptorn för intressekurvor överträffar de bästa tillgängliga deskriptorerna för intressepunkter (SIFT, SURF, BRISK, ORB, och FREAK). Dessutom utformar vi en ny objektdetekteringsalgoritm som bara använder geometri för DICU utan att använda det lokala utseendet. Vi organiserar bildobjekt som kurvkedjor och för att upptäcka ett objekt behöver vi endast söka efter denna kurvkedja i målbilden med hjälp av dynamisk programmering. Kurvkedjematchningen är oberoende av skala och rotationer samt robust vid bilddeformationer. Dessa egenskaper ger möjlighet att lösa problemet med rotationsberoende inom objektdetektering. Vårt ansiktsigenkänningsexperiment visar att kurvkedjematchning är oberoende av skala och rotationer och att den är mycket beräkningseffektiv. / INTRO – INteractive RObotics research network

To guide action, animals anticipate what events will occur, and when they will occur, based on experience. How animals anticipate future events is an unsettled question. Although reinforcement learning is often used to model anticipation, it is resource-intensive outside of the simplest scenarios. In this dissertation, I show evidence of memory that is persistent and carries timing information, and specify an algorithm for how animals might anticipate the identity and timing of future events. This dissertation consists of two studies. In the first study, I found that identity and timing of remembered odors are jointly represented in the same cells in the dentate gyrus and lateral entorhinal cortex. Further, odor memories persist well after new odors emerge. The study analyzed results from an experiment conducted by Woods et al. (2020) on mice passively exposed to separate odors for a period of 20 s per exposure. The results are consistent with a memory framework known as timing using inverse Laplace transform (TILT). In the second study, I constructed a computational algorithm based on the TILT memory framework to anticipate the identity and timing of future events. The algorithm generates predictions based on memories of past events, and stored associations between cues and outcomes. The algorithm is resource-efficient even when the future depends on the indefinite past. The algorithm is scale-invariant and works well with chains of events. Together, the studies support a novel computational mechanism which anticipates what events will occur, and when they will occur. The algorithm could be applied in machine learning in cases of long-range dependence on history. These studies predict that behavioral and neural responses of animals could depend on events well into the past. / 2024-03-13T00:00:00Z

Ce travail de thèse concerne la caractérisation de la structure spatio-temporelle des fortes précipitations dans la région Cévennes-Vivarais. La région est soumise à des événements de pluie catastrophiques dont la magnitude gouverne les conséquences à différentes échelles de temps et d'espace. La détermination de la probabilité d'occurrence des orages est problématique à cause du caractère extrême des ces événements, de leur dimension spatio-temporelle et du manque de données pluviométriques aux échelles d'intérêt. Nous proposons d'adopter des approches d'invariance d'échelles afin d'estimer la fréquence d'occurrence de ces événements. Ces approches permettent d'extrapoler la distribution de la pluie à haute résolution à partir de données d'intensité pluvieuse à plus faible résolution. La paramétrisation de ces modèles étant fortement dépendante de l'incertitude de la mesure, nous avons d'abord caractérisé l'erreur commise dans la mesure de la pluie par un réseau de pluviomètres à augets. Nous avons ensuite exploré le comportement des pluies extrêmes dans la région d'étude, identifiant les gammes d'invariance d'échelles des extrêmes. Dans cette gamme d'échelles, nous présentons un modèle régional Intensité-Durée-Fréquence qui prend en considération l'hétérogénéité spatiale des extrêmes dans la région. Étant donné que le réseau pluviométrique ne permet pas de détecter les propriétés d'invariance d'échelle spatiale des champs de pluie, nous avons adopté une méthode semi-empirique pour modéliser des intensités de pluie intégrés sur des surfaces données (pluie surfacique) sur la base du concept de la mise en échelle dynamique (« dynamic scaling »). Cette modélisation permet la construction d'un modèle régional Intensité-Durée-Fréquence-Surface. Enfin, nous avons appliqué ce modèle à la construction des diagrammes de sévérité pour trois événements marquants en région Cévennes-Vivarais, afin d'identifier les échelles spatio-temporelles critiques pour chaque événement. Grâce aux diagrammes de sévérité, nous avons pu évaluer, pour ces mêmes événements, la performance d'un modèle météorologique de méso-échelle. / The thesis is devoted to the characterization of the space-time structure of heavy rainfall events in the Cévennes-Vivarais area (France). The region is prone to catastrophic storms whose magnitude governs social and economic consequences at different space and time scales. The magnitude of an event cannot be univocally related to a probability of occurrence. The determination of the occurrence probability of storms is problematic because of their extreme character, of their complex space-time development and of the lack of rainfall data at the spatial and temporal scales of interest. We propose to adopt scale-invariant approaches in order to estimate the heavy rainfall frequency assessment. These approaches allow to extrapolate the high resolution rainfall distribution based on low resolution rainfall intensity data. The model estimation being heavily dependent of the data accuracy, the first step consists in the characterization of the error committed in the point and spatial rainfall estimated by tipping-bucket raingage networks. We then explore the extreme rainfall behavior in the region, detecting the range where extremes are scale-invariant. In this range, we present a regional Intensity-Duration-Frequency model for point rainfall maxima taking into account the heterogeneity of extremes in the region. We demonstrate that the rainfall network does not allow to detect scale-invariant properties of extreme rainfall fields, and then we adopt a semi-empirical method based on the concept of « dynamic scaling » to build regional Intensity-Duration-Area-Frequency curves. Finally, we apply this model for the determination of the severity diagrams for three significant storms in the Cévennes-Vivarais region, with the aim to identify the critical space-time scales of each event. Based on severity diagrams, we then evaluate, for the same events, the performances of a mesoscale meteorological model.

PIRES, Rilder de Sousa. Difusão singular em um sistema confinado. 2013. 64 f. Dissertação (Mestrado em Física) - Programa de Pós-Graduação em Física, Departamento de Física, Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2013. / Submitted by Edvander Pires (edvanderpires@gmail.com) on 2015-10-23T19:14:37Z No. of bitstreams: 1 2013_dis_rspires.pdf: 2524951 bytes, checksum: 2a38032e0c2de28e051d588ecd2b47f3 (MD5) / Approved for entry into archive by Edvander Pires(edvanderpires@gmail.com) on 2015-10-23T19:38:52Z (GMT) No. of bitstreams: 1 2013_dis_rspires.pdf: 2524951 bytes, checksum: 2a38032e0c2de28e051d588ecd2b47f3 (MD5) / Made available in DSpace on 2015-10-23T19:38:52Z (GMT). No. of bitstreams: 1 2013_dis_rspires.pdf: 2524951 bytes, checksum: 2a38032e0c2de28e051d588ecd2b47f3 (MD5) Previous issue date: 2013 / Patterns of scale invariance, associated with power laws, are often found in nature, for instance, in the fluctuations of prices of items in stock markets and in the energy spectrum of turbulent systems. These two systems and many others that exhibit scale invariance present some common properties: they are comprised of several elements that interact in a non-linear way, are not in equilibrium, and exhibit self-organization. Scale invariance is also found in the correlations observed in the critical state of systems that present phase transitions. The concept of self-organized criticality suggests that the properties of invariance spontaneously arise in complex systems. Several models exhibit properties of self-organized critically, including invasion percolation, sand-piles and the trough model, however it is not clear what are the necessary ingredients for criticality to arise. It is known that this property appears in some non-linear diffusive systems. In this work, we introduce a confining potential in a one-dimensional diffusion model with a singular non-linearity on diffusion coefficient, and analyze how this affects in the steady state of the system. We then derive a diffusion equation and obtain a solution for stationary density profile. Our analytical solution is in good agreement with the numerical results. We also present a statistical study of the distribution of avalanches sizes in this model, and obtain profiles following power laws, what is not usually observed in other one-dimensional systems. We also investigated how these profiles vary when the confinement increases, and using finite size scaling we found a universal curve for the distribution of avalanche sizes. Our results show that the action of confinement in a one-dimensional system can yield scale invariance. / Padrões de invariância de escala, associados à leis de potência, são frequentemente observados na natureza. Alguns exemplos são: flutuações em preços de itens de bolsa de valores e outros investimentos, além do espectro de energia em sistemas turbulentos. Esses dois sistemas e vários outros que exibem invariância de escala têm propriedades em comum: compõem-se de vários elementos que interagem de forma não linear, estão fora do equilíbrio e exibem auto-organização. Invariância de escala também é encontrada nas correlações observadas no ponto crítico de sistemas que apresentam transições de fase. O conceito de criticalidade auto-organizada sugere que as propriedades de invariância emergem espontaneamente em sistema complexos. Vários modelos exibem propriedades criticamente auto-organizadas, entre eles percolação invasiva, pilhas de areia e o modelo de desníveis, no entanto, não se sabe ao certo quais os ingredientes necessários para criticalidade emergir. Sabe-se que essa propriedade se manifesta em alguns sistemas difusivos não lineares. Nesse trabalho, introduzimos um potencial confinante em um modelo de difusão unidimensional com uma não linearidade singular no coeficiente de difusão e analisamos a influência dessa mudança no estado estacionário do sistema. Conseguimos, então, derivar uma equação de difusão do modelo e obtemos uma solução para o perfil de densidade. Nossa solução analítica concorda perfeitamente com os resultados numéricos. Fizemos, ainda, um estudo estatístico do perfil de avalanches do modelo, e obtemos perfis de avalanche em leis de potência, o que normalmente não é observado em outros sistemas unidimensionais. Analisamos, ainda, como esses perfis variam na medida que se aumenta o confinamento, e usando transformações de escala encontramos uma curva universal para os perfis de distribuição de tamanhos de avalanche. Nossos resultados demonstram que a ação do confinamento em um sistema unidimensional pode levar ao surgimento da invariância de escala.

In this thesis, we first review the current development of optimal regression designs under the second-order least squares estimator in the literature. The criteria include A- and D-optimality. We then introduce a new formulation of A-optimality criterion so the result can be extended to c-optimality which has not been studied before. Following Kiefer's equivalence results, we derive the optimality conditions for A-, c- and D-optimal designs under the second-order least squares estimator. In addition, we study the number of support points for various regression models including Peleg models, trigonometric models, regular and fractional polynomial models. A generalized scale invariance property for D-optimal designs is also explored. Furthermore, we discuss one computing algorithm to find optimal designs numerically. Several interesting applications are presented and related MATLAB code are provided in the thesis. / Graduate

L'arrivée massive de la production décentralisée, l'intégration de technologies d'information et de communication et de convertisseurs d'électronique de puissance permettent aux réseaux électriques de devenir plus flexibles, plus accessibles, plus efficaces. Mais ils deviennent aussi plus complexes et plus difficiles à modéliser, à analyser et à dimensionner. Dans cette thèse, nous allons nous focaliser sur le problème de la modélisation dynamique du réseau électrique. En effet, la complexité du fonctionnement du réseau électrique moderne rend encore plus indispensable de comprendre comment il se comporte suite à des perturbations ou tout simplement à des changements de son état de fonctionnement. C'est cette compréhension qui doit permettre d'éviter que le réseau perde sa stabilité. Grâce aux modèles développés dans la thèse, on veut notamment retrouver des liens de connaissance forts entre le comportement dynamique et les propriétés topologiques du réseau. On espère ainsi pouvoir fournir à termes des préconisations pour l'évolution des topologies de réseaux ou de leurs modes d'exploitation. Pour mener à bien ce travail, l'invariance d'échelle d'un réseau électrique est tout d'abord explorée. Pour cela, des méthodes issues de la géométrie fractale sont exposées et appliquées à des réseaux réalistes. Partant du constat que les réseaux électriques étudiés présentent une invariance d'échelle sur une plage d'observation importante, une nouvelle modélisation dynamique est proposée. Cette modélisation a l'intérêt d'une représentation plus parcimonieuse que les représentations classiques par des approches boite noire et permet de conserver des liens de connaissance avec entre la topologie et les propriétés dynamiques. / The influx of distributed generation, the integration of information as well as communication technologies and the integration of electronic power converters allows electrical grids to become more flexible, more accessible and more effective. However they become at the same time more complex thus making the modeling, analyzing and sizing more difficult. This thesis will focus on the problem of dynamic modeling of electrical networks. Indeed, the operation's complexity of the modern power grid makes it even more essential to understand how it behaves after disturbances or just simply after changes in operation condition. It is this understanding that should allow one to prevent the case that the system loses its stability. With models developed in this thesis, we particularly want to find strong links between the dynamic behavior and the topological properties of the network. It is hoped to provide eventually propositions for evolution of topology or operation modes of networks. To carry through this study, the scale invariance of an electrical network is first explored. For this purpose, methods issued from fractal geometry are presented and applied to realistic networks. Noting that the considered electrical networks exhibit scale invariance over a large observation range, a new dynamic modeling is proposed.

Conselho Nacional de Desenvolvimento CientÃfico e TecnolÃgico / PadrÃes de invariÃncia de escala, associados à leis de potÃncia, sÃo frequentemente observados na natureza. Alguns exemplos sÃo: flutuaÃÃes em preÃos de itens de bolsa de valores e outros investimentos, alÃm do espectro de energia em sistemas turbulentos. Esses dois sistemas e vÃrios outros que exibem invariÃncia de escala tÃm propriedades em comum: compÃem-se de vÃrios elementos que interagem de forma nÃo linear, estÃo fora do equilÃbrio e exibem auto-organizaÃÃo. InvariÃncia de escala tambÃm à encontrada nas correlaÃÃes observadas no ponto crÃtico de sistemas que apresentam transiÃÃes de fase. O conceito de criticalidade auto-organizada sugere que as propriedades de invariÃncia emergem espontaneamente em sistema complexos. VÃrios modelos exibem propriedades criticamente auto-organizadas, entre eles percolaÃÃo invasiva, pilhas de areia e o modelo de desnÃveis, no entanto, nÃo se sabe ao certo quais os ingredientes necessÃrios para criticalidade emergir. Sabe-se que essa propriedade se manifesta em alguns sistemas difusivos nÃo lineares. Nesse trabalho, introduzimos um potencial confinante em um modelo de difusÃo unidimensional com uma nÃo linearidade singular no coeficiente de difusÃo e analisamos a influÃncia dessa mudanÃa no estado estacionÃrio do sistema. Conseguimos, entÃo, derivar uma equaÃÃo de difusÃo do modelo e obtemos uma soluÃÃo para o perfil de densidade. Nossa soluÃÃo analÃtica concorda perfeitamente com os resultados numÃricos. Fizemos, ainda, um estudo estatÃstico do perfil de avalanches do modelo, e obtemos perfis de avalanche em leis de potÃncia, o que normalmente nÃo à observado em outros sistemas unidimensionais. Analisamos, ainda, como esses perfis variam na medida que se aumenta o confinamento, e usando transformaÃÃes de escala encontramos uma curva universal para os perfis de distribuiÃÃo de tamanhos de avalanche. Nossos resultados demonstram que a aÃÃo do confinamento em um sistema unidimensional pode levar ao surgimento da invariÃncia de escala. / Patterns of scale invariance, associated with power laws, are often found in nature, for instance, in the fluctuations of prices of items in stock markets and in the energy spectrum of turbulent systems. These two systems and many others that exhibit scale invariance present some common properties: they are comprised of several elements that interact in a non-linear way, are not in equilibrium, and exhibit self-organization. Scale invariance is also found in the correlations observed in the critical state of systems that present phase transitions. The concept of self-organized criticality suggests that the properties of invariance spontaneously arise in complex systems. Several models exhibit properties of self-organized critically, including invasion percolation, sand-piles and the trough model, however it is not clear what are the necessary ingredients for criticality to arise. It is known that this property appears in some non-linear diffusive systems. In this work, we introduce a confining potential in a one-dimensional diffusion model with a singular non-linearity on diffusion coefficient, and analyze how this affects in the steady state of the system. We then derive a diffusion equation and obtain a solution for stationary density profile. Our analytical solution is in good agreement with the numerical results. We also present a statistical study of the distribution of avalanches sizes in this model, and obtain profiles following power laws, what is not usually observed in other one-dimensional systems. We also investigated how these profiles vary when the confinement increases, and using finite size scaling we found a universal curve for the distribution of avalanche sizes. Our results show that the action of confinement in a one-dimensional system can yield scale invariance.