Lift-and-project ranks of the stable set polytope of joined a-perfect graphs

In this paper we study lift-and-project polyhedral operators defined by Lov?asz and Schrijver and Balas, Ceria and Cornu?ejols on the clique relaxation of the stable set polytope of web graphs. We compute the disjunctive rank of all webs and consequently of antiweb graphs. We also obtain the disjunctive rank of the antiweb constraints for which the complexity of the separation problem is still unknown. Finally, we use our results to provide bounds of the disjunctive rank of larger classes of graphs as joined a-perfect graphs, where near-bipartite graphs belong

Combinatorics

[no abstract available

On the critical nature of plastic flow: one and two dimensional models

Steady state plastic flows have been compared to developed turbulence because the two phenomena share the inherent complexity of particle trajectories, the scale free spatial patterns and the power law statistics of fluctuations. The origin of the apparently chaotic and at the same time highly correlated microscopic response in plasticity remains hidden behind conventional engineering models which are based on smooth fitting functions. To regain access to fluctuations, we study in this paper a minimal mesoscopic model whose goal is to elucidate the origin of scale free behavior in plasticity. We limit our description to fcc type crystals and leave out both temperature and rate effects. We provide simple illustrations of the fact that complexity in rate independent athermal plastic flows is due to marginal stability of the underlying elastic system. Our conclusions are based on a reduction of an over-damped visco-elasticity problem for a system with a rugged elastic energy landscape to an integer valued automaton. We start with an overdamped one dimensional model and show that it reproduces the main macroscopic phenomenology of rate independent plastic behavior but falls short of generating self similar structure of fluctuations. We then provide evidence that a two dimensional model is already adequate for describing power law statistics of avalanches and fractal character of dislocation patterning. In addition to capturing experimentally measured critical exponents, the proposed minimal model shows finite size scaling collapse and generates realistic shape functions in the scaling laws.Comment: 72 pages, 40 Figures, International Journal of Engineering Science for the special issue in honor of Victor Berdichevsky, 201

Robust Network Topology Inference and Processing of Graph Signals

The abundance of large and heterogeneous systems is rendering contemporary data more pervasive, intricate, and with a non-regular structure. With classical techniques facing troubles to deal with the irregular (non-Euclidean) domain where the signals are defined, a popular approach at the heart of graph signal processing (GSP) is to: (i) represent the underlying support via a graph and (ii) exploit the topology of this graph to process the signals at hand. In addition to the irregular structure of the signals, another critical limitation is that the observed data is prone to the presence of perturbations, which, in the context of GSP, may affect not only the observed signals but also the topology of the supporting graph. Ignoring the presence of perturbations, along with the couplings between the errors in the signal and the errors in their support, can drastically hinder estimation performance. While many GSP works have looked at the presence of perturbations in the signals, much fewer have looked at the presence of perturbations in the graph, and almost none at their joint effect. While this is not surprising (GSP is a relatively new field), we expect this to change in the upcoming years. Motivated by the previous discussion, the goal of this thesis is to advance toward a robust GSP paradigm where the algorithms are carefully designed to incorporate the influence of perturbations in the graph signals, the graph support, and both. To do so, we consider different types of perturbations, evaluate their disruptive impact on fundamental GSP tasks, and design robust algorithms to address them.Comment: Dissertatio

Human shape modelling for carried object detection and segmentation

La détection des objets transportés est un des prérequis pour développer des systèmes qui cherchent à comprendre les activités impliquant des personnes et des objets. Cette thèse présente de nouvelles méthodes pour détecter et segmenter les objets transportés dans des vidéos de surveillance. Les contributions sont divisées en trois principaux chapitres. Dans le premier chapitre, nous introduisons notre détecteur d’objets transportés, qui nous permet de détecter un type générique d’objets. Nous formulons la détection d’objets transportés comme un problème de classification de contours. Nous classifions le contour des objets mobiles en deux classes : objets transportés et personnes. Un masque de probabilités est généré pour le contour d’une personne basé sur un ensemble d’exemplaires (ECE) de personnes qui marchent ou se tiennent debout de différents points de vue. Les contours qui ne correspondent pas au masque de probabilités généré sont considérés comme des candidats pour être des objets transportés. Ensuite, une région est assignée à chaque objet transporté en utilisant la Coupe Biaisée Normalisée (BNC) avec une probabilité obtenue par une fonction pondérée de son chevauchement avec l’hypothèse du masque de contours de la personne et du premier plan segmenté. Finalement, les objets transportés sont détectés en appliquant une Suppression des Non-Maxima (NMS) qui élimine les scores trop bas pour les objets candidats. Le deuxième chapitre de contribution présente une approche pour détecter des objets transportés avec une méthode innovatrice pour extraire des caractéristiques des régions d’avant-plan basée sur leurs contours locaux et l’information des super-pixels. Initiallement, un objet bougeant dans une séquence vidéo est segmente en super-pixels sous plusieurs échelles. Ensuite, les régions ressemblant à des personnes dans l’avant-plan sont identifiées en utilisant un ensemble de caractéristiques extraites de super-pixels dans un codebook de formes locales. Ici, les régions ressemblant à des humains sont équivalentes au masque de probabilités de la première méthode (ECE). Notre deuxième détecteur d’objets transportés bénéficie du nouveau descripteur de caractéristiques pour produire une carte de probabilité plus précise. Les compléments des super-pixels correspondants aux régions ressemblant à des personnes dans l’avant-plan sont considérés comme une carte de probabilité des objets transportés. Finalement, chaque groupe de super-pixels voisins avec une haute probabilité d’objets transportés et qui ont un fort support de bordure sont fusionnés pour former un objet transporté. Finalement, dans le troisième chapitre, nous présentons une méthode pour détecter et segmenter les objets transportés. La méthode proposée adopte le nouveau descripteur basé sur les super-pixels pour iii identifier les régions ressemblant à des objets transportés en utilisant la modélisation de la forme humaine. En utilisant l’information spatio-temporelle des régions candidates, la consistance des objets transportés récurrents, vus dans le temps, est obtenue et sert à détecter les objets transportés. Enfin, les régions d’objets transportés sont raffinées en intégrant de l’information sur leur apparence et leur position à travers le temps avec une extension spatio-temporelle de GrabCut. Cette étape finale sert à segmenter avec précision les objets transportés dans les séquences vidéo. Nos méthodes sont complètement automatiques, et font des suppositions minimales sur les personnes, les objets transportés, et les les séquences vidéo. Nous évaluons les méthodes décrites en utilisant deux ensembles de données, PETS 2006 et i-Lids AVSS. Nous évaluons notre détecteur et nos méthodes de segmentation en les comparant avec l’état de l’art. L’évaluation expérimentale sur les deux ensembles de données démontre que notre détecteur d’objets transportés et nos méthodes de segmentation surpassent de façon significative les algorithmes compétiteurs.Detecting carried objects is one of the requirements for developing systems that reason about activities involving people and objects. This thesis presents novel methods to detect and segment carried objects in surveillance videos. The contributions are divided into three main chapters. In the first, we introduce our carried object detector which allows to detect a generic class of objects. We formulate carried object detection in terms of a contour classification problem. We classify moving object contours into two classes: carried object and person. A probability mask for person’s contours is generated based on an ensemble of contour exemplars (ECE) of walking/standing humans in different viewing directions. Contours that are not falling in the generated hypothesis mask are considered as candidates for carried object contours. Then, a region is assigned to each carried object candidate contour using Biased Normalized Cut (BNC) with a probability obtained by a weighted function of its overlap with the person’s contour hypothesis mask and segmented foreground. Finally, carried objects are detected by applying a Non-Maximum Suppression (NMS) method which eliminates the low score carried object candidates. The second contribution presents an approach to detect carried objects with an innovative method for extracting features from foreground regions based on their local contours and superpixel information. Initially, a moving object in a video frame is segmented into multi-scale superpixels. Then human-like regions in the foreground area are identified by matching a set of extracted features from superpixels against a codebook of local shapes. Here the definition of human like regions is equivalent to a person’s probability map in our first proposed method (ECE). Our second carried object detector benefits from the novel feature descriptor to produce a more accurate probability map. Complement of the matching probabilities of superpixels to human-like regions in the foreground are considered as a carried object probability map. At the end, each group of neighboring superpixels with a high carried object probability which has strong edge support is merged to form a carried object. Finally, in the third contribution we present a method to detect and segment carried objects. The proposed method adopts the new superpixel-based descriptor to identify carried object-like candidate regions using human shape modeling. Using spatio-temporal information of the candidate regions, consistency of recurring carried object candidates viewed over time is obtained and serves to detect carried objects. Last, the detected carried object regions are refined by integrating information of their appearances and their locations over time with a spatio-temporal extension of GrabCut. This final stage is used to accurately segment carried objects in frames. Our methods are fully automatic, and make minimal assumptions about a person, carried objects and videos. We evaluate the aforementioned methods using two available datasets PETS 2006 and i-Lids AVSS. We compare our detector and segmentation methods against a state-of-the-art detector. Experimental evaluation on the two datasets demonstrates that both our carried object detection and segmentation methods significantly outperform competing algorithms

A proposed segmented precast concrete spherical cap: geometry, structural stability and construction

This study proposes the design and construction of a concrete spherical cap composed of uniformly-shaped precast doubly-curved panels based on spherical division techniques. A numerical structural analysis is conducted to study the failure behavior of the segmented structure and the capacity of the joints by using finite element modeling techniques to model the concrete material behavior, boundary conditions and intermediate joints of the precast panels. An experimental analysis is conducted to verify the capacity of the structure and the reliability of the modeling techniques, and to study the feasibility of the proposed panel prefabrication and assembly method. The results of this study demonstrate that the proposed precast system and connection design perform efficiently when compared to the monolithically-cast counterpart, particularly under uniform loading conditions. Additional insights on the properties and solution parameters of finite element modelling of concrete shell structures are presented based on the structural analysis of this work. The study concludes the ability of the proposed geometric design and construction method to enhance the prefabrication and construction efficiency with little effect on the structural capacity within the context of the selected geometry and conducted load tests, and recommends further parameters to study for design and construction optimization

Low-Diameter Clusters in Network Analysis

In this dissertation, we introduce several novel tools for cluster-based analysis of complex systems and design solution approaches to solve the corresponding optimization problems. Cluster-based analysis is a subfield of network analysis which utilizes a graph representation of a system to yield meaningful insight into the system structure and functions. Clusters with low diameter are commonly used to characterize cohesive groups in applications for which easy reachability between group members is of high importance. Low-diameter clusters can be mathematically formalized using a clique and an s-club (with relatively small values of s), two concepts from graph theory. A clique is a subset of vertices adjacent to each other and an s-club is a subset of vertices inducing a subgraph with a diameter of at most s. A clique is actually a special case of an s-club with s = 1, hence, having the shortest possible diameter. Two topics of this dissertation focus on graphs prone to uncertainty and disruptions, and introduce several extensions of low-diameter models. First, we introduce a robust clique model in graphs where edges may fail with a certain probability and robustness is enforced using appropriate risk measures. With regard to its ability to capture underlying system uncertainties, finding the largest robust clique is a better alternative to the problem of finding the largest clique. Moreover, it is also a hard combinatorial optimization problem, requiring some effective solution techniques. To this aim, we design several heuristic approaches for detection of large robust cliques and compare their performance. Next, we consider graphs for which uncertainty is not explicitly defined, studying connectivity properties of 2-clubs. We notice that a 2-club can be very vulnerable to disruptions, so we enhance it by reinforcing additional requirements on connectivity and introduce a biconnected 2-club concept. Additionally, we look at the weak 2-club counterpart which we call a fragile 2-club (defined as a 2-club that is not biconnected). The size of the largest biconnected 2-club in a graph can help measure overall system reachability and connectivity, whereas the largest fragile 2-club can identify vulnerable parts of the graph. We show that the problem of finding the largest fragile 2-club is polynomially solvable whereas the problem of finding the largest biconnected 2-club is NP-hard. Furthermore, for the former, we design a polynomial time algorithm and for the latter - combinatorial branch-and-bound and branch-and-cut algorithms. Lastly, we once again consider the s-club concept but shift our focus from finding the largest s-club in a graph to the problem of partitioning the graph into the smallest number of non-overlapping s-clubs. This problem cannot only be applied to derive communities in the graph, but also to reduce the size of the graph and derive its hierarchical structure. The problem of finding the minimum s-club partitioning is a hard combinatorial optimization problem with proven complexity results and is also very hard to solve in practice. We design a branch-and-bound combinatorial optimization algorithm and test it on the problem of minimum 2-club partitioning