2,183 research outputs found

    POTENTIALLY GRAPHIC SEQUENCES OF SPLIT GRAPHS

    Get PDF
    Abstract. A sequence π = (d 1 , d 2 , . . . , d n ) of non-negative integers is said to be graphic if it is the degree sequence of a simple G on n vertices, and such a graph G is referred to as a realization of π. The set of all non-increasing non-negative integer sequences π = (d 1 , d 2 , . . . , d n ) is denoted by N S n . A sequence π ∈ N S n is said to be graphic if it is the degree sequence of a graph G on n vertices, and such a graph G is called a realization of π. The set of all graphic sequences in N S n is denoted by GS n . A split graph K r + K s on r + s vertices is denoted by S r,s . A graphic sequence π is potentially H-graphic if there is a realizaton of π containing H as a subgraph. In this paper, we determine the graphic sequences of subgraphs H, where H is S r1,s1 + S r2,s2 + S r3,s3 + . . . + S rm,sm , S r1,s1 ∨ S r2,s2 ∨ . . . ∨ S rm,sm and S r1,s1 × S r2,s2 × . . . × S rm,sm and +, V and × denotes the standard join operation, the normal join operation and the cartesian product in these graphs respectively

    Topics in random graphs, combinatorial optimization, and statistical inference

    Get PDF
    The manuscript is made of three chapters presenting three differenttopics on which I worked with Ph.D. students. Each chapter can be read independently of the others andshould be relatively self-contained. Chapter 1 is a gentle introduction to the theory of random graphswith an emphasis on contagions on such networks. In Chapter 2, I explain the main ideas of the objectivemethod developed by Aldous and Steele applied to the spectral measure of random graphs and themonomer-dimer problem. This topic is dear to me and I hope that this chapter will convince the readerthat it is an exciting field of research. Chapter 3 deals with problems in high-dimensional statistics whichnow occupy a large proportion of my time. Unlike Chapters 1 and 2 which could be easily extended inlecture notes, I felt that the material in Chapter 3 was not ready for such a treatment. This field ofresearch is currently very active and I decided to present two of my recent contributions

    P-graph Associahedra and Hypercube Graph Associahedra

    Full text link
    A graph associahedron is a polytope dual to a simplicial complex whose elements are induced connected subgraphs called tubes. Graph associahedra generalize permutahedra, associahedra, and cyclohedra, and therefore are of great interest to those who study Coxeter combinatorics. This thesis characterizes nested complexes of simplicial complexes, which we call Δ\Delta-nested complexes. From here, we can define P-nestohedra by truncating simple polyhedra, and in more specificity define P-graph associahedra, which are realized by repeated truncation of faces of simple polyhedra in accordance with tubes of graphs. We then define hypercube-graph associahedra as a special case. Hypercube-graph associahedra are defined by tubes and tubings on a graph with a matching of dashed edges, with tubes and tubings avoiding those dashed edges. These simple rules make hypercube-graph tubings a simple and intuitive extension of classical graph tubings. We explore properties of Δ\Delta-nested complexes and P-nestohedra, and use these results to explore properties of hypercube-graph associahedra, including their facets and faces, as well as their normal fans and Minkowski sum decompositions. We use these properties to develop general methods of enumerating ff-polynomials of families of hypercube-graph associahedra. Several of these hypercube-graphs correspond to previously-studied polyhedra, such as cubeahedra, the halohedron, the type AnA_n linear cc-cluster associahedron, and the type AnA_n linear cc-cluster biassociahedron. We provide enumerations for these polyhedra and others.Comment: PhD Thesis of Jordan Almeter, 2022. https://repository.lib.ncsu.edu/handle/1840.20/3992

    Selected topics in video coding and computer vision

    Get PDF
    Video applications ranging from multimedia communication to computer vision have been extensively studied in the past decades. However, the emergence of new applications continues to raise questions that are only partially answered by existing techniques. This thesis studies three selected topics related to video: intra prediction in block-based video coding, pedestrian detection and tracking in infrared imagery, and multi-view video alignment.;In the state-of-art video coding standard H.264/AVC, intra prediction is defined on the hierarchical quad-tree based block partitioning structure which fails to exploit the geometric constraint of edges. We propose a geometry-adaptive block partitioning structure and a new intra prediction algorithm named geometry-adaptive intra prediction (GAIP). A new texture prediction algorithm named geometry-adaptive intra displacement prediction (GAIDP) is also developed by extending the original intra displacement prediction (IDP) algorithm with the geometry-adaptive block partitions. Simulations on various test sequences demonstrate that intra coding performance of H.264/AVC can be significantly improved by incorporating the proposed geometry adaptive algorithms.;In recent years, due to the decreasing cost of thermal sensors, pedestrian detection and tracking in infrared imagery has become a topic of interest for night vision and all weather surveillance applications. We propose a novel approach for detecting and tracking pedestrians in infrared imagery based on a layered representation of infrared images. Pedestrians are detected from the foreground layer by a Principle Component Analysis (PCA) based scheme using the appearance cue. To facilitate the task of pedestrian tracking, we formulate the problem of shot segmentation and present a graph matching-based tracking algorithm. Simulations with both OSU Infrared Image Database and WVU Infrared Video Database are reported to demonstrate the accuracy and robustness of our algorithms.;Multi-view video alignment is a process to facilitate the fusion of non-synchronized multi-view video sequences for various applications including automatic video based surveillance and video metrology. In this thesis, we propose an accurate multi-view video alignment algorithm that iteratively aligns two sequences in space and time. To achieve an accurate sub-frame temporal alignment, we generalize the existing phase-correlation algorithm to 3-D case. We also present a novel method to obtain the ground-truth of the temporal alignment by using supplementary audio signals sampled at a much higher rate. The accuracy of our algorithm is verified by simulations using real-world sequences

    Subject Index Volumes 1–200

    Get PDF

    Template Based Recognition of On-Line Handwriting

    Get PDF
    Software for recognition of handwriting has been available for several decades now and research on the subject have produced several different strategies for producing competitive recognition accuracies, especially in the case of isolated single characters. The problem of recognizing samples of handwriting with arbitrary connections between constituent characters (emph{unconstrained handwriting}) adds considerable complexity in form of the segmentation problem. In other words a recognition system, not constrained to the isolated single character case, needs to be able to recognize where in the sample one letter ends and another begins. In the research community and probably also in commercial systems the most common technique for recognizing unconstrained handwriting compromise Neural Networks for partial character matching along with Hidden Markov Modeling for combining partial results to string hypothesis. Neural Networks are often favored by the research community since the recognition functions are more or less automatically inferred from a training set of handwritten samples. From a commercial perspective a downside to this property is the lack of control, since there is no explicit information on the types of samples that can be correctly recognized by the system. In a template based system, each style of writing a particular character is explicitly modeled, and thus provides some intuition regarding the types of errors (confusions) that the system is prone to make. Most template based recognition methods today only work for the isolated single character recognition problem and extensions to unconstrained recognition is usually not straightforward. This thesis presents a step-by-step recipe for producing a template based recognition system which extends naturally to unconstrained handwriting recognition through simple graph techniques. A system based on this construction has been implemented and tested for the difficult case of unconstrained online Arabic handwriting recognition with good results

    Graphical Models in Characterizing the Dependency Relationship in Wireless Networks and Social Networks

    Get PDF
    Semi-Markov processes have become increasingly important in probability and statistical modeling, which have found applications in traffic analysis, reliability and maintenance, survival analysis, performance evaluation, biology, DNA analysis, risk processes, insurance and finance, earthquake modeling, etc. In the first part of this thesis, our focus is on applying semi-Markov processes to modeling the on-off duty cycles of different nodes in wireless networks. More specifically, we are interested in restoration of statistics of individual occupancy patterns of specific users based on wireless RF observation traces. In particular, we present a novel approach to finding the statistics of several operations, namely down-sampling, superposition and mislabelling, of a discrete time semi-Markov process in terms of the sojourn time distributions and states transition matrix of the resulting process. The resulting process, after those operations, is also a semi-Markov processes or a Markov renewal process. We show that the statistics of the original sequence before the superposition operation of two semi Markov processes can be generally recovered. However the statistics of the original sequence cannot be recovered under the down-sampling operation, namely the probability transition matrix and the sojourn time distribution properties are distorted after the down-sampling. Simulation and numerical results further demonstrate the validity of our theoretical findings. Our results thus provide a more profound understanding on the limitation of applying semi-Markov models in characterizing and learning the dynamics of nodes\u27 activities in wireless networks. In the second portion of the thesis a review is provided about several graphical models that have been widely used in literature recently to characterize the relationships between different users in social networks, the influence of the neighboring nodes in the networks or the semantic similarity in different contexts

    Numerical Linear Algebra applications in Archaeology: the seriation and the photometric stereo problems

    Get PDF
    The aim of this thesis is to explore the application of Numerical Linear Algebra to Archaeology. An ordering problem called the seriation problem, used for dating findings and/or artifacts deposits, is analysed in terms of graph theory. In particular, a Matlab implementation of an algorithm for spectral seriation, based on the use of the Fiedler vector of the Laplacian matrix associated with the problem, is presented. We consider bipartite graphs for describing the seriation problem, since the interrelationship between the units (i.e. archaeological sites) to be reordered, can be described in terms of these graphs. In our archaeological metaphor of seriation, the two disjoint nodes sets into which the vertices of a bipartite graph can be divided, represent the excavation sites and the artifacts found inside them. Since it is a difficult task to determine the closest bipartite network to a given one, we describe how a starting network can be approximated by a bipartite one by solving a sequence of fairly simple optimization problems. Another numerical problem related to Archaeology is the 3D reconstruction of the shape of an object from a set of digital pictures. In particular, the Photometric Stereo (PS) photographic technique is considered
    • …
    corecore