On vertex adjacencies in the polytope of pyramidal tours with step-backs

We consider the traveling salesperson problem in a directed graph. The pyramidal tours with step-backs are a special class of Hamiltonian cycles for which the traveling salesperson problem is solved by dynamic programming in polynomial time. The polytope of pyramidal tours with step-backs $PSB (n)$ is defined as the convex hull of the characteristic vectors of all possible pyramidal tours with step-backs in a complete directed graph. The skeleton of $PSB (n)$ is the graph whose vertex set is the vertex set of $PSB (n)$ and the edge set is the set of geometric edges or one-dimensional faces of $PSB (n)$. The main result of the paper is a necessary and sufficient condition for vertex adjacencies in the skeleton of the polytope $PSB (n)$ that can be verified in polynomial time.Comment: in Englis

Алгоритм ветвей и границ для задачи коммивояжера не является алгоритмом прямого типа

In this paper, we consider the notion of a direct type algorithm introduced by V. A. Bondarenko in 1983. A direct type algorithm is a linear decision tree with some special properties. the concept of a direct type algorithm is determined using the graph of solutions of a combinatorial optimization problem. e vertices of this graph are all feasible solutions of a problem. Two solutions are called adjacent if there are input data for which these and only these solutions are optimal. A key feature of direct type algorithms is that their complexity is bounded from below by the clique number of the solutions graph. In 2015-2018, there were five papers published, the main results of which are estimates of the clique numbers of polyhedron graphs associated with various combinatorial optimization problems. the main motivation in these works is the thesis that the class of direct type algorithms is wide and includes many classical combinatorial algorithms, including the branch and bound algorithm for the traveling salesman problem, proposed by J. D. C. Little, K. G. Murty, D. W. Sweeney, C. Karel in 1963. We show that this algorithm is not a direct type algorithm. Earlier, in 2014, the author of this paper showed that the Hungarian algorithm for the assignment problem is not a direct type algorithm. us, the class of direct type algorithms is not so wide as previously assumed.В настоящей работе рассматривается понятие линейного разделяющего алгоритма прямого типа, введенное В. А. Бондаренко в 1983 г. Понятие алгоритма прямого типа определяется с помощью графа решений задачи комбинаторной оптимизации. Вершинами этого графа служат все допустимые решения задачи. Два решения называются смежными, если существуют входные данные, для которых эти решения и только они являются оптимальными. Ключевой особенностью алгоритмов прямого типа является то, что их трудоемкость оценивается снизу кликовым числом графа решений. В 2015–2018 гг. было опубликовано пять работ, основными результатами которых являются оценки кликовых чисел графов многогранников, ассоциированных с различными задачами комбинаторной оптимизации. В качестве основной мотивации в этих работах приводится тезис о том, что класс алгоритмов прямого типа является широким и включает в себя многие классические комбинаторные алгоритмы, в том числе алгоритм ветвей и границ для задачи коммивояжера, предложенный J. D. C. Little, K. G. Murty, D. W. Sweeney, C. Karel в 1963 г. Мы покажем, что этот алгоритм не является алгоритмом прямого типа. Ранее, в 2014 г., автором настоящей работы было показано, что венгерский алгоритм для задачи о назначениях не является алгоритмом прямого типа. Таким образом, класс алгоритмов прямого типа не является настолько широким, как предполагалось ранее

Two-Dimensional Matter: Order, Curvature and Defects

Many systems in nature and the synthetic world involve ordered arrangements of units on two-dimensional surfaces. We review here the fundamental role payed by both the topology of the underlying surface and its detailed curvature. Topology dictates certain broad features of the defect structure of the ground state but curvature-driven energetics controls the detailed structured of ordered phases. Among the surprises are the appearance in the ground state of structures that would normally be thermal excitations and thus prohibited at zero temperature. Examples include excess dislocations in the form of grain boundary scars for spherical crystals above a minimal system size, dislocation unbinding for toroidal hexatics, interstitial fractionalization in spherical crystals and the appearance of well-separated disclinations for toroidal crystals. Much of the analysis leads to universal predictions that do not depend on the details of the microscopic interactions that lead to order in the first place. These predictions are subject to test by the many experimental soft and hard matter systems that lead to curved ordered structures such as colloidal particles self-assembling on droplets of one liquid in a second liquid. The defects themselves may be functionalized to create ligands with directional bonding. Thus nano to meso scale superatoms may be designed with specific valency for use in building supermolecules and novel bulk materials. Parameters such as particle number, geometrical aspect ratios and anisotropy of elastic moduli permit the tuning of the precise architecture of the superatoms and associated supermolecules. Thus the field has tremendous potential from both a fundamental and materials science/supramolecular chemistry viewpoint.Comment: Review article, 102 pages, 59 figures, submitted to Advances in Physic

Medical image analysis methods for anatomical surface reconstruction using tracked 3D ultrasound

The thesis focuses on a study of techniques for acquisition and reconstruction of surface data from anatomical objects by means of tracked 3D ultrasound. In the context of the work two experimental scanning systems are developed and tested on both artificial objects and biological tissues. The first system is based on the freehand ultrasound principle and utilizes a conventional 2D ultrasound transducer coupled with an electromechanical 3D position tracker. The main properties and the basic features of this system are discussed. A number of experiments show that its accuracy in the close to ideal conditions reaches 1.2 mm RMS. The second proposed system implements the sequential triggered scanning approach. The system consists of an ultrasound machine, a workstation and a scanning body (a moving tank filled with liquid and a transducer fixation block) that performs transducer positioning and tracking functions. The system is tested on artificial and real bones. The performed experiments illustrate that it provides significantly better accuracy than the freehand ultrasound (about 0.2 mm RMS) and allows acquiring regular data with a good precision. This makes such a system a promising tool for orthopaedic and trauma surgeons during contactless X-ray-free examinations of injured extremities. The second major subject of the thesis concerns development of medical image analysis methods for 3D surface reconstruction and 2D object detection. We introduce a method based on mesh-growing surface reconstruction that is designed for noisy and sparse data received from 3D tracked ultrasound scanners. A series of experiments on synthetic and ultrasound data show an appropriate reconstruction accuracy. The reconstruction error is measured as the averaged distance between the faces of the mesh and the points from the cloud. Dependently on the initial settings of the method the error varies in range 0.04 - 0.2% for artificial data and 0.3 - 0.7 mm for ultrasound bone data. The reconstructed surfaces correctly interpolate the original point clouds and demonstrate proper smoothness. The next significant problem considered in the work is 2D object detection. Although medical object detection is not integrated into the developed scanning systems, it can be used as a possible further extension of the systems for automatic detection of specific anatomical structures. We analyse the existent object detection methods and introduce a modification of the one based on the popular Generalized Hough Transform (GHT). Unlike the original GHT, the developed method is invariant to rotation and uniform scaling, and uses an intuitive two-point parametrization. We propose several implementations of the feature-to-vote conversion function with the corresponding vote analysis principles. Special attention is devoted to a study of the hierarchical vote analysis and its probabilistic properties. We introduce a parameter space subdivision strategy that reduces the probability of vote peak omission, and show that it can be efficiently implemented in practice using the Gumbel probability distribution

Proceedings of the 2018 Canadian Society for Mechanical Engineering (CSME) International Congress

Published proceedings of the 2018 Canadian Society for Mechanical Engineering (CSME) International Congress, hosted by York University, 27-30 May 2018

Proceedings of the Third Edition of the Annual Conference on Wireless On-demand Network Systems and Services (WONS 2006)

Ce fichier regroupe en un seul documents l'ensemble des articles accéptés pour la conférences WONS2006/http://citi.insa-lyon.fr/wons2006/index.htmlThis year, 56 papers were submitted. From the Open Call submissions we accepted 16 papers as full papers (up to 12 pages) and 8 papers as short papers (up to 6 pages). All the accepted papers will be presented orally in the Workshop sessions. More precisely, the selected papers have been organized in 7 session: Channel access and scheduling, Energy-aware Protocols, QoS in Mobile Ad-Hoc networks, Multihop Performance Issues, Wireless Internet, Applications and finally Security Issues. The papers (and authors) come from all parts of the world, confirming the international stature of this Workshop. The majority of the contributions are from Europe (France, Germany, Greece, Italy, Netherlands, Norway, Switzerland, UK). However, a significant number is from Australia, Brazil, Canada, Iran, Korea and USA. The proceedings also include two invited papers. We take this opportunity to thank all the authors who submitted their papers to WONS 2006. You helped make this event again a success