Generating Random Elements of Finite Distributive Lattices

This survey article describes a method for choosing uniformly at random from any finite set whose objects can be viewed as constituting a distributive lattice. The method is based on ideas of the author and David Wilson for using ``coupling from the past'' to remove initialization bias from Monte Carlo randomization. The article describes several applications to specific kinds of combinatorial objects such as tilings, constrained lattice paths, and alternating-sign matrices.Comment: 13 page

Efficient Approach for OS-CFAR 2D Technique Using Distributive Histograms and Breakdown Point Optimal Concept applied to Acoustic Images

In this work, a new approach to improve the algorithmic efficiency of the Order Statistic-Constant False Alarm Rate (OS-CFAR) applied in two dimensions (2D) is presented. OS-CFAR is widely used in radar technology for detecting moving objects as well as in sonar technology for the relevant areas of segmentation and multi-target detection on the seafloor. OS-CFAR rank orders the samples obtained from a sliding window around a test cell to select a representative sample that is used to calculate an adaptive detection threshold maintaining a false alarm probability. Then, the test cell is evaluated to determine the presence or absence of a target based on the calculated threshold. The rank orders allows that OS-CFAR technique to be more robust in multi-target situations and less sensitive than other methods to the presence of the speckle noise, but requires higher computational effort. This is the bottleneck of the technique. Consequently, the contribution of this work is to improve the OS-CFAR 2D with the distributive histograms and the optimal breakdown point optimal concept, mainly from the standpoint of efficient computation. In this way, the OS-CFAR 2D on-line computation was improved, by means of speeding up the samples sorting problem through the improvement in the calculus of the statistics order. The theoretical algorithm analysis is presented to demonstrate the improvement of this approach. Also, this novel efficient OS-CFAR 2D was contrasted experimentally on acoustic images.Fil: Villar, Sebastian Aldo. Universidad Nacional del Centro de la Provincia de Buenos Aires. Centro de Investigaciones en Física e Ingeniería del Centro de la Provincia de Buenos Aires. - Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Tandil. Centro de Investigaciones en Física e Ingeniería del Centro de la Provincia de Buenos Aires. - Provincia de Buenos Aires. Gobernación. Comisión de Investigaciones Científicas. Centro de Investigaciones en Física e Ingeniería del Centro de la Provincia de Buenos Aires; Argentina. Universidad Nacional del Centro de la Provincia de Buenos Aires. Facultad de Ingeniería Olavarría. Departamento de Electromecánica. Grupo INTELYMEC; ArgentinaFil: Menna, Bruno Victorio. Universidad Nacional del Centro de la Provincia de Buenos Aires. Centro de Investigaciones en Física e Ingeniería del Centro de la Provincia de Buenos Aires. - Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Tandil. Centro de Investigaciones en Física e Ingeniería del Centro de la Provincia de Buenos Aires. - Provincia de Buenos Aires. Gobernación. Comisión de Investigaciones Científicas. Centro de Investigaciones en Física e Ingeniería del Centro de la Provincia de Buenos Aires; Argentina. Universidad Nacional del Centro de la Provincia de Buenos Aires. Facultad de Ingeniería Olavarría. Departamento de Electromecánica. Grupo INTELYMEC; ArgentinaFil: Torcida, Sebastián. Universidad Nacional del Centro de la Provincia de Buenos Aires. Facultad de Ciencias Exactas. Departamento de Matemática; ArgentinaFil: Acosta, Gerardo Gabriel. Universidad Nacional del Centro de la Provincia de Buenos Aires. Facultad de Ingeniería Olavarría. Departamento de Electromecánica. Grupo INTELYMEC; Argentina. Universidad Nacional del Centro de la Provincia de Buenos Aires. Centro de Investigaciones en Física e Ingeniería del Centro de la Provincia de Buenos Aires. - Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Tandil. Centro de Investigaciones en Física e Ingeniería del Centro de la Provincia de Buenos Aires. - Provincia de Buenos Aires. Gobernación. Comisión de Investigaciones Científicas. Centro de Investigaciones en Física e Ingeniería del Centro de la Provincia de Buenos Aires; Argentin

Introduction to \u3ci\u3ePhilosophical Foundations of Contract Law\u3c/i\u3e

This Introduction to Philosophical Foundations of Contract Law (Gregory Klass, George Letsas & Prince Saprai eds., Oxford University Press, forthcoming) describes the field of contract theory and locates the essays in the volume within that field. The volume includes chapters from Aditi Bagchi, Randy Barnett, Lisa Bernstein, Mindy Chen-Wishart, Charles Fried, Avery Katz, Dori Kimel, Gregory Klass, George Letsas and Prince Saprai, Daniel Markovits, Liam Murphy, David Owens, J.E. Penner, Margaret Jane Radin, Joseph Raz, Stephen Smith, and Charlie Webb

Variable sets over an algebra of lifetimes: a contribution of lattice theory to the study of computational topology

A topos theoretic generalisation of the category of sets allows for modelling spaces which vary according to time intervals. Persistent homology, or more generally, persistence is a central tool in topological data analysis, which examines the structure of data through topology. The basic techniques have been extended in several different directions, permuting the encoding of topological features by so called barcodes or equivalently persistence diagrams. The set of points of all such diagrams determines a complete Heyting algebra that can explain aspects of the relations between persistent bars through the algebraic properties of its underlying lattice structure. In this paper, we investigate the topos of sheaves over such algebra, as well as discuss its construction and potential for a generalised simplicial homology over it. In particular we are interested in establishing a topos theoretic unifying theory for the various flavours of persistent homology that have emerged so far, providing a global perspective over the algebraic foundations of applied and computational topology.Comment: 20 pages, 12 figures, AAA88 Conference proceedings at Demonstratio Mathematica. The new version has restructured arguments, clearer intuition is provided, and several typos correcte

Contractual Freedom, Contractual Justice, and Contract Law (Theory)

In aircraft control, control allocation can be used to distribute the total control effort among the actuators when the number of actuators exceeds the number of controlled variables. The control allocation problem is often posed as a constrained least squares problem to incorporate the actuator position and rate limits. Most proposed methods for real-time implementation, like there distributed pseudoinverse method, only deliver approximate, and sometimes unreliable solutions. In this paper we investigate the use of classical active set methods for control allocation. We develop active set algorithms that always find the optimal control distribution, and show by simulation that the timing requirements are in the same range as for two previously proposed solvers