Lexicographic identifying codes

An identifying code in a graph is a set of vertices which intersects all the symmetric differences between pairs of neighbourhoods of vertices. Not all graphs have identifying codes; those that do are referred to as twin-free. In this paper, we design an algorithm that finds an identifying code in a twin-free graph on n vertices in O(n^3) binary operations, and returns a failure if the graph is not twin-free. We also determine an alternative for sparse graphs with a running time of O(n^2d log n) binary operations, where d is the maximum degree. We also prove that these algorithms can return any identifying code with minimum cardinality, provided the vertices are correctly sorted

Improving the Lives of Young Children: Meeting Parents' Health and Mental Health Needs Through Medicaid and CHIP So Children Can Thrive

Outlines options for two-generational service delivery to help address parental health issues, especially depression, and minimize developmental or behavioral problems in their children when the parents are ineligible for or not enrolled in Medicaid

Corporate Social Responsibility: Challenges and Opportunities for Trade Unionists

Presents a background of the corporate initiative at self regulation. Criticizes certain components of the concept from the perspective of trade unions

Problems on q-Analogs in Coding Theory

The interest in $q$-analogs of codes and designs has been increased in the last few years as a consequence of their new application in error-correction for random network coding. There are many interesting theoretical, algebraic, and combinatorial coding problems concerning these q-analogs which remained unsolved. The first goal of this paper is to make a short summary of the large amount of research which was done in the area mainly in the last few years and to provide most of the relevant references. The second goal of this paper is to present one hundred open questions and problems for future research, whose solution will advance the knowledge in this area. The third goal of this paper is to present and start some directions in solving some of these problems.Comment: arXiv admin note: text overlap with arXiv:0805.3528 by other author

Compressive and Coded Change Detection: Theory and Application to Structural Health Monitoring

In traditional sparse recovery problems, the goal is to identify the support of compressible signals using a small number of measurements. In contrast, in this thesis the problem of identification of a sparse number of statistical changes in stochastic phenomena is considered when decision makers only have access to compressed measurements, i.e., each measurement is derived by a subset of features. Herein, we propose a new framework that is termed Compressed Change Detection. The main approach relies on integrating ideas from the theory of identifying codes with change point detection in sequential analysis. If the stochastic properties of certain features change, then the changes can be detected by examining the covering set of an identifying code of measurements. In particular, given a large number N of features, the goal is to detect a small set of features that undergoes a statistical change using a small number of measurements. Sufficient conditions are derived for the probability of false alarm and isolation to approach zero in the asymptotic regime where N is large. As an application of compressed change detection, the problem of detection of a sparse number of damages in a structure for Structural Health Monitoring (SHM) is considered. Since only a small number of damage scenarios can occur simultaneously, change detection is applied to responses of pairs of sensors that form an identifying code over a learned damage-sensing graph. Generalizations of the proposed framework with multiple concurrent changes and for arbitrary graph topologies are presented

Large Constant Dimension Codes and Lexicodes

Constant dimension codes, with a prescribed minimum distance, have found recently an application in network coding. All the codewords in such a code are subspaces of \F_q^n with a given dimension. A computer search for large constant dimension codes is usually inefficient since the search space domain is extremely large. Even so, we found that some constant dimension lexicodes are larger than other known codes. We show how to make the computer search more efficient. In this context we present a formula for the computation of the distance between two subspaces, not necessarily of the same dimension.Comment: submitted for ALCOMA1