Metric-locating-dominating sets of graphs for constructing related subsets of vertices

© 2018. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/A dominating set S of a graph is a metric-locating-dominating set if each vertex of the graph is uniquely distinguished by its distances from the elements of S , and the minimum cardinality of such a set is called the metric-location-domination number. In this paper, we undertake a study that, in general graphs and specific families, relates metric-locating-dominating sets to other special sets: resolving sets, dominating sets, locating-dominating sets and doubly resolving sets. We first characterize the extremal trees of the bounds that naturally involve metric-location-domination number, metric dimension and domination number. Then, we prove that there is no polynomial upper bound on the location-domination number in terms of the metric-location-domination number, thus extending a result of Henning and Oellermann. Finally, we show different methods to transform metric-locating-dominating sets into locating-dominating sets and doubly resolving sets. Our methods produce new bounds on the minimum cardinalities of all those sets, some of them concerning parameters that have not been related so farPeer ReviewedPostprint (author's final draft

A páros összehasonlításokon alapuló rangsorolás módszertani és alkalmazási kérdései = Methodological and applicational issues of paired comparison based ranking

A páros összehasonlításokkal történő rangsorolás egyaránt felmerül a döntéselmélet, a preferenciák modellezése, a társadalmi választások elmélete, a tudománymetria, a statisztika, a pszichológia, vagy a sport területén. Ilyen esetekben gyakran nincs lehetőség az alternatívák egyetlen, objektív skálán történő értékelésére, csak azok egymással való összevetésére. Ez három, részben összefüggő kérdést vet fel. Az első a vizsgált gyakorlati probléma matematikai reprezentációja, a második az így keletkező feladat megoldása, a harmadik a kapott eredmény értelmezése. Értekezésünk az első kettőre fókuszál, bár a 7. fejezetben szereplő alkalmazásban az utóbbira is kitérünk. ____ Paired comparison based ranking problems are given by a tournament matrix representing the performance of some objects against each other. They arise in many different fields like social choice theory (Chebotarev and Shamis, 1998), sports (Landau, 1895, 1914; Zermelo, 1929) or psychology (Thurstone, 1927). The usual goal is to determine a winner (possibly a set of winners) or a complete ranking for the objects. There were some attempts to link the two areas (i.e. Bouyssou (2004)), however, they achieved a limited success. We will deal only with the latter issue, allowing for different preference intensities (including ties), incomplete and multiple comparisons among the objects. The ranking includes three areas: representation of the practical problem as a mathematical model, its solution, and interpretation of the results. The third issue strongly depends on the actual application, therefore it is not addressed in the thesis, however, it will appear in Chapter 7

Structural exploration and inference of the network

This dissertation consists of two parts. In the first part, a learning-based method for classification of online reviews that achieves better classification accuracy is extended. Automatic sentiment classification is becoming a popular and effective way to help online users or companies to process and make sense of customer reviews. The method combines two recent developments. First, valence shifters and individual opinion words are combined as bigrams to use in an ordinal margin classifier. Second, relational information between unigrams expressed in the form of a graph is used to constrain the parameters of the classifier. By combining these two components, it is possible to extract more of the unstructured information present in the data than previous methods, like support vector machine, random forest, hence gaining the potential of better performance. Indeed, the results show a higher classification accuracy on empirical real data with ground truth as well as on simulated data. The second part deals with graphical models. Gaussian graphical models are useful to explore conditional dependence relationships between random variables through estimation of the inverse covariance matrix of a multivariate normal distribution. An estimator for such models appropriate for multiple graphs analysis in two groups is developed. Under this setting, inferring networks separately ignores the common structure, while inferring networks identically would mask the disparity. A generalized method which estimates multiple partial correlation matrices through linear regressions is proposed. The method pursues the sparsity for each matrix, similarities for matrices within each group, and the disparities for matrices between groups. This is achieved by a l1 penalty and a 12 penalty for the pursuit of sparseness and clustering, and a metric that learns the true heterogeneity through optimization procedure. Theoretically, the asymptotic consistency for both constrained l0 method and the proposed method to reconstruct the structures is shown. Its superior performance is illustrated via a number of simulated networks. An application to polychromatic flow cytometry data sets for network inference under different sets of conditions is also included