Restrained and Other Domination Parameters in Complementary Prisms.

In this thesis, we will study several domination parameters of a family of graphs known as complementary prisms. We will first present the basic terminology and definitions necessary to understand the topic. Then, we will examine the known results addressing the domination number and the total domination number of complementary prisms. After this, we will present our main results, namely, results on the restrained domination number of complementary prisms. Subsequently results on the distance - k domination number, 2-step domination number and stratification of complementary prisms will be presented. Then, we will characterize when a complementary prism is Eulerian or bipartite, and we will obtain bounds on the chromatic number of a complementary prism. We will finish the thesis with a section on possible future problems

Syntax and semantics: A comparison of the structuralistic language theory of Ebeling with knowledge graph theory

This paper describes a comparison of two structuralistic theories of syntax and semantics of language. Both theories were developed in The Netherlands. One was developed by C.L.Ebeling at the University of Amsterdam about 30 years ago, the other by C.Hoede and students at the University of Twente in the last 20 years

Stratification and domination in graphs.

Thesis (Ph.D.)-University of KwaZulu-Natal, Pietermaritzburg, 2006.In a recent manuscript (Stratification and domination in graphs. Discrete Math. 272 (2003), 171-185) a new mathematical framework for studying domination is presented. It is shown that the domination number and many domination related parameters can be interpreted as restricted 2-stratifications or 2-colorings. This framework places the domination number in a new perspective and suggests many other parameters of a graph which are related in some way to the domination number. In this thesis, we continue this study of domination and stratification in graphs. Let F be a 2-stratified graph with one fixed blue vertex v specified. We say that F is rooted at the blue vertex v. An F-coloring of a graph G is a red-blue coloring of the vertices of G such that every blue vertex v of G belongs to a copy of F (not necessarily induced in G) rooted at v. The F-domination number yF(GQ of G is the minimum number of red vertices of G in an F-coloring of G. Chapter 1 is an introduction to the chapters that follow. In Chapter 2, we investigate the X-domination number of prisms when X is a 2-stratified 4-cycle rooted at a blue vertex where a prism is the cartesian product Cn x K2, n > 3, of a cycle Cn and a K2. In Chapter 3 we investigate the F-domination number when (i) F is a 2-stratified path P3 on three vertices rooted at a blue vertex which is an end-vertex of the F3 and is adjacent to a blue vertex and with the remaining vertex colored red. In particular, we show that for a tree of diameter at least three this parameter is at most two-thirds its order and we characterize the trees attaining this bound. (ii) We also investigate the F-domination number when F is a 2-stratified K3 rooted at a blue vertex and with exactly one red vertex. We show that if G is a connected graph of order n in which every edge is in a triangle, then for n sufficiently large this parameter is at most (n — /n)/2 and this bound is sharp. In Chapter 4, we further investigate the F-domination number when F is a 2- stratified path P3 on three vertices rooted at a blue vertex which is an end-vertex of the P3 and is adjacent to a blue vertex with the remaining vertex colored red. We show that for a connected graph of order n with minimum degree at least two this parameter is bounded above by (n —1)/2 with the exception of five graphs (one each of orders four, five and six and two of order eight). For n > 9, we characterize those graphs that achieve the upper bound of (n — l)/2. In Chapter 5, we define an f-coloring of a graph to be a red-blue coloring of the vertices such that every blue vertex is adjacent to a blue vertex and to a red vertex, with the red vertex itself adjacent to some other red vertex. The f-domination number yz{G) of a graph G is the minimum number of red vertices of G in an f-coloring of G. Let G be a connected graph of order n > 4 with minimum degree at least 2. We prove that (i) if G has maximum degree A where A 4 with maximum degree A where A 5 with maximum degree A where

Modularity and Optimality in Social Choice

Marengo and the second author have developed in the last years a geometric model of social choice when this takes place among bundles of interdependent elements, showing that by bundling and unbundling the same set of constituent elements an authority has the power of determining the social outcome. In this paper we will tie the model above to tournament theory, solving some of the mathematical problems arising in their work and opening new questions which are interesting not only from a mathematical and a social choice point of view, but also from an economic and a genetic one. In particular, we will introduce the notion of u-local optima and we will study it from both a theoretical and a numerical/probabilistic point of view; we will also describe an algorithm that computes the universal basin of attraction of a social outcome in O(M^3 logM) time (where M is the number of social outcomes).Comment: 42 pages, 4 figures, 8 tables, 1 algorithm

Towards a new framework for domination

Dominating concepts constitute a cornerstone in Graph Theory. Part of the efforts in the field have been focused in finding different mathematical frameworks where domination notions naturally arise, providing new points of view about the matter. In this paper, we introduce one of these frameworks based in convexity. The main idea consists of defining a convexity in a graph, already used in image processing, for which the usual parameters of convexity are closely related to domination parameters. Moreover, the Helly number of this convexity may be viewed as a new domination parameter whose study would be of interest

Politics, Power, and Influence: Defense Industries in the Post-Cold War

The post-Cold War era is placing the defense industry at a crossroads. If, on the one hand, it is under great pressure to guarantee warlike efforts around the world, with tight budgets and uncertain lead-times, on the other hand, it is seen as a central instrument for national sovereignty and foreign policy. The purpose of this research is to report the state-of-the-art of the existing literature and explore the most relevant research areas in order to provide the conceptual basis for further empirical research. To do so, this study uses a preferred reporting items for systematic review and meta-analysis (PRISMA), which is an adequate technique as it allows one to discover concepts, ideas, and debates about the defense industry. The results evidenced three different approaches to the defense industry—integration, autarky, and domination. In that regard, we present several case studies in which the defense industry is used as an instrument of foreign policy or national sovereignty. Future studies may focus on empirical research to validate the theoretical findings or to identify variables that lead some defense industries to seek synergies, resorting to mergers and acquisitions, while other defense companies prefer to obtain State funds.info:eu-repo/semantics/publishedVersio

The Governance Grenade: Mass Privatization, State Capacity and Economic Development in Postcommunist and Reforming Communist Societies.

This article critiques neoliberal transition theory from a state-centered perspective. Neoliberal scholars have used cross-national regression analysis to argue that postcommunist economic failure is the result of inadequate adherence to neoliberal precepts. Sociologists, in turn, have relied on case study data to show that postcommunist economic failure is the outcome of too close adherence to neoliberal policy recommendations, which has led to an erosion of state effectiveness, and thus produced underdevelopment. The present paper advances a version of this statist theory based on a quantitative analysis of mass privatization programs in the postcommunist world. We argue that the neoliberal policy of rapid large-scale privatization creates severe supply and demand shocks for enterprises, thereby inducing firm failure. The resulting erosion of tax revenues leads to a fiscal crisis for the state, and severely weakens its capacity and bureaucratic character. This, in turn, reacts back on the enterprise sector, as the state can no longer support the institutions necessary for the effective functioning of a capitalist economy, thus resulting in de-modernization. In this paper, we test the predictions of neoliberal transition theory against those of our statist theory, using cross-national regression techniques. We find that the implementation of mass privatization programs negatively impacts measures of economic growth, state capacity and the security of property rights.