Mark Sequences In Digraphs

In Chapter 1, we present a brief introduction of digraphs and some def- initions. Chapter 2 is a review of scores in tournaments and oriented graphs. Also we have obtained several new results on oriented graph scores and we have given a new proof of Avery's theorem on oriented graph scores. In chap- ter 3, we have introduced the concept of marks in multidigraphs, non-negative integers attached to the vertices of multidigraphs. We have obtained several necessary and su cient conditions for sequences of non-negative integers to be mark sequences of some r-digraphs. We have derived stronger inequalities for these marks. Further we have characterized uniquely mark sequences in r-digraphs. This concept of marks has been extended to bipartite multidi- graphs and multipartite multidigraphs in chapter 4. There we have obtained characterizations for mark sequences in these types of multidigraphs and we have given algorithms for constructing corresponding multidigraphs. Chap- ter 5 deals with imbalances and imbalance sequences in digraphs. We have generalized the concept of imbalances to oriented bipartite graphs and have obtained criteria for a pair of integers to be the pair of imbalance sequences of some oriented bipartite graph. We have shown the existence of an oriented bipartite graph whose imbalance set is the given set of integers

Round-robin tournaments with homogeneous rounds

We study single and double round-robin tournaments for n teams, where in each round a fixed number (g) of teams is present and each team present plays a fixed number (m) of matches in this round. In a single, respectively double, round-robin tournament each pair of teams play one, respectively two, matches. In the latter case the two matches should be played in different rounds. We give necessary combinatorial conditions on the triples (n,g,m) for which such round-robin tournaments can exist, and discuss three general construction methods that concern the cases m=1, m=2 and m=g−1. For n≤20 these cases cover 149 of all 173 non-trivial cases that satisfy the necessary conditions. In 147 of these 149 cases a tournament can be constructed. For the remaining 24 cases the tournament does not exist in 2 cases, and is constructed in all other cases. Finally we consider the spreading of rounds for teams, and give some examples where well-spreading is either possible or impossible

Measuring social dynamics in a massive multiplayer online game

Quantification of human group-behavior has so far defied an empirical, falsifiable approach. This is due to tremendous difficulties in data acquisition of social systems. Massive multiplayer online games (MMOG) provide a fascinating new way of observing hundreds of thousands of simultaneously socially interacting individuals engaged in virtual economic activities. We have compiled a data set consisting of practically all actions of all players over a period of three years from a MMOG played by 300,000 people. This large-scale data set of a socio-economic unit contains all social and economic data from a single and coherent source. Players have to generate a virtual income through economic activities to `survive' and are typically engaged in a multitude of social activities offered within the game. Our analysis of high-frequency log files focuses on three types of social networks, and tests a series of social-dynamics hypotheses. In particular we study the structure and dynamics of friend-, enemy- and communication networks. We find striking differences in topological structure between positive (friend) and negative (enemy) tie networks. All networks confirm the recently observed phenomenon of network densification. We propose two approximate social laws in communication networks, the first expressing betweenness centrality as the inverse square of the overlap, the second relating communication strength to the cube of the overlap. These empirical laws provide strong quantitative evidence for the Weak ties hypothesis of Granovetter. Further, the analysis of triad significance profiles validates well-established assertions from social balance theory. We find overrepresentation (underrepresentation) of complete (incomplete) triads in networks of positive ties, and vice versa for networks of negative ties...Comment: 23 pages 19 figure

An investigation of interregional trade network structures

We provide empirical evidence on the network structure of trade flows between European regions and discuss the theoretical underpinning of such a structure. First, we analyze EU regional trade data using Social Network Analysis. We describe the topology of this network and compute local and global centrality measures. Finally, we consider the distribution of higher order statistics, through the analysis of local clustering and main triadic structures in the triad census of interregional trade flows. In the theoretical part, we explore the relationship between trade costs and trade links. As shown by Behrens (2004, 2005a, 2005b) in a two-region linear new economic geography (NEG) model, trade costs and the local market size determine, even with finite trade costs, unconditional autarky and unilateral trade, that is, a one-directional flow from one region to the other. Following these contributions and guided by the empirical evidence, we clarify the relationship between market competition, trade costs and the patterns of trade in a three-region NEG model. We identify a larger set of trade network configurations other the three elementary ones that occur at the dyadic level between two regions (no trade, one-way trade, reciprocated two-way trade), and relate the model with the triad census

Quality-diversity in dissimilarity spaces

The theory of magnitude provides a mathematical framework for quantifying and maximizing diversity. We apply this framework to formulate quality-diversity algorithms in generic dissimilarity spaces. In particular, we instantiate and demonstrate a very general version of Go-Explore with promising performance.Comment: Minor bug fix: see new appendix J for details. Only small quantitative effects; no significant changes to results (but all redone

Ethnographic Causality

This book explores the problem of causal inference when a sufficient number of comparative cases cannot be found, which would permit the application of frequency based models formulated in terms of explanatory causal generalizations

System development technical interactions and innovation : a network-based investigation

Thesis (S.M.)--Massachusetts Institute of Technology, Engineering Systems Division, 2006.Includes bibliographical references (leaves 70-77).The development of complex engineering systems such as aircraft engines involves many cross functional teams that are usually geographically distributed. These teams interact in several ways but one of the most important set of interactions during the product development phase is the flow of technical information which is largely used for coordination and problem solving. For analytical purposes, these technical information flows can be represented as a directed network. This thesis develops a context and a research design that can help one investigate the impact of the resultant network structure on innovation in complex engineering systems. The broad context can be divided into two: theoretical and real world contexts. The theoretical context is developed by reviewing literature at the intersection of networks and innovation, and the real world context is typified by a modular enterprise developing a complex engineering system. Within this broad context, the research area of interest is framed by a set of hypotheses that lead to precise innovation measures and characterizations. The research design is motivated by the context and intended theoretical contributions. It consists of two major sections.(cont.) The first section discusses and critiques methodologies for constructing networks and proposes a methodology more suited to this engineering systems development context. The second section describes a two-stage model whose variables include network structural properties such as structural holes, nodal degree, tie strength, and innovation output. It also describes a methodology for investigating the relationship between network density and the innovation development subprocess. Finally, the context and research design are tied together to create an instantiation of the measurement and characterization of innovation in complex engineering systems development. The characterization considers product innovation as radical, architectural, modular or incremental, and process innovation as organizational / coordination-based or technical. The measures of innovation include granted patents, implemented employee suggestions, product literature based innovation counts and results from structured interviews with the two leaders from each node in the network.by Pedzisayi O. Makumbe.S.M