The role of bipartite structure in R&D collaboration networks

A number of real-world networks are, in fact, one-mode projections of bipartite networks comprised of two types of nodes. For institutions engaging in collaboration for technological innovation, the underlying network is bipartite with institutions (agents) linked to the patents they have filed (artifacts), while the projection is the co-patenting network. Projected network topology is highly affected by the underlying bipartite structure, hence a lack of understanding of the bipartite network has consequences for the information that might be drawn from the one-mode co-patenting network. Here, we create an empirical bipartite network using data from 2.7 million patents. We project this network onto the agents (institutions) and look at properties of both the bipartite and projected networks that may play a role in knowledge sharing and collaboration. We compare these empirical properties to those of synthetic bipartite networks and their projections in order to understand the processes that might operate in the network formation. A good understanding of the topology is critical for investigating the potential flow of technological knowledge. We show how degree distributions and small cycles affect the topology of the one-mode projected network - specifically degree and clustering distributions, and assortativity. We propose new network-based metrics to quantify how collaborative agents are in the co-patenting network. We find that several large corporations that are the most collaborative agents in the network, however such organisations tend to have a low diversity of collaborators. In contrast, the most prolific institutions tend to collaborate relatively little but with a diverse set of collaborators. This indicates that they concentrate the knowledge of their core technical research, while seeking specific complementary knowledge via collaboration with smaller companies.Comment: 23 pages, 12 figures, 2 table

Bourdieu, networks, and movements: Using the concepts of habitus, field and capital to understand a network analysis of gender differences in undergraduate physics

Current trends suggest that significant gender disparities exist within Science, Technology, Engineering, and Mathematics (STEM) education at university, with female students being underrepresented in physics, but more equally represented in life sciences (e.g., biology, medicine). To understand these trends, it is important to consider the context in which students make decisions about which university courses to enrol in. The current study seeks to investigate gender differences in STEM through a unique approach that combines network analysis of student enrolment data with an interpretive lens based on the sociological theory of Pierre Bourdieu. We generate a network of courses taken by around 9000 undergraduate physics students (from 2009 to 2014) to quantify Bourdieu's concept of field. We explore the properties of this network to investigate gender differences in transverse movements (between different academic fields) and vertical movements (changes in students' achievement rankings within a field). Our findings indicate that female students are more likely to make transverse movements into life science fields. We also find that university physics does a poor job in attracting high achieving students, and especially high achieving female students. Of the students who do choose to study physics, low achieving female students are less likely to continue than their male counterparts. The results and implications are discussed in the context of Bourdieu's theory, and previous research. We argue that in order to remove constraints on female student's study choices, the field of physics needs to provide a culture in which all students feel like they belong.Comment: 23 pages, 6 figures, 1 tabl

Transitivity and degree assortativity explained: The bipartite structure of social networks

Dynamical processes, such as the diffusion of knowledge, opinions, pathogens, "fake news", innovation, and others, are highly dependent on the structure of the social network on which they occur. However, questions on why most social networks present some particular structural features, namely high levels of transitivity and degree assortativity, when compared to other types of networks remain open. First, we argue that every one-mode network can be regarded as a projection of a bipartite network, and show that this is the case using two simple examples solved with the generating functions formalism. Second, using synthetic and empirical data, we reveal how the combination of the degree distribution of both sets of nodes of the bipartite network --- together with the presence of cycles of length four and six --- explains the observed levels of transitivity and degree assortativity in the one-mode projected network. Bipartite networks with top node degrees that display a more right-skewed distribution than the bottom nodes result in highly transitive and degree assortative projections, especially if a large number of small cycles are present in the bipartite structure.Comment: 9 pages, 6 figure

Degree distributions of bipartite networks and their projections

Bipartite (two-mode) networks are important in the analysis of social and economic systems as they explicitly show conceptual links between different types of entities. However, applications of such networks often work with a projected (one-mode) version of the original bipartite network. The topology of the projected network, and the dynamics that take place on it, are highly dependent on the degree distributions of the two different node types from the original bipartite structure. To date, the interaction between the degree distributions of bipartite networks and their one-mode projections is well understood for only a few cases, or for networks that satisfy a restrictive set of assumptions. Here we show a broader analysis in order to fill the gap left by previous studies. We use the formalism of generating functions to prove that the degree distributions of both node types in the original bipartite network affect the degree distribution in the projected version. To support our analysis, we simulate several types of synthetic bipartite networks using a configuration model where node degrees are assigned from specific probability distributions, ranging from peaked to heavy-tailed distributions. Our findings show that when projecting a bipartite network onto a particular set of nodes, the degree distribution for the resulting one-mode network follows the distribution of the nodes being projected on to, but only so long as the degree distribution for the opposite set of nodes does not have a heavier tail. Furthermore, we show that bipartite degree distributions are not the only feature driving topology formation of projected networks, in contrast to what is commonly described in the literature.Comment: 14 pages, 5 figures, 3 table

Search for the Standard Model Higgs Boson with the OPAL Detector at LEP

This paper summarises the search for the Standard Model Higgs boson in e+e- collisions at centre-of-mass energies up to 209 GeV performed by the OPAL Collaboration at LEP. The consistency of the data with the background hypothesis and various Higgs boson mass hypotheses is examined. No indication of a signal is found in the data and a lower bound of 112.7GeV/C^2 is obtained on the mass of the Standard Model Higgs boson at the 95% CL.Comment: 51 pages, 21 figure

Search for Higgs Bosons in e+e- Collisions at 183 GeV

The data collected by the OPAL experiment at sqrts=183 GeV were used to search for Higgs bosons which are predicted by the Standard Model and various extensions, such as general models with two Higgs field doublets and the Minimal Supersymmetric Standard Model (MSSM). The data correspond to an integrated luminosity of approximately 54pb-1. None of the searches for neutral and charged Higgs bosons have revealed an excess of events beyond the expected background. This negative outcome, in combination with similar results from searches at lower energies, leads to new limits for the Higgs boson masses and other model parameters. In particular, the 95% confidence level lower limit for the mass of the Standard Model Higgs boson is 88.3 GeV. Charged Higgs bosons can be excluded for masses up to 59.5 GeV. In the MSSM, mh > 70.5 GeV and mA > 72.0 GeV are obtained for tan{beta}>1, no and maximal scalar top mixing and soft SUSY-breaking masses of 1 TeV. The range 0.8 < tanb < 1.9 is excluded for minimal scalar top mixing and m{top} < 175 GeV. More general scans of the MSSM parameter space are also considered.Comment: 49 pages. LaTeX, including 33 eps figures, submitted to European Physical Journal