Dynamics of technology emergence in innovation networks.

To create the next innovative product, participants in science need to understand which existing technologies can be combined, what new science must be discovered, and what new technologies must be invented. Knowledge of these often arrives by means of expert consensus or popularity metrics, masking key information on how intellectual efforts accumulate into technological progress. To address this shortcoming, we first present a method to establish a mathematical link between technological evolution and complex networks: a path of events that narrates innovation bottlenecks.

Higher-order temporal network effects through triplet evolution.

We study the evolution of networks through 'triplets'-three-node graphlets. We develop a method to compute a transition matrix to describe the evolution of triplets in temporal networks. To identify the importance of higher-order interactions in the evolution of networks, we compare both artificial and real-world data to a model based on pairwise interactions only.

Understanding the transition from paroxysmal to persistent atrial fibrillation.

Atrial fibrillation (AF) is the most common cardiac arrhytmia, characterized by the chaotic motion of electrical wavefronts in the atria. In clinical practice, AF is classified under two primary categories: paroxysmal AF, short intermittent episodes separated by periods of normal electrical activity; and persistent AF, longer uninterrupted episodes of chaotic electrical activity. However, the precise reasons why AF in a given patient is paroxysmal or persistent is poorly understood.

The longest path in the Price model.

The Price model, the directed version of the Barabási-Albert model, produces a growing directed acyclic graph. We look at variants of the model in which directed edges are added to the new vertex in one of two ways: using cumulative advantage (preferential attachment) choosing vertices in proportion to their degree, or with random attachment in which vertices are chosen uniformly at random. In such networks, the longest path is well defined and in some cases is known to be a better approximation to geodesics than the shortest path.

How the network properties of shareholders vary with investor type and country.

We construct two examples of shareholder networks in which shareholders are connected if they have shares in the same company. We do this for the shareholders in Turkish companies and we compare this against the network formed from the shareholdings in Dutch companies. We analyse the properties of these two networks in terms of the different types of shareholder.

Social success of perfumes.

We study data on perfumes and their odour descriptors-notes-to understand how note compositions, called accords, influence successful fragrance formulas. We obtain accords which tend to be present in perfumes that receive significantly more customer ratings. Our findings show that the most popular notes and the most over-represented accords are different to those that have the strongest effect to the perfume ratings.

Collaborative patterns, authorship practices and scientific success in biomedical research: a network analysis.

Objective: To investigate the relationship between biomedical researchers' collaborative and authorship practices and scientific success.

Design: Longitudinal quantitative analysis of individual researchers' careers over a nine-year period.

Setting: A leading biomedical research institution in the United Kingdom.

Embedding graphs in Lorentzian spacetime.

Geometric approaches to network analysis combine simply defined models with great descriptive power. In this work we provide a method for embedding directed acyclic graphs (DAG) into Minkowski spacetime using Multidimensional scaling (MDS). First we generalise the classical MDS algorithm, defined only for metrics with a Riemannian signature, to manifolds of any metric signature.

Uncovering space-independent communities in spatial networks.

Many complex systems are organized in the form of a network embedded in space. Important examples include the physical Internet infrastructure, road networks, flight connections, brain functional networks, and social networks. The effect of space on network topology has recently come under the spotlight because of the emergence of pervasive technologies based on geolocalization, which constantly fill databases with people's movements and thus reveal their trajectories and spatial behavior.