Pattern Formation on Networks:from Localised Activity to Turing Patterns

Systems of dynamical interactions between competing species can be used to model many complex systems, and can be mathematically described by {\em random} networks. Understanding how patterns of activity arise in such systems is important for understanding many natural phenomena. The emergence of patterns of activity on complex networks with reaction-diffusion dynamics on the nodes is studied here. The connection between solutions with a single activated node, which can bifurcate from an undifferentiated state, and the fully developed system-scale patterns are investigated computationally. The different coexisting patterns of activity the network can exhibit are shown to be connected via a snaking type bifurcation structure, similar to those responsible for organising localised pattern formation in regular lattices. These results reveal the origin of the multistable patterns found in systems organised on complex networks. A key role is found to be played by nodes with so called {\em optimal degree}, on which the interaction between the reaction kinetics and the network structure organise the behaviour of the system. A statistical representation of the density of solutions over the parameter space is used as a means to answer important questions about the number of accessible states that can be exhibited in systems with such a high degree of complexity

Understanding the anomalous frequency responses of composite materials using very large random resistor-capacitor networks

In this paper large resistor-capacitor (RC) networks that consist of randomly distributed conductive and capacitive elements which are much larger than those previously explored are studied using an efficient algorithm. We investigate the emergent power-law scaling of the conductance and the percolation and saturation limits of the networks at the high and low frequency bounds in order to compare with a modification of the classical Effective Medium Approximation (EMA) that enables its extension to finite network sizes. It is shown that the new formula provides a simple analytical description of the network response that accurately predicts the effects of finite network size and composition and it agrees well with the new numerical calculations on large networks and is a significant improvement on earlier EMA formulae. Avenues for future improvement and explanation of the formula are highlighted. Finally, the statistical variation of network conductivity with network size is observed and explained. This work provides a deeper insight into the response of large resistor-capacitor networks to understand the AC electrical properties, size effects, composition effects and statistical variation of properties of a range of heterogeneous materials and composite systems

Obeticholic acid for the treatment of non-alcoholic steatohepatitis: interim analysis from a multicentre, randomised, placebo-controlled phase 3 trial

Background Non-alcoholic steatohepatitis (NASH) is a common type of chronic liver disease that can lead to cirrhosis. Obeticholic acid, a farnesoid X receptor agonist, has been shown to improve the histological features of NASH. Here we report results from a planned interim analysis of an ongoing, phase 3 study of obeticholic acid for NASH. Methods In this multicentre, randomised, double-blind, placebo-controlled study, adult patients with definite NASH,non-alcoholic fatty liver disease (NAFLD) activity score of at least 4, and fibrosis stages F2–F3, or F1 with at least oneaccompanying comorbidity, were randomly assigned using an interactive web response system in a 1:1:1 ratio to receive oral placebo, obeticholic acid 10 mg, or obeticholic acid 25 mg daily. Patients were excluded if cirrhosis, other chronic liver disease, elevated alcohol consumption, or confounding conditions were present. The primary endpointsfor the month-18 interim analysis were fibrosis improvement (≥1 stage) with no worsening of NASH, or NASH resolution with no worsening of fibrosis, with the study considered successful if either primary endpoint was met. Primary analyses were done by intention to treat, in patients with fibrosis stage F2–F3 who received at least one dose of treatment and reached, or would have reached, the month 18 visit by the prespecified interim analysis cutoff date. The study also evaluated other histological and biochemical markers of NASH and fibrosis, and safety. This study is ongoing, and registered with ClinicalTrials.gov, NCT02548351, and EudraCT, 20150-025601-6. Findings Between Dec 9, 2015, and Oct 26, 2018, 1968 patients with stage F1–F3 fibrosis were enrolled and received at least one dose of study treatment; 931 patients with stage F2–F3 fibrosis were included in the primary analysis (311 in the placebo group, 312 in the obeticholic acid 10 mg group, and 308 in the obeticholic acid 25 mg group). The fibrosis improvement endpoint was achieved by 37 (12%) patients in the placebo group, 55 (18%) in the obeticholic acid 10 mg group (p=0·045), and 71 (23%) in the obeticholic acid 25 mg group (p=0·0002). The NASH resolution endpoint was not met (25 [8%] patients in the placebo group, 35 [11%] in the obeticholic acid 10 mg group [p=0·18], and 36 [12%] in the obeticholic acid 25 mg group [p=0·13]). In the safety population (1968 patients with fibrosis stages F1–F3), the most common adverse event was pruritus (123 [19%] in the placebo group, 183 [28%] in the obeticholic acid 10 mg group, and 336 [51%] in the obeticholic acid 25 mg group); incidence was generally mild to moderate in severity. The overall safety profile was similar to that in previous studies, and incidence of serious adverse events was similar across treatment groups (75 [11%] patients in the placebo group, 72 [11%] in the obeticholic acid 10 mg group, and 93 [14%] in the obeticholic acid 25 mg group). Interpretation Obeticholic acid 25 mg significantly improved fibrosis and key components of NASH disease activity among patients with NASH. The results from this planned interim analysis show clinically significant histological improvement that is reasonably likely to predict clinical benefit. This study is ongoing to assess clinical outcomes

Pattern Formation on Networks:from Localised Activity to Turing Patterns

Networks of interactions between competing species are used to model many complex systems, such as in genetics, evolutionary biology or sociology and knowledge of the patterns of activity they can exhibit is important for understanding their behaviour. The emergence of patterns on complex networks with reaction-diffusion dynamics is studied here, where node dynamics interact via diffusion via the network edges. Through the application of a generalisation of dynamical systems analysis this work reveals a fundamental connection between small-scale modes of activity on networks and localised pattern formation seen throughout science, such as solitons, breathers and localised buckling. The connection between solutions with a single and small numbers of activated nodes and the fully developed system-scale patterns are investigated computationally using numerical continuation methods. These techniques are also used to help reveal a much larger portion of of the full number of solutions that exist in the system at different parameter values. The importance of network structure is also highlighted, with a key role being played by nodes with a certain so-called optimal degree, on which the interaction between the reaction kinetics and the network structure organise the behaviour of the system

Snaking on Networks: From Local Solutions to Turing Patterns

The emergence of patterns of activity on complex networks with reaction-diffusion dynamics on the nodes is studied. The transition is investigated between the single-node solutions, studied previously [Wolfrum, Physica D (2012)], and the fully developed global activation states (so called Turing states). Numerical continuation reveals snaking bifurcations connecting different solutions, similar to those found in reaction diffusion systems on regular lattice network topologies, shedding light on the origin of the multistable “Turing' patterns reported previously [Nakao & Mikhailov, Nature 2010]

Energy use of urban transport and buildings: A new combined metric

To implement actions to reduce the negative effects of carbon-based energy consumption calls for a good method of measuring that energy.Prior research has always considered urban buildings and transport energy costs separately.A combined energy use metric is developed at a large scale to provide better understanding of energy consumption patterns.Because commuting plays such a substantial role in energy demand, the results show a direct relationship between lower per capita energy consumption and urbanised areas, demonstrating how energy efficient urban living is