An informational approach to the global optimization of expensive-to-evaluate functions

In many global optimization problems motivated by engineering applications, the number of function evaluations is severely limited by time or cost. To ensure that each evaluation contributes to the localization of good candidates for the role of global minimizer, a sequential choice of evaluation points is usually carried out. In particular, when Kriging is used to interpolate past evaluations, the uncertainty associated with the lack of information on the function can be expressed and used to compute a number of criteria accounting for the interest of an additional evaluation at any given point. This paper introduces minimizer entropy as a new Kriging-based criterion for the sequential choice of points at which the function should be evaluated. Based on \emph{stepwise uncertainty reduction}, it accounts for the informational gain on the minimizer expected from a new evaluation. The criterion is approximated using conditional simulations of the Gaussian process model behind Kriging, and then inserted into an algorithm similar in spirit to the \emph{Efficient Global Optimization} (EGO) algorithm. An empirical comparison is carried out between our criterion and \emph{expected improvement}, one of the reference criteria in the literature. Experimental results indicate major evaluation savings over EGO. Finally, the method, which we call IAGO (for Informational Approach to Global Optimization) is extended to robust optimization problems, where both the factors to be tuned and the function evaluations are corrupted by noise.Comment: Accepted for publication in the Journal of Global Optimization (This is the revised version, with additional details on computational problems, and some grammatical changes

Analytical Solution of the Voter Model on Disordered Networks

We present a mathematical description of the voter model dynamics on heterogeneous networks. When the average degree of the graph is $\mu \leq 2$ the system reaches complete order exponentially fast. For $\mu >2$, a finite system falls, before it fully orders, in a quasistationary state in which the average density of active links (links between opposite-state nodes) in surviving runs is constant and equal to $\frac{(\mu-2)}{3(\mu-1)}$, while an infinite large system stays ad infinitum in a partially ordered stationary active state. The mean life time of the quasistationary state is proportional to the mean time to reach the fully ordered state $T$, which scales as $T \sim \frac{(\mu-1) \mu^2 N}{(\mu-2) \mu_2}$, where $N$ is the number of nodes of the network, and $\mu_2$ is the second moment of the degree distribution. We find good agreement between these analytical results and numerical simulations on random networks with various degree distributions.Comment: 20 pages, 8 figure

The impact of the Covid-19 lockdown on the experiences and feeding practices of new mothers in the UK: Preliminary data from the COVID-19 New Mum Study

BACKGROUND: The COVID-19 New Mum Study is recording maternal experiences and infant feeding during the UK lockdown. This report from week 1 of the survey describes and compares the delivery and post-natal experiences of women who delivered before (BL) versus during (DL) the lockdown. METHODS: Women living in the UK aged ≥18 years with an infant ≤12 months of age completed an anonymous online survey (https://is.gd/covid19newmumstudy). Information/links are shared via websites, social media and existing contacts. RESULTS: From 27.5 to 20-3.6.20, 1365 women provided data (94% white, 95% married/with partner, 66% degree/higher qualification, 86% living in house; 1049 (77%) delivered BL and 316 (23%) DL. Delivery mode, skin-to-skin contact and breastfeeding initiation did not differ between groups. DL women had shorter hospital stays (p < 0.001). 39% reported changes to their birth plan. Reflecting younger infant age, 59% of DL infants were exclusively breast-fed/mixed fed versus 39% of BL (p < 0.05). 13% reported a change in feeding; often related to lack of breastfeeding support, especially with practical problems. Important sources of feeding support were the partner (60%), health professional (50%) and online groups (47%). 45% of DL women reported insufficient feeding support. Among BL women, 57% and 69% reported decreased feeding support and childcare, respectively. 40% BL/45% DL women reported insufficient support with their own health, 8%/9% contacted a mental health professional; 11% reported their mental health was affected. 9% highlighted lack of contact/support from family and distress that they had missed seeing the baby. CONCLUSION: Lockdown has impacted maternal experiences, resulting in distress for many women. Our findings suggest the need for better infant feeding support, especially 'face-to-face' support for practical issues; and recognising and supporting mothers who are struggling with mental health challenges or other aspects of their health. The effectiveness of online versus face-to-face contact is currently uncertain, and requires further evaluation

The Bak-Sneppen Model on Scale-Free Networks

We investigate by numerical simulations and analytical calculations the Bak-Sneppen model for biological evolution in scale-free networks. By using large scale numerical simulations, we study the avalanche size distribution and the activity time behavior at nodes with different connectivities. We argue the absence of a critical barrier and its associated critical behavior for infinite size systems. These findings are supported by a single site mean-field analytic treatment of the model.Comment: 5 pages and 3 eps figures. Final version appeared in Europhys. Let