The supernova-regulated ISM. I. The multi-phase structure

We simulate the multi-phase interstellar medium randomly heated and stirred by supernovae, with gravity, differential rotation and other parameters of the solar neighbourhood. Here we describe in detail both numerical and physical aspects of the model, including injection of thermal and kinetic energy by SN explosions, radiative cooling, photoelectric heating and various transport processes. With 3D domain extending 1 kpc^2 horizontally and 2 kpc vertically, the model routinely spans gas number densities 10^-5 - 10^2 cm^-3, temperatures 10-10^8 K, local velocities up to 10^3 km s^-1 (with Mach number up to 25). The thermal structure of the modelled ISM is classified by inspection of the joint probability density of the gas number density and temperature. We confirm that most of the complexity can be captured in terms of just three phases, separated by temperature borderlines at about 10^3 K and 5x10^5 K. The probability distribution of gas density within each phase is approximately lognormal. We clarify the connection between the fractional volume of a phase and its various proxies, and derive an exact relation between the fractional volume and the filling factors defined in terms of the volume and probabilistic averages. These results are discussed in both observational and computational contexts. The correlation scale of the random flows is calculated from the velocity autocorrelation function; it is of order 100 pc and tends to grow with distance from the mid-plane. We use two distinct parameterizations of radiative cooling to show that the multi-phase structure of the gas is robust, as it does not depend significantly on this choice.Comment: 28 pages, 22 figures and 8 table

The supernova-regulated ISM. II. The mean magnetic field

The origin and structure of the magnetic fields in the interstellar medium of spiral galaxies is investigated with 3D, non-ideal, compressible MHD simulations, including stratification in the galactic gravity field, differential rotation and radiative cooling. A rectangular domain, 1x1x2 kpc^{3} in size, spans both sides of the galactic mid-plane. Supernova explosions drive transonic turbulence. A seed magnetic field grows exponentially to reach a statistically steady state within 1.6 Gyr. Following Germano (1992) we use volume averaging with a Gaussian kernel to separate magnetic field into a mean field and fluctuations. Such averaging does not satisfy all Reynolds rules, yet allows a formulation of mean-field theory. The mean field thus obtained varies in both space and time. Growth rates differ for the mean-field and fluctuating field and there is clear scale separation between the two elements, whose integral scales are about 0.7 kpc and 0.3 kpc, respectively.Comment: 5 pages, 10 figures, submitted to Monthly Notices Letter

Allocation in Practice

How do we allocate scarcere sources? How do we fairly allocate costs? These are two pressing challenges facing society today. I discuss two recent projects at NICTA concerning resource and cost allocation. In the first, we have been working with FoodBank Local, a social startup working in collaboration with food bank charities around the world to optimise the logistics of collecting and distributing donated food. Before we can distribute this food, we must decide how to allocate it to different charities and food kitchens. This gives rise to a fair division problem with several new dimensions, rarely considered in the literature. In the second, we have been looking at cost allocation within the distribution network of a large multinational company. This also has several new dimensions rarely considered in the literature.Comment: To appear in Proc. of 37th edition of the German Conference on Artificial Intelligence (KI 2014), Springer LNC

Phase Transition in the Number Partitioning Problem

Number partitioning is an NP-complete problem of combinatorial optimization. A statistical mechanics analysis reveals the existence of a phase transition that separates the easy from the hard to solve instances and that reflects the pseudo-polynomiality of number partitioning. The phase diagram and the value of the typical ground state energy are calculated.Comment: minor changes (references, typos and discussion of results

Random Costs in Combinatorial Optimization

The random cost problem is the problem of finding the minimum in an exponentially long list of random numbers. By definition, this problem cannot be solved faster than by exhaustive search. It is shown that a classical NP-hard optimization problem, number partitioning, is essentially equivalent to the random cost problem. This explains the bad performance of heuristic approaches to the number partitioning problem and allows us to calculate the probability distributions of the optimum and sub-optimum costs.Comment: 4 pages, Revtex, 2 figures (eps), submitted to PR

Optimization by Quantum Annealing: Lessons from hard 3-SAT cases

The Path Integral Monte Carlo simulated Quantum Annealing algorithm is applied to the optimization of a large hard instance of the Random 3-SAT Problem (N=10000). The dynamical behavior of the quantum and the classical annealing are compared, showing important qualitative differences in the way of exploring the complex energy landscape of the combinatorial optimization problem. At variance with the results obtained for the Ising spin glass and for the Traveling Salesman Problem, in the present case the linear-schedule Quantum Annealing performance is definitely worse than Classical Annealing. Nevertheless, a quantum cooling protocol based on field-cycling and able to outperform standard classical simulated annealing over short time scales is introduced.Comment: 10 pages, 6 figures, submitted to PR

Does metformin improve vascular health in children with Type 1 diabetes? Protocol for a one year, double blind, randomised, placebo controlled trial

Background: Cardiovascular disease is the leading cause of mortality in Type 1 diabetes (T1D). Vascular dysfunction is an early and critical event in the development of cardiovascular disease. Children with T1D have vascular dysfunction therefore early interventions to improve vascular health are essential to reduce cardiovascular mortality in T1D. Metformin is an insulin sensitising agent which is known to improve vascular health outcomes in type 2 diabetes (T2D) and other individuals with insulin resistance. It has been used safely in children and adolescents with T2D for over 10 years. This study aims to assess the effect of metformin on vascular health in children with T1D. Methods/Design: This study is a 12 month, double blind, randomised, placebo controlled trial to determine the effect of metformin on vascular health in children (age 8–18) with T1D. The sample size is 76 with 38 children in the metformin group and 38 children in the placebo group. Vascular health and biochemical markers will be measured at baseline, 3, 6 and 12 months. Vascular function will be measured using flow mediated dilatation and glyceryl trinitrate mediated dilatation of the brachial artery and vascular structure will be measured with carotid and aortic intima media thickness, using standardised protocols. Discussion: This study will be the first to investigate the effect of metformin on vascular health in children with T1D. It will provide important information on a potential intervention to improve cardiovascular morbidity and mortality in this population at high risk from cardiovascular disease.Jemma Anderson, Alexia S Peña, Thomas Sullivan, Roger Gent, Bronwen D’Arcy, Timothy Olds, Brian Coppin and Jennifer Coupe