A Unified Framework for Integer Programming Formulation of Graph Matching Problems

Graph theory has been a powerful tool in solving difficult and complex problems arising in all disciplines. In particular, graph matching is a classical problem in pattern analysis with enormous applications. Many graph problems have been formulated as a mathematical program then solved using exact, heuristic and/or approximated-guaranteed procedures. On the other hand, graph theory has been a powerful tool in visualizing and understanding of complex mathematical programming problems, especially integer programs. Formulating a graph problem as a natural integer program (IP) is often a challenging task. However, an IP formulation of the problem has many advantages. Several researchers have noted the need for natural IP formulation of graph theoretic problems. The aim of the present study is to provide a unified framework for IP formulation of graph matching problems. Although there are many surveys on graph matching problems, however, none is concerned with IP formulation. This paper is the first to provide a comprehensive IP formulation for such problems. The framework includes variety of graph optimization problems in the literature. While these problems have been studied by different research communities, however, the framework presented here helps to bring efforts from different disciplines to tackle such diverse and complex problems. We hope the present study can significantly help to simplify some of difficult problems arising in practice, especially in pattern analysis

Linking basin-scale and pore-scale gas hydrate distribution patterns in diffusion-dominated marine hydrate systems

The goal of this study is to computationally determine the potential distribution patterns of diffusion-driven methane hydrate accumulations in coarse-grained marine sediments. Diffusion of dissolved methane in marine gas hydrate systems has been proposed as a potential transport mechanism through which large concentrations of hydrate can preferentially accumulate in coarse-grained sediments over geologic time. Using one-dimensional compositional reservoir simulations, we examine hydrate distribution patterns at the scale of individual sand layers (1-20 m thick) that are deposited between microbially active fine-grained material buried through the gas hydrate stability zone (GHSZ). We then extrapolate to two-dimensional and basin-scale three-dimensional simulations, where we model dipping sands and multilayered systems. We find that properties of a sand layer including pore size distribution, layer thickness, dip, and proximity to other layers in multilayered systems all exert control on diffusive methane fluxes toward and within a sand, which in turn impact the distribution of hydrate throughout a sand unit. In all of these simulations, we incorporate data on physical properties and sand layer geometries from the Terrebonne Basin gas hydrate system in the Gulf of Mexico. We demonstrate that diffusion can generate high hydrate saturations (upward of 90%) at the edges of thin sands at shallow depths within the GHSZ, but that it is ineffective at producing high hydrate saturations throughout thick (greater than 10 m) sands buried deep within the GHSZ. Furthermore, we find that hydrate in fine-grained material can preserve high hydrate saturations in nearby thin sands with burial

Multiscale modelling of ceramic nanoparticle interactions and their influence on the thermal conductivity of nanofluids

There is currently a lack of a reliable theory capable of making accurate predictions of the thermal enhancement in nanofluids (with relatively low solid volume fractions). The work described therefore assesses the thermal conductivity of nanoparticle suspensions in fluids using a Lagrangian particle tracking-based computational modelling technique. A 3D, multiphase fluid-solid model is developed which predicts the motion of suspended nanoparticles. The nanofluid is predicted using an Eulerian-Lagrangian hybrid approach with a constant timestep. This technique takes various multiscale forces into consideration in the calculations, whose characteristic scales are quite different, providing for the first time an analysis of all factors affecting the stability and thermal conductivity of nanofluids. The system considered consists of 71 nm diameter Al2O3 ceramic nanoparticles suspended in water, with homogeneous temperature distributions ranging from 25 °C to 85 °C, at various volume fractions between 1% and 5%. The results of the simulations demonstrate the effectiveness of the presented technique, with predictions elucidating the role of Brownian motion, fluid viscous drag, inter-particle collisions and DLVO attraction and repulsion forces on nanofluid stability. Results indicate that aggregated nanoparticles formed in the suspensions, at various particle concentrations, play an important role in the thermal behaviour of the nanofluids. Predictions are in agreement with theoretical and experimental results obtained in related studies. The thermal characteristics of nanofluids are also considered as a function of temperature, system chemistry and time (measured from an initially homogeneously dispersed state). The proven enhancement in the conductivity of fluids affected by the addition of nanoparticles has great potential to assist the development of commercial nanofluid technology aimed at energy efficient and sustainable processes

The Early Royal Society and Visual Culture

Recent studies have fruitfully examined the intersection between early modern science and visual culture by elucidating the functions of images in shaping and disseminating scientific knowledge. Given its rich archival sources, it is possible to extend this line of research in the case of the Royal Society to an examination of attitudes towards images as artefacts –manufactured objects worth commissioning, collecting and studying. Drawing on existing scholarship and material from the Royal Society Archives, I discuss Fellows’ interests in prints, drawings, varnishes, colorants, images made out of unusual materials, and methods of identifying the painter from a painting. Knowledge of production processes of images was important to members of the Royal Society, not only as connoisseurs and collectors, but also as those interested in a Baconian mastery of material processes, including a “history of trades”. Their antiquarian interests led to discussion of painters’ styles, and they gradually developed a visual memorial to an institution through portraits and other visual records.AH/M001938/1 (AHRC

Genetic mechanisms of critical illness in COVID-19.

Host-mediated lung inflammation is present1, and drives mortality2, in the critical illness caused by coronavirus disease 2019 (COVID-19). Host genetic variants associated with critical illness may identify mechanistic targets for therapeutic development3. Here we report the results of the GenOMICC (Genetics Of Mortality In Critical Care) genome-wide association study in 2,244 critically ill patients with COVID-19 from 208 UK intensive care units. We have identified and replicated the following new genome-wide significant associations: on chromosome 12q24.13 (rs10735079, P = 1.65 × 10-8) in a gene cluster that encodes antiviral restriction enzyme activators (OAS1, OAS2 and OAS3); on chromosome 19p13.2 (rs74956615, P = 2.3 × 10-8) near the gene that encodes tyrosine kinase 2 (TYK2); on chromosome 19p13.3 (rs2109069, P = 3.98 ×  10-12) within the gene that encodes dipeptidyl peptidase 9 (DPP9); and on chromosome 21q22.1 (rs2236757, P = 4.99 × 10-8) in the interferon receptor gene IFNAR2. We identified potential targets for repurposing of licensed medications: using Mendelian randomization, we found evidence that low expression of IFNAR2, or high expression of TYK2, are associated with life-threatening disease; and transcriptome-wide association in lung tissue revealed that high expression of the monocyte-macrophage chemotactic receptor CCR2 is associated with severe COVID-19. Our results identify robust genetic signals relating to key host antiviral defence mechanisms and mediators of inflammatory organ damage in COVID-19. Both mechanisms may be amenable to targeted treatment with existing drugs. However, large-scale randomized clinical trials will be essential before any change to clinical practice

Application of the kinetic theory of partly ionized gases to radiation transfer and ionization in hydrogen nebulae

The problem of ionization produced by a hot star embedded in a hydrogen nebula is studied from basic standpoint. The necessary equation of radiative transfer is derived by introducing a distribution function in photon phase-space, and subjecting it to the procedures of classical kinetic theory. It is found that the distribution function can be separated into a singular part corresponding to “direct” radiation from the star, and a non-singular part corresponding to “diffuse” radiation. The concept of statistical equilibrium is applied to the electron population to provide an auxiliary equation, and the Stromgren equation derived as an approximation. A qualitative discussion of the exact equations shows that for a wide range of physical parameters a well defined ionized region surrounds the star. Ionizing radiation undergoes little absorption within this region, but it is rapidly extinguished at the boundary. The radius of the ionized region and the form of the boundary are discussed, and their dependence on the various physical parameters interpreted. Numerical solutions neglecting the effect of diffuse radiation confirm the predictions for that case.Thesis (M.Sc.) -- University of Adelaide, Dept. of Mathematical Physics, 1963