Phase Transition in Ferromagnetic Ising Models with Non-Uniform External Magnetic Fields

In this article we study the phase transition phenomenon for the Ising model under the action of a non-uniform external magnetic field. We show that the Ising model on the hypercubic lattice with a summable magnetic field has a first-order phase transition and, for any positive (resp. negative) and bounded magnetic field, the model does not present the phase transition phenomenon whenever $\liminf h_i> 0$, where ${\bf h} = (h_i)_{i \in \Z^d}$ is the external magnetic field.Comment: 11 pages. Published in Journal of Statistical Physics - 201

Social impact operations at the global base of the pyramid

In recent years, our field has seen an increase in research that explicitly emphasizes an objective of social impact in the most unprivileged parts of the world—the so-called global base of the pyramid (referring to the 2.7 billion people living on less than $2.50 per day, the largest but most resource-poor economic group globally). This trend seems to cut across the traditional application areas of OM and OR, and it coincides with an increased emphasis on environmental and social governance (ESG) values in industry, a greater prominence of the United Nations' Sustainable Development Goals (UN SDGs) and increases in social impact research in other academic fields. In this paper, we pull together representative examples from our field of what we consider as social impact research aimed at improving living conditions at the base of the pyramid. We first examine the scale and scope of work published in Production and Operations Management over the last 25 years, and then provide a broader summary of the spectrum of research within OM and OR that constitute this stream of literature. We adopt the stance that OM and OR should embrace the current societal emphasis on social responsibility and positive social impact—and strive to contribute to the most pressing problems for those living at the base of the pyramid. Although our field has produced a body of work addressing such problems, individual research projects of this type are usually not viewed as falling under the broad umbrella of Social Impact Operations (SIO), but rather are classified as part of the closest application area. By providing an initial overview of this work we wish to celebrate the contribution of our field to this area, highlight common themes, catalyze a dialogue across application areas among researchers with a common perspective, and identify opportunities for future research

Percolation in invariant Poisson graphs with i.i.d. degrees

Let each point of a homogeneous Poisson process in R^d independently be equipped with a random number of stubs (half-edges) according to a given probability distribution mu on the positive integers. We consider translation-invariant schemes for perfectly matching the stubs to obtain a simple graph with degree distribution mu. Leaving aside degenerate cases, we prove that for any mu there exist schemes that give only finite components as well as schemes that give infinite components. For a particular matching scheme that is a natural extension of Gale-Shapley stable marriage, we give sufficient conditions on mu for the absence and presence of infinite components

Robust combination testing: methods and application to COVID-19 detection

Simple and affordable testing tools are often not accurate enough to be operationally relevant. For COVID-19 detection, rapid point-of-care tests are cheap and provide results in minutes, but largely fail policymakers' accuracy requirements. We propose an analytical methodology, based on robust optimization, that identifies optimal combinations of results from cheap tests for increased predictive accuracy. This methodological tool allows policymakers to credibly quantify the benefits from combination testing and thus break the trade-off between cost and accuracy. Our methodology is robust to noisy and partially missing input data and incorporates operational constraints-relevant considerations in practice. We apply our methodology to two datasets containing individual-level results of multiple COVID-19 rapid antibody and antigen tests, respectively, to generate Pareto-dominating receiver operating characteristic (ROC) curves. We find that combining only three rapid tests increases out-of-sample area under the curve (AUC) by 4% (6%) compared with the best performing individual test for antibody (antigen) detection. We also find that a policymaker who requires a specificity of at least 0.95 can improve sensitivity by 8% and 2% for antibody and antigen testing, respectively, relative to available combination testing heuristics. Our numerical analysis demonstrates that robust optimization is a powerful tool to avoid overfitting, accommodate missing data, and improve out-of-sample performance. Based on our analytical and empirical results, policymakers should consider approving and deploying a curated combination of cheap point-of-care tests in settings where `gold standard' tests are too expensive or too slow

First observations of high-temperature submarine hydrothermal vents and massive anhydrite deposits off the north coast of Iceland

High-temperature (250°C) hydrothermal vents and massive anhydrite deposits have been found in a shallow water, sediment-filled graben near 66°36′N in the Tjornes Fracture Zone north of Iceland. The site is located about 30 km offshore, near the small island of Grimsey. The main vent field occurs at a depth of 400 m and consists of about 20 large-diameter (up to 10 m) mounds and 1–3 m chimneys and spires of anhydrite and talc. A north–south alignment of the mounds over a 1-km strike length of the valley floor suggests that their distribution is controlled by a buried fault. Widespread shimmering water and extensive white patches of anhydrite in the sediment between the mounds indicates that the entire 1-km2 area occupied by the vents is thermally active. A 2-man research submersible JAGO was used to map the area and to sample vent waters, gases, and chimneys. Actively boiling hydrothermal vents occur on most of the mounds, and extensive two-phase venting indicates that the field is underlain by a large boiling zone (200×300 m). The presence of boiling fluids in shallow aquifers beneath the deposits was confirmed by sediment coring. The highest-temperature pore fluids were encountered in talc- and anhydrite-rich sedimentary layers that occur up to 7 m below the mounds. Baked muds underlie the talc and anhydrite layers, and pyrite is common in stockwork-like fractures and veins in the hydrothermally altered sediments. However, massive sulfides (pyrite–marcasite crusts) were found in only one relict mound. Subseafloor boiling has likely affected the metal-carrying capacity of the hydrothermal fluids, and deposition of sulfides may be occurring at greater depth. Although the mounds and chimneys at Grimsey resemble other deposits at sedimented ridges (e.g. Middle Valley, Escanaba Trough, Guaymas Basin), the shallow water setting and extensive boiling of the hydrothermal fluids represent a distinctive new type of seafloor hydrothermal system

White Matter Mapping in DT-MRI Using Geometric Flows

We present a 3D geometric flow designed to evolve in Diffusion Tensor Magnetic Resonance Images(DT-MRI) along fiber tracts by measuring the diffusive similarity between voxels. Therefore we define a front propagation speed that is proportional to the similarity between the tensors lying on the surface and its neighbor in the propagation direction. The method is based on the assumption that successive voxels in a tract have similar diffusion properties. The front propagation is implemented using level set methods by Osher and Sethian [1] to simplify the handling of topology changes and provides an elegant tool for smoothing the segmented tracts. While many methods demand a regularized tensor field, our geometrical flow performs a regularization as it evolves along the fibers. This is done by a curvature dependent smoothing term adapted for thin tubular structures. The purpose of our approach is to get a quantitative measure of the diffusion in segmented fiber tracts. This kind of information can also be used for white matter registration and for surgical planning

Relating Spatial Patterns of Stream Metabolism to Distributions of Juveniles Salmonids at the River Network Scale

Understanding the factors that drive spatial patterns in stream ecosystem processes and the distribution of aquatic biota is important to effective management of these systems and the conservation of biota at the network scale. In this study, we conducted field surveys throughout an extensive river network in NE Oregon that supports diminishing populations of wild salmonids. We collected data on physical habitat, nutrient concentrations, biofilm standing stocks, stream metabolism (gross primary production [GPP] and ecosystem respiration [ER]), and ESA‐listed juvenile salmonid density from approximately 50 sites across two sub‐basins. Our goals were to (1) to evaluate network patterns in these metrics, and (2) determine network‐scale linkages among these metrics, thus providing inference of processes driving observed patterns. Ambient nitrate‐N and phosphate‐P concentrations were low across both sub‐basins (\u3c40 μg/L). Nitrate‐N decreased with watershed area in both sub‐basins, but phosphate‐P only decreased in one sub‐basin. These spatial patterns suggest co‐limitation in one sub‐basin but N limitation in the other; experimental results using nutrient diffusing substrates across both sub‐basins supported these predictions. Solar exposure, temperature, GPP, ER, and GPP:ER increased with watershed area, but biofilm Chl a and ash‐free dry mass (AFDM) did not. Spatial statistical network (SSN) models explained between 70% and 75% of the total variation in biofilm Chl a, AFDM, and GPP, but only 21% of the variation in ER. Temperature and nutrient concentrations were the most supported predictors of Chl aand AFDM standing stocks, but these variables explained little of the total variation compared to spatial autocorrelation. In contrast, solar exposure and temperature were the most supported variables explaining GPP, and these variables explained far more variation than autocorrelation. Solar exposure, temperature, and nutrient concentrations explained almost none of the variation in ER. Juvenile salmonids—a key management focus in these sub‐basins—were most abundant in cool stream sections where rates of GPP were low, suggesting temperature constraints on these species restrict their distribution to oligotrophic areas where energy production at the base of the food web may be limited