Kantorovich-Rubinstein Distance and Barycenter for Finitely Supported Measures: Foundations and Algorithms

The purpose of this paper is to provide a systematic discussion of a generalized barycenter based on a variant of unbalanced optimal transport (UOT) that defines a distance between general non-negative, finitely supported measures by allowing for mass creation and destruction modeled by some cost parameter. They are denoted as Kantorovich–Rubinstein (KR) barycenter and distance. In particular, we detail the influence of the cost parameter to structural properties of the KR barycenter and the KR distance. For the latter we highlight a closed form solution on ultra-metric trees. The support of such KR barycenters of finitely supported measures turns out to be finite in general and its structure to be explicitly specified by the support of the input measures. Additionally, we prove the existence of sparse KR barycenters and discuss potential computational approaches. The performance of the KR barycenter is compared to the OT barycenter on a multitude of synthetic datasets. We also consider barycenters based on the recently introduced Gaussian Hellinger–Kantorovich and Wasserstein–Fisher–Rao distances

Appearance of the Single Gyroid Network Phase in Nuclear Pasta Matter

Nuclear matter under the conditions of a supernova explosion unfolds into a rich variety of spatially structured phases, called nuclear pasta. We investigate the role of periodic network-like structures with negatively curved interfaces in nuclear pasta structures, by static and dynamic Hartree-Fock simulations in periodic lattices. As the most prominent result, we identify for the first time the {\it single gyroid} network structure of cubic chiral $I4_123$ symmetry, a well known configuration in nanostructured soft-matter systems, both as a dynamical state and as a cooled static solution. Single gyroid structures form spontaneously in the course of the dynamical simulations. Most of them are isomeric states. The very small energy differences to the ground state indicate its relevance for structures in nuclear pasta.Comment: 7 pages, 4 figure

Low-temperature statistical mechanics of the QuanTizer problem: fast quenching and equilibrium cooling of the three-dimensional Voronoi Liquid

The Quantizer problem is a tessellation optimisation problem where point configurations are identified such that the Voronoi cells minimise the second moment of the volume distribution. While the ground state (optimal state) in 3D is almost certainly the body-centered cubic lattice, disordered and effectively hyperuniform states with energies very close to the ground state exist that result as stable states in an evolution through the geometric Lloyd's algorithm [Klatt et al. Nat. Commun., 10, 811 (2019)]. When considered as a statistical mechanics problem at finite temperature, the same system has been termed the 'Voronoi Liquid' by [Ruscher et al. EPL 112, 66003 (2015)]. Here we investigate the cooling behaviour of the Voronoi liquid with a particular view to the stability of the effectively hyperuniform disordered state. As a confirmation of the results by Ruscher et al., we observe, by both molecular dynamics and Monte Carlo simulations, that upon slow quasi-static equilibrium cooling, the Voronoi liquid crystallises from a disordered configuration into the body-centered cubic configuration. By contrast, upon sufficiently fast non-equilibrium cooling (and not just in the limit of a maximally fast quench) the Voronoi liquid adopts similar states as the effectively hyperuniform inherent structures identified by Klatt et al. and prevents the ordering transition into a BCC ordered structure. This result is in line with the geometric intuition that the geometric Lloyd's algorithm corresponds to a type of fast quench.Comment: 11 pages, 6 figure

Superconducting Superstructure for the TESLA Collider

We discuss the new layout of a cavity chain (superstructure) allowing, we hope, significant cost reduction of the RF system of both linacs of the TESLA linear collider. The proposed scheme increases the fill factor and thus makes an effective gradient of an accelerator higher. We present mainly computations we have performed up to now and which encouraged us to order the copper model of the scheme, still keeping in mind that experiments with a beam will be necessary to prove if the proposed solution can be used for the acceleration.Comment: 11 page

Spatial patterns and links between microbial community composition and function in cyanobacterial mats

We imaged reflectance and variable fluorescence in 25 cyanobacterial mats from four distant sites around the globe to assess, at different scales of resolution, spatial variabilities in the physiological parameters characterizing their photosynthetic capacity, including the absorptivity by chlorophyll a (Achl), maximum quantum yield of photosynthesis (Ymax), and light acclimation irradiance (Ik). Generally, these parameters significantly varied within individual mats on a sub-millimeter scale, with about 2-fold higher variability in the vertical than in the horizontal direction. The average vertical profiles of Ymax and Ik decreased with depth in the mat, while Achl exhibited a sub-surface maximum. The within-mat variability was comparable to, but often larger than, the between-sites variability, whereas the within-site variabilities (i.e., between samples from the same site) were generally lowest. When compared based on averaged values of their photosynthetic parameters, mats clustered according to their site of origin. Similar clustering was found when the community composition of the mats' cyanobacterial layers were compared by automated ribosomal intergenic spacer analysis (ARISA), indicating a significant link between the microbial community composition and function. Although this link is likely the result of community adaptation to the prevailing site-specific environmental conditions, our present data is insufficient to identify the main factors determining these patterns. Nevertheless, this study demonstrates that the spatial variability in the photosynthetic capacity and light acclimation of benthic phototrophic microbial communities is at least as large on a sub-millimeter scale as it is on a global scale, and suggests that this pattern of variability scaling is similar for the microbial community composition. © 2014 Al-Najjar, Ramette, Kühl, Hamza, Klatt and Polerecky

The Role of Socioeconomic Status, Race, and Gender in Patient-Reported Outcomes Following Total Hip Arthroplasty

Background Disparities in total joint arthroplasty are well-documented. However, much of the research regarding disparities in vulnerable populations receiving total hip arthroplasty (THA) have focused on short-term outcomes. The purpose of this study was to examine the effects of race, gender, and socioeconomic status (SES) on patient-reported outcomes six months following THA. Methods Electronic health record data were retrospectively analyzed for 269 individuals who underwent THA at a large urban hospital from 2013-16. Data retrieved included patient demographics, baseline health information, data regarding hospital length of stay when undergoing THA, post-operative complications, and patient-reported function, measured by the Harris Hip Score (HHS) at baseline (pre-operative) and six months post-operatively. Results Compared to White patients and male patients, non-White (p = .01) and female (p = .02) patients were lower-functioning prior to surgery. At six months post-operatively, White patients had significantly better function than non-White patients, (p = .05) and patients of higher SES had significantly better function than patients of lower SES (p = .05). Regression analyses revealed that, after controlling for race, gender, and SES, the only significant predictor of six-month improvement in HHS was the pre-operative HHS score (p \u3c .001). Conclusion These results indicate that female, non-White, and lower SES patients undergoing THA may have lower function pre-operatively and may not experience as much improvement in physical function post-operatively as their male, White, and higher SES counterparts. Further research is needed to determine if race, gender, and socioeconomic differences in pre-operative function lead to long-term disparities in function following THA, using larger sample sizes and outcomes beyond 6 months post-operatively

Association of Systemic Inflammation With Retinal Vascular Caliber in Patients With AIDS.

PurposeTo evaluate relationships among retinal vascular caliber and biomarkers of systemic inflammation in patients with AIDS.MethodsA total of 454 participants with AIDS had retinal vascular caliber (central retinal artery equivalent and central retinal vein equivalent) determined from enrollment retinal photographs by reading center graders masked to clinical and biomarker information. Cryopreserved plasma specimens were assayed for inflammatory biomarkers, including C-reactive protein (CRP), IL-6, interferon-γ inducible protein (IP)-10, kynurenine/tryptophan (KT) ratio, and intestinal fatty acid binding protein (I-FABP).ResultsIn the simple linear regression of retinal vascular caliber on plasma biomarkers, elevated CRP, IL-6, and IP-10 were associated with retinal venular dilation, and elevated KT ratio with retinal arteriolar narrowing. In the multiple linear regression, including baseline characteristics and plasma biomarkers, AMD was associated with dilation of retinal arterioles (mean difference: 9.1 μm; 95% confidence interval [CI] 5.2, 12.9; P < 0.001) and venules (mean difference, 10.9 μm; 95% CI, 5.3, 16.6; P < 0.001), as was black race (P < 0.001). Hyperlipidemia was associated with retinal venular narrowing (mean difference, -7.5 μm; 95% CI, -13.7, -1.2; P = 0.02); cardiovascular disease with arteriolar narrowing (mean difference, -5.2 μm; 95% CI, -10.3, -0.1; P = 0.05); age with arteriolar narrowing (slope, -0.26 μm/year; 95% CI, -0.46, -0.06; P = 0.009); and IL-6 with venular dilation (slope, 5.3 μm/standard deviation log10[plasma IL-6 concentration]; 95% CI, 2.7, 8.0; P < 0.001).ConclusionsThese data suggest that retinal vascular caliber is associated with age, race, AMD, hyperlipidemia, cardiovascular disease, and selected biomarkers of systemic inflammation