Sylvester's question and the Random Acceleration Process

Let n points be chosen randomly and independently in the unit disk. "Sylvester's question" concerns the probability p_n that they are the vertices of a convex n-sided polygon. Here we establish the link with another problem. We show that for large n this polygon, when suitably parametrized by a function r(phi) of the polar angle phi, satisfies the equation of the random acceleration process (RAP), d^2 r/d phi^2 = f(phi), where f is Gaussian noise. On the basis of this relation we derive the asymptotic expansion log p_n = -2n log n + n log(2 pi^2 e^2) - c_0 n^{1/5} + ..., of which the first two terms agree with a rigorous result due to Barany. The nonanalyticity in n of the third term is a new result. The value 1/5 of the exponent follows from recent work on the RAP due to Gyorgyi et al. [Phys. Rev. E 75, 021123 (2007)]. We show that the n-sided polygon is effectively contained in an annulus of width \sim n^{-4/5} along the edge of the disk. The distance delta_n of closest approach to the edge is exponentially distributed with average 1/(2n).Comment: 29 pages, 4 figures; references added and minor change

Generation of mutation hotspots in ageing bacterial colonies

How do ageing bacterial colonies generate adaptive mutants? Over a period of two months, we isolated on ageing colonies outgrowing mutants able to use a new carbon source, and sequenced their genomes. This allowed us to uncover exquisite details on the molecular mechanism behind their adaptation: most mutations were located in just a few hotspots in the genome and over time, mutations increasingly originated from 8-oxo-guanosine, formed exclusively on the transcribed strand.</jats:p

Consistency between ARPES and STM measurements on SmB6_6

Strongly correlated topological surface states are promising platforms for next-generation quantum applications, but they remain elusive in real materials. The correlated Kondo insulator SmB$_6$ is one of the most promising candidates, with theoretically predicted heavy Dirac surface states supported by transport and scanning tunneling microscopy (STM) experiments. However, a puzzling discrepancy appears between STM and angle-resolved photoemission (ARPES) experiments on SmB$_6$. Although ARPES detects spin-textured surface states, their velocity is an order of magnitude higher than expected, while the Dirac point -- the hallmark of any topological system -- can only be inferred deep within the bulk valence band. A significant challenge is that SmB$_6$ lacks a natural cleavage plane, resulting in ordered surface domains limited to 10s of nanometers. Here we use STM to show that surface band bending can shift energy features by 10s of meV between domains. Starting from our STM spectra, we simulate the full spectral function as an average over multiple domains with different surface potentials. Our simulation shows excellent agreement with ARPES data, and thus resolves the apparent discrepancy between large-area measurements that average over multiple band-shifted domains and atomically-resolved measurements within a single domain

Racial and ethnic disparities in the control of cardiovascular disease risk factors in Southwest American veterans with type 2 diabetes: the Diabetes Outcomes in Veterans Study

BACKGROUND: Racial/ethnic disparities in cardiovascular disease complications have been observed in diabetic patients. We examined the association between race/ethnicity and cardiovascular disease risk factor control in a large cohort of insulin-treated veterans with type 2 diabetes. METHODS: We conducted a cross-sectional observational study at 3 Veterans Affairs Medical Centers in the American Southwest. Using electronic pharmacy databases, we randomly selected 338 veterans with insulin-treated type 2 diabetes. We collected medical record and patient survey data on diabetes control and management, cardiovascular disease risk factors, comorbidity, demographics, socioeconomic factors, psychological status, and health behaviors. We used analysis of variance and multivariate linear regression to determine the effect of race/ethnicity on glycemic control, insulin treatment intensity, lipid levels, and blood pressure control. RESULTS: The study cohort was comprised of 72 (21.3%) Hispanic subjects (H), 35 (10.4%) African Americans (AA), and 226 (67%) non-Hispanic whites (NHW). The mean (SD) hemoglobin A1c differed significantly by race/ethnicity: NHW 7.86 (1.4)%, H 8.16 (1.6)%, AA 8.84 (2.9)%, p = 0.05. The multivariate-adjusted A1c was significantly higher for AA (+0.93%, p = 0.002) compared to NHW. Insulin doses (unit/day) also differed significantly: NHW 70.6 (48.8), H 58.4 (32.6), and AA 53.1 (36.2), p < 0.01. Multivariate-adjusted insulin doses were significantly lower for AA (-17.8 units/day, p = 0.01) and H (-10.5 units/day, p = 0.04) compared to NHW. Decrements in insulin doses were even greater among minority patients with poorly controlled diabetes (A1c ≥ 8%). The disparities in glycemic control and insulin treatment intensity could not be explained by differences in age, body mass index, oral hypoglycemic medications, socioeconomic barriers, attitudes about diabetes care, diabetes knowledge, depression, cognitive dysfunction, or social support. We found no significant racial/ethnic differences in lipid or blood pressure control. CONCLUSION: In our cohort, insulin-treated minority veterans, particularly AA, had poorer glycemic control and received lower doses of insulin than NHW. However, we found no differences for control of other cardiovascular disease risk factors. The diabetes treatment disparity could be due to provider behaviors and/or patient behaviors or preferences. Further research with larger sample sizes and more geographically diverse populations are needed to confirm our findings

Tackling the Root Cause of Surface-Induced Coagulation: Inhibition of FXII Activation to Mitigate Coagulation Propagation and Prevent Clotting

Factor XII (FXII) is a zymogen present in blood that tends to adsorb onto the surfaces of blood-contacting medical devices. Once adsorbed, it becomes activated, initiating a cascade of enzymatic reactions that lead to surface-induced coagulation. This process is characterized by multiple redundancies, making it extremely challenging to prevent clot formation and preserve the properties of the surface. In this study, a novel modulatory coating system based on C1-esterase inhibitor (C1INH) functionalized polymer brushes, which effectively regulates the activation of FXII is proposed. Using surface plasmon resonance it is demonstrated that this coating system effectively repels blood plasma proteins, including FXII, while exhibiting high activity against activated FXII and plasma kallikrein under physiological conditions. This unique property enables the modulation of FXII activation without interfering with the overall hemostasis process. Furthermore, through dynamic Chandler loop studies, it is shown that this coating significantly improves the hemocompatibility of polymeric surfaces commonly used in medical devices. By addressing the root cause of contact activation, the synergistic interplay between the antifouling polymer brushes and the modulatory C1INH is expected to lay the foundation to enhance the hemocompatibility of medical device surfaces.© 2023 The Authors. Macromolecular Bioscience published by Wiley-VCH GmbH

No Fukushima Dai-ichi derived plutonium signal in marine sediments collected 1.5-57km from the reactors

Based on AMS analysis, it is shown that no Pu signals from the Fukushima accident could be discerned in marine sediments collected 1.5-57km away from the Fukushima Da-ichi power plant (FDNPP), which were clearly influenced by accident-derived radiocesium. The 240Pu/239Pu atom ratios (0.21-0.28) were significantly higher than terrestrial global fallout (0.182 ± 0.005), but still in agreement with pre-FDNPP accident baseline data for Pu in near coastal seawaters influenced by global fallout and long-range transport of Pu from the Pacific Proving Grounds.This study has been funded by the Norwegian Research Council through its Centre of Excellence (CoE) funding scheme (Project No. 223268/F50)