Statistical mechanics approach to some problems in conformal geometry

A weak law of large numbers is established for a sequence of systems of N classical point particles with logarithmic pair potential in \bbR^n, or \bbS^n, n\in \bbN, which are distributed according to the configurational microcanonical measure $\delta(E-H)$, or rather some regularization thereof, where H is the configurational Hamiltonian and E the configurational energy. When $N\to\infty$ with non-extensive energy scaling E=N^2 \vareps, the particle positions become i.i.d. according to a self-consistent Boltzmann distribution, respectively a superposition of such distributions. The self-consistency condition in n dimensions is some nonlinear elliptic PDE of order n (pseudo-PDE if n is odd) with an exponential nonlinearity. When n=2, this PDE is known in statistical mechanics as Poisson-Boltzmann equation, with applications to point vortices, 2D Coulomb and magnetized plasmas and gravitational systems. It is then also known in conformal differential geometry, where it is the central equation in Nirenberg's problem of prescribed Gaussian curvature. For constant Gauss curvature it becomes Liouville's equation, which also appears in two-dimensional so-called quantum Liouville gravity. The PDE for n=4 is Paneitz' equation, and while it is not known in statistical mechanics, it originated from a study of the conformal invariance of Maxwell's electromagnetism and has made its appearance in some recent model of four-dimensional quantum gravity. In differential geometry, the Paneitz equation and its higher order n generalizations have applications in the conformal geometry of n-manifolds, but no physical applications yet for general n. Interestingly, though, all the Paneitz equations have an interpretation in terms of statistical mechanics.Comment: 17 pages. To appear in Physica

Destructive fishing : an expert‐driven definition and exploration of this quasi‐concept

Numerous policy and international frameworks consider that “destructive fishing” hampers efforts to reach sustainability goals. Though ubiquitous, “destructive fishing” is undefined and therefore currently immeasurable. Here we propose a definition developed through expert consultation: “Destructive fishing is any fishing practice that causes irrecoverable habitat degradation, or which causes significant adverse environmental impacts, results in long-term declines in target or nontarget species beyond biologically safe limits and has negative livelihood impacts.” We show strong stakeholder support for a definition, consensus on many biological and ecological dimensions, and no clustering of respondents from different sectors. Our consensus definition is a significant step toward defining sustainable fisheries goals and will help interpret and implement global political commitments which utilize the term “destructive fishing.” Our definition and results will help reinforce the Food and Agricultural Organization's Code of Conduct and meaningfully support member countries to prohibit destructive fishing practices

Defining mangrove-fisheries: A typology from the Perancak Estuary, Bali, Indonesia.

This study develops a definition of what mangrove-fisheries can encompass, incorporating a broad range of their possible characteristics. A detailed case study was conducted to develop a typology of mangrove-fishing in the Perancak Estuary, Bali, Indonesia, using interview surveys to investigate the fishing activities associated with mangroves. This case study demonstrated the complexity that a mangrove-fishery can entail, where fishing is connected to the mangrove forest by fishers of multiple sectors, functions, locations and temporal scales. Through a comparison with other mangrove-fishing communities in Bali, it also highlighted that mangrove-fisheries are variable even when in close proximity. With particular reference to this case study, a framework was developed as a flexible tool for identifying the multiple dimensions of a mangrove-fishery in a local context. Following this framework should encourage researchers and managers to look outside of the groups of fishers traditionally expected to benefit from mangrove fishing. This will enable the development of a broader definition of mangrove-fisheries in a site specific way. Identifying the full scope of fishers that contribute to or benefit from a mangrove-fishery is the first step towards building management measures that reflect the interests of groups of fishers that may otherwise remain under-represented. This is in line with international efforts for sustainability, especially in promoting small-scale fishers' access to sustainable resources under the UN Sustainable Development Goals

Plasma Vascular Endothelial Growth Factor Concentrations after Intravitreous Anti–Vascular Endothelial Growth Factor Therapy for Diabetic Macular Edema

© 2018 American Academy of Ophthalmology Purpose: To assess systemic vascular endothelial growth factor (VEGF)-A levels after treatment with intravitreous aflibercept, bevacizumab, or ranibizumab. Design: Comparative-effectiveness trial with participants randomly assigned to 2 mg aflibercept, 1.25 mg bevacizumab, or 0.3 mg ranibizumab after a re-treatment algorithm. Participants: Participants with available plasma samples (N = 436). Methods: Plasma samples were collected before injections at baseline and 4-week, 52-week, and 104-week visits. In a preplanned secondary analysis, systemic-free VEGF levels from an enzyme-linked immunosorbent assay were compared across anti-VEGF agents and correlated with systemic side effects. Main Outcome Measures: Changes in the natural log (ln) of plasma VEGF levels. Results: Baseline free VEGF levels were similar across all 3 groups. At 4 weeks, mean ln(VEGF) changes were −0.30±0.61 pg/ml, −0.31±0.54 pg/ml, and −0.02±0.44 pg/ml for the aflibercept, bevacizumab, and ranibizumab groups, respectively. The adjusted differences between treatment groups (adjusted confidence interval [CI]; P value) were −0.01 (−0.12 to +0.10; P = 0.89), −0.31 (−0.44 to −0.18; P \u3c 0.001), and −0.30 (−0.43 to −0.18; P \u3c 0.001) for aflibercept-bevacizumab, aflibercept-ranibizumab, and bevacizumab-ranibizumab, respectively. At 52 weeks, a difference in mean VEGF changes between bevacizumab and ranibizumab persisted (−0.23 [−0.38 to −0.09]; P \u3c 0.001); the difference between aflibercept and ranibizumab was −0.12 (P = 0.07) and between aflibercept and bevacizumab was +0.11 (P = 0.07). Treatment group differences at 2 years were similar to 1 year. No apparent treatment differences were detected at 52 or 104 weeks in the cohort of participants not receiving injections within 1 or 2 months before plasma collection. Participants with (N = 9) and without (N = 251) a heart attack or stroke had VEGF levels that appeared similar. Conclusions: These data suggest that decreases in plasma free-VEGF levels are greater after treatment with aflibercept or bevacizumab compared with ranibizumab at 4 weeks. At 52 and 104 weeks, a greater decrease was observed in bevacizumab versus ranibizumab. Results from 2 subgroups of participants who did not receive injections within at least 1 month and 2 months before collection suggest similar changes in VEGF levels after stopping injections. It is unknown whether VEGF levels return to normal as the drug is cleared from the system or whether the presence of the drug affects the assay\u27s ability to accurately measure free VEGF. No significant associations between VEGF concentration and systemic factors were noted

Destructive fishing:An expert-driven definition and exploration of this quasi-concept

Numerous policy and international frameworks consider that “destructive fishing” hampers efforts to reach sustainability goals. Though ubiquitous, “destructive fishing” is undefined and therefore currently immeasurable. Here we propose a definition developed through expert consultation: “Destructive fishing is any fishing practice that causes irrecoverable habitat degradation, or which causes significant adverse environmental impacts, results in long-term declines in target or nontarget species beyond biologically safe limits and has negative livelihood impacts.” We show strong stakeholder support for a definition, consensus on many biological and ecological dimensions, and no clustering of respondents from different sectors. Our consensus definition is a significant step toward defining sustainable fisheries goals and will help interpret and implement global political commitments which utilize the term “destructive fishing.” Our definition and results will help reinforce the Food and Agricultural Organization's Code of Conduct and meaningfully support member countries to prohibit destructive fishing practices.</p

Natural History of Drusenoid Pigment Epithelial Detachment Associated with Age-Related Macular Degeneration Age-Related Eye Disease Study 2 Report No. 17

PurposeTo investigate the natural history and genetic associations of drusenoid pigment epithelial detachment (DPED) associated with age-related macular degeneration (AMD).DesignRetrospective analysis of a prospective cohort study.ParticipantsOf the 4203 Age-Related Eye Disease Study 2 (AREDS2) participants, 391 eyes (325 participants) had DPED without late AMD at the time of DPED detection. Genetic analyses included 120 white AREDS2 participants and 145 Age-Related Eye Disease Study (AREDS) participants with DPED.MethodsBaseline and annual stereoscopic fundus photographs were graded centrally to detect DPED, a well-defined yellow elevated mound of confluent drusen ≥433 μm in diameter, and to evaluate progression rates to late AMD: geographic atrophy (GA) and neovascular (NV)-AMD. Five single nucleotide polymorphisms (CFH [rs10611670], C3 [rs2230199], CFI [rs10033900], C2/CFB [rs114254831], ARMS2 [rs10490924]) and genetic risk score (GRS) group were investigated for association with DPED development. Kaplan-Meier analyses and multivariable proportional hazard regressions were performed.Main outcome measuresProgression rates to late AMD and decrease of ≥3 lines in visual acuity (VA) from the time of DPED detection; association of rate of DPED development with genotype.ResultsMean (standard deviation [SD]) follow-up time from DPED detection was 4.7 (0.9) years. DPED was associated with increased risk of progression to late AMD (hazard ratio [HR], 2.36; 95% confidence interval [CI], 1.98-2.82; P &lt; 0.001); 67% of eyes progressed to late AMD 5 years after DPED detection. Drusenoid pigment epithelial detachment was associated with increased risk of ≥3 lines of VA loss (HR, 3.08; CI, 2.41-3.93; P &lt; 0.001) with 46% of eyes experiencing vision loss at 5 years (with or without progression to late AMD). ARMS2 risk alleles (1 vs. 0: HR, 2.72, CI, 1.58-4.70; 2 vs. 0: HR, 3.16, CI, 1.60-6.21, P &lt; 0.001) and increasing GRS group (4 vs. 1) (HR, 12.17, CI, 3.66-40.45, P &lt; 0.001) were significantly associated with DPED development in AREDS. There were no significant genetic results in AREDS2.ConclusionsThis study replicates the results of previous natural history studies of eyes with DPED including the high rates of progression to late AMD and vision loss (regardless of progression to late AMD). The genetic associations are consistent with genes associated with AMD progression