Discrete complex analysis on planar quad-graphs

We develop a linear theory of discrete complex analysis on general quad-graphs, continuing and extending previous work of Duffin, Mercat, Kenyon, Chelkak and Smirnov on discrete complex analysis on rhombic quad-graphs. Our approach based on the medial graph yields more instructive proofs of discrete analogs of several classical theorems and even new results. We provide discrete counterparts of fundamental concepts in complex analysis such as holomorphic functions, derivatives, the Laplacian, and exterior calculus. Also, we discuss discrete versions of important basic theorems such as Green's identities and Cauchy's integral formulae. For the first time, we discretize Green's first identity and Cauchy's integral formula for the derivative of a holomorphic function. In this paper, we focus on planar quad-graphs, but we would like to mention that many notions and theorems can be adapted to discrete Riemann surfaces in a straightforward way. In the case of planar parallelogram-graphs with bounded interior angles and bounded ratio of side lengths, we construct a discrete Green's function and discrete Cauchy's kernels with asymptotics comparable to the smooth case. Further restricting to the integer lattice of a two-dimensional skew coordinate system yields appropriate discrete Cauchy's integral formulae for higher order derivatives.Comment: 49 pages, 8 figure

Inverse problem and Bertrand's theorem

The Bertrand's theorem can be formulated as the solution of an inverse problem for a classical unidimensional motion. We show that the solutions of these problems, if restricted to a given class, can be obtained by solving a numerical equation. This permit a particulary compact and elegant proof of Bertrand's theorem.Comment: 11 pages, 3 figure

Making morbidity multiple: History, legacies, and possibilities for global health

Multimorbidity has been framed as a pressing global health challenge that exposes the limits of systems organised around single diseases. This article seeks to expand and strengthen current thinking around multimorbidity by analysing its construction within the field of global health. We suggest that the significance of multimorbidity lies not only in challenging divisions between disease categories but also in what it reveals about the culture and history of transnational biomedicine. Drawing on social research from sub-Saharan Africa to ground our arguments, we begin by describing the historical processes through which morbidity was made divisible in biomedicine and how the single disease became integral not only to disease control but to the extension of biopolitical power. Multimorbidity, we observe, is hoped to challenge single disease approaches but is assembled from the same problematic, historically-loaded categories that it exposes as breaking down. Next, we highlight the consequences of such classificatory legacies in everyday lives and suggest why frameworks and interventions to integrate care have tended to have limited traction in practice. Finally, we argue that efforts to align priorities and disciplines around a standardised biomedical definition of multimorbidity risks retracing the same steps. We call for transdisciplinary work across the field of global health around a more holistic, reflexive understanding of multimorbidity that foregrounds the culture and history of translocated biomedicine, the intractability of single disease thinking, and its often-adverse consequences in local worlds. We outline key domains within the architecture of global health where transformation is needed, including care delivery, medical training, the organisation of knowledge and expertise, global governance, and financing

SURVEY OF THE DEPENDENCE ON TEMPERATURE OF THE COERCIVITY OF GARNET-FILMS

The temperature dependence of the domain-wall coercive field of epitaxial magnetic garnets films has been investigated in the entire temperature range of the ferrimagnetic phase, and has been found to be described by a set of parametric exponents. In subsequent temperature regions different slopes were observed, with breaking points whose position was found to be sample dependent. A survey ba.ed on literature Data as well as on a large number of our own samples shows the general existence of this piecewise exponential dependence and the presence of the breaking points. This type of domain-wall coercive field temperature dependence was found in all samples in the large family of the epitaxial garnets (about 30 specimens of more than ten chemical compositionsj and also in another strongly anisotropic material (TbFeCo)

Carriage of extended-spectrum beta-lactamase-producing Enterobacteriaceae in HIV-infected children in Zimbabwe.

BACKGROUND: Antimicrobial resistance is an emerging global health issue. Data on the epidemiology of multidrug-resistant organisms are scarce for Africa, especially in HIV-infected individuals who often have frequent contact with healthcare. We investigated the prevalence of extended-spectrum beta-lactamase-producing Enterobacteriaceae (ESBL-E) carriage in stool among HIV-infected children attending an HIV outpatient department in Harare, Zimbabwe. METHODS: We recruited children who were stable on antiretroviral therapy (ART) attending a HIV clinic from August 2014 to June 2015. Information was collected on antibiotic use and hospitalization. Stool was tested for ESBL-E through combination disc diffusion. API20E identification and antimicrobial susceptibility was performed on the positive samples followed by whole genome sequencing. RESULTS: Stool was collected from 175/202 (86.6 %) children. Median age was 11 [inter-quartile range (IQR) 9-12] years. Median time on ART was 4.6 years (IQR 2.4-6.4). ESBL-Es were found in 24/175 samples (13.7 %); 50 % of all ESBL-Es were resistant to amoxicillin-clavulanate, 100 % to co-trimoxazole, 45.8 % to chloramphenicol, 91.6 % to ceftriaxone, 20.8 % to gentamicin and 62.5 % to ciprofloxacin. ESBL-Es variously encoded CTX-M, OXA, TEM and SHV enzymes. The odds of ESBL-E carriage were 8.5 times (95 % CI 2.2-32.3) higher in those on ART for less than one year (versus longer) and 8.5 times (95 % CI 1.1-32.3) higher in those recently hospitalized for a chest infection. CONCLUSION: We found a 13.7 % prevalence of ESBL-E carriage in a population where ESBL-E carriage has not been described previously. Antimicrobial resistance (AMR) in Africa merits further study, particularly given the high HIV prevalence and limited diagnostic and therapeutic options available