Block-Goettsche invariants from wall-crossing

We show how some of the refined tropical counts of Block and Goettsche emerge from the wall-crossing formalism. This leads naturally to a definition of a class of putative q-deformed Gromov-Witten invariants. We prove that this coincides with another natural q-deformation, provided by a result of Reineke and Weist in the context of quiver representations, when the latter is well defined

Sustainable Production of Stiff and Crystalline Bacterial Cellulose from Orange Peel Extract

In this work, a potentially economic and environmentally friendly method for the synthesis of bacterial cellulose (BC) by Gluconacetobacter xylinus from a biomass containing orange peel extract was evaluated. Orange peel extract was used as a culture medium without any hydrolysis treatment, thus speeding up the synthesis procedure. The efficacy of orange peel as a carbon source was compared with that of sucrose. The orange peel extract formed thicker cellulose gels than those formed using sucrose. X-ray diffraction (XRD) revealed both a high crystallinity index and crystallite size of BC nanofibers in samples obtained from orange peel (BC_Orange). Field emission scanning electron microscopy (FE-SEM) revealed a highly densely packed nanofibrous structure (50 nm in diameter). BC_Orange presented a two-fold increase in water holding capacity (WHC), and dynamic mechanical analysis (DMA) showed a 44% increase in storage modulus compared to sucrose derived BC. These results showed that the naturally available carbon sources derived from orange peel extract can be effectively used for BC production. The orange-based culture medium can be considered a profitable alternative to the generation of high-value products in a virtuous circular economy model

Increased risk of breast cancer among female relatives of patients with ataxia-telangiectasia: a causal relationship?

International audienc

A construction of Frobenius manifolds from stability conditions

© 2018 London Mathematical Society A finite quiver Q without loops or 2-cycles defines a CY3 triangulated category D(Q) and a finite heart A(Q)⊂D(Q). We show that if Q satisfies some (strong) conditions, then the space of stability conditions (A(Q))) supported on this heart admits a natural family of semisimple Frobenius manifold structures, constructed using the invariants counting semistable objects in D(Q). In the case of An evaluating the family at a special point, we recover a branch of the Saito Frobenius structure of the An singularity y2=xn+1. We give examples where applying the construction to each mutation of Q and evaluating the families at a special point yields a different branch of the maximal analytic continuation of the same semisimple Frobenius manifold. In particular, we check that this holds in the case of An, n5

Determination of zeolite-group mineral compositions by electron probe microanalysis

A new protocol for the quantitative determination of zeolite-group mineral compositions by electron probe microanalysis (wavelength-dispersive spectrometry) under ambient conditions, is presented. The method overcomes the most serious challenges for this mineral group, including new confidence in the fundamentally important Si-Al ratio. Development tests were undertaken on a set of natural zeolite candidate reference samples, representing the compositional extremes of Na, K, Cs, Mg, Ca, Sr and Ba zeolites, to demonstrate and assess the extent of beam interaction effects on each oxide component for each mineral. These tests highlight the variability and impact of component mobility due to beam interaction, and show that it can be minimized with recommended operating conditions of 15 kV, 2 nA, a defocused, 20 μm spot size, and element prioritizing with the spectrometer configuration. The protocol represents a pragmatic solution that works, but provides scope for additional optimization where required. Vital to the determination of high-quality results is the attention to careful preparations and the employment of strict criteria for data reduction and quality control, including the monitoring and removal of non-zeolitic contaminants from the data (mainly Fe and clay phases). Essential quality criteria include the zeolite-specific parameters of R value (Si/(Si + Al + Fe3+), the ‘E%’ charge-balance calculation, and the weight percent of non-hydrous total oxides. When these criteria are applied in conjunction with the recommended analytical operating conditions, excellent inter-batch reproducibility is demonstrated. Application of the method to zeolites with complex solid-solution compositions is effective, enabling more precise geochemical discrimination for occurrence-composition studies. Phase validation for the reference set was conducted satisfactorily with the use of X-ray diffraction and laser-ablation inductively-coupled plasma mass spectroscopy

A quantized Riemann-Hilbert problem in Donaldson-Thomas theory

We introduce Riemann-Hilbert problems determined by refined Donaldson-Thomas theory. They involve piecewise holomorphic maps from the complex plane to the group of automorphisms of a quantum torus algebra. We study the simplest case in detail and use the Barnes double gamma function to construct a solution

Microvascular dysfunction in pediatric patients with SARS-COV-2 pneumonia: report of three severe cases

The coronavirus 19 (COVID-19) pandemic has affected hundreds of millions of people worldwide: in most of cases children and young people developed asymptomatic or pauci-symptomatic clinical pictures. However authors have showed that there are some categories of childhood more vulnerable to COVID-19 infection such as newborns or children with comorbidities. We report for the first time to the best of our knowledge about microvascular dysfunction in three pediatric clinical cases who developed COVID-19 infections with need of pediatric critical care. We found that sublingual microcirculation is altered in children with severe COVID-19 infection. Our findings confirmed most of data already observed by other authors in adult population affected by severe COVID-19 infection, but with distinct characteristics than microcirculation alterations previous observed in a clinical case of MIS-C. However we cannot establish direct correlation between microcirculation analysis and clinical or laboratory parameters in our series, by our experience we have found that sublingual microcirculation analysis allow clinicians to report directly about microcirculation dysfunction in COVID-19 patients and it could be a valuable bedside technique to monitor thrombosis complication in this population

Stability data, irregular connections and tropical curves

We study a class of meromorphic connections nabla(Z) on P^1, parametrised by the central charge Z of a stability condition, with values in a Lie algebra of formal vector fields on a torus. Their definition is motivated by the work of Gaiotto, Moore and Neitzke on wall-crossing and three-dimensional field theories. Our main results concern two limits of the families nabla(Z) as we rescale the central charge Z to RZ. In the R to 0 ``conformal limit'' we recover a version of the connections introduced by Bridgeland and Toledano Laredo (and so the Joyce holomorphic generating functions for enumerative invariants), although with a different construction yielding new explicit formulae. In the R to infty ``large complex structure" limit the connections nabla(Z) make contact with the Gross-Pandharipande-Siebert approach to wall-crossing based on tropical geometry. Their flat sections display tropical behaviour, and also encode certain tropical/relative Gromov-Witten invariants