Random graph asymptotics on high-dimensional tori. II. Volume, diameter and mixing time

For critical bond-percolation on high-dimensional torus, this paper proves sharp lower bounds on the size of the largest cluster, removing a logarithmic correction in the lower bound in Heydenreich and van der Hofstad (2007). This improvement finally settles a conjecture by Aizenman (1997) about the role of boundary conditions in critical high-dimensional percolation, and it is a key step in deriving further properties of critical percolation on the torus. Indeed, a criterion of Nachmias and Peres (2008) implies appropriate bounds on diameter and mixing time of the largest clusters. We further prove that the volume bounds apply also to any finite number of the largest clusters. The main conclusion of the paper is that the behavior of critical percolation on the high-dimensional torus is the same as for critical Erdos-Renyi random graphs. In this updated version we incorporate an erratum to be published in a forthcoming issue of Probab. Theory Relat. Fields. This results in a modification of Theorem 1.2 as well as Proposition 3.1.Comment: 16 pages. v4 incorporates an erratum to be published in a forthcoming issue of Probab. Theory Relat. Field

Benzylic fluorination induced by a charge-transfer complex with a solvent-dependent selectivity switch

We present a divergent strategy for the fluorination of phenylacetic acid derivatives that is induced by a charge-transfer complex between Selectfluor and 4-(dimethylamino)pyridine. A comprehensive investigation of the conditions revealed a critical role of the solvent on the reaction outcome. In the presence of water, decarboxylative fluorination through a single-electron oxidation is dominant. Non-aqueous conditions result in the clean formation of α-fluoro-α-arylcarboxylic acids

Benzylic fluorination induced by N–F bond activation of Selectfluor^® with a solvent-dependent selectivity switch

We present a divergent radical strategy for the fluorination of phenylacetic acid derivatives through N–F bond activation of Selectfluor® with 4-(dimethylamino)pyridine. Comprehensive reaction investigation revealed the critical role of reaction media on selectivity. In presence of water, decarboxylative fluorination through a single electron oxidation is dominant. Non-aqueous conditions result in the clean formation of α-fluoro-α-arylcarboxylic acids through hydrogen atom transfer

What is the super-sample covariance? A fresh perspective for second-order shear statistics

Cosmological analyses of second-order weak lensing statistics require precise and accurate covariance estimates. These covariances are impacted by two sometimes neglected terms: A negative contribution to the Gaussian covariance due to finite survey area and the super-sample covariance (SSC) which for the power spectrum contains the impact by Fourier modes larger than the survey window. We show here that these two effects are connected and can be seen as correction terms to the ``large-field-approximation'', the asymptotic case of an infinitely large survey area. We describe the two terms collectively as ``Finite-Field-Terms''. We derive the covariance of second-order shear statistics from first principles. For this, we use an estimator in real space without relying on an estimator for the power spectrum. The resulting covariance does not scale inversely with the survey area, as naively assumed. This scaling is only correct under the large-field approximation when the contribution of the finite-field terms tends to zero. Furthermore, all parts of the covariance, not only the SSC, depend on the power- and trispectrum at all modes, including those larger than the survey. We also show that it is generally impossible to transform an estimate for the power spectrum covariance into the covariance of a real-space statistic. Such a transformation is only possible in the asymptotic case of the `large-field approximation'. Additionally, we find that the total covariance of a real-space statistic can be calculated using correlation functions estimates on spatial scales smaller than the survey window. Consequently, estimating covariances of real-space statistics, in principle, does not require information on spatial scales larger than the survey area. We demonstrate that this covariance estimation method is equivalent to the standard sample covariance method.Comment: 8 pages + appendix, 3 figures, submitted to Astronomy & Astrophysics, Major revision after comments by referee and communit

Metabolic Equivalent in Adolescents, Active Adults and Pregnant Women.

"Metabolic Equivalent" (MET) represents a standard amount of oxygen consumed by the body under resting conditions, and is defined as 3.5 mL O₂/kg × min or ~1 kcal/kg × h. It is used to express the energy cost of physical activity in multiples of MET. However, universal application of the 1-MET standard was questioned in previous studies, because it does not apply well to all individuals. Height, weight and resting metabolic rate (RMR, measured by indirect calorimetry) were measured in adolescent males (n = 50) and females (n = 50), women during pregnancy (gestation week 35-41, n = 46), women 24-53 weeks postpartum (n = 27), and active men (n = 30), and were compared to values predicted by the 1-MET standard. The RMR of adolescent males (1.28 kcal/kg × h) was significantly higher than that of adolescent females (1.11 kcal/kg × h), with or without the effects of puberty stage and physical activity levels. The RMR of the pregnant and post-pregnant subjects were not significantly different. The RMR of the active normal weight (0.92 kcal/kg × h) and overweight (0.89 kcal/kg × h) adult males were significantly lower than the 1-MET value. It follows that the 1-MET standard is inadequate for use not only in adult men and women, but also in adolescents and physically active men. It is therefore recommended that practitioners estimate RMR with equations taking into account individual characteristics, such as sex, age and Body Mass Index, and not rely on the 1-MET standard

8-Methoxyneorautenol and radical scavenging flavonoids from Erythrina abyssinica

A new pterocarpan (named 8-methoxyneorautenol) was isolated from the acetone extract of the root bark of Erythrina abyssinica. In addition, the known isoflavonoid derivatives eryvarin L, erycristagallin and shinpterocarpin were identified for the first time from the roots of this plant. The structures were determined on the basis of spectroscopic evidence. The new compound showed selective antimicrobial activity against Trichophyton mentagrophytes. The acetone extract of the root bark of E. abyssinica showed radical scavenging activity towards 2,2-diphenyl-1-picrylhydrazyl radical (DPPH). The pterocarpenes, 3-hydroxy-9-methoxy-10-(3,3- dimethylallyl)pterocarpene and erycristagallin, were the most active constituents of the roots of this plant and showing dose-dependent activities similar to that of the standard quercetin

Antiplasmodial and larvicidal flavonoids from Derris trifoliata

From the dichloromethane-methanol (1:1) extract of the seed pods of Derris trifoliata, a new flavanone derivative (S)-lupinifolin 4´-methyl ether was isolated. In addition, the known flavonoids lupinifolin and rotenone were identified. The structures were determined on the basis of spectroscopic evidence. Lupinfolin showed moderate in vitro antiplasmodial activity against the D6 (chloroquine-sensitive) and W2 (chloroquineresistant)strains of Plasmodium falciparum. The different parts of this plant showed larvicidal activities against Aedes aegypti and rotenoids were identified as the active principles

KiDS-1000 cosmology: Combined second- and third-order shear statistics

This paper performs the first cosmological parameter analysis of the KiDS-1000 data with second- and third-order shear statistics. This work builds on a series of papers that describe the roadmap to third-order shear statistics. We derive and test a combined model of the second-order shear statistic, namely the COSEBIs and the third-order aperture mass statistics $\langle M_\mathrm{ap}^3\rangle$ in a tomographic set-up. We validate our pipeline with $N$-body simulations that mock the fourth Kilo Degree survey data release. To model the second- and third-order statistics, we use the latest version of \textsc{HMcode2020} for the power spectrum and \textsc{BiHalofit} for the bispectrum. Furthermore, we use an analytic description to model intrinsic alignments and hydro-dynamical simulations to model the effect of baryonic feedback processes. Lastly, we decreased the dimension of the data vector significantly by considering for the $\langle M_\mathrm{ap}^3\rangle$ part of the data vector only equal smoothing radii, making a data analysis of the fourth Kilo Degree survey data release using a combined analysis of COSEBIs third-order shear statistic possible. We first validate the accuracy of our modelling by analysing a noise-free mock data vector assuming the KiDS-1000 error budget, finding a shift in the maximum-a-posterior of the matter density parameter $\Delta \Omega_m< 0.02\, \sigma_{\Omega_m}$ and of the structure growth parameter $\Delta S_8 < 0.05\, \sigma_{S_8}$. Lastly, we performed the first KiDS-1000 cosmological analysis using a combined analysis of second- and third-order shear statistics, where we constrained $\Omega_m=0.248^{+0.062}_{-0.055}$ and $S_8=\sigma_8\sqrt{\Omega_m/0.3}=0.772\pm0.022$. The geometric average on the errors of $\Omega_\mathrm{m}$ and $S_8$ of the combined statistics increased compared to the second-order statistic by 2.2.Comment: 19 pages, 15 figures. Updated version with arXiv ID of our companion paper Porth et at. 202

Oxidation of isodrimeninol with PCC yields drimane derivatives with activity against candida yeast by inhibition of lanosterol 14-alpha demethylase

Indexación: Scopus.Candida species cause an opportunistic yeast infection called Candidiasis, which is responsible for more than 50,000 deaths every year around the world. Effective treatments against candidiasis caused by non-albicans Candida species such as C. glabrata, C. parapsilosis, C. aureus, and C. krusei are limited due to severe resistance to conventional antifungal drugs. Natural drimane sesquiterpenoids have shown promising antifungal properties against Candida yeast and have emerged as valuable candidates for developing new candidiasis therapies. In this work, we isolated isodrimeninol (C1) from barks of Drimys winteri and used it as starting material for the hemi-synthesis of four sesquiterpenoids by oxidation with pyridinium chlorochromate (PCC). The structure of the products (C2, C3, C4, and C5) was elucidated by 1D and 2D NMR spectroscopy resulting in C4 being a novel compound. Antifungal activity assays against C. albicans, C. glabrata, and C. krusei revealed that C4 exhibited an increased activity (IC50 of 75 µg/mL) compared to C1 (IC50 of 125 µg/mL) in all yeast strains. The antifungal activity of C1 and C4 was rationalized in terms of their capability to inhibit lanosterol 14-alpha demethylase using molecular docking, molecular dynamics simulations, and MM/GBSA binding free energy calculations. In silico analysis revealed that C1 and C4 bind to the outermost region of the catalytic site of 14-alpha demethylase and block the entrance of lanosterol (LAN) to the catalytic pocket. Binding free energy estimates suggested that C4 forms a more stable complex with the enzyme than C1, in agreement with the experimental evidence. Based on this new approach it is possible to design new drimane-type sesquiterpenoids for the control of Candida species as inhibitors of 14-alpha demethylase. © 2020 by the authors. Licensee MDPI, Basel, Switzerland.https://www.mdpi.com/2218-273X/10/8/110

The Alexander-Orbach conjecture holds in high dimensions

We examine the incipient infinite cluster (IIC) of critical percolation in regimes where mean-field behavior has been established, namely when the dimension d is large enough or when d>6 and the lattice is sufficiently spread out. We find that random walk on the IIC exhibits anomalous diffusion with the spectral dimension d_s=4/3, that is, p_t(x,x)= t^{-2/3+o(1)}. This establishes a conjecture of Alexander and Orbach. En route we calculate the one-arm exponent with respect to the intrinsic distance.Comment: 25 pages, 2 figures. To appear in Inventiones Mathematica