On the variational problem for upper tails in sparse random graphs

What is the probability that the number of triangles in , the Erd?s‐Rényi random graph with edge density p , is at least twice its mean? Writing it as , already the order of the rate function r (n, p ) was a longstanding open problem when p = o (1), finally settled in 2012 by Chatterjee and by DeMarco and Kahn, who independently showed that for ; the exact asymptotics of r (n, p ) remained unknown. The following variational problem can be related to this large deviation question at : for δ > 0 fixed, what is the minimum asymptotic p‐relative entropy of a weighted graph on n vertices with triangle density at least (1 + δ )p ³? A beautiful large deviation framework of Chatterjee and Varadhan (2011) reduces upper tails for triangles to a limiting version of this problem for fixed p . A very recent breakthrough of Chatterjee and Dembo extended its validity to for an explicit α > 0, and plausibly it holds in all of the above sparse regime. In this note we show that the solution to the variational problem is when vs. when (the transition between these regimes is expressed in the count of triangles minus an edge in the minimizer). From the results of Chatterjee and Dembo, this shows for instance that the probability that for has twice as many triangles as its expectation is where . Our results further extend to k‐cliques for any fixed k , as well as give the order of the upper tail rate function for an arbitrary fixed subgraph when . © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 50, 420–436, 2017     

Single-walled carbon nanotubes embedded in oriented polymeric nanofibers by electrospinning

The electrospinning process was used successfully to embed single-walled carbon nanotubes (SWCNTs) in a poly(ethylene oxide) (PEO) matrix, forming composite nanofibers. Initial dispersion of SWCNTs in water was achieved by the use of an amphiphilic alternating copolymer of styrene and sodium maleate. The resulting dispersions were stable, having a dark, smooth, ink-like appearance. For electrospinning, the dispersions were mixed with PEO solution in an ethanol/water mixture. The distribution and conformation of the nanotubes in the nanofibers were studied by transmission electron microscopy (TEM). Oxygen plasma etching was used to expose the nanotubes within the nanofibers to facilitate direct observation. Nanotube alignment within the nanofibers was shown to depend strongly on the quality of the initial dispersions. Well-dispersed and separated nanotubes were embedded in a straight and aligned form, while entangled nonseparated nanotubes were incorporated as dense aggregates. X-ray diffraction demonstrated a high degree of orientation of the PEO crystals in the electrospun nanofibers with embedded SWCNTs. This result is in pronounced distinction to the detrimental effect of incorporation of multiwalled carbon nanotubes on polymer orientation in electrospun nanofibers, as reported previously.     

Elastic scattering of 17, 18O on 12, 13C at Ec.m. = 12.6 – 14.0 MeV

The angular distributions of the elastic scattering of ^{17, 18}O on ^{12, 13}C were measured at c.m. energies between 12.6 to 14.0 MeV. A rise of the cross section at backward angles was observed. Standard optical-model fits were found to reproduce reasonably well the forward part of the cross section, but fail at backward angles. Possible contributions of first-order cluster exchange and compound-nucleus reactions are discussed. Excitation functions of various exit channels in the ¹⁸O + ¹²C system were measured at backward angles in the energy range of 12.0 to 14.8 MeV c.m. No significant correlation was found between any of these cross sections.     

Optimal Treatment with Cannabis Extracts Formulations Is Gained via Knowledge of Their Terpene Content and via Enrichment with Specifically Selected Monoterpenes and Monoterpenoids

Differences between therapeutic effects of medical cannabis inflorescences and those of their extracts are generally attributed to the differences in administration form and in the resultant pharmacokinetics. We hypothesized that difference may further extend to the composition of the actually consumed drug. Cannabinoid and terpene contents were compared between commercial cannabis inflorescences (n = 19) and decarboxylated extracts (n = 12), and between inflorescences and decarboxylated extracts produced from them (n = 10). While cannabinoid content was preserved in the extracts, a significant loss of terpenes was evident, mainly in the more volatile monoterpenes and monoterpenoids (representing a loss of about 90%). This loss changes the total terpene content, the proportion of monoterpenes out of the total terpenes, and the monoterpene/cannabinoid ratio. Terpene deficiency might impair extracts’ pharmacological efficacy and might contribute to the patients’ preference to inflorescences-smoking. This argues against the validity of terms such as “whole plant” and “full spectrum” extracts and creates a misleading assumption that extracts represent the pharmacological profile of the sourced inflorescences. Furthermore, it reduces the diversity in extracts, such as loss of differences between sativa-type and indica-type. Enriching cannabis extracts with selected terpenes may provide a suitable solution, generating a safe, precise, and reproducible drug with tailored cannabinoid and terpene contents. Careful selection of terpenes to be added enables tailor-made extracts, adjusted for various medicinal aims and for different populations.     

pH‐Controlled network formation in a mixture of oppositely charged cellulose nanocrystals and poly(allylamine)

The behavior of a mixture of negatively charged cellulose nanocrystals (CNCs) and positively charged poly(allylamine) (PAAm) is examined in aqueous media. By modulating the pH, the acting Coulomb forces can be varied that can lead not only to adsorption of PAAm chains on the CNC surface but also to the development of a supermolecular structure by bridging of CNC rods by extended PAAm chains. This bridging can result in the formation of CNC clusters, which was demonstrated experimentally. Light scattering and rheological studies showed that these clusters begin to grow and merge, ultimately forming a global percolated network above a critical degree of PAAm ionization. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 1527–1536     

Studies on Electronic Effects in O‐, N‐ and S‐Chelated Ruthenium Olefin‐Metathesis Catalysts

A short overview on the structural design of the Hoveyda–Grubbs‐type ruthenium initiators chelated through oxygen, nitrogen or sulfur atoms is presented. Our aim was to compare and contrast O‐, N‐ and S‐chelated ruthenium complexes to better understand the impact of electron‐withdrawing and ‐donating substituents on the geometry and activity of the ruthenium complexes and to gain further insight into the trans–cis isomerisation process of the S‐chelated complexes. To evaluate the different effects of chelating heteroatoms and to probe electronic effects on sulfur‐ and nitrogen‐chelated latent catalysts, we synthesised a series of novel complexes. These catalysts were compared against two well‐known oxygen‐chelated initiators and a sulfoxide‐chelated complex. The structures of the new complexes have been determined by single‐crystal X‐ray diffraction and analysed to search for correlations between the structural features and activity. The replacement of the oxygen‐chelating atom by a sulfur or nitrogen atom resulted in catalysts that were inert at room temperature for typical ring‐closing metathesis (RCM) and cross‐metathesis reactions and showed catalytic activity only at higher temperatures. Furthermore, one nitrogen‐chelated initiator demonstrated thermo‐switchable behaviour in RCM reactions, similar to its sulfur‐chelated counterparts.     

Critical Ising on the Square Lattice Mixes in Polynomial Time

The Ising model is widely regarded as the most studied model of spin-systems in statistical physics. The focus of this paper is its dynamic (stochastic) version, the Glauber dynamics, introduced in 1963 and by now the most popular means of sampling the Ising measure. Intensive study throughout the last three decades has yielded a rigorous understanding of the spectral-gap of the dynamics on everywhere except at criticality. While the critical behavior of the Ising model has long been the focus for physicists, mathematicians have only recently developed an understanding of its critical geometry with the advent of SLE, CLE and new tools to study conformally invariant systems.     

Shot-noise limited single-molecule FRET histograms: comparison between theory and experiments

We describe a simple approach and present a straightforward numerical algorithm to compute the best fit shot-noise limited proximity ratio histogram (PRH) in single-molecule fluorescence resonant energy transfer diffusion experiments. The key ingredient is the use of the experimental burst size distribution, as obtained after burst search through the photon data streams. We show how the use of an alternated laser excitation scheme and a correspondingly optimized burst search algorithm eliminates several potential artifacts affecting the calculation of the best fit shot-noise limited PRH. This algorithm is tested extensively on simulations and simple experimental systems. We find that dsDNA data exhibit a wider PRH than expected from shot noise only and hypothetically account for it by assuming a small Gaussian distribution of distances with an average standard deviation of 1.6 A. Finally, we briefly mention the results of a future publication and illustrate them with a simple two-state model system (DNA hairpin), for which the kinetic transition rates between the open and closed conformations are extracted.