Diameters in preferential attachment models

In this paper, we investigate the diameter in preferential attachment (PA-) models, thus quantifying the statement that these models are small worlds. The models studied here are such that edges are attached to older vertices proportional to the degree plus a constant, i.e., we consider affine PA-models. There is a substantial amount of literature proving that, quite generally, PA-graphs possess power-law degree sequences with a power-law exponent \tau>2. We prove that the diameter of the PA-model is bounded above by a constant times \log{t}, where t is the size of the graph. When the power-law exponent \tau exceeds 3, then we prove that \log{t} is the right order, by proving a lower bound of this order, both for the diameter as well as for the typical distance. This shows that, for \tau>3, distances are of the order \log{t}. For \tau\in (2,3), we improve the upper bound to a constant times \log\log{t}, and prove a lower bound of the same order for the diameter. Unfortunately, this proof does not extend to typical distances. These results do show that the diameter is of order \log\log{t}. These bounds partially prove predictions by physicists that the typical distance in PA-graphs are similar to the ones in other scale-free random graphs, such as the configuration model and various inhomogeneous random graph models, where typical distances have been shown to be of order \log\log{t} when \tau\in (2,3), and of order \log{t} when \tau>3

A novel NADPH-dependent aldehyde reductase gene from Vigna radiata confers resistance to the grapevine fungal toxin eutypine.

Eutypine, 4-hydroxy-3-(3-methyl-3-butene-1-ynyl) benzyl aldehyde, is a toxin produced by Eutypa lata, the causal agent of eutypa dieback of grapevines. It has previously been demonstrated that tolerance of some cultivars to this disease was correlated with their capacity to convert eutypine to the corresponding alcohol, eutypinol, which lacks phytotoxicity. We have thus purified to homogeneity a protein from Vigna radiata that exhibited eutypinereducing activity and have isolated the corresponding cDNA. This encodes an NADPH-dependent reductase of 36 kDa that we have named Vigna radiata eutypine-reducing enzyme (VR-ERE), based on the capacity of a recombinant form of the protein to reduce eutypine into eutypinol. The strongest homologies (86.8%) of VR-ERE at the amino acid level were found with CPRD14, a drought-inducible gene of unknown function, isolated from Vigna unguiculata and with an aromatic alcohol dehydrogenase (71.7%) from Eucalyptus gunnii. Biochemical characterization of VR-ERE revealed that a variety of compounds containing an aldehyde group can act as substrates. However, the highest affinity was observed with 3-substituted benzaldehydes. Expression of a VR-ERE transgene in Vitis vinifera cells cultured in vitro conferred resistance to the toxin. This discovery opens up new biotechnological approaches for the generation of grapevines resistant to eutypa dieback

An introductory electrochemical approach to studying hydrometallurgical reactions

Many hydrometallurgical processes are electrochemical phenomena. Although this fact is well known, electrochemical methods are under-utilized when studying these processes. One possible reason is the confusion surrounding the number of electrochemical techniques available. We present an insight into how one technique can be used to study a variety of hydrometallurgical processes. This article details how to perform experiments, interpret data, and recognize complications with results. Examples where this approach has been highly successful are presented

Infrared supercontinuum from a large mode area PCF under extreme picosecond excitation

Evolution of the long-wavelength edge of supercontinuum (SC) in a large mode-area photonic crystal fiber (LMA PCF) under extreme (close to the fiber damage threshold) picosecond excitation is analyzed for the first time to our knowledge. The obtained results are interpreted on the basis of the numerical simulations explaining both spectral and temporal characteristics of SC in dependence on the pulse power and the fiber length. An existence of the minimum LMA PCF length providing the broadest spectrum under the highest picosecond excitations is predicted. The multimode cross-modulation inside the LMA PCF is analyzed, as well