Gradient and Passive Circuit Structure in a Class of Non-linear Dynamics on a Graph

We consider a class of non-linear dynamics on a graph that contains and generalizes various models from network systems and control and study convergence to uniform agreement states using gradient methods. In particular, under the assumption of detailed balance, we provide a method to formulate the governing ODE system in gradient descent form of sum-separable energy functions, which thus represent a class of Lyapunov functions; this class coincides with Csisz\'{a}r's information divergences. Our approach bases on a transformation of the original problem to a mass-preserving transport problem and it reflects a little-noticed general structure result for passive network synthesis obtained by B.D.O. Anderson and P.J. Moylan in 1975. The proposed gradient formulation extends known gradient results in dynamical systems obtained recently by M. Erbar and J. Maas in the context of porous medium equations. Furthermore, we exhibit a novel relationship between inhomogeneous Markov chains and passive non-linear circuits through gradient systems, and show that passivity of resistor elements is equivalent to strict convexity of sum-separable stored energy. Eventually, we discuss our results at the intersection of Markov chains and network systems under sinusoidal coupling

Frequent burning promotes invasions of alien plants into a mesic African savanna

Fire is both inevitable and necessary for maintaining the structure and functioning of mesic savannas. Without disturbances such as fire and herbivory, tree cover can increase at the expense of grass cover and over time dominate mesic savannas. Consequently, repeated burning is widely used to suppress tree recruitment and control bush encroachment. However, the effect of regular burning on invasion by alien plant species is little understood. Here, vegetation data from a long-term fire experiment, which began in 1953 in a mesic Zimbabwean savanna, were used to test whether the frequency of burning promoted alien plant invasion. The fire treatments consisted of late season fires, lit at 1-, 2-, 3-, and 4-year intervals, and these regularly burnt plots were compared with unburnt plots. Results show that over half a century of frequent burning promoted the invasion by alien plants relative to areas where fire was excluded. More alien plant species became established in plots that had a higher frequency of burning. The proportion of alien species in the species assemblage was highest in the annually burnt plots followed by plots burnt biennially. Alien plant invasion was lowest in plots protected from fire but did not differ significantly between plots burnt triennially and quadrennially. Further, the abundance of five alien forbs increased significantly as the interval (in years) between fires became shorter. On average, the density of these alien forbs in annually burnt plots was at least ten times as high as the density of unburnt plots. Plant diversity was also altered by long-term burning. Total plant species richness was significantly lower in the unburnt plots compared to regularly burnt plots. These findings suggest that frequent burning of mesic savannas enhances invasion by alien plants, with short intervals between fires favouring alien forbs. Therefore, reducing the frequency of burning may be a key to minimising the risk of alien plant spread into mesic savannas, which is important because invasive plants pose a threat to native biodiversity and may alter savanna functioning

The role of cholesterol metabolism and various steroid abnormalities in autism spectrum disorders : A hypothesis paper

© 2017 The Authors Autism Research published by Wiley Periodicals, Inc. on behalf of International Society for Autism Research.Peer reviewedPublisher PD

Measurement of the production cross section of prompt j/psi mesons in association with a W (+/-) boson in pp collisions root s=7 TeV with the ATLAS detector

The process pp -> W (+/-) J/psi provides a powerful probe of the production mechanism of charmonium in hadronic collisions, and is also sensitive to multiple parton interactions in the colliding protons. Using the 2011 ATLAS dataset of 4.5 fb(-1) of root s= 7 TeV pp collisions at the LHC, the first observation is made of the production of W (+/-) + prompt J/psi events in hadronic collisions, using W (+/-) -> mu nu(mu) and J/psi -> mu(+)mu(-) center dot A yield of W (+/-) + prompt J/psi events is observed, with a statistical significance of 5.1 sigma. The production rate as a ratio to the inclusive W (+/-) boson production rate is measured, and the double parton scattering contribution to the cross section is estimated

On the Spanish main,

Mode of access: Internet

The brown book for boys /

A collection of short stories for boys."Reprinted 1921 in Great Britain by R. Clay and Sons, Ltd., Bungay, Suffolk"--T.p. verso.A collection of short stories for boys.Mode of access: Internet.Gift of William A. Gosling