The GHS and other correlation inequalities for a class of even ferromagnets

We prove the GHS inequality for families of random variables which arise in certain ferromagnetic models of statistical mechanics and quantum field theory. These include spin –1/2 Ising models, ⁴ field theories, and other continuous spin models. The proofs are based on the properties of a classG ^– of probability measures which contains all measures of the form const exp(–V(x))dx, whereV is even and continuously differentiable anddV/dx is convex on [0, ). A new proof of the GKS inequalities using similar ideas is also given.Supported in part by National Science Foundation Grant MPS 71-02838 A 04.Supported by National Science Foundation Grant MPS 74-24696.Supported in part by National Science Foundation Grant MPS 74-04870.     

Narrow band quantitative and multivariate electroencephalogram analysis of peri-adolescent period

ABSTRACT: BACKGROUND: The peri-adolescent period is a crucial developmental moment of transition from childhood to emergent adulthood. The present report analyses the differences in Power Spectrum (PS) of the Electroencephalogram (EEG) between late childhood (24 children between 8 and 13 years old) and young adulthood (24 young adults between 18 and 23 years old). RESULTS: The narrow band analysis of the Electroencephalogram was computed in the frequency range of 0--20 Hz. The analysis of mean and variance suggested that six frequency ranges presented a different rate of maturation at these ages, namely: low delta, delta-theta, low alpha, high alpha, low beta and high beta. For most of these bands the maturation seems to occur later in anterior sites than posterior sites. Correlational analysis showed a lower pattern of correlation between different frequencies in children than in young adults, suggesting a certain asynchrony in the maturation of different rhythms. The topographical analysis revealed similar topographies of the different rhythms in children and young adults. Principal Component Analysis (PCA) demonstrated the same internal structure for the Electroencephalogram of both age groups. Principal Component Analysis allowed to separate four subcomponents in the alpha range. All these subcomponents peaked at a lower frequency in children than in young adults. CONCLUSIONS: The present approaches complement and solve some of the incertitudes when the classical brain broad rhythm analysis is applied. Children have a higher absolute power than young adults for frequency ranges between 0-20 Hz, the correlation of Power Spectrum (PS) with age and the variance age comparison showed that there are six ranges of frequencies that can distinguish the level of EEG maturation in children and adults. The establishment of maturational order of different frequencies and its possible maturational interdependence would require a complete series including all the different ages.     

Polymersomes, smaller than you think: ferrocene as a TEM probe to determine core structure

By incorporating ferrocene into the hydrophobic membrane of PEG-b-PCL polymersome nanoparticles it is possible to selectively visualize their core using Transmission Electron Microscopy (TEM). Two different sizes of ferrocene-loaded polymersomes with mean hydrodynamic diameters of approximately 40 and 90 nm were prepared. Image analysis of TEM pictures of these polymersomes found that the mean diameter of the core was 4–5 times smaller than the mean hydrodynamic diameter. The values obtained also allow the surface diameter and internal volume of the core to be calculated.     

A Short,Affordable, One-Pot Synthesis of a Camphor-Derived Amino Alcohol

The commercially available α-ketoxime of camphorquinone (1) was reduced to the corresponding exo,exo-amino alcohol (2) in a two-step, one-pot procedure using sodium borohydride and nickel(II) chloride hexahydrate.     

A New Reaction Involving the Formation of Unsaturated Carbenes

Treatment of 5,5-dialkyl-N-nitrosooxazolidones (1) with Lithium ethoxide (and other bases) under certain conditions yields reaction products the formation of which seems best explained by assuming that unsaturated carbenes [A] are involved.^3–5     

Assortative mixing in networks

A network is said to show assortative mixing if the nodes in the network that have many connections tend to be connected to other nodes with many connections. Here we measure mixing patterns in a variety of networks and find that social networks are mostly assortatively mixed, but that technological and biological networks tend to be disassortative. We propose a model of an assortatively mixed network, which we study both analytically and numerically. Within this model we find that networks percolate more easily if they are assortative and that they are also more robust to vertex removal.