Enumeration of coloured plane trees with a given type partition

Tutte's result for the number of planted plane trees with a given degree partition is rederived by a variety of methods and in particular by a simple piecewise construction technique. A theorem of Gordon and Temple is applied in order to give a general relationship between the number of planted plane trees and the number of rooted plane trees and the degree partition restriction is generalised to type partition. The piecewise construction method is successfully used to derive the number of planted plane trees with a given 2-colour degree partition, also derived by Tutte, and an algorithm for the k-coloured case is developed. This algorithm may be used to obtain more specific results. These models are relevant to the statistical mechanics of polymers and this is discussed briefly.     

Determination of the α parameter for the decay Ξ− → Λπ−

The α parameter for Ξ^? → Λπ^? decay has been determined to be α_Ξ^?=?0.462 ± 0.015, from a sample of 1.5 × 10⁵ events recorded in the CERN SPS hyperon beam. This value is 2.5 standard deviations higher than the current world average.     

Dysregulation of Na+/K+ ATPase by amyloid in APP+PS1 transgenic mice

Background  

The pathology of Alzheimer's disease (AD) is comprised of extracellular amyloid plaques, intracellular tau tangles, dystrophic neurites and neurodegeneration. The mechanisms by which these various pathological features arise are under intense investigation. Here, expanding upon pilot gene expression studies, we have further analyzed the relationship between Na+/K+ ATPase and amyloid using APP+PS1 transgenic mice, a model that develops amyloid plaques and memory deficits in the absence of tangle formation and neuronal or synaptic loss.     

Critical behavior of light in mode-locked lasers

Light is shown to exhibit critical and tricritical behavior in passively mode-locked lasers with externally injected pulses. It is a first and unique example of critical phenomena in a one-dimensional many-body light-mode system. The phase diagrams consist of regimes with continuous wave, driven parapulses, spontaneous pulses via mode condensation, and heterogeneous pulses, separated by phase transition lines that terminate with critical or tricritical points. Enhanced non-Gaussian fluctuations and collective dynamics are present at the critical and tricritical points, showing a mode system analog of the critical opalescence phenomenon. The critical exponents are calculated and shown to comply with the mean field theory, which is rigorous in the light system.     

Limit on the electron electric dipole moment in gadolinium-iron garnet

A new method for the detection of the electron electric dipole moment (EDM) using a solid is described. The method involves the measurement of a voltage induced across the solid by the alignment of the sample's magnetic dipoles in an applied magnetic field, H. A first application of the method to GdIG has resulted in a limit on the electron EDM of 5 x 10(-24)e cm, which is a factor of 40 below the limit obtained from the only previous solid-state EDM experiment. The result is limited by the imperfect discrimination of an unexpectedly large voltage that is even upon the reversal of the sample magnetization.     

A new direction in carbon-rich organometallic wires: diruthenium compounds bridged by E-hex-3-ene-1,5-diyn-diyl

New organometallic wires were obtained from two diruthenium units bridged by E-hex-3-ene-1,5-diyn-dyl.     

Micromachined array tip for multifocus fiber-based optical coherence tomography

High-resolution optical coherence tomography demands a large detector bandwidth and a high numerical aperture for real-time imaging, which is difficult to achieve over a large imaging depth. To resolve these conflicting requirements we propose a novel multifocus fiber-based optical coherence tomography system with a micromachined array tip. We demonstrate the fabrication of a prototype four-channel tip that maintains a 9-14-microm spot diameter with more than 500 microm of imaging depth. Images of a resolution target and a human tooth were obtained with this tip by use of a four-channel cascaded Michelson fiber-optic interferometer, scanned simultaneously at 8 kHz with geometric power distribution across the four channels.