Analytic measures and Bochner measurability

Let $\Sigma$ be a $\sigma$-algebra over $\Omega$, and let $M(\Sigma)$ denote the Banach space of complex measures. Consider a representation $T_t$ for $t\in\Bbb R$ acting on $M(\Sigma)$. We show that under certain, very weak hypotheses, that if for a given $\mu \in M(\Sigma)$ and all $A \in \Sigma$ the map $t \mapsto T_t \mu(A)$ is in $H^\infty(\Bbb R)$, then it follows that the map $t \mapsto T_t \mu$ is Bochner measurable. The proof is based upon the idea of the Analytic Radon Nikod\'ym Property. Straightforward applications yield a new and simpler proof of Forelli's main result concerning analytic measures ({\it Analytic and quasi-invariant measures}, Acta Math., {\bf 118} (1967), 33--59)

Synaptic Reorganization of Inhibitory Hilar Interneuron Circuitry After Traumatic Brain Injury in Mice

Functional plasticity of synaptic networks in the dentate gyrus has been implicated in the development of posttraumatic epilepsy and in cognitive dysfunction after traumatic brain injury, but little is known about potentially pathogenic changes in inhibitory circuits. We examined synaptic inhibition of dentate granule cells and excitability of surviving GABAergic hilar interneurons 8–13 weeks after cortical contusion brain injury in transgenic mice that express enhanced green fluorescent protein in a subpopulation of inhibitory neurons. Whole-cell voltage-clamp recordings in granule cells revealed a reduction in spontaneous and miniature IPSC frequency after head injury; no concurrent change in paired-pulse ratio was found in granule cells after paired electrical stimulation of the hilus. Despite reduced inhibitory input to granule cells, action potential and EPSC frequencies were increased in hilar GABA neurons from slices ipsilateral to the injury versus those from control or contralateral slices. Furthermore, increased excitatory synaptic activity was detected in hilar GABA neurons ipsilateral to the injury after glutamate photostimulation of either the granule cell or CA3 pyramidal cell layers. Together, these findings suggest that excitatory drive to surviving hilar GABA neurons is enhanced by convergent input from both pyramidal and granule cells, but synaptic inhibition of granule cells is not fully restored after injury. This rewiring of circuitry regulating hilar inhibitory neurons may reflect an important compensatory mechanism, but it may also contribute to network destabilization by increasing the relative impact of surviving individual interneurons in controlling granule cell excitability in the posttraumatic dentate gyrus

Observation of ferromagnetism above 900 K in Cr-GaN and Cr-AlN

We report the observation of ferromagnetism at over 900K in Cr-GaN and Cr-AlN thin films. The saturation magnetization moments in our best films of Cr-GaN and Cr-AlN at low temperatures are 0.42 and 0.6 u_B/Cr atom, respectively, indicating that 14% and 20%, of the Cr atoms, respectively, are magnetically active. While Cr-AlN is highly resistive, Cr-GaN exhibits thermally activated conduction that follows the exponential law expected for variable range hopping between localized states. Hall measurements on a Cr-GaN sample indicate a mobility of 0.06 cm^2/V.s, which falls in the range characteristic of hopping conduction, and a free carrier density (1.4E20/cm^3), which is similar in magnitude to the measured magnetically-active Cr concentration (4.9E19/cm^3). A large negative magnetoresistance is attributed to scattering from loose spins associated with non-ferromagnetic impurities. The results indicate that ferromagnetism in Cr-GaN and Cr-AlN can be attributed to the double exchange mechanism as a result of hopping between near-midgap substitutional Cr impurity bands.Comment: 14 pages, 4 figures, submitted to AP

Profiles

Short biographical sketches of Henry Whitcom Sweeney by A.N. Mosich, DR Scott by James R. Morton, John Bennett Canning by William Robert Smith, and F.R.M. de Paula by Stephen A. Zeff

Landscape as a Model: The Importance of Geometry

In all models, but especially in those used to predict uncertain processes (e.g., climate change and nonnative species establishment), it is important to identify and remove any sources of bias that may confound results. This is critical in models designed to help support decisionmaking. The geometry used to represent virtual landscapes in spatially explicit models is a potential source of bias. The majority of spatial models use regular square geometry, although regular hexagonal landscapes have also been used. However, there are other ways in which space can be represented in spatially explicit models. For the first time, we explicitly compare the range of alternative geometries available to the modeller, and present a mechanism by which uncertainty in the representation of landscapes can be incorporated. We test how geometry can affect cell-to-cell movement across homogeneous virtual landscapes and compare regular geometries with a suite of irregular mosaics. We show that regular geometries have the potential to systematically bias the direction and distance of movement, whereas even individual instances of landscapes with irregular geometry do not. We also examine how geometry can affect the gross representation of real-world landscapes, and again show that individual instances of regular geometries will always create qualitative and quantitative errors. These can be reduced by the use of multiple randomized instances, though this still creates scale-dependent biases. In contrast, virtual landscapes formed using irregular geometries can represent complex real-world landscapes without error. We found that the potential for bias caused by regular geometries can be effectively eliminated by subdividing virtual landscapes using irregular geometry. The use of irregular geometry appears to offer spatial modellers other potential advantages, which are as yet underdeveloped. We recommend their use in all spatially explicit models, but especially for predictive models that are used in decisionmaking