What Makes Educational Campaings Succeed?

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Extensions and block decompositions for finite-dimensional representations of equivariant map algebras

Suppose a finite group acts on a scheme $X$ and a finite-dimensional Lie algebra $\mathfrak{g}$. The associated equivariant map algebra is the Lie algebra of equivariant regular maps from $X$ to $\mathfrak{g}$. The irreducible finite-dimensional representations of these algebras were classified in previous work with P. Senesi, where it was shown that they are all tensor products of evaluation representations and one-dimensional representations. In the current paper, we describe the extensions between irreducible finite-dimensional representations of an equivariant map algebra in the case that $X$ is an affine scheme of finite type and $\mathfrak{g}$ is reductive. This allows us to also describe explicitly the blocks of the category of finite-dimensional representations in terms of spectral characters, whose definition we extend to this general setting. Applying our results to the case of generalized current algebras (the case where the group acting is trivial), we recover known results but with very different proofs. For (twisted) loop algebras, we recover known results on block decompositions (again with very different proofs) and new explicit formulas for extensions. Finally, specializing our results to the case of (twisted) multiloop algebras and generalized Onsager algebras yields previously unknown results on both extensions and block decompositions.Comment: 41 pages; v2: minor corrections, formatting changed to match published versio

Ozone Depletion from Nearby Supernovae

Estimates made in the 1970's indicated that a supernova occurring within tens of parsecs of Earth could have significant effects on the ozone layer. Since that time, improved tools for detailed modeling of atmospheric chemistry have been developed to calculate ozone depletion, and advances have been made in theoretical modeling of supernovae and of the resultant gamma-ray spectra. In addition, one now has better knowledge of the occurrence rate of supernovae in the galaxy, and of the spatial distribution of progenitors to core-collapse supernovae. We report here the results of two-dimensional atmospheric model calculations that take as input the spectral energy distribution of a supernova, adopting various distances from Earth and various latitude impact angles. In separate simulations we calculate the ozone depletion due to both gamma-rays and cosmic rays. We find that for the combined ozone depletion roughly to double the ``biologically active'' UV flux received at the surface of the Earth, the supernova must occur at <8 pc. Based on the latest data, the time-averaged galactic rate of core-collapse supernovae occurring within 8 pc is ~1.5/Gyr. In comparing our calculated ozone depletions with those of previous studies, we find them to be significantly less severe than found by Ruderman (1974), and consistent with Whitten et al. (1976). In summary, given the amplitude of the effect, the rate of nearby supernovae, and the ~Gyr time scale for multicellular organisms on Earth, this particular pathway for mass extinctions may be less important than previously thought.Comment: 24 pages, 4 Postscript figures, to appear in The Astrophysical Journal, 2003 March 10, vol. 58

Development of Readout Interconnections for the Si-W Calorimeter of SiD

The SiD collaboration is developing a Si-W sampling electromagnetic calorimeter, with anticipated application for the International Linear Collider. Assembling the modules for such a detector will involve special bonding technologies for the interconnections, especially for attaching a silicon detector wafer to a flex cable readout bus. We review the interconnect technologies involved, including oxidation removal processes, pad surface preparation, solder ball selection and placement, and bond quality assurance. Our results show that solder ball bonding is a promising technique for the Si-W ECAL, and unresolved issues are being addressed.Comment: 8 pages + title, 6 figure

On the action potential as a propagating density pulse and the role of anesthetics

The Hodgkin-Huxley model of nerve pulse propagation relies on ion currents through specific resistors called ion channels. We discuss a number of classical thermodynamic findings on nerves that are not contained in this classical theory. Particularly striking is the finding of reversible heat changes, thickness and phase changes of the membrane during the action potential. Data on various nerves rather suggest that a reversible density pulse accompanies the action potential of nerves. Here, we attempted to explain these phenomena by propagating solitons that depend on the presence of cooperative phase transitions in the nerve membrane. These transitions are, however, strongly influenced by the presence of anesthetics. Therefore, the thermodynamic theory of nerve pulses suggests a explanation for the famous Meyer-Overton rule that states that the critical anesthetic dose is linearly related to the solubility of the drug in the membranes.Comment: 13 pages, 8 figure

Poisson transition rates from time-domain measurements with finite bandwidth

In time-domain measurements of a Poisson two-level system, the observed transition rates are always smaller than those of the actual system, a general consequence of finite measurement bandwidth in an experiment. This underestimation of the rates is significant even when the measurement and detection apparatus is ten times faster than the process under study. We derive here a quantitative form for this correction using a straightforward state-transition model that includes the detection apparatus, and provide a method for determining a system's actual transition rates from bandwidth-limited measurements. We support our results with computer simulations and experimental data from time-domain measurements of quasiparticle tunneling in a single-Cooper-pair transistor.Comment: 4 pages, 5 figure

Correctly validating results from single molecule data: the case of stretched exponential decay in the catalytic activity of single lipase B molecules

The question of how to validate and interpret correctly the waiting time probability density functions (WT-PDFs) from single molecule data is addressed. It is shown by simulation that when a stretched exponential WT-PDF, with a stretched exponent alfa and a time scale parameter tau, generates the off periods of a two-state trajectory, a reliable recovery of the input WT-PDF from the trajectory is obtained even when the bin size used to define the trajectory, dt, is much larger than the parameter tau. This holds true as long as the first moment of the WT-PDF is much larger than dt. Our results validate the results in an earlier study of the activity of single Lipase B molecules and disprove recent related critique

Correlation studies of open and closed states fluctuations in an ion channel: Analysis of ion current through a large conductance locust potassium channel

Ion current fluctuations occurring within open and closed states of large conductance locust potassium channel (BK channel) were investigated for the existence of correlation. Both time series, extracted from the ion current signal, were studied by the autocorrelation function (AFA) and the detrended fluctuation analysis (DFA) methods. The persistent character of the short- and middle-range correlations of time series is shown by the slow decay of the autocorrelation function. The DFA exponent $\alpha$ is significantly larger than 0.5. The existence of strongly-persistent long-range correlations was detected only for closed-states fluctuations, with $\alpha=0.98\pm0.02$. The long-range correlation of the BK channel action is therefore determined by the character of closed states. The main outcome of this study is that the memory effect is present not only between successive conducting states of the channel but also independently within the open and closed states themselves. As the ion current fluctuations give information about the dynamics of the channel protein, our results point to the correlated character of the protein movement regardless whether the channel is in its open or closed state.Comment: 12 pages, 5 figures; to be published in Phys. Rev.