Exact Nonperturbative Unitary Amplitudes for 1->N Transitions

I present an extension to arbitrary N of a previously proposed field theoretic model, in which unitary amplitudes for $1->8$ processes were obtained. The Born amplitude in this extension has the behavior $A(1->N)^{tree}\ =\ g^{N-1}\ N!$ expected in a bosonic field theory. Unitarity is violated when $|A(1->N)|>1$, or when $N>\N_crit\simeq e/g.$ Numerical solutions of the coupled Schr\"odinger equations shows that for weak coupling and a large range of N>\ncrit, the exact unitary amplitude is reasonably fit by a factorized expression |A(1->N)| \sim (0.73 /N) \cdot \exp{(-0.025/\g2)}. The very small size of the coefficient 1/\g2 , indicative of a very weak exponential suppression, is not in accord with standard discussions based on saddle point analysis, which give a coefficient $\sim 1.\$ The weak dependence on $N$ could have experimental implications in theories where the exponential suppression is weak (as in this model). Non-perturbative contributions to few-point correlation functions in this theory would arise at order $K\ \simeq\ \left((0.05/\g2)+ 2\ ln{N}\right)/ \ ln{(1/\g2)}$in an expansion in powers of$\g2.$Comment: 11 pages, 3 figures (not included

Richards' Transformation and Positive Real Functions

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/113745/1/sapm1962411191.pd

Particle Physics on Ice: Constraints on Neutrino Interactions Far Above the Weak Scale

Ultra-high energy cosmic rays and neutrinos probe energies far above the weak scale. Their usefulness might appear to be limited by astrophysical uncertainties; however, by simultaneously considering up- and down-going events, one may disentangle particle physics from astrophysics. We show that present data from the AMANDA experiment in the South Pole ice already imply an upper bound on neutrino cross sections at energy scales that will likely never be probed at man-made accelerators. The existing data also place an upper limit on the neutrino flux valid for any neutrino cross section. In the future, similar analyses of IceCube data will constrain neutrino properties and fluxes at the O(10%) level.Comment: 4 pages, 1 figure, published versio

Atmospheric X-ray emission experiment for shuttle

An experiment designed to measure the spatial, temporal, and energy distribution of X-ray aurorae produced by precipitating electrons, is presented. The experiment will provide vital data on solar-terrestrial relationships that may lead to defining the transfer mechanism that causes certain terrestrial weather events and climatological behavior. An instrument concept is discussed, and is based on a spatially sensitive multiwire proportional counter, combined with collimators to produce X-ray images of the aurorae. An instrument pointing system, on which the counter can be mounted, will provide the required altitude control, and can be operated by a Spacelab payload specialist for full control over its observing and data taking modes

Properties of Nucleon Resonances by means of a Genetic Algorithm

We present an optimization scheme that employs a Genetic Algorithm (GA) to determine the properties of low-lying nucleon excitations within a realistic photo-pion production model based upon an effective Lagrangian. We show that with this modern optimization technique it is possible to reliably assess the parameters of the resonances and the associated error bars as well as to identify weaknesses in the models. To illustrate the problems the optimization process may encounter, we provide results obtained for the nucleon resonances $\Delta$(1230) and $\Delta$(1700). The former can be easily isolated and thus has been studied in depth, while the latter is not as well known experimentally.Comment: 12 pages, 10 figures, 3 tables. Minor correction

Improved sampling of the pareto-front in multiobjective genetic optimizations by steady-state evolution: a Pareto converging genetic algorithm

Previous work on multiobjective genetic algorithms has been focused on preventing genetic drift and the issue of convergence has been given little attention. In this paper, we present a simple steady-state strategy, Pareto Converging Genetic Algorithm (PCGA), which naturally samples the solution space and ensures population advancement towards the Pareto-front. PCGA eliminates the need for sharing/niching and thus minimizes heuristically chosen parameters and procedures. A systematic approach based on histograms of rank is introduced for assessing convergence to the Pareto-front, which, by definition, is unknown in most real search problems. We argue that there is always a certain inheritance of genetic material belonging to a population, and there is unlikely to be any significant gain beyond some point; a stopping criterion where terminating the computation is suggested. For further encouraging diversity and competition, a nonmigrating island model may optionally be used; this approach is particularly suited to many difficult (real-world) problems, which have a tendency to get stuck at (unknown) local minima. Results on three benchmark problems are presented and compared with those of earlier approaches. PCGA is found to produce diverse sampling of the Pareto-front without niching and with significantly less computational effort

Unfair competition governs the interaction of pCPI-17 with myosin phosphatase (PP1-MYPT1).

The small phosphoprotein pCPI-17 inhibits myosin light-chain phosphatase (MLCP). Current models postulate that during muscle relaxation, phosphatases other than MLCP dephosphorylate and inactivate pCPI-17 to restore MLCP activity. We show here that such hypotheses are insufficient to account for the observed rapidity of pCPI-17 inactivation in mammalian smooth muscles. Instead, MLCP itself is the critical enzyme for pCPI-17 dephosphorylation. We call the mutual sequestration mechanism through which pCPI-17 and MLCP interact inhibition by unfair competition: MLCP protects pCPI-17 from other phosphatases, while pCPI-17 blocks other substrates from MLCP\u27s active site. MLCP dephosphorylates pCPI-17 at a slow rate that is, nonetheless, both sufficient and necessary to explain the speed of pCPI-17 dephosphorylation and the consequent MLCP activation during muscle relaxation

The Inverse Shapley Value Problem

For $f$ a weighted voting scheme used by $n$ voters to choose between two candidates, the $n$ \emph{Shapley-Shubik Indices} (or {\em Shapley values}) of $f$ provide a measure of how much control each voter can exert over the overall outcome of the vote. Shapley-Shubik indices were introduced by Lloyd Shapley and Martin Shubik in 1954 \cite{SS54} and are widely studied in social choice theory as a measure of the "influence" of voters. The \emph{Inverse Shapley Value Problem} is the problem of designing a weighted voting scheme which (approximately) achieves a desired input vector of values for the Shapley-Shubik indices. Despite much interest in this problem no provably correct and efficient algorithm was known prior to our work. We give the first efficient algorithm with provable performance guarantees for the Inverse Shapley Value Problem. For any constant \eps > 0 our algorithm runs in fixed poly$(n)$ time (the degree of the polynomial is independent of \eps) and has the following performance guarantee: given as input a vector of desired Shapley values, if any "reasonable" weighted voting scheme (roughly, one in which the threshold is not too skewed) approximately matches the desired vector of values to within some small error, then our algorithm explicitly outputs a weighted voting scheme that achieves this vector of Shapley values to within error \eps. If there is a "reasonable" voting scheme in which all voting weights are integers at most \poly(n) that approximately achieves the desired Shapley values, then our algorithm runs in time \poly(n) and outputs a weighted voting scheme that achieves the target vector of Shapley values to within error $\eps=n^{-1/8}.

Statistics of Oscillator Strengths in Chaotic Systems

The statistical description of oscillator strengths for systems like hydrogen in a magnetic field is developed by using the supermatrix nonlinear $\sigma$-model. The correlator of oscillator strengths is found to have a universal parametric and frequency dependence, and its analytical expression is given. This universal expression applies to quantum chaotic systems with the same generality as Wigner-Dyson statistics.Comment: 11 pages, REVTeX3+epsf, two EPS figures. Replaced by the published version. Minor changes