Symmetrization in Geometry

The concept of an $i$-symmetrization is introduced, which provides a convenient framework for most of the familiar symmetrization processes on convex sets. Various properties of $i$-symmetrizations are introduced and the relations between them investigated. New expressions are provided for the Steiner and Minkowski symmetrals of a compact convex set which exhibit a dual relationship between them. Characterizations of Steiner, Minkowski and central symmetrization, in terms of natural properties that they enjoy, are given and examples are provided to show that none of the assumptions made can be dropped or significantly weakened. Other familiar symmetrizations, such as Schwarz symmetrization, are discussed and several new ones introduced.Comment: A chacterization of central symmetrization has been added and several typos have been corrected. This version has been accepted for publication on Advances in Mathematic

Evaluation of AIS Data for Agronomic and Rangeland Vegetation: Preliminary Results for August 1984 Flight over Nebraska Sandhills Agricultural Laboratory

Since 1978 scientists from the Center for Agricultural Meteorology and Climatology at the University of Nebraska have been conducting research at the Sandhills Agricultural Laboratory on the effects of water stress on crop growth, development and yield using remote sensing techniques. We have been working to develop techniques, both remote and ground-based, to monitor water stress, phenological development, leaf area, phytomass production and grain yields of corn, soybeans and sorghum. Because of the sandy soils and relatively low rainfall at the site it is an excellent location to study water stress without the necessity of installing expensive rainout shelters. The primary objectives of research with the airborne imaging spectrometer (AIS) data collected during an August 1984 flight over the Sandhills Agricultural Laboratory are to evaluate the potential of using AIS to: (1) discriminate crop type; (2) to detect subtle architectural differences that exist among different cultivars or hybrids of agronomic crops; (3) to detect and quantify, if possible, the level of water stress imposed on the crops; and (4) to evaluate leaf area and biomass differences for different crops

Absence of anomalous negative lattice-expansion for polycrystalline sample of Tb2Ti2O7

High resolution X-ray powder-diffraction experiments on a well-characterized polycrystalline sample of the spin liquid Tb2Ti2O7 reveal that it shows normal positive thermal-expansion above 4 K, which does not agree with the intriguing anomalous negative thermal-expansion due to a magneto-elastic coupling reported for a single crystal sample below 20 K. We also performed a Rietveld profile refinement of a powder-diffraction pattern taken at a room temperature, and confirmed that it is consistent with the fully ordered cubic pyrochlore structure.Comment: 2 pages, 3 figure

Design specification for LARSYS procedure 1

There are no author-identified significant results in this report

A polynomial training algorithm for calculating perceptrons of optimal stability

Recomi (REpeated COrrelation Matrix Inversion) is a polynomially fast algorithm for searching optimally stable solutions of the perceptron learning problem. For random unbiased and biased patterns it is shown that the algorithm is able to find optimal solutions, if any exist, in at worst O(N^4) floating point operations. Even beyond the critical storage capacity alpha_c the algorithm is able to find locally stable solutions (with negative stability) at the same speed. There are no divergent time scales in the learning process. A full proof of convergence cannot yet be given, only major constituents of a proof are shown.Comment: 11 pages, Latex, 4 EPS figure

Kinematic Evolution of Simulated Star-Forming Galaxies

Recent observations have shown that star-forming galaxies like our own Milky Way evolve kinematically into ordered thin disks over the last ~8 billion years since z=1.2, undergoing a process of "disk settling." For the first time, we study the kinematic evolution of a suite of four state of the art "zoom in" hydrodynamic simulations of galaxy formation and evolution in a fully cosmological context and compare with these observations. Until now, robust measurements of the internal kinematics of simulated galaxies were lacking as the simulations suffered from low resolution, overproduction of stars, and overly massive bulges. The current generation of simulations has made great progress in overcoming these difficulties and is ready for a kinematic analysis. We show that simulated galaxies follow the same kinematic trends as real galaxies: they progressively decrease in disordered motions (sigma_g) and increase in ordered rotation (Vrot) with time. The slopes of the relations between both sigma_g and Vrot with redshift are consistent between the simulations and the observations. In addition, the morphologies of the simulated galaxies become less disturbed with time, also consistent with observations, and they both have similarly large scatter. This match between the simulated and observed trends is a significant success for the current generation of simulations, and a first step in determining the physical processes behind disk settling.Comment: ApJ accepted; 6 pages; A pdf with full resolution figures can be found at https://db.tt/8y4Vzaff (2.8M

Stability of the replica symmetric solution for the information conveyed by by a neural network

The information that a pattern of firing in the output layer of a feedforward network of threshold-linear neurons conveys about the network's inputs is considered. A replica-symmetric solution is found to be stable for all but small amounts of noise. The region of instability depends on the contribution of the threshold and the sparseness: for distributed pattern distributions, the unstable region extends to higher noise variances than for very sparse distributions, for which it is almost nonexistant.Comment: 19 pages, LaTeX, 5 figures. Also available at http://www.mrc-bbc.ox.ac.uk/~schultz/papers.html . Submitted to Phys. Rev. E Minor change