Stable subnorms revisited

Let A be a finite-dimensional, power-associative algebra over a field F, either R or C, and let S, a subset of A, be closed under scalar multiplication. A real-valued function f defined on S, shall be called a subnorm if f(a) > 0 for all 0 not equal a is an element of S, and f(alpha a) = |alpha| f(a) for all a is an element of S and alpha is an element of F. If in addition, S is closed under raising to powers, then a subnorm f shall be called stable if there exists a constant sigma > 0 so that f(a(m)) less than or equal to sigma f(a)(m) for all a is an element of S and m = 1, 2, 3.... The purpose of this paper is to provide an updated account of our study of stable subnorms on subsets of finite-dimensional, power-associative algebras over F. Our goal is to review and extend several of our results in two previous papers, dealing mostly with continuous subnorms on closed sets

A modeling analysis program for the JPL Table Mountain Io sodium cloud data

Progress and achievements in the second year are discussed in three main areas: (1) data quality review of the 1981 Region B/C images; (2) data processing activities; and (3) modeling activities. The data quality review revealed that almost all 1981 Region B/C images are of sufficient quality to be valuable in the analyses of the JPL data set. In the second area, the major milestone reached was the successful development and application of complex image-processing software required to render the original image data suitable for modeling analysis studies. In the third area, the lifetime description of sodium atoms in the planet magnetosphere was improved in the model to include the offset dipole nature of the magnetic field as well as an east-west electric field. These improvements are important in properly representing the basic morphology as well as the east-west asymmetries of the sodium cloud

A modeling analysis program for the JPL table mountain Io sodium cloud

Progress and achievements in the first year are discussed in three main areas: (1) review and assessment of the massive JPL Table Mountain Io sodium cloud data set, (2) formulation and execution of a plan to perform further processing of this data set, and (3) initiation of modeling activities. The complete 1976-79 and 1981 data sets are reviewed. Particular emphasis is placed on the superior 1981 Region B/C images which provide a rich base of information for studying the structure and escape of gases from Io as well as possible east-west and magnetic longitudinal asymmetries in the plasma torus. A data processing plan is developed and is undertaken by the Multimission Image Processing Laboratory of JPL for the purpose of providing a more refined and complete data set for our modeling studies in the second year. Modeling priorities are formulated and initial progress in achieving these goals is reported

A modeling analysis program for the JPL table mountain Io sodium cloud

A data quality review for the entire set of the 1981 Region B/C images has been completed and is presented. The review indicates that almost all images are of sufficient quality to be valuable in our analysis of this data set. Five data-correlation studies for the same data set have also been completed and are useful in classifying and studying the sodium cloud morphology and its interactions with solar radiation pressure and the plasma torus. Additional progress in developing new image processing techniques and in improving the Io sodium cloud model is also discussed

A modeling analysis program for the JPL Table Mountain Io sodium cloud data

The abundant Io sodium cloud data obtained at JPL Table Mountain was reviewed. Images of the sodium cloud important to this modeling analysis program are contained in the 1976-1979 data set and the 1981 data set. A preliminary assessment of the 263 images in the 1981 data set for Region B/C was initiated. The spatial morphology of some of these images revealed the presence of the forward sodium cloud (Region B) and the directional features (Region C) as expected. Plans for the second quarter to initiate preliminary modeling analysis and to define further data processing are discussed

Constructing computer virus phylogenies

There has been much recent algorithmic work on the problem of reconstructing the evolutionary history of biological species. Computer virus specialists are interested in finding the evolutionary history of computer viruses - a virus is often written using code fragments from one or more other viruses, which are its immediate ancestors. A phylogeny for a collection of computer viruses is a directed acyclic graph whose nodes are the viruses and whose edges map ancestors to descendants and satisfy the property that each code fragment is "invented" only once. To provide a simple explanation for the data, we consider the problem of constructing such a phylogeny with a minimum number of edges. In general this optimization problem is NP-complete; some associated approximation problems are also hard, but others are easy. When tree solutions exist, they can be constructed and randomly sampled in polynomial time

General relativity on a null surface: Hamiltonian formulation in the teleparallel geometry

The Hamiltonian formulation of general relativity on a null surface is established in the teleparallel geometry. No particular gauge conditons on the tetrads are imposed, such as the time gauge condition. By means of a 3+1 decomposition the resulting Hamiltonian arises as a completely constrained system. However, it is structurally different from the the standard Arnowitt-Deser-Misner (ADM) type formulation. In this geometrical framework the basic field quantities are tetrads that transform under the global SO(3,1) and the torsion tensor.Comment: 15 pages, Latex, no figures, to appear in the Gen. Rel. Gra

Community detection in complex networks using Extremal Optimization

We propose a novel method to find the community structure in complex networks based on an extremal optimization of the value of modularity. The method outperforms the optimal modularity found by the existing algorithms in the literature. We present the results of the algorithm for computer simulated and real networks and compare them with other approaches. The efficiency and accuracy of the method make it feasible to be used for the accurate identification of community structure in large complex networks.Comment: 4 pages, 4 figure

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

Reionization Revisited: Secondary CMB Anisotropies and Polarization

Secondary CMB anisotropies and polarization provide a laboratory to study structure formation in the reionized epoch. We consider the kinetic Sunyaev-Zel'dovich effect from mildly nonlinear large-scale structure and show that it is a natural extension of the perturbative Vishniac effect. If the gas traces the dark matter to overdensities of order 10, as expected from simulations, this effect is at least comparable to the Vishniac effect at arcminute scales. On smaller scales, it may be used to study the thermal history-dependent clustering of the gas. Polarization is generated through Thomson scattering of primordial quadrupole anisotropies, kinetic (second order Doppler) quadrupole anisotropies and intrinsic scattering quadrupole anisotropies. Small scale polarization results from the density and ionization modulation of these sources. These effects generically produce comparable E and B-parity polarization, but of negligible amplitude (0.001-0.01 uK) in adiabatic CDM models. However, the primordial and kinetic quadrupoles are observationally comparable today so that a null detection of B-polarization would set constraints on the evolution and coherence of the velocity field. Conversely, a detection of a cosmological B-polarization even at large angles does not necessarily imply the presence of gravity waves or vorticity. For these calculations, we develop an all-sky generalization of the Limber equation that allows for an arbitrary local angular dependence of the source for both scalar and symmetric trace-free tensor fields on the sky.Comment: 14 pages, 12 figures, minor changes and typo fixes reflect published versio