NASA SBIR abstracts of 1991 phase 1 projects

The objectives of 301 projects placed under contract by the Small Business Innovation Research (SBIR) program of the National Aeronautics and Space Administration (NASA) are described. These projects were selected competitively from among proposals submitted to NASA in response to the 1991 SBIR Program Solicitation. The basic document consists of edited, non-proprietary abstracts of the winning proposals submitted by small businesses. The abstracts are presented under the 15 technical topics within which Phase 1 proposals were solicited. Each project was assigned a sequential identifying number from 001 to 301, in order of its appearance in the body of the report. Appendixes to provide additional information about the SBIR program and permit cross-reference of the 1991 Phase 1 projects by company name, location by state, principal investigator, NASA Field Center responsible for management of each project, and NASA contract number are included

NASA SBIR abstracts of 1990 phase 1 projects

The research objectives of the 280 projects placed under contract in the National Aeronautics and Space Administration (NASA) 1990 Small Business Innovation Research (SBIR) Phase 1 program are described. The basic document consists of edited, non-proprietary abstracts of the winning proposals submitted by small businesses in response to NASA's 1990 SBIR Phase 1 Program Solicitation. The abstracts are presented under the 15 technical topics within which Phase 1 proposals were solicited. Each project was assigned a sequential identifying number from 001 to 280, in order of its appearance in the body of the report. The document also includes Appendixes to provide additional information about the SBIR program and permit cross-reference in the 1990 Phase 1 projects by company name, location by state, principal investigator, NASA field center responsible for management of each project, and NASA contract number

Do Community-Level Models Account for the Effects of Biotic Interactions? A Comparison of Community-Level and Species Distribution Modeling of Rocky Mountain Conifers

Community-level models (CLMs) aim to improve species distribution modeling (SDM) methods by attempting to explicitly incorporate the influences of interacting species. However, the ability of CLMs to appropriately account for biotic interactions is unclear. We applied CLM and SDM methods to predict the distributions of three dominant conifer tree species in the U.S. Rocky Mountains and compared CLM and SDM predictive accuracy as well as the ability of each approach to accurately reproduce species co-occurrence patterns. We specifically evaluated the performance of two statistical algorithms, MARS and CForest, within both CLM and SDM frameworks. Across all species, differences in SDM and CLM predictive accuracy were slight and can be attributed to differences in model structure rather than accounting for the effects of biotic interactions. In addition, CLMs generally over-predicted species cooccurrence, while SDMs under-predicted cooccurrence. Our results demonstrate no real improvement in the ability of CLMs to account for biotic interactions relative to SDMs. We conclude that alternative modeling approaches are needed in order to accurately account for the effects of biotic interactions on species distributions

Flora and Fauna in East Asian Art

Flora and Fauna in East Asian Art is the fourth annual exhibition curated by students enrolled in the Art History Methods course. This exhibition highlights the academic achievements of six student curators: Samantha Frisoli ’18, Daniella Snyder ’18, Gabriella Bucci ’19, Melissa Casale ’19, Keira Koch ’19, and Paige Deschapelles ’20. The selection of artworks in this exhibition considers how East Asian artists portrayed similar subjects of flora and fauna in different media including painting, prints, embroidery, jade, and porcelain. This exhibition intends to reveal the hidden meanings behind various representations of flora and fauna in East Asian art by examining the iconography, cultural context, aesthetic and function of each object.https://cupola.gettysburg.edu/artcatalogs/1025/thumbnail.jp

Phase diagram and aggregation dynamics of a monolayer of paramagnetic colloids

We have developed a tunable colloidal system and a corresponding simulation model for studying the phase behavior of particles assembling under the influence of long-range magnetic interactions. A monolayer of paramagnetic particles is subjected to a spatially uniform magnetic field with a static perpendicular component and rapidly rotating in-plane component. The sign and strength of the interactions vary with the tilt angle $\theta$ of the rotating magnetic field. For a purely in-plane field, $\theta=90^{\circ}$, interactions are attractive and the experimental results agree well with both equilibrium and out-of-equilibrium predictions based on a two-body interaction model. For tilt angles $50^{\circ}\lesssim \theta\lesssim 55^{\circ}$, the two-body interaction gives a short-range attractive and long-range repulsive (SALR) interaction, which predicts the formation of equilibrium microphases. In experiments, however, a different type of assembly is observed. Inclusion of three-body (and higher-order) terms in the model does not resolve the discrepancy. We thus further characterize the anomalous behavior by measuring the time-dependent cluster size distribution.Comment: 12 pages, 8 figure

The NASA SBIR product catalog

The purpose of this catalog is to assist small business firms in making the community aware of products emerging from their efforts in the Small Business Innovation Research (SBIR) program. It contains descriptions of some products that have advanced into Phase 3 and others that are identified as prospective products. Both lists of products in this catalog are based on information supplied by NASA SBIR contractors in responding to an invitation to be represented in this document. Generally, all products suggested by the small firms were included in order to meet the goals of information exchange for SBIR results. Of the 444 SBIR contractors NASA queried, 137 provided information on 219 products. The catalog presents the product information in the technology areas listed in the table of contents. Within each area, the products are listed in alphabetical order by product name and are given identifying numbers. Also included is an alphabetical listing of the companies that have products described. This listing cross-references the product list and provides information on the business activity of each firm. In addition, there are three indexes: one a list of firms by states, one that lists the products according to NASA Centers that managed the SBIR projects, and one that lists the products by the relevant Technical Topics utilized in NASA's annual program solicitation under which each SBIR project was selected

Dimension Reduction via Colour Refinement

Colour refinement is a basic algorithmic routine for graph isomorphism testing, appearing as a subroutine in almost all practical isomorphism solvers. It partitions the vertices of a graph into "colour classes" in such a way that all vertices in the same colour class have the same number of neighbours in every colour class. Tinhofer (Disc. App. Math., 1991), Ramana, Scheinerman, and Ullman (Disc. Math., 1994) and Godsil (Lin. Alg. and its App., 1997) established a tight correspondence between colour refinement and fractional isomorphisms of graphs, which are solutions to the LP relaxation of a natural ILP formulation of graph isomorphism. We introduce a version of colour refinement for matrices and extend existing quasilinear algorithms for computing the colour classes. Then we generalise the correspondence between colour refinement and fractional automorphisms and develop a theory of fractional automorphisms and isomorphisms of matrices. We apply our results to reduce the dimensions of systems of linear equations and linear programs. Specifically, we show that any given LP L can efficiently be transformed into a (potentially) smaller LP L' whose number of variables and constraints is the number of colour classes of the colour refinement algorithm, applied to a matrix associated with the LP. The transformation is such that we can easily (by a linear mapping) map both feasible and optimal solutions back and forth between the two LPs. We demonstrate empirically that colour refinement can indeed greatly reduce the cost of solving linear programs

Bounds on changes in Ritz values for a perturbed invariant subspace of a Hermitian matrix

The Rayleigh-Ritz method is widely used for eigenvalue approximation. Given a matrix $X$ with columns that form an orthonormal basis for a subspace \X, and a Hermitian matrix $A$, the eigenvalues of $X^HAX$ are called Ritz values of $A$ with respect to \X. If the subspace \X is $A$-invariant then the Ritz values are some of the eigenvalues of $A$. If the $A$-invariant subspace \X is perturbed to give rise to another subspace \Y, then the vector of absolute values of changes in Ritz values of $A$ represents the absolute eigenvalue approximation error using \Y. We bound the error in terms of principal angles between \X and \Y. We capitalize on ideas from a recent paper [DOI: 10.1137/060649070] by A. Knyazev and M. Argentati, where the vector of absolute values of differences between Ritz values for subspaces \X and \Y was weakly (sub-)majorized by a constant times the sine of the vector of principal angles between \X and \Y, the constant being the spread of the spectrum of $A$. In that result no assumption was made on either subspace being $A$-invariant. It was conjectured there that if one of the trial subspaces is $A$-invariant then an analogous weak majorization bound should only involve terms of the order of sine squared. Here we confirm this conjecture. Specifically we prove that the absolute eigenvalue error is weakly majorized by a constant times the sine squared of the vector of principal angles between the subspaces \X and \Y, where the constant is proportional to the spread of the spectrum of $A$. For many practical cases we show that the proportionality factor is simply one, and that this bound is sharp. For the general case we can only prove the result with a slightly larger constant, which we believe is artificial.Comment: 12 pages. Accepted to SIAM Journal on Matrix Analysis and Applications (SIMAX