A special form of a generalized inverse of an arbitrary complex matrix

Equations for inversion of singular matrix - special form of generalized inverse of arbitrary complex matri

Accumulation and Dynamics of Petrogenic PAHs on Leaves of Black Mangrove (Avicennia germinans)

Crude oil from Deepwater Horizon Macondo oil spill is currently present in Louisiana coastal surface sediments and its effects on the coastal ecosystem are still being realized. Deposition of 2- and 3-ring PAHs (alkylated naphthalenes and phenanthrenes) on the exterior of Spartina alterniflora and Avicennia germinans leaves have been demonstrated in marshes impacted by Macondo spill. Whether these deposition events result from contaminated tidal water or volatilization followed by deposition onto the leaf surface has not been conclusively established. Measurements of PAH deposition on the leaf surface of black mangrove (Avicennia germinans) can provide important evidence of the mechanism of deposition since these plants are rarely submerged by tidal water. Study objectives were to quantify and observe the uptake mechanisms of PAH accumulation as a function of time, leaf age, and leaf fraction in mangrove leaves from a heavily oiled site at Bay Jimmy marsh in Barataria Basin, LA. PAHs did not accumulate over time or leaf age indicating diffusion and equilibrium processes dominated and occurred quickly. PAHs accumulated in the inner tissue of the leaf posing a potential for long-term internal cycling of PAHs in a sediment-vegetation-biota system. Semipermeable membrane devices (SPMDs) were utilized in air and marsh surface in the field as a simple analogue to investigate the transfer process. Higher correlations between leaves and SPMDs were observed for C1-naphthalenes than the other PAHs studied. The plant – air partitioning coefficient (KPA) for various PAHs in field contaminated mangrove leaves was quantified using an experimental partitioning apparatus and compared to respective KPA values calculated for Spartina alterniflora. All KPA coefficients were well below 8 which supports the dominant uptake process of air phase PAHs is equilibrium partitioning between the vegetation and the gas phase

On the variational equations for Householder transformations in feature selection

Results that suggest the possibility of using a sequential monotone process for solving the feature selection problem using Householder transformations are applied to the divergence separability criterion and an expression for the gradient of the divergence with respect to the generator of a single Householder transformation will be developed. This expression for the gradient is used in any number of differential correction schemes (iterators) that attempt to extremize the divergence. Data sets provided by the Earth Observations Division-JSC are used to demonstrate selecting the Householder transformations that generate the kxn matrix defining the best (in the sense of extremizing the divergence) k linear combinations of features. The tests allow initial comparisons to be made with results. In particular, this technique does not appear to require initial guesses for the iterator to be generated without replacement, exhaustive search, or other similar schemes

Feature combinations and the divergence criterion

Classifying large quantities of multidimensional remotely sensed agricultural data requires efficient and effective classification techniques and the construction of certain transformations of a dimension reducing, information preserving nature. The construction of transformations that minimally degrade information (i.e., class separability) is described. Linear dimension reducing transformations for multivariate normal populations are presented. Information content is measured by divergence

Feature combinations and the Bhattacharyya criterion

A procedure for calculating a kxn rank k matrix B for data compression using the Bhattacharyya bound on the probability of error and an iterative construction using Householder transformation was developed. Two sets of remotely sensed agricultural data are used to demonstrate the application of the procedure. The results of the applications gave some indication of the extent to which the Bhattacharyya bound on the probability of error is affected by such transformations for multivariate normal populations

Householder transformations and optimal linear combinations

Several theorems related to the Householder transformation and separability criteria are proven. Orthogonal transformations, topology, divergence, mathematical matrices, and group theory are discussed

Linear feature selection with applications

There are no author-identified significant results in this report

Image 100 procedures manual development: Applications system library definition and Image 100 software definition

An outline for an Image 100 procedures manual for Earth Resources Program image analysis was developed which sets forth guidelines that provide a basis for the preparation and updating of an Image 100 Procedures Manual. The scope of the outline was limited to definition of general features of a procedures manual together with special features of an interactive system. Computer programs were identified which should be implemented as part of an applications oriented library for the system

Characterizations of linear sufficient statistics

A surjective bounded linear operator T from a Banach space X to a Banach space Y must be a sufficient statistic for a dominated family of probability measures defined on the Borel sets of X. These results were applied, so that they characterize linear sufficient statistics for families of the exponential type, including as special cases the Wishart and multivariate normal distributions. The latter result was used to establish precisely which procedures for sampling from a normal population had the property that the sample mean was a sufficient statistic