Spot Form of Net Blotch Resistance in a Diverse Set of Barley Lines in Australia and Canada.

The responses of 95 barley lines and cultivars to spot form of net blotch (SFNB) caused by Pyrenophora teres f. maculata were analyzed as seedlings and adults in Australia and Canada. Cluster analyses revealed complex reaction responses. Only 2 lines (Esperance Orge 289 and TR3189) were resistant to all isolates at the seedling stage, whereas 15 lines and cultivars (81-82/033, Arimont, BYDV-018, CBSS97M00855T-B2-M1-Y1-M2-Y-1M-0Y, C19776, Keel, Sloop, Torrens, TR326, VB0111, Yarra, VB0229, WI-2477, WI2553, and Wisconsin Pedigree) were resistant toward the two Canadian isolates and mixture of Australian isolates at the adult stages. In Australian field experiments, the effectiveness of SFNB resistance in three barley cultivars (Barque. Cowabbie, and Schooner) and one breeding line (VB9104) with a different source of resistance was tested. Barque, which possessed a resistance gene that provided complete resistance to SFNB, was the most effective and showed no effect on grain yield or quality in the presence of inoculum. Generally, cultivars with seedling or adult resistance had less disease and better grain quality than the susceptible control. Dash, but they were not as effective as Barque. A preliminary differential set of 19 barley lines and cultivars for P teres I. maculata is proposed.

Analytical method for solving a set of inhomogeneous infinite simultaneous equations

It is shown that a method based on the principle of analytic continuation can be used to solve a set of inhomogeneous infinite simultaneous equations encountered in the analysis of surface acoustic wave propagation along the periodically perturbed surface of a piezoelectric medium.

Analytical method for solving a set of infinite simultaneous equations

It is shown that a method based on the principle of analytic continuation can be used to solve a set of infinite simultaneous equations encountered in solving for the electric field of a periodic electrode structure.

Minimal set of generators for the derivation module of certain monomial curves

Let K be a field of characteristic zero and let m(0),..., m(e-1) be a sequence of positive integers. Let C be an algebroid monomial curve in the affine e-space A(K)(e) defined parametrically by X-0 = T-m0,..., Xe-1 = Tme-1 and let A be the coordinate ring of C. In this paper, we assume that some e - 1 terms of m(0),..., m(e-1) form an arithmetic sequence and construct a minimal set of generators for the derivation module Der(K)(A) of A and write an explicit formula for mu (Der(K)(A)).

On finding a set of healthy individuals from a large population

In this paper, we explore fundamental limits on the number of tests required to identify a given number of ``healthy'' items from a large population containing a small number of ``defective'' items, in a nonadaptive group testing framework. Specifically, we derive mutual information-based upper bounds on the number of tests required to identify the required number of healthy items. Our results show that an impressive reduction in the number of tests is achievable compared to the conventional approach of using classical group testing to first identify the defective items and then pick the required number of healthy items from the complement set. For example, to identify L healthy items out of a population of N items containing K defective items, when the tests are reliable, our results show that O(K(L - 1)/(N - K)) measurements are sufficient. In contrast, the conventional approach requires O(K log(N/K)) measurements. We derive our results in a general sparse signal setup, and hence, they are applicable to other sparse signal-based applications such as compressive sensing also.

Intramolecular hydrogen bond: Can it be part of the basis set of valence internal coordinates in normal mode analysis?

It has been shown earlier1] that the relaxed force constants (RFCs) could be used as a measure of bond strength only when the bonds form a part of the complete valence internal coordinates (VIC) basis. However, if the bond is not a part of the complete VIC basis, its RFC is not necessarily a measure of bond strength. Sometimes, it is possible to have a complete VIC basis that does not contain the intramolecular hydrogen bond (IMHB) as part of the basis. This means the RFC of IMHB is not necessarily a measure of bond strength. However, we know that IMHB is a weak bond and hence its RFC has to be a measure of bond strength. We resolve this problem of IMHB not being part of the complete basis by postulating `equivalent' basis sets where IMHB is part of the basis at least in one of the equivalent sets of VIC. As long as a given IMHB appears in one of the equivalent complete VIC basis sets, its RFC could be used as a measure of bond strength parameter.

User’s Guide to ADMB2R: A Set of AD Model Builder Output Routines Compatible with the R Statistics Language

ADMB2R is a collection of AD Model Builder routines for saving complex data structures into a file that can be read in the R statistics environment with a single command.1 ADMB2R provides both the means to transfer data structures significantly more complex than simple tables, and an archive mechanism to store data for future reference. We developed this software because we write and run computationally intensive numerical models in Fortran, C++, and AD Model Builder. We then analyse results with R. We desired to automate data transfer to speed diagnostics during working-group meetings. We thus developed the ADMB2R interface to write an R data object (of type list) to a plain-text file. The master list can contain any number of matrices, values, dataframes, vectors or lists, all of which can be read into R with a single call to the dget function. This allows easy transfer of structured data from compiled models to R. Having the capacity to transfer model data, metadata, and results has sharply reduced the time spent on diagnostics, and at the same time, our diagnostic capabilities have improved tremendously. The simplicity of this interface and the capabilities of R have enabled us to automate graph and table creation for formal reports. Finally, the persistent storage in files makes it easier to treat model results in analyses or meta-analyses devised months—or even years—later. We offer ADMB2R to others in the hope that they will find it useful. (PDF contains 30 pages)

User’s Guide to C2R: A Set of C Language Output Routines Compatible with the R Statistics Language

C2R is a collection of C routines for saving complex data structures into a file that can be read in the R statistics environment with a single command.1 C2R provides both the means to transfer data structures significantly more complex than simple tables, and an archive mechanism to store data for future reference. We developed this software because we write and run computationally intensive numerical models in Fortran, C++, and AD Model Builder. We then analyse results with R. We desired to automate data transfer to speed diagnostics during working-group meetings. We thus developed the C2R interface to write an R data object (of type list) to a plain-text file. The master list can contain any number of matrices, values, dataframes, vectors or lists, all of which can be read into R with a single call to the dget function. This allows easy transfer of structured data from compiled models to R. Having the capacity to transfer model data, metadata, and results has sharply reduced the time spent on diagnostics, and at the same time, our diagnostic capabilities have improved tremendously. The simplicity of this interface and the capabilities of R have enabled us to automate graph and table creation for formal reports. Finally, the persistent storage in files makes it easier to treat model results in analyses or meta-analyses devised months—or even years—later. We offer C2R to others in the hope that they will find it useful. (PDF contains 27 pages)

On the set of eigenvalues of a class of equimodular matrices

The structure of the set ϐ(A) of all eigenvalues of all complex matrices (elementwise) equimodular with a given n x n non-negative matrix A is studied. The problem was suggested by O. Taussky and some aspects have been studied by R. S. Varga and B.W. Levinger.

If every matrix equimodular with A is non-singular, then A is called regular. A new proof of the P. Camion-A.J. Hoffman characterization of regular matrices is given.

The set ϐ(A) consists of m ≤ n closed annuli centered at the origin. Each gap, ɤ, in this set can be associated with a class of regular matrices with a (unique) permutation, π(ɤ). The association depends on both the combinatorial structure of A and the size of the a_ii. Let A be associated with the set of r permutations, π₁, π₂,…, π_r, where each gap in ϐ(A) is associated with one of the π_k. Then r ≤ n, even when the complement of ϐ(A) has n+1 components. Further, if π(ɤ) is the identity, the real boundary points of ɤ are eigenvalues of real matrices equimodular with A. In particular, if A is essentially diagonally dominant, every real boundary point of ϐ(A) is an eigenvalues of a real matrix equimodular with A.

Several conjectures based on these results are made which if verified would constitute an extension of the Perron-Frobenius Theorem, and an algebraic method is introduced which unites the study of regular matrices with that of ϐ(A).