On the bottleneck linear programming problem

In this paper, the results on primal methods for Bottleneck Linear Programming (BLP) problem are briefly surveyed, the primal method is presented and the degenerate case related to Bottleneck Transportation Problem (BTP) is explicitly considered. The algorithm is based on the idea of using auxiliary coefficients as is done by Garfinkel and Rao [6]. The modification presented for the BTP rectifies the defect in Hammer's method in the case of degenerate basic feasible solution. Illustrative numerical examples are also given.

On various types of decoupling for time-varying system

This paper deals with the problem of decoupling a class of linear time-varying multi-variable systems, based on the defining property that the impulse response matrix of a decoupled system is diagonal. Depending on the properties of the coefficient matrices of the vector differential equation of the open-loop system, the system may be uniformly or totally decoupled. The necessary and sufficient conditions that permit a system to be uniformly or totally decoupled by state variable feedback are given. The main contribution of this paper is the precise definition of these two classes of decoupling and a rigorous derivation of the necessary and sufficient conditions which show the necessity of requiring that the system be of constant ordered rank with respect to observability. A simple example illustrates the importance of having several definitions of decoupling. Finally, the results are specialized to the case of time invariant systems.

Comments on a decentralized control of linear multivariable systems

A strongly connected decentralized control system may be made single channel controllable and observable with respect to any channel by decentralized feedbacks. It is noted here that the system example considered by Corfmat and Morse to illustrate this fact is already single channel controllable and observable, with respect to one of the channels. An alternate example which fits into the situation is presented in this item.

Validation of a new spot form of net blotch differential set and evidence for hybridisation between the spot and net forms of net blotch in Australia

A recently developed spot form of blotch differential set of 16 barley lines was tested for reaction response to 60 Pyrenophora teres f. maculata isolates from geographically disperse barley crops of Australia. Twelve barley lines (Arimont, Barque, Chebec, CI5286, CI5791, CI9214, CII6150, Dairokkaku, Esperance Orge 289, Galleon, Keel, Skiff, Torrens and TR250) provided differential response between the isolates. The susceptible controls Gairdner and Kombar provided indication of isolate virulence or avirulence. Abundant pathogenic diversity was revealed with 33 designated pathotypes, some of which related to geographic region. AFLP analysis also revealed abundant diversity with each of the isolates representing a unique genotype and one isolate that contained both AFLP bands unique to P. teres f. maculata and P. teres f. teres, the cause of spot form and net form of net blotch respectively, suggesting that sexual recombination between the net form and spot form isolates may have occurred naturally in the field.

L2-stability of nonstationary feedback systems: Frequency-domain criteria

A frequency-domain positivity condition is derived for linear time-varying operators in2and is used to develop2stability criteria for linear and nonlinear feedback systems. These criteria permit the use of a very general class of operators in2with nonstationary kernels, as multipliers. More specific results are obtained by using a first-order differential operator with a time-varying coefficient as multiplier. Finally, by employing periodic multipliers, improved stability criteria are derived for the nonlinear damped Mathieu equation with a forcing function.

Velocity ratio in the analysis of linear dynamical systems

The transfer matrix method is known to be well suited for a complete analysis of a lumped as well as distributed element, one-dimensional, linear dynamical system with a marked chain topology. However, general subroutines of the type available for classical matrix methods are not available in the current literature on transfer matrix methods. In the present article, general expressions for various aspects of analysis-viz., natural frequency equation, modal vectors, forced response and filter performance—have been evaluated in terms of a single parameter, referred to as velocity ratio. Subprograms have been developed for use with the transfer matrix method for the evaluation of velocity ratio and related parameters. It is shown that a given system, branched or straight-through, can be completely analysed in terms of these basic subprograms, on a stored program digital computer. It is observed that the transfer matrix method with the velocity ratio approach has certain advantages over the existing general matrix methods in the analysis of one-dimensional systems.

An algebraic algorithm for the design and analysis of linear dynamical systems

In an earlier paper [1], it has been shown that velocity ratio, defined with reference to the analogous circuit, is a basic parameter in the complete analysis of a linear one-dimensional dynamical system. In this paper it is shown that the terms constituting velocity ratio can be readily determined by means of an algebraic algorithm developed from a heuristic study of the process of transfer matrix multiplication. The algorithm permits the set of most significant terms at a particular frequency of interest to be identified from a knowledge of the relative magnitudes of the impedances of the constituent elements of a proposed configuration. This feature makes the algorithm a potential tool in a first approach to a rational design of a complex dynamical filter. This algorithm is particularly suited for the desk analysis of a medium size system with lumped as well as distributed elements.

On linear order and computation : The expressiveness of interactive computations on linear orders and computations indexed by ordinals

We solve the Dynamic Ehrenfeucht-Fra\"iss\'e Game on linear orders for both players, yielding a normal form for quantifier-rank equivalence classes of linear orders in first-order logic, infinitary logic, and generalized-infinitary logics with linearly ordered clocks. We show that Scott Sentences can be manipulated quickly, classified into local information, and consistency can be decided effectively in the length of the Scott Sentence. We describe a finite set of linked automata moving continuously on a linear order. Running them on ordinals, we compute the ordinal truth predicate and compute truth in the constructible universe of set-theory. Among the corollaries are a study of semi-models as efficient database of both model-theoretic and formulaic information, and a new proof of the atomicity of the Boolean algebra of sentences consistent with the theory of linear order -- i.e., that the finitely axiomatized theories of linear order are dense.

Stochastic Filtering

The stochastic filtering has been in general an estimation of indirectly observed states given observed data. This means that one is discussing conditional expected values as being one of the most accurate estimation, given the observations in the context of probability space. In my thesis, I have presented the theory of filtering using two different kind of observation process: the first one is a diffusion process which is discussed in the first chapter, while the third chapter introduces the latter which is a counting process. The majority of the fundamental results of the stochastic filtering is stated in form of interesting equations, such the unnormalized Zakai equation that leads to the Kushner-Stratonovich equation. The latter one which is known also by the normalized Zakai equation or equally by Fujisaki-Kallianpur-Kunita (FKK) equation, shows the divergence between the estimate using a diffusion process and a counting process. I have also introduced an example for the linear gaussian case, which is mainly the concept to build the so-called Kalman-Bucy filter. As the unnormalized and the normalized Zakai equations are in terms of the conditional distribution, a density of these distributions will be developed through these equations and stated by Kushner Theorem. However, Kushner Theorem has a form of a stochastic partial differential equation that needs to be verify in the sense of the existence and uniqueness of its solution, which is covered in the second chapter.

Sequence diversity and differential expression of major phenylpropanoid-flavonoid biosynthetic genes among three mango varieties

Background: Mango fruits contain a broad spectrum of phenolic compounds which impart potential health benefits; their biosynthesis is catalysed by enzymes in the phenylpropanoid-flavonoid (PF) pathway. The aim of this study was to reveal the variability in genes involved in the PF pathway in three different mango varieties Mangifera indica L., a member of the family Anacardiaceae: Kensington Pride (KP), Irwin (IW) and Nam Doc Mai (NDM) and to determine associations with gene expression and mango flavonoid profiles. Results: A close evolutionary relationship between mango genes and those from the woody species poplar of the Salicaceae family (Populus trichocarpa) and grape of the Vitaceae family (Vitis vinifera), was revealed through phylogenetic analysis of PF pathway genes. We discovered 145 SNPs in total within coding sequences with an average frequency of one SNP every 316bp. Variety IW had the highest SNP frequency (one SNP every 258bp) while KP and NDM had similar frequencies (one SNP every 369bp and 360bp, respectively). The position in the PF pathway appeared to influence the extent of genetic diversity of the encoded enzymes. The entry point enzymes phenylalanine lyase (PAL), cinnamate 4-mono-oxygenase (C4H) and chalcone synthase (CHS) had low levels of SNP diversity in their coding sequences, whereas anthocyanidin reductase (ANR) showed the highest SNP frequency followed by flavonoid 3'-hydroxylase (F3'H). Quantitative PCR revealed characteristic patterns of gene expression that differed between mango peel and flesh, and between varieties. Conclusions: The combination of mango expressed sequence tags and availability of well-established reference PF biosynthetic genes from other plant species allowed the identification of coding sequences of genes that may lead to the formation of important flavonoid compounds in mango fruits and facilitated characterisation of single nucleotide polymorphisms between varieties. We discovered an association between the extent of sequence variation and position in the pathway for up-stream genes. The high expression of PAL, C4H and CHS genes in mango peel compared to flesh is associated with high amounts of total phenolic contents in peels, which suggest that these genes have an influence on total flavonoid levels in mango fruit peel and flesh. In addition, the particularly high expression levels of ANR in KP and NDM peels compared to IW peel and the significant accumulation of its product epicatechin gallate (ECG) in those extracts reflects the rate-limiting role of ANR on ECG biosynthesis in mango. © 2015 Hoang et al.

Application of ultraspherical polynomials to forced oscillations of a third-order non-linear system

In this paper the method of ultraspherical polynomial approximation is applied to study the steady-state response in forced oscillations of a third-order non-linear system. The non-linear function is expanded in ultraspherical polynomials and the expansion is restricted to the linear term. The equation for the response curve is obtained by using the linearized equation and the results are presented graphically. The agreement between the approximate solution and the analog computer solution is satisfactory. The problem of stability is not dealt with in this paper.

Numerical studies on quasilinear and linear elliptic equations

We explore here the acceleration of convergence of iterative methods for the solution of a class of quasilinear and linear algebraic equations. The specific systems are the finite difference form of the Navier-Stokes equations and the energy equation for recirculating flows. The acceleration procedures considered are: the successive over relaxation scheme; several implicit methods; and a second-order procedure. A new implicit method—the alternating direction line iterative method—is proposed in this paper. The method combines the advantages of the line successive over relaxation and alternating direction implicit methods. The various methods are tested for their computational economy and accuracy on a typical recirculating flow situation. The numerical experiments show that the alternating direction line iterative method is the most economical method of solving the Navier-Stokes equations for all Reynolds numbers in the laminar regime. The usual ADI method is shown to be not so attractive for large Reynolds numbers because of the loss of diagonal dominance. This loss can however be restored by a suitable choice of the relaxation parameter, but at the cost of accuracy. The accuracy of the new procedure is comparable to that of the well-tested successive overrelaxation method and to the available results in the literature. The second-order procedure turns out to be the most efficient method for the solution of the linear energy equation.

Non-linear bending of beams of variable cross-section

For the non-linear bending of cantilever beams of variable cross-section, the effect of large deformations, but with linear elasticity, is considered. The governing integral equation is solved by a numerical iterative procedure. Results for some typical cases are obtained and compared with some of those available in the literature.

Genome-wide association analysis and differential expression analysis of resistance to Sclerotinia stem rot in Brassica napus

Brassica napus is one of the most important oil crops in the world, and stem rot caused by the fungus Sclerotinia sclerotiorum results in major losses in yield and quality. To elucidate resistance genes and pathogenesis-related genes, genome-wide association analysis of 347 accessions was performed using the Illumina 60K Brassica SNP (single nucleotide polymorphism) array. In addition, the detached stem inoculation assay was used to select five highly resistant (R) and susceptible (S) B. napus lines, 48 h postinoculation with S. sclerotiorum for transcriptome sequencing. We identified 17 significant associations for stem resistance on chromosomes A8 and C6, five of which were on A8 and 12 on C6. The SNPs identified on A8 were located in a 409-kb haplotype block, and those on C6 were consistent with previous QTL mapping efforts. Transcriptome analysis suggested that S. sclerotiorum infection activates the immune system, sulphur metabolism, especially glutathione (GSH) and glucosinolates in both R and S genotypes. Genes found to be specific to the R genotype related to the jasmonic acid pathway, lignin biosynthesis, defence response, signal transduction and encoding transcription factors. Twenty-four genes were identified in both the SNP-trait association and transcriptome sequencing analyses, including a tau class glutathione S-transferase (GSTU) gene cluster. This study provides useful insight into the molecular mechanisms underlying the plant's response to S. sclerotiorum.

Constrained linear minimax filter for systems with large plant uncertainties

This paper presents a method of designing a minimax filter in the presence of large plant uncertainties and constraints on the mean squared values of the estimates. The minimax filtering problem is reformulated in the framework of a deterministic optimal control problem and the method of solution employed, invokes the matrix Minimum Principle. The constrained linear filter and its relation to singular control problems has been illustrated. For the class of problems considered here it is shown that the filter can he constrained separately after carrying out the mini maximization. Numorieal examples are presented to illustrate the results.