Formal description, compression and transformation of digital pictures II. Picture algebra and geometry

In an earlier paper (Part I) we described the construction of Hermite code for multiple grey-level pictures using the concepts of vector spaces over Galois Fields. In this paper a new algebra is worked out for Hermite codes to devise algorithms for various transformations such as translation, reflection, rotation, expansion and replication of the original picture. Also other operations such as concatenation, complementation, superposition, Jordan-sum and selective segmentation are considered. It is shown that the Hermite code of a picture is very powerful and serves as a mathematical signature of the picture. The Hermite code will have extensive applications in picture processing, pattern recognition and artificial intelligence.

On the Geometry of Infinite-Dimensional Grassmannian Manifolds and Gauge Theory

This PhD Thesis is about certain infinite-dimensional Grassmannian manifolds that arise naturally in geometry, representation theory and mathematical physics. From the physics point of view one encounters these infinite-dimensional manifolds when trying to understand the second quantization of fermions. The many particle Hilbert space of the second quantized fermions is called the fermionic Fock space. A typical element of the fermionic Fock space can be thought to be a linear combination of the configurations m particles and n anti-particles . Geometrically the fermionic Fock space can be constructed as holomorphic sections of a certain (dual)determinant line bundle lying over the so called restricted Grassmannian manifold, which is a typical example of an infinite-dimensional Grassmannian manifold one encounters in QFT. The construction should be compared with its well-known finite-dimensional analogue, where one realizes an exterior power of a finite-dimensional vector space as the space of holomorphic sections of a determinant line bundle lying over a finite-dimensional Grassmannian manifold. The connection with infinite-dimensional representation theory stems from the fact that the restricted Grassmannian manifold is an infinite-dimensional homogeneous (Kähler) manifold, i.e. it is of the form G/H where G is a certain infinite-dimensional Lie group and H its subgroup. A central extension of G acts on the total space of the dual determinant line bundle and also on the space its holomorphic sections; thus G admits a (projective) representation on the fermionic Fock space. This construction also induces the so called basic representation for loop groups (of compact groups), which in turn are vitally important in string theory / conformal field theory. The Thesis consists of three chapters: the first chapter is an introduction to the backround material and the other two chapters are individually written research articles. The first article deals in a new way with the well-known question in Yang-Mills theory, when can one lift the action of the gauge transformation group on the space of connection one forms to the total space of the Fock bundle in a compatible way with the second quantized Dirac operator. In general there is an obstruction to this (called the Mickelsson-Faddeev anomaly) and various geometric interpretations for this anomaly, using such things as group extensions and bundle gerbes, have been given earlier. In this work we give a new geometric interpretation for the Faddeev-Mickelsson anomaly in terms of differentiable gerbes (certain sheaves of categories) and central extensions of Lie groupoids. The second research article deals with the question how to define a Dirac-like operator on the restricted Grassmannian manifold, which is an infinite-dimensional space and hence not in the landscape of standard Dirac operator theory. The construction relies heavily on infinite-dimensional representation theory and one of the most technically demanding challenges is to be able to introduce proper normal orderings for certain infinite sums of operators in such a way that all divergences will disappear and the infinite sum will make sense as a well-defined operator acting on a suitable Hilbert space of spinors. This research article was motivated by a more extensive ongoing project to construct twisted K-theory classes in Yang-Mills theory via a Dirac-like operator on the restricted Grassmannian manifold.

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.

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.

Differential scanning calorimetric studies on ammonium perchlorate

Differential scanning calorimetric studies on ammonium perchlorate have been carried out. The enthalpy values for the phase transition endotherm and the two exotherms have been reported in the present communication. A new method has been developed for the estimation of kinetic parameters from DSC the mograms. The values for activation energy as calculated by the above method for low temperature and high temperature exotherms are in close agreement with literature values. The present studies also confirm the presence of small exothermic peaks at the initial stages of high temperature exotherm. Explanation for the same has been given.

Generalised quaternion methods in conformal geometry

A new approach to Penrose's twistor algebra is given. It is based on the use of a generalised quaternion algebra for the translation of statements in projective five-space into equivalent statements in twistor (conformal spinor) space. The formalism leads toSO(4, 2)-covariant formulations of the Pauli-Kofink and Fierz relations among Dirac bilinears, and generalisations of these relations.

Vibration of Non-Uniform Thin-Walled Beams of Arbitrary Shape

A generalised theory for the natural vibration of non-uniform thin-walled beams of arbitrary cross-sectional geometry is proposed. The governing equations are obtained as four partial, linear integro-differential equations. The corresponding boundary conditions are also obtained in an integro-differential form. The formulation takes into account the effect of longitudinal inertia and shear flexibility. A method of solution is presented. Some numerical illustrations and an exact solution are included.

Inductor realisation using a finite gain differential amplifier

A finite gain differential amplifier is used along with a few passive RC elements to simulate an inductor. Methods for obtaining low Q inductance and frequency dependent high QI inductance are described. Sensitivity analysis when the gain varies is also included.

A differential transformation technique for the analysis of a class of non-linear time varying systems

The scope of the differential transformation technique, developed earlier for the study of non-linear, time invariant systems, has been extended to the domain of time-varying systems by modifications to the differential transformation laws proposed therein. Equivalence of a class of second-order, non-linear, non-autonomous systems with a linear autonomous model of second order is established through these transformation laws. The feasibility of application of this technique in obtaining the response of such non-linear time-varying systems is discussed.

Negative differential resistance in GaN nanocrystals above room temperature

Negative differential resistance (NDR) has been observed for the first time above room temperature in gallium nitride nanocrystals synthesized by a simple chemical route. Current-voltage characteristics have been used to investigate this effect through a metal-semiconductor-metal (M-S-M) configuration on SiO2. The NDR effect is reversible and reproducible through many cycles. The threshold voltage is similar to 7 V above room temperature.

Computation of turbulent flow in an IFRF quarl burner

A computational model for isothermal axisymmetric turbulent flow in a quarl burner is set up using the CFD package FLUENT, and numerical solutions obtained from the model are compared with available experimental data. A standard k-e model and and two versions of the RNG k-e model are used to model the turbulence. One of the aims of the computational study is to investigate whether the RNG based k-e turbulence models are capable of yielding improved flow predictions compared with the standard k-e turbulence model. A difficulty is that the flow considered here features a confined vortex breakdown which can be highly sensitive to flow behaviour both upstream and downstream of the breakdown zone. Nevertheless, the relatively simple confining geometry allows us to undertake a systematic study so that both grid-independent and domain-independent results can be reported. The systematic study includes a detailed investigation of the effects of upstream and downstream conditions on the predictions, in addition to grid refinement and other tests to ensure that numerical error is not significant. Another important aim is to determine to what extent the turbulence model predictions can provide us with new insights into the physics of confined vortex breakdown flows. To this end, the computations are discussed in detail with reference to known vortex breakdown phenomena and existing theories. A major conclusion is that one of the RNG k-e models investigated here is able to correctly capture the complex forward flow region inside the recirculating breakdown zone. This apparently pathological result is in stark contrast to the findings of previous studies, most of which have concluded that either algebraic or differential Reynolds stress modelling is needed to correctly predict the observed flow features. Arguments are given as to why an isotropic eddy-viscosity turbulence model may well be able to capture the complex flow structure within the recirculating zone for this flow setup. With regard to the flow physics, a major finding is that the results obtained here are more consistent with the view that confined vortex breakdown is a type of axisymmetric boundary layer separation, rather than a manifestation of a subcritical flow state.

Geometry of the de-Sitter universe

By making use of the fact that the de-Sitter metric corresponds to a hyperquadric in a five-dimensional flat space, it is shown that the three Robertson-Walker metrics for empty spacetime and positive cosmological constant, corresponding to 3-space of positive, negative and zero curvative, are geometrically equivalent. The 3-spaces correspond to intersections of the hyperquadric by hyperplanes, and the time-like geodesics perpendicular to them correspond to intersections by planes, in all three cases.

The fully implicit stochastic-alpha method for stiff stochastic differential equations

A fully implicit integration method for stochastic differential equations with significant multiplicative noise and stiffness in both the drift and diffusion coefficients has been constructed, analyzed and illustrated with numerical examples in this work. The method has strong order 1.0 consistency and has user-selectable parameters that allow the user to expand the stability region of the method to cover almost the entire drift-diffusion stability plane. The large stability region enables the method to take computationally efficient time steps. A system of chemical Langevin equations simulated with the method illustrates its computational efficiency.

The alpha method for solving differential algebraic inequality (DAI) systems

This paper describes an algorithm for ``direct numerical integration'' of the initial value Differential-Algebraic Inequalities (DAI) in a time stepping fashion using a sequential quadratic programming (SQP) method solver for detecting and satisfying active path constraints at each time step. The activation of a path constraint generally increases the condition number of the active discretized differential algebraic equation's (DAE) Jacobian and this difficulty is addressed by a regularization property of the alpha method. The algorithm is locally stable when index 1 and index 2 active path constraints and bounds are active. Subject to available regularization it is seen to be stable for active index 3 active path constraints in the numerical examples. For the high index active path constraints, the algorithm uses a user-selectable parameter to perturb the smaller singular values of the Jacobian with a view to reducing the condition number so that the simulation can proceed. The algorithm can be used as a relatively cheaper estimation tool for trajectory and control planning and in the context of model predictive control solutions. It can also be used to generate initial guess values of optimization variables used as input to inequality path constrained dynamic optimization problems. The method is illustrated with examples from space vehicle trajectory and robot path planning.

Synthesis of liquid crystalline benzothiazole base derivatives: A study of their optical and electrical properties

Two new donor-acceptor type liquid crystalline semiconductors based on benzothiazole have been synthesized. Their structural, photophysical and electronic properties were investigated using X-ray diffraction, atomic force microscopy, cyclic voltammetry, UV-Vis, photoluminescence, and Raman spectroscopy. The liquid crystalline behaviour of the molecules was thoroughly examined by differential scanning calorimetry (DSC) and optical polarizing microscope. The DSC and thermogravimetric analysis (TGA) show that these materials posses excellent thermal stability and have decomposition temperatures in excess of 300 degrees C. Beyond 160 degrees C both molecules show a smectic A liquid crystalline phase that exists till about 240 degrees C. Field-effect transistors were fabricated by vacuum evaporating the semiconductor layer using standard bottom gate/top contact geometry. The devices exhibit p-channel behaviour with hole mobilities of 10(-2) cm(2)/Vs. (C) 2009 Elsevier B.V. All rights reserved.