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.

Solution of a class of vibration problems by flowgraph methods

A 4-degree-of-freedom single-input system and a 3-degree-of-freedom multi-input system are solved by the Coates', modified Coates' and Chan-Mai flowgraph methods. It is concluded that the Chan-Mai flowgraph method is superior to other flowgraph methods in such cases.

Mechanistic Aspects of Shape Selection and Symmetry Breaking during Nanostructure Growth by Wet Chemical Methods

The control of shapes of nanocrystals is crucial for using them as building blocks for various applications. In this paper, we present a critical overview of the issues involved in shape-controlled synthesis of nanostructures. In particular, we focus on the mechanisms by which anisotropic structures of high-symmetry materials (fcc crystals, for instance) could be realized. Such structures require a symmetry-breaking mechanism to be operative that typically leads to selection of one of the facets/directions for growth over all the other symmetry-equivalent crystallographic facets. We show how this selection could arise for the growth of one-dimensional structures leading to ultrafine metal nanowires and for the case of two-dimensional nanostructures where the layer-by-layer growth takes place at low driving forces leading to plate-shaped structures. We illustrate morphology diagrams to predict the formation of two-dimensional structures during wet chemical synthesis. We show the generality of the method by extending it to predict the growth of plate-shaped inorganics produced by a precipitation reaction. Finally, we present the growth of crystals under high driving forces that can lead to the formation of porous structures with large surface areas.

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.

Comparison of Prediction Based LSF Quantization Methods using Split VQ

Further improvement in performance, to achieve near transparent quality LSF quantization, is shown to be possible by using a higher order two dimensional (2-D) prediction in the coefficient domain. The prediction is performed in a closed-loop manner so that the LSF reconstruction error is the same as the quantization error of the prediction residual. We show that an optimum 2-D predictor, exploiting both inter-frame and intra-frame correlations, performs better than existing predictive methods. Computationally efficient split vector quantization technique is used to implement the proposed 2-D prediction based method. We show further improvement in performance by using weighted Euclidean distance.

Application of optimization methods to vibration control of stretched strings

In this paper, non-linear programming techniques are applied to the problem of controlling the vibration pattern of a stretched string. First, the problem of finding the magnitudes of two control forces applied at two points l1 and l2 on the string to reduce the energy of vibration over the interval (l1, l2) relative to the energy outside the interval (l1, l2) is considered. For this problem the relative merits of various methods of non-linear programming are compared. The more complicated problem of finding the positions and magnitudes of two control forces to obtain the desired energy pattern is then solved by using the slack unconstrained minimization technique with the Fletcher-Powell search. In the discussion of the results it is shown that the position of the control force is very important in controlling the energy pattern of the string.

Solution NMR studies of acetohydroxy acid synthase I: Identification of the sites of inter-subunit interactions using multidimensional NMR methods

The novel multidomain organization in the multimeric Escherichia coli AHAS I (ilvBN) enzyme has been dissected to generate polypeptide fragments. These fragments when cloned, expressed and purified reassemble in the presence of cofactors to yield a catalytically competent enzyme. Structural characterization of AHAS has been impeded due to the fact that the holoenzyme is prone to dissociation leading to heterogeneity in samples. Our approach has enabled the structural characterization using high-resolution nuclear magnetic resonance methods. Near complete sequence specific NMR assignments for backbone H-N, N-15, C-13 alpha and C-13(beta) atoms of the FAD binding domain of ilvB have been obtained on samples isotopically enriched in H-2, C-13 and N-15. The secondary structure determined on the basis of observed C-13(alpha) secondary chemical shifts and sequential NOEs indicates that the secondary structure of the FAD binding domain of E. coli AHAS large Subunit (ilvB) is similar to the structure of this domain in the catalytic subunit of yeast AHAS. Protein-protein interactions involving the regulatory subunit (ilvN) and the domains of the catalytic subunit (ilvB) were studied using circular dichroic and isotope edited solution nuclear magnetic resonance spectroscopic methods. Observed changes in circular dichroic spectra indicate that the regulatory subunit (ilvN) interacts with ilvB alpha and ilvB beta domains of the catalytic subunit and not with the ilvB gamma domain. NMR chemical shift mapping methods show that ilvN binds close to the FAD binding site in ilvB beta and proximal to the intrasubunit ilvB alpha/ilvB beta domain interface. The implication of this interaction on the role of the regulatory subunit oil the activity of the holoenzyme is discussed. NMR studies of the regulatory domains show that these domains are structured in solution. Preliminary evidence for the interaction of ilvN with the metabolic end product of the pathway, viz., valine is also presented.

Serum proteomics of glioma: methods and applications

The prognosis of patients with glioblastoma, the most malignant adult glial brain tumor, remains poor in spite of advances in treatment procedures, including surgical resection, irradiation and chemotherapy.Genetic heterogeneity of glioblastoma warrants extensive studies in order to gain a thorough understanding of the biology of this tumor. While there have been several studies of global transcript profiling of glioma with the identification of gene signatures for diagnosis and disease management, translation into clinics is yet to happen. Serum biomarkers have the potential to revolutionize the process of cancer diagnosis, grading, prognostication and treatment response monitoring. Besides having the advantage that serum can be obtained through a less invasive procedure, it contains molecules at an extraordinary dynamic range of ten orders of magnitude in terms of their concentrations. While the conventional methods, such as 2DE, have been in use for many years, the ability to identify the proteins through mass spectrometry techniques such as MALDI-TOF led to an explosion of interest in proteomics. Relatively new high-throughput proteomics methods such as SELDI-TOF and protein microarrays are expected to hasten the process of serum biomarker discovery. This review will highlight the recent advances in the proteomics platform in discovering serum biomarkers and the current status of glioma serum markers. We aim to provide the principles and potential of the latest proteomic approaches and their applications in the biomarker discovery process. Besides providing a comprehensive list of available serum biomarkers of glioma, we will also propose how these markers will revolutionize the clinical management of glioma patients.

Crystallization kinetics of SrBi2B2O7 glasses by non-isothermal methods

Transparent glasses of SrBi2B2O7 (SBBO) were fabricated via the conventional melt-quenching technique. The amorphous and the glassy nature of the as-quenched samples were, respectively, confirmed by X-ray powder diffraction (XRD) and differential scanning calorimetry (DSC). The glass transition (T (g)) and the crystallization parameters [crystallization activation energy (E (cr)) and Avrami exponent (n)] were evaluated under non-isothermal conditions using DSC. There was a close agreement between the activation energies for the crystallization process determined by Augis and Bennet and Kissinger methods. The variation of local activation energy [E (c)(x)] that was determined by Ozawa method, decreased with the fraction of crystallization (x). The Avrami exponent (n(x)) increased with the increase in fraction of crystallization (x) suggesting that there was a change over in the crystallization process from the surface to the bulk.

Shortcomings of discontinuous-pressure finite element methods on a class of transient problems

Past studies that have compared LBB stable discontinuous- and continuous-pressure finite element formulations on a variety of problems have concluded that both methods yield Solutions of comparable accuracy, and that the choice of interpolation is dictated by which of the two is more efficient. In this work, we show that using discontinuous-pressure interpolations can yield inaccurate solutions at large times on a class of transient problems, while the continuous-pressure formulation yields solutions that are in good agreement with the analytical Solution.

Stereoselective Formal Total Synthesis of (-)-Didemniserinolipid B

A formal total synthesis of (-)-didemniserinolipid B from L-(+)-tartaric acid is presented. Key features of the synthesis include construction of the bicyclic acetal core from bisdimethyl amide of tartaric acid and further elaboration by cross metathesis.

A multistep transversal linearization (MTL) method in non-linear dynamics through a Magnus characterization

A new form of a multi-step transversal linearization (MTL) method is developed and numerically explored in this study for a numeric-analytical integration of non-linear dynamical systems under deterministic excitations. As with other transversal linearization methods, the present version also requires that the linearized solution manifold transversally intersects the non-linear solution manifold at a chosen set of points or cross-section in the state space. However, a major point of departure of the present method is that it has the flexibility of treating non-linear damping and stiffness terms of the original system as damping and stiffness terms in the transversally linearized system, even though these linearized terms become explicit functions of time. From this perspective, the present development is closely related to the popular practice of tangent-space linearization adopted in finite element (FE) based solutions of non-linear problems in structural dynamics. The only difference is that the MTL method would require construction of transversal system matrices in lieu of the tangent system matrices needed within an FE framework. The resulting time-varying linearized system matrix is then treated as a Lie element using Magnus’ characterization [W. Magnus, On the exponential solution of differential equations for a linear operator, Commun. Pure Appl. Math., VII (1954) 649–673] and the associated fundamental solution matrix (FSM) is obtained through repeated Lie-bracket operations (or nested commutators). An advantage of this approach is that the underlying exponential transformation could preserve certain intrinsic structural properties of the solution of the non-linear problem. Yet another advantage of the transversal linearization lies in the non-unique representation of the linearized vector field – an aspect that has been specifically exploited in this study to enhance the spectral stability of the proposed family of methods and thus contain the temporal propagation of local errors. A simple analysis of the formal orders of accuracy is provided within a finite dimensional framework. Only a limited numerical exploration of the method is presently provided for a couple of popularly known non-linear oscillators, viz. a hardening Duffing oscillator, which has a non-linear stiffness term, and the van der Pol oscillator, which is self-excited and has a non-linear damping term.

Fusion of Multisensor Data:Review and Comparative Analysis

Image fusion is a formal framework which is expressed as means and tools for the alliance of multisensor, multitemporal, and multiresolution data. Multisource data vary in spectral, spatial and temporal resolutions necessitating advanced analytical or numerical techniques for enhanced interpretation capabilities. This paper reviews seven pixel based image fusion techniques - intensity-hue-saturation, brovey, high pass filter (HPF), high pass modulation (HPM), principal component analysis, fourier transform and correspondence analysis.Validation of these techniques on IKONOS data (Panchromatic band at I m spatial resolution and Multispectral 4 bands at 4 in spatial resolution) reveal that HPF and HPM methods synthesises the images closest to those the corresponding multisensors would observe at the high resolution level.

Formal Verification of Full-Wave Rectifier: A Case Study

We present a case study of formal verification of full-wave rectifier for analog and mixed signal designs. We have used the Checkmate tool from CMU [1], which is a public domain formal verification tool for hybrid systems. Due to the restriction imposed by Checkmate it necessitates to make the changes in the Checkmate implementation to implement the complex and non-linear system. Full-wave rectifier has been implemented by using the Checkmate custom blocks and the Simulink blocks from MATLAB from Math works. After establishing the required changes in the Checkmate implementation we are able to efficiently verify, the safety properties of the full-wave rectifier.

Evaluation of methods to estimate foliage density in the understorey of a tropical evergreen forest

Foliage density and leaf area index are important vegetation structure variables. They can be measured by several methods but few have been tested in tropical forests which have high structural heterogeneity. In this study, foliage density estimates by two indirect methods, the point quadrat and photographic methods, were compared with those obtained by direct leaf counts in the understorey of a wet evergreen forest in southern India. The point quadrat method has a tendency to overestimate, whereas the photographic method consistently and ignificantly underestimates foliage density. There was stratification within the understorey, with areas close to the ground having higher foliage densities.