Formal description, compression and transformation of digital pictures

This paper describes the application of vector spaces over Galois fields, for obtaining a formal description of a picture in the form of a very compact, non-redundant, unique syntactic code. Two different methods of encoding are described. Both these methods consist in identifying the given picture as a matrix (called picture matrix) over a finite field. In the first method, the eigenvalues and eigenvectors of this matrix are obtained. The eigenvector expansion theorem is then used to reconstruct the original matrix. If several of the eigenvalues happen to be zero this scheme results in a considerable compression. In the second method, the picture matrix is reduced to a primitive diagonal form (Hermite canonical form) by elementary row and column transformations. These sequences of elementary transformations constitute a unique and unambiguous syntactic code-called Hermite code—for reconstructing the picture from the primitive diagonal matrix. A good compression of the picture results, if the rank of the matrix is considerably lower than its order. An important aspect of this code is that it preserves the neighbourhood relations in the picture and the primitive remains invariant under translation, rotation, reflection, enlargement and replication. It is also possible to derive the codes for these transformed pictures from the Hermite code of the original picture by simple algebraic manipulation. This code will find extensive applications in picture compression, storage, retrieval, transmission and in designing pattern recognition and artificial intelligence systems.

An exponential stability criterion for certain nonlinear systems

Improved sufficient conditions are derived for the exponential stability of a nonlinear time varying feedback system having a time invariant blockG in the forward path and a nonlinear time varying gain ϕ(.)k(t) in the feedback path. φ(.) being an odd monotone nondecreasing function. The resulting bound on is less restrictive than earlier criteria.

On energy-momentum tensors as sources of spin-2 fields

The improvement terms in the generalised energy-momentum tensor of Callan, Coleman and Jackiw can be derived from a variational principle if the Lagrangian is generalised to describe coupling between ‘matter’ fields and a spin-2 boson field. The required Lorentz-invariant theory is a linearised version of Kibble-Sciama theory with an additional (generally-covariant) coupling term in the Lagrangian. The improved energy-momentum tensor appears as the source of the spin-2 field, if terms of second order in the coupling constant are neglected.

Conformal invariance and scalar-tensor theories

A new generalisation of Einstein’s theory is proposed which is invariant under conformal mappings. Two scalar fields are introduced in addition to the metric tensor field, so that two special choices of gauge are available for physical interpretation, the ‘Einstein gauge’ and the ‘atomic gauge’. The theory is not unique but contains two adjustable parameters ζ anda. Witha=1 the theory viewed from the atomic gauge is Brans-Dicke theory (ω=−3/2+ζ/4). Any other choice ofa leads to a creation-field theory. In particular the theory given by the choicea=−3 possesses a cosmological solution satisfying Dirac’s ‘large numbers’ hypothesis.

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.

An exponential stability criterion for certain nonlinear systems

Improved sufficient conditions are derived for the exponential stability of a nonlinear time varying feedback system having a time invariant blockG in the forward path and a nonlinear time varying gain ϕ(.)k(t) in the feedback path. φ(.) being an odd monotone nondecreasing function. The resulting bound on $$\left( {{{\frac{{dk}}{{dt}}} \mathord{\left/ {\vphantom {{\frac{{dk}}{{dt}}} k}} \right. \kern-\nulldelimiterspace} k}} \right)$$ is less restrictive than earlier criteria.

A method for separation of stresses in Two- and three-dimensional photoelasticity

A method for separation of stresses in two and three-dimensional photo elasticity using the harmonisation ofjrst stress invariant along a straight section is deve- ,dped. For two-dimensions, the equations of equilibrium are reformulated in terms ojsum and difference of normal stresses and relations are obtained which can be used for harmonisation of the first invariant of stress along a straight section. A similar procedure is adopted for three-dimensions by making use of the Beltrmi-MicheN equations. The new relations are used in finite d~yerencefo rm to evaluate the sum of normal stresses along straight sections in a three-dimensional body. The method requires photoelastic data along the section as well ~rra djacent sections. This method could be used as an alternative to the shear d@erence method for separation of stresses in photoelasticity. 7he accuracy and reliability of the method is ver$ed by applying the method to problems whose solutions are known.

On the stability of a nonlinear system with periodic coefficients

A quasi-geometric stability criterion for feedback systems with a linear time invariant forward block and a periodically time varying nonlinear gain in the feedback loop is developed.

A Generalized Approach to Multiresolution Complex SAR Signal Processing

Multiresolution synthetic aperture radar (SAR) image formation has been proven to be beneficial in a variety of applications such as improved imaging and target detection as well as speckle reduction. SAR signal processing traditionally carried out in the Fourier domain has inherent limitations in the context of image formation at hierarchical scales. We present a generalized approach to the formation of multiresolution SAR images using biorthogonal shift-invariant discrete wavelet transform (SIDWT) in both range and azimuth directions. Particularly in azimuth, the inherent subband decomposition property of wavelet packet transform is introduced to produce multiscale complex matched filtering without involving any approximations. This generalized approach also includes the formulation of multilook processing within the discrete wavelet transform (DWT) paradigm. The efficiency of the algorithm in parallel form of execution to generate hierarchical scale SAR images is shown. Analytical results and sample imagery of diffuse backscatter are presented to validate the method.

Influence of Hydrophilic Surface Specificity on the Structural Properties of Confined Water

The influence of chemical specificity of hydrophilic surfaces on the structure of confined water in the subnanometer regime is investigated using grand canonical Monte Carlo Simulations. The structural variations for water confined between hydroxylated silica surfaces are contrasted with water confined between mica surfaces. Although both surfaces are hydrophilic, our Study shows that hydration of potassium ions on the mica surface has a strong influence on the water Structure and solvation force response of confined water. In contrast to the disrupted hydrogen bond network observed for water confined between Mica Surfaces, water between silica surfaces retains its hydrogen bond network displaying bulklike structural features down to surface separations as small as 0.45 nm. Hydrogen bonding of all invariant contact water layer with the surface silanol groups aids in maintaining a constant number of hydrogen bonds per water molecule for the silica surfaces. As a consequence water depletion and rearrangement upon decreasing confinement is a strong function of the hydrophilic surface specificity, particularly at smaller separations. An oscillatory solvation force response is only observed for water confined between Silica surfaces, and bulklike features are observed for both Surfaces above a surface separation of about 1.2 nm. We evaluate and contrast the water density, dipole moment distributions, pi pair correlation functions, and solvation forces as a function of the surface separation.

Spatial correlation in grain misorientation distribution

Grain misorientation was studied in relation to the nearest neighbor's mutual distance using electron back-scattered diffraction measurements. The misorientation correlation function was defined as the probability density for the occurrence of a certain misorientation between pairs of grains separated by a certain distance. Scale-invariant spatial correlation between neighbor grains was manifested by a power law dependence of the preferred misorientation vs. inter-granular distance in various materials after diverse strain paths. The obtained negative scaling exponents were in the range of -2 +/- 0.3 for high-angle grain boundaries. The exponent decreased in the presence of low-angle grain boundaries or dynamic recrystallization, indicating faster decay of correlations. The correlations vanished in annealed materials. The results were interpreted in terms of lattice incompatibility and continuity conditions at the interface between neighboring grains. Grain-size effects on texture development, as well as the implications of such spatial correlations on texture modeling, were discussed.

Harmonic Analysis On Heisenberg Nilmanifolds

In these lectures we plan to present a survey of certain aspects of harmonic analysis on a Heisenberg nilmanifold Gammakslash}H-n. Using Weil-Brezin-Zak transform we obtain an explicit decomposition of L-2 (Gammakslash}H-n) into irreducible subspaces invariant under the right regular representation of the Heisenberg group. We then study the Segal-Bargmann transform associated to the Laplacian on a nilmanifold and characterise the image of L-2 (GammakslashH-n) in terms of twisted Bergman and Hermite Bergman spaces.

Free and ATP-bound structures of Ap(4)A hydrolase from Aquifex aeolicus V5

Asymmetric diadenosine tetraphosphate (Ap(4)A) hydrolases degrade the metabolite Ap(4)A back into ATP and AMP. The three-dimensional crystal structure of Ap(4)A hydrolase (16 kDa) from Aquifex aeolicus has been determined in free and ATP-bound forms at 1.8 and 1.95 angstrom resolution, respectively. The overall three-dimensional crystal structure of the enzyme shows an alpha beta alpha-sandwich architecture with a characteristic loop adjacent to the catalytic site of the protein molecule. The ATP molecule is bound in the primary active site and the adenine moiety of the nucleotide binds in a ring-stacking arrangement equivalent to that observed in the X-ray structure of Ap(4)A hydrolase from Caenorhabditis elegans. Binding of ATP in the active site induces local conformational changes which may have important implications in the mechanism of substrate recognition in this class of enzymes. Furthermore, two invariant water molecules have been identified and their possible structural and/or functional roles are discussed. In addition, modelling of the substrate molecule at the primary active site of the enzyme suggests a possible path for entry and/or exit of the substrate and/or product molecule.

Structure of Mycobacterium tuberculosis RuvA, a protein involved in recombination

The process of recombinational repair is crucial for maintaining genomic integrity and generating biological diversity. In association with RuvB and RuvC, RuvA plays a central role in processing and resolving Holliday junctions, which are a critical intermediate in homologous recombination. Here, the cloning, purification and structure determination of the RuvA protein from Mycobacterium tuberculosis (MtRuvA) are reported. Analysis of the structure and comparison with other known RuvA proteins reveal an octameric state with conserved subunit-subunit interaction surfaces, indicating the requirement of octamer formation for biological activity. A detailed analysis of plasticity in the RuvA molecules has led to insights into the invariant and variable regions, thus providing a framework for understanding regional flexibility in various aspects of RuvA function.

Free-volume dependent pressure sensitivity of Zr-based bulk metallic glass

Instrumented indentation experiments on a Zr-based bulk metallic glass (BMG) in as-cast, shot-peened and structurally relaxed conditions were conducted to examine the dependence of plastic deformation on its structural state. Results show significant differences in hardness, H, with structural relaxation increasing it and shot peening markedly reducing it, and slightly changed morphology of shear bands around the indents. This is in contrast to uniaxial compressive yield strength, sigma(y), which remains invariant with the change in the structural state of the alloys investigated. The plastic constraint factor, C = H/sigma(y), of the relaxed BMG increases compared with that of the as-cast glass, indicating enhanced pressure sensitivity upon annealing. In contrast, C of the shot-peened layer was found to be similar to that observed in crystalline metals, indicating that severe plastic deformation could eliminate pressure sensitivity. Microscopic origins for this result, in terms of shear transformation zones and free volume, are discussed.