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.

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.

Ising ferromagnet with biquadratic exchange

A spin one Ising system with biquadratic exchange, is investigated, using Green's function technique in random phase approximation (RPA). Transition temperature Tc and <(Sz)2> at Tc, are found to increase with biquadratic exchange parameter α for sc, bcc and fcc lattices. The variation of <(Sz)2> at Tc with α is found to be the same for the above lattices.

Magnetic behaviour in metal-organic frameworks-Some recent examples

The article describes the synthesis, structure and magnetic investigations of a series of metal-organic framework compounds formed with Mn+2 and Ni+2 ions. The structures, determined using the single crystal X-ray diffraction, indicated that the structures possess two- and three-dimensional structures with magnetically active dimers, tetramers, chains, two-dimensional layers connected by polycarboxylic acids. These compounds provide good examples for the investigations of magnetic behaviour. Magnetic studies have been carried out using SQUID magnetometer in the range of 2-300 K and the behaviour indicates a predominant anti-ferromagnetic interactions, which appears to differ based on the M-O-C-O-M and/or the M-O-M (M = metal ions) linkages. Thus, compounds with carboxylate (Mn-O-C-O-Mn) connected ones, [C3N2H [Mn(H2O)''C6H3(COO)(3)''], I, [''Mn(H2O (3)''aEuroeC(12)H(8)O(COO)(2)'']center dot H2O, II, [''Mn(H2O)''aEuroeC(12)H(8)O(COO)(2)''], III, show simple anti-ferromagnetic behaviour. The compounds with Mn-O/OH-Mn connected dimer and tetramer units in [NaMn''C6H3(COO)(3)''], IV, [Mn-2(A mu(3)-OH) (H2O)(2)''C6H3(COO)(3)'']center dot 2H(2)O, V, show canted-antiferromagnetic and anti-ferromagnetic behaviour, respectively. The presence of infinite one-dimensional -Ni-OH-Ni- chains in the compound, [Ni-2(H2O)(A mu(3)-OH)(2)(C8H5NO4], VI, gives rise to ferromagnet-like behaviour at low temperatures. The compounds, [Mn-3''C6H3(COO)(3)''(2)], VII and [''Mn(OH)''(2)''C12H8O(COO)(2)''], VIII, have two-dimensional infinite -Mn-O/OH-Mn- layers with triangular magnetic lattices, which resemble the Kagome and brucite-like layer. The magnetic studies indicated canted-antiferromagnetic behaviour in both the cases. Variable temperature EPR and theoretical magnetic modelling studies have been carried out on selected compounds to probe the nature of the magnetic species and their interactions with them.

Analysis of multiple crystal forms of Bacillus subtilis BacB suggests a role for a metal ion as a nucleant for crystallization

Bacillus subtilis BacB is an oxidase that is involved in the production of the antibiotic bacilysin. This protein contains two double-stranded beta-helix (cupin) domains fused in a compact arrangement. BacB crystallizes in three crystal forms under similar crystallization conditions. An interesting observation was that a slight perturbation of the crystallization droplet resulted in the nucleation of a different crystal form. An X-ray absorption scan of BacB suggested the presence of cobalt and iron in the crystal. Here, a comparative analysis of the different crystal forms of BacB is presented in an effort to identify the basis for the different lattices. It is noted that metal ions mediating interactions across the asymmetric unit dominate the different packing arrangements. Furthermore, a normalized B-factor analysis of all the crystal structures suggests that the solvent-exposed metal ions decrease the flexibility of a loop segment, perhaps influencing the choice of crystal form. The residues coordinating the surface metal ion are similar in the triclinic and monoclinic crystal forms. The coordinating ligands for the corresponding metal ion in the tetragonal crystal form are different, leading to a tighter packing arrangement. Although BacB is a monomer in solution, a dimer of BacB serves as a template on which higher order symmetrical arrangements are formed. The different crystal forms of BacB thus provide experimental evidence for metal-ion-mediated lattice formation and crystal packing.

Ordering near the percolation threshold in models of two-dimensional interacting bosons with quenched dilution

Randomly diluted quantum boson and spin models in two dimensions combine the physics of classical percolation with the well-known dimensionality dependence of ordering in quantum lattice models. This combination is rather subtle for models that order in two dimensions but have no true order in one dimension, as the percolation cluster near threshold is a fractal of dimension between 1 and 2: two experimentally relevant examples are the O(2) quantum rotor and the Heisenberg antiferromagnet. We study two analytic descriptions of the O(2) quantum rotor near the percolation threshold. First a spin-wave expansion is shown to predict long-ranged order, but there are statistically rare points on the cluster that violate the standard assumptions of spin-wave theory. A real-space renormalization group (RSRG) approach is then used to understand how these rare points modify ordering of the O(2) rotor. A new class of fixed points of the RSRG equations for disordered one-dimensional bosons is identified and shown to support the existence of long-range order on the percolation backbone in two dimensions. These results are relevant to experiments on bosons in optical lattices and superconducting arrays, and also (qualitatively) for the diluted Heisenberg antiferromagnet La-2(Zn,Mg)(x)Cu1-xO4.

Fourfold Helical Structures for Polypeptides

Fourfold helical structures for polypeptides and their association in regular lattices with interchain hydrogen bonds were investigated by model building studies. These studies revealed that stereochemically satisfactory fourfold helical sturctures are possible for polyglycine, polyproline, and copolymers of glycine and proline with two and four units in the monomer. In these structures the unit height h for the backbone has been found to be restricted from 2.7 to 3.1 k, with four peptide units per turn of the helix. Energetically both fourfold and threefold helical structures are equally favorable.

Probing disorder in cubic pyrochlore Bi-1 Zn-5(1) Nb-0(1) O-5(7) (BZN) thin films

The dielectric response of pulsed laser ablated Bi-1 Zn-5(1) Nb-0(1) O-5(7) (BZN) thin films are investigated within the temperature range of 300-660 K and frequency range of 100 Hz-100 kHz Thin film exhibited a strong dielectric relaxation behavior A sharp rise in dielectric constant of BZN thin film at high temperatures is related to disorder in canon and anion lattices Observed dielectric relaxation implies a redistribution of charges within the unit cell This phenomenon suggests that the large change in dielectric constant is due to a dynamical rise of dipolar fluctuations in the unit cell XPS spectra of BZN (A(2)B(2)O(6)O') cubic pyrochlore confirm that the relaxation corresponds to the ionic hopping among the A and O' positions of several local potential minima Barrier height for hopping is distributed between 0 and 0 94 eV The O is spectrum confirms presence of two types of oxygen in BZN thin film The disorder in charge neutralized thin film is correlated with XPS spectra (C) 2010 Elsevier Ltd All rights reserved

Eu2+ luminescence in MAl3BO7 aluminoborates (M=Ca, Sr, Ba)

Three new aluminoborates having the composition MAl3BO7, where M = Ca,Sr or Ba, have been prepared. X-ray diffraction data indicate that all the phases are monoclinic, with close structural similarity to the meta stable aluminate, SrAl4O7. These aluminoborates are good host lattices for Eu2+ luminescence. The emission spectra show multiple bands in the blue region, corresponding to two inequivalent sites in each case, with one of them having quantum efficiency greater-than or equivalent to 75%. In the case of SrAl3BO7:Eu2+, the d–f band emission dominates at 300 K whereas at 77 K both d–f band and f–f line emissions are observed. Efficient Eu2+→Mn2+ energy transfer is observed in MAl3BO7 leading to strong green emission of Mn2+in the tetrahedral sites.aluminoborates; europium

Role of silver doping in oxygen incorporation of oxide thin film

A distinctive characteristic of silver in oxygen incorporation of oxide thin films during pulsed laser ablation has been discovered. Optical emission spectroscopy studies of laser-induced plume of Ag-target indicates the presence of AgO species whose concentration increases with an increase in oxygen partial pressure. The formation of AgO in laser-plume has been found to be very useful for the realization of high temperature superconducting YBa2Cu3O7-delta (YBCO) and giant magnetoresistive La0.7MnO3-delta (LMO) thin films with dramatically superior quality if the target materials contained a small amount of silver. The improvement in the quality of these films is brought about by the supply of atomic oxygen to oxide lattices during their formation. This becomes possible due to the fact that Ag, after it is ablated with other constituent materials in the target, gets moderately oxidized in an oxygen atmosphere and the oxidized species dissociate back into Ag and nascent O at the substrate surface. The nascent oxygen is very highly reactive and is easily assimilated into the lattice of these compounds. (C) 1997 Elsevier Science S.A.

The studies on micro-structural defects in deformed composite matrix of Al-Si-Mg and SiC

Detailed Fourier line shape analysis has been performed on three different compositions of the composite matrix of Al-Si-Mg and SiC. The alloy composition in wt% is Al-7%Si, 0.35%Mg, 0.14%Fe and traces of copper and titanium (similar to 0.01%) with SiC varying from 0 to 30wt% in three steps i.e., 0, 10 and 30wt%. The line shift analysis has been performed by considering 111, 200, 220, 311 and 222 reflections after estimating their relative shift. Peak asymmetry analysis has been performed considering neighbouring 111 and 200 reflections and Fourier line shape analysis has been performed after considering the multiple orders 111 and 222, 200 and 400 reflections. Combining all these three analyses it has been found that the deformation stacking faults both intrinsic alpha' and extrinsic alpha " are absent in this alloy system whereas the deformation twin beta has been found to be positive and increases with the increase of SiC concentration. So, like other Al-base alloys this ternary alloy also shows high stacking fault energy, and the addition of SiC introduces deformation twin which increases with its concentration in the deformed lattices.

Percolation and Connectivity in AB Random Geometric Graphs

Given two independent Poisson point processes ©(1);©(2) in Rd, the AB Poisson Boolean model is the graph with points of ©(1) as vertices and with edges between any pair of points for which the intersection of balls of radius 2r centred at these points contains at least one point of ©(2). This is a generalization of the AB percolation model on discrete lattices. We show the existence of percolation for all d ¸ 2 and derive bounds for a critical intensity. We also provide a characterization for this critical intensity when d = 2. To study the connectivity problem, we consider independent Poisson point processes of intensities n and cn in the unit cube. The AB random geometric graph is de¯ned as above but with balls of radius r. We derive a weak law result for the largest nearest neighbour distance and almost sure asymptotic bounds for the connectivity threshold.

Confinement-deconfinement transition and spin correlations in a generalized Kitaev model

We present a spin model, namely, the Kitaev model augmented by a loop term and perturbed by an Ising Hamiltonian, and show that it exhibits both confinement-deconfinement transitions from spin liquid to antiferromagnetic/spin-chain/ferromagnetic phases and topological quantum phase transitions between gapped and gapless spin-liquid phases. We develop a fermionic resonating-valence-bonds (RVB) mean-field theory to chart out the phase diagram of the model and estimate the stability of its spin-liquid phases, which might be relevant for attempts to realize the model in optical lattices and other spin systems. We present an analytical mean-field theory to study the confinement-deconfinement transition for large coefficient of the loop term and show that this transition is first order within such mean-field analysis in this limit. We also conjecture that in some other regimes, the confinement-deconfinement transitions in the model, predicted to be first order within the mean-field theory, may become second order via a defect condensation mechanism. Finally, we present a general classification of the perturbations to the Kitaev model on the basis of their effect on it's spin correlation functions and derive a necessary and sufficient condition, within the regime of validity of perturbation theory, for the spin correlators to exhibit a long-ranged power-law behavior in the presence of such perturbations. Our results reproduce those of Tikhonov et al. [Phys. Rev. Lett. 106, 067203 (2011)] as a special case.

Transport through an electrostatically defined quantum dot lattice in a two-dimensional electron gas

Quantum dot lattices (QDLs) have the potential to allow for the tailoring of optical, magnetic, and electronic properties of a user-defined artificial solid. We use a dual gated device structure to controllably tune the potential landscape in a GaAs/AlGaAs two-dimensional electron gas, thereby enabling the formation of a periodic QDL. The current-voltage characteristics, I (V), follow a power law, as expected for a QDL. In addition, a systematic study of the scaling behavior of I (V) allows us to probe the effects of background disorder on transport through the QDL. Our results are particularly important for semiconductor-based QDL architectures which aim to probe collective phenomena.

The inhomogeneous extended Bose-Hubbard model: A mean-field theory

We develop an inhomogeneous mean-field theory for the extended Bose-Hubbard model with a quadratic, confining potential. In the absence of this potential, our mean-field theory yields the phase diagram of the homogeneous extended Bose-Hubbard model. This phase diagram shows a superfluid (SF) phase and lobes of Mott-insulator (MI), density-wave (DW), and supersolid (SS) phases in the plane of the chemical potential mu and on-site repulsion U; we present phase diagrams for representative values of V, the repulsive energy for bosons on nearest-neighbor sites. We demonstrate that, when the confining potential is present, superfluid and density-wave order parameters are nonuniform; in particular, we obtain, for a few representative values of parameters, spherical shells of SF, MI, DW, and SS phases. We explore the implications of our study for experiments on cold-atom dipolar condensates in optical lattices in a confining potential.