Saša Krešić-Jurić

Noncommutative differential forms on the kappa-deformed space

We construct a differential algebra of forms on the kappa-deformed space. For a given realization of noncommutative coordinates as formal power series in the Weyl algebra we find an infinite family of one-forms and nilpotent exterior derivatives. We derive explicit expressions for the exterior derivative and one-forms in covariant and noncovariant realizations. We also introduce higher order forms and show that the exterior derivative satisfies the graded Leibniz rule. The differential forms are generally not graded commutative, but they satisfy the graded Jacobi identity. We also consider the star-product of classical differential forms. The star-product is well defined if the commutator between the noncommutative coordinates and one-forms is closed in the space of one-forms alone. In addition, we show that in certain realizations the exterior derivative acting on the star-product satisfies the undeformed Leibniz rule.

Applications of hidden Markov models in bar code decoding

We present a novel approach to edge detection in bar code signals using a hidden Markov model (HMM). We also present an algorithm for selection of an optimal filter scale used in smoothing the data. Experimental results show that the proposed HMM is superior in performance compared with existing algorithms in commercial scanners.

Analysis of speckle noise in bar-code scanning systems

Laser beams used for bar-code scanning exhibit speckle noise generated by the roughness of the surface on which bar codes are printed. Statistical properties of a photodetector signal that integrates a time-varying speckle pattern falling on its aperture are analyzed in detail. We derive simple closed-form expressions for the autocorrelation function and the power spectral density of the detector current for scanning beams with arbitrary field distributions. Theoretical calculations are illustrated by numerical simulations as well.

Edge detection in bar code signals corrupted by integrated time-varying speckle

Accurate edge localization is of primary importance in bar code decoding. In this paper we investigate statistical properties of edge localization error when a bar code signal is corrupted by additive noise which is a weakly stationary random process. We derive a first order approximation for the expected value and standard deviation of the error in terms of the power spectral density (PSD) of the noise. This result is used to estimate the edge localization error caused by speckle noise. We show that the standard deviation of the error is determined by the intensity distribution of a scanning beam and the positions of neighboring edges. We discuss how the error analysis determines the detection rates of a scanning system, and how it can be used in the system design. Analytical examples are provided for UPCA bar code symbols and a scanning beam with Gaussian distribution.

Speckle noise in bar-code scanning systems—power spectral density and SNR

Laser-based flying-spot scanners are strongly affected by speckle that is intrinsic to coherent illumination of diffusing targets. In such systems information is usually extracted by processing the derivative of a photodetector signal that results from collecting over the detectors aperture the scattered light of a laser beam scanning a bar code. Because the scattered light exhibits a time-varying speckle pattern, the signal is corrupted by speckle noise. In this paper we investigate the power spectral density and total noise power of such signals. We also analyze the influence of speckle noise on edge detection and derive estimates for a signal-to-noise ratio when a laser beam scans different sequences of edges. The theory is illustrated by applying the results to Gaussian scanning beams for which we derive closed form expressions.

A loop group approach to the C. Neumann problem and Moser–Veselov factorization

A geometrical description of continuous and discrete versions of the Neumann oscillator in terms of a loop group framework is investigated. It is shown that the continuous Neumann oscillator can be integrated by the Riemann–Hilbert factorization on the “twisted” loop group of O(3), LO(3). The solution of the problem is given in terms of a special class of flows on the quotient space LO(3)/LO(3)+ where LO(3)+ is a subgroup of positive loops in LO(3). It is also shown that the Moser–Veselov algorithm for integrating a discrete version of the Neumann oscillator (Heisenberg XYZ chain) is induced by a discrete flow in this space. The flow can be explicitly integrated by solving the matrix Riccati equation. In both cases, discrete and continuous, conservation laws are derived from time invariance of a relation that holds for coefficients of the Fourier expansion of the flows.

Gauge transformations and symmetries of integrable systems

We analyse several integrable systems in zero-curvature form within the framework of invariant gauge theory. In the Drinfeld–Sokolov gauge, we derive a two-parameter family of nonlinear evolution equations which as special cases include the Korteweg–de Vries (KdV) and Harry Dym (HD) equations. We find residual gauge transformations which lead to infinitesimal symmetries of this family of equations. For KdV and HD equations we find an infinite hierarchy of such symmetry transformations, and we investigate their relation with local conservation laws, constants of the motion and the bi-Hamiltonian structure of the equations. Applying successive gauge transformations of Miura type we obtain a sequence of gauge-equivalent integrable systems, among them the modified KdV and Calogero KdV equations.

Speckle revisited: analysis of speckle noise in bar-code scanning systems

Laser beams used for bar-code scanning exhibit speckle noise generated by the roughness of the surface on which bar-codes are printed. Statistical properties of a photodetector signal that integrates a time-varying speckle pattern falling on its aperture are analyzed in detail. We derive simple closed form expressions for the auto-correlation function and power spectral density of the detector current for general form scanning beams with arbitrary field distributions. Theoretical calculations are illustrated by numerical simulations.

Hamiltonians and zero-curvature equations for integrable partial differential equations

We discuss the relationship between two approaches to integrable partial differential equations, one using formal affine Lie algebras and the other Banach–Lie groups. In the first approach integrability of the equations follows from commutativity of Hamiltonian flows on the Lie algebra, while in the second it follows from commutativity of certain flows induced by an action on the Banach–Lie group. We show that these two methods are essentially equivalent since one can calculate one type of the flows from the other. The classes of solutions encompassed by the two methods, however, vary significantly. We demonstrate this relationship specifically with the nonlinear Schrodinger equation.

Generalization of Weyl realization to a class of Lie superalgebras

This paper generalizes Weyl realization to a class of Lie superalgebras