Spectral decomposition and matrix-valued orthogonal polynomials

The relation between the spectral decomposition of a self-adjoint operator which is realizable as a higher order recurrence operator and matrix-valued orthogonal polynomials is investigated. A general construction of such operators from scalar-valued orthogonal polynomials is presented. Two examples of matrix-valued orthogonal polynomials with explicit orthogonality relations and three-term recurrence relation are presented, which both can be considered as $2\times 2$-matrix-valued analogues of subfamilies of Askey-Wilson polynomials.Comment: 15 page

Wilson function transforms related to Racah coefficients

The irreducible $*$-representations of the Lie algebra $su(1,1)$ consist of discrete series representations, principal unitary series and complementary series. We calculate Racah coefficients for tensor product representations that consist of at least two discrete series representations. We use the explicit expressions for the Clebsch-Gordan coefficients as hypergeometric functions to find explicit expressions for the Racah coefficients. The Racah coefficients are Wilson polynomials and Wilson functions. This leads to natural interpretations of the Wilson function transforms. As an application several sum and integral identities are obtained involving Wilson polynomials and Wilson functions. We also compute Racah coefficients for U_q(\su(1,1)), which turn out to be Askey-Wilson functions and Askey-Wilson polynomials.Comment: 48 page

LU factorizations, q=0 limits, and p-adic interpretations of some q-hypergeometric orthogonal polynomials

For little q-Jacobi polynomials and q-Hahn polynomials we give particular q-hypergeometric series representations in which the termwise q=0 limit can be taken. When rewritten in matrix form, these series representations can be viewed as LU factorizations. We develop a general theory of LU factorizations related to complete systems of orthogonal polynomials with discrete orthogonality relations which admit a dual system of orthogonal polynomials. For the q=0 orthogonal limit functions we discuss interpretations on p-adic spaces. In the little 0-Jacobi case we also discuss product formulas.Comment: changed title, references updated, minor changes matching the version to appear in Ramanujan J.; 22 p

Sensor data classification for the indication of lameness in sheep

Lameness is a vital welfare issue in most sheep farming countries, including the UK. The pre-detection at the farm level could prevent the disease from becoming chronic. The development of wearable sensor technologies enables the idea of remotely monitoring the changes in animal movements which relate to lameness. In this study, 3D-acceleration, 3D-orientation, and 3D-linear acceleration sensor data were recorded at ten samples per second via the sensor attached to sheep neck collar. This research aimed to determine the best accuracy among various supervised machine learning techniques which can predict the early signs of lameness while the sheep are walking on a flat field. The most influencing predictors for lameness indication were also addressed here. The experimental results revealed that the Decision Tree classifier has the highest accuracy of 75.46%, and the orientation sensor data (angles) around the neck are the strongest predictors to differentiate among severely lame, mildly lame and sound classes of sheep

Decomposition algorithms for submodular optimization with applications to parallel machine scheduling with controllable processing times

In this paper we present a decomposition algorithm for maximizing a linear function over a submodular polyhedron intersected with a box. Apart from this contribution to submodular optimization, our results extend the toolkit available in deterministic machine scheduling with controllable processing times. We demonstrate how this method can be applied to developing fast algorithms for minimizing total compression cost for preemptive schedules on parallel machines with respect to given release dates and a common deadline. Obtained scheduling algorithms are faster and easier to justify than those previously known in the scheduling literature

Simulated preferential water flow and solute transport in shrinking soils

We present follow-up work to previous work extending the classical rigid (RGD) approach formerly proposed by Gerke and van Genuchten, to account for shrinking effects (SHR) in modeling water flow and solute transport in dualpermeability porous media. In this study we considered three SHR scenarios, assuming that aggregate shrinkage may change either: (i) the hydraulic properties of the two pore domains, (ii) their relative fractions, or (iii) both hydraulic properties and fractions of the two domains. The objective was to compare simulation results obtained under the RGD and the SHR assumptions to illustrate the impact of matrix volume changes on water storage, water fluxes, and solute concentrations during an infiltration process bringing an initially dry soil to saturation and a drainage process starting from an initially saturated soil. For an infiltration process, the simulated wetting front and the solute concentration propagation velocity, as well as the water fluxes and water and solute exchange rates, for the three SHR scenarios significantly deviated from the RGD. By contrast, relatively similar water content profiles evolved under all scenarios during drying. Overall, compared to the RGD approach, the effect of changing the hydraulic properties and the weight of the two domains according to the shrinkage behavior of the soil aggregates induced a much more rapid response in terms of water fluxes and solute travel times, as well as a larger and deeper water and solute transfer from the fractures to the matrix during wetting processes

Sensor data classification for the indication of lameness in sheep

Lameness is a vital welfare issue in most sheep farming countries, including the UK. The pre-detection at the farm level could prevent the disease from becoming chronic. The development of wearable sensor technologies enables the idea of remotely monitoring the changes in animal movements which relate to lameness. In this study, 3D-acceleration, 3D-orientation, and 3D-linear acceleration sensor data were recorded at ten samples per second via the sensor attached to sheep neck collar. This research aimed to determine the best accuracy among various supervised machine learning techniques which can predict the early signs of lameness while the sheep are walking on a flat field. The most influencing predictors for lameness indication were also addressed here. The experimental results revealed that the Decision Tree classifier has the highest accuracy of 75.46%, and the orientation sensor data (angles) around the neck are the strongest predictors to differentiate among severely lame, mildly lame and sound classes of sheep