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

On a pair of difference equations for the 4F3_4F_3 type orthogonal polynomials and related exactly-solvable quantum systems

We introduce a pair of novel difference equations, whose solutions are expressed in terms of Racah or Wilson polynomials depending on the nature of the finite-difference step. A number of special cases and limit relations are also examined, which allow to introduce similar difference equations for the orthogonal polynomials of the $_3 F_2$ and $_2 F_1$ types. It is shown that the introduced equations allow to construct new models of exactly-solvable quantum dynamical systems, such as spin chains with a nearest-neighbour interaction and fermionic quantum oscillator models.Comment: 8 pages, to be published in Springer Proceedings in Mathematics & Statistic

Laminitis in dairy goats (Capra aegagrus hircus) on a low-forage diet

Dairy goats on high-concentrate diets attain high production levels, but at what cost? Here, ongoing lameness problems in a herd offered ad lib concentrates and roughages throughout their lifetime were investigated. Five severely affected, chronically lame animals were euthanased and examined postmortem. Foot pathology consisted of distortion of the claw shape and irregular fissures over the solar and bulbar horn with the distal phalanx rotated downwards on two claws. Rumen pH was measured between 5.26 and 5.46 with moderate rumen mucosa hyperkeratosis, and ulcerative, mild lymphocytic rumenitis. Feet showed irregular hyperplasia of the epidermal laminae with parakeratotic hyperkeratosis, especially in solar regions. Dense clusters of lymphocytes expanded the dermal laminae. Based on these findings, chronic laminitis was suspected. Ruminal hyperkeratosis was likely a result of prolonged periods of acidosis. The consequences of feeding a high-concentrate ration throughout the life of dairy goats need more research

Temporal networks of face-to-face human interactions

The ever increasing adoption of mobile technologies and ubiquitous services allows to sense human behavior at unprecedented levels of details and scale. Wearable sensors are opening up a new window on human mobility and proximity at the finest resolution of face-to-face proximity. As a consequence, empirical data describing social and behavioral networks are acquiring a longitudinal dimension that brings forth new challenges for analysis and modeling. Here we review recent work on the representation and analysis of temporal networks of face-to-face human proximity, based on large-scale datasets collected in the context of the SocioPatterns collaboration. We show that the raw behavioral data can be studied at various levels of coarse-graining, which turn out to be complementary to one another, with each level exposing different features of the underlying system. We briefly review a generative model of temporal contact networks that reproduces some statistical observables. Then, we shift our focus from surface statistical features to dynamical processes on empirical temporal networks. We discuss how simple dynamical processes can be used as probes to expose important features of the interaction patterns, such as burstiness and causal constraints. We show that simulating dynamical processes on empirical temporal networks can unveil differences between datasets that would otherwise look statistically similar. Moreover, we argue that, due to the temporal heterogeneity of human dynamics, in order to investigate the temporal properties of spreading processes it may be necessary to abandon the notion of wall-clock time in favour of an intrinsic notion of time for each individual node, defined in terms of its activity level. We conclude highlighting several open research questions raised by the nature of the data at hand.Comment: Chapter of the book "Temporal Networks", Springer, 2013. Series: Understanding Complex Systems. Holme, Petter; Saram\"aki, Jari (Eds.

The gait profile score characterises walking performance impairments in young stroke survivors

Background: The Gait Profile Score (GPS) provides a composite measure of the quality of joint movement during walking, but the relationship between this measure and metabolic cost, temporal (e.g. walking speed) and spatial (e.g. stride length) parameters in stroke survivors has not been reported. Research Question: The aims of this study were to compare the GPS (paretic, non-paretic, and overall score) of young stroke survivors to the healthy able-bodied control and determine the relationship between the GPS and metabolic cost, temporal (walking speed, stance time asymmetry) and spatial (stride length, stride width, step length asymmetry) parameters in young stroke survivors to understand whether the quality of walking affects walking performance in stroke survivors. Methods: Thirty-nine young stroke survivors aged between 18 and 65years and 15 healthy age-matched able-bodied controls were recruited from six hospital sites in Wales, UK. Joint range of motion at the pelvis, hip, knee and ankle, and temporal and spatial parameters were measured during walking on level ground at self-selected speed with calculation of the Gait Variable Score and then the GPS. Results: GPS for the paretic leg (9.40° (8.60–10.21) p < 0.001), non-paretic leg (11.42° (10.20–12.63) p < 0.001) and overall score (11.18° (10.26–12.09) p < 0.001)) for stroke survivors were significantly higher than the control (4.25° (3.40–5.10), 5.92° (5.11 (6.73)). All parameters with the exception of step length symmetry ratio correlated moderate to highly with the GPS for the paretic, non-paretic, and/or overall score (ρ = <−0.732 (p < 0.001)). Significance: The quality of joint movement during walking measured via the GPS is directly related to the speed and efficiency of walking, temporal (stance time symmetry) and spatial (stride length, stride width) parameters in young stroke survivors

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

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