Addenda and corrections to work done on the path-integral approach to classical mechanics

In this paper we continue the study of the path-integral formulation of classical mechanics and in particular we better clarify, with respect to previous papers, the geometrical meaning of the variables entering this formulation. With respect to the first paper with the same title, we {\it correct} here the set of transformations for the auxiliary variables $\lambda_{a}$. We prove that under this new set of transformations the Hamiltonian ${\widetilde{\cal H}}$, appearing in our path-integral, is an exact scalar and the same for the Lagrangian. Despite this different transformation, the variables $\lambda_{a}$ maintain the same operatorial meaning as before but on a different functional space. Cleared up this point we then show that the space spanned by the whole set of variables ($\phi, c, \lambda,\bar c$) of our path-integral is the cotangent bundle to the {\it reversed-parity} tangent bundle of the phase space ${\cal M}$ of our system and it is indicated as $T^{\star}(\Pi T{\cal M})$. In case the reader feel uneasy with this strange {\it Grassmannian} double bundle, we show in this paper that it is possible to build a different path-integral made only of {\it bosonic} variables. These turn out to be the coordinates of $T^{\star}(T^{\star}{\cal M})$ which is the double cotangent bundle of phase-space.Comment: Title changed, appendix expanded, few misprints fixe

Hilbert Space Structure in Classical Mechanics: (II)

In this paper we analyze two different functional formulations of classical mechanics. In the first one the Jacobi fields are represented by bosonic variables and belong to the vector (or its dual) representation of the symplectic group. In the second formulation the Jacobi fields are given as condensates of Grassmannian variables belonging to the spinor representation of the metaplectic group. For both formulations we shall show that, differently from what happens in the case presented in paper no. (I), it is possible to endow the associated Hilbert space with a positive definite scalar product and to describe the dynamics via a Hermitian Hamiltonian. The drawback of this formulation is that higher forms do not appear automatically and that the description of chaotic systems may need a further extension of the Hilbert space.Comment: 45 pages, RevTex; Abstract and Introduction improve

'Customers were not objects to suck blood from': Social relations in UK retail banks under changing performance management systems

Utilising an analytical framework informed by a moral economy approach, this article examines the social relationships between bank workers and customers in the context of changing performance management. Informed by 46 in‐depth interviews with branch workers and branch managers from UK banks, this article focusses on the interplay of the pressures arising from an intensified and all‐encompassing performance management system and bank workers lay morality. The article seeks to analyse why one group of bank workers engages with customers in a primarily instrumental manner, while another group tends to mediate and engage in oppositional practices which aim to avoid such an instrumentalisation. The article argues that moral economy gives voice to the agency of workers and the critical concerns of the social, economic and moral consequences of market‐driven and purely profit‐oriented workplace regimes

Cell compaction is not required for the development of gradient refractive index profiles in the embryonic chick lens

The development of the eye requires the co-ordinated integration of optical and neural elements to create a system with requisite optics for the given animal. The eye lens has a lamellar structure with gradually varying protein concentrations that increase towards the centre, creating a gradient refractive index or GRIN. This provides enhanced image quality compared to a homogeneous refractive index lens. The development of the GRIN during ocular embryogenesis has not been investigated previously. This study presents measurements using synchrotron X-ray Talbot interferometry and scanning electron microscopy of chick eyes from embryonic day 10: midway through embryonic development to E18: a few days before hatching. The lens GRIN profile is evident from the youngest age measured and increases in magnitude of refractive index at all points as the lens grows. The profile is parabolic along the optic axis and has two distinct regions in the equatorial plane. We postulate that these may be fundamental for the independent central and peripheral processes that contribute to the optimisation of image quality and the development of an eye that is emmetropic. The spatial distributions of the distinct GRIN profile regions match with previous measurements on different fibre cell groups in chick lenses of similar developmental stages. Results suggest that tissue compaction may not be necessary for development of the GRIN in the chick eye lens

Chondroitin sulfate as a potential modulator of the stem cell niche in cornea

Chondroitin sulfate (CS) is an important component of the extracellular matrix in multiple biological tissues. In cornea, the CS glycosaminoglycan (GAG) exists in hybrid form, whereby some of the repeating disaccharides are dermatan sulfate (DS). These CS/DS GAGs in cornea, through their presence on the proteoglycans, decorin and biglycan, help control collagen fibrillogenesis and organization. CS also acts as a regulatory ligand for a spectrum of signaling molecules, including morphogens, cytokines, chemokines, and enzymes during corneal growth and development. There is a growing body of evidence that precise expression of CS or CS/DS with specific sulfation motifs helps define the local extracellular compartment that contributes to maintenance of the stem cell phenotype. Indeed, recent evidence shows that CS sulfation motifs recognized by antibodies 4C3, 7D4, and 3B3 identify stem cell populations and their niches, along with activated progenitor cells and transitional areas of tissue development in the fetal human elbow. Various sulfation motifs identified by some CS antibodies are also specifically located in the limbal region at the edge of the mature cornea, which is widely accepted to represent the corneal epithelial stem cell niche. Emerging data also implicate developmental changes in the distribution of CS during corneal morphogenesis. This article will reflect upon the potential roles of CS and CS/DS in maintenance of the stem cell niche in cornea, and will contemplate the possible involvement of CS in the generation of eye-like tissues from human iPS (induced pluripotent stem) cells

Living with the h-index? Metric assemblages in the contemporary academy

This paper examines the relationship between metrics, markets and affect in the contemporary UK academy. It argues that the emergence of a particular structure of feeling amongst academics in the last few years has been closely associated with the growth and development of ‘quantified control’. It examines the functioning of a range of metrics: citations; workload models; transparent costing data; research assessments; teaching quality assessments; and commercial university league tables. It argues that these metrics, and others, although still embedded within an audit culture, increasingly function autonomously as a data assemblage able not just to mimic markets but, increasingly, to enact them. It concludes by posing some questions about the possible implications of this for the future of academic practice

The Short-Term Effect of Weight Loss Surgery on Volumetric Breast Density and Fibroglandular Volume

Purpose: Obesity and breast density are both associated with an increased risk of breast cancer and are potentially modifiable. Weight loss surgery (WLS) causes a significant reduction in the amount of body fat and a decrease in breast cancer risk. The effect of WLS on breast density and its components has not been documented. Here, we analyze the impact of WLS on volumetric breast density (VBD) and on each of its components (fibroglandular volume and breast volume) by using three-dimensional methods. Materials and Methods: Fibroglandular volume, breast volume, and their ratio, the VBD, were calculated from mammograms before and after WLS by using Volpara™ automated software. Results: For the 80 women included, average body mass index decreased from 46.0 ± 7.22 to 33.7 ± 7.06 kg/m2. Mammograms were performed on average 11.6 ± 9.4 months before and 10.1 ± 7 months after WLS. There was a significant reduction in average breast volume (39.4 % decrease) and average fibroglandular volume (15.5 % decrease), and thus, the average VBD increased from 5.15 to 7.87 % (p < 1 × 10−9) after WLS. When stratified by menopausal status and diabetic status, VBD increased significantly in all groups but only perimenopausal and postmenopausal women and non-diabetics experienced a significant reduction in fibroglandular volume. Conclusions: Breast volume and fibroglandular volume decreased, and VBD increased following WLS, with the most significant change observed in postmenopausal women and non-diabetics. Further studies are warranted to determine how physical and biological alterations in breast density components after WLS may impact breast cancer risk.ECU Open Access Publishing Support Fun