On discrete integrable equations with convex variational principles

We investigate the variational structure of discrete Laplace-type equations that are motivated by discrete integrable quad-equations. In particular, we explain why the reality conditions we consider should be all that are reasonable, and we derive sufficient conditions (that are often necessary) on the labeling of the edges under which the corresponding generalized discrete action functional is convex. Convexity is an essential tool to discuss existence and uniqueness of solutions to Dirichlet boundary value problems. Furthermore, we study which combinatorial data allow convex action functionals of discrete Laplace-type equations that are actually induced by discrete integrable quad-equations, and we present how the equations and functionals corresponding to (Q3) are related to circle patterns.Comment: 39 pages, 8 figures. Revision of the whole manuscript, reorder of sections. Major changes due to additional reality conditions for (Q3) and (Q4): new Section 2.3; Theorem 1 and Sections 3.5, 3.6, 3.7 update

Discrete Nonholonomic Lagrangian Systems on Lie Groupoids

This paper studies the construction of geometric integrators for nonholonomic systems. We derive the nonholonomic discrete Euler-Lagrange equations in a setting which permits to deduce geometric integrators for continuous nonholonomic systems (reduced or not). The formalism is given in terms of Lie groupoids, specifying a discrete Lagrangian and a constraint submanifold on it. Additionally, it is necessary to fix a vector subbundle of the Lie algebroid associated to the Lie groupoid. We also discuss the existence of nonholonomic evolution operators in terms of the discrete nonholonomic Legendre transformations and in terms of adequate decompositions of the prolongation of the Lie groupoid. The characterization of the reversibility of the evolution operator and the discrete nonholonomic momentum equation are also considered. Finally, we illustrate with several classical examples the wide range of application of the theory (the discrete nonholonomic constrained particle, the Suslov system, the Chaplygin sleigh, the Veselova system, the rolling ball on a rotating table and the two wheeled planar mobile robot).Comment: 45 page

Towards practice-based studies of HRM: an actor-network and communities of practice informed approach

HRM may have become co-terminus with the new managerialism in the rhetorical orthodoxies of the HRM textbooks and other platforms for its professional claims. However, we have detailed case-study data showing that HR practices can be much more complicated, nuanced and indeed resistive toward management within organizational settings. Our study is based on ethnographic research, informed by actor-network theory and community of practice theory conducted by one of the authors over an 18-month period. Using actor-network theory in a descriptive and critical way, we analyse practices of managerial resistance, enrolment and counter-enrolment through which an unofficial network of managers used a formal HRM practice to successfully counteract the official strategy of the firm, which was to close parts of a production site. As a consequence, this network of middle managers effectively changed top management strategy and did so through official HRM practices, coupled with other actor-network building processes, arguably for the ultimate benefit of the organization, though against the initial views of the top management. The research reported here, may be characterized as a situated study of HRM-in-practice and we draw conclusions which problematize the concept of HRM in contemporary management literature

Secular dynamics of a planar model of the Sun-Jupiter-Saturn-Uranus system; effective stability into the light of Kolmogorov and Nekhoroshev theories

We investigate the long-time stability of the Sun-Jupiter-Saturn-Uranus system by considering a planar secular model, that can be regarded as a major refinement of the approach first introduced by Lagrange. Indeed, concerning the planetary orbital revolutions, we improve the classical circular approximation by replacing it with a solution that is invariant up to order two in the masses; therefore, we investigate the stability of the secular system for rather small values of the eccentricities. First, we explicitly construct a Kolmogorov normal form, so as to find an invariant KAM torus which approximates very well the secular orbits. Finally, we adapt the approach that is at basis of the analytic part of the Nekhoroshev's theorem, so as to show that there is a neighborhood of that torus for which the estimated stability time is larger than the lifetime of the Solar System. The size of such a neighborhood, compared with the uncertainties of the astronomical observations, is about ten times smaller.Comment: 31 pages, 2 figures. arXiv admin note: text overlap with arXiv:1010.260

Generalized Calogero-Moser systems from rational Cherednik algebras

We consider ideals of polynomials vanishing on the W-orbits of the intersections of mirrors of a finite reflection group W. We determine all such ideals which are invariant under the action of the corresponding rational Cherednik algebra hence form submodules in the polynomial module. We show that a quantum integrable system can be defined for every such ideal for a real reflection group W. This leads to known and new integrable systems of Calogero-Moser type which we explicitly specify. In the case of classical Coxeter groups we also obtain generalized Calogero-Moser systems with added quadratic potential.Comment: 36 pages; the main change is an improvement of section 7 so that it now deals with an arbitrary complex reflection group; Selecta Math, 201

Surface Roughness and Effective Stick-Slip Motion

The effect of random surface roughness on hydrodynamics of viscous incompressible liquid is discussed. Roughness-driven contributions to hydrodynamic flows, energy dissipation, and friction force are calculated in a wide range of parameters. When the hydrodynamic decay length (the viscous wave penetration depth) is larger than the size of random surface inhomogeneities, it is possible to replace a random rough surface by effective stick-slip boundary conditions on a flat surface with two constants: the stick-slip length and the renormalization of viscosity near the boundary. The stick-slip length and the renormalization coefficient are expressed explicitly via the correlation function of random surface inhomogeneities. The effective stick-slip length is always negative signifying the effective slow-down of the hydrodynamic flows by the rough surface (stick rather than slip motion). A simple hydrodynamic model is presented as an illustration of these general hydrodynamic results. The effective boundary parameters are analyzed numerically for Gaussian, power-law and exponentially decaying correlators with various indices. The maximum on the frequency dependence of the dissipation allows one to extract the correlation radius (characteristic size) of the surface inhomogeneities directly from, for example, experiments with torsional quartz oscillators.Comment: RevTeX4, 14 pages, 3 figure

Local structure of the set of steady-state solutions to the 2D incompressible Euler equations

It is well known that the incompressible Euler equations can be formulated in a very geometric language. The geometric structures provide very valuable insights into the properties of the solutions. Analogies with the finite-dimensional model of geodesics on a Lie group with left-invariant metric can be very instructive, but it is often difficult to prove analogues of finite-dimensional results in the infinite-dimensional setting of Euler's equations. In this paper we establish a result in this direction in the simple case of steady-state solutions in two dimensions, under some non-degeneracy assumptions. In particular, we establish, in a non-degenerate situation, a local one-to-one correspondence between steady-states and co-adjoint orbits.Comment: 81 page

Picturing the nation : The Celtic periphery as discursive other in the archaeological displays of the museum of Scotland

Using the archaeological displays at the Museum of Scotland in Edinburgh, this paper examines the exhibition as a site of identity creation through the negotiations between categories of same and Other. Through an analysis of the poetics of display, the paper argues that the exhibition constructs a particular relationship between the Celtic Fringe and Scottish National identity that draws upon the historical discourses of the Highlands and Islands of Scotland as a place and a time \u27apart\u27. This will be shown to have implications for the display of archaeological material in museums but also for contemporary understandings of Scottish National identity. <br /

An Integrated TCGA Pan-Cancer Clinical Data Resource to Drive High-Quality Survival Outcome Analytics

For a decade, The Cancer Genome Atlas (TCGA) program collected clinicopathologic annotation data along with multi-platform molecular profiles of more than 11,000 human tumors across 33 different cancer types. TCGA clinical data contain key features representing the democratized nature of the data collection process. To ensure proper use of this large clinical dataset associated with genomic features, we developed a standardized dataset named the TCGA Pan-Cancer Clinical Data Resource (TCGA-CDR), which includes four major clinical outcome endpoints. In addition to detailing major challenges and statistical limitations encountered during the effort of integrating the acquired clinical data, we present a summary that includes endpoint usage recommendations for each cancer type. These TCGA-CDR findings appear to be consistent with cancer genomics studies independent of the TCGA effort and provide opportunities for investigating cancer biology using clinical correlates at an unprecedented scale. Analysis of clinicopathologic annotations for over 11,000 cancer patients in the TCGA program leads to the generation of TCGA Clinical Data Resource, which provides recommendations of clinical outcome endpoint usage for 33 cancer types