Block designs for experiments with non-normal response

Many experiments measure a response that cannot be adequately described by a linear model withnormally distributed errors and are often run in blocks of homogeneous experimental units. Wedevelop the first methods of obtaining efficient block designs for experiments with an exponentialfamily response described by a marginal model fitted via Generalized Estimating Equations. Thismethodology is appropriate when the blocking factor is a nuisance variable as, for example, occursin industrial experiments. A D-optimality criterion is developed for finding designs robust to thevalues of the marginal model parameters and applied using three strategies: unrestricted algorithmicsearch, use of minimum-support designs, and blocking of an optimal design for the correspondingGeneralized Linear Model. Designs obtained from each strategy are critically compared and shownto be much more efficient than designs that ignore the blocking structure. The designs are comparedfor a range of values of the intra-block working correlation and for exchangeable, autoregressive andnearest neighbor structures. An analysis strategy is developed for a binomial response that allows es-timation from experiments with sparse data, and its efectiveness demonstrated. The design strategiesare motivated and demonstrated through the planning of an experiment from the aeronautics industr

Load-depth sensing of isotropic, linear viscoelastic materials using rigid axisymmetric indenters

An indentation experiment involves five variables: indenter shape, material behavior of the substrate, contact size, applied load and indentation depth. Only three variable are known afterwards, namely, indenter shape, plus load and depth as function of time. As the contact size is not measured and the determination of the material properties is the very aim of the test; two equations are needed to obtain a mathematically solvable system. For elastic materials, the contact size can always be eliminated once and for all in favor of the depth; a single relation between load, depth and material properties remains with the latter variable as unknown. For viscoelastic materials where hereditary integrals model the constitutive behavior, the relation between depth and contact size usually depends also on the (time-dependent) properties of the material. Solving the inverse problem, i.e., determining the material properties from the experimental data, therefore needs both equations. Extending Sneddon's analysis of the indentation problem for elastic materials to include viscoelastic materials, the two equations mentioned above are derived. To find the time dependence of the material properties the feasibility of Golden and Graham's method of decomposing hereditary integrals (J.M. Golden and G.A.C. Graham. Boundary value problems in linear viscoelasticity, Springer, 1988) is investigated and applied to a single load-unload process and to sinusoidally driven stationary state indentation processes.Comment: 116 pages, 29 figure

The dynamical distance and intrinsic structure of the globular cluster omega Centauri

We determine the dynamical distance D, inclination i, mass-to-light ratio M/L and the intrinsic orbital structure of the globular cluster omega Cen, by fitting axisymmetric dynamical models to the ground-based proper motions of van Leeuwen et al. and line-of-sight velocities from four independent data-sets. We correct the observed velocities for perspective rotation caused by the space motion of the cluster, and show that the residual solid-body rotation component in the proper motions can be taken out without any modelling other than assuming axisymmetry. This also provides a tight constraint on D tan i. Application of our axisymmetric implementation of Schwarzschild's orbit superposition method to omega Cen reveals no dynamical evidence for a significant radial dependence of M/L. The best-fit dynamical model has a stellar V-band mass-to-light ratio M/L_V = 2.5 +/- 0.1 M_sun/L_sun and an inclination i = 50 +/- 4 degrees, which corresponds to an average intrinsic axial ratio of 0.78 +/- 0.03. The best-fit dynamical distance D = 4.8 +/- 0.3 kpc (distance modulus 13.75 +/- 0.13 mag) is significantly larger than obtained by means of simple spherical or constant-anisotropy axisymmetric dynamical models, and is consistent with the canonical value 5.0 +/- 0.2 kpc obtained by photometric methods. The total mass of the cluster is (2.5 +/- 0.3) x 10^6 M_sun. The best-fit model is close to isotropic inside a radius of about 10 arcmin and becomes increasingly tangentially anisotropic in the outer region, which displays significant mean rotation. This phase-space structure may well be caused by the effects of the tidal field of the Milky Way. The cluster contains a separate disk-like component in the radial range between 1 and 3 arcmin, contributing about 4% to the total mass.Comment: 37 pages (23 figures), accepted for publication in A&A, abstract abridged, for PS and PDF file with full resolution figures, see http://www.strw.leidenuniv.nl/~vdven/oc

Optimal Tradeoff Between Exposed and Hidden Nodes in Large Wireless Networks

Wireless networks equipped with the CSMA protocol are subject to collisions due to interference. For a given interference range we investigate the tradeoff between collisions (hidden nodes) and unused capacity (exposed nodes). We show that the sensing range that maximizes throughput critically depends on the activation rate of nodes. For infinite line networks, we prove the existence of a threshold: When the activation rate is below this threshold the optimal sensing range is small (to maximize spatial reuse). When the activation rate is above the threshold the optimal sensing range is just large enough to preclude all collisions. Simulations suggest that this threshold policy extends to more complex linear and non-linear topologies

Triaxial orbit-based modelling of the Milky Way Nuclear Star Cluster

We construct triaxial dynamical models for the Milky Way nuclear star cluster using Schwarzschild's orbit superposition technique. We fit the stellar kinematic maps presented in Feldmeier et al. (2014). The models are used to constrain the supermassive black hole mass M_BH, dynamical mass-to-light ratio M/L, and the intrinsic shape of the cluster. Our best-fitting model has M_BH = (3.0 +1.1 -1.3)x10^6 M_sun, M/L = (0.90 +0.76 -0.08) M_sun/L_{sun,4.5micron}, and a compression of the cluster along the line-of-sight. Our results are in agreement with the direct measurement of the supermassive black hole mass using the motion of stars on Keplerian orbits. The mass-to-light ratio is consistent with stellar population studies of other galaxies in the mid-infrared. It is possible that we underestimate M_BH and overestimate the cluster's triaxiality due to observational effects. The spatially semi-resolved kinematic data and extinction within the nuclear star cluster bias the observations to the near side of the cluster, and may appear as a compression of the nuclear star cluster along the line-of-sight. We derive a total dynamical mass for the Milky Way nuclear star cluster of M_MWNSC = (2.1 +-0.7)x10^7 M_sun within a sphere with radius r = 2 x r_eff = 8.4 pc. The best-fitting model is tangentially anisotropic in the central r = 0.5-2 pc of the nuclear star cluster, but close to isotropic at larger radii. Our triaxial models are able to recover complex kinematic substructures in the velocity map.Comment: 14 pages, 10 figures. Accepted for publication in MNRA

General solution of the Jeans equations for triaxial galaxies with separable potentials

The Jeans equations relate the second-order velocity moments to the density and potential of a stellar system. For general three-dimensional stellar systems, there are three equations and six independent moments. By assuming that the potential is triaxial and of separable Staeckel form, the mixed moments vanish in confocal ellipsoidal coordinates. Consequently, the three Jeans equations and three remaining non-vanishing moments form a closed system of three highly-symmetric coupled first-order partial differential equations in three variables. These equations were first derived by Lynden-Bell, over 40 years ago, but have resisted solution by standard methods. We present the general solution here. We consider the two-dimensional limiting cases first. We solve their Jeans equations by a new method which superposes singular solutions. The singular solutions, which are new, are standard Riemann-Green functions. The two-dimensional solutions are applied to non-axisymmetric discs, oblate and prolate spheroids, and also to the scale-free triaxial limit. We then extend the method of singular solutions to the triaxial case, and obtain a full solution. The general solution can be expressed in terms of complete (hyper)elliptic integrals which can be evaluated in a straightforward way, and provides the full set of second moments which can support a triaxial density distribution in a separable triaxial potential. (abridged)Comment: 28 pages (7 figures), LaTeX MN2e, accepted for publication in MNRA