Scale Models

Introduction: Without being informed of the expected product, the students will make a Play-doh model of the Earth-Moon system, scaled to size and distance. The facilitator will reveal the true identity of the system at the conclusion of the activity. During the construction phase, students try to guess what members of the solar system their model represents. Each group receives different amounts of Play-doh, with each group assigned a color (red, blue, yellow, white). At the end, groups set up their models and inspect the models of other groups. They report patterns of scale that they notice; as the amount of Play-doh increases, for example, so do the size and distance of the model.McDonald Observator

Large Scale Variational Bayesian Inference for Structured Scale Mixture Models

Natural image statistics exhibit hierarchical dependencies across multiple scales. Representing such prior knowledge in non-factorial latent tree models can boost performance of image denoising, inpainting, deconvolution or reconstruction substantially, beyond standard factorial "sparse" methodology. We derive a large scale approximate Bayesian inference algorithm for linear models with non-factorial (latent tree-structured) scale mixture priors. Experimental results on a range of denoising and inpainting problems demonstrate substantially improved performance compared to MAP estimation or to inference with factorial priors.Comment: Appears in Proceedings of the 29th International Conference on Machine Learning (ICML 2012

Chiral Models of Weak Scale Supersymmetry

I discuss supersymmetric extensions of the Standard Model containing an extra U(1)' gauge symmetry which provide a solution to the mu-problem and at the same time protect the proton from decaying via dimension 4 operators. Moreover, all fields are protected by chirality and supersymmetry from acquiring high scale masses. The additional requirements of anomaly cancellation and gauge coupling unification imply the existence of extra matter multiplets and that several fields participate in U(1)' symmetry breaking simultaneously. While there are several studies addressing subsets of these requirements, this work uncovers simultaneous solutions to all of them. It is surprising and encouraging that extending the Minimal Supersymmetric Standard Model by a simple U(1) factor solves its major drawbacks with respect to the non-supersymmetric Standard Model, especially as current precision data seem to offer a hint to the existence of its corresponding Z' boson. It is also remarkable that there are many solutions where the U(1)' charges of the known quarks and leptons are predicted to be identical to those E_6 motivated Z' bosons which give the best fit to the data. I discuss the solutions to these constraints including some phenomenological implications.Comment: 19 page

Warped metrics for location-scale models

This paper argues that a class of Riemannian metrics, called warped metrics, plays a fundamental role in statistical problems involving location-scale models. The paper reports three new results : i) the Rao-Fisher metric of any location-scale model is a warped metric, provided that this model satisfies a natural invariance condition, ii) the analytic expression of the sectional curvature of this metric, iii) the exact analytic solution of the geodesic equation of this metric. The paper applies these new results to several examples of interest, where it shows that warped metrics turn location-scale models into complete Riemannian manifolds of negative sectional curvature. This is a very suitable situation for developing algorithms which solve problems of classification and on-line estimation. Thus, by revealing the connection between warped metrics and location-scale models, the present paper paves the way to the introduction of new efficient statistical algorithms.Comment: preprint of a submission to GSI 2017 conferenc

Holography for chiral scale-invariant models

Deformation of any d-dimensional conformal field theory by a constant null source for a vector operator of dimension (d + z -1) is exactly marginal with respect to anisotropic scale invariance, of dynamical exponent z. The holographic duals to such deformations are AdS plane waves, with z=2 being the Schrodinger geometry. In this paper we explore holography for such chiral scale-invariant models. The special case of z=0 can be realized with gravity coupled to a scalar, and is of particular interest since it is related to a Lifshitz theory with dynamical exponent two upon dimensional reduction. We show however that the corresponding reduction of the dual field theory is along a null circle, and thus the Lifshitz theory arises upon discrete light cone quantization of an anisotropic scale invariant field theory.Comment: 62 pages; v2, published version, minor improvements and references adde

Scale Factor Self-Dual Cosmological Models

We implement a conformal time scale factor duality for Friedmann-Robertson-Walker cosmological models, which is consistent with the weak energy condition. The requirement for self-duality determines the equations of state for a broad class of barotropic fluids. We study the example of a universe filled with two interacting fluids, presenting an accelerated and a decelerated period, with manifest UV/IR duality. The associated self-dual scalar field interaction turns out to coincide with the "radiation-like" modified Chaplygin gas models. We present an equivalent realization of them as gauged K\"ahler sigma models (minimally coupled to gravity) with very specific and interrelated K\"ahler- and super-potentials. Their applications in the description of hilltop inflation and also as quintessence models for the late universe are discussed.Comment: v3, improved and extended version to be published in JHEP; new results added to sect.2; 4 figures; 17pg