Modular synthesis of discrete controllers

This paper presents supervisory control theory in a process-algebraic setting, and proposes a way of synthesising modular supervisors that guarantee nonblocking. The framework used includes the possibility of hiding actions which results in nondeterminism. As modularity crucially depends on the process equivalence used, the paper studies possible equivalences and points out that, in order to be consistent with respect to the nonblocking property and to supervisor synthesis, a conflict-preserving equivalence must be used. It applies the results to synthesise nonblocking modular supervisors for a manufacturing system

Cosmological perturbations

We review the study of inhomogeneous perturbations about a homogeneous and isotropic background cosmology. We adopt a coordinate based approach, but give geometrical interpretations of metric perturbations in terms of the expansion, shear and curvature of constant-time hypersurfaces and the orthogonal timelike vector field. We give the gauge transformation rules for metric and matter variables at first and second order. We show how gauge invariant variables are constructed by identifying geometric or matter variables in physically-defined coordinate systems, and give the relations between many commonly used gauge-invariant variables. In particular we show how the Einstein equations or energy-momentum conservation can be used to obtain simple evolution equations at linear order, and discuss extensions to non-linear order. We present evolution equations for systems with multiple interacting fluids and scalar fields, identifying adiabatic and entropy perturbations. As an application we consider the origin of primordial curvature and isocurvature perturbations from field perturbations during inflation in the very early universe.Comment: 96 pages, submitted to Phys. Rep; v2: minor changes, typos corrected, references added, 1 figure added, corresponds to published versio

Determination of biogeochemical properties of marine particles using above water measurements of the degree of polarization at the Brewster angle

Retrieval of biogeochemical parameters from remotely sensed data in optically complex waters such as those found in coastal zones is a challenging task due to the effects of various water constituents (biogenic, nonalgal and inorganic particles, dissolved matter) on the radiation exiting the ocean. Since scattering by molecules, aerosols, hydrosols and reflection at the sea surface introduce and modify the polarization state of light, the polarized upward radiation contains embedded information about the intrinsic nature of aerosols and suspended matter in the ocean. In this study, shipborne above water angularly resolved visible/near infrared multiband measurements of the degree of polarization are analysed against their corresponding in-situ biogeochemically characterized water samples for the first time. Water samples and radiometric data were collected in the English Channel along an inshore-offshore transect. Angular variations in the degree of polarization P are found to be consistent with theory. Maximum values of P are observed near the Brewster viewing angle in the specular direction. Variations in the degree of polarization at the Brewster angle (PB) with water content revealed that the suspended particulate matter, which is mainly composed of inorganic particles during the experiment, contributes to depolarise the skylight reflection, thus reducing PB. An empirical polarization-based approach is proposed to determine biogeochemical properties of the particles. The concentration of inorganic particles can be estimated using PB to within ±13% based on the dataset used. Larger sets of polarized measurements are recommended to corroborate the tendency observed in this study

End-to-end Recovery of Human Shape and Pose

We describe Human Mesh Recovery (HMR), an end-to-end framework for reconstructing a full 3D mesh of a human body from a single RGB image. In contrast to most current methods that compute 2D or 3D joint locations, we produce a richer and more useful mesh representation that is parameterized by shape and 3D joint angles. The main objective is to minimize the reprojection loss of keypoints, which allow our model to be trained using images in-the-wild that only have ground truth 2D annotations. However, the reprojection loss alone leaves the model highly under constrained. In this work we address this problem by introducing an adversary trained to tell whether a human body parameter is real or not using a large database of 3D human meshes. We show that HMR can be trained with and without using any paired 2D-to-3D supervision. We do not rely on intermediate 2D keypoint detections and infer 3D pose and shape parameters directly from image pixels. Our model runs in real-time given a bounding box containing the person. We demonstrate our approach on various images in-the-wild and out-perform previous optimization based methods that output 3D meshes and show competitive results on tasks such as 3D joint location estimation and part segmentation.Comment: CVPR 2018, Project page with code: https://akanazawa.github.io/hmr

A Concise Introduction to Perturbation Theory in Cosmology

We give a concise, self-contained introduction to perturbation theory in cosmology at linear and second order, striking a balance between mathematical rigour and usability. In particular we discuss gauge issues and the active and passive approach to calculating gauge transformations. We also construct gauge-invariant variables, including the second order tensor perturbation on uniform curvature hypersurfaces.Comment: revtex4, 16 pages, 3 figures; v2: minor changes, typos corrected, reference added, version accepted by CQ