Stress-Energy-Momentum Tensors and the Belinfante-Rosenfeld Formula

We present a new method of constructing a stress-energy-momentum tensor for a classical field theory based on covariance considerations and Noether theory. The stress-energy-momentum tensor T ^μ _ν that we construct is defined using the (multi)momentum map associated to the spacetime diffeomorphism group. The tensor T ^μ _ν is uniquely determined as well as gauge-covariant, and depends only upon the divergence equivalence class of the Lagrangian. It satisfies a generalized version of the classical Belinfante-Rosenfeld formula, and hence naturally incorporates both the canonical stress-energy-momentum tensor and the “correction terms” that are necessary to make the latter well behaved. Furthermore, in the presence of a metric on spacetime, our T^(μν) coincides with the Hilbert tensor and hence is automatically symmetric

Concatenating Variational Principles and the Kinetic Stress-Energy-Momentum Tensor

We show how to "concatenate" variational principles over dierent bases into one over a single base, thereby providing a unied Lagrangian treatment of interacting systems. As an example we study a Klein{ Gordon eld interacting with a mesically charged particle. We employ our method to give a novel group-theoretic derivation of the kinetic stress-energy-momentum tensor density corresponding to the particle

Energy dependent Schrödinger operators and complex Hamiltonian systems on Riemann surfaces

We use so-called energy-dependent Schrödinger operators to establish a link between special classes of solutions on N-component systems of evolution equations and finite dimensional Hamiltonian systems on the moduli spaces of Riemann surfaces. We also investigate the phase-space geometry of these Hamiltonian systems and introduce deformations of the level sets associated to conserved quantities, which results in a new class of solutions with monodromy for N-component systems of PDEs. After constructing a variety of mechanical systems related to the spatial flows of nonlinear evolution equations, we investigate their semiclassical limits. In particular, we obtain semicalssical asymptotics for the Bloch eigenfunctions of the energy dependent Schrödinger operators, which is of importance in investigating zero-dispersion limits of N-component systems of PDEs

An upper limit to [C II] emission in a z ~= 5 galaxy

Low-ionization-state far-infrared (FIR) emission lines may be useful diagnostics of star-formation activity in young galaxies, and at high redshift may be detectable from the ground. In practice, however, very little is known concerning how strong such line emission might be in the early Universe. We attempted to detect the 158 micron [C II] line from a lensed galaxy at z = 4.926 using the Caltech Submillimeter Observatory. This source is an ordinary galaxy, in the sense that it shows high but not extreme star formation, but lensing makes it visible. Our analysis includes a careful consideration of the calibrations and weighting of the individual scans. We find only modest improvement over the simpler reduction methods, however, and the final spectrum remains dominated by systematic baseline ripple effects. We obtain a 95 per cent confidence upper limit of 33 mJy for a 200 km/s full width at half maximum line, corresponding to an unlensed luminosity of 1x10^9 L_sun for a standard cosmology. Combining this with a marginal detection of the continuum emission using the James Clerk Maxwell Telescope, we derive an upper limit of 0.4 per cent for the ratio of L_CII/L_FIR in this object.Comment: 5 pages, 2 figures, accepted for publication in MNRA

People, Penguins and Petri Dishes: Adapting Object Counting Models To New Visual Domains And Object Types Without Forgetting

In this paper we propose a technique to adapt a convolutional neural network (CNN) based object counter to additional visual domains and object types while still preserving the original counting function. Domain-specific normalisation and scaling operators are trained to allow the model to adjust to the statistical distributions of the various visual domains. The developed adaptation technique is used to produce a singular patch-based counting regressor capable of counting various object types including people, vehicles, cell nuclei and wildlife. As part of this study a challenging new cell counting dataset in the context of tissue culture and patient diagnosis is constructed. This new collection, referred to as the Dublin Cell Counting (DCC) dataset, is the first of its kind to be made available to the wider computer vision community. State-of-the-art object counting performance is achieved in both the Shanghaitech (parts A and B) and Penguins datasets while competitive performance is observed on the TRANCOS and Modified Bone Marrow (MBM) datasets, all using a shared counting model.Comment: 10 page

The Maxwell–Vlasov equations in Euler–Poincaré form

Low's well-known action principle for the Maxwell–Vlasov equations of ideal plasma dynamics was originally expressed in terms of a mixture of Eulerian and Lagrangian variables. By imposing suitable constraints on the variations and analyzing invariance properties of the Lagrangian, as one does for the Euler equations for the rigid body and ideal fluids, we first transform this action principle into purely Eulerian variables. Hamilton's principle for the Eulerian description of Low's action principle then casts the Maxwell–Vlasov equations into Euler–Poincaré form for right invariant motion on the diffeomorphism group of position-velocity phase space, [openface R]6. Legendre transforming the Eulerian form of Low's action principle produces the Hamiltonian formulation of these equations in the Eulerian description. Since it arises from Euler–Poincaré equations, this Hamiltonian formulation can be written in terms of a Poisson structure that contains the Lie–Poisson bracket on the dual of a semidirect product Lie algebra. Because of degeneracies in the Lagrangian, the Legendre transform is dealt with using the Dirac theory of constraints. Another Maxwell–Vlasov Poisson structure is known, whose ingredients are the Lie–Poisson bracket on the dual of the Lie algebra of symplectomorphisms of phase space and the Born–Infeld brackets for the Maxwell field. We discuss the relationship between these two Hamiltonian formulations. We also discuss the general Kelvin–Noether theorem for Euler–Poincaré equations and its meaning in the plasma context

Crowd behaviour and congestion analysis through deep machine learning

This thesis looks to advance understanding in the field of computer vision based crowd analysis through a combination of deep learning techniques, multi-task learning, and domain adaptation. Issues that have limited progress in this field to date include visual occlusion, scale and perspective issues, variation in scene content as well as a lack of labelled training data. Another negative trend that has emerged in this field as well as in computer vision in general is the development of bespoke, single-task techniques that cannot be easily extended or re-used. The core contributions of this work are as follows. First, deep learning methods are developed for several crowd analysis tasks including crowd counting, crowd density level estimation, crowd behaviour recognition and crowd behaviour anomaly detection. The proposed data-driven methods are shown to be superior to techniques which rely on hand-crafted features, overcoming many of the observed challenges and achieving state-of-the-art results. Second, multi-task learning strategies are applied to crowd behaviour and congestion analysis tasks, increasing the overall predictive performance and removing redundant model parameters. Finally, domain adaptation techniques are investigated as a means to extend a given crowd analysis model to perform the same task in new visual domains (e.g. medical, wildlife) and vice-versa, with original domain performance preserved