Autocalibration with the Minimum Number of Cameras with Known Pixel Shape

In 3D reconstruction, the recovery of the calibration parameters of the cameras is paramount since it provides metric information about the observed scene, e.g., measures of angles and ratios of distances. Autocalibration enables the estimation of the camera parameters without using a calibration device, but by enforcing simple constraints on the camera parameters. In the absence of information about the internal camera parameters such as the focal length and the principal point, the knowledge of the camera pixel shape is usually the only available constraint. Given a projective reconstruction of a rigid scene, we address the problem of the autocalibration of a minimal set of cameras with known pixel shape and otherwise arbitrarily varying intrinsic and extrinsic parameters. We propose an algorithm that only requires 5 cameras (the theoretical minimum), thus halving the number of cameras required by previous algorithms based on the same constraint. To this purpose, we introduce as our basic geometric tool the six-line conic variety (SLCV), consisting in the set of planes intersecting six given lines of 3D space in points of a conic. We show that the set of solutions of the Euclidean upgrading problem for three cameras with known pixel shape can be parameterized in a computationally efficient way. This parameterization is then used to solve autocalibration from five or more cameras, reducing the three-dimensional search space to a two-dimensional one. We provide experiments with real images showing the good performance of the technique.Comment: 19 pages, 14 figures, 7 tables, J. Math. Imaging Vi

Locally finite groups containing a 2 -element with Chernikov centralizer

Suppose that a locally finite group G has a 2-element g with Chernikov centralizer. It is proved that if the involution in ⟨g⟩ has nilpotent centralizer, then G has a soluble subgroup of finite index

Covariant spinor representation of iosp(d,2/2)iosp(d,2/2) and quantization of the spinning relativistic particle

A covariant spinor representation of $iosp(d,2/2)$ is constructed for the quantization of the spinning relativistic particle. It is found that, with appropriately defined wavefunctions, this representation can be identified with the state space arising from the canonical extended BFV-BRST quantization of the spinning particle with admissible gauge fixing conditions after a contraction procedure. For this model, the cohomological determination of physical states can thus be obtained purely from the representation theory of the $iosp(d,2/2)$ algebra.Comment: Updated version with references included and covariant form of equation 1. 23 pages, no figure

Three manifestations of the pulsed harmonic potential

We consider, in turn, three systems being acted upon by a regularly pulsed harmonic potential (PHP). These are i) a classical particle, ii) a quantum particle, and iii) a directed line. We contrast the mechanics of the first two systems by parameterizing their bands of stability and periodicity. Interesting differences due to quantum fluctuations are examined in detail. The fluctuations of the directed line are calculated in the two cases of a binding PHP, and an unbinding PHP. In the latter case there is a finite maximum line length for a given potential strength.Comment: 34 Revtex pages, with 5 attached figure

Historical Criminology and the Explanatory Power of the Past

To what extent can the past ‘explain’ the present? This deceptively simple question lies at the heart of historical criminology (research which incorporates historical primary sources while addressing present-day debates and practices in the criminal justice field). This article seeks first to categorise the ways in which criminologists have used historical data thus far, arguing that it is most commonly deployed to ‘problematize’ the contemporary rather than to ‘explain’ it. The article then interrogates the reticence of criminologists to attribute explicative power in relation to the present to historical data. Finally, it proposes the adoption of long time-frame historical research methods, outlining three advantages which would accrue from this: the identification and analysis of historical continuities; a more nuanced, shared understanding of micro/macro change over time in relation to criminal justice; and a method for identifying and analysing instances of historical recurrence, particularly in perceptions and discourses around crime and justice

Covariant scalar representation of iosp(d,2/2)iosp(d,2/2) quantization of the scalar relativistic particle

A covariant scalar representation of $iosp(d,2/2)$ is constructed and analysed in comparison with existing methods for the quantization of the scalar relativistic particle. It is found that, with appropriately defined wavefunctions, this $iosp(d,2/2)$ produced representation can be identified with the state space arising from the canonical BFV-BRST quantization of the modular invariant, unoriented scalar particle (or antiparticle) with admissible gauge fixing conditions. For this model, the cohomological determination of physical states can thus be obtained purely from the representation theory of the $iosp(d,2/2)$ algebra.Comment: 16 pages Late

Assessing the impact of peat erosion on growing season CO2 fluxes by comparing erosional peat pans and surrounding vegetated haggs (article)

This is the author accepted manuscript. The final version is available from International Mire Conservation Group and International Peat Society via the DOI in this record.The research data supporting this publication are openly available from the University of Exeter's institutional repository at: https://doi.org/10.24378/exe.1143.Peatlands are recognised as an important but vulnerable ecological resource. Understanding the effects of existing damage, in this case erosion, enables more informed land management decisions to be made. Over the growing seasons of 2013 and 2014 photosynthesis and ecosystem respiration were measured using closed chamber techniques within vegetated haggs and erosional peat pans in Dartmoor National Park, southwest England. Below-ground total and heterotrophic respiration were measured and autotrophic respiration estimated from the vegetated haggs. The mean water table was significantly higher in the peat pans than in the vegetated haggs; because of this, and the switching from submerged to dry peat, there were differences in vegetation composition, photosynthesis and ecosystem respiration. In the peat pans photosynthetic CO2 uptake and ecosystem respiration were greater than in the vegetated haggs and strongly dependent on the depth to water table (r2>0.78, p<0.001). Whilst in the vegetated haggs, photosynthesis and ecosystem respiration had the strongest relationships with normalised difference vegetation index (NDVI) (r2=0.82, p<0.001) and soil temperature at 15 cm depth (r2=0.77, p=0.001). Autotrophic and total below-ground respiration in the vegetated haggs varied with soil temperature; heterotrophic respiration increased as water tables fell. An empirically derived net ecosystem model estimated that over the two growing seasons both the vegetated haggs (29 and 20 gC m 2; 95 % confidence intervals of -570 to 762 and -873 to 1105 gC m-2) and the peat pans (7 and 8 gC m 2; 95 % confidence intervals of -147 to 465 and -136 to 436 gC m 2) were most likely net CO2 sources. This study suggests that not only the visibly degraded bare peat pans but also the surrounding vegetated haggs are losing carbon to the atmosphere, particularly during warmer and drier conditions, highlighting a need for ecohydrological restoration.MomentaSouth West Water (SWW)Dartmoor National Park Authorit

Synchronization of fractional order chaotic systems

The chaotic dynamics of fractional order systems begin to attract much attentions in recent years. In this brief report, we study the master-slave synchronization of fractional order chaotic systems. It is shown that fractional order chaotic systems can also be synchronized.Comment: 3 pages, 5 figure

Long-range pollution transport during the MILAGRO-2006 campaign: a case study of a major Mexico City outflow event using free-floating altitude-controlled balloons

One of the major objectives of the Megacities Initiative: Local And Global Research Observations (MILAGRO-2006) campaign was to investigate the long-range transport of polluted Mexico City Metropolitan Area (MCMA) outflow and determine its downwind impacts on air quality and climate. Six research aircraft, including the National Center for Atmospheric Research (NCAR) C-130, made extensive chemical, aerosol, and radiation measurements above MCMA and more than 1000 km downwind in order to characterize the evolution of the outflow as it aged and dispersed over the Mesa Alta, Sierra Madre Oriental, Coastal Plain, and Gulf of Mexico. As part of this effort, free-floating Controlled-Meteorological (CMET) balloons, commanded to change altitude via satellite, made repeated profile measurements of winds and state variables within the advecting outflow. In this paper, we present an analysis of the data from two CMET balloons that were launched near Mexico City on the afternoon of 18 March 2006 and floated downwind with the MCMA pollution for nearly 30 h. The repeating profile measurements show the evolving structure of the outflow in considerable detail: its stability and stratification, interaction with other air masses, mixing episodes, and dispersion into the regional background. Air parcel trajectories, computed directly from the balloon wind profiles, show three transport pathways on 18–19 March: (a) high-altitude advection of the top of the MCMA mixed layer, (b) mid-level outflow over the Sierra Madre Oriental followed by decoupling and isolated transport over the Gulf of Mexico, and (c) low-level outflow with entrainment into a cleaner northwesterly jet above the Coastal Plain. The C-130 aircraft intercepted the balloon-based trajectories three times on 19 March, once along each of these pathways; in all three cases, peaks in urban tracer concentrations and LIDAR backscatter are consistent with MCMA pollution. In comparison with the transport models used in the campaign, the balloon-based trajectories appear to shear the outflow far more uniformly and decouple it from the surface, thus forming a thin but expansive polluted layer over the Gulf of Mexico that is well aligned with the aircraft observations. These results provide critical context for the extensive aircraft measurements made during the 18–19 March MCMA outflow event and may have broader implications for modelling and understanding long-range transport

Squeezed States of the Generalized Minimum Uncertainty State for the Caldirola-Kanai Hamiltonian

We show that the ground state of the well-known pseudo-stationary states for the Caldirola-Kanai Hamiltonian is a generalized minimum uncertainty state, which has the minimum allowed uncertainty $\Delta q \Delta p = \hbar \sigma_0/2$, where $\sigma_0 (\geq 1)$ is a constant depending on the damping factor and natural frequency. The most general symmetric Gaussian states are obtained as the one-parameter squeezed states of the pseudo-stationary ground state. It is further shown that the coherent states of the pseudo-stationary ground state constitute another class of the generalized minimum uncertainty states.Comment: RevTex4, 9 pages, no fingure; to be published in Journal of Physics