The symbolic model for algebra : functions and mechanisms

The symbolic mode of reasoning in algebra, as it emerged during the sixteenth century, can be considered as a form of model-based reasoning. In this paper we will discuss the functions and mechanisms of this model and show how the model relates to its arithmetical basis. We will argue that the symbolic model was made possible by the epistemic justification of the basic operations of algebra as practiced within the abbaco tradition. We will also show that this form of model-based reasoning facilitated the expansion of the number concept from Renaissance interpretations of number to the full notion of algebraic numbers

Nonlinear directional coupler for polychromatic light

We demonstrate that nonlinear directional coupler with special bending of waveguide axes can be used for all-optical switching of polychromatic light with very broad spectrum covering all visible region. The bandwidth of suggested device is enhanced five times compared to conventional couplers. Our results suggest novel opportunities for creation of all-optical logical gates and switches for polychromatic light with white-light and super-continuum spectrum.Comment: 3 pages, 3 figure

The application of graph theory and percolation analysis for assessing change in the spatial configuration of pond networks

Pond networks support high levels of biodiversity when compared to other freshwater ecosystems such as rivers, lakes and streams. The persistence of species in these small, sometimes ephemeral, aquatic habitats depends on the dispersal of individuals among ponds in the landscape. However, the number of ponds across the landscape is at a historical low as urbanisation and intensified agricultural practices have led to a substantial loss of ponds (nodes in the pond network) over more than a century. Here, we examine the extent and drivers of pond loss in a heavily urbanised landscape (Birmingham, UK) over 105 years and determine how pond loss influences key structural properties of the pond network using graph theoretic approaches. Specifically, we calculated minimum spanning trees (MST) and performed percolation analyses to determine changes in both the spatial configuration and resilience of the pond network through time. Pond numbers declined by 82% between ca1904 and 2009, such that pond density decreased from 7.1 km-2 to 1.3 km-2. The MST analyses revealed increased distance between ponds in the network (i.e. edge length increased) by up to 49% over the 105-year period, indicating that ponds in the modern landscape (2009) were considerably more isolated, with fewer neighbours. This study demonstrates that graph theory has an excellent potential to inform the management of pond networks in order to support ecological communities that are less vulnerable to environmental change

A new era of wide-field submillimetre imaging: on-sky performance of SCUBA-2

SCUBA-2 is the largest submillimetre wide-field bolometric camera ever built. This 43 square arc-minute field-of-view instrument operates at two wavelengths (850 and 450 microns) and has been installed on the James Clerk Maxwell Telescope on Mauna Kea, Hawaii. SCUBA-2 has been successfully commissioned and operational for general science since October 2011. This paper presents an overview of the on-sky performance of the instrument during and since commissioning in mid-2011. The on-sky noise characteristics and NEPs of the 450 and 850 micron arrays, with average yields of approximately 3400 bolometers at each wavelength, will be shown. The observing modes of the instrument and the on-sky calibration techniques are described. The culmination of these efforts has resulted in a scientifically powerful mapping camera with sensitivities that allow a square degree of sky to be mapped to 10 mJy/beam rms at 850 micron in 2 hours and 60 mJy/beam rms at 450 micron in 5 hours in the best weather.Comment: 18 pages, 15 figures.SPIE Conference series 8452, Millimetre, Submillimetre and Far-infrared Detectors and Instrumentation for Astronomy VI 201

Quantum limits to center-of-mass measurements

We discuss the issue of measuring the mean position (center-of-mass) of a group of bosonic or fermionic quantum particles, including particle number fluctuations. We introduce a standard quantum limit for these measurements at ultra-low temperatures, and discuss this limit in the context of both photons and ultra-cold atoms. In the case of fermions, we present evidence that the Pauli exclusion principle has a strongly beneficial effect, giving rise to a 1/N scaling in the position standard-deviation -- as opposed to a $1/\sqrt{N}$ scaling for bosons. The difference between the actual mean-position fluctuation and this limit is evidence for quantum wave-packet spreading in the center-of-mass. This macroscopic quantum effect cannot be readily observed for non-interacting particles, due to classical pulse broadening. For this reason, we also study the evolution of photonic and matter-wave solitons, where classical dispersion is suppressed. In the photonic case, we show that the intrinsic quantum diffusion of the mean position can contribute significantly to uncertainties in soliton pulse arrival times. We also discuss ways in which the relatively long lifetimes of attractive bosons in matter-wave solitons may be used to demonstrate quantum interference between massive objects composed of thousands of particles.Comment: 12 pages, 6 figures. Submitted to PRA. Revised to include more references as well as a discussion of fermionic center-of-mas

Work disability before and after a major cardiovascular event: a ten-year study using nationwide medical and insurance registers

We examined the trajectories of work disability before and after IHD and stroke events. New IHD (n = 13521) and stroke (n = 7162) cases in 2006-2008 were retrieved from nationwide Swedish hospital records and their annual work disability days five years before and after the date of diagnosis were retrieved from a nationwide disability register. There was no pre-event differences in disability days between the IHD and stroke cases and five years prior to the event, they were close to those observed in the general population. In the first post-event year, the adjusted mean days increased to 83.9 (95% CI 80.6-86.5) in IHD; to 179.5 (95% CI 172.4-186.8) in stroke, a six-fold increase in IHD and 14-fold in stroke. Work disability leveled off among the IHD cases but not among those who had stroke. The highest disability levels for the fifth post-event year after a stroke event was associated with pre-existing diabetes (146.9), mental disorder (141.2), non-employment (137.0), and immigrant status (117.9). In a working-age population, the increase in work disability after a cardiovascular event decreases close to the pre-event level in IHD but remains particularly high after stroke; among patients with comorbid depression or diabetes, immigrants, and those not in employment

Mode structure and photon number correlations in squeezed quantum pulses

The question of efficient multimode description of optical pulses is studied. We show that a relatively very small number of nonmonochromatic modes can be sufficient for a complete quantum description of pulses with Gaussian quadrature statistics. For example, a three-mode description was enough to reproduce the experimental data of photon number correlations in optical solitons [S. Spalter et al., Phys. Rev. Lett. 81, 786 (1998)]. This approach is very useful for a detailed understanding of squeezing properties of soliton pulses with the main potential for quantum communication with continuous variables. We show how homodyne detection and/or measurements of photon number correlations can be used to determine the quantum state of the multi-mode field. We also discuss a possible way of physical separation of the nonmonochromatic modes.Comment: 14 pages, 4 figures; minor revisions of the text, new references; to appear in the Phys. Rev.

Color separate singlets in e+e−e^+e^- annihilation

We use the method of color effective Hamiltonian to study the properties of states in which a gluonic subsystem forms a color singlet, and we will study the possibility that such a subsystem hadronizes as a separate unit. A parton system can normally be subdivided into singlet subsystems in many different ways, and one problem arises from the fact that the corresponding states are not orthogonal. We show that if only contributions of order $1/N_c^2$ are included, the problem is greatly simplified. Only a very limited number of states are possible, and we present an orthogonalization procedure for these states. The result is simple and intuitive and could give an estimate of the possibility to produce color separated gluonic subsystems, if no dynamical effects are important. We also study with a simple MC the possibility that configurations which correspond to "short strings" are dynamically favored. The advantage of our approach over more elaborate models is its simplicity, which makes it easier to estimate color reconnection effects in reactions which are more complicated than the relatively simple $e^+e^-$ annihilation.Comment: Revtex, 24 pages, 7 figures; Compared to the previous version, 1 new figure is added and Monte-Carlo results are re-analyzed, as suggested by the referee; To appear in Phys. Rev.

Resolving the inner jet structure of 1924-292 with the EVENT HORIZON TELESCOPE

We present the first 1.3 mm (230 GHz) very long baseline interferometry model image of an AGN jet using closure phase techniques with a four-element array. The model image of the quasar 1924-292 was obtained with four telescopes at three observatories: the James Clerk Maxwell Telescope (JCMT) on Mauna Kea in Hawaii, the Arizona Radio Observatory's Submillimeter Telescope (SMT) in Arizona, and two telescopes of the Combined Array for Research in Millimeterwave Astronomy (CARMA) in California in April 2009. With the greatly improved resolution compared with previous observations and robust closure phase measurement, the inner jet structure of 1924-292 was spatially resolved. The inner jet extends to the northwest along a position angle of $-53^\circ$ at a distance of 0.38\,mas from the tentatively identified core, in agreement with the inner jet structure inferred from lower frequencies, and making a position angle difference of $\sim 80^{\circ}$ with respect to the cm-jet. The size of the compact core is 0.15\,pc with a brightness temperature of $1.2\times10^{11}$\,K. Compared with those measured at lower frequencies, the low brightness temperature may argue in favor of the decelerating jet model or particle-cascade models. The successful measurement of closure phase paves the way for imaging and time resolving Sgr A* and nearby AGN with the Event Horizon Telescope.Comment: 6 pages, 4 figures, accepted for publication in ApJ