Revisiting the radio interferometer measurement equation. IV. A generalized tensor formalism

The radio interferometer measurement equation (RIME), especially in its 2x2 form, has provided a comprehensive matrix-based formalism for describing classical radio interferometry and polarimetry, as shown in the previous three papers of this series. However, recent practical and theoretical developments, such as phased array feeds (PAFs), aperture arrays (AAs) and wide-field polarimetry, are exposing limitations of the formalism. This paper aims to develop a more general formalism that can be used to both clearly define the limitations of the matrix RIME, and to describe observational scenarios that lie outside these limitations. Some assumptions underlying the matrix RIME are explicated and analysed in detail. To this purpose, an array correlation matrix (ACM) formalism is explored. This proves of limited use; it is shown that matrix algebra is simply not a sufficiently flexible tool for the job. To overcome these limitations, a more general formalism based on tensors and the Einstein notation is proposed and explored both theoretically, and with a view to practical implementations. The tensor formalism elegantly yields generalized RIMEs describing beamforming, mutual coupling, and wide-field polarimetry in one equation. It is shown that under the explicated assumptions, tensor equations reduce to the 2x2 RIME. From a practical point of view, some methods for implementing tensor equations in an optimal way are proposed and analysed. The tensor RIME is a powerful means of describing observational scenarios not amenable to the matrix RIME. Even in cases where the latter remains applicable, the tensor formalism can be a valuable tool for understanding the limits of such applicability.Comment: 16 pages, no figures, accepted by A&

Assessing the food preference of the brushtail possum (Trichosurus vulpecular) using fixed-ratio schedules

The quality of different foods has been found in previous studies to effect an animal’s performance on fixed-ratio schedules. Foods that are of a higher quality should maintain behaviour to larger fixed-ratio values than foods of a lower quality. The present study examined the performance maintained by increasing fixed-ratio schedules by four different foods (Rolled Oats, Cocoa Puffs™ and flaked barley, All Bran™ and Soy Protein) with six brushtail possum (Trischosurus vulpecula). Overall response rates and running response rates both generally showed a bitonic function, and post-reinforcement pauses showed a modest increase with increases in the fixed-ratio. The equations of two quantitative models; Behavioural economics and mathematical principles of reinforcement (MPR) were fitted to the data to see how different food types affected the two models ability to predict behaviour. This was measured through two parameter estimates, alpha (α) and specific activation (αs). Both demand equations and the MPR equation described the data fairly well. The parameter estimates for specific activation (αs) showed a significant difference in value across the foods, but there was no significant difference across foods for parameter estimates of alpha (α). There was a weak correlation between parameter estimates of α and αs (r =-0.245, p =0.0926) . The four foods used in this study were also tested in a paired-stimulus preference assessment. The foods that were assessed as being of more value in the behavioural economic equations and the MPR model, for some possums were identified as being more preferred, but this was not consistent for all possums

Revisiting the radio interferometer measurement equation. I. A full-sky Jones formalism

Since its formulation by Hamaker et al., the radio interferometer measurement equation (RIME) has provided a rigorous mathematical basis for the development of novel calibration methods and techniques, including various approaches to the problem of direction-dependent effects (DDEs). This series of papers aims to place recent developments in the treatment of DDEs into one RIME-based mathematical framework, and to demonstrate the ease with which the various effects can be described and understood. It also aims to show the benefits of a RIME-based approach to calibration. Paper I re-derives the RIME from first principles, extends the formalism to the full-sky case, and incorporates DDEs. Paper II then uses the formalism to describe self-calibration, both with a full RIME, and with the approximate equations of older software packages, and shows how this is affected by DDEs. It also gives an overview of real-life DDEs and proposed methods of dealing with them. Applying this to WSRT data (Paper III) results in a noise-limited image of the field around 3C 147 with a very high dynamic range (1.6 million), and none of the off-axis artifacts that plague regular selfcal. The resulting differential gain solutions contain significant information on DDEs, and can be used for iterative improvements of sky models. Perhaps most importantly, sources as faint as 2 mJy have been shown to yield meaningful differential gain solutions, and thus can be used as potential calibration beacons in other DDE-related schemes.Comment: 12 pages, no figures, published in A&

Nonlinear optical properties of functionalized DNA

Third-order nonlinear optical properties of functionalized deoxyribonucleic acid (DNA) are studied by optical third harmonic generation at 1 0642 nm fundamental wavelength. The studies were performed on thin films of DNA-CTMA and DNA-CTMA doped with a charge transfer molecules DR1 and with a cobalt phthalocyanine. They show that DNA, similarly as synthetic polymers, can be used as matrix for highly active NLO chromophores

Ischemic preconditioning attenuates portal venous plasma concentrations of purines following warm liver ischemia in man

Background/Aims: Degradation of adenine nucleotides to adenosine has been suggested to play a critical role in ischemic preconditioning (IPC). Thus, we questioned in patients undergoing partial hepatectomy whether (i) IPC will increase plasma purine catabolites and whether (ii) formation of purines in response to vascular clamping (Pringle maneuver) can be attenuated by prior IPC. Methods: 75 patients were randomly assigned to three groups: group I underwent hepatectomy without vascular clamping; group II was subjected to the Pringle maneuver during resection, and group III was preconditioned (10 min ischemia and 10 min reperfusion) prior to the Pringle maneuver for resection. Central, portal venous and arterial plasma concentrations of adenosine, inosine, hypoxanthine and xanthine were determined by high-performance liquid chromatography. Results: Duration of the Pringle maneuver did not differ between patients with or without IPC. Surgery without vascular clamping had only a minor effect on plasma purine transiently increased. After the Pringle maneuver alone, purine plasma concentrations were most increased. This strong rise in plasma purines caused by the Pringle maneuver, however, was significantly attenuated by IPC. When portal venous minus arterial concentration difference was calculated for inosine or hypoxanthine, the respective differences became positive in patients subjected to the Pringle maneuver and were completely prevented by preconditioning. Conclusion: These data demonstrate that (i) IPC increases formation of adenosine, and that (ii) the unwanted degradation of adenine nucleotides to purines caused by the Pringle maneuver can be attenuated by IPC. Because IPC also induces a decrease of portal venous minus arterial purine plasma concentration differences, IPC might possibly decrease disturbances in the energy metabolism in the intestine as well. Copyright (C) 2005 S. Karger AG, Basel

Groundwater flow system analysis in the regolith of Dodowa on the Accra Plains, Ghana

Study Region: Accra Plains. Study Focus: We conducted a field geology mapping, a well inventory exercise, used ERT, drilled boreholes at 8 locations (15–60 m depth), took drill core samples which we subjected to dilute acid leaching experiments, installed piezometers and equipped them with pressure transducers, analyzed tidal signals in high frequency groundwater hydrographs, carried out pumping tests, and, finally, took 49 groundwater samples. New Insights: Our results indicated a diverse groundwater system. On the one hand, groundwater was found at shallow depths in the saprolite of the Togo Structural Unit (TSU), which, in unweathered state, is composed of phyllites, schists, and quartzites. This system was shallow and predominantly unconfined, as revealed by tidal analysis. In addition, transmissivities of TSU saprolite, all in the order of < 6e-5 m2/s, reduced with depth, which indicated either the lack of a stratiform fractured layer or the presence of such layer beyond drilled depths. On the other hand, groundwater was found in fractures of the gneisses of the Dahomeyan Structural Unit (DSU). This system was potentially deeper, but DSU transmissivities were significantly lower than those of TSU saprolite. Hydrochemically, groundwater was mainly characterized by infiltration of wastewater, evidenced by elevated ion concentrations, including nitrate. Due to the thinly weathered basement, groundwater system development in the area is local and restricted to the Dodowa area

Виртуальная лаборатория на базе стенда AVR-микролаб

В статті розглянуті шляхи створення сучасної учбової лабораторії враховуючи матеріальні труднощі сучасної освіти.This paper is devoted to consider ways of making a modern student’s laboratory, taking into account financial troubles in the modern education

Technical note: Disentangling the groundwater response to Earth and atmospheric tides to improve subsurface characterisation

The groundwater response to Earth tides and atmospheric pressure changes can be used to understand subsurface processes and estimate hydraulic and hydro-mechanical properties. We develop a generalised frequency domain approach to disentangle the impacts of Earth and atmospheric tides on groundwater level responses. By considering the complex harmonic properties of the signal, we improve upon a previous method for quantifying barometric efficiency (BE), while simultaneously assessing system confinement and estimating hydraulic conductivity and specific storage. We demonstrate and validate this novel approach using an example barometric and groundwater pressure record with strong Earth tide influences. Our method enables improved and rapid assessment of subsurface processes and properties using standard pressure measurements

Four-level and two-qubit systems, sub-algebras, and unitary integration

Four-level systems in quantum optics, and for representing two qubits in quantum computing, are difficult to solve for general time-dependent Hamiltonians. A systematic procedure is presented which combines analytical handling of the algebraic operator aspects with simple solutions of classical, first-order differential equations. In particular, by exploiting $su(2) \oplus su(2)$ and $su(2) \oplus su(2) \oplus u(1)$ sub-algebras of the full SU(4) dynamical group of the system, the non-trivial part of the final calculation is reduced to a single Riccati (first order, quadratically nonlinear) equation, itself simply solved. Examples are provided of two-qubit problems from the recent literature, including implementation of two-qubit gates with Josephson junctions.Comment: 1 gzip file with 1 tex and 9 eps figure files. Unpack with command: gunzip RSU05.tar.g

NLO properties of functionalized DNA thin films

In this paper we investigate the third-order nonlinear optical properties of spin deposited thin films of DNA-based complexes using the optical third harmonic generation (THG) technique at a fundamental wavelength of 1064 nm. We found that the third-order susceptibility, χ(3)(− 3ω;ω,ω,ω), of DNA-based films was about one order of magnitude larger than that of our reference, a pure silica slab. In thin films doped with 5% of the chromophore disperse red 1 (DR1), a two order of magnitude larger value of χ(3)(− 3ω;ω,ω,ω) was observed