Finite dimensional semigroup quadratic algebras with the minimal number of relations

A quadratic semigroup algebra is an algebra over a field given by the generators x_1, . . . , x_n and a finite set of quadratic relations each of which either has the shape x_j x_k = 0 or the shape x_j x_k = x_l x_m . We prove that a quadratic semigroup algebra given by n generators and d=(n^2+n)/4 relations is always infinite dimensional. This strengthens the Golod–Shafarevich estimate for the above class of algebras. Our main result however is that for every n, there is a finite dimensional quadratic semigroup algebra with n generators and d_n relations, where d_n is the first integer greater than (n^2+n)/4 . That is, the above Golod–Shafarevich-type estimate for semigroup algebras is sharp.

DNA damage responses following exposure to modulated radiation fields

During the delivery of advanced radiotherapy treatment techniques modulated beams are utilised to increase dose conformity across the target volume. Recent investigations have highlighted differential cellular responses to modulated radiation fields particularly in areas outside the primary treatment field that cannot be accounted for by scattered dose alone. In the present study, we determined the DNA damage response within the normal human fibroblast AG0-1522B and the prostate cancer cell line DU-145 utilising the DNA damage assay. Cells plated in slide flasks were exposed to 1 Gy uniform or modulated radiation fields. Modulated fields were delivered by shielding 25%, 50% or 75% of the flask during irradiation. The average number of 53BP1 or ?H2AX foci was measured in 2 mm intervals across the slide area. Following 30 minutes after modulated radiation field exposure an increase in the average number of foci out-of-field was observed when compared to non-irradiated controls. In-field, a non-uniform response was observed with a significant decrease in the average number of foci compared to uniformly irradiated cells. Following 24 hrs after exposure there is evidence for two populations of responding cells to bystander signals in-and out-of-field. There was no significant difference in DNA damage response between 25%, 50% or 75% modulated fields. The response was dependent on cellular secreted intercellular signalling as physical inhibition of intercellular communication abrogated the observed response. Elevated residual DNA damage observed within out-of-field regions decreased following addition of an inducible nitric oxide synthase inhibitor (Aminoguanidine). These data show, for the first time, differential DNA damage responses in-and out-of-field following modulated radiation field delivery. This study provides further evidence for a role of intercellular communication in mediating cellular radiobiological response to modulated radiation fields and may inform the refinement of existing radiobiological models for the optimization of advanced radiotherapy treatment plans. © 2012 Trainor et al.

The dynamics of arsenic in four paddy fields in the Bengal delta

Irrigation with arsenic contaminated groundwater in the Bengal Delta may lead to As accumulation in the soil and rice grain. The dynamics of As concentration and speciation in paddy fields during dry season (boro) rice cultivation were investigated at 4 sites in Bangladesh and West Bengal, India. Three sites which were irrigated with high As groundwater had elevated As concentrations in the soils, showing a significant gradient from the irrigation inlet across the field. Arsenic concentration and speciation in soil pore water varied temporally and spatially; higher As concentrations were associated with an increasing percentage of arsenite, indicating a reductive mobilization. Concentrations of As in rice grain varied by 2-7 fold within individual fields and were poorly related with the soil As concentration. A field site employing alternating flooded-dry irrigation produced the lowest range of grain As concentration, suggesting a lower soil As availability caused by periodic aerobic conditions.

Arsenic accumulation and phosphorus status in two rice (Oryza sativa L.) cultivars surveyed from fields in South China

The consumption of paddy rice (Oryza sativa L.) is a major inorganic arsenic exposure pathway in S.E. Asia. A multi-location survey was undertaken in Guangdong Province, South China to assess arsenic accumulation and speciation in 2 rice cultivars, one an Indica and the other a hybrid Indica. The results showed that arsenic concentrations in rice tissue increased in the order grain <husk <straw <root. Rice grain arsenic content of 2 rice cultivars was significant different and correlated with phosphorus concentration and molar ratio of P/As in shoot, being higher for the Indica cultivar than for the hybrid Indica, which suggests altering shoot phosphorus status as a promising route for breeding rice cultivars with reduced grain arsenic. Speciation of grain arsenic, performed using HPLC-ICP-MS, identified inorganic arsenic as the dominant arsenic species present in the rice grain.

Dynamics of Self-Generated, Large Amplitude Magnetic Fields Following High-Intensity Laser Matter Interaction

The dynamics of magnetic fields with an amplitude of several tens of megagauss, generated at both sides of a solid target irradiated with a high-intensity (~1019W/cm2) picosecond laser pulse, has been spatially and temporally resolved using a proton imaging technique. The amplitude of the magnetic fields is sufficiently large to have a constraining effect on the radial expansion of the plasma sheath at the target surfaces. These results, supported by numerical simulations and simple analytical modeling, may have implications for ion acceleration driven by the plasma sheath at the rear side of the target as well as for the laboratory study of self-collimated high-energy plasma jets. © 2012 American Physical Society.

A study of velocity fields in the transition region of ε Eri (K2 V)

Analyses of the widths and shifts of optically thin emission lines in the ultraviolet spectrum of the active dwarf e Eri (K2 V) are presented. The spectra were obtained using the Space Telescope Imaging Spectrograph on the Hubble Space Telescope and the Far Ultraviolet Spectroscopic Explorer. The linewidths are used to find the non-thermal energy density and its variation with temperature from the chromosphere to the upper transition region. The energy fluxes that could be carried by Alfvén and acoustic waves are investigated, to test their possible roles in coronal heating. Acoustic waves do not appear to be a viable means of coronal heating. There is, in principle, ample flux in Alfvén waves, but detailed calculations of wave propagation are required before definite conclusions can be drawn concerning their viability. The high sensitivity and spectral resolution of the above instruments have allowed two-component Gaussian fits to be made to the profiles of the stronger transition region lines. The broad and narrow components that result share some similarities with those observed in the Sun, but in e Eri the broad component is redshifted relative to the narrow component and contributes more to the total line flux. The possible origins of the two components and the energy fluxes implied are discussed. On balance our results support the conclusion of Wood, Linsky & Ayres, that the narrow component is related to Alfvén waves reaching to the corona, but the origin of the broad component is not clear.

Selectable linear or quadratic coupling in an optomechanical system

There has been much interest recently in the analysis of optomechanical systems incorporating dielectric nano- or microspheres inside a cavity field. We analyse here the situation when one of the mirrors of the cavity itself is also allowed to move. We reveal that the interplay between the two oscillators yields a cross-coupling that results in, e.g., appreciable cooling and squeezing of the motion of the sphere, despite its nominal quadratic coupling. We also discuss a simple modification that would allow this cross-coupling to be removed at will, thereby yielding a purely quadratic coupling for the sphere.

The spark of life:The role of electric fields in regulating cell behaviour using the eye as a model system

Endogenous electric fields (EF) have long been known to influence cell behaviour during development, neural cell tropism, wound healing and cell behaviour generally. The effect is based on short circuiting of electrical potential differences across cell and tissue boundaries generated by ionic segregation. Recent in vitro and in vivo studies have shown that EF regulate not only cell movement but orientation of cells during mitosis, an effect which may underlie shaping of tissues and organs. The molecular basis of this effect is founded on receptor-mediated cell signalling events and alterations in cytoskeletal function as revealed in studies of gene deficient cells. Remarkably, not all cells respond directionally to EF in the same way and this has consequences, for instance, for lens development and vascular remodelling. The physical basis of EF effect may be related to changes induced in 'bound water' at the cell surface, whose organisation in association with trans-membrane proteins (e.g. receptors) is disrupted when EF are generated. Copyright © 2007 S. Karger AG.

Quantification of interpoint topographic correlations of threshold values in glaucomatous visual fields

Purpose: The authors sought to quantify neighboring and distant interpoint correlations of threshold values within the visual field in patients with glaucoma. Methods: Visual fields of patients with confirmed or suspected glaucoma were analyzed (n = 255). One eye per patient was included. Patients were examined using the 32 program of the Octopus 1-2-3. Linear regression analysis among each of the locations and the rest of the points of the visual field was performed, and the correlation coefficient was calculated. The degree of correlation was categorized as high (r > 0.66), moderate (0.66 = r > 0.33), or low (r = 0.33). The standard error of threshold estimation was calculated. Results: Most locations of the visual field had high and moderate correlations with neighboring points and with distant locations corresponding to the same nerve fiber bundle. Locations of the visual field had low correlations with those of the opposite hemifield, with the exception of locations temporal to the blind spot. The standard error of threshold estimation increased from 0.6 to 0.9 dB with an r reduction of 0.1. Conclusion: Locations of the visual field have highest interpoint correlation with neighboring points and with distant points in areas corresponding to the distribution of the retinal nerve fiber layer. The quantification of interpoint correlations may be useful in the design and interpretation of visual field tests in patients with glaucoma.

Comparison of two fast strategies, SITA fast and TOP, for the assessment of visual fields in glaucoma patients

Purpose: To compare two fast threshold strategies of visual field assessment; SITA Fast (HSF) and Tendency Orientated Perimetry (TOP), in detecting visual field loss in patients with glaucoma. Methods: Seventy-six glaucoma, ocular hypertensive and normal patients had HSF and TOP performed in random order. Quantitative comparisons for the global visual field indices - mean deviation and defect (MD) for HSF and TOP, and pattern standard deviation (PSD) for HSF and loss variance (LV) for TOP - were made using correlation coefficients. Humphrey global parameters were converted to Octopus equivalents, and method comparison analysis was used to determine agreement between the two strategies. Test duration times were compared using t-test. Sensitivity and specificity for these two algorithms were determined according to predetermined criteria. Results: High correlation coefficient values were obtained for MD measurements between HSF and TOP (r=-0.89, P

Generation of scaled protogalactic seed magnetic fields in laser-produced shock waves

The standard model for the origin of galactic magnetic fields is through the amplification of seed fields via dynamo or turbulent processes to the level consistent with present observations. Although other mechanisms may also operate, currents from misaligned pressure and temperature gradients (the Biermann battery process) inevitably accompany the formation of galaxies in the absence of a primordial field. Driven by geometrical asymmetries in shocks associated with the collapse of protogalactic structures, the Biermann battery is believed to generate tiny seed fields to a level of about 10 gauss (refs 7, 8). With the advent of high-power laser systems in the past two decades, a new area of research has opened in which, using simple scaling relations, astrophysical environments can effectively be reproduced in the laboratory. Here we report the results of an experiment that produced seed magnetic fields by the Biermann battery effect. We show that these results can be scaled to the intergalactic medium, where turbulence, acting on timescales of around 700 million years, can amplify the seed fields sufficiently to affect galaxy evolution.

Soil Moisture Deficit as a predictor of the trend in soil water status of grass fields

Nutrient loss from agricultural land following organic fertilizer spreading can lead to eutrophication and poor water quality. The risk of pollution is partly related to the soil water status during and after spreading. In response to these issues, a decision support system (DSS) for nutrient management has been developed to predict when soil and weather conditions are suitable for slurry spreading. At the core of the DSS, the Hybrid Soil Moisture Deficit (HSMD) model estimates soil water status relative to field capacity (FC) for three soil classes (well, moderately and poorly drained) and has potential to predict the occurrence of a transport vector when the soil is wetter than FC. Three years of field observation of volumetric water content was used to validate HSMD model predictions of water status and to ensure correct use and interpretation of the drainage classes. Point HSMD model predictions were validated with respect to the temporal and spatial variations in volumetric water content and soil strength properties. It was found that the HSMD model predictions were well related to topsoil water content through time, but a new class intermediate between poor and moderate, perhaps ‘imperfectly drained’, was needed. With correct allocations of a field into a drainage class, the HSMD model predictions reflect field scale trends in water status and therefore the model is suitable for use at the core of a DSS.