The Berry-Tabor conjecture for spin chains of Haldane-Shastry type

According to a long-standing conjecture of Berry and Tabor, the distribution of the spacings between consecutive levels of a "generic'' integrable model should follow Poisson's law. In contrast, the spacings distribution of chaotic systems typically follows Wigner's law. An important exception to the Berry-Tabor conjecture is the integrable spin chain with long-range interactions introduced by Haldane and Shastry in 1988, whose spacings distribution is neither Poissonian nor of Wigner's type. In this letter we argue that the cumulative spacings distribution of this chain should follow the "square root of a logarithm'' law recently proposed by us as a characteristic feature of all spin chains of Haldane-Shastry type. We also show in detail that the latter law is valid for the rational counterpart of the Haldane-Shastry chain introduced by Polychronakos.Comment: LaTeX with revtex4, 6 pages, 6 figure

Fouling control in membrane bioreactors with sewage-sludge based adsorbents

The potential application of powdered activated carbon (PAC) to mitigate membrane fouling has been tested in membrane bioreactors (MBRs) fed with cosmetic wastewater. Inexpensive powder activated carbon was prepared from sewage sludge biosolids (B-PAC) by pyrolysis (750 °C; 0.5 h) and air-activation (400 °C; 2 h). Adsorption capacities of 143 and 570 mg g −1 were reached for carbohydrates and proteins, respectively, quite similar to those of a commercial activated carbon (C-PAC). To check the effect of PAC addition on membrane fouling, three MBRs were simultaneously operated without (control-MBR) and with PAC (B-MBR and C-MBR) for 150 days in continuous mode at 8 L m −2  h −1 flux. Similar COD removal efficiencies were achieved in these three MBR systems. After 100 days of operation, the effect of the PACs on the sludge filterability was studied in the MBRs for 10 days. B-MBR showed stable transmembrane pressure (TMP) after 9 days of operation, unlike of control-MBR and C-MBR, where the TMP increased after the 2nd and 5th days, respectively. Therefore, operational cost saving can be achieved in the membrane cleaning due to decrease of fouling rate. Operating at stable state condition the addition of PAC gave rise to an increase of the critical flux of 25%. In an extra shear test, carried out at the end of the continuous experiment, a clear reduction in mean size of the flocs from 45 to 28 μm was observed in control-MBR. However, the extra shear led to a slight reduction of the mean size of flocs (less than 5%) in MBRs with PAC, with average sizes of 62 and 71 μm in C-MBR and B-MBR, respectively. The molecular weight fractionation of the MBR demonstrated a higher selectivity of B-PAC toward the adsorption of proteins smaller than 1 μm which prevents the irreversible fouling of the membranes. The membranes lifetime was increased because the B-PAC extended the filtration for a longer period than C-PAC, probably due to its easier in-situ regenerationThe authors greatly appreciatefinancial support by the SpanishMinisterio de Economia y Competitividad and Comunidad deMadrid through the projects CTM2013-43803-P and P2013/MAE-2716, respectivel

3D reconstruction of medical images from slices automatically landmarked with growing neural models

In this study, we utilise a novel approach to segment out the ventricular system in a series of high resolution T1-weighted MR images. We present a brain ventricles fast reconstruction method. The method is based on the processing of brain sections and establishing a fixed number of landmarks onto those sections to reconstruct the ventricles 3D surface. Automated landmark extraction is accomplished through the use of the self-organising network, the growing neural gas (GNG), which is able to topographically map the low dimensionality of the network to the high dimensionality of the contour manifold without requiring a priori knowledge of the input space structure. Moreover, our GNG landmark method is tolerant to noise and eliminates outliers. Our method accelerates the classical surface reconstruction and filtering processes. The proposed method offers higher accuracy compared to methods with similar efficiency as Voxel Grid