Complementary methods to investigate the development of clogging within a horizontal sub-surface flow tertiary treatment wetland

A combination of experimental methods was applied at a clogged, horizontal subsurface flow (HSSF) municipal wastewater tertiary treatment wetland (TW) in the UK, to quantify the extent of surface and subsurface clogging which had resulted in undesirable surface flow. The three dimensional hydraulic conductivity profile was determined, using a purpose made device which recreates the constant head permeameter test in-situ. The hydrodynamic pathways were investigated by performing dye tracing tests with Rhodamine WT and a novel multi-channel, data-logging, flow through Fluorimeter which allows synchronous measurements to be taken from a matrix of sampling points. Hydraulic conductivity varied in all planes, with the lowest measurement of 0.1 md1 corresponding to the surface layer at the inlet, and the maximum measurement of 1550 md1 located at a 0.4m depth at the outlet. According to dye tracing results, the region where the overland flow ceased received five times the average flow, which then vertically short-circuited below the rhizosphere. The tracer break-through curve obtained from the outlet showed that this preferential flow-path accounted for approximately 80% of the flow overall and arrived 8 h before a distinctly separate secondary flow-path. The overall volumetric efficiencyof the clogged system was 71% and the hydrology was simulated using a dual-path, dead-zone storage model. It is concluded that uneven inlet distribution, continuous surface loading and high rhizosphere resistance is responsible for the clog formation observed in this system. The average inlet hydraulic conductivity was 2 md1, suggesting that current European design guidelines, which predict that the system will reach an equilibrium hydraulic conductivity of 86 md1, do not adequately describe the hydrology of mature systems.

Generalized methods and solvers for noise removal from piecewise constant signals. I. Background theory

Removing noise from piecewise constant (PWC) signals is a challenging signal processing problem arising in many practical contexts. For example, in exploration geosciences, noisy drill hole records need to be separated into stratigraphic zones, and in biophysics, jumps between molecular dwell states have to be extracted from noisy fluorescence microscopy signals. Many PWC denoising methods exist, including total variation regularization, mean shift clustering, stepwise jump placement, running medians, convex clustering shrinkage and bilateral filtering; conventional linear signal processing methods are fundamentally unsuited. This paper (part I, the first of two) shows that most of these methods are associated with a special case of a generalized functional, minimized to achieve PWC denoising. The minimizer can be obtained by diverse solver algorithms, including stepwise jump placement, convex programming, finite differences, iterated running medians, least angle regression, regularization path following and coordinate descent. In the second paper, part II, we introduce novel PWC denoising methods, and comparisons between these methods performed on synthetic and real signals, showing that the new understanding of the problem gained in part I leads to new methods that have a useful role to play.

Critical noise levels for low-density parity check decoding

We determine the critical noise level for decoding low-density parity check error-correcting codes based on the magnetization enumerator (M), rather than on the weight enumerator (W) employed in the information theory literature. The interpretation of our method is appealingly simple, and the relation between the different decoding schemes such as typical pairs decoding, MAP, and finite temperature decoding (MPM) becomes clear. In addition, our analysis provides an explanation for the difference in performance between MN and Gallager codes. Our results are more optimistic than those derived using the methods of information theory and are in excellent agreement with recent results from another statistical physics approach.

Representational difference analysis:Critical appraisal and method development for the identification of unique DNA sequences from prokaryotes

Representational difference analysis (RDA) has great potential for preferential amplification of unique but uncharacterised DNA sequences present in one source such as a whole genome, but absent from a related genome or other complex population of sequences. While a few examples of its successful exploitation have been published, the method has not been well dissected and robust, detailed published protocols are lacking. Here we examine the method in detail, suggest improvements and provide a protocol that has yielded key unique sequences from a pathogenic bacterial genome. © 2003 Elsevier Science B.V. All rights reserved.

An efficient, approximate path-following algorithm for elastic net based nonlinear spike enhancement

Unwanted spike noise in a digital signal is a common problem in digital filtering. However, sometimes the spikes are wanted and other, superimposed, signals are unwanted, and linear, time invariant (LTI) filtering is ineffective because the spikes are wideband - overlapping with independent noise in the frequency domain. So, no LTI filter can separate them, necessitating nonlinear filtering. However, there are applications in which the noise includes drift or smooth signals for which LTI filters are ideal. We describe a nonlinear filter formulated as the solution to an elastic net regularization problem, which attenuates band-limited signals and independent noise, while enhancing superimposed spikes. Making use of known analytic solutions a novel, approximate path-following algorithm is given that provides a good, filtered output with reduced computational effort by comparison to standard convex optimization methods. Accurate performance is shown on real, noisy electrophysiological recordings of neural spikes.