Creating social entrepreneurship in local government The public sector is often considered synonym with inefficiency and a lack of motivation to be innovative. This paper seeks to contribute towards the literature surrounding social entrepreneurship in the public sector, through using institutional theory to underpin an e-Innovations model that promotes social entrepreneurship, while recognising how the adoption of innovation within the public sector is fostered. The proposed model seeks to serve as a process that threatens the conservative and risk-averse culture endemic in the public sector. This research note has sought to develop a process to support local authorities in their quest to become more entrepreneurial and thus supportive of innovation through a structured process. The underpinning rationale is well grounded theoretically, with the emergent model practically applicable within the public sector. Indeed, the next phase of the research is to move into a more applied phase that will allow the testing and refinement of the model; thus, leading to a process where innovation can be fostered and nurtured. All through the ODPM initiative in 2003-2005 and in its follow-up evaluation as reported by Anon (2007) , the administration of e-Government has struggled with creating an environment where innovation can be nurtured and thus, occur. The need for Central Government to be 'in the driving seat' and for processes to be perceived as publicly accountable produces a conservative and risk-averse culture that only seeks to stifle innovation and thus, maintain the status quo. The paradox is that management can only stimulate innovation by standing back and not trying to manage the flow of ideas. The key under the proposed model is to manage the process and let the ideas flourish.. Although it is recognised that the proposal is an unproven process, it does seek to serve as a process that threatens the conservative and risk-averse culture endemic in the public sector. This is clear through the way it enfranchises people with the new ideas, irrespective of their place in the hierarchy. It was originally conceived as a national process but there is no reason why it should not be adopted over a smaller administrative area. Nor need it be driven from the top -a collective like the 'Yorkshire Digital eco-system' and 'PIE ' (Topham, 2008) could easily adopt the process.. Having tabled the challenge, the authors await the public body innovative enough to adopt it, so that the process can be refined in operation. A. D. (Tony) Elliman is a reader in Information Systems and Computing with an interest in the development of information systems for the public sector. He is a founding member of the ISEing (http://www.iseing.org) and has experience of using simulation techniques in a variety of contexts, including IT project evaluation. He is also actively involved with the European Mediterranean Conference on Information Systems (emcis.org). He works closely with the Chartered Institute of Public Finance and Accountancy (CIPFA) Improvement and Quality Network on e-Government projects. Having trained as an electrical engineer with International Computers Limited, Dr. Elliman has a broad background, having taught many aspects of computing including information systems development, software engineering, distributed systems and hybrid simulation. As a chartered engineer, he has provided software consultancy services to Government, academic and private sector organisations, and has benefited from funding sources that include EPSRC, QinetiQ and the EU.

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Compressed Sensing Off the Grid This paper investigates the problem of estimating the frequency components of a mixture of complex sinusoids from a random subset of regularly spaced samples. Unlike previous work in compressed sensing, the frequencies are not assumed to lie on a grid, but can assume any values in the normalized frequency domain . An atomic norm minimization approach is proposed to exactly recover the unobserved samples and identify the unknown frequencies, which is then reformulated as an exact semidefinite program. Even with this continuous dictionary, it is shown that random samples are sufficient to guarantee exact frequency localization with high probability, provided the frequencies are well separated. Extensive numerical experiments are performed to illustrate the effectiveness of the proposed method. C OMPRESSED sensing has demonstrated that data acquisition and compression can often be combined, dramatically reducing the time and space needed to acquire many signals of interest [1] - [4] . Despite the tremendous impact of compressed sensing on signal processing theory and practice, its development thus far has focused on signals with sparse representations in finite discrete dictionaries. However, signals encountered in applications such as radar, array processing, communication, seismology, and remote sensing are usually specified by parameters in a continuous domain [5] - [7] . In order to apply the theory of compressed sensing to such applications, researchers typically adopt a discretization procedure to reduce the continuous parameter space to a finite set of grid points [8] - [16] . While this simple strategy yields state-of-the-art performance for problems where the true parameters lie on the grid, discretization has several significant drawbacks-1) In cases where the true parameters do not fall onto the finite grid, the Manuscript signal cannot often be sparsely represented by the discrete dictionary [13] , [17] , [18] .. 2) It is difficult to characterize the performance of discretization using standard compressed sensing analyses since the dictionary becomes very coherent as we increase the number of grid points. 3) Although finer grids may improve the reconstruction error in theory, very fine grids often lead to numerical instability issues. We sidestep the issues arising from discretization by working directly on the continuous parameter space for estimating the continuous frequencies and amplitudes of a mixture of complex sinusoids from partially observed time samples. In particular, the frequencies are not assumed to lie on a grid, and can instead take arbitrary values across the bandwidth of the signal. With a time-frequency exchange, our model is exactly the same as the one in Candès et al.'s foundational work on compressed sensing [1] , except that we do not assume the spikes to lie on an equispaced grid. This major difference presents a significant technical challenge as the resulting dictionary is no longer an orthonormal Fourier basis, but is an infinite dictionary with continuously many atoms and arbitrarily high correlation between candidate atoms. We demonstrate that a sparse sum of complex sinusoids can be reconstructed exactly from a small sampling of its time samples provided the frequencies are sufficiently far apart from one another.. Our computational method and theoretical analysis is based upon the atomic norm induced by samples of complex exponentials [19] . Chandrasekaran et al. argue that the atomic norm is the best convex heuristic for underdetermined, structured linear inverse problems, and it generalizes the norm for sparse recovery and the nuclear norm for low-rank matrix completion. The norm is a convex function, and in the case of complex exponentials, can be computed via semidefinite programming. We show how the atomic norm for moment sequences can be derived either from the perspective of sparse approximation or rank minimization [20] , illuminating new ties between these related areas of study. Much as was the case in other problems where the atomic norm has been studied, we prove that atomic norm minimization achieves nearly optimal recovery bounds for reconstructing sums of sinusoids from incomplete data.. To be precise, we consider signals whose spectra consist of spike trains with unknown locations in the normalized interval (we identify 0 and 1). Rather than sampling the signal at all times we sample the signal at a subset of times with each . Our main contribution is summarized by the following theorem.. Theorem I. 1 : Suppose we observe the signal (I.1) 0018-9448 © 2013 IEEE with unknown frequencies on an index set of size selected uniformly at random. Additionally, assume are drawn i.i.d. from the uniform distribution on the complex unit circle and where the distance is understood as the wrap-around distance on the unit circle. If , then there exists a numerical constant such that is sufficient to guarantee that we can recover and localize the frequencies via a semidefinite program with probability at least with respect to the random samples and signs. The frequencies may be identified directly using the dual solution of the atomic norm minimization problem we propose in this paper. Alternatively, once the missing entries are recovered exactly, the frequencies can be identified by Prony's method [21] , a matrix pencil approach [22] , or other linear prediction methods [23] . After identifying the frequencies, the coefficients can be obtained by solving a linear system. Remark I.2 (Resolution): An interesting artifact of using convex optimization methods is the necessity of a particular resolution condition on the spectrum of the underlying signal. For the signal to be recoverable via our methods using random time samples from the set , the spikes in the spectrum need to be separated by roughly . In contrast, if one chose to acquire consecutive samples from this set (equispaced sampling), the required minimum separation would be ; this sampling regime was studied by Candès and Fernandez-Granda [24] . Therefore, in some sense, the resolution is determined by the region over which we take the samples, either in full or in a uniform random manner. We comment that numerical simulations of Section V suggest that the critical separation is actually . We leave tightening our bounds by the extra constant of 4 to future work.

B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Validation of Canopy Height Profile methodology for small-footprint full-waveform airborne LiDAR data in a discontinuous canopy environment A Canopy Height Profile (CHP) procedure presented in Harding et al. (2001) for large footprint LiDAR data was tested in a closed canopy environment as a way of extracting vertical foliage profiles from LiDAR raw-waveform. In this study, an adaptation of this method to small-footprint data has been shown, tested and validated in an Australian sparse canopy forest at plot-and site-level. Further, the methodology itself has been enhanced by implementing a dataset-adjusted reflectance ratio calculation according to Armston et al. (2013) in the processing chain, and tested against a fixed ratio of 0.5 estimated for the laser wavelength of 1550nm. As a by-product of the methodology, effective leaf area index (LAIe) estimates were derived and compared to hemispherical photography-derived values. To assess the influence of LiDAR aggregation area size on the estimates in a sparse canopy environment, LiDAR CHPs and LAIes were generated by aggregating waveforms to plot-and site-2 level footprints (plot/site-aggregated) as well as in 5m grids (grid-processed). LiDAR profiles were then compared to leaf biomass field profiles generated based on field tree measurements. The correlation between field and LiDAR profiles was very high, with a mean R 2 of 0.75 at plot-level and 0.86 at site-level for 55 plots and the corresponding 11 sites. Gridding had almost no impact on the correlation between LiDAR and field profiles (only marginally improvement), nor did the datasetadjusted reflectance ratio. However, gridding and the dataset-adjusted reflectance ratio were found to improve the correlation between raw-waveform LiDAR and hemispherical photography LAIe estimates, yielding the highest correlations of 0.61 at plot-level and of 0.83 at site-level. This proved the validity of the approach and superiority of dataset-adjusted reflectance ratio of Armston et al.(2013) over a fixed ratio of 0.5 for LAIe estimation, as well as showed the adequacy of small-footprint LiDAR data for LAIe estimation in discontinuous canopy forests. Vegetation plays a very important role on Earth, as through its interaction with the atmosphere it is responsible for the exchange of energy fluxes (Breda, 2003, Levy and Jarvis, 1999) . The information about its amount and spatial distribution is a key factor in many environmental studies and applications including flood modelling, fire risk assessment, carbon stock modelling (Lefsky et al., 2005b , Koetz et al., 2006 and global environmental change . With the foliage distribution variable in horizontal and vertical directions as well as with time (seasonally and over years) (Breda, 2003) , vegetation's complicated structure is very difficult to quantify and map in a timely manner. Field inventories are time consuming, laborious, expensive and not always accurate enough, often relying on allometric equations or other ground-based indirect methods while direct methods are highly destructive. Such field methods are therefore unsuitable for long-term monitoring of large areas due to low frequency of sampling and high costs. Remote sensing methods on the other hand, both airborne and spaceborne, provide non-destructive and fast tools for obtaining better and wider coverage and therefore they are particularly useful for monitoring and inventories of vegetation at regional and global scales.. The two parameters commonly used to describe vegetation amount, derived from remote sensing observations are: normalized difference vegetation index (NDVI) and leaf area index (LAI). NDVI is a well-established passive optical remote sensing technique relying on the difference in vegetation's reflectance in the red and infrared parts of the electromagnetic spectrum. NDVI and other optical remote sensing techniques provide no information on the vertical distribution of the canopy, though, due to their two-dimensional character (no elevation information) . They are therefore incapable of providing vertical foliage profiles. They are also sensitive to many factors such as e.g. atmospheric and soil effects, and their accuracy depends on the pixel size relation to the size of vegetation components (Riaño et al., 2004) . This method has also been reported to saturate at high level vegetation biomass (Chen and Cihlar, 1996) .. Leaf area index (LAI), defined as half the total leaf area per unit ground area (Lang et al., 1991, Chen and Black, 1992) , has also been a widely studied parameter. Despite the simplicity of its definition, it is still one of the most difficult parameters to measure (Breda, 2003 , Richardson et al., 2009 ). The methods of obtaining LAI are commonly divided into two groups: direct and indirect measurements (Breda, 2003 , Levy and Jarvis, 1999 , Chen et al., 1997 . Extensive reviews of ground-based direct and indirect methods of LAI retrievals with their advantages and disadvantages are presented in Jonckheere et al. (2004) and Breda (2003) , with a background theory summary described in Weiss et al. (2004) . This study has presented a validation of the Canopy Height Profile methodology (based on Harding et al. 2001) for leaf area index and vertical foliage retrieval, using small-footprint (0.2m) fullwaveform airborne LiDAR data in a discontinuous canopy cover environment, at plot (30m diameter) and site-levels (100m diameter). The methodology has been enhanced to include a dataset-adjusted reflectance ratio according to Armston et al. (2013) and tested against a fixed ratio of 0.5. This study has also looked at the influence of the aggregation area on LAIe and CHP retrievals in discontinuous canopy cover environments by carrying out calculations of LAIe and CHPs on grid-processed (5m) and plot/site-aggregated (15m/50m radius) datasets. The analyses have shown that this methodology is relevant and suitable for its purpose.. The LAIe extracted as an intermediate step of the methodology was compared to hemisphericalphotography estimates. The analysis has shown that the method produced LAIe values which were close to those of hemispherical photography with some degree of underestimation. The correlation values were somewhat moderate (however still significant) at the plot-level owing most likely to geocoding uncertainties and a lack of GPS measurements of the hemispherical photography locations. At site-level the correlation improved significantly. Due to the fact that hemi-photo LAIe estimates at site-level were derived as a mean value of plot-level LAIes, the comparison to LiDAR site-level estimates was always better when the site-level LiDAR estimates were derived in the same way, rather than from a cylinder with 50m radius. The highest R 2 value of 0.83 at site-level was reached by WF1 with dataset-adjusted reflectance ratio. Using a dataset-adjusted reflectance ratio as opposed to a fixed ratio of 0.5 did considerably improve the correlation with hemispherical photography values both at plot-and site-level, proving the importance of accurate estimation of the vegetationground reflectance ratio in LAIe estimation and the value of the Armston et al. (2013) methodology for this application.. The influence of the aggregation area on LAIe estimates of discontinuous canopies was assessed by performing the calculation of LAIe in 5m by 5m grids versus datasets aggregated to plot (15m radius) and site-level (50m radius). Gridding improved the correlation between LiDAR and hemi-photoderived LAIe estimates both at plot-and site-level especially when fixed reflectance ratio was used.. The study has, therefore, shown that in the case of discontinuous canopies it is important to consider heterogeneity of vegetation by choosing the aggregation size of LiDAR data that enables depiction of its sparseness. This may suggest that for such environments small-footprint LiDAR data (here with a footprint diameter of 0.2m) may be particularly suitable as they offer the possibility of selecting a cylinder radius or grid size for aggregation that ensures homogeneity of the area covered by it.. Choosing an aggregation area that is larger and does not depict the heterogeneity of vegetation or using LiDAR data with a footprint size that does not allow for it will most likely lead to underestimation of the LAIe due to the logarithmic transformation involved in the LAIe calculation.. For areas with DTM variations and significant slopes, the use of small-footprint LiDAR data would be even more advantageous as it would help to avoid the influence of the terrain on the shape of the received waveforms and in consequence inaccuracies in the estimates. As a final remark, it is worth pointing out that due to its better spatial coverage and less effort in terms of collecting data LiDAR-based estimation of LAIe should provide better estimates than hemispherical photography , Richardson et al., 2009 ).. Comparison of LiDAR CHPs to field biomass profiles generated based on field measurements made at the time of LiDAR acquisition, has proven that this methodology is also appropriate for description of the vertical distribution of vegetation. The correlation between field and LiDAR profiles was very high and reached a maximum mean R 2 of 0.75 at plot-level and 0.86 at site-level when 55 plots and the corresponding 11 sites were considered. All LiDAR plot-level profiles but one and all site-level profiles were also found to be not statistically significantly different (at 5% significance level) to field biomass profiles. Unlike the results of the LAIe determination, due to relative character of the CHP, using dataset-adjusted or constant reflectance ratio had almost no impact on the correlation of LiDAR with field biomass profiles (the fixed ratio gave marginally better correlation by 0.01). Furthermore, the profiles generated with different ratios were found to be not significantly different between each other (with p-values close to 1), regardless of the aggregation type and both at plot-and site-level. In the case of the grid-processed datasets, the correlation between LiDAR and leaf biomass field data was usually marginally higher (by 0.01-0.02) than that of plot/site-aggregated datasets (both at plot and site-level). Moreover, around one third of the grid-processed LiDAR canopy height profiles were found to be statistically significantly different from the corresponding plot/site-aggregated profiles.. This suggests that not only for LAIe but also for foliage vertical profiles, using small-footprint airborne data may be advantageous in discontinuous canopy environments. Further experiments are, however, required in order to verify the performance and the use of the methodology at denser forest areas and at areas with a wider range of LAIe values. The raw-waveform LiDAR methodology used in this study is based on the SLICER Canopy Height. Profile processing presented in Harding et al. (2001) . This methodology, originally applied to largefootprint data over a closed canopy environment, was adapted to small-footprint LiDAR and initially tested by Fieber et al. (2013b) at plot-and site-level in four forest sites for LAIe estimates (one of the stages of the procedure), in a comparative study of discrete point LAIe extraction methods. The technique was also tested for LAIe and vertical profile generation, however, only at single-tree-level (Fieber et al., 2014 ) with a very promising result (R 2 of 0.86 with field profile). Here, the validation of LAIe and vertical foliage profiles (CHPs) was performed at plot and site-level using 11 fieldmeasured sites in the discontinuous canopy cover of Gillenbah forest. The methodology was also enhanced by using the dataset-adjusted vegetation-ground reflectance ratio proposed by Armston et al. (2013) (WF1) and compared to the results of the procedure with a constant ratio of 0.5 (WF2) for the laser wavelength 1550nm. The LAIe estimates were then compared to hemispherical photography derived values, and the vertical foliage profiles were compared to field biomass profiles.. To assess the quality of the results, ordinary least square regression analysis was carried out, and root mean squared error was calculated for each LiDAR LAIe comparison. Furthermore, a set of paired two-tailed t-tests (at the 5% significance level) of the null hypothesis that the differences between LiDAR and hemi-photo estimates were a random sample from a normal distribution with mean 0, against the alternative that the mean is not 0 were performed. Similarly to the LAIe analysis, for vertical foliage profiles a bin-wise ordinary least squares regression was undertaken, and root mean squared error calculated. Furthermore, a set of paired bin-wise two-tailed t-tests was carried out in order to assess whether the LiDAR profiles were significantly different from field-biomass profiles. T-tests were also performed between CHPs extracted using different vegetation ratios and between plot/site-aggregated and grid-processed CHPs.

O O O O O O O B B O B O O O O O O O B I I I O O O O O O O O O O B O O O O O O O O O O O O O O O O O B O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I I I O O O O O O O O O O O O O O B O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O B O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O B B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O


An evaluation of ANN methods for estimating the lengths of hydraulic jumps in U-shaped channel Modelling of hydraulic characteristics of jump using theoretical and empirical models has always been a difficult task. The length of jump may be defined as the distance measured from the toe of the jump to the location of the surface rise. Due to high turbulence this length cannot be determined easily by theory. However, it has been investigated experimentally so as to design the stilling basins with hydraulic jumps. In this work, the control of a hydraulic jump by broad-crested sills in a Ushaped channel is recalled theoretically and experimentally examined. The study begins with a multiple regression (MR) analysis. Then, and in order to model the relative lengths of hydraulic jumps, we have implemented and evaluated two different artificial neural networks (ANN): multilayer perceptron neural network (MLPNN) and generalized regression neural network (GRNN). The results demonstrate the predictive strength of GRNN and its potential to predict hydraulic problems with an adaptive spread value. However, the MLPNN model remains best classified by these indexes of performance. Key words | artificial neural network, GRNN, lengths of hydraulic jump, MLPNN, MR, U-channel NOMENCLATURE A Cross-sectional area of flow [m 2 ] D Diameter [m] Fr Froude number [-] L j Length of jump [m] Q Discharge [m 3 /s] g Acceleration due to gravity [m/s 2 ] h Depth of flow [m] q Specific discharge [-] y Relative depth of flow [-] θ 1 Angle for semicircular cross-sectional area [rad] ABBREVIATIONS ANN Artificial neural networks GRNN Generalized regression neural network MLPNN Multilayer perceptron neural network MR Multiple regression ). Some of the other practical applications are: e.g. flow-metering flume, mixing of chemicals for water purification and aerating water (Chow ; Kucukali & Cokgor ). In practice, the stilling basin is seldom designed to confine the entire length of a free hydraulic jump on the paved apron, because such a basin would be too expensive.Consequently, accessories to control the jump are usually installed in the basin. The main purpose of such control is to shorten the range within which the jump will take place The hydraulic jump is the discontinuous transition between supercritical and subcritical flow with varied or fixed location (Vischer & Hager ) , it is characterized by a sudden increasing of the water surface with high turbulence production. This phenomenon is an example of steady nonuniform flow. Principally, the hydraulic jump is well known to hydraulic engineers as a useful means of dissipating excess energy of flowing water downstream of hydraulic structures, such as spillways, chutes and sluices (Hager and thus to reduce the size and cost of the stilling basin (Chow ) .. The hydraulic jump in open non-rectangular channels has been studied by many researchers. Mentioning in this context the circular and U-shaped channel; in the circular one, the jump was considered by Hager (), Stahl & Hager () , Achour (), Dey (), Gargano & Hager () and Mitchell () . Moreover in the Ushaped one, the jump was also considered by Silvester (), Rajaratnam (), Hager (), Houichi (), Achour & Debabeche () and Afzal & Bushra () .. The length of jump may be defined as the distance measured from the toe of the jump to the location of the surface rise (Rajaratnam ) . This definition was adopted and used within the current study. In theory, the length cannot be determined easily because of the effects of highly turbulent flow. This phenomenon continuously modifies the internal jump characteristics. Yet, it has been investigated experimentally (Chow ; Kréménetsky et al. ) . In nature, turbulent flow, rollers and eddies, the random nature of surface disturbances, and air entrainment, complicate the exact determination of the two ends of a hydraulic jump. In practice, the end of a hydraulic jump is considered to be the point from which the concrete coating is not necessary any more (Lencastre ). The main objective of the present study is the presentation and evaluation of two different ANN techniques: multilayer perceptron neural network (MLPNN) and GRNN, in order to predict the relative length for hydraulic jumps in a U-shaped channel controlled by broad-crested sills.

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O B O O O O O O O B O O O O O O O O O O O O O O B O O O O O O O O O O O O B I I B B I I I B B B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O B O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O B O O O O O O O O O O O O O O O O O O


SAGA: A hybrid search algorithm for Bayesian Network structure learning of transcriptional regulatory networks Bayesian Networks have been used for the inference of transcriptional regulatory relationships among genes, and are valuable for obtaining biological insights. However, finding optimal Bayesian Network (BN) is NP-hard. Thus, heuristic approaches have sought to effectively solve this problem. In this work, we develop a hybrid search method combining Simulated Annealing with a Greedy Algorithm (SAGA). SAGA explores most of the search space by undergoing a two-phase search: first with a Simulated Annealing search and then with a Greedy search. Three sets of background-corrected and normalized microarray datasets were used to test the algorithm. BN structure learning was also conducted using the datasets, and other established search methods as implemented in BANJO (Bayesian Network Inference with Java Objects). The Bayesian Dirichlet Equivalence (BDe) metric was used to score the networks produced with SAGA. SAGA predicted transcriptional regulatory relationships among genes in networks that evaluated to higher BDe scores with high sensitivities and specificities. Thus, the proposed method competes well with existing search algorithms for Bayesian Network structure learning of transcriptional regulatory networks. Bayesian Networks (BNs) are useful for reverse-engineering gene networks from microarray data. BNs are probabilistic in nature. BNs are, therefore, becoming increasingly useful for the inference of cellular networks, modeling signaling pathways and analyzing genetic data [1] [2] [3] . Unlike other algorithms for inferring relationships among genes such as the ordinary differential equation (ODE)-based methods which generally involve time series data and low dimensional datasets, BNs (including dynamic BNs) can effectively infer relationships from both large steady-state expression measurements (and time series measurements) [4] [5] [6] [7] [8] . Furthermore, clustering algorithms and information-theoreticbased methods only establish the existence of relationships among variables in the dataset but do not describe the specific directionality of relationships [9] . On the other hand, BNs infer causal relationships (when the causal Markov assumption holds) making them more desirable than many inference algorithms.. However, structure learning of BNs from data is an NP-hard problem and so many heuristic methods have been proposed to solve search problems [10, 11] . Most of the proposed methods are local search methods. The number of possible direct acyclic graphs (DAGs) grows exponentially for increasing numbers of nodes [12] . For this reason, we review below a number of search approaches that have been proposed to search for BN structures among DAGs. SAGA recorded the highest sensitivities in the breast cancer and mouse whole brain datasets in the second and last experiments where smaller and larger prior relationships respectively were supplied. The performance of all the algorithms varied with respect to each dataset. In particular, for larger datasets where numbers of variables are large, SAGA is able to infer models with high rates of truly recovered relationships when used to infer BNs over longer periods with larger prior relationships. Therefore, SAGA is recommended for reverse-engineering networks from datasets where Fig. 5 . Specificity comparison in the human airway smooth muscle dataset. All methods are able to distinguish false relationships. SAGA is Simulated Annealing with a Greedy Algorithm, GR is Greedy search with random restarts, SAR is Simulated Annealing with re-annealing, GS is Greedy Search and SA is Simulated Annealing. Fig. 6 . Sensitivity comparison mouse whole brain dataset. SAGA is able to discover higher true relationships for all the experimental designs with prior networks in large datasets. SAGA is Simulated Annealing with a Greedy Algorithm, GR is Greedy search with random restarts, SAR is Simulated Annealing with re-annealing, GS is Greedy Search and SA is Simulated Annealing. Fig. 7 . Specificity comparison in mouse whole brain dataset. All methods are able to distinguish false discoveries from true relationships. SAGA is Simulated Annealing with a Greedy Algorithm, GR is Greedy search with random restarts, SAR is Simulated Annealing with re-annealing, GS is Greedy Search and SA is Simulated Annealing. Fig. 8 . Evolution of Performance metrics in the human airway smooth muscle dataset without prior network. Each experiment is repeated 10 times and the average is used. SAGA is Simulated Annealing with a Greedy Algorithm, GR is Greedy search with random restarts, SAR is Simulated Annealing with re-annealing, GS is Greedy Search and SA is Simulated Annealing. Fig. 9 . Evolution of performance metrics in the human airway smooth muscle dataset with prior network with 30 edges. Each experiment is repeated 10 times and the average is used. SAGA is Simulated Annealing with a Greedy Algorithm, GR is Greedy search with random restarts, SAR is Simulated Annealing with reannealing, GS is Greedy Search and SA is Simulated Annealing.. there are large numbers of variables, and where some priors are available. Moreover, GR has greater capacity to clearly distinguish false relationships from true relationships than SAGA. Thus, GR may be used to infer models which clearly distinguish false relationships from true relationships (for datasets where there are large numbers of variables, and where some prior knowledge is available).. On a smaller dataset as observed in the human airway smooth muscle dataset, SAGA is able to recover higher true positives since it had the highest sensitivities for all the experiments with priors. However, GR and GS are useful for such smaller datasets because of their higher specificity values on this dataset. In the absence of priors, all methods had low or no sensitivity values. This indicates that these methods are most effective in the presence of prior knowledge. We propose a sequential-based hybrid search method, SAGA for BN structure learning. SAGA uses known prior relationships to infer transcriptional regulatory relationships. The results of the evaluations of BN structure learning algorithms confirm that structure learning in BNs is effectively done with smaller datasets. However, when presented with real world problems, with prior knowledge reflecting prior relationships and large datasets of high ratios of variables to arrays, then SAGA will generally provide superior BN structure learning with high sensitivities and specificities. This is largely demonstrated by the results of the experiments performed on the datasets employed in this study. Therefore, in realistic contexts, identification of transcriptional regulatory networks could be enhanced with BN structure learning with SAGA.

O O O O O O B I O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Adaptive reduced basis finite element heterogeneous multiscale method An adaptive reduced basis finite element heterogeneous multiscale method (RB-FE-HMM) is proposed for elliptic problems with multiple scales. The multiscale method is based on the RB-FE-HMM introduced in [A. Abdulle and Y. Bai, J. Comput. Phys, 2012, in press]. It couples a macroscopic solver with effective data recovered from the solution of micro problems solved on sampling domains. Unlike classical numerical homogenization methods, the micro problems are computed in a finite dimensional space spanned by a small number of accurately computed representative micro solutions (the reduced basis) obtained by a greedy algorithm in an offline stage. In this paper we present a residual-based a posteriori error analysis in the energy norm as well as an a posteriori error analysis in quantities of interest. For both type of adaptive strategies, rigorous a posteriori error estimates are derived and corresponding error estimators are proposed. In contrast to the adaptive finite element heterogeneous multiscale method (FE-HMM), there is no need to adapt the micro mesh simultaneously to the macroscopic mesh refinement. Up to an offline preliminary stage, the RB-FE-HMM has the same computational complexity as a standard adaptive FEM for the effective problem. Two and three dimensional numerical experiments confirm the efficiency of the RB-FE-HMM and illustrate the improvements compared to the adaptive FE-HMM. A basic problem for many applications is the characterization of effective properties of a physical process occurring on multiple scales (e.g., elastic properties of composite materials, fluid flow through heterogeneous porous media, thermal diffusion in composite structures, etc). Such problems are often modeled by partial differential equations (PDEs) with highly oscillating coefficients varying over multiples scales, whose numerical solution is difficult to compute (if not impossible) with classical numerical methods such as the finite element method (FEM). Indeed, the computational cost needed to resolve the smallest scale in the problem is often overwhelming. Simply ignoring the fine scales does usually not allow to capture the correct effective behavior. The development of multiscale methods capable of capturing the effective behavior of a problem without scale resolution on the whole computational domain has therefore received major attention during the past few years [1, 2, 3, 4, 5] .. In this paper we focus on the finite element heterogeneous multiscale method (FE-HMM), a numerical homogenization method developed in the framework of the heterogeneous multiscale method (HMM) proposed in [6] . The main idea of the FE-HMM is to apply a macro FEM based on a macro partition of the computational domain with effective coefficients recovered (on the fly) by solving micro finite element (FE) problems defined on sampling domains located at quadrature points within each element of the macro partition (see [7] for a review). The fully discrete error analysis in [8] indicates that the optimal convergence rates can be obtained only when the macro and micro meshes are refined simultaneously.. This simultaneous mesh refinement leads to superlinear growth (in the macro degrees of freedom) of the computational work. This becomes an issue (as for most of the numerical homogenization methods) for high dimensional problems or high order macro FEMs.. To address the computational issue of simultaneous macro and micro mesh refinement the reduced basis finite element heterogeneous multiscale method (RB-FE-HMM) has been introduced in [9] . Departing from the approach used in the FE-HMM, the RB-FE-HMM allows one to design an efficient numerical method relying only on a small number of micro problems selected by a rigorous a posteriori error estimator computed accurately in an socalled offline stage. In a so-called online stage, the effective solution is obtained from the macro solver of the FE-HMM with effective coefficients recovered from micro problems solved in the precomputed RB space. This method, that follows the offline-online strategy of reduced basis (RB) method [10, 11, 12, 13, 14] , does no longer require the simultaneous refinement of macro and micro meshes. As illustrated in [9] , the RB-FE-HMM is specially attractive for high order macro methods or three dimensional multiscale computations.. In this paper we discuss a posteriori error control and mesh refinement strategy for the RB-FE-HMM. In practice, being able to refine the computational mesh adaptively, based on a given actual numerical solution is of prime importance. Adaptive methods not only provide a criterion that indicates whether a certain prescribed accuracy is met, but also estimate local errors that allow to drive a mesh refinement that equi-distributes the approximation error (e.g., refining in the region where singularity in the solution or in the domain occur). The general adaptive strategy for the adaptive FEM is based on the following cycle Solve → Estimate → Mark → Refine.. The procedure can be understood as follows. One first solves the partial differential equation numerically on the current mesh and compute an a posteriori error by defining suitable error estimators that give an estimation of the actual error between the computed and the true solution (in a certain norm). Then, according to the distribution of the error estimator in each element, one marks the elements which have the largest contribution to the estimated error, refines the marked elements and goes back to the step 'Solve'. The essential step for adaptive method is the construction of reliable error estimator. While there is a large literature for single scale adaptive methods (see for example [15, 16, 17, 18] and the references therein), adaptive multiscale methods are still at an early stage of development. One difficulty is that the error estimator (that first need to be suitably modeled) depends on multiple scales and the reliability of such error estimator depends on the accuracy of the resolution of the fine scale.. A posteriori error analysis for the FE-HMM has first been given in [19] based on a twoscale analysis [20] . A posteriori error analysis for the FE-HMM in the physical energy-norm has been derived in [21] and the extension of the FE-HMM to goal oriented adaptivity (in quantities of interest) has been discussed in [22] . For this latter adaptive method, the solution of dual problems (in a higher macro FE space) are required. Both adaptive methods [21, 22] have proved to be useful and more efficient than the FE-HMM with uniform refinement when the macroscopic domain or the macroscopic solution exhibit singularities. But as mentioned above, the simultaneous mesh refinement still represents a significant computational overhead that prevents to solve efficiently three-dimensional problems adaptively, or to use adaptive higher order macro FEM. In this paper we discuss a new adaptive method that combines RB techniques with the FE-HMM. This method, that allows to drive a macroscopic mesh refinement using the same precomputed set of RB micro functions to estimate the effective data, improves significantly the adaptive FE-HMM and provides a highly efficient adaptive multiscale computational strategy.. The paper is organized as follows. In Section 2, we briefly review the FE-HMM and the RB-FE-HMM. The residual based adaptive RB-FE-HMM is discussed in Section 3 and the corresponding a posteriori estimates for the upper and lower bound are derived in the energy norm. The goal-oriented adaptive RB-FE-HMM is presented in Section 4, where an exact representation of the error in a quantity of interest is derived. Numerical examples for the proposed method in two and three dimensions and comparison with the adaptive FE-HMM are presented in section 5. Notations Let Ω ⊂ R. d be an open set, and Y = (− . We also have the property that. where the tensor a ε oscillates on a small spatial scale ε and f ∈ H −1 (Ω). Here, a zero Dirichlet boundary condition is taken for simplicity. We emphasize that the numerical method presented below can be readily generalized to other boundary conditions such as non-zero Dirichlet or Neumann boundnary conditions. The d × d matrix a ε (x) is assumed to be uniformly elliptic and bounded, i.e.,. for a.e x ∈ Ω. Using homogenization theory, one can prove that there exists. , where u 0 is the solution of the homogenized equation (for example, see [23, 24] for detail),. where a 0 is the homogenized tensor. As a 0 is usually unknown, we need to introduce numerical methods for its approximation. One well-known method is the FE-HMM which is based on a macroscopic FEM with quadrature formula (QF) defined on a macro partition of the domain Ω, supplemented by microscopic FEMs applied on sampling domains centered at the macroscopic quadrature points of the QF to estimate the unknown data in the macro system. We have presented an efficient adaptive FEM, the RB-FE-HMM, for elliptic homogenization problems based on micro-macro solvers combined with a RB strategy. We have shown that repeated FEM computations of micro problems are avoided during the macro mesh refinement, in contrast to the adaptive FE-HMM, as the micro solutions are computed in a finite dimensional space spanned by a small number of accurately computed representative micro solutions (the reduced basis) obtained by a greedy algorithm in an offline stage. This methodology allows to bypass the derivation of micro a posterior error estimates to calibrate the micro mesh during the macro mesh adaptive cycles. We have presented an a posteriori error analysis for a residual based adaptive RB-FE-HMM. Error estimation for the RB-FE-HMM in quantities of interest has also been presented. The efficiency and the sharpness of the derived error bounds have been illustrated by several numerical examples in two and three dimensions. These examples show the significant advantage of the adaptive RB-FE-HMM over the adaptive FE-HMM.

O O O O O B I I O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O B I O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Exploring the functional significance of dendritic inhibition in cortical pyramidal cells Inhibitory synapses contacting the soma and axon initial segment are commonly presumed to participate in shaping the response properties of cortical pyramidal cells. Such an inhibitory mechanism has been explored in numerous computational models. However, the majority of inhibitory synapses target the dendrites of pyramidal cells, and recent physiological data suggests that this dendritic inhibition affects tuning properties. We describe a model that can be used to investigate the role of dendritic inhibition in the competition between neurons. With this model we demonstrate that dendritic inhibition significantly enhances the computational and representational properties of neural networks. Lateral inhibition between cortical cells is known to play an important role in determining the receptive field properties of those cells (Eysel et al., 1998; Jagadeesh, 2000) . Such lateral inhibition provides a mechanism through which neurons compete to respond to the current pattern of stimulation. The vast majority (93%) of inhibitory synapses targeting neocortical pyramidal cells terminate on the dendrites (DeFelipe and Fariñas, 1992; Fiala and Harris, 1999) . This dendritic inhibition is likely to have strong effects only on more distal inputs along the same dendritic branch (Borg-Graham et al., 1998; Koch et al., 1983; Koch and Segev, 2000; Rall, 1964; Segev, 1995; Spruston et al., 1999) , and will thus selectively inhibit specific groups of excitatory inputs, or dendritic compartments. In contrast, many neural network models assume that dendrites have passive conductance properties (Mel, 1999) , and hence, that all inhibitory contacts are equally effective at suppressing responses to any excitatory inputs. For such point-neuron models, all inhibitory contacts act as if they target the soma or axon initial segment.. While somatic inhibition non-selectively inhibits responses to all stimuli, dendritic inhibition selectively inhibits specific patterns of excitatory inputs. Recent physiological data suggests that the latter mechanism is important in determining the response properties of cortical pyramidal cells since the blockade of GABAergic synapses (in monkey area TE) results in specific dis-inhibition of responses to particular stimulus features rather than removal of non-specific inhibition (Wang et al., 2000) . We propose a simple neural network architecture which can be used to explore the role of dendritic inhibition as a mechanism of competition between pyramidal cells. A network of neurons competing through dendritic lateral inhibition is capable of generating correct representations based on the 'knowledge' stored in the synaptic weights of the neurons. Specifically, it is capable of generating a local encoding of individual input patterns as well as responding simultaneously to multiple patterns, , 'e', and 'f') is wired up so that nodes are selective to the patterns 'a', 'ab', 'abc', 'cd', 'de', and 'def'. The response of the network to each of these input patterns is shown on the top row. Dendritic inhibition (lateral weights have been omitted from the figures) enables each node to respond exclusively to its preferred pattern. In addition, the response to multiple and partial patterns is shown on the bottom row. Pattern 'abcd' causes the nodes representing 'ab' and 'cd' to be active simultaneously, despite the fact that this pattern overlaps strongly with pattern 'abc'. Input 'abcde' is parsed as 'abc' together with 'de', and input 'abcdef' is parsed as 'abc' + 'def'. Input 'abcdf' is parsed as 'abc' + two-thirds of 'def', hence the addition of 'f' to the pattern 'abcd' radically changes the representation that is generated. Input 'bcde' is parsed as two-thirds of 'abc' plus pattern 'de'. Input 'acef' is parsed as 'a' + one half of 'cd' + two-thirds of pattern 'def'. (Földiák, 1990) . Each plot shows the change, over the course of training, in the number of bars correctly represented by exactly one node in the neural network. Mean performance, over ten trials (using different randomly generated sequences of training patterns) is shown. Performance is plotted for networks containing 16 and 20 nodes trained with the standard bars data (like that illustrated in (a)), and for 16-node networks trained with images each containing a single bar, with images which contained only horizontal or only vertical bars, and with images in which horizontal bars occurred with half the probability of vertical bars. For each of these variations the dendritic inhibition model learns reliably and quickly, while the model using the conventional mechanism for lateral inhibition fails to learn any of the tasks except the standard bars problem for which it was specifically designed. The error bars show the best and worst performance over all trials for a 16-node network trained on the standard bars problem.. when they are present, in order to generate a distributed encoding. It can produce an appropriate representation even when patterns overlap and respond to partial patterns such that the response is proportional to how well that input matches the stored pattern. Not only can dendritic inhibition provide appropriate coding properties, it can also be used to efficiently learn such representations. Hence, competition via dendritic inhibition significantly enhances the computational and representational capacities of networks of neurons and may be exploited by cortical circuits. Furthermore, such a neural network has significant practical advantages over algorithms that employ the conventional mechanism of competition.. Our architecture assumes that all afferent synapses, carrying information about a feature of the input space, can be modelled as a single input to a node. This can be justified since it is presumed that related synapses cluster together within dendritic trees so that local operations are performed by multiple, functionally distinct, dendritic subunits before integration at the soma (Koch and Segev, 2000; Segev and Rall, 1998; Segev, 1995; Häusser et al., 2000; Häusser, 2001; Mel, 1994 Mel, , 1999 . Dendritic inhibition could thus act to 'block' the output from individual functional compartments. It has long been recognized that a dendrite composed of multiple subunits would provide a significant enhancement to the computational powers of an individual neuron (Mel, 1994 (Mel, , 1999 and that dendritic inhibition could contribute to this enhancement (Koch et al., 1983; Koch and Segev, 2000; Segev and Rall, 1998) . However, the role of dendritic inhibition in competition between cells and its subsequent effect on neural coding and receptive field properties has not previously been investigated.. The idea embodied in our model is that pyramidal cells inhibit the activity of dendritic compartments in other pyramidal cells within the same cortical area. It has been shown that cortical pyramidal cells innervate inhibitory cell types which in turn form synapses on the dendrites of pyramidal cells . Our model predicts that it should be possible to find pairs of pyramidal cells for which action potentials generated by one cell induce inhibitory post-synaptic potentials within the dendrites of the other. More complex models, which include a separate inhibitory cell population, and which use multi-compartmental models of dendritic processes could relate our proposal more directly with physiology. We hope that our demonstration of the computational and representational advantages that could arise from dendritic inhibition will serve to stimulate more detailed studies of this type. By making the lateral weights equal in strength to the corresponding afferent weights (as shown in figure 1(c)) each node can 'block' its preferred inputs from activating other nodes. With this arrangement of weights, if a node is strongly activated by the stimulus, and it has a strong synaptic weight to a certain feature of that stimulus, then it will inhibit other nodes from responding to that feature. On the other hand, if an active node receives a weak synapse from a certain input, then it will weakly inhibit other nodes from responding to that specific input. Hence, if individual nodes have learnt weights that are selective to certain stimuli then when multiple stimuli are simultaneously presented to the network each of the nodes representing one of these stimuli can be simultaneously active. A network using dendritic inhibition can thus respond appropriately to any combination of input patterns. Furthermore, such a network deals naturally with stimuli which share sub-features in common (i.e., patterns which overlap in the input space). This capacity is important if different sets of neurons are to respond to distinct sensory events which may share many features in common. Both these properties are illustrated in figure 2. In this example six nodes each represent one of six patterns defined across six input features (labelled 'a' to 'f'). Each node responds exclusively to its preferred input pattern despite the strong overlap between stimuli. Furthermore, multiple nodes responds when multiple stimuli are presented.. Competition not only makes responses more selective (in the short-term), but since learning is activitydependent it also makes the receptive fields of individual nodes more distinct (in the long-term). Improved response properties result in more correct learning episodes (Marshall, 1995) , and hence, the advantageous coding properties that arise from using dendritic inhibition can result in efficient, unsupervised, learning (Spratling and Johnson, 2002) . For example, figure 3(b) shows the performance of our algorithm when applied to the bars problem (Földiák, 1990) . Corresponding results for a conventional neural network architecture are shown in figure 3(c) . The speed of learning when using dendritic inhibition compares favourably, not only to networks that use the conventional form of lateral inhibition, but with all neural network algorithms that have been applied to this task (Spratling and Johnson, 2002) . More significantly, a single algorithm can learn to represent the independent components of the training data (i.e., the individual bars) under a number of different conditions (such as the number of nodes in the network, the frequency with which bars appear and the number of bars making up each image). In contrast, a conventional network architecture requires a priori information about the task in order to define learning rules that will find appropriate weights for a particular task. For example, to solve the bars problem, Földiák (Földiák, 1990) found it is necessary to use the value for the probability of a bar being active within the learning rules. Hence, this algorithm fails to learn even when the statistics of the input data are only slightly different from that expected (as illustrated in figure 3(c) ). Furthermore, even with a priori knowledge of each task, it would not be possible to define appropriate learning rules for each case. Algorithms which use the conventional mechanism of lateral inhibition are thus severely restricted in the class of problems that they can successfully learn, and require a priori knowledge to succeed even on those tasks. Figure 1(a) illustrates the architecture used by conventional models of lateral inhibition. In some implementations, competition is achieved (as shown) by using explicit lateral connections between the nodes (von der Malsburg, 1973; Földiák, 1990; Marshall, 1995) , while in others, competition is implemented implicitly through a selection process which chooses the 'winning' node(s) (Rumelhart and Zipser, 1985; Kohonen, 1997; Grossberg, 1987) . In all of these algorithms, nodes attempt to 'block' other nodes from generating a response to the current stimulus. A node's success in this competition is dependent on the total strength of the stimulation it receives and nodes which compete unsuccessfully have their output activity suppressed.. Figure 1(b) shows the architecture of our model of dendritic inhibition. As with conventional models, we simplify reality by assuming that the role of interneurons can be approximated by direct inhibitory connections between excitatory nodes. Furthermore, we group together all the synapses contributing to a dendritic compartment to form a single input to the node. Dendritic inhibition is then modeled as (linear) inhibition of this input. This mechanism thus enables nodes to selectively inhibit other nodes from responding to particular input features. Full details of this algorithm can be found in (Spratling and Johnson, 2002)

O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O B O O O O O O O O O O O O O O O O O B O O B O O O O O O O O O B O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O B O O O O B O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O B O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O B O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O B O O O O O O B I O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O B O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O B O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O B O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Unified Bundling and Registration of Brain White Matter Fibers Abstract-Magnetic resonance diffusion tensor imaging is being widely used to reconstruct brain white matter fiber tracts. To characterize structural properties of the tracts, reconstructed fibers are often grouped into bundles that correspond to coherent anatomic structures. For further group analysis of fiber bundles, it is desirable that corresponding bundles from different studies are coregistered. To address these needs simultaneously, a unified fiber bundling and registration (UFIBRE) framework is proposed in this work. The framework is based on maximizing a posteriori Bayesian probabilities using an expectation maximization algorithm. Given a set of segmented template bundles and a whole-brain target fiber set, the UFIBRE algorithm optimally bundles the target fibers and registers them with the template. The bundling component in the UFIBRE algorithm simplifies fiber-based registration into bundle-to-bundle registration, and the registration component in turn guides the bundling process to find bundles consistent with the template. Experiments with in vivo data demonstrate that the estimated bundles have an 80% consistency with ground truth and the root mean square error between their bundle medial axes is less than one voxel. The proposed algorithm is highly efficient, offering potential routine use for group analysis of white matter fibers. In summary, we proposed an algorithm to automatically bundle a whole-brain fiber set and register it with a template bundle set. The resulting fiber bundles are consistent across subjects and share a common space, which facilitates further group analysis of the bundle properties. Experiments with in vivo human brain DTI data demonstrate that the algorithm we proposed is capable of bundling WM fibers in a consistent manner, and registering fiber bundles with subvoxel accuracy. Future work along this line includes development of a reliable parametric bundle atlas for fully automated implementation of this algorithm, and further applications of the automated algorithm to group analysis. We proposed in this paper a novel algorithm for joint bundling and registration of WM fibers reconstructed from DTI data. Given a set of segmented template bundles and a whole-brain target fiber set, the algorithm optimally bundles the target fibers and registers them with those in the template. Experiments with in vivo human DTI data show that, postregistration, 80% of fibers are correctly clustered, and the root mean square error of the bundle central fiber reaches subvoxel accuracy. The algorithm is highly efficient, converging within 15 iterations of parameter optimization at a speed of 60 s per iteration. This offers the potential of using the algorithm as a routine tool for laboratory research.. The framework we proposed has two salient and mutually beneficial features. First, the registration process guides fibers in the target to converge to bundles that are consistent with the template. This consistency is not guaranteed in conventional fiber clustering algorithms, which exclusively operate on individual datasets separately. Second, the bundling process helps simplify fiber-based registration to bundle-to-bundle registration. This avoids the process of fiber preclustering, and considerably improves the computational efficiency.. Image registration as a general image processing problem has long been the interest of many researchers. Essentially, it involves searches in a high dimensional space for transformation parameters that deform one image to optimally match another. The image registration problem, however, is ill-posed since a unique solution may not exist, and has very high computational complexity due to the high dimensional searches needed. The situation is worse for WM fiber registration, as the structures to be registered are finer and hence more complicated scenarios may occur. To approach the ill-posed, highly complex problem, it is typical to employ some regularization mechanisms and iterative optimizations, so that practically useful solutions can be obtained.. In this work, we also use regularization and iterative optimization, but further make three assumptions on fiber distributions for WM fiber registration: 1) a set of fibers in the human brain observe a Gaussian mixture model, 2) fibers in a bundle and points along the fibers are identically and independently distributed, and 3) the probability distribution of errors between the central fiber of a target and that of a template is Gaussian. These assumptions offer considerable computational benefits to parameter optimization, which renders the fiber registration problem more tractable. Although the validity of these assumptions still warrants further proof, experiments in this work demonstrate that quite appealing results can be obtained based on them. We recognize, however, more sophisticated models may better describe WM fiber distributions. For example, it was reported that a Gamma mixture distribution [9] may model the WM fiber distribution more accurately. Since parameters in the Gamma model can also be estimated by the EM algorithm, it can be in principle incorporated into our framework as well. A major drawback of using this or other more sophisticated models is disproportionally increased complication in the parameter optimization. We, therefore, note that, for fiber registration, the fiber distribution model should be chosen judiciously so that an optimal trade-off between the accuracy of model representation and the efficiency of parameter optimization is achieved.. It should be mentioned that, in this work, alignment of fiber bundles between the template and the target is only based on matching of the first order statistics (central fibers) of the bundles. The central fiber alone, however, does not carry complete information about the morphology of the fiber bundle. To align two fiber bundles more accurately, higher order statistics need to be considered. For instance, minimizing the difference in the second order statistics (covariance matrices) would provide better matching of bundle cross-sectional profiles. However, using higher order statistics may create difficulties in modeling the conditional probability,. . A solution to this exists for the second-order statistics (i.e., using Kullback Leibler divergence), but optimization of the target bundle parameters becomes too complicated. Therefore, high order statistics are not included in this work, in order to achieve a compromise between the accuracy of bundle alignment and the efficiency of parameter optimization.. A most direct and useful application of joint bundling and registration of WM fibers is group analysis. It allows fibers from different subjects to be bundled consistently and registered into a common space, in which statistical characterization of bundle structural, architectural or geometric properties can be conveniently implemented. In addition, consistent and coregistered bundles from a group of subjects may be used to construct a parametric bundle atlas, which can be further utilized to guide other processes such as fiber tracking, bundling/labeling and registration. This application has been debuted in the present work with construction of a bundle atlas using eight human datasets.. Finally, we point out that the initial template bundles are segmented manually in this work. As mentioned earlier, this offers great flexibility in selecting or defining the bundles of interest. Notwithstanding this flexibility, the manual initial segmentation has the drawback of potentially producing subjective errors, and involving a certain amount of human labor. Manual segmentation can be avoided by using an atlas that contains well defined bundle models of interest for initialization. We have demonstrated the possibility of constructing an atlas of this kind, and plan to develop a more reliable atlas with more comprehensively defined fiber bundle models from a larger group of subjects, to enable our UFIBRE algorithm to work in a fully automated and objective fashion.

O B O B O O B I I O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O B O O B O O B O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O B O O B O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


The cybernetics of design and the design of cybernetics Purpose – The purpose of this paper is to connect two discourses, the discourse of cybernetics and that of design.Design/methodology/approach – The paper takes a comparative analysis of relevant definitions, concepts, and entailments in both discourse, and an integration of these into a cybernetically informed concept of human‐centered design, on the one hand, and a design‐informed concept of second‐order cybernetics, on the other hand. In the course of this conceptual exploration, the distinction between science and design is explored with cybernetics located in the dialectic between the two. Technology‐centered design is distinguished from human‐centered design, and several axioms of the latter are stated and discussed.Findings – This paper consists of recommendations to think and do things differently. In particular, a generalization of interface is suggested as a replacement for the notion of products; a concept of meaning is developed to substitute for the meaninglessness of physical properties; a th...

O B O B O O B O B O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O B O O O O O O O O O O O O O O O O B O O O B O O O O O O O O B O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


A simple correction method of inner filter effects affecting FEEM and its application to the PARAFAC decomposition In this paper we introduce a new inner filters correction method for standard fluorometer. The Controlled Dilution Approach (CDA) deals with highly absorbing solutions using the Fluorescent Excitation-Emission Matrix of a controlled weak dilution. Along with the non linear FEEM of the original solution, these two informations allow to estimate the linearized FEEM. The method relies on inner filter effects modelization. Beyond its numerical simplicity, the main interest is that CDA only requires fluorescence measurements. The method was validated using a set of known mixtures and a set of dissolved organic matter samples. In addition we show that the corrected FEEM can be used efficiently for advanced multilinear analysis. Therefore CDA is presented here as a relevant pretreatment to the PARAFAC decomposition of highly absorbing mixtures. Emission (nm) . The absorbance spectrum of the solution is then defined by

O O O O O B I I O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O