Natural coordinate descent algorithm for L1-penalised regression in generalised linear models ABSTRACT. The problem of finding the maximum likelihood estimates for the regression coefficients in generalised linear models with an 1 sparsity penalty is shown to be equivalent to minimising the unpenalised maximum log-likelihood function over a box with boundary defined by the 1 -penalty parameter. In oneparameter models or when a single coefficient is estimated at a time, this result implies a generic soft-thresholding mechanism which leads to a novel coordinate descent algorithm for generalised linear models that is entirely described in terms of the natural formulation of the model and is guaranteed to converge to the true optimum. A prototype implementation for logistic regression tested on two largescale cancer gene expression datasets shows that this algorithm is efficient, particularly so when a solution is computed at set values of the 1 -penalty parameter as opposed to along a regularisation path. Source code and test data are available from http://glmnat.googlecode.com. In high-dimensional regression problems where the number of potential model parameters greatly exceeds the number of training samples, the use of an 1 penalty which augments standard objective functions with a term that sums the absolute effect sizes of all parameters in the model has emerged as a hugely successful and intensively studied variable selection technique, particularly for the ordinary least squares (OLS) problem (e.g. Efron et al. (2004); El Ghaoui et al. (2012) ; Friedman et al. (2010) ; Johnstone and Titterington (2009) ; Osborne et al. (2000a,b) ; Tibshirani (1996 Tibshirani ( , 2013 ; Tibshirani et al. (2012) ; Zou and Hastie (2005) ). Generalised linear models (GLMs) relax the implicit OLS assumption that the response variable is normally distributed and can be applied to, for instance, binomially distributed binary outcome data or poisson distributed count data (Nelder and Wedderburn, 1972) . However, the most popular and efficient algorithm for 1 -penalised regression in GLMs uses a quadratic approximation to the log-likelihood function to map the problem back to an OLS problem and although it works well in practice, it is not guaranteed to converge to the optimal solution (Friedman et al., 2010) . Here it is shown that calculating the maximum likelihood coefficient estimates for 1 -penalised regression in generalised linear models can be done via a coordinate descent algorithm consisting of successive soft-thresholding operations on the unpenalised maximum log-likelihood function without requiring an intermediate OLS approximation. Because this algorithm can be expressed entirely in terms of the natural formulation of the GLM, it is proposed to call it the natural coordinate descent algorithm.. To make these statements precise, let us start by introducing a response variable Y ∈ R and predictor vector X ∈ R p . It is assumed that Y has a probability distribution from the exponential family, written in canonical form as. Research supported by Roslin Institute Strategic Grant funding from the BBSRC.. where η ∈ R is the natural parameter of the distribution, φ is a dispersion parameter and h, α > 0 and A convex are known functions. The expectation value of Y is a function of the natural parameter, E(Y) = A (η), and linked to the predictor variables by the assumption of a linear relation η = X T β, where β ∈ R p is the vector of regression coefficients. It is tacitly assumed that X 1 ≡ 1 such that β 1 represents the intercept parameter. Suppose now that we have n observation pairs (x i , y i ) (with x i1 = 1 fixed for all i). The minus log-likelihood of the observations for a given set of regression coefficients β under the GLM is given by. where any terms not involving β have been omitted,. y i x i ∈ R p , and the dependence of U and w on the data (x i , y i ) has been suppressed for notational simplicity. In the penalised regression setting, this cost function is augmented with 1 and 2 penalty terms to achieve regularity and sparsity of the minimum-energy solution, i.e. H is replaced by. where. |β j | are the 2 and 1 norm, respectively, and λ and µ are positive constants. The 2 term merely adds a quadratic function to U which serves to make its Hessian matrix non-singular and it will not need to be treated explicitly in our analysis. Furthermore a slight generalisation is made where instead of a fixed parameter µ, a vector of predictor-specific penalty parameters µ j is used. This allows for instance to account for the usual situation where the intercept coefficient is unpenalised (µ 1 = 0). The problem we are interested in is thus to findβ. with H a function of the form. where U : R p → R is a smooth convex function, w ∈ R p is an arbitrary vector and µ ∈ R p , µ 0 is a vector of non-negative parameters. The notation u v is used to indicate that u j ≥ v j for all j and likewise the notation u · v will be used to indicate elementwise multiplication, i.e. (u · v) j = u j v j . The maximum of the unpenalised log-likelihood, considered as a function of w, is of course the Legendre transform of the convex function U,. and standard results from convex analysis (Boyd and Vandenberghe, 2004) imply that the unpenalised regression coefficients satisfŷ. where ∇ is the usual gradient operator. We have the following key result:. whereû(w, µ) is the solution of the constrained convex optimisation problem u(w, µ) = argmin. Furthermore the sparsity patterns ofβ andû − w + sgn(β) · µ are complementary,. The proof of this Theorem consists of a straightforward application of Fenchel's duality theorem and is provided in Appendix A. The popularity of 1 -penalised regression as a variable selection technique owes a great deal to the availability of highly efficient coordinate descent algorithms. For generalised linear models, the best existing algorithm uses a quadratic least squares approximation where the coordinate update step can be solved analytically as a linear soft-thresholding operation. This analytic solution has been understood primarily as a consequence of the quadratic nature of the problem. Here it has been shown however that in the dual picture where the penalised optimisation problem is expressed in terms of its Legendre transform, this soft-thresholding mechanism is generic and a direct consequence of the presence of an 1 -penalty term. Incorporating this analytic result in a standard coordinate descent algorithm leads to a method that is not only theoretically attractive and easy to implement, but also appears to offer practical advantages compared to the existing quadraticapproximation algorithm. In particular it is more robust to the choice of starting vector and therefore considerably more efficient when it is cold-started, i.e. when a solution is computed at set values of the 1 -penalty parameter as opposed to along a regularisation path of descending 1 -penalties. This can be exploited for instance NCD cold NCD warm Glmnet cold Glmnet warm FIGURE 2. Numerical evaluation of the natural coordinate descent algorithm. a. Runtime in seconds of the linear approximation on the BRCA (red circles) and COAD (blue squares) dataset and of the exact algorithm on the BRCA (red asterisks) and COAD (blue diamonds) dataset vs. convergence threshold parameter . The insert shows the maximum relative score difference between both algorithms for the same convergence thresholds. b. Maximum relative score difference between the natural coordinate descent algorithm and glmnet vs. convergence threshold parameter for the BRCA (red circles) and COAD (blue squares) dataset. The horizontal lines indicate the minimum, mean and maximum of the relative score difference over 10 comparisons between the original glmnet result and glmnet applied to data with randomly permuted order of predictors. c,d. Runtime in seconds of the natural coordinate descent algorithm with cold (green circles) and warm (orange squares) starts and of glmnet with cold (blue asterisks) and warm (magenta diamonds) starts on the BRCA (c) and COAD (d) dataset vs. index k of the penalty parameter vector. See main text for details.. in situations where prior knowledge or other constraints dictate the choice of 1 -penalty parameter or in situations where distributing the computations for sweeping the 1 -penalty parameter space over multiple processors can lead to significant gains in computing time.

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Feedback control strategies for spatial navigation revealed by dynamic modelling of learning in the Morris water maze The Morris water maze is an experimental procedure in which animals learn to escape swimming in a pool using environmental cues. Despite its success in neuroscience and psychology for studying spatial learning and memory, the exact mnemonic and navigational demands of the task are not well understood. Here, we provide a mathematical model of rat swimming dynamics on a behavioural level. The model consists of a random walk, a heading change and a feedback control component in which learning is reflected in parameter changes of the feedback mechanism. The simplicity of the model renders it accessible and useful for analysis of experiments in which swimming paths are recorded. Here, we used the model to analyse an experiment in which rats were trained to find the platform with either three or one extramaze cue. Results indicate that the 3-cues group employs stronger feedback relying only on the actual visual input, whereas the 1-cue group employs weaker feedback relying to some extent on memory. Because the model parameters are linked to neurological processes, identifying different parameter values suggests the activation of different neuronal pathways. The Morris water maze (Morris et al. 1982 ) is a standard test for studying spatial learning and memory. In order to escape swimming in the surrounding water, animals are required to locate a hidden platform (positioned just below the surface of the water). They do this by making use of the available cues in the environment. Although the task is widely used in neuroscience and experimental psychology to understand the behavioural and neural underpinnings of spatial learning, the exact mnemonic and navigational demands of the task are unclear. There is general acceptance that animals rely on distal cues to infer the platform location (often referred to as an allocentric learning), the exact strategy used depends on the number, location and availability of the cues (see Kealy et al. 2008 and references therein) . Further, animals can adopt strategies that use cues in a beacon-like fashion or that are solely based on self movements and memorised motor actions (egocentric learning; see Moghaddam and Bures 1996) . However, the dissociation of spatial from nonspatial strategies is not always possible (Harrison et al. 2006) . It is therefore crucial for any study of spatial learning and memory, to understand the navigational demands of the tasks and the strategies solving it. The present study clarifies the navigational demands of the Morris water maze and quantifies the effectiveness of different strategies using a (data-driven) dynamic modelling approach. In contrast to other modelling studies in the field of neuroscience that utilise and examine complex networks of neurons (Burgess 2008) , the approach presented here focuses on whole behaviour (Cain and Saucier 1996) and offers a simple model that is identifiable from experimental data of swimming paths.. Traditionally, rather crude performance measures are employed to assess learning, such as escape latencies or the time spend in different areas of the pool (Maei et al. 2009 ). In contrast, we provide a more comprehensive time series analysis of rat swimming dynamics and propose a mathematical model of navigation as a stochastic process. The basic idea is that prior to training, rats exhibit random movements and with learning these movements become increasingly goal oriented. Between two measuring points, a rat moves a certain distance (step size) in a certain direction (heading). This movement can be described by a directed random walk, whereby the step size and heading change are random processes.. The dynamic modelling approach offers full control over multiple variables and a much richer analysis compared to measuring only simple performance statistics. For example it allows testing whether a purely egocentric strategy would be sufficient to solve the task. Real animals in the watermaze may employ a variety of different strategies (even in a single trial) such as avoiding the pool border, approaching a cue, etc (Harvey et al. 2009 ), which makes it very difficult to assess the effectiveness of these individual strategies experimentally. Using a modelling approach, one can formally specify different strategies, and then analyse these in simulations, either individually or in combination. As such the effectiveness of different strategies and their relative contribution to the performance in terms of escape latencies can be assessed effectively. Our modelling results concerning the 3-cues and 1-cue group are in concordance with earlier reports. Harvey et al. (2009) revealed no significant difference between the groups in terms of the gross measures used (e.g escape latencies) demonstrating that both groups learned the task effectively, but also found different behavioural patterns. Here we provide a mathematical model explaining the group differences and revealing that both groups control their movements differently.. The parameters of the heading change model were identified in open loop and seem not to differ considerably. In contrast, the feedback parameters as identified in closed loop are clearly distinct. This demonstrates that the model can reveal inherent procedural differences not visible in gross measures. The model parameters are influenced by several factors that could be controlled in experiments (e.g. brain lesions, training schemes). This makes the model a useful tool for analysis of experiments for which swimming paths are recorded. The fitted model parameters can be understood as higher level measures reflecting behavioural and neurophysiological differences. This section identifies the mathematical model from experimental data and analyses different navigational strategies. Estimating all parameters from the recorded swimming paths is possible because the described model is simple and largely linear (except for Eq. (1)).

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Application of the asymptotic solution to EM field scattering problem for creation of media with prescribed permeability Scattering of electromagnetic (EM) waves by many small impedance particles (bodies), embedded in a homogeneous medium, is studied. Physical properties of the particles are described by their boundary impedances. The limiting equation is obtained for the effective EM field in the limiting medium, in the limit a→0, where a is the characteristic size of a particle and the number M(a) of the particles tends to infinity at a suitable rate. The proposed theory allows one to create a medium with a desirable spatially inhomogeneous permeability. The main new physical result is the explicit analytical formula for the permeability μ(x) of the limiting medium. The computational results confirm a possibility to create the media with various distributions of μ(x). A theory of electromagnetic (EM) wave scattering by many small impedance particles (bodies) embedded in a homogeneous medium with a constant permittivity ε 0 > 0, permeability µ 0 > 0 and, possibly, constant conductivity σ 0 ≥ 0 is applied for creating a media with a prescribed permeability. The computational procedure for numerical solution of the scattering problem were developed in [1] .. In [9] there is a mathematical analysis of the Maxwell's equations, and in [10] theory of the wave scattering by obstacles is developed. The small particles are embedded in a finite domain D. The medium, created by the embedding of the small particles, has new physical properties. In particular, it has a spatially inhomogeneous magnetic permeability µ(x), which can be controlled by the choice of the boundary impedances of the embedded small particles and their distribution density. An analytic formula for the permeability of the new medium is obtained (see Subsection 2.3) .. Although the initial medium has a constant permeability µ 0 , the limiting medium, obtained as a result of embedding many small particles with prescribed boundary impedances, has a non-homogeneous permeability which is expressed analytically in terms of the distribution density of the small particles and their boundary impedances. Therefore, a new physical phenomenon is predicted theoretically, namely, appearance of a spatially inhomogeneous permeability as a result of embedding of many small particles whose physical properties are described by their boundary impedances.. We assume that in any sub-domain ∆, the number N (∆) of the embedded particles is given by the formula:. where N (x) ≥ 0 is a continuous function, vanishing outside of the finite domain D in which small particles (bodies) are distributed, κ ∈ (0, 1) is a number that one can choose as one wishes, and the boundary impedances of the small particles are defined by the formula:. where x m is a point inside m-th particle, and h(x) is a continuous function vanishing outside D which satisfies only the physical restriction Reh(x) ≥ 0. The function h, used in our numerical examples satisfies this restriction. The impedance boundary condition on the surface S m of the m-th particle D m is E t = ζ m [H t , N ], where E t (H t ) is the tangential component of E(H) on S m , and N is the unit normal to S m , pointing out of D m .. Since one can choose the functions N (x) and h(x), one can create a desired magnetic permeability in D. This is a novel idea proposed originally in [14] , [15] . It has led to a recipe for creating materials with a desired refraction coefficient in [19] , [20] . [21] .. Materials with negative permittivity and permeability are of interest in applications, see [11] , [23] , [24] ).. We also derive an analytic formula for the refraction coefficient of the medium in D created by the embedding of many small particles. An equation for the effective EM field in the limiting medium is derived. This medium is created when the size a of small particles tends to zero while the total number M = M (a) of the particles tends to infinity at a suitable rate.. The refraction coefficient n 2 (x) in the limiting medium is spatially inhomogeneous.. The proposed theory may be viewed as a "homogenization theory", but it differs from the usual homogenization theory (see, e.g., [3] , [10] , [5] , and references therein) in several respects: we do not assume any periodic structure in the distribution of small bodies, our problem does not have a discrete spectrum, our operators are non-selfadjoint, to mention some of the differences. The ideas, methods, and techniques are also quite different from the usual methods. These ideas are similar to the ideas developed in papers [15] , [16] , where scalar wave scattering by small bodies was studied. More on this one can find in the forthcoming monograph [22] .. However, the scattering of EM waves brought new technical difficulties which are resolved in this paper. The difficulties come from the vectorial nature of the boundary conditions. Our approach is valid for small particles of arbitrary shape, but for simplicity we assume that the small bodies are balls of radius a [18] . The numerical procedures for solving the EM wave scattering problem by one and many small impedance particles of an arbitrary shape are given. On this basis a method for creating the media with non-uniform distribution of magnetic permeability µ(x) is developed and tested numerically. It is shown that the relative error of the asymptotic solution (17) compared with the Mie-type solution (52) in the paper [2] depends on the radius a of the particle, the distance r to the observation point, and on the parameter h which defines the surface impedance ζ of the particle.. The numerical results show that the assumptions DivE t = 0 and Divσ m = 0 on the surfaces of the particles are practically accurate: the relative error of these assumptions does not exceed 1.85% in the considered range of the parameters used for the solution of the scattering problem.

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


Automatic recognition of lower facial action units The face is an important source of information in multimodal communication.Facial expressions are generated by contractions of facial muscles, which lead to subtle changes in the area of the eyelids, eye brows, nose, lips and skin texture, often revealed by wrinkles and bulges. The Facial Action Coding System (FACS) [5] is a humanobserver-based system designed to detect subtle changes in facial features, and describes facial expressions by 44 anatomically based Action Units (AUs). AUs can occur individually or in combinations. When AUs occur in combination they may be nonadditive, in which case the combination changes the appearance of the constituents. FACS coding is very labor-intensive; automating this process has attracted a lot ofattention since the early 1990s. Automatic facial analysis requires extraction of features from static images or image sequences, and classification into AUs, or AU combinations. Basically, there are two main approaches for feature extraction: geometry-, and appearance-based.. Geometry-based featureextraction consists of detecting and tracking facial feature points.. Appearance-based features concern motion and texture changes. Methods to extract these features are Gabor Wavelets Analysis, optical flow analysis, PCA, ICA.. It has been shown that the combination ofgeometry-and appearance-based features give better recognition results, [4, 10, 13] .. State of the art classification methods are Support Vector Machines (SVM) [1, 10] , Neural Networks, Hidden Markov Models, and DiscriminantAnalysis. Our system was trained on the Cohn and Kanade's DFAT-504 dataset [9] . This databaseconsists of 486 sequences of facial displays that are produced by 98 University students from 18 to 30 years old,of which 65% is female. All sequences areannotated by certified FACS coders. We selected all sequences where at least one of the analyzed AUs is present. This resulted in 364 sequences from 94 subjects (66% female). Training and evaluation is doneon the last frame of each sequence, which contains the apex of the expression.. Our final goal is to develop a system that detects behavioral patterns in communication between two persons, more specifically between mother and infant. We therefore selected a set of AUs from state of the art work in mother-infant communication, e.g. [11] . As lower facial AUs do not involve lots of wrinkles and furrows, which need appearance-based features, we started with the analysis of the lower AUs. Table 3 shows the AUswe analyze.

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 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


Interval feature extraction for classification of event-related potentials (ERP) in EEG data analysis Abstract Event-related potential data can be used to index perceptual and cognitive operations. However, they are typically high-dimensional and noisy. This study examines the original raw data and six feature-extraction methods as a pre-processing step before classification. Four traditionally used feature-extraction methods were considered: principal component analysis, independent component analysis, autoregression, and wavelets. We add to these a less well-known method called interval feature extraction. It overproduces features from the ERP signal and then eliminates irrelevant and redundant features by the fast correlation-based filter. To make the comparisons fair, the other feature-extraction methods were also run with the filter. An experiment on two EEG datasets (four classification scenarios) was carried out to examine the classification accuracy of four classifiers on the extracted features: support vector machines with linear and perceptron kernel, the nearest neighbour classifier and the random forest ensemble method. The interval features led to the best classification accuracy in most of the configurations, specifically when used with the Random Forest classifier ensemble. Event-related potentials (ERP) are stereotyped electrophysiological responses to a volitional activity or an external stimulus. ERPs are derived by averaging the spontaneous electroencephalogram (EEG) across several occurrences of the same event, for example, repeated presentations of the same stimulus. Assuming that the onset of the event is known, the ERP is a time series containing the ensuing brain reaction, termed an epoch. ERP can be used to distinguish between the brain states of the subject in response to the different stimuli within the particular examination context. This makes ERP analysis an ideal, long-standing tool in brain-computer interface (BCI) [2] , ranging from predicting the laterality of imminent left-versus right-hand finger movements [1] to distinguishing between musical segments [22] .. Classification of ERP data is challenging due to the high dimensionality and noise contamination of the raw data. Here, we study the classification accuracy of the original data and four feature-extraction methods used as a preprocessing step, and argue that ERP data benefits from interval feature extraction.. ERP are associated to different electrodes. For each electrode, a different classification problem is considered. The ERP time series is regarded as a collection of measurements, x 1 , . . . , x T , each measurement is considered to be a feature. Thus, each ERP series becomes a point in a T -dimensional space, x ∈ T . A training dataset is a collection of points x 1 , . . . x N and the corresponding labels y 1 . . . y N .. Section 2 explains the feature-extraction methods, Sect. 3 lists the four classifiers, and Sect. 4 details the data, the experimental protocol and the results. Feature-extraction methods are likely to enhance the classification accuracy in ERP classification. We showed that interval features followed by an FCBF are a suitable tool for this task. The first step over-produces interval-based features, a large part of which are redundant, irrelevant or both. The second step picks the most relevant and uncorrelated features. The resultant feature set works well with various classifier models, including SVM and classifier ensembles, represented here by random forest.. Compared to the other feature-extraction methods, the interval method is simple and intuitive. The simplicity is important in view of the large variability of the raw data, as illustrated in Fig. 1 . A more intricate and versatile model such as wavelets may overfit the noise. Unlike PCA and ICA, the interval-extraction method is non-linear, which gives it additional flexibility. Finally, the method does not rely on a parameter of significant importance as does auto-regression extraction method.. An interesting future direction is joining the electrode data and extracting interval features from the multidimensional ERP. This reflects the fact that brain activity is typically not localised but involves spatially coordinated brain-activation patterns. We grouped the results by classifiers and show in Table 2 the maximum achieved accuracies along with the respective electrode labels for the methods without FCBF. Table 3 has the same format but this time, FCBF has been applied after the selection. The interval method is the same because FCBF is an integral part of it. Wilcoxon signed rank tests were run to determine whether the difference with the interval features accuracies are statistically significant at level 0.05. A mark of • in the tables means that the respective methods is significantly better than the interval features method, • means that it is significantly worse and − means that the difference is not statistically significant. The tables show that the top accuracies with the interval features are often larger than these with the other featureextraction methods, and in many experimental configurations, these differences are statistically significant (level 0.05). The Interval method was found significantly worse only in four cases (two in Table 2 and two in Table 3 ). It is interesting to note that the differences in favour of the Interval methods are most pronounced in the bottom block-row of both tables. These rows correspond to the random forest ensembles, which give the highest classification accuracies across the classification models. We chose the Face/Car dataset to illustrate the results further. Figure 3 shows the distribution of the classification accuracy across the electrodes on the scalp for two combinations of a feature-extraction method and a classifier. The anatomical reference of the electrode with the best accuracy is also shown. 5 Subplot (a) shows the combination with the highest maximal accuracy and subplot (b), the combination with the highest average accuracy across all electrodes.. The maximum of the classification accuracy for this dataset (Experiment 1), achieved by the interval features with FCBF and the Random Forest classifier ensembles, falls in the parietooccipital electrode site, which is the expected brain area for distinguishing face from non-face objects [5] . The method that we recommend in this study is interval feature extraction followed by FCBF. To the best of the authors' knowledge, interval features have not been applied previously to ERP classification, either as a full set or after FCBF filtering. The purpose of this experiment is to compare the interval features + FCBF with the traditional featureextraction methods for pre-processing of ERP data for classification. To make the comparisons fair, we applied FCBF to all competing methods as well.

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


Bringing cross-layer MIMO to today's wireless LANs Recent years have seen major innovations in cross-layer wireless designs. Despite demonstrating significant throughput gains, hardly any of these technologies have made it into real networks. Deploying cross-layer innovations requires adoption from Wi-Fi chip manufacturers. Yet, manufacturers hesitate to undertake major investments without a better understanding of how these designs interact with real networks and applications.This paper presents the first step towards breaking this stalemate, by enabling the adoption of cross-layer designs in today's networks with commodity Wi-Fi cards and actual applications. We present OpenRF, a cross-layer architecture for managing MIMO signal processing. OpenRF enables access points on the same channel to cancel their interference at each other's clients, while beamforming their signal to their own clients. OpenRF is self-configuring, so that network administrators need not understand MIMO or physical layer techniques.We patch the iwlwifi driver to support OpenRF on off-the-shelf Intel cards. We deploy OpenRF on a 20-node network, showing how it manages the complex interaction of cross-layer design with a real network stack, TCP, bursty traffic, and real applications. Our results demonstrate an average gain of 1.6× for TCP traffic and a significant reduction in response time for real-time applications, like remote desktop. This paper introduces OpenRF, the first system that enables the deployment of physical-layer MIMO techniques on commodity Wi-Fi cards. It is also the first cross-layer design that is demonstrated using a fully operational network stack with real applications. While our current implementation of OpenRF demonstrates interference nulling, interference alignment and beamforming, we believe OpenRF can be extended to support other PHYaware techniques such as multi-user MIMO and frequency diversity schemes [29] , when future wireless cards support them. We compare OpenRF in various settings with a standard 802.11n baseline that uses block-aggregation but does not perform interference nulling, coherent beamforming or interference alignment. We implemented OpenRF by modifying the iwlwifi driver for Intel Wi-Fi cards on Ubuntu 10.04 LTS. We built our solution over the University of Washington's 802.11 CSI tool [12] . Our APs also use the transmit beamforming feature of the Intel 5300 Wi-Fi cards. 8 To support the OpenRF Interface, we made the following modifications to the driver: First, we implemented the OpenRF table (Sec. §4.1) as a debugfs file that interfaces between user and kernel modes. Second, OpenRF uses the 802.11 CSI tool to calculate the reciprocal channels from the clients, which are used to maintain the coherence and interference spaces in the OpenRF table for various flows at this AP. Finally, we employ the transmit beamforming feature to set precoding vectors for various flows in real-time, using the coherence and interference spaces as in §4.2.. To support the OpenRF Controller at each AP, we first employ block aggregation to implement time slots spanning 5 ms. We use NTP over the wired Ethernet backbone to synchronize the block aggregation slots across APs in the network. We observed that this was sufficient to synchronize blocks spanning 5 ms each, within tens of microseconds. We intercept packets from the higher layers into per-flow queues at the driver and apply the local controller algorithm as described in §4.3. Our controller and scheduler algorithms are implemented using high resolution timers to minimize waste of airtime. The central controller is implemented on a Linux workstation, and coordinates APs in the network over the Ethernet backbone using the algorithm described in §4.3.. Finally, our implementation fully complies with 802.11n and handles concurrent transmissions, carrier sense, and ACKs as in §5. We deployed OpenRF on a network of 20 nodes, each containing an Intel Wireless-N series card connected to a PC or laptop. Our network has six 3-antenna APs, spread out on a single floor of a large building as shown in Fig. 11 . Each AP is a Linux PC running hostapd, and implementing our patched iwlwifi driver. We deploy 14 clients, including seven single-antenna, five 2-antenna and two 3-antenna wireless nodes. We randomize the locations of the clients on the floor across different experiments (a candidate set of client locations is shown in Fig. 11 ). All APs in the network share the same wireless channel, potentially causing interference at some clients, that are at the edge of their AP's communication range.

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


A New Construction of Permutation Arrays Let PA(n, d) be a permutation array (PA) of order n and the minimum distance d. We propose a new construction of the permutation array PA p m , p m−1 k for a given prime number p, a positive integer k < p and a positive integer m. The resulted array has |PA(p, k)| · p (m−1)(p−k) m rows. Compared to the other constructions, the new construction gives a permutation array of far bigger size with a large minimum distance, for example, when k ≥ 2p/3. Moreover the proposed construction provides an algorithm to find the i-th row of PA p m , p m−1 k for a given index i very simply. Permutation codes were introduced first in [1] for communications over discrete channels such as powerlines [19] . Let n be a positive integer and S n be the symmetric group of order n. An element η ∈ S n is usually represented as an n-tuple of integers from its images: η = (η(1), η(2), . . . , η(n)) .. With this representation, we define a Hamming distance function d H on S n as follows:. for η 1 , η 2 ∈ S n . Since (S n , d H ) is a metric space, we can construct a permutation code with a minimum distance d on S n by considering each permutation as a codeword. If we write them as rows, we obtain an array with n columns whose rows are permutations with a minimum distance d. In the research of permutation arrays, the most important issue is to construct a permutation array with a large number of rows for given n and d, see e.g., [1] , [2] , [4] , [6] - [12] and [18] . Another issue, which is considered less in literature, is to find the row of the array corresponding to a given index. This issue has been treated explicitly in only [6] , and in no others, as far as authors are aware.. In this paper we first propose a new construction of permutation arrays PA p 2 , pk from PA(p, k) for a prime number p and a positive integer k < p. Then we extend the construction to PA p m , p m−1 k for a integer m ≥ 2. We also show that all the proposed construction provide algorithms to pick up the designated row from the arrays for a given index in a natural way.

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 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 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 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Nonparametric

Scene

Parsing

via

Label

Transfer

Abstract-While

there

has

been

a

lot

of

recent

work

on

object

recognition

and

image

understanding,

the

focus

has

been

on

carefully

establishing

mathematical

models

for

images,

scenes,

and

objects.

In

this

paper,

we

propose

a

novel,

nonparametric

approach

for

object

recognition

and

scene

parsing

using

a

new

technology

we

name

label

transfer.

For

an

input

image,

our

system

first

retrieves

its

nearest

neighbors

from

a

large

database

containing

fully

annotated

images.

Then,

the

system

establishes

dense

correspondences

between

the

input

image

and

each

of

the

nearest

neighbors

using

the

dense

SIFT

flow

algorithm

which

aligns

two

images

based

on

local

image

structures.

Finally,

based

on

the

dense

scene

correspondences

obtained

from

SIFT

flow,

our

system

warps

the

existing

annotations

and

integrates

multiple

cues

in

a

Markov

random

field

framework

to

segment

and

recognize

the

query

image.

Promising

experimental

results

have

been

achieved

by

our

nonparametric

scene

parsing

system

on

challenging

databases.

Compared

to

existing

object

recognition

approaches

that

require

training

classifiers

or

appearance

models

for

each

object

category,

our

system

is

easy

to

implement,

has

few

parameters,

and

embeds

contextual

information

naturally

in

the

retrieval/alignment

procedure.

S

CENE

parsing,

or

recognizing

and

segmenting

objects

in

an

image,

is

one

of

the

core

problems

of

computer

vision.

Traditional

approaches

to

object

recognition

begin

by

specifying

an

object

model,

such

as

template

matching

constellations

bags

of

features

or

shape

models

etc.

These

approaches

typically

work

with

a

fixed

number

of

object

categories

and

require

training

generative

or

discriminative

models

for

each

category

from

training

data.

In

the

parsing

stage,

these

systems

try

to

align

the

learned

models

to

the

input

image

and

associate

object

category

labels

with

pixels,

windows,

edges,

or

other

image

representations.

Recently,

context

information

has

also

been

carefully

modeled

to

capture

the

relationship

between

objects

at

the

semantic

level

Encouraging

progress

has

been

made

by

these

models

on

a

variety

of

object

recognition

and

scene

parsing

tasks..

However,

these

learning-based

methods

do

not,

in

general,

scale

well

with

the

number

of

object

categories.

For

example,

to

include

more

object

categories

in

an

existing

system,

we

need

to

train

new

models

for

the

new

categories

and,

typically,

adjust

system

parameters.

Training

can

be

a

tedious

job

if

we

want

to

include

thousands

of

object

categories

in

a

scene

parsing

system.

In

addition,

the

complexity

of

contextual

relationships

among

objects

also

increases

rapidly

as

the

quantity

of

object

categories

expands..

Recently,

the

emergence

of

large

databases

of

images

has

opened

the

door

to

a

new

family

of

methods

in

computer

vision.

Large

database-driven

approaches

have

shown

the

potential

for

nonparametric

methods

in

several

applications.

Instead

of

training

sophisticated

parametric

models,

these

methods

try

to

reduce

the

inference

problem

for

an

unknown

image

to

that

of

matching

to

an

existing

set

of

annotated

images.

In

the

authors

estimate

the

pose

of

a

human,

relying

on

million

training

examples.

In

the

proposed

algorithm

can

fill

holes

on

an

input

image

by

introducing

elements

that

are

likely

to

be

semantically

correct

through

searching

a

large

image

database.

In

a

system

is

designed

to

infer

the

possible

object

categories

that

may

appear

in

an

image

by

retrieving

similar

images

in

a

large

database

Moreover,

the

authors

in

showed

that

with

a

database

of

million

images,

even

simple

SSD

match

can

give

semantically

meaningful

parsing

for

Â

images..

In

this

paper,

we

propose

a

novel,

nonparametric

scene

parsing

system

to

transfer

the

labels

from

existing

samples

in

a

large

database

to

annotate

an

image,

as

illustrated

in

Fig.

For

a

query

image

(Fig.

our

system

first

retrieves

the

top

matches

in

a

large,

annotated

image

database

using

a

combination

of

GIST

matching

and

SIFT

flow

Since

these

top

matches

are

labeled,

we

transfer

the

annotation

(Fig.

of

the

top

matches

to

the

query

image

and

obtain

the

scene

parsing

result

in

(Fig.

For

comparison,

the

groundtruth

user

annotation

of

the

query

is

displayed

in

(Fig.

Our

system

is

able

to

generate

promising

scene

parsing

results

if

images

from

the

same

scene

type

as

the

query

are

retrieved

in

the

annotated

database..

However,

it

is

nontrivial

to

build

an

efficient

and

reliable

scene

parsing

system

using

dense

scene

alignment.

To

account

for

the

multiple

annotation

suggestions

from

the

top

matches,

a

Markov

random

field

model

is

used

to

merge

multiple

cues

(e.g.,

likelihood,

prior,

and

spatial

smoothness)

into

a

robust

annotation.

Promising

experimental

results

are

achieved

on

images

from

the

LabelMe

database

Our

goal

is

to

explore

the

performance

of

scene

parsing

through

the

transfer

of

labels

from

existing

annotated

images,

rather

than

building

a

comprehensive

object

recognition

system.

We

show,

however,

that

the

performance

of

our

system

outperforms

existing

approaches

on

our

databases.

Our

code

and

databases

can

be

downloaded

at

This

paper

is

organized

as

follows:

In

Section

we

briefly

survey

the

object

recognition

and

detection

literature.

After

giving

a

system

overview

in

Section

we

describe,

in

detail,

each

component

of

our

system

in

Section

Thorough

experiments

are

conducted

in

Section

for

evaluation,

and

in-depth

discussion

is

provided

in

Section

We

conclude

our

paper

in

Section

We

have

presented

a

novel,

nonparametric

scene

parsing

system

to

integrate

and

transfer

the

annotations

from

a

large

database

to

an

input

image

via

dense

scene

alignment.

A

coarse-to-fine

SIFT

flow

matching

scheme

is

proposed

to

reliably

and

efficiently

establish

dense

correspondences

between

images

across

scenes.

Using

the

dense

scene

correspondences,

we

warp

the

pixel

labels

of

the

existing

samples

to

the

query.

Furthermore,

we

integrate

multiple

cues

to

segment

and

recognize

the

query

image

into

the

object

categories

in

the

database.

Promising

results

have

been

achieved

by

our

scene

alignment

and

parsing

system

on

challenging

databases.

Compared

to

existing

approaches

that

require

training

for

each

object

category,

our

nonparametric

scene

parsing

system

is

easy

to

implement,

has

only

a

few

parameters,

and

embeds

contextual

information

naturally

in

the

retrieval/alignment

procedure.

Fig.

Some

scene

parsing

results

on

the

SUN

database

following

the

same

notation

as

in

Fig.

Note

that

the

LabelMe

Outdoor

database

is

a

subset

of

the

SUN

database,

but

the

latter

contains

a

larger

proportion

of

indoor

and

activity-based

scenes.

As

it

is

in

all

cases,

the

success

of

the

final

parsing

depends

on

the

semantic

similarity

of

the

query

in

(a)

to

the

warped

support

image

(d).

Examples

and

For

more

information

on

this

or

any

other

computing

topic,

please

visit

our

Digital

Library

at

Object

recognition

is

an

area

of

research

that

has

greatly

evolved

over

the

last

decade.

Many

works

focusing

on

single-class

modeling,

such

as

faces

digits,

characters,

and

pedestrians

have

been

proven

successful

and,

in

some

cases,

the

problems

have

been

mostly

deemed

as

solved.

Recent

efforts

have

turned

to

mainly

focusing

in

the

area

of

multiclass

object

recognition.

In

creating

an

object

detection

system,

there

are

many

basic

building

blocks

to

take

into

account;

feature

description

and

extraction

is

the

first

stepping

stone.

Examples

of

descriptors

include

gradient-based

features

such

as

SIFT

and

HOG

shape

context

and

patch

statistics

Consequently,

selected

feature

descriptors

can

be

further

applied

to

images

in

either

a

sparse

manner

by

selecting

the

top

key

points

containing

the

highest

response

from

the

feature

descriptor,

or

densely

by

observing

feature

statistics

across

the

image

Sparse

key

point

representations

are

often

matched

among

pairs

of

images.

Since

the

generic

problem

of

matching

two

sets

of

key

points

is

NP-hard,

approximation

algorithms

have

been

developed

to

efficiently

compute

key

point

matches

minimizing

error

rates

(e.g.,

the

pyramid

match

kernel

and

vocabulary

trees

On

the

other

hand,

dense

representations

have

been

handled

by

modeling

distributions

of

the

visual

features

over

neighborhoods

in

the

image

or

in

the

image

as

a

whole

We

chose

the

dense

representation

in

the

paper

due

to

recent

advances

in

dense

image

matching

At

a

higher

level,

we

can

also

distinguish

two

types

of

object

recognition

approaches:

parametric

approaches

that

consist

of

learning

generative/discriminative

models,

and

nonparametric

approaches

that

rely

on

image

retrieval

and

matching.

In

the

parametric

family

we

can

find

numerous

template-matching

methods,

where

classifiers

are

trained

to

discriminate

between

an

image

window

containing

an

object

or

a

background

However,

these

methods

assume

that

objects

are

mostly

rigid

and

are

susceptible

to

little

or

no

deformation.

To

account

for

articulated

objects,

constellation

models

have

been

designed

to

model

objects

as

ensembles

of

parts

considering

spatial

information

depth

ordering

information

and

multiresolution

modes

Recently,

a

new

idea

of

integrating

humans

in

the

loop

via

crowd

sourcing

for

visual

recognition

of

specialized

classes

such

as

plants

and

animal

species

has

emerged

this

method

integrates

the

description

of

an

object

in

less

than

discriminative

questions

that

humans

can

answer

after

visually

inspecting

the

image..

In

the

realm

of

nonparametric

methods

we

find

systems

such

as

Video

Google

a

system

that

allows

users

to

specify

a

visual

query

of

an

object

in

a

video

and

subsequently

retrieve

instances

of

the

same

object

across

the

movie.

Another

nonparametric

system

is

the

one

in

where

a

previously

unknown

query

image

is

matched

against

a

densely

labeled

image

database;

the

nearest

neighbors

are

used

to

build

a

label

probability

map

for

the

query,

which

is

further

used

to

prune

out

object

detectors

of

classes

that

are

unlikely

to

take

place

in

the

image.

Nonparametric

methods

have

also

been

widely

used

in

web

data

to

retrieve

similar

images.

For

example,

in

a

customized

distance

function

is

used

at

a

retrieval

stage

to

compute

the

distance

between

a

query

image

and

images

in

the

training

set,

which

subsequently

cast

votes

to

infer

the

object

class

of

the

query.

In

the

same

spirit,

our

nonparametric

label

transfer

system

avoids

modeling

object

appearances

explicitly

as

our

system

parses

a

query

image

using

the

annotation

of

similar

images

in

a

training

database

and

dense

image

correspondences..

Recently,

several

works

have

also

considered

contextual

information

in

object

detections

to

clean

and

reinforce

individual

results.

Among

contextual

cues

that

have

been

used

are

object-level

co-occurrences,

spatial

relationships

and

scene

layout

For

a

more

detailed

and

comprehensive

study

and

benchmark

of

contextual

works,

we

refer

to

Instead

of

explicitly

modeling

context,

our

model

incorporates

context

implicitly

as

object

co-occurrences

and

spatial

relationships

are

retained

in

label

transfer..

An

earlier

version

of

our

work

appeared

at

in

this

paper,

we

will

explore

the

label-transfer

framework

indepth

with

more

thorough

experiments

and

insights.

Other

recent

papers

have

also

introduced

similar

ideas.

For

instance,

in

oversegmentation

is

performed

to

the

query

image

and

segment-based

classifiers

trained

on

the

nearest

neighbors

are

applied

to

recognize

each

segment.

In

scene

boundaries

are

discovered

by

the

common

edges

shared

by

nearest

neighbors.

Fig.

For

a

query

image

(a),

our

system

finds

the

top

matches

(b)

(three

are

shown

here)

using

scene

retrieval

and

a

SIFT

flow

matching

algorithm

The

annotations

of

the

top

matches

(c)

are

transferred

and

integrated

to

parse

the

input

image,

as

shown

in

(d).

For

comparison,

the

ground-truth

user

annotation

of

(a)

is

shown

in

(e)..

The

core

idea

of

our

nonparametric

scene

parsing

system

is

recognition-by-matching.

To

parse

an

input

image,

we

match

the

visual

objects

in

the

input

image

to

the

images

in

a

database.

If

images

in

the

database

are

annotated

with

object

category

labels

and

if

the

matching

is

semantically

meaningful,

i.e.,

building

corresponds

to

building,

window

to

window,

person

to

person,

then

we

can

simply

transfer

the

labels

of

the

images

in

the

database

to

parse

the

input.

Nevertheless,

we

need

to

deal

with

many

practical

issues

in

order

to

build

a

reliable

system.

Fig.

shows

the

pipeline

of

our

system,

which

consists

of

the

following

three

algorithmic

modules:.

Scene

retrieval:

Given

a

query

image,

use

scene

retrieval

techniques

to

find

a

set

of

nearest

neighbors

that

share

similar

scene

configuration

(including

objects

and

their

relationships)

with

the

query.

Dense

scene

alignment:

Establish

dense

scene

correspondence

between

the

query

image

and

each

of

the

retrieved

nearest

neighbors.

Choose

the

nearest

neighbors

with

the

top

matching

scores

as

voting

candidates.

Label

transfer:

Warp

the

annotations

from

the

voting

candidates

to

the

query

image

according

to

estimated

dense

correspondence.

Reconcile

multiple

labeling

and

impose

spatial

smoothness

under

a

Markov

random

field

(MRF)

model.

Although

we

are

going

to

choose

concrete

algorithms

for

each

module

in

this

paper,

any

algorithm

that

fits

to

the

module

can

be

plugged

into

our

nonparametric

scene

parsing

system.

For

example,

we

use

SIFT

flow

for

dense

scene

alignment,

but

it

would

also

suffice

to

use

sparse

feature

matching

and

then

propagate

sparse

correspondences

to

produce

dense

counterparts..

A

key

component

of

our

system

is

a

large,

dense,

and

annotated

image

database.

In

this

paper,

we

use

two

sets

of

databases,

both

annotated

using

the

LabelMe

online

annotation

tool

to

build

and

evaluate

our

system.

The

first

is

the

LabelMe

Outdoor

(LMO)

database

containing

fully

annotated

images,

most

of

which

are

outdoor

scenes

including

street,

beach,

mountains,

fields,

and

buildings.

The

second

is

the

SUN

database

containing

fully

annotated

images,

covering

both

indoor

and

outdoor

scenes;

in

fact,

LMO

is

a

subset

of

SUN..

We

use

the

LMO

database

to

explore

our

system

in-depth,

and

also

report

the

results

on

the

SUN

database.

Before

jumping

into

the

details

of

our

system,

it

is

helpful

to

look

at

the

statistics

of

the

LMO

database.

The

images

in

LMO

are

randomly

split

into

for

training

and

for

testing.

We

chose

the

top

object

categories

with

the

most

labeled

pixels.

The

pixels

that

are

not

labeled,

or

labeled

as

other

object

categories,

are

treated

as

the

category:

"unlabeled."

The

per

pixel

frequency

count

of

these

object

categories

in

the

training

set

is

shown

at

the

top

of

Fig.

The

color

of

each

bar

is

the

average

RGB

value

of

the

corresponding

object

category

from

the

training

data

with

saturation

and

brightness

boosted

for

visualization

purposes.

The

top

object

categories

are

sky,

building,.

Other

scene

parsing

and

image

understanding

systems

also

require

such

a

database.

We

do

not

require

more

than

others.

Fig.

System

pipeline.

There

are

three

key

algorithmic

components

(rectangles)

in

our

system:

scene

retrieval,

dense

scene

alignment,

and

label

transfer.

The

ovals

denote

data

representations.

Fig.

Top:

The

per-pixel

frequency

counts

of

the

object

categories

in

our

data

set

(sorted

in

descending

order).

The

color

of

each

bar

is

the

average

RGB

value

of

each

object

category

from

the

training

data

with

saturation

and

brightness

boosted

for

visualization.

Bottom:

The

spatial

priors

of

the

object

categories

in

the

database.

White

means

zero

and

the

saturated

color

means

high

probability.

mountain,

tree,

unlabeled,

road,

sea,

field,

grass,

and

river.

The

spatial

priors

of

these

object

categories

are

displayed

at

the

bottom

of

Fig.

where

white

denotes

zero

probability

and

the

saturation

of

color

is

directly

proportional

to

its

probability.

Note

that,

consistent

with

common

knowledge,

sky

occupies

the

upper

part

of

the

image

grid

and

field

occupies

the

lower

part.

Furthermore,

there

are

only

limited

samples

for

the

sun,

cow,

bird,

and

moon

classes.

Extensive

experiments

were

conducted

to

evaluate

our

system.

We

shall

first

report

the

results

on

a

small

scale

database

which

we

will

refer

to

as

the

LabelMe

Outdoor

(LMD)

database

in

Section

this

database

will

aid

us

for

an

in-depth

exploration

of

our

model.

Furthermore,

we

will

Fig.

For

a

query

image,

we

first

find

a

hK;

i-nearest

neighbor

set

in

the

database

using

GIST

matching

The

nearest

neighbors

are

reranked

using

SIFT

flow

matching

scores,

and

form

a

top

M-voting

candidate

set.

The

annotations

are

transferred

from

the

voting

candidates

to

parse

the

query

image..

report

results

on

the

SUN

database,

a

larger

and

more

challenging

data

set

in

Section

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


On the (n, m, k)-cast capacity of wireless ad hoc networks and compute the (n, m, k)-cast communications. Next, the achievable throughput capacity is computed when receiver nodes are endowed with multipacket reception (MPR) capability. We adopt maximum likelihood decoding (MLD) and successive interference cancellation as optimal and suboptimal decoding schemes for MPR. We also demonstrate that physical and protocol models for MPR render the same capacity when we utilize MLD for decoding.Index Terms: Capacity, maximum likelihood decoding (MLD), scaling law, wireless ad hoc network. The seminal work by Gupta and Kumar [2] demonstrated that throughput capacity is bounded by O (1/ √ n) and throughput capacity scaling as 1/(n log n) is achievable when the number of nodes n increases. Later this gap is closed by Franceschetti et al. [3] by utilizing the percolation theory. Zheng et al. [4] proved that the throughput capacity under physical model can be increased by a factor of Θ (log n) α−2 2α compared to Gupta and Kumar's result when nodes are equipped with multipacket reception and a successive interference cancellation decoding scheme. Zheng [5] studied the behaviour of information dissemination in power-constrained wireless networks in terms of the broadcast capacity and information diffusion rate in both random extended and dense networks. Keshavarz et al. [6] extended Zheng's work by considering the interference effect in general wireless networks and proposed the most general case for broadcast capacity results with multihop routing under the protocol model. In [7] , they extended the broadcast capacity for the physical model and the generalized physical model based on Shannon's formula [8] . Li et al. [9] unified the capacity of wireless ad hoc networks utiliz-ing unicast, multicast, and broadcast routing schemes. Recent work [1] has shown that all forms of information dissemination in wireless ad hoc networks can be unified into a single (n, m, k)-cast model. (n, m, k)-cast is a general communication model where n is the number of nodes in the network, m is the number of destinations, and k (k ≤ m) is the actual number of the closest destinations that receive packets from source in each (n, m, k)-cast group. The (n, m, k)-cast communication was investigated under protocol model in [1] . Recent work [10] demonstrated that the throughput capacity can be improved by utilizing multipacket reception (MPR) at the receiver. However, all the results from prior work [1] , [10] concentrated on the protocol model. This paper presents the throughput capacity of (n, m, k)-cast under the physical model when both single packet reception (SPR) and multipacket reception (MPR) schemes are considered.. As the first contribution of this paper, we study the throughput capacity of (n, m, k)-cast under the physical model when nodes are communicating based on point-to-point communication. As our second contribution, we propose the optimum decoding scheme at the receiver node and compute (n, m, k)-cast throughput capacity both under the proposed optimum decoding and successive interference cancellation schemes. The result corresponds to the throughput capacity result in [10] based on the protocol model with MPR which implies that protocol model is equivalent to physical model under the optimal maximum likelihood decoding (MLD) constraint. We presented the throughput capacity of (n, m, k)-casting model when nodes are communicating based on point to point packet transmission. A new upper bound of O ( √ m/ √ nk) and similar lower bound results to [1] were derived. The lower bound capacity consists of three different regions with values of Ω( √ m/k √ n log n), Ω(1/k log n), and Ω(1/n) when m = O(n/ log n), Ω(k) = (n/ log n) = O(m), and Ω(n/ log n) = k, respectively. It is worth investigating as future work, if the gap in the physical model for (n, m, k)-cast can be closed using percolation theory. The achievable throughput capacity assuming MPR scheme is also provided for (n, m, k)-casting. Based on MLD, we proved that in case of D(n) = R(n), the protocol and physical models actually render the same achievable throughput capacity. On the other hand, the suboptimum SIC decoding reduces the capacity under the physical model by a factor of T (n). As a future work, we investigate the upper bound of the throughput capacity for both MLD and SIC.

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


Dynamic, unbalanced distribution of tasks on a PS3 cluster system for double precision calculation The article aims to describe an algorithm for dynamic distribution of tasks in a parallel computing system consisting of a network of 9 PlayStation3 (PS3) stations. Due to the fact that the SPU cores do not have units of double precision calculation, these calculations require a longer time. Therefore, an unbalanced distribution of computing tasks on a heterogeneous cluster system as 9 × PS3 is necessary. The algorithm produces an estimation of the value of π by calculating the integral π = 1 0 4 1+x 2 and makes PPU-SPU empirical distribution of tasks on a smaller number of intervals. After determining the optimum loading between cores 18 × PPU (PowerPC Unit) and 54 × SPU (Synergetic Processor Unit), the integral calculation algorithm goes to a larger number of intervals. By introducing the SPU units in calculating the value of π and using an unbalanced loading distribution between PPU-SPU units, we obtain the following values of cal- (Fig. 12) . The follows conclusions are derived from analysis of the two graphs: -The introduction of the SPU units into the calculation of (DP-Double Precision) improves calculation time by about 50 % but is well below of SPU units potential if they had a unit DP. -Also, we get a lower error in calculating of the π value.. -To obtain maximum efficiency of computing time, you must use an unbalanced distribution formula calculations between SPU and PPU units. -Distribution coefficient k takes different values depending on the number and complexity of the calculations. -Preferably use SPU units in double precision calculations, but reserve their use to a lower level.. This algorithm can be used to increase the speed of double precision calculation in scientific computing.

O B I 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 B I 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 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 B I O O O O


Pseudo-Codeword Analysis of Tanner Graphs From Projective and Euclidean Planes Abstract-We consider coded data transmission over a binary-input output-symmetric memoryless channel using a binary linear code. In order to understand the performance of maximum-likelihood (ML) decoding, one studies the codewords, in particular the minimal codewords, and their Hamming weights. In the context of linear programming (LP) decoding, one's attention needs to be shifted to the pseudo-codewords, in particular, to the minimal pseudo-codewords and their pseudo-weights. In this paper, we investigate some families of codes that have good properties under LP decoding, namely certain families of low-density parity-check (LDPC) codes that are derived from projective and Euclidean planes: we study the structure of their minimal pseudo-codewords and give lower bounds on their pseudo-weight. Besides this main focus, we also present some results that hold for pseudo-codewords and minimal pseudo-codewords of any Tanner graph, and we highlight how the importance of minimal pseudo-codewords under LP decoding varies depending on which binary-input output-symmetric memoryless channel is used. We have investigated the minimal pseudo-codewords of some codes whose Tanner graphs are derived from projective and Euclidean planes and we have introduced the notion of pseudoweight spectrum gap for a parity-check matrix, a concept which is certainly worthwhile to be further explored. Although our numerical results are for codes of modest length, to the best of our knowledge, this is the first study that tries to analytically quantify the behavior of -and -based binary linear codes under LP decoding. Extending these results to somewhat longer codes has the potential to explain many experimental observations made in the past. Moreover, we have obtained a clearer picture on the structure of the minimal pseudo-codewords of the Tanner graphs under investigation, nevertheless, more work is required to get a sufficiently tight characterization of them. Throughout the text, we have also listed some conjectures and statements of open problems; we hope that they stimulate some research toward a better understanding of minimal pseudo-codewords, be it for codes from the code families that we have considered or any other codes. Let us remark that Chertkov and Stepanov [44] have recently proposed a heuristic algorithm for enumerating minimal pseudo-codewords. In their paper, they show some interesting (approximate) spectra of other families of codes than the ones presented here.. In order to classify which minimal pseudo-codewords can be the solution of LP decoding and which ones cannot, we have introduced the notion of the effectiveness of a minimal pseudocodeword. In the case of the AWGNC, all minimal pseudo-codewords are effective (of the first kind and the second kind); however, we have seen that in the case of non-AWGNC channels there are minimal pseudo-codewords that are not effective, i.e., not effective of the first kind or not even effective of the second kind. Interestingly, for deriving that result, we were able to use the canonical completion, a tool that so far has been very useful for characterizing families of -regular LDPC codes, with , bounded when the block length goes to infinity, i.e., code families where the Tanner graph diameter grows with the block length. (This is in contrast to the -based Tanner graphs which have girth and diameter , independently of ).

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


An analysis of the performance of a high-order stabilised finite element method for simulating compressible flows Stabilised finite element methods are now well established and are used in both industrial and commercial flow solvers. However, these methods have traditionally been restricted to linear approximations in space and they are rarely implemented within a high-order context. In the present work, the numerical performance of a higher-order approach is investigated for the simulation of some inviscid and laminar viscous two dimensional subsonic and transonic flows. The results produced clearly demonstrate the benefits that the higher-order approach has to offer, in terms of a reduction in both the degrees of freedom and, more importantly, the CPU time required, when compared with a low-order finite element or finite volume method. Second order finite volume methods remain the predominant numerical technique employed in industrial aerodynamic flow computations. However, the necessity of simulating high Reynolds number flows over complex configurations presents a major challenge for such methods, as a large number of degrees of freedom is generally required to obtain sufficiently accurate results.. During the last decade, there has been a great interest in developing efficient high-order methods for computational fluid dynamics. An example is the EU supported ADIGMA project [1] , which was aimed at developing innovative adaptive high-order methods for the next generation of industrial aerodynamic flow solvers. The results of this project indicated that highorder methods are able to reduce drastically the required number of degrees of freedom but, normally, at the price of increasing the computational cost. It is worth noting that a large part of the research undertaken in ADIGMA was focused on high-order discontinuous Galerkin methods [2] and it was concluded that further research development was required before this approach could be employed as the basis for an industrial code [3] .. Stabilised finite element methods, such as the streamline upwind/PetrovGalerkin (SUPG) method [4] or the Galerkin/least-squares (GLS) method [5] , are well established and already employed in certain industrial and commercial codes [6, 7] . However, stabilised finite element methods have, traditionally, been employed with linear elements [8] . A comparison of low and higher order stabilised finite elements for the incompressible Navier-Stokes equations is presented in [9] , where it is shown that cubic elements are between six and seven times more efficient than linear elements. The combination of high-order approximations and stabilised methods for the compressible Navier-Stokes equations is considered in [10] . In a variety of test cases, the authors show the advantages that higher order approximations bring, in terms efficiency, for obtaining a given accuracy. In fact, it is worth remarking that this work showed the potential advantages of a high-order stabilised finite element solver with respect to high-order DG solvers in the context of the ADIGMA project.. In the present work, the SUPG formulation is considered and it is employed with continuous linear, quadratic or cubic polynomial approximations in space and a discontinuous approximation in time. The performance of the resulting space-time stabilised finite element formulation is studied for two dimensional steady inviscid and laminar viscous flow simulations. Linear and higher-order approximations are compared, in terms of the convergence behaviour of aerodynamic quantities of practical interest, such as lift and drag coefficients. The comparisons concentrate upon the number of degrees of freedom employed and the CPU time required. The results produced are encouraging and show that higher-order finite element approximations are competitive, not only with respect to linear (second order accurate) finite element approximations, but also with respect to second order finite volume methods.. The remainder of the paper is organised as follows. Section 2 details the Euler and Navier-Stokes equations governing the flow of a compressible fluid. Sections 3 and 4 briefly summarise the space-time SUPG formulation and its numerical implementation. In Section 5, a number of two dimensional inviscid and low Reynolds viscous subsonic and transonic flows are considered in order to analyse the performance of the method. Finally, Section 6 presents the main conclusions of the work that has been presented. The application of the stabilised SUPG formulation, combined with higherorder polynomial approximations in space and discontinuous approximations in time, has been considered. The resulting method is high-order accurate 28 Preprint of R. Sevilla, O. Hassan and K. Morgan An analysis of the performance of a high-order stabilised finite element method for simulating compressible flows Computer Methods in Applied Mechanics and Engineering. 253 (1); [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] 2013 in space and provides an implicit unconditionally stable time marching algorithm.. Optimal convergence of the higher-order SUPG formulation has been illustrated in the case of a simple subsonic inviscid flow example. More complex two dimensional examples, involving inviscid and viscous subsonic and transonic compressible flows, have been employed to compare and discuss the performance of the linear and higher-order approximations. The relative performance of the linear and higher-order approaches has been compared in terms of the number of degrees of freedom and the CPU time required to converge lift and drag coefficients. The performance of the SUPG formulation has also been compared to that of a standard second order finite volume solution algorithm.. The presented results show the advantages of higher-order approximations in this context. They are able not only to reduce drastically the necessary number of degrees of freedom but, more importantly, to reduce the CPU time required to reach the desired accuracy. The possibilities offered by the higher-order stabilised finite element approach for industrial applications have been demonstrated by the results of the comparison with the performance of the second order finite volume method.

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


Development of maraviroc, a CCR5 antagonist for treatment of HIV, using a novel tropism assay Assays to identify infectious organisms are critical for diagnosis and enabling the development of therapeutic agents. The demonstration that individuals with a 32-bp deletion within the CCR5 locus were resistant to human immunodeficiency virus (HIV) infection, while those heterozygous for the mutation progressed more slowly, led to the discovery of maraviroc (MVC), a CCR5 antagonist. As MVC is only active against CCR5-tropic strains of HIV, it was critical to develop a diagnostic assay to identify appropriate patients. Trofile TM , a novel phenotypic tropism assay, was used to identify patients with CCR5-tropic virus for the MVC development program. Results of these clinical studies demonstrated that the assay correctly identified patients likely to respond to MVC. Over time, the performance characteristics of the phenotypic assay were enhanced, necessitating retesting of study samples. Genotypic tropism tests that have the potential to allow for local use and more rapid turnaround times are also being developed. The development and utilization of a diagnostic assay to accurately determine HIV-1 coreceptor tropism was critical to the development of the CCR5 antagonist MVC. On the other hand, the results of the MVC registrational clinical studies demonstrated the utility of the Trofile assay for the selection of patients most likely to benefit from treatment with a CCR5 antagonist, thereby confirming both its clinical positive and negative predictive value. Retrospective evaluation of stored clinical samples from the MVC clinical studies have also been useful in the evaluation of genotypic tropism tests that are cheaper, more convenient to use, and can be utilized closer to the point of clinical care, allowing quicker turnaround times and more rapid clinical decision making. Altogether, scientific advances have led to more sensitive and accessible options for tropism testing, either as phenotypic-or genotypic-based methods, and this provides a good example of the simultaneous development of a new treatment for HIV and an enabling diagnostic assay.

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