Supine and Prone Colon Registration Using Quasi-Conformal Mapping Abstract-In virtual colonoscopy, CT scans are typically acquired with the patient in both supine (facing up) and prone (facing down) positions. The registration of these two scans is desirable so that the user can clarify situations or confirm polyp findings at a location in one scan with the same location in the other, thereby improving polyp detection rates and reducing false positives. However, this supine-prone registration is challenging because of the substantial distortions in the colon shape due to the patient's change in position. We present an efficient algorithm and framework for performing this registration through the use of conformal geometry to guarantee that the registration is a diffeomorphism (a one-to-one and onto mapping). The taeniae coli and colon flexures are automatically extracted for each supine and prone surface, employing the colon geometry. The two colon surfaces are then divided into several segments using the flexures, and each segment is cut along a taenia coli and conformally flattened to the rectangular domain using holomorphic differentials. The mean curvature is color encoded as texture images, from which feature points are automatically detected using graph cut segmentation, mathematic morphological operations, and principal component analysis. Corresponding feature points are found between supine and prone and are used to adjust the conformal flattening to be quasi-conformal, such that the features become aligned. We present multiple methods of visualizing our results, including 2D flattened rendering, corresponding 3D endoluminal views, and rendering of distortion measurements. We demonstrate the efficiency and efficacy of our registration method by illustrating matched views on both the 2D flattened colon images and in the 3D volume rendered colon endoluminal view. We analytically evaluate the correctness of the results by measuring the distance between features on the registered colons. Colorectal cancer is the third most incident cancer and the second leading cause of cancer related mortality in the United States [15] . Optical colonoscopy (OC), whereby precancerous polyps can be located and removed, has been recommended for screening and has helped to greatly reduce the mortality rate of colorectal cancer [4] . Virtual colonoscopy (VC) techniques have been developed as viable non-invasive alternatives to OC for screening purposes [12, 19] . For a VC procedure, computed tomography (CT) scans of the abdomen are commonly acquired with the patient in both supine (facing up) and prone (facing down) positions. From these scans, the colon wall can be extracted as in Figure 2 and visualized by the VC user as a volume rendered endoluminal view, mimicing the endoscopic view of an OC. The use of computer-aided detection (CAD) of colonic polyps has also been suggested [14, 38, 39] . A CAD scheme can help to reduce the necessary reading and interpretation time of the user and can act as a second reader to improve detection rates in VC. Though various CAD methods can achieve different accuracies, a common problem among them is the presence of false positives in the results. A reduction of these false positives would help the user to focus on true suspicious areas and not waste time on unimportant regions.. In addition to the general VC and CAD techniques, researchers have worked to find new ways of visualizing the data to aid the user in identifying polyps or assisting with interventional needs. Volumetric curved planar reformation has been used to aid the viewer in locating polyps with a 3D surface superimposed over the standard CT slices [35] . For simulating intestinal surgery, a system has been developed to visualize the colon and provide collision processing [27] . There has also been work in creating a correlation between the VC navigation view and the OC view based upon the different view paths [23] . In this work, we aim to add another visualization tool to the doctor's toolbelt. The main goal of our work is to allow the user to view one location on the colon (whether in a 2D flattened view or a 3D endoluminal view) in one scan, and then jump to and view the identical region in the other scan. We also show how the user can visualize the deformation of the colon surface if such a utility is desired.. Throughout the development of VC, the registration of the supine and prone scans has remained a constant and challenging problem [1, 6, 25] . Being able to register these two scans is useful for both a routine VC system and for a CAD system. In the case of a VC system, providing the user the ability to jump from one area in one scan to the same area in the other scan would allow for the easy comparison of these areas when something might be unclear in one of the scans, or for confirming a finding. For a CAD system, a proper registration could help achieve greater accuracy while at the same time reducing false positive results. We are presently interested in performing supine-prone registration due to the visualization possibilities that it presents, both for viewing corresponding regions of the colon surface as well as for visualizing the elastic deformation of the colon.. In this paper, we present a method of supine-prone registration using conformal colon flattening. Conformal colon flattening has been introduced as an enhancement for VC navigation [13] and has been utilized successfully for CAD [14] . According to conformal geometry theory, there exists an angle preserving map which periodically flattens the colon surface onto a planar rectangle. This mapping minimizes the total stretching energy. Because the conformal mapping is locally shape preserving, it offers an effective way to visualize the entire colon surface and exposes all of the geometric structures hidden in the original shape embedded in 3D.. The characteristics of the deformation between supine and prone is determined by the elasticity properties of the tissues and muscles. The strain-stress relations for different types of tissues or muscles are different. If the strain-stress relation deformation is independent of the orientation, then local deformation is practically a scaling, and the global deformation is conformal. In that case, we can flatten each supine and prone surface to a planar rectangle conformally, and those two rectangles should be similar. By aligning the planar rectangles, we can get a one-to-one and onto mapping, and obtain the registration between them. In this work, we introduce this registration approach and carefully design experiments to test whether the deformation between supine and prone is conformal or not. Our experimental results show that the deformation is not conformal, but close to conformal.. An elastic deformation with bounded angle distortion is called a quasi-conformal map. The angle distortion for a quasi-conformal map can be represented as a complex valued function, the so-called Beltrami coefficient. The Beltrami coefficient fully controls the quasiconformal map, which is determined by the elasticity of the underlying material. By better understanding the deformation between supine and prone, we can understand the elasticity of the tissues and muscles and vice versa.. The non-rigid elastic deformation between supine and prone colons poses a great challenge for shape registration. In this work, we locate and match the anatomical landmarks and internal features on conformally flattened supine and prone surfaces, and compute a harmonic map with these feature constraints in linear computational complexity. The resulting supine-prone registration is a quasi-conformal map (diffeomorphism), which reflects the elastic deformation of the muscle and tissue. The distortion is evaluated by the Beltrami coefficients. Our experiments on 6 pairs of supine-prone colons obtained an average R 3 distance error of 7.85mm for the feature points and polyps evaluated. To the best of our knowledge, this is the first work to apply geometric mapping for supine-prone colon registration by converting the 3D registration problem to a 2D image matching problem. The whole process is efficient and automatic, and our registration method performs better than other existing methods (see Section 6.1). Figure 3 shows our registration pipeline, which primarily consists of five stages. As the input, the supine and prone CT scans are subjected to the pre-processing steps, including cleansing, segmentation with topological simplification, and surface mesh reconstruction, which have been studied previously and are outside the scope of this paper. Given the supine and prone surfaces, anatomical landmarks are extracted (see Section 4.1). Using these landmarks, the colon surfaces of both supine and prone are decomposed to segments. For each segment, a flat rectangular conformal mapping is obtained (see Section 4.2). Based on these flat images, feature points are detected and their correspondences between supine and prone are obtained (see Section 4.3). With the feature correspondence constraints, the supine-prone registration is performed using a harmonic map (see Section 4.4) .. Given the completed supine-prone registration, we present the methods in which we visualize the results of our registration algorithm. We firs demonstrate flattened rendering of the colon in the native 2D registration format (see Section 5.1). For the endoluminal views which would be used by a radiologist reading a case, we detail a method to provide correlated views between supine and prone (see Section 5.2). To better understand where the deformation occurs most on the colon surface, we show the visualization of the Beltrami coefficient both in 2D and 3D (see Section 5.3). The results of our registration are analyzed and discussed in Section 6. We verify the efficacy of our work using both objective analytic and subjective visual methods. We present the related work in the next section and brief background information on conformal mapping and quasi-conformal mapping in Section 3 to familiarize the reader with the terms. Shape registration is very fundamental for shape analysis problems, especially for abnormality detection in medical applications. We introduce an efficient framework for the registration of supine and prone colons, through the use of conformal geometry, to improve the accuracy of polyp detection. We automatically extract the anatomical landmarks, namely the taeniae coli and flexures, for consistent segmentation. We then conformally flatten the colon surfaces to the rectangular domain using holomorphic differentials. The feature points are automatically detected from mean-curvature encoded images using graph cut segmentation, and their correspondence between supine and prone are obtained by graph matching. These feature constraints are used to align the flattened domains by adjusting the conformal mapping to be quasi-conformal through the harmonic map. We demonstrate the efficiency of our method by both analytic evaluation and the 2D and 3D consistent registration views. The Beltrami coefficient is employed to analyze the physical deformation of the colon muscle and tissue. To our best knowledge, this is the first work to use a geometric mapping method for the supine and prone colon surface registration problem.. With the ability to measure and view the elastic distortion between segments of the supine and prone colons, we are seeking further outlets to which this work can be applied. We are looking at applying this registration to our CAD work to achieve better sensitivity and specificity. Additionally, we are looking to extend our work from 2D surface registration to 3D volumetric registration for colon wall segmenations which contain thickness. Early work on supine-prone registration for VC applications focused on using the centerlines and various landmarks. A basic method applies linear stretching and shrinking operations to the centerline, where local extrema are matched and used to drive the deformations [1] . Improved methods of centerline correlation were also investigated for use in reducing false positive results [25] . Correlating individual points along the centerline through the use of dynamic programming has also been suggested [6, 24] .. More recently, the taeniae coli (three bands of smooth muscle along the colon surface) have been used as features which can be correlated between the two scans [16, 17] . This relies on a manual identification of one of the three taeniae coli, and then an automatic algorithm repeats the line representing the identified taenia coli at equal distances. Further progress has been made where the haustral folds and the points between them can be automatically detected, and the taeniae coli are identified by connecting these points [32] . However, this method is only feasible on the ascending and transverse portions of the colon.. Deformation fields have also been suggested for use in supine-prone registration. Motion vectors can be identified for matched centerline regions, interpolated for non-matched regions, and then propagated to the entire volume [28] . It has also been proposed to use a free-form deformation grid to model the possible changes in the colon shape from supine to prone [26] .. Conformal mapping has been successfully used for many medical applications, such as brain cortex surface morphology study [10] and colonic polyp detection [14] . In this work, we perform the supineprone registration through conformal mapping based on holomorphic 1-forms. The colon surface is reconstructed from CT images, represented as a topological cylinder in the discrete form of a triangular mesh, and conformally mapped to a planar rectangle. The computation of the conformal mapping using holomorphic 1-forms has linear complexity. The subsequent registration is carried out through the 2D conformal mapping images of the supine and prone colons.. Discrete holomorphic forms have been introduced to compute global conformal surface parameterizations for general surfaces [11] . Optimal holomorphic 1-forms have been used to reduce area distortion for visualization purposes [18] . Work has been done to generalize 1-forms to parameterize genus one meshes [9] and to incorporate cone singularities [30] . Discrete 1-forms have been applied for meshing point clouds [29] , surface tiling [7] , and quadriangulation [30] . It has also been applied in computer vision for 3D shape matching, recognition, and stitching [33, 37] . The holomorphic 1-form method has been applied for CAD of colonic polyps, where the use of planar conformal mapping improved the efficiency and accuracy in detecting polyps [14] . In terms of surface registration by conformal mapping, the smooth one-to-one maps between closed surfaces of the same topology have been computed [22] . However, that work employed non-linear mapping computation and did not provide a solution to handle open surfaces.. Because the deformation from supine to prone is not conformal, we generalize the conformal colon flattening method to a quasi-conformal flattening for registration purpose. Most existing colon registration methods cannot guarantee the mapping to be a diffeomorphism (oneto-one and onto mapping). Due to the complicated geometric structure of the colon surface, the existing methods often introduce folding or singularities in the mapping. Our method is based on the biophysical nature of the deformation from supine to prone, which is physically elastic and anisotropic. Due to the material properties of the muscles and tissues, the deformation can be exactly modeled as a quasiconformal map. Our experimental results validate that the mapping is indeed quasi-conformal. To the best of our knowledge, this work is the first to use quasi-conformal mapping for supine-prone registration.

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


Nonlinear Fourier analysis for discontinuous conductivities: computational results Two reconstruction methods of Electrical Impedance Tomography (EIT) are numerically compared for nonsmooth conductivities in the plane based on the use of complex geometrical optics (CGO) solutions to D-bar equations involving the global uniqueness proofs for Calder\'on problem exposed in [Nachman; Annals of Mathematics 143, 1996] and [Astala and P\"aiv\"arinta; Annals of Mathematics 163, 2006]: the Astala-P\"aiv\"arinta theory-based"low-pass transport matrix method"implemented in [Astala et al.; Inverse Problems and Imaging 5, 2011] and the"shortcut method"which considers ingredients of both theories. The latter method is formally similar to the Nachman theory-based regularized EIT reconstruction algorithm studied in [Knudsen, Lassas, Mueller and Siltanen; Inverse Problems and Imaging 3, 2009] and several references from there. New numerical results are presented using parallel computation with size parameters larger than ever, leading mainly to two conclusions as follows. First, both methods can approximate piecewise constant conductivities better and better as the cutoff frequency increases, and there seems to be a Gibbs-like phenomenon producing ringing artifacts. Second, the transport matrix method loses accuracy away from a (freely chosen) pivot point located outside of the object to be studied, whereas the shortcut method produces reconstructions with more uniform quality. We study a widely applicable nonlinear Fourier transform in dimension two. We perform numerical tests related to the nonlinear Gibbs phenomenon with much larger cutoff frequencies than before. Furthermore, we compare two computational inverse transformations, called low-pass transport matrix method and shortcut method in terms of accuracy.. The inverse conductivity problem of Calderón [10] is the main source of applications of the nonlinear Fourier transform we consider. Let Ω ⊂ R 2 be the unit disc and let σ : Ω → (0, ∞) be an essentially bounded measurable function satisfying σ(x) ≥ c > 0 for almost every x ∈ Ω. Let u ∈ H 1 (Ω) be the unique solution to the following elliptic Dirichlet problem:. ∇ · σ∇u = 0 in Ω, (1.1). The inverse conductivity problem consists on recovering σ from the Dirichlet-toNeumann (DN) map or voltage-to-current map defined by. Here ν is the unit outer normal to the boundary. Note that the map Λ : σ → Λ σ is nonlinear. The inverse conductivity problem is related to many practical applications, including the medical imaging technique called electrical impedance tomography (EIT). There one attaches electrodes to the skin of a patient, feeds electric currents into the body and measures the resulting voltages at the electrodes. Repeating the measurement with several current patterns yields a current-to-voltage data matrix that can be used to compute an approximation Λ δ σ to Λ σ . Since different organs and tissues have different conductivities, recovering σ computationally from Λ δ σ amounts to creating an image of the inner structure of the patient. See [41, 12] for more information on EIT and its applications.. Recovering σ from Λ δ σ is a nonlinear and ill-posed inverse problem, whose computational solution requires regularization. Several categories of solution methods have been suggested and tested in the literature; in this work we focus on so-called D-bar methods based on complex geometrical optics (CGO) solutions. There are three main flavors of D-bar methods for EIT:. • Schrödinger equation approach for twice differentiable σ. Introduced by Nachman in 1996 [43] , implemented numerically in [45, 40, 31, 30, 34, 41] .. • First-order system approach for once differentiable σ. Introduced by Brown and Uhlmann in 1997 [7] , implemented numerically in [32, 36, 19] .. • Beltrami equation approach assuming no smoothness (σ ∈ L ∞ (Ω)). Introduced by Astala and Päivärinta in 2006 [6] , implemented numerically in [5, 4, 3, 41] . The assumption σ ∈ L ∞ (Ω) was the one originally used by Calderón in [10] .. Using these approaches, a number of conditional stability results have been studied for the Calderón problem. The most recent results in the plane were obtained by Clop, Faraco and Ruiz in [13] , where stability in L 2 -norm was proven for conductivities on Lipschitz domains in the fractional Sobolev spaces W α,p with α > 0, 1 < p < ∞, and in [15] , where the Lipschitz condition on the boundary of the domain was removed. In dimension d ≥ 3, conditional stability in Hölder norm for just C 1+ε conductivities on bounded Lipschitz domains was proved by Caro, García and the third author in [11] using the method presented in [18] .. The three aforementioned D-bar methods for EIT in the two-dimensional case are based on the use of nonlinear Fourier transforms specially adapted to the inverse conductivity problem. Schematically, the idea looks like this:. T r a n s f o r m¨¨¨¨¨¨¨B. The main point above is that the nonlinear Fourier transform can be calculated from the infinite-precision data Λ σ , typically via solving a second-kind Fredholm boundary integral equation for the traces of the CGO solutions on ∂Ω.. In practice one is not given the infinite-precision data Λ σ , but rather the noisy and finite-dimensional approximation Λ δ σ . Typically all we know about Λ δ σ is that Λ σ − Λ δ σ Y < δ for some (known) noise level δ > 0 measured in an appropriate norm · Y . Most CGO-based EIT methods need to be regularized by a truncation |k| < R in the nonlinear frequency-domain as illustrated in Figure 1 .. The regularization step results in a smooth reconstruction. This smoothing property of the nonlinear low-pass filter resembles qualitatively the effect of linear low-pass filtering of images. In particular, the smaller R is, the blurrier the reconstruction becomes.. The cut-off frequency R is determined by the noise amplitude δ, and typically R cannot exceed 7 in practical situations. However, it is interesting to understand how the conductivity is represented by its nonlinear Fourier transform. To study this numerically, we compute nonlinear Fourier transforms in large discs such as . Figure 1: Schematic illustration of the nonlinear low-pass filtering approach to regularized EIT. This image corresponds to the so-called shortcut method defined below. The simulated heart-and-lungs phantom σ(z) (bottom left) gives rise to a finite voltage-to-current matrix Λ δ σ (orange square), which can be used to determine the nonlinear Fourier transform. Measurement noise causes numerical instabilities in the transform (irregular white patches), leading to a bad reconstruction (a). However, multiplying the transform by the characteristic function of the disc |k| < 4 yields a lowpass-filtered transform, which in turn gives a noise-robust approximate reconstruction (b).. |k| < 60 and compute low-pass filtered reconstructions using inverse nonlinear Fourier transform and observe the results.. We compare two reconstruction methods based on the use of the CGO solutions (2.1): the low-pass transport matrix method implemented in [3] , and a shortcut method based on solving a D-bar equation. The latter method does not have rigorous analysis available yet, but it is formally similar to the regularized EIT reconstruction algorithm studied in [43, 45, 40, 31, 30, 33, 34] .. Our new computational findings can be roughly summarized by the following two points. First, both methods can approximate piecewise constant conductivities better and better as the cutoff frequency R increases, and there seems to be a Gibbs-like phenomenon producing ringing artifacts. Second, the transport matrix method loses accuracy away from a (freely chosen) pivot point located R = 20 R = 40 R = 50 True Figure 2 : Convergence of nonlinearly low-pass filtered conductivity to the true discontinuous conductivity. Note the ringing artefacts reminiscent of the Gibbs effect of linear low-pass filtering. This picture illustrates the so-called shortcut method, and it is the first-ever computation of this kind with cutoff frequencies larger than 20.. outside of Ω, whereas the shortcut method produces reconstructions with more uniform quality. Figure 2 shows some of our numerical results via the shortcut method for a nonsymmetric conductivity distribution.. The rotationally symmetric examples presented in Section 4.1 provide numerical evidence of the fact that discontinuous conductivities can be reconstructed with the shortcut method more and more accurately when R tends to infinity.. In the computational experiments we show in this paper, the truncated scattering transform is computed with a very large cutoff frequency through the Beltrami equation solver. In practice, it is not possible to obtain such scattering data from boundary measurements unless we had unrealistically high-precision EIT measurements available.. Notwithstanding the aforesaid, our new results are relevant for applications at least in these two ways:. (1) We provide strong new evidence suggesting that the shortcut method can recover organ boundaries at the low-noise limit. Even with practical noise levels we can recover low-pass filtered jumps in the cases of nested inclusions or checkerboard-type discontinuity curves. While there are many dedicated methods for inclusion detection in EIT, for example [16, 9, 28, 8, 29, 25, 27, 39, 21, 17, 46, 22, 26, 23] , none of them can locate nested inclusions. (2) The nonlinear Fourier transform studied here can be used to solve the nonlinear Noviko-Veselov (NV) equation. It is a nonlinear evolution equation generalizing the celebrated Korteweg-de Vries (KdV) equation into dimension (2+1). There has been significant recent progress in linearizing the NV equation using inverse scattering methods, see [38, 37, 44, 42, 14] . In the potential applications of the NV equation there should be no restriction to as low frequencies as in EIT. We remark that all our numerical experiments have been computed using either a 192 Gigabyte computer with Linux or parallel computation provided by Techila. 1 Regarding the radially symmetric examples studied in Section 4.1, the conclusion is clear: numerical evidence suggests that discontinuous conductivities can be reconstructed with the shortcut method more and more accurately when R tends to infinity.. The errors in the reconstructions are very similar to the Gibbs phenomenon observed with truncated linear Fourier transforms.. The numerical study of the nonsymmetric examples comparing both reconstruction types leads us to two observations: -For these discontinuous conductivity examples, the shortcut method generates considerably better reconstructions than the transport matrix method.. -The approximate solution computed by the transport matrix method is reliable on an area within the unit disc close enough to the selected z 0 point outside the unit disc.. Finally, since errors (4.4) are small and plots for both functions f µ (z, k 0 ), f µ (z, k 0 ) are similar in view of Figure 14 , we have numerical evidence supporting the fact that the transport matrix method "transports well" and the worse results by the transport matrix method are explained by the final algebraic steps, including numerical differentiation in (3.12), just after the computation of the solutions u In Figure 15 the profiles of E p (r) for p = 0.1%, 0.5%, 1%, 5% are shown in black, blue, green and red colour, respectively. The maximum value shown on the vertical axis is 1. Accuracy of the DN map to compute t(k) on D(0, 50) How many correct significant digits would one need in the DN map for computing the scattering transform t(k) for |k| < 50? It is well-known [1] that there is a logarithmic relation between measurement accuracy and details in conductivity. In other words, EIT is an exponentially ill-posed inverse problem. In terms of scattering transforms, a fixed noise level p% in the EIT measurement leads to, roughly speaking, the computation of t(k) to be stable and accurate in a disc |k| < R(p) and unstable outside that disc. See [34, Figure 2 ]. The exponential ill-posedness shows up as a logarithmic dependence of R on p, see [34, Figure 3 ]. Improving the measurement accuracy so that the DN matrix entries have one more significant digit increases the stability radius from R to R + Γ with Γ > 0 a fixed real number.. Let us make a crude quantitative estimation based on [34, Figure 3 ]. Two significant digits in the DN map corresponds to R = 3 and six significant digits to R = 7. A quick computation shows that achieving the stability radius R = 50 would require 49 correct significant digits in the elements of the DN matrix (and, actually, using a larger matrix with more oscillatory basis functions involved as well).

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 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 B I I 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 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 B I I 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 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 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 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 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 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 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 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 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 identification of heart failure diagnostic criteria, using text analysis of clinical notes from electronic health records Objective: Early detection of Heart Failure (HF) could mitigate the enormous individual and societal burden from this disease. Clinical detection is based, in part, on recognition of the multiple signs and symptoms comprising the Framingham HF diagnostic criteria that are typically documented, but not necessarily synthesized, by primary care physicians well before more specific diagnostic studies are done. We developed a natural language processing (NLP) procedure to identify Framingham HF signs and symptoms among primary care patients, using electronic health record (EHR) clinical notes, as a prelude to pattern analysis and clinical decision support for early detection of HF.Design: We developed a hybrid NLP pipeline that performs two levels of analysis: (1) At the criteria mention level, a rule-based NLP system is constructed to annotate all affirmative and negative mentions of Framingham criteria. (2) At the encounter level, we construct a system to label encounters according to whether any Framingham criterion is asserted, denied, or unknown.Measurements: Precision, recall, and F-score are used as performance metrics for criteria mention extraction and for encounter labeling.Results: Our criteria mention extractions achieve a precision of 0.925, a recall of 0.896, and an F-score of 0.910. Encounter labeling achieves an F-score of 0.932.Our system accurately identifies and labels affirmations and denials of Framingham diagnostic criteria in primary care clinical notes and may help in the attempt to improve the early detection of HF. With adaptation and tooling, our development methodology can be repeated in new problem settings.2 The Framingham criteria extractors are effective at finding criteria mentions with high precision and recall. Furthermore, those criteria can serve as the basis for accurately labeling clinical notes with respect to the criteria that they document, a prerequisite for downstream clinical applications of EHRs. Iterative annotation refinement is an effective tool for creating criteria extraction systems for applications where there is no preexisting dataset of suitably annotated text. Evaluation results reveal a few general error types, involving data quality, human anatomy, and syntactic complexity.. One manifestation of the data quality issue was that 26 of the 237 errors encountered in the final evaluation run -over 10% -were due to spelling errors. These include simple typographical errors, as in Figure 2 . Further errors occurred when text was dumped from the EHR system and reassembled in the PredMED analysis environment, a process that introduced sentence boundary errors that misled the extractors' algorithms. elsewhere is often impossible, because of institutional and EHR system differences and HIPAA constraints, and (3) creating such a dataset locally often taxes the skill and resources of the institution. In such a situation, IAR has the following advantages:. • The error analysis step provides for excellent communication between the expert and the computational linguist who develops the extractor. This is much broader bandwidth communication than separately written annotation guidelines would provide.. • The process produces a (rule-based) extractor that is consistent with the annotation guidelines.. • The extractor can be used for pre-annotation to assist coders in creating higherquality reference standards, by improving their recall.. • The resulting annotations may be used to train machine-learning systems, if desired.. One use case for our development approach is in the creation of criteria extraction systems for medical criteria beyond the Framingham HF set. The NYHA [39] and the ESC [40] , as well as the MedicalCriteria.com website [41] , present hundreds of sets of medical criteria, many of which could be addressed with systems like PredMED and would benefit from IAR. Furthermore, many specific criteria reappear in multiple criteria sets, pointing to further opportunities for re-use. With appropriate tooling for reusing extractors, for managing expert annotations, and for IAR error analysis, our approach can be an attractive alternative to current development methods. Our development and evaluation process comprised the following steps:. • A cardiologist and a linguist analyzed a development dataset of 65 encounter documents rich in Framingham criteria, to learn the linguistics of criteria mentions.. • The linguist used the NLP tools to build initial extractors for assertions and denials of Framingham criteria (this section).. • The clinical expert and linguist incrementally measured and improved the performance of the extractors on the development documents (the Iterative Annotation Refinement section).. • The clinical expert used annotation guidelines he developed to train coders, who manually created gold standard annotations on an evaluation dataset of 400 randomly selected encounter documents (the Evaluation Setup section).. • The linguist used the gold standard to measure the performance of the final extractors on two tasks, criteria extraction and encounter labeling (the Results section).. Text analysis involved the following tasks: In addition to FramSymptomVocab, there are dictionaries for:. (1) negating words and counterfactual triggers, such as denies and if.. (2) segment header words.. (3) weight loss phrases, time value words, weight unit words, and diuretic words, used in the WeightLoss criterion extractor.

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Two-phase porous media flows with dynamic capillary effects and hysteresis: Uniqueness of weak solutions In this paper, we obtain the uniqueness of weak solutions for a two phase flow model in a porous medium. A particularity of the model is that the dynamic effects and hysteresis are included in the capillary pressure. We consider a mathematical model for two-phase flow in a porous medium. Two immiscible fluid phases are flowing through a porous medium occupying a bounded, connected domain Ω ⊂ R d (d = 1, 2, 3). UsingΩ and ∂Ω denote the closure and boundary of Ω. Let T > 0 be a given time. The phase pressures are denoted by p w , p n . The non-wetting phase saturation is s. We assume the porous medium is saturated by the two phases. Then from the Darcy law and mass conservation for each fluid give the system (see [1, 16] ) ∂ t s − ∇ · (k n (s)∇p n ) − ∇ · (k n (s) − → g ) = 0,. Here − → g ∈ R d is the gravity vector in direction − − → e d = (0, ..., 0, −1) ∈ R d . k n (s), k w (s) are the permeabilities -two nonlinear functions depending on s. The system is closed by the relation between the phase pressures and saturation. Standardly, equilibrium models assume p w − p n = p c (s), p c -decreasing with respect to s (see [12] ). While experiments [3, 7, 17] have proved the limitation of this approach. Alternatively, models involving non-equilibrium effects are proposed in [2] :. Here γ ≥ 0, τ > 0 are given and sign denotes the multi-valued function. The second term on the right in (3) models a play-type hysteresis (see [2, 18] ), while the last one accounts for dynamic effects in the phase pressure difference (see [15] ). Following [11] , for τ > 0, the multi-valued function Φ : ξ −→ τ ξ + γsign(ξ) can be inverted. Its inverse Ψ : Φ −1 : R → R is a Lipschitz continuous function satisfying. With this notation, (3) transforms into. The model (1), (2), (6) is complemented by initial and boundary conditions. p n = p w = 0 at ∂Ω, for all t ≥ 0.. Remark 1.1: Other boundary conditions are possible, but for clarity, we restrict the presentation to (8) .. The following assumptions are made:. • A1: The functions k w , k n : R → R are Lipschitz continuous. Further, δ, M k > 0 exist such that δ ≤ k w (s), k n (s) ≤ M k < ∞, for all s ∈ R.. • A2: p c (·) ∈ C 1 (R) is increasing and Lipschitz continuous, there exist m p , M p > 0 such that m p ≤ p c (s) ≤ M p , for all s ∈ R.. • A3: Ω is a C 1,α (0 < α ≤ 1) domain.. • A4: γ(x) ∈ C 0,1 (Ω).. • A5: s 0 ∈ C 0,α (Ω). Then A1 is not satisfied when s approaches to 0 or 1. We consider here a regularized approximation of these functions. In this paper, we have proved the uniqueness of weak solutions to a non-degenerate system which models two-phase flow in porous media including hysteresis and dynamic effects in the capillary pressure. In doing so, we use arguments based on Green's function.

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Vector-valued image regularization with PDEs: a common framework for different applications Abstract-In this paper, we focus on techniques for vector-valued image regularization, based on variational methods and PDEs. Starting from the study of PDE-based formalisms previously proposed in the literature for the regularization of scalar and vector-valued data, we propose a unifying expression that gathers the majority of these previous frameworks into a single generic anisotropic diffusion equation. On one hand, the resulting expression provides a simple interpretation of the regularization process in terms of local filtering with spatially adaptive Gaussian kernels. On the other hand, it naturally disassembles any regularization scheme into the smoothing process itself and the underlying geometry that drives the smoothing. Thus, we can easily specialize our generic expression into different regularization PDEs that fulfill desired smoothing behaviors, depending on the considered application: image restoration, inpainting, magnification, flow visualization, etc. Specific numerical schemes are also proposed, allowing us to implement our regularization framework with accuracy by taking the local filtering properties of the proposed equations into account. Finally, we illustrate the wide range of applications handled by our selected anisotropic diffusion equations with application results on color images.

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Getting virtual 3D landscapes out of the lab Increasingly realistic virtual three dimensional (3D) models have been created that demonstrate a variety of landscape designs. They have supported a more collaborative and participative approach in planning and design. However, these 3D landscape models are often developed for use in bespoke virtual reality labs that tie the models to expensive graphics hardware, or complex arrays of screens, with the viewer spatially detached from the actual site. Given the increase in prevalence of advanced "smartphone" and tablet technology with GPS and compass functionality, this paper demonstrates two methods for on-demand dissemination of existing virtual 3D landscape models using: (1) a touch based interface with integrated mapping; (2) a standard web browser interface on mobile phones. The latter method demonstrates the potential to reduce the complexity of accessing an existing 3D landscape model on-site to simply pointing a smartphone in a particular direction, loading a web page and seeing the relevant view of the model as an image. A prototype system was developed to demonstrate both methods successfully, but it was also ascertained that the accuracy of GPS positional data can have a negative effect on the browser based method. Finally, potential developments are presented exploring the future of the technology underpinning the method and possible extensions to the prototype as a technique for increasing public participation in planning and design. Public participation is an approach for making the landscape planning and design process more inclusive. In recent decades, this approach has been adopted into government policy, for instance as articulated in the European Landscape Convention (Lange & Hehl-Lange, 2011) , or in the UK Localism Act (Localism Act, 2011) , which aims to devolve decision making powers to a local level, e.g. to neighbourhood planning groups. However, one of the major tasks for public participation in landscape planning and design is the dissemination of the information to the population. Typically, in the Western world, planning departments hold the records pertaining to landscape proposals and distribute this information through formal planning meetings, public displays, or by sending documentation directly to the public. Widely adopted digital connectivity via the Internet has aided this dispersal by providing online access to planning documents through local governmental planning portals. Nevertheless, WarrenKretzschmar and von Haaren argue that when planners attempt to engage with the public, there can be a disconnection between perceived and actual participation of the public, although this can potentially be overcome through the use of visualisations (Warren-Kretzschmar & Von Haaren, 2014) . In comparison to the written or spoken word, visualisations have lower barriers in terms of communicating contents thus helping to improve citizens' understanding and ability to respond towards planning issues.. Landscape visualisations are a means to graphically represent the landscape. There is a long tradition of analogue techniques including physical models, sketches and so on. In recent decades, digital representations of landscapes have become more commonplace in the communication of possible future landscape designs, with the digital photomontage (Lange, 1990) widely employed. In addition, interactive 3D landscape visualisation technologies are increasingly being used by planners and landscape designers. In 1995, Danahy and Hoinkes demonstrated interactive landscape visualisations using their POLYTRIM software running on then state of the art graphical computer hardware (Danahy & Hoinkes, 1995) . Since then, digital landscape visualisations have been used to represent a variety of differing future scenarios from large scale environments (Perrin, Beauvais, & Puppo, 2001) down to highly detailed site design (Morgan, Gill, Lange, & Romano, 2009) . Research surrounding interactive landscape models has tended to concentrate on techniques to improve photo-realism (House, Schmidt, Arvin, & Kitagawa-DeLeon, 1998) , user immersion (Bishop & Dave, 2001 ) and model complexity without degrading rendering speed (Deussen, 2003) . This has led to successful solutions for immersive Virtual Reality (VR) laboratories, but ones that require complex bespoke computer hardware, such as the 13 workstations and 13 projector configurations described by Zehner (Zehner, 2009) . The advent of laptops with powerful graphical resources and portable projectors has meant that it is possible to move interactive 3D landscape models to multiple locations. For example, a model originally created for use in a VR lab was also used as an interactive learning tool at a natural history museum using a laptop (Morgan, Gill, Lange, & Dallimer, 2012) . Internet based dissemination of interactive landscape models has also been undertaken (Shojaei, Rajabifard, Kalantari, Bishop, & Aien, 2014) , but this tends to require a reasonable level of computing hardware at the client side to render the downloaded models together with the ability to navigate the model using the supplied user interface.. Thus, although there are now the tools to construct and render detailed landscape models, their intrinsic information is often locked in VR laboratories (Zehner, 2009) , or may contain a barrier to use through requisite hardware and the need to learn a user interface (Paar, 2006) . All of which can also make it difficult to integrate with existing online planning portals and none of these methods make it simple for the public to interrogate existing models quickly on-site. On-site access of landscape visualisations would allow the public to contrast the future vision of landscape designers with the reality on the ground and it may also help engage with more people who actively pass through a site.. In 2001, Rakkolainen and Vainio examined the usefulness of 2D maps and 3D models in a mobile environment as an aid for navigation of an unknown urban environment. The results from their trial showed both 2D maps and 3D elements were interchangeably consulted by participants (Rakkolainen & Vainio, 2001) . They were hampered however by the lack of computation resource in the handsets available to them, but predicted the arrival of more computationally powerful devices.. Nowadays, new opportunities arise for transmission of landscape visualisations with the advent of 'smartphone' and 'tablet' technologies that can derive their location, have high resolution screens, internet connectivity and enough computing power available to render graphical images (Evans-Cowley, 2012) . These devices are becoming increasingly commonplace and offer an opportunity to present landscape visualisation to the public in an easily accessible manner. This has been demonstrated with 'apps' that can overlay information on video feeds, presenting Augmented Reality (AR), e.g. Layar (Layar, 2009 ). However, these can suffer from occlusion issues or poor video quality (Takacs et al., 2008) . Alternatively, apps are available that can present pre-prepared visualisations of future scenarios whilst on-site (Lange, 2011 , Bilge, Hehl-Lange, & Lange, 2014 , Priestnall, 2009 ). These methods can provide either the visual fidelity of VR lab based models or the interactivity of viewpoint, but not both.. Therefore, the aim of the work presented in this paper is to illustrate a method that disseminates highly detailed and interactive 3D visualisations of landscape and urban design proposals via smartphones and tablets on site. Such an approach could be highly advantageous to planners and designers (Graham-Rowe, 2011) , both in potentially reducing costs of delivery and increasing inclusiveness in decision making.. In Section 2, a theoretical discussion is presented that explains how the new method relates to existing visualisation techniques. Section 3 details the implementation of several different prototypes that provide on-site visualisations by re-using existing virtual 3D landscape models. Section 4 highlights the results of using the prototype system out at a location. Finally, future work, discussion and conclusions are presented. The prototype as currently implemented would not provide a highly scalable solution for high demand scenarios as it relies on the Simmetry3d API to move the viewer to a particular position and then render that view, so requests for visualisation by multiple clients would be queued as the server processed each request one at a time. However, this could be overcome in the future with a multithreaded rendering solution.. There are a number of possibilities for extending the prototypes presented. The integration of social networks and online planning portals to the web site interface on the smartphone provides the possibility of allowing users to give their feedback on landscape proposals instantaneously. Recording locations in the proposal when people request views may provide insight into areas of concern or popularity. This data would end up being able to produce tracking maps that could be overlaid on the 3D model to give designers and planners an insight into popular, or potentially controversial areas or aspects of a design, especially in conjunction with an analysis of comments and feedback on social networks. Although graphics hardware on mobile devices continues to improve, it is likely the geometric complexity of 3D landscape models will continue to remain beyond the capacity of mobile devices to render interactively. In addition, the rollout of 4G connectivity and other future technologies will reduce the time taken in delivering on-demand streamed visualisations. Therefore, to further enhance the interactivity of feedback to the user it may be possible to consider a "cloud" based rendering solution that sends video to the client device rather than geometric data, such as the scheme presented by Lamberti and Sanna (Lamberti & Sanna, 2007) .. It is worth stating that, as this on-demand prototype uses standard Internet protocols (HTTP over TCP/IP), this method is not limited to merely mobile browsers. It could easily be used in standard web browsers too, but some method for specifying location and direction would have to be introduced. Another usage pattern could be to allow users to connect their mobile devices to an interactive walk-through running in the VR lab and be able to save views without having to interrupt proceedings, or for use in further discussions later away from the VR lab. It is now possible to create detailed visualisations of possible changes to our environment through interactive 3D landscape models. These can be shared with the public in one of the six methods (VR lab, PC mobile, internet PC, AR mobile, pre-prepared mobile, on-demand mobile) detailed in this paper. Each method has advantages and disadvantages associated with it, but determining which method to use in which circumstance is not yet clear.. 3D models were previously restricted to being explored in a remote lab or office environment, in that the 3D or virtual environment is mainly restricted to a purely visual representation. While an aural component can also be part of the representation (Lindquist & Lange, 2014) , being on site provides a multi-sensory environment that is very difficult to recreate faithfully in a remote location. This isolation from the actual site can lead to divergent responses to visualisations (Wergles & Muhar, 2009 ). The approach presented here allows interactive exploration of landscape visualisations amongst the current context.. The different methods that can be pursued open up a number of routes in research, development and application that need exploring further (Gill, Lange, Morgan, & Romano, 2013) . These efforts need to involve the general public, experts in software engineering and the planning and design disciplines in order to understand the suitability and to get maximum benefit of these methods for public participation in planning and design.. be taken as indicative in any way of the position of the funders or of colleagues and partners. It has been demonstrated that it is possible to disseminate visualisations from existing detailed virtual 3D landscape models both on-demand and on-site through touch based user interfaces. Given this, it seems a sensible strategy to ascertain whether it does indeed provide benefits over more traditional forms of public consultation, or over VR labs with 3D navigational interface devices.. The different methods for disseminating virtual 3D landscape models all have varying strengths and weaknesses. For example, it must be clearly stated that one obvious drawback to the on-demand streaming system is that fast mobile data networks do not provide universal coverage. So, if a proposal were located outside data network coverage, the above system would fail to operate. Visualisation on-site could still be possible if an ad-hoc wireless network were to be set up to a base computer that hosted the model and the user stayed in range.. It may mean this on-demand streaming system is currently more suited to urban sites rather than more rural ones. In this sense, at the moment the presented software developments are more suited to design-related urban projects, such as new housing, a new urban park and so on, but less suited for projects in rural areas that typically require assessing their impact including e.g. wind parks, hydro power projects, etc. However, as was mentioned in the Results section signals can suffer from inaccuracy, especially in dense urban or forested environments. Therefore, the layout of urban site being visualised may have a significant effect on the use of any system (AR, or on-demand streaming) that relies on accurate location determination. The introduction of higher accuracy GPS systems, such as the European Galileo project (Ji et al., 2010) , means the positioning in smartphones may become more precise and overcome this issue. Another option would be to augment the GPS location using information gleaned from sensors based on the mobile device (Dalla Mura, Zanin, Andreatta, & Chippendale, 2012) .. In either situation, urban or rural, projects can be highly contentious and would benefit from improved public participation. In the setting of a VR lab the stakeholders involved in a participatory process are removed from the actual site. It is not only hard for them to imagine the context but also other sensory experiences, other than visual, are normally excluded. In contrast, a prototype as it is presented here allows consideration of not only the visual appearance of a project, but also of other sensory experiences while on site (Lindquist & Lange, 2014) . The authors suggest that the suitability of each method of visualisation delivery be examined based on the type of proposal, the sensitivity of the proposal, the level of detail contained in the available models, screen size and any other relevant criteria.. Being able to access multiple options in a planning and design seems extremely important as it allows a comparison of alternatives and highlighting of differences at that viewpoint. Further research to determine how to present multiple design options to the user for each of the different visualisation delivery methods would seem another sensible direction to pursue. The tablet app and the mobile web browser application were tested remotely and connected to several existing virtual 3D landscape models in a central area of Sheffield. It proved possible to use both the tablet app and the web browser on-site to navigate and view multiple remote 3D landscape models via a 3G data connection. The production and transmission of the 3D views would take several seconds due to the rendering of the model to an image and the transmission speeds of the mobile data network. The panorama files took even longer to produce as they require multiple views to be rendered and the resultant file size was on average approximately 10 times larger. This system performance cannot therefore be deemed fully interactive, although it did provide an easy method of viewing the model remotely and within the context of the site.. Using the GPS and the compass automatically to both ascertain and transmit location and direction was possible. When the mobile device accurately determined the GPS position, it provided a very easy to use method of accessing a 3D landscape model. However, there can be inaccuracy in the detected position, which could mean when standing by the riverside, the server returned a view of the model from one or two metres into the river. Moving position would often rectify this. For this study, detailed virtual landscape models were available. However, due to the complexity and size of these models they would not render on the mobile devices available. Therefore, it was decided to attempt to implement the "streaming" of visualisations to the remote smartphones. This ensures the same graphical style of visualisation that would have been available to a user in the VR lab viewing the same model. The prototype was developed as a client/server architecture where the mobile "clients" would request visualisations from a "server" computer. To re-use the existing models, three pieces of software development were undertaken: a visualisation server hosted in existing landscape visualisation software; a tablet based "app"; a web browser based interface for mobile devices. An overview of the implemented architecture can be seen in Fig. 1 . Each element is further detailed below.

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Computing matrix functions arising in engineering models with orthogonal matrix polynomials Trigonometric matrix functions play a fundamental role in the solution of second order differential equations. Hermite series truncation together with Paterson-Stockmeyer method and the double angle formula technique allow efficient computation of the matrix cosine. A careful error bound analysis of the Hermite approximation is given and a theoretical estimate for the optimal value of its parameters is obtained. Based on the ideas above, an efficient and highly-accurate Hermite algorithm is presented. A MATLAB implementation of this algorithm has also been developed and made available online. This implementation has been compared to other efficient state-ofthe-art implementations on a large class of matrices for different dimensions, obtaining higher accuracy and lower computational costs in the majority of cases. Matrix functions play a relevant role in different areas of science and technology. They arise most frequently in connection with the solution of differential systems and control theory. For example, it is well known that the wave equation. plays an important role in many areas of engineering and applied sciences. When we use the spatially semi-discretization method of the wave equation (1), we obtain the matrix differential problem. where A is a square matrix and Y 0 and Y 1 are vectors, see [1] for details. Matrix problem (2) has the solution. where √ A denotes any square root of a non-singular matrix A (see e.g. expression (1.2) of [2] ). More general problems of type (2) , with a forcing term F (t) on the right-hand side arise from mechanical systems without damping, and their solutions can be expressed in terms of integrals involving the matrix sine and cosine [3] . Thus, trigonometric matrix functions play an important role in second order differential systems, similar to matrix exponential e At in first order differential systems [4] .. Moreover, the matrix cosine is used in the method of Yau-Lu for reducing the symmetric eigenvalue problem (finding all the eigenvalues and eigenvectors of a dense symmetric matrix) to a number of matrix multiplications [5] .. Computing the matrix sine reduces to computing the matrix cosine through sin (A) = cos (A − π 2 I). Thus we concentrate on the matrix cosine. Serbin and Blalock proposed a general algorithm for computing the matrix cosine in [1] , which uses rational approximations and the double angle formula. In [6] new methods for computing matrix exponential, sine and cosine based on Hermite matrix polynomial series were presented. A new bound for Hermite matrix polynomials was provided and it was used to give expressions for obtaining the number of Hermite series terms depending on the desired approximation error in exact arithmetic. Later, Higham, Smith and Hargreaves developed two algorithms based on (4) and Padé approximation in [7, 2] , including truncation and rounding error analysis. Recently, in [8] the authors introduced a new parameter in the matrix cosine and sine Hermite series from [6] and new error bounds, improving both accuracy and efficiency.. In this paper we use the new matrix cosine Hermite series from [8] , providing sharper bounds for Hermite matrix polynomials and the approximation error, and computing the optimal values of the series parameter to develop a competitive Hermite algorithm for computing the matrix cosine in IEEE double precision arithmetic that uses: matrix scaling based on (4), Paterson-Stockmeyer's method for the evaluation of Hermite series [9, 10] , and accuracy bound tests similar to those proposed in [10, p. 6456-6457] . A MATLAB implementation of this algorithm is made available online and it is compared with the MATLAB function funm [11] and a MATLAB implementation based on the Padé algorithm given in [2] , i.e. function cosm, providing higher accuracy and efficiency than both methods in the majority of test matrices. This paper is organized as follows. Section 2 summarizes previous results of Hermite matrix polynomial series expansion of cos (A) and the development of a new error bound. In Section 3, an algorithm based on that error bound is described. Numerical experiments are presented in Section 4. Finally, conclusions are given in Section 5.. Throughout this paper, [x] denotes the integer part of x. To obtain the above mentioned error bound, we will use any subordinate matrix norm ∥ A ∥, A ∈ C r×r , and in the subsequent error analysis, we will use the 1-norm ∥ A ∥ 1 . If A(k, n) is a matrix in C r×r for n ≥ 0, k ≥ 0, the following identity holds [6] :. 2. Hermite matrix polynomial series expansions of matrix cosine. In this section we describe Algorithm 1 (cosher), based on Hermite series, which uses bound (14) for choosing the scaling factor for computing the matrix cosine.

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


ARCHITECTURES AND FPGA IMPLEMENTATIONS OF THE 64-BIT MISTY1 BLOCK CIPHER In this paper, we present two alternative architectures and FPGA implementations of the 64-bit NESSIE proposal, MISTY1 block cipher. The first architecture is suitable for applications with high-performance requirements. A throughput of up to 12.6 Gbps can be achieved at a clock frequency of 168 MHz. The main characteristic of this architecture is that uses RAM blocks embedded in modern FPGA devices in order to implement the S-boxes defined in the block cipher algorithm. The second architecture can be used in implementing applications on area-constrained systems. It utilizes feedback logic and inner pipeline with negative edge-triggered register. This technique shortens the critical path, without increasing the latency of the MISTY1 algorithm execution. Compared with an implementation without inner pipeline, performance improvement of 97% is achieved. The measured throughput of the second architecture implementation is 561 Mbps at 79 MHz. Due to the rapid development of wireless standards, security in mobile communications has gained more importance. However, it is far more difficult to develop new highly qualitative cryptography methods for wireless standards. Some security features have been added and some existing ones have been improved compared with previous mobile systems, in order to achieve more efficient and secure offered services.. Many attempts have taken place in order to establish qualitative cryptography methods. The New European Schemes for Signatures, Integrity, and Encryption (NESSIE) project 1 had a goal to establish a portfolio of strong cryptographic primitives of various types. For block ciphers, a third security level, normal-legacy, has been specified, which means a block size of 64 bits instead of 128 (the AES 2 does not specify smaller block size than 128-bit). This was suggested by the project industry board, because the market will still need this block size for compatibility with 818 P. Kitsos, M. D. Galanis & O. Koufopavlou present applications (e.g., payments with 8-byte personal identification numbers). It is used in 64-bit block ciphers which are more secure and efficient than the ones presently used. In February 2003, it was announced that the 64-bit block cipher included in the NESSIE portfolio is MISTY1. 3, 4 This cipher is designed in order to provide high-level security against differential and linear cryptanalysis.. In the third NESSIE workshop, 1 a paper on some NESSIE proposal algorithms was presented. 5 The main purpose of that work was the evaluation of these algorithms in terms of hardware implementation performance. In that evaluation, only the encryption mode of operation was implemented and not the decryption one. In addition, only the unrolled architecture of the algorithm was considered.. Besides our work, some other architectures and implementations of the MISTY1 cipher have been proposed. 6, 7 The work in Ref. 6 is exactly the same as the MISTY1 implementation proposed in Ref. 5 . As previously mentioned, these implementations do not support the decryption mode of the cipher. In Ref. 7, two MISTY1 software implementations on a Digital Alpha processor were proposed. Nevertheless, it is well known that the software implementations of security algorithms are much slower than the hardware ones.. In this paper, two architectures and efficient FPGA implementations of the 64-bit NESSIE proposal MISTY1 block cipher are proposed. These two architectures realize both encryption and decryption modes in the same hardware unit. The first architecture is suitable for applications with high-performance requirements. The main feature of this implementation is the unrolling of the cipher rounds in a 75-stage pipeline. Due to the increased critical path delay of the logical expressions, for the S-boxes implementation, the RAM blocks embedded in the considered FPGA devices are utilized.. The second architecture can be used in applications where an area-constrained design is desirable. It uses feedback logic and inner pipeline with negative edgetriggered register. 8, 9 This method shortens the critical path, without increasing the cipher's latency, thus the cipher's throughput is increased.. The rest of the paper is organized as follows: In Sec. 2, the MISTY1 block cipher is described. In Sec. 3, the two proposed hardware architectures are presented and explained in detail. Performance analysis of the FPGA implementations of the two architectures and comparison results with existing works are given in Sec. 4. Finally, Sec. 5 concludes the paper. Two different hardware architectures and FPGA implementations of the MISTY1 block cipher were presented. These architectures support encryption and decryption modes of operations which is not the case in existing works. The eight rounds architecture, which is suitable for high-performance designs, achieves a maximum throughput of 12.6 Gbps at an clock frequency of 168 MHz. Additionally, this architecture is more hardware efficient compared with previous hardware architectures.

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


Coexpression and coregulation analysis of time-series gene expression data in estrogen-induced breast cancer cell Background: Estrogen is a chemical messenger that has an influence on many breast cancers as it helps cells to grow and divide. These cancers are often known as estrogen responsive cancers in which estrogen receptor occupies the surface of the cells. The successful treatment of breast cancers requires understanding gene expression, identifying of tumor markers, acquiring knowledge of cellular pathways, etc. In this paper we introduce our proposed triclustering algorithm δ-TRIMAX that aims to find genes that are coexpressed over subset of samples across a subset of time points. Here we introduce a novel mean-squared residue for such 3D dataset. Our proposed algorithm yields triclusters that have a mean-squared residue score below a threshold δ. Results: We have applied our algorithm on one simulated dataset and one real-life dataset. The real-life dataset is a time-series dataset in estrogen induced breast cancer cell line. To establish the biological significance of genes belonging to resultant triclusters we have performed gene ontology, KEGG pathway and transcription factor binding site enrichment analysis. Additionally, we represent each resultant tricluster by computing its eigengene and verify whether its eigengene is also differentially expressed at early, middle and late estrogen responsive stages. We also identified hub-genes for each resultant triclusters and verified whether the hub-genes are found to be associated with breast cancer. Through our analysis CCL2, CD47, NFIB, BRD4, HPGD, CSNK1E, NPC1L1, PTEN, PTPN2 and ADAM9 are identified as hub-genes which are already known to be associated with breast cancer. The other genes that have also been identified as hub-genes might be associated with breast cancer or estrogen responsive elements. The TFBS enrichment analysis also reveals that transcription factor POU2F1 binds to the promoter region of ESR1 that encodes estrogen receptor α. Transcription factor E2F1 binds to the promoter regions of coexpressed genes MCM7, ANAPC1 and WEE1. Conclusions: Thus our integrative approach provides insights into breast cancer prognosis. In this work we have proposed δ-TRIMAX triclustering algorithm that aims to retrieve large and coherent groups of genes, having an MSR score below a threshold δ. Genes belonging to each tricluster are coexpressed over a subset of samples/ experimental conditions and across subset of time points. The results of GO and KEGG pathway enrichment analysis show that our proposed algorithm is able to extract group of coexpressed genes that are biologically significant. We have performed TFBS enrichment analysis to establish the fact that the promoter regions of the genes having similar expression profile are bound by the same transcription factors. We have compared the performance of our algorithm with that of existing algorithm using one artificial dataset in terms of affirmation score and one real-life dataset in terms of coverage, statistical difference from background and triclustering quality index score. In case of these two datasets our proposed algorithm outperformed the existing one. Additionally, here we have represented the expression profiles of genes belonging to each tricluster by eigengene and then identified hub genes using the profile of eigengene. We have observed that most of the identified hub-genes are previously reported to be associated with breast cancer and estrogen responsive elements. The other identified hub genes might be associated with breast cancer and need to be verified experimentally. Hence our integrative approach and findings might provide new insights into breast cancer prognosis. In the context of genomics research, the functional approach is based on the ability to analyze genomewide patterns of gene expression and the mechanisms by which gene expression is coordinated. Microarray technology and other high-throughput methods are used to measure expression values of thousands of genes over different samples/experimental conditions. In recent years the microarray technology has been used to measure in a single experiment expression values of thousands of genes under a huge variety of experimental conditions across different time points. This kind of datasets can be referred to as time series microarray datasets. Because of the large data volume, computational methods are used to analyze such datasets. Clustering is one of the most common methods for identifying coexpressed genes [1] . This kind of analysis is facilitative for constructing gene regulatory networks in which single or groups of genes interact with other genes. Besides this, coexpression analysis also reveals information about some unknown genes that form a cluster with some known genes.. A clustering algorithm is used to group genes that are coexpressed over all conditions/samples or to group experimental conditions over all genes based on some similarity/dissimilarity metric. However clustering may fail to find the group of genes that are similarly expressed over a subset of samples/experimental conditions i.e. clustering algorithms are unable to find such local patterns in the gene expression dataset. To deal with that problem, biclustering algorithms are used. A bicluster can be defined as a subset of genes that are coexpressed over a subset of samples/experimental conditions. The first biclustering algorithm that was used to analyse gene expression datasets was proposed by Cheng and Church and they used a greedy search heuristic approach to retrieve largest possible bicluster having mean squared residue (MSR) under a predefined threshold value δ (δ-bicluster) [2] . But nowadays, biologists are eager to analyze 3D microarray dataset to answer the question: "Which genes are coexpressed under which subset of experimental conditions/samples across which subset of time points?" Biclustering is not able to deal with such 3D datasets. So, in this case we need some other clustering technique that can mine 3D datasets. Hence the term Triclustering has been defined and a tricluster can be delineated as a subset of genes that are similarly expressed across a subset of experimental conditions/samples over a subset of time points. Zhao and Zaki proposed a triclustering algorithm TRICLUSTER that is based on graphbased approach. They defined coherence of a tricluster as max(e ib /e ia ,e jb /e ja ) min(e ib /e ia ,e jb /e ja ) − 1, where e ia , e ib denote the expression values of two columns a and b respectively for a row i. A tricluster is valid if it has a ratio below a maximum ratio threshold [3] .. Here we introduce an efficient triclustering algorithm δ-TRIMAX [4] that aims to cope with noisy 3D gene expression dataset and is less sensitive to input parameters. The normalization method does not influence the performance of our algorithm, as it produces the same results for both normalized and raw datasets. Here we propose a novel extension of MSR [2] for 3D gene expression data and use a greedy search heuristic approach to retrieve triclusters, having MSR values below a threshold δ. Hence the triclusters can be defined as δ-tricluster.. In this work we have applied our proposed δ-TRIMAX algorithm on a time-series gene expression data in estrogen induced breast cancer cell. Estrogen, a chemical messenger plays an instrumental role in normal sexual development, regulating woman's menstrual cycles and normal development of the breast. Estrogen is also needed for heart and healthy bones. As estrogen plays vital role in stimulating breast cell division, has an effect on other hormones implicated in breast cell division and provides support to the growth of estrogen-responsive tumors, it may be involved in risk for breast cancer [5] . Though since last decade, some research has been done to decipher some unknown questions on breast cancer risk, still some questions such as involvement of genes in breast cancer risk etc. remain unanswered. Here our coexpression analysis reveals some genes that have already been found to be associated with estrogen induced breast cancer and some other genes that might play an important role in this context. Additionally, our coregulation analysis brings out some important information such as which transcription factor binds the promoter regions of genes and play an important role in this context.. In section 2, we have described our proposed triclustering algorithm in detail. Section 3 shows results of our algorithm using one artificial dataset and one real-life dataset. In section 4, we conclude our work. Cheng and Church proposed an algorithm for retrieving large and maximal biclusters that have mean squared residue score (MSR) below a threshold δ in 2D microarray gene expression dataset. They also showed that MSR of a perfect δ-bicluster and perfect shifting bicluster is zero (S = δ = 0) [2, 6]

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