Piecewise Linear Transformation Research Articles

Cost-Effectiveness of a Novel e-Health Depression Service

A recent trial assessed feasibility of an e-health service (" Improvehealth.eu ") to support depression care and reported positive outcomes. Our objective was to examine cost-effectiveness of the Improvehealth.eu service. A baseline model was used to evaluate cost and effects of the intervention. Given the high uncertainty in the input space, a series of alternative scenarios were evaluated to challenge the result. The aim was to find if conservative or even pessimistic estimates and assumptions could result in a change of the cost-effectiveness from the baseline model. A probabilistic depression model combined with bootstrapping was built and populated with data from the literature and from the pilot efficacy trial of the e-health service. The core of the model was a stochastic mapping function that translated depression-specific outcomes to quality-adjusted life years. Correlated sampling was used to obtain unbiased and consistent piecewise linear transformation of Beck Depression Inventory scores to utilities. The results are shown as cost-effectiveness acceptability curves with value of information data. An extreme scenario analysis was then performed to deal with parameter, structural, and modeling uncertainty. Cost-effectiveness of the e-health service was favorable because of low cost and high efficacy of the intervention. Apart from the most pessimistic one, none of the 13 alternative scenarios changed the preferred alternative. Improvehealth.eu is cost-effective relative to usual care, given the available efficacy data. Results of the health economic evaluation were robust to alternative assumptions, despite considerable uncertainty in input data.

Wideband Re-synthesis of Narrowband Speech Using Discriminative Piecewise Linear Transformation

Wideband Re-synthesis of Narrowband Speech Using Discriminative Piecewise Linear Transformation

Minkowski Polynomials and Mutations

Given a Laurent polynomial f, one can form the period of f: this is a function of one complex variable that plays an important role in mirror symmetry for Fano manifolds. Mutations are a particular class of birational transformations acting on Laurent polynomials in two variables; they preserve the period and are closely connected with cluster algebras. We propose a higher-dimensional analog of mutation acting on Laurent polynomials f in n variables. In particular we give a combinatorial description of mutation acting on the Newton polytope P of f, and use this to establish many basic facts about mutations. Mutations can be understood combinatorially in terms of Minkowski rearrangements of slices of P, or in terms of piecewise-linear transformations acting on the dual polytope P^* (much like cluster transformations). Mutations map Fano polytopes to Fano polytopes, preserve the Ehrhart series of the dual polytope, and preserve the period of f. Finally we use our results to show that Minkowski polynomials, which are a family of Laurent polynomials that give mirror partners to many three-dimensional Fano manifolds, are connected by a sequence of mutations if and only if they have the same period.

Towards an improved description of ocean uncertainties: effect of local anamorphic transformations on spatial correlations

Abstract. The objective of this paper is to investigate if the description of ocean uncertainties can be significantly improved by applying a local anamorphic transformation to each model variable, and by making the assumption of joint Gaussianity for the transformed variables, rather than for the original variables. For that purpose, it is first argued that a significant improvement can already be obtained by deriving the local transformations from a simple histogram description of the marginal distributions. Two distinctive advantages of this solution for large size applications are the conciseness and the numerical efficiency of the description. Second, various oceanographic examples are used to evaluate the effect of the resulting piecewise linear local anamorphic transformations on the spatial correlation structure. These examples include (i) stochastic ensemble descriptions of the effect of atmospheric uncertainties on the ocean mixed layer, and of wind uncertainties or parameter uncertainties on the ecosystem, and (ii) non-stochastic ensemble descriptions of forecast uncertainties in current sea ice and ecosystem pre-operational developments. The results indicate that (i) the transformation is accurate enough to faithfully preserve the correlation structure if the joint distribution is already close to Gaussian, and (ii) the transformation has the general tendency of increasing the correlation radius as soon as the spatial dependence between random variables becomes nonlinear, with the important consequence of reducing the number of degrees of freedom in the uncertainties, and thus increasing the benefit that can be expected from a given observation network.

Combined Piecewise Linear Recursive Convolution-Bilinear Transform Implementation of the CFS-PML for Unmagnetized Plasma

The complex frequency shifted (CFS) perfectly matched layer (PML) has been proven to be more efficient in attenuating evanescent waves and reducing late-time reflections than the original PML. In this letter, the piecewise linear recursive convolution (PLRC) method is combined with the bilinear transform (BT) to implement the CFS-PML for unmagnetized plasma simulation. Compared to the original bilinear transform implementation, the computational cost of the PLRC CFS-PML is greatly reduced with the same absorbing performance.

Aligning archive maps and extracting footprints for analysis of historic urban environments

Archive cartography and archaeologist's sketches are invaluable resources when analysing a historic town or city. A virtual reconstruction of a city provides the user with the ability to navigate and explore an environment which no longer exists to obtain better insight into its design and purpose. However, the process of reconstructing the city from maps depicting features such as building footprints and roads can be labour intensive. In this paper we present techniques to aid in the semi-automatic extraction of building footprints from digital images of archive maps and sketches. Archive maps often exhibit problems in the form of inaccuracies and inconsistencies in scale which can lead to incorrect reconstructions. By aligning archive maps to accurate modern vector data one may reduce these problems. Furthermore, the efficiency of the footprint extraction methods may be improved by aligning either modern vector data or previously extracted footprints, since common elements can be identified between maps of differing time periods and only the difference between the two needs to be extracted. An evaluation of two alignment approaches is presented: using a linear affine transformation and a set of piecewise linear affine transformations.

Control and dynamics of linear systems under finite quantised feedback

This paper addresses control problems and analyses dynamics for linear systems under finite quantised feedback. The optimal one-bit control laws are developed, which minimise either an asymptotic time-averaged expected cost function or an asymptotic expected cost function. The closed-loop system with one-bit controller is a piecewise linear transformation. In the paper, the dynamical behaviour of the closed-loop system is investigated via invariant measures. The invariant distribution can be obtained from the induced matrix when the closed-loop system is a Markov transformation. It is shown that there are infinitely many cases of Markov transformations.

A free group of piecewise linear transformations

A free group of piecewise linear transformations

On the Combinatorics of Rigid Objects in 2-Calabi-Yau Categories

Given a triangulated 2-Calabi-Yau category C and a cluster-tilting subcategory T, the index of an object X of C is a certain element of the Grothendieck group of the additive category T. In this note, we show that a rigid object of C is determined by its index, that the indices of the indecomposables of a cluster-tilting subcategory T′ form a basis of the Grothendieck group of T and that, if T and T′ are related by a mutation, then the indices with respect to T and T′ are related by a certain piecewise linear transformation introduced by Fomin and Zelevinsky in their study of cluster algebras with coefficients. This allows us to give a combinatorial construction of the indices of all rigid objects reachable from the given cluster-tilting subcategory T. Conjecturally, these indices coincide with Fomin-Zelevinsky's g-vectors.

Equivalent configurations of optical transformation media

We demonstrate that a medium consisting of two adjoining distinct layers of transformation materials, corresponding respectively to two linear coordinate transformations, can behave effectively as that of the same region transformed by another linear transformation. The equivalence means that, irrespective of the direction of incident wave, the fields of the medium exterior to the transformed regions of the two configurations are exactly the same. This property can also apply to a domain that is transformed by a piecewise linear transformation function, and to a medium that is mapped by a general curved function. This proof is shown analytically based on a rigorous Fourier-Bessel analysis. The equivalence suggests that, for a given transformed domain, one can find an infinite number of complementary media that altogether can give a desired effective response of certain transformation path.

A natural extension for the greedy β-transformation with three arbitrary digits

We construct a planar version of the natural extension of the piecewise linear transformation T generating greedy β-expansions with digits in an arbitrary set of real numbers A = {a0, a1, a2}. As a result, we derive in an easy way a closed formula for the density of the unique T-invariant measure µ absolutely continuous with respect to Lebesgue measure. Furthermore, we show that T is exact and weak Bernoulli with respect to µ.

Improving Piecewise Linear Registration of High-Resolution Satellite Images Through Mesh Optimization

Piecewise linear transformation is a powerful technique for coping with the registration of images affected by local geometric distortions, as it is usually the case of high-resolution satellite images. A key point when applying this technique is to divide the images to register according to a suitable common triangular mesh. This comprises two different aspects: where to place the mesh vertices (i.e., the mesh geometrical realization) and to set an appropriate topology upon these vertices (i.e., the mesh topological realization). This paper focuses on the latter and presents a novel method that improves the registration of two images by an iterative optimization process that modifies the mesh connectivity by swapping edges. For detecting if an edge needs to be swapped or not, we evaluate the registration improvement of that action on the two triangles connected by the edge. Another contribution of our proposal is the use of the mutual information for measuring the registration consistency within the optimization process, which provides more robustness to image changes than other well-known metrics such as normalized cross-correlation or sum of square differences. The proposed method has been successfully tested with different pairs of panchromatic QuickBird images (0.6 m/pixel of spatial resolution) of a variety of land covers (urban, residential, and rural) acquired under different lighting conditions and viewpoints.

Contrast enhancement by automatic and parameter-free piecewise linear transformation for color images

Conventional contrast enhancement methods have four shortcomings. First, most of them need transformation functions and parameters which are specified manually. Second, most of them are application-oriented methods. Third, most of them are performed on gray level images. Fourth, the histogram equalization (HE) based enhancement methods use non-linear transform function. Thus, this paper proposes an automatic and parameter-free contrast enhancement algorithm for color images. This method includes following steps: First, RGB color space is transformed to HSV color space. Second, image content analysis is used to analyze the image illumination distribution. Third, the original image is enhanced by piecewise linear based enhancement method. Finally, the enhancement image is transformed back to RGB color space. This novel enhancement is automatic and parameter-free. Our experiments included various color images with low and high contrast. Experiment results show that the performance of the proposed method is better than histogram equalization (HE) and its six variations in non-over enhancement and natural clearly revealed. Moreover, the proposed algorithm can be run on an embedded environment (such as mobile device, digital camera, or other consumer products) and processed in real-time system due to its simplicity and efficiently.

A fast and fully automatic registration approach based on point features for multi-source remote-sensing images

Automatic registration of multi-source remote-sensing images is a difficult task as it must deal with the varying illuminations and resolutions of the images, different perspectives and the local deformations within the images. This paper proposes a fully automatic and fast non-rigid image registration technique that addresses those issues. The proposed technique performs a pre-registration process that coarsely aligns the input image to the reference image by automatically detecting their matching points by using the scale invariant feature transform (SIFT) method and an affine transformation model. Once the coarse registration is completed, it performs a fine-scale registration process based on a piecewise linear transformation technique using feature points that are detected by the Harris corner detector. The registration process firstly finds in succession, tie point pairs between the input and the reference image by detecting Harris corners and applying a cross-matching strategy based on a wavelet pyramid for a fast search speed. Tie point pairs with large errors are pruned by an error-checking step. The input image is then rectified by using triangulated irregular networks (TINs) to deal with irregular local deformations caused by the fluctuation of the terrain. For each triangular facet of the TIN, affine transformations are estimated and applied for rectification. Experiments with Quickbird, SPOT5, SPOT4, TM remote-sensing images of the Hangzhou area in China demonstrate the efficiency and the accuracy of the proposed technique for multi-source remote-sensing image registration.

Construction of Keyless Attack on Cryptosystem Based on Piecewise-linear Transformation

Construction of Keyless Attack on Cryptosystem Based on Piecewise-linear Transformation

A Spectral Conversion Approach to Single-Channel Speech Enhancement

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> In this paper, a novel method for single-channel speech enhancement is proposed, which is based on a spectral conversion feature denoising approach. Spectral conversion has been applied previously in the context of voice conversion, and has been shown to successfully transform spectral features with particular statistical properties into spectral features that best fit (with the constraint of a piecewise linear transformation) different target statistics. This spectral transformation is applied as an initialization step to two well-known single channel enhancement methods, namely the iterative Wiener filter (IWF) and a particular iterative implementation of the Kalman filter. In both cases, spectral conversion is shown here to provide a significant improvement as opposed to initializations using the spectral features directly from the noisy speech. In essence, the proposed approach allows for applying these two algorithms in a user-centric manner, when “clean” speech training data are available from a particular speaker. The extra step of spectral conversion is shown to offer significant advantages regarding output signal-to-noise ratio (SNR) improvement over the conventional initializations, which can reach 2 dB for the IWF and 6 dB for the Kalman filtering algorithm, for low input SNRs and for white and colored noise, respectively. </para>

Study of Automatic Enhancement for Chest Radiograph

Because of the large difference of the densities in the lung and other structures, the chest x-ray image behaves as a wide-range intensity distribution, which brings on a bit of difficulty to investigate the focus. In the paper, according to the intensity properties of the chest radiograph, the chest radiographic image is divided into three subregions, and a piecewise linear transformation model is established. An approach of automatic enhancement is presented, based on the gray-level normalization. The average enhanced ratios of three subregions of the normal and severe acute respiratory syndrome image are increased by 10.70% and 25.55%, respectively. The technique is proved to be effective through the evaluation of the improved images.

Transport Properties of a Piecewise Linear Transformation and Deterministic Levy Flights

The transport properties of a 1-dimensional piecewise linear dynamical system are investigated through the spectrum of its Frobenius-Perron operator. For a class of initial densities, eigenvalues and eigenfunctions of the Frobenius-Perron operator are obtained explicitly. It is also found that in the long length wave limit, this system exhibits normal diffusion and super diffusion called Levy flight. The diffusion constant and stable index are derived from the eigenvalues.

Tree-Structured Clustering Methods for Piecewise Linear-Transformation-Based Noise Adaptation

This paper proposes the application of tree-structured clustering to the processing of noisy speech collected under various SNR conditions in the framework of piecewise-linear transformation (PLT)-based HMM adaptation for noisy speech. Three kinds of clustering methods are described: a one-step clustering method that integrates noise and SNR conditions and two two-step clustering methods that construct trees for each SNR condition. According to the clustering results, a noisy speech HMM is made for each node of the tree structure. Based on the likelihood maximization criterion, the HMM that best matches the input speech is selected by tracing the tree from top to bottom, and the selected HMM is further adapted by linear transformation. The proposed methods are evaluated by applying them to a Japanese dialogue recognition system. The results confirm that the proposed methods are effective in recognizing digitally noise-added speech and actual noisy speech issued by a wide range of speakers under various noise conditions. The results also indicate that the one-step clustering method gives better performance than the two-step clustering methods.

Hausdorff Dimension of Trees Generated by Piecewise Linear Transformations

Trees are constructed by one--dimensional piecewise linear transformations, and the Hausdorff dimension of trees are calculated.