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Because haplotype information is of widespread interest in biomedical applications, effort has been put into their reconstruction. Here, we propose an efficient method, called haploSep, that is able to accurately infer major haplotypes and their frequencies just from multiple samples of allele frequency data. Even the accuracy of experimentally obtained allele frequencies can be improved by re-estimating them from our reconstructed haplotypes. From a methodological point of view, we model our problem as a multivariate regression problem where both the design matrix and the coefficient matrix are unknown. Compared to other methods, haploSep is very fast, with linear computational complexity in the haplotype length. We illustrate our method on simulated and real data focusing on experimental evolution and microbial data. haploSep is a computationally efficient method to infer major haplotypes and their frequencies from multiple samples of allele frequency data, and to provide improved estimates of experimentally obtained allele frequencies.

Dilated cardiomyopathy (DCM) is a major risk factor for heart failure and is associated with the development of life-threatening cardiac arrhythmias. Using a patient-specific induced pluripotent stem cell-derived cardiomyocyte (iPSC-CM) model harbouring a mutation in cardiac troponin T (R173W), we aim to examine the cellular basis of arrhythmogenesis in DCM patients with this mutation. iPSC from control (Ctrl) and DCM-TnT-R173W donors from the same family were differentiated into iPSC-CM and analysed through optical action potential (AP) recordings, simultaneous measurement of cytosolic calcium concentration ([Ca2+]i) and membrane currents and separately assayed using field stimulation to detect the threshold for AP- and [Ca2+]i-alternans development. AP duration was unaltered in TnT-R173W iPSC-CM. Nevertheless, TnT-R173W iPSC-CM showed a strikingly low stimulation threshold for AP- and [Ca2+]i-alternans. Myofilaments are known to play a role as intracellular Ca2+ buffers and here we show increased Ca2+ affinity of intracellular buffers in TnT-R173W cells, indicating increased myofilament sensitivity to Ca2+. Similarly, EMD57033, a myofilament Ca2+ sensitiser, replicated the abnormal [Ca2+]i dynamics observed in TnT-R173W samples and lowered the threshold for alternans development. In contrast, application of a Ca2+ desensitiser (blebbistatin) to TnT-R173W iPSC-CM was able to phenotypically rescue Ca2+ dynamics, normalising Ca2+ transient profile and minimising the occurrence of Ca2+ alternans at physiological frequencies. This finding suggests that increased Ca2+ buffering likely plays a major arrhythmogenic role in patients with DCM, specifically in those with mutations in cardiac troponin T. In addition, we propose that modulation of myofilament Ca2+ sensitivity could be an effective anti-arrhythmic target for pharmacological management of this disease.

Since haplotype information is of widespread interest in biomedical applications, effort has been put into their reconstruction. Here, we propose a new, computationally efficient method, called haploSep, that is able to accurately infer major haplotypes and their frequencies just from multiple samples of allele frequency data. Our approach seems to be the first that is able to estimate more than one haplotype given such data. Even the accuracy of experimentally obtained allele frequencies can be improved by re-estimating them from our reconstructed haplotypes. From a methodological point of view, we model our problem as a multivariate regression problem where both the design matrix and the coefficient matrix are unknown. The design matrix, with 0/1 entries, models haplotypes and the columns of the coefficient matrix represent the frequencies of haplotypes, which are non-negative and sum up to one. We illustrate our method on simulated and real data focusing on experimental evolution and microbial data.

In this chapter we discuss how to obtain statistical guarantees in photonic imaging. We start with an introduction to hypothesis testing in the context of imaging, more precisely we describe how to test if there is signal in a specific region of interest (RoI) or just noise. Afterwards we extend this approach to a family of RoIs and examine the occurring problems such as inflation of type I error and dependency issues. We discuss how to control the family-wise error rate by different modifications, and provide a connection to extreme value theory. Afterwards we present possible extension to inverse problems. Moving from testing to estimation, we finally introduce a method which constructs an estimator of the desired quantity of interest with automatic smoothness guarantees.

Computing the inverse of pentadiagonal Toeplitz matrices has numerous applications. However, in some cases, we only need to obtain the diagonal of the inverse rather than the whole inverse. This paper presents a new approach to compute the diagonal of the pentadiagonal Toeplitz matrix inverse by Matrix Mobius Transformations. The proposed algorithm meticulously handles two cases of matrices. We have shown that the complexity of the proposed algorithm is O(n) for matrices of sizes n x n. We investigate the efficiency of the proposed algorithm via numerical simulations and make Matlab codes publicly available.

Purpose In real-time MRI serial images are generally reconstructed from highly undersampled datasets as the iterative solutions of an inverse problem. While practical realizations based on regularized nonlinear inversion (NLINV) have hitherto been surprisingly successful, strong assumptions about the continuity of image features may affect the temporal fidelity of the estimated reconstructions. Theory and Methods The proposed method for real-time image reconstruction integrates the deformations between nearby frames into the data consistency term of the inverse problem. The aggregated motion estimation (AME) is not required to be affine or rigid and does not need additional measurements. Moreover, it handles multi-channel MRI data by simultaneously determining the image and its coil sensitivity profiles in a nonlinear formulation which also adapts to non-Cartesian (e.g., radial) sampling schemes. The new method was evaluated for real-time MRI studies using highly undersampled radial gradient-echo sequences. Results AME reconstructions for a motion phantom with controlled speed as well as for measurements of human heart and tongue movements demonstrate improved temporal fidelity and reduced residual undersampling artifacts when compared with NLINV reconstructions without motion estimation. Conclusion Nonlinear inverse reconstructions with aggregated motion estimation offer improved image quality and temporal acuity for visualizing rapid dynamic processes by real-time MRI. Magn Reson Med 72:1039–1048, 2014. © 2013 Wiley Periodicals, Inc.

Designing fast singular value decomposition (SVD) is significantly interesting in applications. The random direct SVD (RSVD) has provided a fast scheme to compute the well-approximate SVD by unilateral randomized sampling. In this paper, we present an efficient random algorithm in a bilateral sampling way. We also prove that the proposed algorithms can be bounded well and have less computational complexity compared to RSVD when the objective matrix is approximately square. Numerical experiments on graph Laplacian and Hilbert matrix demonstrate the efficiency and stability of the proposed methods.

Polynomials are widely used in scientific computing and engineering. In this paper, we present an accurate and fast compensated algorithm to evaluate bivariate polynomials with floating-point coefficients. This algorithm is applying error free transformations to the bivariate Horner scheme and sum the final decomposition accurately. We also prove the proposed algorithm's accuracy with forward error analysis that the accuracy of the computed result is similar to the result computed by the bivariate Horner scheme in twice the working precision. Numerical experiments illustrate the behavior and it has higher efficiency than the bivariate Horner scheme implemented in double-double library.

Fast multiple change-point segmentation methods, which additionally provide faithful statistical statements on the number, locations and sizes of the segments, have recently received great attention. In this paper, we propose a multiscale segmentation method, FDRSeg, which controls the false discovery rate (FDR) in the sense that the number of false jumps is bounded linearly by the number of true jumps. In this way, it adapts the detection power to the number of true jumps. We prove a non-asymptotic upper bound for its FDR in a Gaussian setting, which allows to calibrate the only parameter of FDRSeg properly. Change-point locations, as well as the signal, are shown to be estimated in a uniform sense at optimal minimax convergence rates up to a log-factor. The latter is w.r.t. $L^p$-risk, $p \ge 1$, over classes of step functions with bounded jump sizes and either bounded, or possibly increasing, number of change-points. FDRSeg can be efficiently computed by an accelerated dynamic program; its computational complexity is shown to be linear in the number of observations when there are many change-points. The performance of the proposed method is examined by comparisons with some state of the art methods on both simulated and real datasets. An R-package is available online., An R-package "FDRSeg" is available at http://www.stochastik.math.uni-goettingen.de/fdrs

This paper presents a compensated algorithm to accurately evaluate a polynomial expressed in Chebyshev basis of the first and second kind with floating-point coefficients. The principle is to apply error-free transformations to improve the traditional Clenshaw algorithm. The new algorithm is as accurate as the Clenshaw algorithm performed in twice the working precision. Forward error analysis and numerical experiments illustrate the accuracy and properties of the proposed algorithm.

Recent years have witnessed great success of manifold learning methods in understanding the structure of multidimensional patterns. However, most of these methods operate in a batch mode and cannot be effectively applied when data are collected sequentially. In this paper, we propose a general incremental learning framework, capable of dealing with one or more new samples each time, for the so-called spectral embedding methods. In the proposed framework, the incremental dimensionality reduction problem reduces to an incremental eigen-problem of matrices. Furthermore, we present, using this framework as a tool, an incremental version of Hessian eigenmaps, the IHLLE method. Finally, we show several experimental results on both synthetic and real world datasets, demonstrating the efficiency and accuracy of the proposed algorithm.

This paper presents a second-order and two-scale computation method of initial-boundary value problem for heat conduction equation with rapidly oscillating coefficients. This method can be applied to heat conduction analysis of composite materials. The main advantages of this method are that it can greatly save computer memory and CPU time, and it possesses good precision at the same time. Finally numerical results show that the presented method is effective and reliable.

In this paper, we present two new families of third-order methods for finding multiple roots of nonlinear equations. Each of them is based on a variant of the Halley's method (for simple roots) free from second derivative. One of the families requires one evaluation of the function and two of its first derivative per iteration, and the other family requires two evaluations of the function and one of its first derivative. Several numerical examples are given to illustrate the performance of the presented methods.

Tensor-driven anisotropic diffusion and regularisation have been successfully applied to a wide range of image processing and computer vision tasks such as denoising, inpainting, and optical flow. Empirically it has been shown that anisotropic models with a diffusion tensor perform better than their isotropic counterparts with a scalar-valued diffusivity function. However, the reason for this superior performance is not well understood so far. Moreover, the specific modelling of the anisotropy has been carried out in a purely heuristic way. The goal of our paper is to address these problems. To this end, we use the statistics of natural images to derive a unifying framework for eight isotropic and anisotropic diffusion filters that have a corresponding variational formulation. In contrast to previous statistical models, we systematically investigate structure-adaptive statistics by analysing the eigenvalues of the structure tensor. With our findings, we justify existing successful models and assess the relationship between accurate statistical modelling and performance in the context of image denoising.