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This report provides a global view of how gene expression is affected by DNA replication. We analyzed synchronized cultures of Saccharomyces cerevisiae under conditions that prevent DNA replication initiation without delaying cell cycle progression. We use a higher‐order singular value decomposition to integrate the global mRNA expression measured in the multiple time courses, detect and remove experimental artifacts and identify significant combinations of patterns of expression variation across the genes, time points and conditions. We find that, first, ∼88% of the global mRNA expression is independent of DNA replication. Second, the requirement of DNA replication for efficient histone gene expression is independent of conditions that elicit DNA damage checkpoint responses. Third, origin licensing decreases the expression of genes with origins near their 3′ ends, revealing that downstream origins can regulate the expression of upstream genes. This confirms previous predictions from mathematical modeling of a global causal coordination between DNA replication origin activity and mRNA expression, and shows that mathematical modeling of DNA microarray data can be used to correctly predict previously unknown biological modes of regulation. In this first global view of how DNA replication affects transcription, ∼88% of global gene expression is found to be independent of DNA replication, significantly lowering the recently measured upper bound to replication‐dependent mRNA expression. The requirement of DNA replication for efficient histone gene expression is found to be independent of conditions that elicit DNA damage checkpoint responses. Origin licensing is found to decrease expression of genes with origins near their 3′ ends, experimentally revealing for the first time that downstream origins can regulate the expression of upstream genes, and demonstrating that mathematical modeling of DNA microarray data can be used to correctly predict previously unknown biological modes of regulation. The recent analogy of the tensor higher‐order singular value decomposition (HOSVD) with the matrix singular value decomposition (SVD), which already enables the interpretation of the HOSVD in terms of the cellular states, biological processess and experimental artifacts that compose the data tensor, is extended by mathematically defining the operation of HOSVD data reconstruction, and by computationally using this operation to remove experimental artifacts from the data.

This survey provides an overview of higher-order tensor decompositions, their applications, and available software. A tensor is a multidimensional or N-way array. Decompositions of higher-order tensors (i.e., N-way arrays with N ≥ 3) have applications in psychometrics, chemometrics, signal processing, numerical linear algebra, computer vision, numerical analysis, data mining, neuroscience, graph analysis, and elsewhere. Two particular tensor decompositions can be considered to be higher-order extensions of the matrix singular value decomposition: CANDECOMP/PARAFAC (CP) decomposes a tensor as a sum of rank-one tensors, and the Tucker decomposition is a higher-order form of principal component analysis. There are many other tensor decompositions, including INDSCAL, PARAFAC2, CANDELINC, DEDICOM, and PARATUCK2 as well as nonnegative variants of all of the above. The N-way Toolbox, Tensor Toolbox, and Multilinear Engine are examples of software packages for working with tensors.

Noise usually affects the reliability of quantitative analysis in diffusion-weighted (DW) magnetic resonance imaging (MRI), especially at high b-values and/or high spatial resolution. Higher-order singular value decomposition (HOSVD) has recently emerged as a simple, effective, and adaptive transform to exploit sparseness within multidimensional data. In particular, the patch-based HOSVD denoising has demonstrated superb performance when applied to T1-, T2-, and proton density-weighted MRI data. In this study, we aim to investigate the feasibility of denoising DW data using the HOSVD transform. With the low signal-to-noise ratio in typical DW data, the patch-based HOSVD denoising suffers from stripe artifacts in homogeneous regions because of the HOSVD bases learned from the noisy patches. To address this problem, we propose a novel denoising method. It first introduces a global HOSVD-based denoising as a prefiltering stage to guide the subsequent patch-based HOSVD denoising stage. The HOSVD bases from the patch groups in prefiltered images are then used to transform the noisy patch groups in original DW data. Experiments were performed using simulated and in vivo DW data. Results show that the proposed method significantly reduces stripe artifacts compared with conventional patch-based HOSVD denoising methods, and outperforms two state-of-the-art denoising methods in terms of denoising quality and diffusion parameters estimation.

In this paper, we present a novel four-dimensional (4D) parameter estimation method to localize the mixed far-field (FF) and near-field (NF) targets using bistatic MIMO arrays and higher-order singular value decomposition (HOSVD). The estimated four parameters include the angle-of-departure (AOD), angle-of-arrival (AOA), range-of-departure (ROD), and range-of-arrival (ROA). In the method, we store array data in a tensor form to preserve the inherent multidimensional properties of the array data. First, the observation data are arranged into a third-order tensor and its covariance tensor is calculated. Then, the HOSVD of the covariance tensor is performed. From the left singular vector matrices of the corresponding module expansion of the covariance tensor, the subspaces with respect to transmit and receive arrays are obtained, respectively. The AOD and AOA of the mixed FF and NF targets are estimated with signal-subspace, and the ROD and ROA of the NF targets are achieved using noise-subspace. Finally, the estimated four parameters are matched via a pairing method. The Cramér–Rao lower bound (CRLB) of the mixed target parameters is also derived. The numerical simulations demonstrate the superiority of the tensor-based method.

Coherent imaging systems, such as synthetic aperture radar (SAR), often suffer from granular speckle noise due to inherent defects, which can make interpretation challenging. Although numerous despeckling methods have been proposed in the past three decades, SAR image despeckling remains a challenging task. With the extensive use of non-local self-similarity, despeckling methods under the non-local framework have become increasingly mature. However, effectively utilizing patch similarities remains a key problem in SAR image despeckling. This paper proposes a three-dimensional (3D) SAR image despeckling method based on searching for similar patches and applying the high-order singular value decomposition (HOSVD) theory to better utilize the high-dimensional information of similar patches. Specifically, the proposed method extends two-dimensional (2D) to 3D for SAR image despeckling using tensor patches. A new, non-local similar patch-searching measure criterion is used to classify the patches, and similar patches are stacked into 3D tensors. Lastly, the iterative adaptive weighted tensor cyclic approximation is used for SAR image despeckling based on the HOSVD method. Experimental results demonstrate that the proposed method not only effectively reduces speckle noise but also preserves fine details.

One of the most important tasks in seismic data interpretation is the detection of salt bodies since most of the important reservoirs are trapped around such bodies. However, the accurate interpretation and analysis of such data depends heavily upon the robustness of the attributes/features used and the efficiency of the classification/segmentation stage. In this paper, we present a novel salt dome detection and tracking algorithm which combines the Hidden Markov Model (HMM) with the Active Contour Model (ACM). The HMM is used with a set of new features based on the Higher Order Singular Value Decomposition (HOSVD) of 3D seismic volumes to accurately delineate the boundaries of salt domes. The model parameters of the HMM are estimated using the Expectation-Maximization (EM) algorithm. The new HOSVD based features ensure that the proposed workflow overcomes the limitations of edge-based and texture-based methods. Furthermore, in order to alleviate the computational burden of the HMM, an ACM is applied on consecutive seismic images to track the changes of the salt dome boundary across the 3D seismic volume. We tested the proposed algorithm on real seismic data from the Netherlands offshore F3 block. Our algorithm, with only a small set of features, produces excellent results as compared to existing edge-based, texture-based, and fusion-based methods.

Background Positron emission tomography (PET) always suffers from high levels of noise due to the constraints of the injected dose and acquisition time, especially in the studies of dynamic PET imaging. To improve the quality of PET image, several approaches have been introduced to suppress noise. However, traditional filters often blur the image edges, or erase small detail, or rely on multiple parameters. In order to solve such problems, nonlocal denoising methods have been adapted to denoise PET images. Methods In this paper, we propose to use the weighted higher-order singular value decomposition for PET image denoising. We first modeled the noise in the PET image as Poisson distribution. Then, we transformed the noise to an additive Gaussian noise by use of the anscombe root transformation. Finally, we denoised the transformed image using the proposed higher-order singular value decomposition (HOSVD)-based algorithms. The denoised results were compared with results from some general filters by performing physical phantom and mice studies. Results Compared to other commonly used filters, HOSVD-based denoising algorithms can preserve boundaries and quantitative accuracy better. The spatial resolution and the low activity features in PET image also can be preserved by use of HOSVD-based methods. Comparing with the standard HOSVD-based algorithm, the proposed weighted HOSVD algorithm can suppress the stair-step artifact, and the time-consumption is about half of that needed by the Wiener-augmented HOSVD algorithm. Conclusions The proposed weighted HOSVD denoising algorithm can suppress noise while better preserving of boundary and quantity in PET images.

With the increasing availability of location-based services, location-based social networks and smart phones, standard rating schema of recommender systems that involve user and item dimensions is extended to three-dimensional (3-D) schema involving context information. Although there are models proposed for dealing with data in this form, the problem of combining it with additional features and constructing a general model suitable for different forms of recommendation system techniques has not been fully explored. This work proposes a technique to reduce 3-D rating data into 2-D for two reasons: employing already developed efficient methods for 2-D on a 3-D data and expanding it with additional features, which are usually 2-D also, if it is necessary. Our experiments show that this reduction is effective. The proposed 2-D model supports content-based, collaborative filtering and hybrid recommendation approaches effectively, whereas we have achieved the best accuracy results for pure collaborative filtering recommendation model. Since our method was built on efficient singular value decomposition-based dimension reduction idea, it also works very efficiently, and in our experiments, we have obtained better run-time results than standard methods developed for 3-D data using higher-order singular value decomposition.

In this chapter we cover the detailed implementation of PGD methods for the simplest problem, the Poisson equation. Detailed code is provided and its results compared with data available in the bibliography.