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Sparse signal restoration is usually formulated as the minimization of a quadratic cost function \Vert \mbi y - \mbi A \mbi x \Vert2^{2} where \mbi A is a dictionary and \mbi x is an unknown sparse vector. It is well-known that imposing an \ell 0 constraint leads to an NP-hard minimization problem. The convex relaxation approach has received considerable attention, where the \ell 0-norm is replaced by the \ell 1-norm. Among the many effective \ell 1 solvers, the homotopy algorithm minimizes \Vert \mbi y - \mbi A \mbi x \Vert2^{2}+\lambda \Vert \mbi x \Vert 1 with respect to \mbi x for a continuum of \lambda ’s. It is inspired by the piecewise regularity of the \ell 1-regularization path, also referred to as the homotopy path. In this paper, we address the minimization problem \Vert \mbi y - \mbi A \mbi x \Vert2^{2}+\lambda \Vert \mbi x \Vert 0 for a continuum of \lambda ’s and propose two heuristic search algorithms for \ell 0-homotopy. Continuation Single Best Replacement is a forward–backward greedy strategy extending the Single Best Replacement algorithm, previously proposed for \ell 0-minimization at a given \lambda . The adaptive search of the \lambda -values is inspired by \ell 1-homotopy. \ell 0 Regularization Path Descent is a more complex algorithm exploiting the structural properties of the \ell 0-regularization path, which is piecewise constant with respect to \lambda . Both algorithms are empirically evaluated for difficult inverse problems involving ill-conditioned dictionaries. Finally, we show that they can be easily coupled with usual methods of model order selection. [ABSTRACT FROM PUBLISHER]

Common copy number variations (CNVs) refid="ref1"/ are small regions of genomic variations at the same loci across multiple samples, which can be detected with high resolution from next-generation sequencing (NGS) technique. Multiple sequencing data samples are often available from genomic studies; examples include sequences from multiple platforms and sequences from multiple individuals. By integrating complementary information from multiple data samples, detection power can be potentially improved. However, most of current CNV detection methods often process an individual sequence sample, or two samples in an abnormal versus matched normal study; researches on detecting common CNVs across multiple samples have been very limited but are much needed. In this paper, we propose a novel method to detect common CNVs from multiple sequencing samples by exploiting the concurrency of genomic variations in read depth signals derived from multiple NGS data. We use a penalized sparse regression model to fit multiple read depth profiles, based on which common CNV identification is formulated as a change-point detection problem. Finally, we validate the proposed method on both simulation and real data, showing that it can give both higher detection power and better break point estimation over several published CNV detection methods. [ABSTRACT FROM PUBLISHER]

Integrated analysis of multiple types of genomic data has received increasing attention in recently years, due to the rapid development of new genetic techniques and the strong demand for improvement of the reliability of these techniques. In this work, we proposed a sparse representation based clustering (SRC) method for joint analysis of gene expression and copy number data with the purpose to select significant genes/variables for identification of genes susceptible to a disease. Different from traditional gene selections methods, the proposed SRC model employs information of multifeatures and clusters the data into multi-groups, and then selects significant genes/variables in a particular group. By using joint features extracted from both types of data, the proposed SRC method provides an efficient approach to integrate different types of genomic measurements for comprehensive analysis. Our method has been tested on both breast cancer cell lines and breast tumors data. In addition, simulated data sets were used to test the robustness of the method to several factors such as noise, data sizes and data types. Experiments showed that our proposed method can effectively identify genes/variables with interesting characteristics, e.g., genes/variables with large variations across all genes, and genes/variables that are statistically significant in both measurements with strong correlations. The proposed method can be applicable to a wide variety of biological problems where joint analysis of biological measurements is a common challenge. [ABSTRACT FROM AUTHOR]

Reticular 2-bromo-2-methylpropionic acid (BMPA) modified Fe 3 O 4 nanoparticle aggregates with novel acoustic properties, namely the photoexcited audible sound (PEAS) effect, were prepared by a laser-induced irradiation method. Their morphology was observed by Lorentz transmission electron microscopy. Their chemical structure, crystal composition, and magnetic properties were analyzed using infrared spectroscopy, X-ray diffraction, and a magnetic property measurement instrument, respectively. It is found that the nanoparticle aggregates appeared reticular, with the size of the BMPA modified Fe 3 O 4 nanoparticles being 5.5 ± 0.4 nm. The saturation magnetization values of the BMPA modified Fe 3 O 4 nanoparticles and associated aggregates were 59.99 and 63.51 emu g -1 , respectively. The reticular BMPA modified nanoparticle aggregates can produce strong PEAS signals under very weak laser irradiation with great stability and repeatability. The emitted PEAS signals possessed strong specificity, suitable decay time and a large amount of information under a very weak laser power and can be detected by the human ear without any special detection equipment. Subsequently, a heat transfer model was constructed for the simulation of the possible mechanism of the PEAS effect using COMSOL software. The simulation results showed that the aggregates have a fast heat transfer rate with the temperature increasing to 480 K in only 0.25 s and 600 K in 5 s, respectively, meeting the requirements of the vapor explosion mechanism. Therefore, we realized that the possible mechanism of the PEAS effect of the reticular BMPA modified Fe 3 O 4 nanoparticle aggregates is laser-induced fast heat transfer and vapor explosion in situ , resulting in the observed audible sound phenomenon. This novel PEAS effect has potential for application in materials science, biomedical engineering and other fields.

To analyze the next generation sequencing data, the so-called read depth signal is often segmented with standard segmentation tools. However, these tools usually assume the signal to be a piecewise constant signal and contaminated with zero mean Gaussian noise, and therefore modeling error occurs. This paper models the read depth signal with piecewise Poisson distribution, which is more appropriate to the next generation sequencing mechanism. Based on the proposed model, an opti- mal dynamic programming algorithm with parallel computing is proposed to segment the piecewise signal, and furthermore detect the copy number variation.

It is realized that a combined analysis of different types of genomic measurements tends to give more reliable classification results. However, how to efficiently combine data with different resolutions is challenging. We propose a novel compressed sensing based approach for the combined analysis of gene expression and copy number variants data for the purpose of subtyping six types of Gliomas. Experimental results show that the proposed combined approach can substantially improve the classification accuracy compared to that of using either of individual data type. The proposed approach can be applicable to many other types of genomic data.

Copy number variation (CNV) is a structural variation in human genome that has been associated with many complex diseases. In this paper we present a method to detect common copy number variation from next generation sequencing data. First, copy number variations are detected from each individual sample, which is formulated as a total variation penalized least square problem. Second, the common copy number discovery from multiple samples is obtained using source separation techniques such as the non-negative matrix factorization (NMF). Finally, the method is applied to population clustering. The results on real data analysis show that two family trio with different ancestries can be clustered into two ethnic groups based on their common CNVs, demonstrating the potential of the proposed method for application to population genetics.