A fast approach for overcomplete sparse decomposition based on smoothed L0 norm

In this paper, a fast algorithm for overcomplete sparse decomposition, called SL0, is proposed. The algorithm is essentially a method for obtaining sparse solutions of underdetermined systems of linear equations, and its applications include underdetermined Sparse Component Analysis (SCA), atomic decomposition on overcomplete dictionaries, compressed sensing, and decoding real field codes. Contrary to previous methods, which usually solve this problem by minimizing the L1 norm using Linear Programming (LP) techniques, our algorithm tries to directly minimize the L0 norm. It is experimentally shown that the proposed algorithm is about two to three orders of magnitude faster than the state-of-the-art interior-point LP solvers, while providing the same (or better) accuracy.Comment: Accepted in IEEE Transactions on Signal Processing. For MATLAB codes, see (http://ee.sharif.ir/~SLzero). File replaced, because Fig. 5 was missing erroneousl

Myocardial infarct-sparing effect of ischemic preconditioning abrogated in cirrhotic rat through involvement of mitochondrial permeability transition pore

Despite all studies undertaken mechanism of cirrhotic cardiomyopathy the role of cirrhosis on ischemia-reperfusion (I/R) injury and ischemic preconditioning (IPC) phenomenon hasn't been explored yet. The aim of present study is to assess the relation between cirrhosis and IPC and the mitochondrial permeability transition pore (mPTP) role in IPC cardioprotective effects in cirrhotic rats. Material and method: Rat's heart were isolated and perfused with Krebs buffer by Langendorff method. Animals were equally divided into six groups (n=6): (I) I/R; hearts were subjected to 30 min ischemia and 45 min reperfusion, (II) IPC; IPC was induced via four cycle of 5 min regional ischemia followed by 5 min of reperfusion (III) common bile duct ligated (CBDL); hearts were subjected ischemia and reperfusion in cirrhotic rats, (IV) IPC-CBDL; four cycle of 5 min regional ischemia followed by 5 min of reperfusion in cirrhotic rats (V) CSA; Cyclosporine A was added 40 min prior to main ischemia (VI) CBDL+CSA. Results: Infarct size was increased significantly in IPC-CBDL group in comparison with IPC group (p< 0.05). Addition of CSA in CBDL+CSA group significantly decreased infarct size in comparison with IPC-CBDL group (p< 0.05). Ventricular arrhythmia severity was decreased significantly in IPC group compared to IR group, whereas it was increased significantly in IPC-CBDL group compared to IPC group (p< 0.05). CSA did not decrease arrhythmia score in CBDL group. Conclusion: The results showed that the cardioprotective effects of IPC are eliminated in cirrhosis. MPTP signaling in partly involve in cirrhotic cardiomyopathy

On the error of estimating the sparsest solution of underdetermined linear systems

Let A be an n by m matrix with m>n, and suppose that the underdetermined linear system As=x admits a sparse solution s0 for which ||s0||_0 < 1/2 spark(A). Such a sparse solution is unique due to a well-known uniqueness theorem. Suppose now that we have somehow a solution s_hat as an estimation of s0, and suppose that s_hat is only `approximately sparse', that is, many of its components are very small and nearly zero, but not mathematically equal to zero. Is such a solution necessarily close to the true sparsest solution? More generally, is it possible to construct an upper bound on the estimation error ||s_hat-s0||_2 without knowing s0? The answer is positive, and in this paper we construct such a bound based on minimal singular values of submatrices of A. We will also state a tight bound, which is more complicated, but besides being tight, enables us to study the case of random dictionaries and obtain probabilistic upper bounds. We will also study the noisy case, that is, where x=As+n. Moreover, we will see that where ||s0||_0 grows, to obtain a predetermined guaranty on the maximum of ||s_hat-s0||_2, s_hat is needed to be sparse with a better approximation. This can be seen as an explanation to the fact that the estimation quality of sparse recovery algorithms degrades where ||s0||_0 grows.Comment: To appear in December 2011 issue of IEEE Transactions on Information Theor

Linking genomics and metabolomics to chart specialized metabolic diversity

Microbial and plant specialized metabolites constitute an immense chemical diversity, and play key roles in mediating ecological interactions between organisms. Also referred to as natural products, they have been widely applied in medicine, agriculture, cosmetic and food industries. Traditionally, the main discovery strategies have centered around the use of activity-guided fractionation of metabolite extracts. Increasingly, omics data is being used to complement this, as it has the potential to reduce rediscovery rates, guide experimental work towards the most promising metabolites, and identify enzymatic pathways that enable their biosynthetic production. In recent years, genomic and metabolomic analyses of specialized metabolic diversity have been scaled up to study thousands of samples simultaneously. Here, we survey data analysis technologies that facilitate the effective exploration of large genomic and metabolomic datasets, and discuss various emerging strategies to integrate these two types of omics data in order to further accelerate discovery

Nonlinear mixture-wise expansion approach to underdetermined blind separation of nonnegative dependent sources

Underdetermined blind separation of nonnegative dependent sources consists in decomposing set of observed mixed signals into greater number of original nonnegative and dependent component (source) signals. That is an important problem for which very few algorithms exist. It is also practically relevant for contemporary metabolic profiling of biological samples, such as biomarker identification studies, where sources (a.k.a. pure components or analytes) are aimed to be extracted from mass spectra of complex multicomponent mixtures. This paper presents method for underdetermined blind separation of nonnegative dependent sources. The method performs nonlinear mixture-wise mapping of observed data in high-dimensional reproducible kernel Hilbert space (RKHS) of functions and sparseness constrained nonnegative matrix factorization (NMF) therein. Thus, original problem is converted into new one with increased number of mixtures, increased number of dependent sources and higher-order (error) terms generated by nonlinear mapping. Provided that amplitudes of original components are sparsely distributed, that is the case for mass spectra of analytes, sparseness constrained NMF in RKHS yields, with significant probability, improved accuracy relative to the case when the same NMF algorithm is performed on original problem. The method is exemplified on numerical and experimental examples related respectively to extraction of ten dependent components from five mixtures and to extraction of ten dependent analytes from mass spectra of two to five mixtures. Thereby, analytes mimic complexity of components expected to be found in biological samples

HypoRiPPAtlas as an Atlas of hypothetical natural products for mass spectrometry database search

Recent analyses of public microbial genomes have found over a million biosynthetic gene clusters, the natural products of the majority of which remain unknown. Additionally, GNPS harbors billions of mass spectra of natural products without known structures and biosynthetic genes. We bridge the gap between large-scale genome mining and mass spectral datasets for natural product discovery by developing HypoRiPPAtlas, an Atlas of hypothetical natural product structures, which is ready-to-use for in silico database search of tandem mass spectra. HypoRiPPAtlas is constructed by mining genomes using seq2ripp, a machine-learning tool for the prediction of ribosomally synthesized and post-translationally modified peptides (RiPPs). In HypoRiPPAtlas, we identify RiPPs in microbes and plants. HypoRiPPAtlas could be extended to other natural product classes in the future by implementing corresponding biosynthetic logic. This study paves the way for large-scale explorations of biosynthetic pathways and chemical structures of microbial and plant RiPP classes

Integrating genomics and metabolomics for scalable non-ribosomal peptide discovery.

Non-Ribosomal Peptides (NRPs) represent a biomedically important class of natural products that include a multitude of antibiotics and other clinically used drugs. NRPs are not directly encoded in the genome but are instead produced by metabolic pathways encoded by biosynthetic gene clusters (BGCs). Since the existing genome mining tools predict many putative NRPs synthesized by a given BGC, it remains unclear which of these putative NRPs are correct and how to identify post-assembly modifications of amino acids in these NRPs in a blind mode, without knowing which modifications exist in the sample. To address this challenge, here we report NRPminer, a modification-tolerant tool for NRP discovery from large (meta)genomic and mass spectrometry datasets. We show that NRPminer is able to identify many NRPs from different environments, including four previously unreported NRP families from soil-associated microbes and NRPs from human microbiota. Furthermore, in this work we demonstrate the anti-parasitic activities and the structure of two of these NRP families using direct bioactivity screening and nuclear magnetic resonance spectrometry, illustrating the power of NRPminer for discovering bioactive NRPs