Block-wise Approach Research Articles

$$\mathcal H$$ H -FAINV: hierarchically factored approximate inverse preconditioners

Given a sparse matrix, its LU-factors, inverse and inverse factors typically suffer from substantial fill-in, leading to non-optimal complexities in their computation as well as their storage. In the past, several computationally efficient methods have been developed to compute approximations to these otherwise rather dense matrices. Many of these approaches are based on approximations through sparse matrices, leading to well-known ILU, sparse approximate inverse or factored sparse approximate inverse techniques and their variants. A different approximation approach is based on blockwise low rank approximations and is realized, for example, through hierarchical ($$\mathcal H$$H-) matrices. While $$\mathcal H$$H-inverses and $$\mathcal H$$H-LU factors have been discussed in the literature, this paper will consider the construction of an approximation of the factored inverse through $$\mathcal H$$H-matrices ($$\mathcal H$$H-FAINV). We will describe a blockwise approach that permits to replace (exact) matrix arithmetic through approximate efficient $$\mathcal H$$H-arithmetic. We conclude with numerical results in which we use approximate factored inverses as preconditioners in the iterative solution of the discretized convection---diffusion problem.

Performance of a blockwise approach in variable selection using linkage disequilibrium information.

BackgroundGenome-wide association studies (GWAS) aim at finding genetic markers that are significantly associated with a phenotype of interest. Single nucleotide polymorphism (SNP) data from the entire genome are collected for many thousands of SNP markers, leading to high-dimensional regression problems where the number of predictors greatly exceeds the number of observations. Moreover, these predictors are statistically dependent, in particular due to linkage disequilibrium (LD).We propose a three-step approach that explicitly takes advantage of the grouping structure induced by LD in order to identify common variants which may have been missed by single marker analyses (SMA). In the first step, we perform a hierarchical clustering of SNPs with an adjacency constraint using LD as a similarity measure. In the second step, we apply a model selection approach to the obtained hierarchy in order to define LD blocks. Finally, we perform Group Lasso regression on the inferred LD blocks. We investigate the efficiency of this approach compared to state-of-the art regression methods: haplotype association tests, SMA, and Lasso and Elastic-Net regressions.ResultsOur results on simulated data show that the proposed method performs better than state-of-the-art approaches as soon as the number of causal SNPs within an LD block exceeds 2. Our results on semi-simulated data and a previously published HIV data set illustrate the relevance of the proposed method and its robustness to a real LD structure. The method is implemented in the R package BALD (Blockwise Approach using Linkage Disequilibrium), available from http://www.math-evry.cnrs.fr/publications/logiciels.ConclusionsOur results show that the proposed method is efficient not only at the level of LD blocks by inferring well the underlying block structure but also at the level of individual SNPs. Thus, this study demonstrates the importance of tailored integration of biological knowledge in high-dimensional genomic studies such as GWAS.Electronic supplementary materialThe online version of this article (doi:10.1186/s12859-015-0556-6) contains supplementary material, which is available to authorized users.

A block-wise random sampling approach: Compressed sensing problem

The focus of this paper is to consider the compressed sensing problem. It is stated that the compressed sensing theory, under certain conditions, helps relax the Nyquist sampling theory and takes smaller samples. One of the important tasks in this theory is to carefully design measurement matrix (sampling operator). Most existing methods in the literature attempt to optimize a randomly initialized matrix with the aim of decreasing the amount of required measurements. However, these approaches mainly lead to sophisticated structure of measurement matrix which makes it very difficult to implement. In this paper we propose an intermediate structure for the measurement matrix based on random sampling. The main advantage of block-based proposed technique is simplicity and yet achieving acceptable performance obtained through using conventional techniques. The experimental results clearly confirm that in spite of simplicity of the proposed approach it can be competitive to the existing methods in terms of reconstruction quality. It also outperforms existing methods in terms of computation time.

Synthesis of a pentasaccharide and neoglycoconjugates related to fungal α-(1→3)-glucan and their use in the generation of antibodies to trace Aspergillus fumigatus cell wall.

3-Aminopropyl α-(1→3)-pentaglucoside, a fragment of α-(1→3)-glucan of the cell wall of Aspergillus fumigatus, has been synthesized in a blockwise approach. The application of mono- and disaccharide N-phenyltrifluoroacetimidates bearing a stereodirecting 6-O-benzoyl group was essential for stereoselective α-glucosylations. In the products, p-methoxyphenyl and levulinoyl groups served as orthogonal protecting groups for the anomeric position and 3-OH group, respectively. Their removal from shared blocks led to donors and acceptors that were used for the synthesis of pentasaccharides. Coupling of free α-(1→3)-pentaglucoside with biotin and bovine serum albumin (BSA) gave glycoconjugate tools for mycological studies. Immunization of mice with the BSA conjugate induced the generation of antibodies that recognize α-(1→3)-glucan on A. fumigatus cell wall and distinguish its morphotypes. This discovery represents a first step to the development of a diagnostic test system and a vaccine to detect and fight this life-threatening pathogen.

Block-Wise Two-Dimensional Maximum Margin Criterion for Face Recognition

Maximum margin criterion (MMC) is a well-known method for feature extraction and dimensionality reduction. However, MMC is based on vector data and fails to exploit local characteristics of image data. In this paper, we propose a two-dimensional generalized framework based on a block-wise approach for MMC, to deal with matrix representation data, that is, images. The proposed method, namely, block-wise two-dimensional maximum margin criterion (B2D-MMC), aims to find local subspace projections using unilateral matrix multiplication in each block set, such that in the subspace a block is close to those belonging to the same class but far from those belonging to different classes. B2D-MMC avoids iterations and alternations as in current bilateral projection based two-dimensional feature extraction techniques by seeking a closed form solution of one-side projection matrix for each block set. Theoretical analysis and experiments on benchmark face databases illustrate that the proposed method is effective and efficient.

Ultrasound echocardiography despeckling with non-local means time series filter

Ultrasound imaging is one of the most important instruments of modern medical imaging modalities. However, the usefulness of ultrasound imaging is degraded due to the presence of a signal-dependent noise known as speckle. Recently, lots of algorithms have been proposed for despeckling. Unfortunately, few attentions have been paid on time series of ultrasound images like echocardiography. In this paper, we address this problem by developing a time series non-local means (NLM) filter algorithm. A distance measure relevant to a speckle model is firstly introduced to take place of the Gaussian-weighted Euclidian distance according to a Bayesian formulation. By taking the information along the temporal axis into account, we further extend the NLM filter from single frame to image time series. To lighten the computational burden, a blockwise approach and a pre-classification process are used to accelerate the algorithm. In order to evaluate our method, experiments are conducted on both synthetic and in vivo ultrasound images. Experiments show that the proposed method achieves satisfactory results in terms of removing the speckle and preserving the edges and image details, compared with the state-of-the-art methods.

Disparity-based space-variant image deblurring

Obtaining a good-quality image requires exposure to light for an appropriate amount of time. If there is camera or object motion during the exposure time, the image is blurred. To remove the blur, some recent image deblurring methods effectively estimate a point spread function (PSF) by acquiring a noisy image additionally, and restore a clear latent image with the PSF. Since the groundtruth PSF varies with the location, a blockwise approach for PSF estimation has been proposed. However, the block to estimate a PSF is a straightly demarcated rectangle which is generally different from the shape of an actual region where the PSF can be properly assumed constant. We utilize the fact that a PSF is substantially related to the local disparity between two views. This paper presents a disparity-based method of space-variant image deblurring which employs disparity information in image segmentation, and estimates a PSF, and restores a latent image for each region. The segmentation method firstly over-segments a blurred image into sufficiently many regions based on color, and then merges adjacent regions with similar disparities. Experimental results show the effectiveness of the proposed method.

Efficient block-wise independent component analysis with optimal learning rate

Independent component analysis (ICA) is a potential solution for blind source separation (BSS) problems and has proven to be effective in many practical applications. One major drawback for ICA algorithms is its heavy computation load which is especially deteriorated in long-term signals. To solve this problem, the block-wise approach is proposed to improve the computational efficiency in this study. As ambiguities of variances and order of the separated components exist for ICA algorithms, signal reconstruction is an issue for block-wise approach. In this study, correlation coefficients (CC) of the short-term Fourier transform (STFT) among those acquired from the neighboring blocks are adopted for order permutation and phase correction of the separated signals. The weights of the separated signals are then normalized by the maximum amplitude of the corresponding one in previous block to avoid the variance ambiguity. Two robust ICA algorithms based on iterative matrix inversion approach, one with fixed nonlinear functions whereas another one with flexibly selected nonlinear functions, are implemented in both batch and block-wise processing for performance evaluation. Linearly mixed biopotential signals (ECG and EMG) and 60-Hz sinusoid are incorporated for the experiments. The results reveal that the proposed block-wise approach can attain the desired requirements in a more efficient way without loss of the separation performance. The proposed approach may be a potential tool for which the computational efficiency is an important issue.

Tracking survival of institutional births for neonatal period-feasibility at district hospitals

We assessed the feasibility of involving routine district health system personnel in tracking survival of institutional births for neonatal period in two district hospitals (Nagaur in Rajasthan and Chhatarpur in Madhya Pradesh) for the month of March 2010. A centralized district level tracking system was used in Nagaur, whereas in Chattarpur, block-wise tracking of births was performed. A total of 607 live births were tracked with 17 identified neonatal deaths. Prematurity and infections were commonest causes of deaths with majority occurring within first week of life. The block-wise approach resulted in identifying extra neonatal deaths.

Synthesis of octyl S-glycosides of tri- to pentasaccharide fragments related to the GPI anchor of Trypanosoma brucei

The three oligosaccharide octyl-S-glycosides Man-α1,6-Man-α1,4-GlcNH 2-α1, S-Octyl ( 19), Man-α1,6-(Gal-α1,3)Man-α1,4-GlcNH 2-α1, S-Octyl ( 27) and Man-α1,2-Man-α1,6-(Gal-α1,3)Man-α1,4-GlcNH 2-α1, S-Octyl ( 37), related to the GPI anchor of Trypanosoma brucei were prepared by a stepwise and block-wise approach from octyl 2-azido-2-deoxy-3,6-di- O-benzyl-1-thio-α- d-glucopyranoside ( 8) and octyl 2- O-benzoyl-4,6- O-(1,1,3,3-tetraisopropyl-1,3-disiloxane-1,3-diyl)-1-thio-α- d-mannopyransoside ( 9). Glucosamine derivative 8 was obtained from 1,3,4,6-tetra- O-acetyl-2-azido-2-desoxy-β- d-glucopyranose ( 1) in five steps. Mannoside 9 was converted into the corresponding imidate 12 and coupled with 8 to give disaccharide octyl-S-glycoside 13 which was further mannosylated to afford trisaccharide 19 upon deprotection. Likewise, mannoside 9 was galactosylated, converted into the corresponding imidate and coupled with 8 to give trisaccharide 25. Mannosylation of the latter afforded tetrasaccharide 27 upon deprotection. Condensation of 25 with disaccharide imidate 35 gave, upon deprotection of the intermediates, the corresponding pentasaccharide octyl-S-glycoside 37. Saccharides 19, 27 and 37 are suitable substrates for studying the enzymatic glycosylation pattern of the GPI anchor of T. brucei.

Synthesis of five nona-β-(1→6)- d-glucosamines with various patterns of N-acetylation corresponding to the fragments of exopolysaccharide of Staphylococcus aureus

A series of five 3-acetamidopropyl β-glycosides of nona-β-(1→6)-glucosamines containing two N-acetylglucosamine residues separated by a different number of glucosamine units with free amino groups have been synthesized using a convergent blockwise approach. Oxazoline glycosylation was used to introduce N-acetylglucosamine residues. These nonasaccharides are structurally related to the poly- N-acetylglucosamine (PNAG) extracellular polysaccharide of Staphylococcus aureus and can be used as models for biochemical and immunological studies.

Block-wise construction of tree-like relational features with monotone reducibility and redundancy

We describe an algorithm for constructing a set of tree-like conjunctive relational features by combining smaller conjunctive blocks. Unlike traditional level-wise approaches which preserve the monotonicity of frequency, our block-wise approach preserves monotonicity of feature reducibility and redundancy, which are important in propositionalization employed in the context of classification learning. With pruning based on these properties, our block-wise approach efficiently scales to features including tens of first-order atoms, far beyond the reach of state-of-the art propositionalization or inductive logic programming systems.

Block-wise 2D kernel PCA/LDA for face recognition

Direct extension of (2D) matrix-based linear subspace algorithms to kernel-induced feature space is computationally intractable and also fails to exploit local characteristics of input data. In this letter, we develop a 2D generalized framework which integrates the concept of kernel machines with 2D principal component analysis (PCA) and 2D linear discriminant analysis (LDA). In order to remedy the mentioned drawbacks, we propose a block-wise approach based on the assumption that data is multi-modally distributed in so-called block manifolds. Proposed methods, namely block-wise 2D kernel PCA (B2D-KPCA) and block-wise 2D generalized discriminant analysis (B2D-GDA), attempt to find local nonlinear subspace projections in each block manifold or alternatively search for linear subspace projections in kernel space associated with each blockset. Experimental results on ORL face database attests to the reliability of the proposed block-wise approach compared with related published methods.

Synthesis of β-(1→6)-linked glucosamine oligosaccharides corresponding to fragments of the bacterial surface polysaccharide poly- N-acetylglucosamine

A series of 3-β-acetamidopropyl oligo-β-(1→6)-glucosamines consisting of 5, 7, 9 and 11 glucosamine residues, and a series of corresponding per-N-acetylated derivatives were synthesized using a convergent blockwise approach. These compounds represent fragments of a bacterial surface polysaccharide produced by numerous bacterial pathogens, including Staphylococcus aureus, and will be used as models for its biochemical and immunological properties.

Synthesis of Ligands Related to the O‐Specific Polysaccharides of Shigella flexneri Serotype 2a and Shigella flexneri Serotype 5a. Part 10. Blockwise Approach to Fragments of the O‐Specific Polysaccharide of Shigella flexneri Serotype 2a: Convergent Synthesis of a Decasaccharide Representative of a Dimer of the Branched Repeating Unit.

Synthesis of Ligands Related to the O‐Specific Polysaccharides of Shigella flexneri Serotype 2a and Shigella flexneri Serotype 5a. Part 10. Blockwise Approach to Fragments of the O‐Specific Polysaccharide of Shigella flexneri Serotype 2a: Convergent Synthesis of a Decasaccharide Representative of a Dimer of the Branched Repeating Unit.

Synthesis of Streptococcus pneumoniae Type 3 Neoglycoproteins Varying in Oligosaccharide Chain Length, Loading and Carrier Protein

The preparation is described of a range of neoglycoproteins containing synthesised fragments of the capsular polysaccharide of Streptococcus pneumoniae type 3, that is β-D-GlcpA-(1→4)-β-D-Glcp-(1→O)-(CH2)3NH2 (1), β-D-Glcp-(1→3)-β-D-GlcpA-(1→4)-β-D-Glcp-(1→O)-(CH2)3NH2 (2), and β-D-GlcpA-(1→4)-β-D-Glcp-(1→3)-β-D-GlcpA-(1→4)-β-D-Glcp-(1→O)-(CH2)3NH2 (3). A blockwise approach was developed for the synthesis of the protected carbohydrate chains, in which the carboxylic groups were introduced prior to deprotection by selective oxidation of HO-6 in the presence of HO-4 by using TEMPO (2,2,6,6-tetramethyl-1-piperidinyloxy radical). After deprotection, the 3-aminopropyl spacer of the fragments was elongated with diethyl squarate (3,4-diethoxy-3-cyclobutene-1,2-dione) and the elongated oligosaccharides were conjugated to CRM197 (cross-reacting material of diphtheria toxin), KLH (keyhole limpet hemocyanin) or TT (tetanus toxoid). The resulting neoglycoconjugates varied in oligosaccharide chain length, oligosaccharide loading and protein carrier. These well-defined conjugates are ideal probes for evaluating the influence of the different structural parameters in immunological tests.

Synthesis of Streptococcus pneumoniae type 3 neoglycoproteins varying in oligosaccharide chain length, loading and carrier protein.

The preparation is described of a range of neoglycoproteins containing synthesised fragments of the capsular polysaccharide of Streptococcus pneumoniae type 3, that is beta-D-GlcpA-(1-->4)-beta-D-Glcp-(1-->O)-(CH2)3NH2 (1), beta-D-Glcp-(1-->3)-beta-D-GlcpA-(1-->4)-beta-D-Glcp-(1-->O)-(CH2)3NH2 (2), and beta-D-GlcpA-(1-->4)-beta-D-Glcp-(1-->3)-beta-D-GlcpA-(1-->4)-beta-D-Glcp-(1-->O)-(CH4)NH2 (3). A blockwise approach was developed for the synthesis of the protected carbohydrate chains, in which the carboxylic groups were introduced prior to deprotection by selective oxidation of HO-6 in the presence of HO-4 by using TEMPO (2,2,6,6-tetramethyl-1-piperidinyloxy radical). After deprotection, the 3-aminopropyl spacer of the fragments was elongated with diethyl squarate (3,4-diethoxy-3-cyclobutene-1,2-dione) and the elongated oligosaccharides were conjugated to CRM197 (cross-reacting material of diphtheria toxin), KLH (keyhole limpet hemocyanin) or TT (tetanus toxoid). The resulting neoglycoconjugates varied in oligosaccharide chain length, oligosaccharide loading and protein carrier. These well-defined conjugates are ideal probes for evaluating the influence of the different structural parameters in immunological tests.

Block-wise physical model synthesis for musical acoustics

A block-wise approach to sound synthesis based on nonlinear wave digital modelling is proposed. Starting from a semantic description of the physical model, the technique generates, validates and initialises appropriate simulation source code with time-varying parameters.

Glycosylated peptoids as prototypical HIV-1 protease inhibitors

Using a blockwise approach, N-substituted oligoglycine (NSGs) peptoids bearing N-acetylglucosamine residues in different position of the side chain were efficiently synthesized by a reiterative strategy involving mono N-alkylation and bromoacetylation.

Oligomeric glycopeptidomimetics bearing the cancer related T N-antigen

α- O-Linked N-acetylgalatosamine clusters with 2, 3, 4, 6, and 8 repeating units were synthesized using a reiterative blockwise approach and N-substituted oligoglycine peptoid backbones. Orthogonally protected glycopeptide 5 and 7 were used as key building blocks.