Improving the efficiency of multidimensional scaling in the analysis of high-dimensional data using singular value decomposition

MOTIVATION: Multidimensional scaling (MDS) is a well-known multivariate statistical analysis method used for dimensionality reduction and visualization of similarities and dissimilarities in multidimensional data. The advantage of MDS with respect to singular value decomposition (SVD) based methods such as principal component analysis is its superior fidelity in representing the distance between different instances specially for high-dimensional geometric objects. Here, we investigate the importance of the choice of initial conditions for MDS, and show that SVD is the best choice to initiate MDS. Furthermore, we demonstrate that the use of the first principal components of SVD to initiate the MDS algorithm is more efficient than an iteration through all the principal components. Adding stochasticity to the molecular dynamics simulations typically used for MDS of large datasets, contrary to previous suggestions, likewise does not increase accuracy. Finally, we introduce a k nearest neighbor method to analyze the local structure of the geometric objects and use it to control the quality of the dimensionality reduction. RESULTS: We demonstrate here the, to our knowledge, most efficient and accurate initialization strategy for MDS algorithms, reducing considerably computational load. SVD-based initialization renders MDS methodology much more useful in the analysis of high-dimensional data such as functional genomics datasets.     

Identification of soil quality indicators for assessing the effect of different tillage practices through a soil quality index in a semi-arid environment

Tillage is known to potentially affect soil quality in various ways. In this study, a soil quality index (SQI) was developed by quantifying several soil attributes either sensitive or insensitive to physical disturbance, using factor analysis as a dimension reduction technique, in order to discriminate different tillage systems. Soil properties including physical (MWD), chemical (pH, organic C, total N, available P and POM contents) and microbial (MBC, MBN, PCM, PNM and three enzymes) parameters were measured to establish a minimum data set (MDS) for the assessment of overall SQI. The soil attributes were determined on samples (0–20 cm depth) collected under moldboard (MP) and disk (DP) plows as conventional tillage (CT), and rotary (RP) and chisel (CP) plows as reduced tillage (RT) systems with a similar plant C input rate and cover crop over a period of six years (2005–2011) in a semi-arid calcareous soil (Calcixerepts) from Central Iran. Results indicated a clear difference in soil quality among the tillage systems with a significant increase of SQI under RT over time, particularly under CP practices. Although RT improved most soil microbial attributes, not all attributes contributed to SQI because of their close interrelationship. The final SQI consisted only of geometric mean of microbial activity (GMA, the square root of the product of PCM and PNM) and geometric mean of enzyme activity (GME, the cube root of the product of enzyme activities). Soil GME and GMA were found to be as key indicators contributing 55% and 36% to SQI, respectively. Therefore, the GME and GMA were the most important indicators effectively discriminating tillage systems, and could be used to monitor the enhancement of soil quality under RT in this semiarid environment. The influence of tillage year on SQI was greater than that of tillage practices. In conclusion, RT systems were characterized by a higher value of SQI, suggesting a good recovery of soil capacity and functions after abandoning CT in the studied area. Smallholder farmers should therefore be aware of the potential for high soil quality in future as a result of continuing RT systems, especially with surface tillage using CP practices.     

Multidimensional scaling for large genomic data sets

Background  

Multi-dimensional scaling (MDS) is aimed to represent high dimensional data in a low dimensional space with preservation of the similarities between data points. This reduction in dimensionality is crucial for analyzing and revealing the genuine structure hidden in the data. For noisy data, dimension reduction can effectively reduce the effect of noise on the embedded structure. For large data set, dimension reduction can effectively reduce information retrieval complexity. Thus, MDS techniques are used in many applications of data mining and gene network research. However, although there have been a number of studies that applied MDS techniques to genomics research, the number of analyzed data points was restricted by the high computational complexity of MDS. In general, a non-metric MDS method is faster than a metric MDS, but it does not preserve the true relationships. The computational complexity of most metric MDS methods is over O(N ² ), so that it is difficult to process a data set of a large number of genes N, such as in the case of whole genome microarray data.     

Cytogenetic characteristics of patients with signs and symptoms of myelodysplastic syndromes in the State of Pará, Brazil

The myelodysplastic syndromes (MDS) are clonal hematopoietic diseases characterized by medullary dysplasia, cytopenias, and frequent evolution to acute myeloid leukemia. In 1982, the French-American-British (FAB) group proposed a classification for the MDS, based on morphological characteristics of peripheral blood and of the bone marrow. Later, cytogenetics proved to be a useful tool for the refinement of prognosis, through the use of the International Prognosis Score System (IPSS), as well as through evidence of clonality. Recently, the World Health Organization (WHO) proposed a new classification for the MDS, based on significant modifications of the FAB proposal, with the inclusion of chromosome analysis. A cytogenetic analysis was made of 17 patients with symptoms of MDS in the State of Para, based on WHO recommendations, and application of the IPSS. Good metaphases were obtained for 13 patients; 12 had a normal karyotype and only one had a clonal abnormality, del(3)(p25). The genes related to neoplastic processes that have been mapped to 3p are: XPC in 3p25.1 and FANCD2 and VHL in 3p25-26. Four patients had classic symptoms of MDS; in the rest the possibility of MDS was excluded or several months of observation before diagnosis were recommended. Among those with MDS, it was not possible to apply IPSS and WHO recommendations, because fundamental data were lacking, specifically the medullary blast and ring sideroblast counts. We advocate the implementation of routine cytogenetic analyses for the study of MDS, especially in patients with moderate hematopoietic dysplasia.     

基于茎干直径微变化制定苹果灌溉制度

茎干直径的动态微变化是研究植物体水分和生长状况的重要指标。利用测树器监测西北旱区盛果期苹果树茎干直径微变化规律,根据监测记录获得茎干直径日最大值(MXTD)、茎干直径日最大收缩量(MDS)数据,并探讨茎干直径微变化规律及其对环境因素的响应,为茎干直径微变化用于指导精确灌溉提供科学依据。实验结果表明,晴天或多云天气下,苹果树茎干直径在每天的7:00或8:00时刻达到一天最大值,在16:00左右达到一天的最小值,茎干直径年增长量与果实产量成反比例关系。整个生育期MXTD呈先快速增加后平稳的变化特征。2010年MDS与茎干水势(φstem)呈显著负相关关系(r2=0.76***,n=14),这表明MDS可以反映苹果树的水势状况。生育后期的MDS对环境因素响应比生育前期敏感,全生育期MDS与气象因素的决定系数大小顺序为日最大水汽压差(VPDmax)日最高温度(Tmax)净辐射(Rn)。茎干直径微变化规律可以反映西北旱区盛果期果树的水分状况,可以为果园灌溉制度的确定提供科学依据。     

Thionin Staining of Paraffin and Plastic Embedded Sections of Cartilage

The usefulness of thionin for staining cartilage sections embedded in glycol meth-acrylate (GMA) and the effect of decalcification on cartilage sections embedded in paraffin and GMA were assessed. Short decalcification periods using 5% formic acid or 10% EDTA did not influence the staining properties or the morphology of cartilage matrix and chondrocytes. The standard stain safranin O-fast green for differential staining of cartilage was used as control in these experiments. Prolonged exposure of safranin P stained sections to fast green resulted in disappearance of the safranin O stained matrix, thereby hampering the quantitative measurement of negatively charged glycosaminoglycans (GAG). Thionin stained evenly throughout all cartilage layers, independent of the staining times. In contrast to safranin 0, thionin did not show meta-chromasia in nondehydrated cartilage sections, which made it more suitable for assessing cartilage quality in GMA embedded cartilage. To evaluate the selectivity of thionin staining in cartilage, chondroitinase ABC and trypsin digestions were carried out. Thionin staining was prevented by these enzymes in the territorial matrix, representing the interlacunar network and the chondrocyte capsule. Staining with thionin of the interterritorial matrix was only slightly reduced, possibly representing keratan sulfate and hyaluronic acid in cartilage of elderly patients. Comparison of thionin stained GMA embedded cartilage with safranin O stained paraffin embedded sections showed significant similarity in optical densitometry, indicative of the specificity of thionin bound to negatively charged GAG in cartilage. In GMA embedded cartilage morphology was relatively intact compared to paraffin embedded sections due to less shrinkage of chondrocytes and the interlacunar network.     

Do multivariate analyses incorporating changes in pattern across taxonomic levels reveal anthropogenic stress in Mediterranean lagoons?

It is accepted that observed patterns in community structure change as analyses are carried out at higher taxonomic levels. Univariate analyses which incorporate higher taxonomic structure within assemblages have been shown to be informative. In this paper we suggest ways in which changes in multivariate relationships at higher taxonomic levels and associated with higher taxonomic/phylogenetic structure of the community may be incorporated into multivariate analyses, an aspect never occurred before in this type of analysis. Four approaches, namely: biodiversity MDS (bdMDS), number of taxa MDS (ntMDS), delta MDS (δMDS) and lambda MDS (λMDS), are proposed, and applied to theoretical data as well as to data collected from the literature on the Mediterranean lagoonal environment. Results show that these approaches have the capacity to distinguish severely impacted lagoons from naturally disturbed ones, although in practice the simplest method (ntMDS) was the most successful. Analyses based on the most abundant groups (polychaetes, molluscs, crustaceans) did not always match analyses based on the entire macrofauna, mirroring the performance of taxonomic distinctness indices in the Mediterranean lagoons. The important characteristics of the approaches introduced, as well as potential criticisms are provided. Application of these techniques on smaller scales and to other habitats, is suggested prior to their wider use in the region.     

Thionin Staining of Paraffin and Plastic Embedded Sections of Cartilage

The usefulness of thionin for staining cartilage sections embedded in glycol meth-acrylate (GMA) and the effect of decalcification on cartilage sections embedded in paraffin and GMA were assessed. Short decalcification periods using 5% formic acid or 10% EDTA did not influence the staining properties or the morphology of cartilage matrix and chondrocytes. The standard stain safranin O-fast green for differential staining of cartilage was used as control in these experiments. Prolonged exposure of safranin P stained sections to fast green resulted in disappearance of the safranin O stained matrix, thereby hampering the quantitative measurement of negatively charged glycosaminoglycans (GAG). Thionin stained evenly throughout all cartilage layers, independent of the staining times. In contrast to safranin 0, thionin did not show meta-chromasia in nondehydrated cartilage sections, which made it more suitable for assessing cartilage quality in GMA embedded cartilage. To evaluate the selectivity of thionin staining in cartilage, chondroitinase ABC and trypsin digestions were carried out. Thionin staining was prevented by these enzymes in the territorial matrix, representing the interlacunar network and the chondrocyte capsule. Staining with thionin of the interterritorial matrix was only slightly reduced, possibly representing keratan sulfate and hyaluronic acid in cartilage of elderly patients. Comparison of thionin stained GMA embedded cartilage with safranin O stained paraffin embedded sections showed significant similarity in optical densitometry, indicative of the specificity of thionin bound to negatively charged GAG in cartilage. In GMA embedded cartilage morphology was relatively intact compared to paraffin embedded sections due to less shrinkage of chondrocytes and the interlacunar network.     

Dynamic models of gene expression and classification

Powerful new methods, like expression profiles using cDNA arrays, have been used to monitor changes in gene expression levels as a result of a variety of metabolic, xenobiotic or pathogenic challenges. This potentially vast quantity of data enables, in principle, the dissection of the complex genetic networks that control the patterns and rhythms of gene expression in the cell. Here we present a general approach to developing dynamic models for analyzing time series of whole genome expression. In this approach, a self-consistent calculation is performed that involves both linear and non-linear response terms for interrelating gene expression levels. This calculation uses singular value decomposition (SVD) not as a statistical tool but as a means of inverting noisy and near-singular matrices. The linear transition matrix that is determined from this calculation can be used to calculate the underlying network reflected in the data. This suggests a direct method of classifying genes according to their place in the resulting network. In addition to providing a means to model such a large multivariate system this approach can be used to reduce the dimensionality of the problem in a rational and consistent way, and suppress the strong noise amplification effects often encountered with expression profile data. Non-linear and higher-order Markov behavior of the network are also determined in this self-consistent method. In data sets from yeast, we calculate the Markov matrix and the gene classes based on the linear-Markov network. These results compare favorably with previously used methods like cluster analysis. Our dynamic method appears to give a broad and general framework for data analysis and modeling of gene expression arrays. Electronic Publication     

Inbreeding effective population size and parentage analysis without parents

An important use of genetic parentage analysis is the ability to directly calculate the number of offspring produced by each parent (k(i)) and hence effective population size, N(e). But what if parental genotypes are not available? In theory, given enough markers, it should be possible to reconstruct parental genotypes based entirely on a sample of progeny, and if so the vector of parental k(i) values. However, this would provide information only about parents that actually contributed offspring to the sample. How would ignoring the 'null' parents (those that produced no offspring) affect an estimate of N(e)? The surprising answer is that null parents have no effect at all. We show that: (i) The standard formula for inbreeding N(e) can be rewritten so that it is a function only of sample size and ∑(k(2)(i)); it is not necessary to know the total number of parents (N). This same relationship does not hold for variance N(e). (ii) This novel formula provides an unbiased estimate of N(e) even if only a subset of progeny is available, provided the parental contributions are accurately determined, in which case precision is also high compared to other single-sample estimators of N(e). (iii) It is not necessary to actually reconstruct parental genotypes; from a matrix of pairwise relationships (as can be estimated by some current software programs), it is possible to construct the vector of k(i) values and estimate N(e). The new method based on parentage analysis without parents (PwoP) can potentially be useful as a single-sample estimator of contemporary N(e), provided that either (i) relationships can be accurately determined, or (ii) ∑(k(2)(i)) can be estimated directly.     

Monoclonal antibody panels for acute leukemia and myelodysplastic syndrome diagnosis. Results of a co-operative quality control group

The need for standardization criteria and result reproducibility in immunophenotyping hematological diseases has increased along with their clinical importance. Our group "Policentric Study Group on Immunological Markers", is composed of 40 laboratories. Its aim, over recent years, has been to find a standardized way of immunophenotypic analysis applicable to various hematological diseases. The objective of this study is to contribute to the debate concerning standardization of monoclonal antibody panels and immunophenotypic analysis procedures in acute leukemia (AL) and myelodysplastic syndrome (MDS), with the following targets: to improve interlaboratory reproducibility of the immunophenotyping data, and interpretative results; to study, with improved feasibility, correlation between immunophenotype and clinical or biological findings on a large number of AL and MDS cases; to verify the utility of the proposed monoclonal antibody panels for proper AL and MDS classification, and to detect minimal residual disease. In the field of AL and MDS our experience is based on about 1800 and 700 cases respectively analyzed over the last five years. Starting from these experiences and data of the literature we have elaborated the proposed panels of monoclonal antibodies and the methods of analysis. We have suggested a standardized immunophenotypic approach to study AL and MDS. In particular our work has focused on the gating strategy. This aims at drawing a gate of analysis having high purity and recovery, and on the choice of monoclonal antibody combinations for multiparametric analysis, particularly the normal antigen expression on each step of lineage differentiation or their clinically relevant aberrant expressions. A standardized criteria has become a necessary starting point in any kind of analytical process. In the field of acute leukemias and myelodysplastic syndromes the work of this polycentric group has focused on the pre-analytical and analytical steps to be taken in cytometric evaluation of hematological malignancies. The results obtained may contribute to reaching intra and inter-laboratory reproducibility.     

A New Method for Flat Embedding in Glycol Methacrylate

Glycol methacrylate (GMA) is a useful polymer for embedding tissue because of its stability, hydrophilic properties, and resistance to many solvents (Feder a d O'Brien 1968, Bennett et a/. 1976). Undue solvent extraction is also avoided as GMA contains water, making complete dehydration unnecessary (Cole and Sykes 1974). This property shows some evidence that GMA embedded sections may be useful in energy dispersive analysis by X-ray for some elements (DeNee et al. 1977). GMA also does not exclude water soluble dye molecules and has thus become a useful medium for histochemical studies (Bennett et al. 1976).     

Analysis and visualization of tree space

We explored the use of multidimensional scaling (MDS) of tree-to-tree pairwise distances to visualize the relationships among sets of phylogenetic trees. We found the technique to be useful for exploring "tree islands" (sets of topologically related trees among larger sets of near-optimal trees), for comparing sets of trees obtained from bootstrapping and Bayesian sampling, for comparing trees obtained from the analysis of several different genes, and for comparing multiple Bayesian analyses. The technique was also useful as a teaching aid for illustrating the progress of a Bayesian analysis and as an exploratory tool for examining large sets of phylogenetic trees. We also identified some limitations to the method, including distortions of the multidimensional tree space into two dimensions through the MDS technique, and the definition of the MDS-defined space based on a limited sample of trees. Nonetheless, the technique is a useful approach for the analysis of large sets of phylogenetic trees.     

Rapid diagnosis of Miller-Dieker syndrome and isolated lissencephaly sequence by the polymerase chain reaction

Summary Probe YNZ22 (D17S5) is a highly polymorphic, variable number tandem repeat (VNTR) marker previously shown to be deleted in all patients with the Miller-Dieker syndrome (MDS) but not in patients with isolated lissencephaly sequence (ILS). Primers were constructed to the unique sequence flanking the polymorphic, repetitive region of YNZ22 for amplification by the polymerase chain reaction (PCR). Analysis of 118 normal individuals revealed 12 alleles (differing in copy number of a 70-bp repeat unit) ranging in size from 168 to 938 bp. A retrospective study of eight MDS and six ILS patients was consistent with Southern blot analysis in all cases except one. In the latter, a very large allele (12 copies of the repeat unit) in a patient and her mother failed to amplify on initial attempts, but was successfully amplified by reducing the concentration of genomic DNA used in the reaction. Prospective studies on two MDS and five ILS patients were successfully performed and confirmed in all cases by Southern blot analysis. From the total sample, restriction fragment length polymorphism (RFLP) analysis was fully informative in four of ten MDS patients and showed a deletion in all four cases. Nine of eleven ILS patients were heterozygous and therefore not deleted for YNZ22. Development of primers for additional polymorphic markers in the Miller-Dieker region will lead to a rapid PCR-based diagnostic approach for all MDS and ILS patients. PCR typing of YNZ22 will also facilitate use of this marker in other applications, including genetic linkage, paternity and forensic studies, and analysis of loss of heterozygosity in tumors.     

Substrate Access to Cytochrome P450cam: A Comparison of a Thermal Motion Pathway Analysis with Molecular Dynamics Simulation Data

Cytochrome P450 enzymes are hemoprotein monooxygenases that catalyse the oxidation of a variety of compounds. The mechanism by which camphor, the natural substrate of Cytochrome P450cam (P450cam), accesses the active site is a long-standing puzzle, although putative access channels have been proposed. A thermal motion pathway (TMP) analysis was performed on the crystal structure of P450cam with camphor bound. Hereby, three distinct thermal motion pathway families (TMPFs) were found. Possible substrate access channels obtained by this analysis based on B-factors are compared with exit channels explored by molecular dynamics simulations (MDS) by imposing an artificial expulsion force on the substrate in addition to the standard MD force field. Two out of three TMPFs are supported by results obtained with the random expulsion MDS method. However, the pathway found by the TMP method to have the highest average B-factor could not be observed by MDS. The pathway proposed from crystallographic data, which is a small opening above the active site located near residues 185, 87 and 395 corresponds to the TMPF with the second highest average B-factor.     

Fast computing betweenness centrality with virtual nodes on large sparse networks

Betweenness centrality is an essential index for analysis of complex networks. However, the calculation of betweenness centrality is quite time-consuming and the fastest known algorithm uses O(N(M + N log N)) time and O(N + M) space for weighted networks, where N and M are the number of nodes and edges in the network, respectively. By inserting virtual nodes into the weighted edges and transforming the shortest path problem into a breadth-first search (BFS) problem, we propose an algorithm that can compute the betweenness centrality in O(wDN2) time for integer-weighted networks, where w is the average weight of edges and D is the average degree in the network. Considerable time can be saved with the proposed algorithm when w < log N/D + 1, indicating that it is suitable for lightly weighted large sparse networks. A similar concept of virtual node transformation can be used to calculate other shortest path based indices such as closeness centrality, graph centrality, stress centrality, and so on. Numerical simulations on various randomly generated networks reveal that it is feasible to use the proposed algorithm in large network analysis.     

Trends of classification,incidence, mortality,and survival of MDS patients in Switzerland between 2001 and 2012

Myelodysplastic syndromes (MDS) are emerging disorders of the elderly with an increasing burden on healthcare systems. He we report on the first population-based, epidemiological analysis of patients diagnosed with MDS in Switzerland between 2001 and 2012. The aim of this study was to characterize the extent and limitations of currently available population-based, epidemiological data and formulate recommendations for future health services research. The investigated outcomes comprised trends of annual case frequency, classification of morphological subtypes, incidence, mortality and survival. Annual case frequency increased by 20% (from 263 to 315 cases per year), whereas age-standardized incidence-/mortality-rates remained stable (2.5/1.1 per 100′000 person-years). This observation reflects population growth as well as higher diagnostic awareness and not an increase of age-specific risk. However, it will inevitably influence the future prevalence of MDS and the impact on healthcare systems. Reporting of classification in MDS subtypes was poor with modest improvement from 20% to 39% and increased awareness for mainly higher-risk diseases. Relative survival for all patients at 5-years (RS) ranged between 37 and 40%. Significant better RS was found for younger compared to older higher-risk MDS patients (48% vs. 17%), reflecting the effect of allogeneic hematopoietic stem-cell transplantation. However, no survival advantage was found in elderly patients after introduction of hypomethylating agents as standard for care in this patient group. Our data is in line with results from other MDS and cancer registries. It allows formulating recommendations for future collaborative health services research on MDS patients with national and international partners.     

Emulsion templated scaffolds that include gelatin and glycosaminoglycans

Gelatin is one of the most commonly used biopolymer for creating cellular scaffolds due to its innocuous nature. To create stable gelatin scaffolds at physiological temperature (37 degrees C), chemical cross-linking is a necessary step. In a previous paper (Biomacromolecules 2006, 7, 3059-3068), cross-linking was carried out by either radical polymerization of the methacrylated derivative of gelatin (GMA) or through the formation of isopeptide bonds catalyzed by transglutaminase. The method of scaffold production was based on emulsion templating in which an organic phase is dispersed in the form of discrete droplets into a continuous aqueous solution of the biopolymer. Both kinds of scaffolds were tested as culture medium for hepatocytes. It turned out that the enzymatic cross-linked scaffold performed superiorily in this respect, even though it was mechanically less stable than the GMA scaffold. In the present paper, in an attempt to improve the biocompatibility of the GMA-based scaffold, biopolymers present in the extracellular matrix (ECM) were included in scaffold formulation, namely, chondroitin sulfate and hyaluronic acid. These biopolymers were derivatized with methacrylic moieties to undergo radical polymerization together with GMA. The morphology of the scaffolds was tuned to some extent by varying the volume fraction of the internal phase and to a larger extent by inducing a controlled destabilization of the precursor emulsion through the use of additives. In this way, scaffolds with 44% of the void volume attributable to voids with a diameter exceeding 60 microm and with 79% of the interconnect area attributable to interconnects with a diameter exceeding 20 microm in diameter could be successfully synthesized. To test whether the inclusion of ECM components into scaffold formulation resolves in an improvement of their biocompatibility with respect to GMA scaffolds, hepatocytes were seeded on both kinds of scaffolds and cell viability and function assays were carried out and compared.     

Sparsity as Cellular Objective to Infer Directed Metabolic Networks from Steady-State Metabolome Data: A Theoretical Analysis

Since metabolome data are derived from the underlying metabolic network, reverse engineering of such data to recover the network topology is of wide interest. Lyapunov equation puts a constraint to the link between data and network by coupling the covariance of data with the strength of interactions (Jacobian matrix). This equation, when expressed as a linear set of equations at steady state, constitutes a basis to infer the network structure given the covariance matrix of data. The sparse structure of metabolic networks points to reactions which are active based on minimal enzyme production, hinting at sparsity as a cellular objective. Therefore, for a given covariance matrix, we solved Lyapunov equation to calculate Jacobian matrix by a simultaneous use of minimization of Euclidean norm of residuals and maximization of sparsity (the number of zeros in Jacobian matrix) as objective functions to infer directed small-scale networks from three kingdoms of life (bacteria, fungi, mammalian). The inference performance of the approach was found to be promising, with zero False Positive Rate, and almost one True positive Rate. The effect of missing data on results was additionally analyzed, revealing superiority over similarity-based approaches which infer undirected networks. Our findings suggest that the covariance of metabolome data implies an underlying network with sparsest pattern. The theoretical analysis forms a framework for further investigation of sparsity-based inference of metabolic networks from real metabolome data.