Eigenvector Decomposition Research Articles

Nearshore Ship Detection in PolSAR Images by Integrating Superpixel-Level GP-PNF and Refined Polarimetric Decomposition

Nearshore ship detection has significant applications in both the military and civilian domains. Compared to synthetic aperture radar (SAR), polarimetric synthetic aperture radar (PolSAR) provides richer information for analyzing the scattering mechanisms of ships and enables better detection of ship targets. However, ships in nearshore areas tend to be highly concentrated, and ship detection is often affected by adjacent strong scattering, resulting in false alarms or missed detections. While the GP-PNF detector performs well in PolSAR ship detection, it cannot obtain satisfactory results in these scenarios, and it also struggles in the presence of azimuthal ambiguity or strong clutter interference. To address these challenges, we propose a nearshore ship detection method named ECD-PNF by integrating superpixel-level GP-PNF and refined polarimetric decomposition. Firstly, polarimetric superpixel segmentation and sea–land segmentation are performed to reduce the influence of land on ship detection. To estimate the sea clutter more accurately, an automatic censoring (AC) mechanism combined with superpixels is used to select the sea clutter superpixels. By utilizing refined eight-component polarimetric decomposition to improve the scattering vector, the physical interpretability of the detector is enhanced. Additionally, the expression of polarimetric coherence is improved to enhance the target clutter ratio (TCR). Finally, this paper combines the third eigenvalue of eigenvalue–eigenvector decomposition to reduce the impact of azimuthal ambiguity. Three spaceborne PolSAR datasets from Radarsat-2 and GF-3 are adopted in the experiments for comparison. The proposed ECD-PNF method achieves the highest figure of merit (FoM) value of 0.980, 1.000, and 1.000 for three datasets, validating the effectiveness of the proposed method.

Autoignition Problem in Homogeneous Combustion Systems: GQL versus QSSA Combined with DRG

The global quasi-linearization (GQL) is used as a method to study and to reduce the complexity of mathematical models of mechanisms of chemical kinetics. Similar to standard methodologies, such as the quasi-steady-state assumption (QSSA), the GQL method defines the fast and slow invariant subspaces and uses slow manifolds to gain a reduced representation. It does not require empirical inputs and is based on the eigenvalue and eigenvector decomposition of a linear map approximating the nonlinear vector field of the original system. In the present work, the GQL-based slow/fast decomposition is applied for different combustion systems. The results are compared with the standard QSSA approach. For this, an implicit implementation strategy described by differential algebraic equations (DAEs) systems is suggested and used, which allows for treating both approaches within the same computational framework. Hydrogen–air (with 9 species) and ethanol–air (with 57 species) combustion systems are considered representative examples to illustrate and verify the GQL. The results show that 4D GQL for hydrogen–air and 14D GQL ethanol–air slow manifolds outperform the standard QSSA approach based on a DAE-based reduced computation model.

Ship Detection in PolSAR Images Based on a Modified Polarimetric Notch Filter

Ship detection based on synthetic aperture radar (SAR) imagery is one of the key applications for maritime security. Compared with single-channel SAR images, polarimetric SAR (PolSAR) data contains the fully-polarized information, which better facilitates better discriminating between targets, sea clutter, and interference. Therefore, many ship detection methods based on the polarimetric scattering mechanism have been studied. To deal with the false alarms caused by the existence of ghost targets, resulting from azimuth ambiguities and interference from side lobes, a modified polarimetric notch filter (PNF) is proposed for PolSAR ship detection. In the proposed method, the third eigenvalue obtained by the eigenvalue–eigenvector decomposition of the polarimetric covariance matrix is utilized to construct a new feature vector. Then, the target power can be computed to construct the modified PNF detector. On the one hand, the detection rate of ship targets can be enhanced by target-to-clutter contrast. On the other hand, false alarms resulting from azimuth ambiguities and side lobes can be reduced to an extent. Experimental results based on three C-band AIRSAR PolSAR datasets demonstrated the capability of the proposed PNF detector to improve detection performance while reducing false alarms. To be specific, the figure of merit (FoM) of the proposed method is the highest among comparative approaches with results of 80%, 100%, and 100% for the tested datasets, respectively.

Optimization of diffuse reflectance spectroscopy measurements for direct and rapid screening of pesticides: A case study of spinach

Although diffuse reflectance spectroscopy (DRS) measurements can be collected rapidly and simultaneously, the resulting datasets are imbalanced and redundant due to the highly correlated spectral features collected on relatively few samples. Consequently, modelling these datasets using machine learning (ML) techniques is challenging and necessitates longer training times and more computational resources. Furthermore, models developed with such data are frequently prone to overfitting, resulting in promising but often non-reproducible results. We demonstrate the advantage of using an eigenvector decomposition principal component analysis (PCA) in reducing the dimensionality and data mining of DRS measurements in the short near-infrared region (750–900 nm). A total of 547 DRS measurements consisting of 151 wavelengths were acquired from spinach samples sprayed with two different pesticides and control samples. The measurements were later preprocessed with a Savitzky-Golay filter and multiplicative scatter analysis. After performing PCA on the preprocessed data, two principal components (PCs) that explained 77% of the cumulative variance and maximized the interclass variation were extracted and used as inputs to three ML models namely; artificial neural networks, support vector machine and random forest, to classify the samples. Re-sampling was used to tune the models and avoid overfitting. The performance of the models was compared using raw DRS data, pre-processed (PP) DRS data, and PCs data. The results show that pesticide classification using PCs data requires the least amount of training time (average 2.4 s) for all the models, and achieves 100% classification accuracy. In addition, it was observed that spectral data pre-processing improves accuracy and training time when compared to using raw spectral data. These findings are particularly encouraging since they demonstrate the possibility of developing rapid and accurate classification models for screening pesticide residues in fresh produce based on DRS measurements with minimal computational resources.

Genome-wide association study of eigenvectors provides genetic insights into selective breeding for tomato metabolites

BackgroundLong-term domestication and intensive breeding of crop plants aim to establish traits desirable for human needs, and characteristics related to yield, disease resistance, and postharvest storage have traditionally received considerable attention. These processes have led also to negative consequences, as is the case of loss of variants controlling fruit quality, for instance in tomato. Tomato fruit quality is directly associated to metabolite content profiles; however, a full understanding of the genetics affecting metabolite content during tomato domestication and improvement has not been reached due to limitations of the single detection methods previously employed. Here, we aim to reach a broad understanding of changes in metabolite content using a genome-wide association study (GWAS) with eigenvector decomposition (EigenGWAS) on tomato accessions.ResultsAn EigenGWAS was performed on 331 tomato accessions using the first eigenvector generated from the genomic data as a “phenotype” to understand the changes in fruit metabolite content during breeding. Two independent gene sets were identified that affected fruit metabolites during domestication and improvement in consumer-preferred tomatoes. Furthermore, 57 candidate genes related to polyphenol and polyamine biosynthesis were discovered, and a major candidate gene chlorogenate: glucarate caffeoyltransferase (SlCGT) was identified, which affected the quality and diseases resistance of tomato fruit, revealing the domestication mechanism of polyphenols.ConclusionsWe identified gene sets that contributed to consumer liking during domestication and improvement of tomato. Our study reports novel evidence of selective sweeps and key metabolites controlled by multiple genes, increasing our understanding of the mechanisms of metabolites variation during those processes. It also supports a polygenic selection model for the application of tomato breeding.

Dielectric characterization and polarimetric analysis of lunar north polar crater Hermite-A using Chandrayaan-1 Mini-SAR, Lunar Reconnaissance Orbiter (LRO) Mini-RF, and Chandrayaan-2 DFSAR data

Studies of the lunar surface from Synthetic Aperture Radar (SAR) data have played a prominent role in the exploration of the lunar surface in recent times. This study uses data from SAR sensors from three Moon missions: Chandrayaan-1 Mini-SAR, Lunar Reconnaissance Orbiter (LRO) Mini-RF and Chandrayaan-2 Dual Frequency Synthetic Aperture Radar (DFSAR). DFSAR sensor is the first of its kind to operate at L-band and S-band in fully and hybrid polarimetric modes. Due to the availability of only L-band data out of the two bands (L-and S-band) for the study site, this study only used DFSAR's L-band data. The dielectric characterization and polarimetric analysis of the lunar north polar crater Hermite-A was performed in this study using Chandrayaan-1 Mini-SAR, LRO Mini-RF and Chandrayaan-2 DFSAR data. Hermite-A lies in the Permanently Shadowed Region (PSR) of the lunar north pole and whose PSR ID is NP_879520_3076780. Because of its location within the PSR of the lunar north pole, the Hermite-A makes an ideal candidate for a probable location of water-ice deposits. This work utilizes S-band hybrid polarimetric data of Mini-SAR and Mini-RF and L-band fully polarimetric data of DFSAR for the lunar north polar crater Hermite-A. This study characterizes the scattering mechanisms from three decomposition techniques of Hybrid Polarimetry namely m-delta, m-chi, and m-alpha decompositions, and for fully polarimetric data Barnes decomposition technique was applied which is based on wave dichotomy. Eigenvector and Eigenvalue-based decomposition model (H-A-Alpha decomposition) was also applied to characterize the scattering behavior of the crater. This study utilizes the hybrid-pol and fully polarimetric data-based Integral Equation Model (IEM) to retrieve the values of dielectric constant for Hermite-A crater. The dielectric constant values for the Hermite-A crater from Chandrayaan-1 Mini-SAR and LRO Mini-RF are similar, which goes further in establishing the presence of water-ice in the region. The values of the dielectric constant for Chandrayaan-2 in some regions of the crater especially on the left side of the crater is also around 3 but overall the range is relatively higher than the compact/hybrid polarimetric data. The dielectric characterization and polarimetric analysis of the Hermite-A indicatively illustrate that the crater may have surface ice clusters in its walls and on some areas of the crater floor, which can be explored in the future from the synergistic use of remote sensing data and in-situ experiments to confirm the presence of the surface ice clusters.

NOMA Computation Over Multi-Access Channels for Multimodal Sensing

An improved mean squared error (MSE) minimization solution based on eigenvector decomposition approach is conceived for wideband non-orthogonal multiple-access based computation over multi-access channel (NOMA-CoMAC) framework. This work aims at further developing NOMA-CoMAC for next-generation multimodal sensor networks, where a multimodal sensor monitors several environmental parameters such as temperature, pollution, humidity, or pressure. We demonstrate that our proposed scheme achieves an MSE value approximately 0.7 lower at <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${E}_{b}/{N}_{o} {\pmb =} \textrm {1}$ </tex-math></inline-formula> dB in comparison to that for the average sum-channel based method. Moreover, the MSE performance gain of our proposed solution increases even more for larger values of subcarriers and sensor nodes due to the benefit of the diversity gain. This, in return, suggests that our proposed scheme is eminently suitable for multimodal sensor networks.

An optimised one-way wave migration method for complex media with arbitrarily varying velocity based on eigen-decomposition

Abstract The classical one-way generalised screen propagator (GSP) and Fourier finite-difference (FFD) schemes have limitations in imaging large angles in complex media with substantial lateral variations in wave velocity. Some improvements to the classical one-way wave scheme have been proposed with optimised methods. However, the performance of these methods in imaging complex media remains unsatisfying. To overcome this issue, a new strategy for wavefield extrapolation based on the eigenvalue and eigenvector decomposition of the Helmholtz operator is presented herein. In this method, the square root operator is calculated after the decomposition of the Helmholtz operator at the product of the eigenvalues and eigenvectors. Then, Euler transformation is applied using the best polynomial approximation of the trigonometric function based on the infinite norm, and the propagator for one-way wave migration is calculated. According to this scheme, a one-way operator can be computed more accurately with a lower-order expansion. The imaging performance of this scheme was compared with that of the classical GSP, FFD and the recently developed full-wave-equation depth migration (FWDM) schemes. The impulse responses in media with arbitrary velocity inhomogeneity demonstrate that the proposed migration scheme performs better at large angles than the classical GSP scheme. The wavefronts calculated in the dipping and salt dome models illustrate that this scheme can provide a precise wavefield calculation. The applications of the Marmousi model further demonstrate that the proposed approach can achieve better-migrated results in imaging small-scale and complex structures, especially in media with steep-dipping faults.

Computational Experience with Piecewise Linear Relaxations for Petroleum Refinery Planning

Refinery planning optimization is a challenging problem as regards handling the nonconvex bilinearity, mainly due to pooling operations in processes such as crude oil distillation and product blending. This work investigated the performance of several representative piecewise linear (or piecewise affine) relaxation schemes (referred to as McCormick, bm, nf5, and nf6t) and de (which is a new approach proposed based on eigenvector decomposition) that mainly give rise to mixed-integer optimization programs to convexify a bilinear term using predetermined univariate partitioning for instances of uniform and non-uniform partition sizes. The computational results showed that applying these schemes improves the relaxation tightness compared to only applying convex and concave envelopes as estimators. Uniform partition sizes typically perform better in terms of relaxation solution quality and convergence behavior. It was also seen that there is a limit on the number of partitions that contribute to relaxation tightness, which does not necessarily correspond to a larger number of partitions, while a direct relationship between relaxation size and tightness does not always hold for non-uniform partition sizes.

Local Manifold Embedding Cross-Domain Subspace Learning for Drift Compensation of Electronic Nose Data

The gas sensor drift problem arises from the bias of data, which is known as a significant problem in the artificial olfactory community. Traditionally, hardware calibration methods are laborious and ineffective due to frequent recalibration actions involving different gases, and some calibration transfer and baseline calibration methods are not effective enough. In this work, a local manifold embedding cross-domain subspace learning (LME-CDSL) model is proposed based on domain distribution alignment. It is a unified subspace learning model combined with manifold learning and domain adaptation, which tends to explore a latent transform matrix that not only enforces the drifted target domain data to learn the manifold of nondrifted source domain data but also adopts the domain adaptation method to align the domain data distribution. In general, the LME-CDSL model has three features: 1) the unsupervised and adaptation distribution subspace projection can be easily computed through eigenvector decomposition; 2) the local linear manifold learns to achieve the compact representations of high-dimensional data and is capable of preserving the local features of nondrifted samples; and 3) the domain adaptation part utilizes the maximum mean discrepancy (MMD) and variance maximization to make the sample distributions of different domains more similar and preserve the intrinsic properties. For long-term and short-term drift compensation on a single E-nose system, the local manifold embedding cross-domain subspace learning (LME-CDSL) model obtains the average recognition accuracy of 70.95% and 74.09%, respectively, while 71.71% and 73.96%, respectively for multiple identical E-nose systems with both long-term and interplate drift, which are higher than several comparative methods and proves the its effectiveness and superiority on anti-drift and gas recognition.

Data processing pipeline for Tianlai experiment

The Tianlai project is a 21cm intensity mapping experiment aimed at detecting dark energy by measuring the baryon acoustic oscillation (BAO) features in the large scale structure power spectrum. This experiment provides an opportunity to test the data processing methods for cosmological 21cm signal extraction, which is still a great challenge in current radio astronomy research. The 21cm signal is much weaker than the foregrounds and easily affected by the imperfections in the instrumental responses. Furthermore, processing the large volumes of interferometer data poses a practical challenge. We have developed a data processing pipeline software called {\tt tlpipe} to process the drift scan survey data from the Tianlai experiment. It performs offline data processing tasks such as radio frequency interference (RFI) flagging, array calibration, binning, and map-making, etc. It also includes utility functions needed for the data analysis, such as data selection, transformation, visualization and others. A number of new algorithms are implemented, for example the eigenvector decomposition method for array calibration and the Tikhonov regularization for $m$-mode analysis. In this paper we describe the design and implementation of the {\tt tlpipe} and illustrate its functions with some analysis of real data. Finally, we outline directions for future development of this publicly code.

Modeling human thinking about similarities by neuromatrices in the perspective of fuzzy logic

In this work, we propose a new method for modeling human reasoning about objects’ similarities. We assume that similarity depends on perceived intensities of objects’ attributes expressed by natural language expressions such as low, medium, and high. We show how to find the underlying structure of the matrix with intensities of objects’ similarities in the factor-analysis-like manner. The demonstrated approach is based on fuzzy logic and set theory principles, and it uses only maximum and minimum operators. Similarly to classic eigenvector decomposition, we aim at representing the initial linguistic ordinal-scale (LOS) matrix as a max–min product of other LOS matrix and its transpose. We call this reconstructing matrix a neuromatrix because we assume that such a process takes place at the neural level in our brain. We show and discuss on simple, illustrative examples, how the presented way of modeling grasps natural way of reasoning about similarities. The unique characteristics of our approach are treating smaller attribute intensities as less important in making decisions about similarities. This feature is consistent with how the human brain is functioning at a biological level. A neuron fires and passes information further only if input signals are strong enough. The proposal of the heuristic algorithm for finding the decomposition in practice is also introduced and applied to exemplary data from classic psychological studies on perceived similarities between colors and between nations. Finally, we perform a series of simulation experiments showing the effectiveness of the proposed heuristic.

Characterization of Genetic Diversity and Genome-Wide Association Mapping of Three Agronomic Traits in Qingke Barley (Hordeum Vulgare L.) in the Qinghai-Tibet Plateau.

Barley (Hordeum vulgare L.) is one of the most important cereal crops worldwide. In the Qinghai-Tibet Plateau, six-rowed hulless (or naked) barley, called “qingke” in Chinese or “nas” in Tibetan, is produced mainly in Tibet. The complexity of the environment in the Qinghai-Tibet Plateau has provided unique opportunities for research on the breeding and adaptability of qingke barley. However, the genetic architecture of many important agronomic traits for qingke barley remains elusive. Heading date (HD), plant height (PH), and spike length (SL) are three prominent agronomic traits in barley. Here, we used genome-wide association (GWAS) mapping and GWAS with eigenvector decomposition (EigenGWAS) to detect quantitative trait loci (QTL) and selective signatures for HD, PH, and SL in a collection of 308 qingke barley accessions. The accessions were genotyped using a newly-developed, proprietary genotyping-by-sequencing (tGBS) technology, that yielded 14,970 high quality single nucleotide polymorphisms (SNPs). We found that the number of SNPs was higher in the varieties than in the landraces, which suggested that Tibetan varieties and varieties in the Tibetan area may have originated from different landraces in different areas. We have identified 62 QTLs associated with three important traits, and the observed phenotypic variation is well-explained by the identified QTLs. We mapped 114 known genes that include, but are not limited to, vernalization, and photoperiod genes. We found that 83.87% of the identified QTLs are located in the non-coding regulatory regions of annotated barley genes. Forty-eight of the QTLs are first reported here, 28 QTLs have pleotropic effects, and three QTL are located in the regions of the well-characterized genes HvVRN1, HvVRN3, and PpD-H2. EigenGWAS analysis revealed that multiple heading-date-related loci bear signatures of selection. Our results confirm that the barley panel used in this study is highly diverse, and showed a great promise for identifying the genetic basis of adaptive traits. This study should increase our understanding of complex traits in qingke barley, and should facilitate genome-assisted breeding for qingke barley improvement.

Terahertz imaging and vibro-thermography for impact response in carbon fiber reinforced plastics

In this paper, terahertz (THz) imaging and vibro-thermography (VT) are implemented for non-destructive evaluation (NDE) of CFRP subjected to impact damage. THz inspection is well-known for its outstanding detection depth in dielectric materials but unreliable in conductive materials like carbon fiber reinforced plastics (CFRP): an unwanted electro-magnetic wave will be excited under the irradiation of THz waves in conductive molecules and interrupted the reflective waves leading to a blur in the detection results. However, our experimental results showed THz imaging is comparable when it’s used to detect surface defects and shallow ones caused by impact loads. We conducted a set of VT tests as a contrast test, and the VT data are processed by Fourier transform and eigenvector decomposition algorithms, i.e. independent component analysis (ICA). Compared with VT, THz imaging show more details on surface defects and shallow-buried ones due to the absence of thermal diffusion effects. THz imaging could perform non-invasive, non-ionizing and non-contact inspection on the impact damage based on the differences in reflective index. In the end, signal-to-noise (SNR) evaluation is used as an effective means to quantitatively compare the results of these two techniques.

Frobenius correlation based u-shapelets discovery for time series clustering

An u-shapelet is a sub-sequence of a time series used for the clustering of time series datasets. The purpose of this paper is to discover u-shapelets on uncertain time series. To achieve this goal, we propose a dissimilarity score called FOTS whose computation is based on the eigenvector decomposition and the comparison of the autocorrelation matrices of the time series. This score is robust to the presence of uncertainty; it is not very sensitive to transient changes; it allows capturing complex relationships between time series such as oscillations and trends, and it is also well adapted to the comparison of short time series. The FOTS score is used with the Scalable Unsupervised Shapelet Discovery algorithm for the clustering of 63 datasets, and it has shown a substantial improvement in the quality of the clustering with respect to the Rand Index. This work defines a novel framework for the clustering of uncertain time series.

The magnetic gradient tensor of a triaxial ellipsoid, its derivation and its application to the determination of magnetisation direction

This paper presents a theory for the anomalous magnetic gradient tensor due to a uniformly magnetised general triaxial ellipsoid. Expressions for the magnetic field vector and its gradient tensor are derived from expressions for the gravitational field or the gravity gradient tensor via an application of Poisson’s theorem. This theory provides increased capability in forward modelling, inversion and equivalent source applications in both magnetic and gravimetric exploration. It provides an accurate and computationally efficient means of modelling the magnetic gradient tensor of ellipsoidal bodies which may possess isotropic or anisotropic magnetic susceptibility, remanent magnetisation and, in the case of highly magnetic ellipsoids, may be subject to the effect of self-demagnetisation. This paper presents a novel method based on the eigenvector decomposition of the magnetic gradient tensor to provide estimates of the magnetisation direction over an ellipsoidal source. This includes an investigation of the influence of shape detail, observation height and inclination of magnetisation on the positioning of global maxima in normalised source strength and how this affects the problem of estimating magnetisation direction. This study confirms that magnetisation directions may be accurately estimated for extremely elongated ellipsoidal bodies where the ratio of smallest observation height to maximum elongation (in plan view) is greater than 1.

Letter to the Editor: Ending the Use of Obsolete Data Analysis Methods

ABSTRACT Aerosol and Air Quality Research is taking an editorial stand with regards to outdated data analysis methods, specifically principal component analysis (PCA) and related techniques and enrichment factors (EF). In both cases, they have been replaced with more quantitative data analytical tools that provide much greater information on sources of variation in the data. Enrichment factors were first used in the 1960s when we basically did not have computers. It was a simple way of using double ratios to see if an element were substantially enriched over crustal abundances that had been reported by one of several authors. However, the information is quite crude since it simply says that the element is higher than typical crustal values and does not account for local variations in elemental abundances. When we now have the capabilities to look at correlations, statistical assessment of differences in means or medians, etc., we should provide appropriate quantitative estimates of significance of differences among samples. In the case of PCA and other eigenvector-based methods, it has been shown by Lawson and Hanson (1974) and Malinowski (2002) that an eigenvector analysis is an unweighted least-square fit to the data. Such fits are going to create problems with heteroskedastic data such as is commonly encountered in atmospheric measurements. Typically, the measurement uncertainties are proportional to the measured values rather than a fixed value for all of the measurements (homoscedastic data). Thus, unweighted least squares fits will not provide the best estimators of the parameters of interest. PCA also typically uses a default of subtracting the mean value from the data points and scales them by the variance such that it apportions the variance rather than the variation of the actual measured concentrations. Although methods like Target-Transformation Factor Analysis (TTFA) avoided subtracting the mean, it still suffers from the problem of improper (absence of) data point weights. In the 1970s when mainframe computing power was less than what we carry in our pockets as a telephone, it was necessary to use simplifying methods like eigenvector decompositions to be able to obtain results in a reasonable time. However, we have long since gained sufficient computing power in personal computers to be able to perform full, explicit least-squares fits with proper data weighting. Factor analysis tools like non-negative constrained alternating least square (Tauler et al., 1993, 1994), positive matrix factorization (Paatero and Tapper, 1993, 1994), and non-negative least squares (e.g., Lee and Seung, 1999; Camp, 2019) have been available for more than 25 years that allow proper weighting of individual data points. Software for these techniques are readily available for download: MCR-ALS (http://www.mcrals.info), PMF (https://www.epa.gov/air-research/positive-matrix-factorization-model-environmental-data-analyses; https://www.psi.ch/lac/sofi-sourcefinder), and NNLS (https://pages.nist.gov/pyMCR/; https://cran.r-project.org/package=NMF) While PCA has value as a preliminary screening tool (e.g., Roscoe et al., 1982) and as an exploratory tool, but it should not be used as a receptor model. For quantitative analyses that form the basis of conclusions in a paper, we strongly recommend more modern and statistically appropriate methods be used.

NormGAM: an R package to remove systematic biases in genome architecture mapping data

BackgroundThe genome architecture mapping (GAM) technique can capture genome-wide chromatin interactions. However, besides the known systematic biases in the raw GAM data, we have found a new type of systematic bias. It is necessary to develop and evaluate effective normalization methods to remove all systematic biases in the raw GAM data.ResultsWe have detected a new type of systematic bias, the fragment length bias, in the genome architecture mapping (GAM) data, which is significantly different from the bias of window detection frequency previously mentioned in the paper introducing the GAM method but is similar to the bias of distances between restriction sites existing in raw Hi-C data. We have found that the normalization method (a normalized variant of the linkage disequilibrium) used in the GAM paper is not able to effectively eliminate the new fragment length bias at 1 Mb resolution (slightly better at 30 kb resolution). We have developed an R package named normGAM for eliminating the new fragment length bias together with the other three biases existing in raw GAM data, which are the biases related to window detection frequency, mappability, and GC content. Five normalization methods have been implemented and included in the R package including Knight-Ruiz 2-norm (KR2, newly designed by us), normalized linkage disequilibrium (NLD), vanilla coverage (VC), sequential component normalization (SCN), and iterative correction and eigenvector decomposition (ICE).ConclusionsBased on our evaluations, the five normalization methods can eliminate the four biases existing in raw GAM data, with VC and KR2 performing better than the others. We have observed that the KR2-normalized GAM data have a higher correlation with the KR-normalized Hi-C data on the same cell samples indicating that the KR-related methods are better than the others for keeping the consistency between the GAM and Hi-C experiments. Compared with the raw GAM data, the normalized GAM data are more consistent with the normalized distances from the fluorescence in situ hybridization (FISH) experiments. The source code of normGAM can be freely downloaded from http://dna.cs.miami.edu/normGAM/.

The Eminence of Co-Expressed Ties in Schizophrenia Network Communities

Exploring gene networks is crucial for identifying significant biological interactions occurring in a disease condition. These interactions can be acknowledged by modeling the tie structure of networks. Such tie orientations are often detected within embedded community structures. However, most of the prevailing community detection modules are intended to capture information from nodes and its attributes, usually ignoring the ties. In this study, a modularity maximization algorithm is proposed based on nonlinear representation of local tangent space alignment (LTSA). Initially, the tangent coordinates are computed locally to identify k-nearest neighbors across the genes. These local neighbors are further optimized by generating a nonlinear network embedding function for detecting gene communities based on eigenvector decomposition. Experimental results suggest that this algorithm detects gene modules with a better modularity index of 0.9256, compared to other traditional community detection algorithms. Furthermore, co-expressed genes across these communities are identified by discovering the characteristic tie structures. These detected ties are known to have substantial biological influence in the progression of schizophrenia, thereby signifying the influence of tie patterns in biological networks. This technique can be extended logically on other diseases networks for detecting substantial gene “hotspots”.

Multi-dimensional Resource Optimal Allocation Method for Service Function Chain Deployment

Aiming at the problem of multi-dimensional resource service function chain deployment in a resource-limited network, a resource allocation method based on optimal weighted graph matching is proposed. The node and link resources are embodied as weights of the weighted graph, and the eigenvector decomposition of the adjacency matrix is used to get graph matching method. The simulation results show that the algorithm optimizes the bandwidth required for the deployment of the service function chain, optimizes the balance of node load and link bandwidth, supports more service requests, and has low algorithm complexity.