Pairwise Matrices Research Articles

Ricci Semi-symmetric Hypersurfaces in Complex Two-Plane Grassmannians

In this paper, we considered Ricci semi-symmetric real hypersurface in complex two-plane Grassmannians. Then we prove the non-existence of Ricci semi-symmetric Hopf hypersurfaces in complex two-plane Grassmannians by using the method of simultaneous diagonalization for pairwise commutative matrices.

Combining diversity measures for ensemble pruning

Multiple Classifier Systems (MCSs) have been widely used in the area of pattern recognition due to the difficult task that is to find a single classifier that has a good performance on a great variety of problems. Studies have shown that MCSs generate a large quantity of classifiers and that those classifiers have redundancy between each other. Various methods proposed to decrease the number of classifiers without worsening the performance of the ensemble succeeded when using diversity to drive the pruning process. In this work we propose a pruning method that combines different pairwise diversity matrices through a genetic algorithm. The combined diversity matrix is then used to group similar classifiers, i.e., those with low diversity, that should not belong to the same ensemble. In order to generate candidate ensembles, we transform the combined diversity matrix into one or more graphs and then apply a graph coloring method. The proposed method was assessed on 21 datasets from the UCI Machine Learning Repository and its results were compared with five state-of-the-art techniques in ensemble pruning. Results have shown that the proposed pruning method obtains smaller ensembles than the state-of-the-art techniques while improving the recognition rates.

Reconstruction methods for AHP pairwise matrices: How reliable are they?

Habitually, decision-makers are exposed to situations that require a lot of knowledge and expertise. Therefore, they need tools to help them choose the best possible alternatives. Analytic hierarchical process (AHP) is one of those tools and it is widely used in many fields. While the use of AHP is very simple, there is a situation that becomes complex: the consistency of the pairwise matrices. In order to obtain the consistent pairwise matrix from the inconsistent one, reconstruction methods can be used, but they cannot guarantee getting the right matrix according to the judgments of the decision maker. This situation does not allow proper evaluation of methods reliability, i.e. it is not possible to obtain a reliable ranking of alternatives based on an inconsistent matrix. In this work, a new way to evaluate the reliability of matrix reconstruction methods is proposed. This technique uses a novel measure for alternatives ranking comparison (based on element positions and distances), which is introduced in order to compare several matrix reconstruction methods. Finally, in order to demonstrate the extensibility of this new reliability measure, two reconstruction methods based on bio-inspired models (a Genetic Algorithm and the Firefly Algorithm) are presented and evaluated by using the aforementioned reliability measure.

Defining Immune Response Signatures in DLBCL As Potential Predictive Biomarkers for Outcome to Immunotherapy

PurposeTo assess whether comparative gene network analysis can reveal characteristic immune response signatures that predict clinical response in Diffuse large B-cell lymphoma (DLBCL).BackgroundThe wealth of available gene expression data sets for DLBCL and other cancer types provides a resource to define recurrent pathological processes at the level of gene expression and gene correlation neighbourhoods. This is of particular relevance in the context of cancer immune responses, where convergence onto common patterns may drive shared gene expression profiles. Where existing and novel immunotherapies harness the immune response for therapeutic benefit such responses may provide predictive biomarkers.MethodsWe independently analysed publically available DLBCL gene expression data sets and a wide compendium of gene expression data from diverse cancer types, and then asked whether common elements of cancer host response could be identified from resulting networks. Using 10 DLBCL gene expression data sets, encompassing 2030 cases, we established pairwise gene correlation matrices per data set, which were merged to generate median correlations of gene pairs across all data sets. Gene network analysis and unsupervised clustering was then applied to define global representations of DLBCL gene expression neighbourhoods. In parallel a diverse range of solid and lymphoid malignancies including; breast, colorectal, oesophageal, head and neck, non-small cell lung, prostate, pancreatic cancer, Hodgkin lymphoma, Follicular lymphoma and DLBCL were independently analysed using an orthogonal weighted gene correlation network analysis of gene expression data sets from which correlated modules across diverse cancer types were identified. The biology of resulting gene neighbourhoods was assessed by signature and ontology enrichment, and the overlap between gene correlation neighbourhoods and WGCNA derived modules associated with immune/host responses was analysed.ResultsAmongst DLBCL data, we identified distinct gene correlation neighbourhoods associated with the immune response. These included both elements of IFN-polarised responses, core T-cell, and cytotoxic signatures as well as distinct macrophage responses. Neighbourhoods linked to macrophages separated CD163 from CD68 and CD14. In the WGCNA analysis of diverse cancer types clusters corresponding to these immune response neighbourhoods were independently identified including a highly similar cluster related to CD163. The overlapping CD163 clusters in both analyses linked to diverse Fc-Receptors, complement pathway components and patterns of scavenger receptors potentially linked to alternative macrophage activation. The relationship between the CD163 macrophage gene expression cluster and outcome was tested in DLBCL data sets, identifying a poor response in CD163 -cluster high patients, which reached statistical significance in one data set (GSE10846). Notably, the effect of the CD163-associated gene neighbourhood which correlates with poor outcome post rituximab containing immunochemotherapy is distinct from the effect of IFNG-STAT1-IRF1 polarised cytotoxic responses. The latter represents the predominant immune response pattern separating cell of origin unclassifiable (Type-III) DLBCL from either ABC or GCB DLBCL subsets, and is associated with a trend toward positive outcome.ConclusionComparative gene expression network analysis identifies common immune response signatures shared between DLBCL and other cancer types. Gene expression clusters linked to CD163 macrophage responses and IFNG-STAT1-IRF1 polarised cytotoxic responses are common patterns with apparent divergent outcome association. DisclosuresDavies:CTI: Honoraria; GIlead: Consultancy, Honoraria, Research Funding; Mundipharma: Honoraria, Research Funding; Bayer: Research Funding; Takeda: Honoraria, Research Funding; Janssen: Honoraria, Research Funding; Roche: Honoraria, Research Funding; GSK: Research Funding; Pfizer: Honoraria; Celgene: Honoraria, Research Funding. Jack:Jannsen: Research Funding.

On the use of convolutional neural networks and augmented CSP features for multi-class motor imagery of EEG signals classification.

Learning the deep structures and unknown correlations is important for the detection of motor imagery of EEG signals (MI-EEG). This study investigates the use of convolutional neural networks (CNNs) for the classification of multi-class MI-EEG signals. Augmented common spatial pattern (ACSP) features are generated based on pair-wise projection matrices, which covers various frequency ranges. We propose a frequency complementary feature map selection (FCMS) scheme by constraining the dependency among frequency bands. Experiments are conducted on BCI competition IV dataset IIa with 9 subjects. Averaged cross-validation accuracy of 68.45% and 69.27% is achieved for FCMS and all feature maps, respectively, which is significantly higher (4.53% and 5.34%) than random map selection and higher (1.44% and 2.26%) than filter-bank CSP (FBCSP). The results demonstrate that the CNNs are capable of learning discriminant, deep structure features for EEG classification without relying on the handcrafted features.

A prioritization model for locating relief logistic centers using analytic hierarchy process with interval comparison matrix

When natural disasters happen, relief logistic centers (RLCs) and the quality of their services become absolutely important. In other words, choosing proper locations for RLCs has a direct impact on operating costs and timeliness of responses to the rising demands. This paper aims at proposing a decision support system for prioritizing RLC’s locations to facilitate providing emergency helps when natural disasters occur. The present study, focuses on considering availability, risk, technical issues, cost and coverage in locating RLCs. It is assumed that applying analytic hierarchy process (AHP) can facilitate the problem of locating these centers. The most important step in this process is establishing pair-wise comparisons for the criteria and alternatives. As it is more logical to use interval comparisons instead of crisp ones in real-world problems due to some considerations, this paper has used two decision-making methods known as lexicographic goal programming (LGP) and two-step logarithmic goal programming (TLGP) to derive priorities from pair-wise matrices. To assess the proposed method, a case study of Tehran, the capital city of Iran has also been discussed.

Some extensions of the precise consistency consensus matrix

The Precise Consensus Consistency Matrix (PCCM) is an AHP-Group Decision Making (AHP-GDM) tool, defined by Aguarón et al. [2] and developed in a local context (a single criterion) in which the decision makers are assigned the same weights. Using the Row Geometric Mean as the prioritisation procedure, consensus is sought between the different decision makers when the modifications of their initial positions or judgements are guaranteed to be within the range of values accepted for a given inconsistency level. This paper upgrades the algorithm initially proposed for obtaining the PCCM in two ways: (i) it considers the case of different weights for the decision makers; and (ii) it strengthens the idea of consistency in the design of the algorithm. One of the drawbacks of this decisional tool is that it is sometimes impossible to achieve a complete matrix. To address this, we propose a procedure for attaining a complete common consensus judgement matrix or, at least, a matrix with the minimum number of entries that are required to derive the priorities. Finally, we compare the results obtained when applying the extensions of the PCCM with those obtained using the two traditional procedures (AIJ and AIP) usually employed in AHP-GDM. In order to do this, we use a set of indicators that measure the violations in consistency of the group pairwise matrices and the compatibility between the individuals and group positions in four cases associated with two scenarios (weighted and non-weighted decision makers) and two situations (complete and incomplete PCCMs).

An asymptotic existence result on compressed sensing matrices

For any rational number h and all sufficiently large n we give a deterministic construction for an n×⌊hn⌋ compressed sensing matrix with (ℓ1,t)-recoverability where t=O(n). Our method uses pairwise balanced designs and complex Hadamard matrices in the construction of ϵ-equiangular frames, which we introduce as a generalisation of equiangular tight frames. The method is general and produces good compressed sensing matrices from any appropriately chosen pairwise balanced design. The (ℓ1,t)-recoverability performance is specified as a simple function of the parameters of the design. To obtain our asymptotic existence result we prove new results on the existence of pairwise balanced designs in which the numbers of blocks of each size are specified.

Representation of solutions of neutral differential equations with delay and linear parts defined by pairwise permutable matrices

Representation of solutions of neutral differential equations with delay and linear parts defined by pairwise permutable matrices

Fredholm boundary-value problems for linear delay systems defined by pairwise permutable matrices

Fredholm boundary-value problems for linear delay systems defined by pairwise permutable matrices

Massive fungal biodiversity data re-annotation with multi-level clustering.

With the availability of newer and cheaper sequencing methods, genomic data are being generated at an increasingly fast pace. In spite of the high degree of complexity of currently available search routines, the massive number of sequences available virtually prohibits quick and correct identification of large groups of sequences sharing common traits. Hence, there is a need for clustering tools for automatic knowledge extraction enabling the curation of large-scale databases. Current sophisticated approaches on sequence clustering are based on pairwise similarity matrices. This is impractical for databases of hundreds of thousands of sequences as such a similarity matrix alone would exceed the available memory. In this paper, a new approach called MultiLevel Clustering (MLC) is proposed which avoids a majority of sequence comparisons, and therefore, significantly reduces the total runtime for clustering. An implementation of the algorithm allowed clustering of all 344,239 ITS (Internal Transcribed Spacer) fungal sequences from GenBank utilizing only a normal desktop computer within 22 CPU-hours whereas the greedy clustering method took up to 242 CPU-hours.

SPIKY: A graphical user interface for tracking spike train similarity

Modern electrophysiology is developing fast and it sometimes provides more data than available algorithms and methods can handle and process. In particular, there is an increasing demand for methods which provide the possibility to study similarity patterns of activity across many neurons. Accordingly, a wide variety of approaches to quantify the similarity (or dissimilarity) between two or more spike trains has been suggested. Recently, the ISI- and the SPIKE-distance [1,2] have been proposed as parameter-free and time-scale independent measures of spike train synchrony. The key property of both measures is that they are time-resolved since they rely on instantaneous estimates of spike train dissimilarity. This makes it possible to track changes in instantaneous clustering, i.e., time-localized patterns of (dis)similarity among multiple spike trains. The SPIKE-distance also comes in a causal variant [2] which is defined such that the instantaneous values of dissimilarity are defined from past information only so that time-resolved spike train synchrony can be estimated in real-time. For both the regular and the real-time SPIKE-distance, there are several levels of information reduction [3]. The starting point is the most detailed representation in which one instantaneous value is obtained for each pair of spike trains. This results in a matrix of size ’number of sampled time instants’ × ’squared number of spike trains’ (i.e. #(tn)N2). By selecting a pair of spike trains one obtains a bivariate dissimilarity profile whereas the selection of a time instant yields an instantaneous matrix of pairwise spike train dissimilarities which can be used to divide the spike trains into instantaneous clusters, i.e., groups of spike trains with low intra-group and high inter-group dissimilarity. Another way to reduce the information is averaging. The spatial average over spike train pairs yields a dissimilarity profile for the selected (sub)population, whereas temporal averaging leads to a bivariate distance matrix for the selected interval or the selected trigger points. Finally, application of the remaining average results in one distance value which describes the overall level of synchrony for a group of spike trains over a given time interval. The Matlab source codes for calculating and visualizing both the ISI- and the SPIKE-distance have been made publicly available and have already been widely used in various contexts. However, the use of these codes is not very intuitive and their application requires some basic knowledge of Matlab. Thus it became desirable to provide a more user-friendly and accessible interface. Here we address this need and present an advanced version of the graphical user interface SPIKY [4,5]. This interactive program facilitates the application of the ISI- and the SPIKE-distance to both simulated and real data. Once given a set of spike train data (importable from many different formats), SPIKY calculates the desired measure and allows visualization of different representations such as measure profiles and pairwise dissimilarity matrices. SPIKY also includes the possibility to generate movies which are very useful in order to track the varying patterns of (dis)similarity. Finally, SPIKY has been optimized with respect to both computation speed (by using MEX-files, i.e. C-based Matlab executables) and memory demand (by taking advantage of the piecewise linear nature of the dissimilarity profiles).

A Group Fuzzy Analytic Network Process to Prioritize Low Carbon Energy Systems in the Philippines

Low-carbon energy systems are being proposed as portfolio of solutions to mitigate CO2 emissions from the electricity-generating power sector. Stakeholder's perception on such technology plays a crucial role in its successful implementation. Not only the technological and economic aspects, but also the environmental and social aspects that surround these technologies should be considered in in determining which of these energy systems should be promoted, invested in, and subsidized. This decision problem should take into consideration the trade-offs due to several conflicting aspects involved in the prioritization. This paper thus proposes Fuzzy Analytic Network Process as a decision modeling tool in a group decision making environment to address the complexity of the decision structure and the uncertainty inherent in eliciting value judgments from stakeholders or experts. Fuzzy numbers are used to model the uncertainty, vagueness and incompleteness of information thus derived. The method then extends the fuzzy preference programming technique to derive the group priorities or weights from fuzzy pairwise comparative judgment matrices. A numerical example is presented to illustrate the proposed approach in prioritizing low carbon energy systems in the Philippines.

On exponential stability of nonlinear fractional multidelay integro-differential equations defined by pairwise permutable matrices

In this paper, systems of nonlinear differential equations with Caputo fractional derivative and multiple delays are considered. Using representation of a solution of differential equation with multiple delays in the form of matrix polynomial and stability results such as Gronwall’s and Pinto’s inequality, sufficient conditions for the exponential stability of a trivial solution of nonlinear multidelay fractional differential equations are proved.

The Geographic Mosaic of Sex and Infection in Lake Populations of a New Zealand Snail at Multiple Spatial Scales

Understanding how sexual and asexual forms of the same species coexist is a challenge for evolutionary biology. The Red Queen hypothesis predicts that sex is favored by parasite-mediated selection against common asexual genotypes, leading to the coexistence of sexual and asexual hosts. In a geographic mosaic, where the risk of infection varies in space, the theory also predicts that sexual reproduction would be positively correlated with disease prevalence. We tested this hypothesis in lake populations of a New Zealand freshwater snail, Potamopyrgus antipodarum, by comparing pairwise difference matrices for infection frequency and male frequency using partial Mantel tests. We conducted the test at three spatial scales: among lakes on the South Island, among depths within an intensively sampled lake (Lake Alexandrina), and within depths at Lake Alexandrina. We found that the difference in infection risk and the difference in the proportion of sexual snails were significantly and positively correlated at all spatial scales. Our results thus suggest that parasite-mediated selection contributes to the long-term coexistence of sexual and asexual individuals in coevolutionary hotspots, and that the "warmth" of hotspots can vary on small spatial scales.

PyRMSD: a Python package for efficient pairwise RMSD matrix calculation and handling

We introduce pyRMSD, an open source standalone Python package that aims at offering an integrative and efficient way of performing Root Mean Square Deviation (RMSD)-related calculations of large sets of structures. It is specially tuned to do fast collective RMSD calculations, as pairwise RMSD matrices, implementing up to three well-known superposition algorithms. pyRMSD provides its own symmetric distance matrix class that, besides the fact that it can be used as a regular matrix, helps to save memory and increases memory access speed. This last feature can dramatically improve the overall performance of any Python algorithm using it. In addition, its extensibility, testing suites and documentation make it a good choice to those in need of a workbench for developing or testing new algorithms. The source code (under MIT license), installer, test suites and benchmarks can be found at https://pele.bsc.es/ under the tools section. victor.guallar@bsc.es Supplementary data are available at Bioinformatics online.

SPIKY: a graphical user interface for monitoring spike train synchrony

With the growing availability of multi-unit recordings there is increasing demand for methods which provide the possibility to study similarity patterns of activity across many neurons. Accordingly, a wide variety of approaches to quantify the similarity (or dissimilarity) between two or more spike trains has been suggested. Recently, the ISI- and the SPIKE-distance [1,2] have been proposed as parameter-free and time-scale independent measures of spike train synchrony. The key property of both measures is that they are time-resolved since they rely on instantaneous estimates of spike train dissimilarity. This makes it possible to track changes in instantaneous clustering, i.e., time-localized patterns of (dis)similarity among multiple spike trains. The SPIKE-distance also comes in a causal variant [2] which is defined such that the instantaneous values of dissimilarity are defined from past information only so that time-resolved spike train synchrony can be estimated in real-time. For both the regular and the real-time SPIKE-distance, there are several levels of information reduction [3]. The starting point is the most detailed representation in which one instantaneous value is obtained for each pair of spike trains. This results in a matrix of size 'number of sampled time instants' × 'squared number of spike trains' (i.e. #(tn)N2). By selecting a pair of spike trains one obtains a bivariate dissimilarity profile whereas the selection of a time instant yields an instantaneous matrix of pairwise spike train dissimilarities which can be used to divide the spike trains into instantaneous clusters, i.e., groups of spike trains with low intra-group and high inter-group dissimilarity. Another way to reduce the information is averaging. The spatial average over spike train pairs yields a dissimilarity profile for the selected (sub)population, whereas temporal averaging leads to a bivariate distance matrix for the selected interval or the selected trigger points. Finally, application of the remaining average results in one distance value which describes the overall level of synchrony for a group of spike trains over a given time interval. The Matlab source codes for calculating and visualizing both the ISI- and the SPIKE-distance have been made publicly available and have already been widely used in various contexts. However, the use of these codes is not very intuitive and their application requires some basic knowledge of Matlab. Thus it became desirable to provide a more user-friendly and accessible interface. Here we address this need and present the graphical user interface SPIKY [4,5]. This interactive program facilitates the application of the ISI- and the SPIKE-distance to both simulated and real data. SPIKY includes a spike train generator for testing purposes, as well as masks for selecting the analysis window and the neuronal subpopulation of interest. Once given a set of spike train data, it calculates the desired measure and allows visualization of all the different representations mentioned above (such as measure profiles and pairwise dissimilarity matrices). It even includes the possibility to generate movies which are very useful in order to track the varying patterns of (dis)similarity. Finally, we also have increased the high computation speed even further by transferring the most time-consuming parts of the original Matlab code to Matlab executables (MEX) with the new subroutines written in C.

Representation of a Solution of the Cauchy Problem for an Oscillating System with Multiple Delays and Pairwise Permutable Matrices

Nonhomogeneous system of linear differential equations of second order with multiple different delays and pairwise permutable matrices defining the linear parts is considered. Solution of corresponding initial value problem is represented using matrix polynomials.

Genetic structuring of the common shrew,Sorex araneus(Soricomorpha: Soricidae) in the Polish Sudetes may suggest ways of northwards colonization

An effect of geographical barriers on the level of population structuring and ways of northwards colonization in the common shrew Sorex araneus was investigated by contrasting gene flow inferred by one Y-linked and eight autosomal microsatellites. A total of 102 shrews trapped at eight localities separated by mountain ridges of the Śnieżnik Massif (East Sudetes, Poland) were studied. The genetic structure of populations was estimated using the standard analysis of molecular variance based on F-statistic, as well as two clustering methods implemented in Structure and Geneland. In pair-wise population comparisons both FST and RST were estimated. A Mantel-test was used to investigate the patterns and causes of structuring. No significant correlation between genetic differentiation and geographical distance was found for autosomal loci and for the Y-linked locus. Significant genetic structuring was found in four out of six pairs of populations. Studying autosomal loci we found nonsignificant correlations between pair-wise matrices of FST and RST and the presence of the barrier. On the other hand, for the Y-linked locus these correlations were significant, both for FST and RST, suggesting reduced gene flow between populations for males. Patterns of genetic structuring in the common shrew of the Massif of Śnieżnik may suggest two possible ways of northwards colonization, which promoted genetic distinction of shrews migrating different routes.

Analysis of genetic relationship among Arbutus unedo L. genotypes using RAPD and SSR markers

The strawberry tree (Arbutus unedo L.) is an underutilized, drought tolerant, fire resistant species with a south western distribution in Europe, and with ecological and putative socio-economical impact in Portugal and Mediterranean countries. Our aim was to develop an appropriate set of molecular markers to enable genetic diversity to be assessed and to fingerprint Arbutus unedo genotypes for breeding and conservation purposes in Portugal. Twenty-seven trees from a broad geographic range were screened with 20 random amplified polymorphic DNA (RAPD primers) and 11 microsatellite markers (SSR). The RAPDs generated 124 bands, 57.3% of which were polymorphic, with an expected heterozygosity of 27%. We cross-amplified 11 SSR primers developed for Vaccinium spp., and 5 were found to be polymorphic in A. unedo, with 75% of expected heterozygosity, a number of alleles of 11.6, a null allele frequency of 7.6% and a polymorphic information content of 71%. Although the SSRs were more polymorphic and informative than the RAPDs, both markers displayed high genetic variability with the gathered data. No geographic pattern was observed in the genetic variation distribution based on both marker systems, and the lack of correlation between genetic and geographical matrices was confirmed by Mantel tests. Likely, no correlation was found between pairwise SSR and RAPD band-sharing matrices. These results and their implications on A. unedo breeding and conservation programs are discussed.