Multivariate genetic architecture reveals testosterone-driven sexual antagonism in contemporary humans.

Sex difference (SD) is ubiquitous in humans despite shared genetic architecture (SGA) between the sexes. A univariate approach, i.e., studying SD in single traits by estimating genetic correlation, does not provide a complete biological overview, because traits are not independent and are genetically correlated. The multivariate genetic architecture between the sexes can be summarized by estimating the additive genetic (co)variance across shared traits, which, apart from the cross-trait and cross-sex covariances, also includes the cross-sex-cross-trait covariances, e.g., between height in males and weight in females. Using such a multivariate approach, we investigated SD in the genetic architecture of 12 anthropometric, fat depositional, and sex-hormonal phenotypes. We uncovered sexual antagonism (SA) in the cross-sex-cross-trait covariances in humans, most prominently between testosterone and the anthropometric traits - a trend similar to phenotypic correlations. 27% of such cross-sex-cross-trait covariances were of opposite sign, contributing to asymmetry in the SGA. Intriguingly, using multivariate evolutionary simulations, we observed that the SGA acts as a genetic constraint to the evolution of SD in humans only when selection is sexually antagonistic and not concordant. Remarkably, we found that the lifetime reproductive success in both the sexes shows a positive genetic correlation with anthropometric traits, but not with testosterone. Moreover, we demonstrated that genetic variance is depleted along multivariate trait combinations in both the sexes but in different directions, suggesting absolute genetic constraint to evolution. Our results indicate that testosterone drives SA in contemporary humans and emphasize the necessity and significance of using a multivariate framework in studying SD.

Diffusion tensor imaging metrics as natural markers of multiple sclerosis-induced brain disorders with a low Expanded Disability Status Scale score.

Non-invasive and effective differentiation along with determining the degree of deviations compared to the healthy cohort is important in the case of various brain disorders, including multiple sclerosis (MS). Evaluation of the effectiveness of diffusion tensor metrics (DTM) in 3T DTI for recording MS-related deviations was performed using a time-acceptable MRI protocol with unique comprehensive detection of systematic errors related to spatial heterogeneity of magnetic field gradients. In a clinical study, DTMs were acquired in segmented regions of interest (ROIs) for 50 randomly selected healthy controls (HC) and 50 multiple sclerosis patients. Identical phantom imaging was performed for each clinical measurement to estimate and remove the influence of systematic errors using the b-matrix spatial distribution in the DTI (BSD-DTI) technique. In the absence of statistically significant differences due to age in healthy volunteers and patients with multiple sclerosis, the existence of significant differences between groups was proven using DTM. Moreover, a statistically significant impact of spatial systematic errors occurs for all ROIs and DTMs in the phantom and for approximately 90 % in the HC and MS groups. In the case of a single patient measurement, this appears for all the examined ROIs and DTMs. The obtained DTMs effectively discriminate healthy volunteers from multiple sclerosis patients with a low mean score on the Expanded Disability Status Scale. The magnitude of the group differences is typically significant, with an effect size of approximately 0.5, and similar in both the standard approach and after elimination of systematic errors. Differences were also observed between metrics obtained using these two approaches. Despite a small alterations in mean DTMs values for groups and ROIs (1-3 %), these differences were characterized by a huge effect (effect size ∼0.8 or more). These findings indicate the importance of determining the spatial distribution of systematic errors specific to each MR scanner and DTI acquisition protocol in order to assess their impact on DTM in the ROIs examined. This is crucial to establish accurate DTM values for both individual patients and mean values for a healthy population as a reference. This approach allows for an initial reliable diagnosis based on DTI metrics.

A novel framework for in-vivo diffusion tensor distribution MRI of the human brain.

Neural tissue microstructure plays an important role in developmental, physiological and pathophysiological processes. Diffusion tensor distribution (DTD) MRI helps probe subvoxel heterogeneity by describing water diffusion within a voxel using an ensemble of non-exchanging compartments characterized by a probability density function of diffusion tensors. In this study, we provide a new framework for acquiring multiple diffusion encoding (MDE) images and estimating DTD from them in the human brain in vivo. We interfused pulsed field gradients (iPFG) in a single spin echo to generate arbitrary b-tensors of rank one, two, or three without introducing concomitant gradient artifacts. Employing well-defined diffusion encoding parameters we show that iPFG retains salient features of a traditional multiple-PFG (mPFG/MDE) sequence while reducing the echo time and coherence pathway artifacts thereby extending its applications beyond DTD MRI. Our DTD is a maximum entropy tensor-variate normal distribution whose tensor random variables are constrained to be positive definite to ensure their physicality. In each voxel, the second-order mean and fourth-order covariance tensors of the DTD are estimated using a Monte Carlo method that synthesizes micro-diffusion tensors with corresponding size, shape, and orientation distributions to best fit the measured MDE images. From these tensors we obtain the spectrum of diffusion tensor ellipsoid sizes and shapes, and the microscopic orientation distribution function (µODF) and microscopic fractional anisotropy (µFA) that disentangle the underlying heterogeneity within a voxel. Using the DTD-derived µODF, we introduce a new method to perform fiber tractography capable of resolving complex fiber configurations. The results revealed microscopic anisotropy in various gray and white matter regions and skewed MD distributions in cerebellar gray matter not observed previously. DTD MRI tractography captured complex white matter fiber organization consistent with known anatomy. DTD MRI also resolved some degeneracies associated with diffusion tensor imaging (DTI) and elucidated the source of diffusion heterogeneity which may help improve the diagnosis of various neurological diseases and disorders.

The genetic architecture of sexual dimorphism in the moss Ceratodon purpureus.

A central problem in evolutionary biology is to identify the forces that maintain genetic variation for fitness in natural populations. Sexual antagonism, in which selection favours different variants in males and females, can slow the transit of a polymorphism through a population or can actively maintain fitness variation. The amount of sexually antagonistic variation to be expected depends in part on the genetic architecture of sexual dimorphism, about which we know relatively little. Here, we used a multivariate quantitative genetic approach to examine the genetic architecture of sexual dimorphism in a scent-based fertilization syndrome of the moss Ceratodon purpureus. We found sexual dimorphism in numerous traits, consistent with a history of sexually antagonistic selection. The cross-sex genetic correlations (rmf) were generally heterogeneous with many values indistinguishable from zero, which typically suggests that genetic constraints do not limit the response to sexually antagonistic selection. However, we detected no differentiation between the female- and male-specific trait (co)variance matrices (Gf and Gm, respectively), meaning the evolution of sexual dimorphism may be constrained. The cross-sex cross-trait covariance matrix B contained both symmetric and asymmetric elements, indicating that the response to sexually antagonistic or sexually concordant selection, and the constraint to sexual dimorphism, are highly dependent on the traits experiencing selection. The patterns of genetic variances and covariances among these fitness components is consistent with partly sex-specific genetic architectures having evolved in order to partially resolve multivariate genetic constraints (i.e. sexual conflict), enabling the sexes to evolve towards their sex-specific multivariate trait optima.

Predicting Multivariate Responses of Sexual Dimorphism to Direct and Indirect Selection.

AbstractSexual dimorphism is often assumed to result from balancing the strength of antagonistic selection in favor of dimorphism against the degree of constraint imposed by the shared genome of the sexes, reflected in the B matrix of genetic intersexual covariances. To investigate the totality of forces shaping dimorphism, we reparameterized the Lande equation to predict changes in trait averages and trait differences between the sexes. As genetic constraints on the evolution of dimorphism in response to antagonistic selection become larger, dimorphism will tend to respond more rapidly to concordant selection (which favors the same direction of change in male and female traits) than to antagonistic selection. When we apply this theory to four empirical estimates of B in Drosophila melanogaster, the indirect responses of dimorphism to concordant selection are of comparable or larger magnitude than the direct responses of dimorphism to antagonistic selection in two suites of traits with typical levels of intersex correlation. Antagonistic selection is more important in two suites of traits where the intersex correlations are unusually low. This suggests that the evolution of sexual dimorphism may sometimes be dominated by concordant selection rather than antagonistic selection.

Assessment of the systematic errors caused by diffusion gradient inhomogeneity in DTI-computer simulations.

Diffusion tensor imaging (DTI) is a powerful MRI modality that allows the investigation of the microstructure of tissues both in vivo and noninvasively. Its reliability is strictly dependent on the performance of diffusion-sensitizing gradients, of which spatial nonuniformity is a known issue in the case of virtually all clinical MRI scanners. The influence of diffusion gradient inhomogeneity on the accuracy of the diffusion tensor imaging was investigated by means of computer simulations supported by an MRI experiment performed at the isocenter and 15 cm away. The DTI measurements of two diffusion phantoms were simulated assuming a nonuniform diffusion-sensitizing gradient and various levels of noise. Thereafter, the tensors were calculated by two methods: (i) assuming a spatially constant b-matrix (standard DTI) and (ii) applying the b-matrix spatial distribution in the DTI (BSD-DTI) technique, a method of indicating the b-matrix for each voxel separately using an anisotropic phantom as a standard of diffusion. The average eigenvalues and fractional anisotropy across the homogeneous region of interest were calculated and compared with the expected values. Diffusion gradient inhomogeneity leads to overestimation of the largest eigenvalue, underestimation of the smallest one and thus overestimation of fractional anisotropy. The effect is similar to that caused by noise; however, it could not be corrected by increasing SNR. The MRI measurements, performed using a 3 T clinical scanner, revealed that the split of the eigenvalues measured 15 cm away from the isocenter is significant (up to 25%). The BSD-DTI calibration allowed the reduction of the measured fractional anisotropy of the isotropic medium from 0.174 to 0.031, suggesting that gradient inhomogeneity was the main cause of this error. For the phantom measured at the isocenter, however, the split was almost not observed; the average eigenvalues were shifted from the expected value by ~ 5%.

The effects of stress and sex on selection, genetic covariance, and the evolutionary response.

The capacity of a population to adapt to selection (evolvability) depends on whether the structure of genetic variation permits the evolution of fitter trait combinations. Selection, genetic variance and genetic covariance can change under environmental stress, and males and females are not genetically independent, yet the combined effects of stress and dioecy on evolvability are not well understood. Here, we estimate selection, genetic (co)variance and evolvability in both sexes of Tribolium castaneum flour beetles under stressful and benign conditions, using a half-sib breeding design. Although stress uncovered substantial latent heritability, stress also affected genetic covariance, such that evolvability remained low under stress. Sexual selection on males and natural selection on females favoured a similar phenotype, and there was positive intersex genetic covariance. Consequently, sexual selection on males augmented adaptation in females, and intralocus sexual conflict was weak or absent. This study highlights that increased heritability does not necessarily increase evolvability, suggests that selection can deplete genetic variance for multivariate trait combinations with strong effects on fitness, and tests the recent hypothesis that sexual conflict is weaker in stressful or novel environments.

Multivariate genetic architecture of the Anolis dewlap reveals both shared and sex-specific features of a sexually dimorphic ornament.

Darwin viewed the ornamentation of females as an indirect consequence of sexual selection on males and the transmission of male phenotypes to females via the 'laws of inheritance'. Although a number of studies have supported this view by demonstrating substantial between-sex genetic covariance for ornament expression, the majority of this work has focused on avian plumage. Moreover, few studies have considered the genetic basis of ornaments from a multivariate perspective, which may be crucial for understanding the evolution of sex differences in general, and of complex ornaments in particular. Here, we provide a multivariate, quantitative-genetic analysis of a sexually dimorphic ornament that has figured prominently in studies of sexual selection: the brightly coloured dewlap of Anolis lizards. Using data from a paternal half-sibling breeding experiment in brown anoles (Anolis sagrei), we show that multiple aspects of dewlap size and colour exhibit significant heritability and a genetic variance-covariance structure (G) that is broadly similar in males (Gm ) and females (Gf ). Whereas sexually monomorphic aspects of the dewlap, such as hue, exhibit significant between-sex genetic correlations (rmf ), sexually dimorphic features, such as area and brightness, exhibit reduced rmf values that do not differ from zero. Using a modified random skewers analysis, we show that the between-sex genetic variance-covariance matrix (B) should not strongly constrain the independent responses of males and females to sexually antagonistic selection. Our microevolutionary analysis is in broad agreement with macroevolutionary perspectives indicating considerable scope for the independent evolution of coloration and ornamentation in males and females.

Sexually antagonistic selection on genetic variation underlying both male and female same-sex sexual behavior.

BACKGROUND: Intralocus sexual conflict, arising from selection for different alleles at the same locus in males and females, imposes a constraint on sex-specific adaptation. Intralocus sexual conflict can be alleviated by the evolution of sex-limited genetic architectures and phenotypic expression, but pleiotropic constraints may hinder this process. Here, we explored putative intralocus sexual conflict and genetic (co)variance in a poorly understood behavior with near male-limited expression. Same-sex sexual behaviors (SSBs) generally do not conform to classic evolutionary models of adaptation but are common in male animals and have been hypothesized to result from perception errors and selection for high male mating rates. However, perspectives incorporating sex-specific selection on genes shared by males and females to explain the expression and evolution of SSBs have largely been neglected. RESULTS: We performed two parallel sex-limited artificial selection experiments on SSB in male and female seed beetles, followed by sex-specific assays of locomotor activity and male sex recognition (two traits hypothesized to be functionally related to SSB) and adult reproductive success (allowing us to assess fitness consequences of genetic variance in SSB and its correlated components). Our experiments reveal both shared and sex-limited genetic variance for SSB. Strikingly, genetically correlated responses in locomotor activity and male sex-recognition were associated with sexually antagonistic fitness effects, but these effects differed qualitatively between male and female selection lines, implicating intralocus sexual conflict at both male- and female-specific genetic components underlying SSB. CONCLUSIONS: Our study provides experimental support for the hypothesis that widespread pleiotropy generates pervasive intralocus sexual conflict governing the expression of SSBs, suggesting that SSB in one sex can occur due to the expression of genes that carry benefits in the other sex.

Between-sex genetic covariance constrains the evolution of sexual dimorphism in Drosophila melanogaster.

Males and females share much of their genome, and as a result, intralocus sexual conflict is generated when selection on a shared trait differs between the sexes. This conflict can be partially or entirely resolved via the evolution of sex-specific genetic variation that allows each sex to approach, or possibly achieve, its optimum phenotype, thereby generating sexual dimorphism. However, shared genetic variation between the sexes can impose constraints on the independent expression of a shared trait in males and females, hindering the evolution of sexual dimorphism. Here, we examine genetic constraints on the evolution of sexual dimorphism in Drosophila melanogaster cuticular hydrocarbon (CHC) expression. We use the extended G matrix, which includes the between-sex genetic covariances that constitute the B matrix, to compare genetic constraints on two sets of CHC traits that differ in the extent of their sexual dimorphism. We find significant genetic constraints on the evolution of further dimorphism in the least dimorphic traits, but no such constraints for the most dimorphic traits. We also show that the genetic constraints on the least dimorphic CHCs are asymmetrical between the sexes. Our results suggest that there is evidence both for resolved and ongoing sexual conflict in D. melanogaster CHC profiles.

A multivariate view of the evolution of sexual dimorphism.

Sexual differences are often dramatic and widespread across taxa. Their extravagance and ubiquity can be puzzling because the common underlying genome of males and females is expected to impede rather than foster phenotypic divergence. Widespread dimorphism, despite a shared genome, may be more readily explained by considering the multivariate, rather than univariate, framework governing the evolution of sexual dimorphism. In the univariate formulation, differences in genetic variances and a low intersexual genetic correlation (rMF) can facilitate the evolution of sexual dimorphism. However, studies that have analysed sex-specific differences in heritabilities or genetic variances do not always find significant differences. Furthermore, many of the reported estimates of rMF are very high and positive. When monomorphic heritabilities and a high rMF are present together, the evolution of sexual dimorphism on a trait-by-trait basis is severely constrained. By contrast, the multivariate formulation has greater generality and more flexibility. Although the number of multivariate sexual dimorphism studies is low, almost all support sex-specific differences in the G (variance-covariance) matrix; G matrices can differ with respect to size and/or orientation, affecting the response to selection differently between the sexes. Second, whereas positive values of the univariate quantity rMF only hinder positive changes in sexual dimorphism, positive covariances in the intersexual covariance B matrix can either help or hinder. Similarly, the handful of studies reporting B matrices indicate that it is often asymmetric, so that B can affect the evolution of single traits differently between the sexes. Multivariate approaches typically demonstrate that genetic covariances among traits can strongly constrain trait evolution when compared with univariate approaches. By contrast, in the evolution of sexual dimorphism, a multivariate view potentially reveals more opportunities for sexual dimorphism to evolve by considering the effect sex-specific selection has on sex-specific G matrices and an asymmetric B matrix.

Hormonal pleiotropy structures genetic covariance.

Quantitative genetic theory proposes that phenotypic evolution is shaped by G, the matrix of genetic variances and covariances among traits. In species with separate sexes, the evolution of sexual dimorphism is also shaped by B, the matrix of between-sex genetic variances and covariances. Despite considerable focus on estimating these matrices, their underlying biological mechanisms are largely speculative. We experimentally tested the hypothesis that G and B are structured by hormonal pleiotropy, which occurs when one hormone influences multiple phenotypes. Using juvenile brown anole lizards (Anolis sagrei) bred in a paternal half-sibling design, we elevated the steroid hormone testosterone with slow-release implants while administering empty implants to siblings as a control. We quantified the effects of this manipulation on the genetic architecture of a suite of sexually dimorphic traits, including body size (males are larger than females) and the area, hue, saturation, and brightness of the dewlap (a colorful ornament that is larger in males than in females). Testosterone masculinized females by increasing body size and dewlap area, hue, and saturation, while reducing dewlap brightness. Control females and males differed significantly in G, but treatment of females with testosterone rendered G statistically indistinguishable from males. Whereas B was characterized by low between-sex genetic correlations when estimated between control females and males, these same correlations increased significantly when estimated between testosterone females and either control or testosterone males. The full G matrix (including B) for testosterone females and either control or testosterone males was significantly less permissive of sexually dimorphic evolution than was G estimated between control females and males, suggesting that natural sex differences in testosterone help decouple genetic variance between the sexes. Our results confirm that hormonal pleiotropy structures genetic covariance, implying that hormones play an important yet overlooked role in mediating evolutionary responses to selection.

Genetic covariances promote climatic adaptation in Australian Drosophila.

Evolutionary potential for adaptation hinges upon the orientation of genetic variation for traits under selection, captured by the additive genetic variance-covariance matrix (G), as well as the evolutionary stability of G. Yet studies that assess both the stability of G and its alignment with selection are extraordinarily rare. We evaluated the stability of G in three Drosophila melanogaster populations that have adapted to local climatic conditions along a latitudinal cline. We estimated population- and sex-specific G matrices for wing size and three climatic stress-resistance traits that diverge adaptively along the cline. To determine how G affects evolutionary potential within these populations, we used simulations to quantify how well G aligns with the direction of trait divergence along the cline (as a proxy for the direction of local selection) and how genetic covariances between traits and sexes influence this alignment. We found that G was stable across the cline, showing no significant divergence overall, or in sex-specific subcomponents, among populations. G also aligned well with the direction of clinal divergence, with genetic covariances strongly elevating evolutionary potential for adaptation to climatic extremes. These results suggest that genetic covariances between both traits and sexes should significantly boost evolutionary responses to environmental change.

Cross-sex genetic covariances limit the evolvability of wing-shape within and among species of Drosophila.

The independent evolution of males and females is potentially constrained by both sexes inheriting the same alleles from their parents. This genetic constraint can limit the evolvability of complex traits; however, there are few studies of multivariate evolution that incorporate cross-sex genetic covariances in their predictions. Drosophila wing-shape has emerged as a model high-dimensional phenotype; wing-shape is highly evolvable in contemporary populations, and yet perplexingly stable across phylogenetic timescales. Here, we show that cross-sex covariances in Drosophila melanogaster, given by the B-matrix, may considerably bias wing-shape evolution. Using random skewers, we show that B would constrain the response to antagonistic selection by 90%, on average, but would double the response to concordant selection. Both cross-sex within-trait and cross-sex cross-trait covariances determined the predicted response to antagonistic selection, but only cross-sex within-trait covariances facilitated the predicted response to concordant selection. Similar patterns were observed in the direction of extant sexual dimorphism in D. melanogaster, and in directions of most and least dimorphic variation across the Drosophila phylogeny. Our results highlight the importance of considering between-sex genetic covariances when making predictions about evolution on both macro- and microevolutionary timescales, and may provide one more explanatory piece in the puzzle of stasis.

The generalized Stejskal-Tanner equation for non-uniform magnetic field gradients.

The intensity of the diffusion weighted NMR signal is described by the Stejskal-Tanner equation, which was derived under the assumption that the gradients are uniform throughout the sample. Nevertheless, it has been demonstrated numerous times that this condition is not fulfilled in the cases of virtually any clinical or research MRI scanners. Therefore, technically, the Stejskal-Tanner equation is valid only for a very specific case of homogeneous gradients. In this paper the Stejskal-Tanner equation was derived for the general case on non-uniform diffusion gradients. To this end, the magnetic field was expressed as linear in a curvilinear coordinate system defined by a vector function p(r). Thereafter, the expression for the non-linear magnetic field was put into the Bloch-Torrey equation and solved. Moreover, the meaning of so-called coil tensor, which is used for the gradients inhomogeneity correction, was explained. It was proven that in the case of the spin echo-based sequences, the Stejskal-Tenner equation is still valid, even if the diffusion gradients are non-uniform. However, in such a case, the b-matrix should be derived for each voxel separately. For other sequence, the derived relation possesses an imaginary term, which corresponds do the phase shift of the diffusion weighted signal.

Analysis and correction of errors in DTI-based tractography due to diffusion gradient inhomogeneity.

The DTI-based tractography, despite its restrictions, is the most widely utilized fiber tracking method in clinical practice. Its fidelity is strictly dependent on the precision and accuracy of the DTI measurement, which in turn is limited by the linearity of the diffusion sensitizing gradient. The influence of the gradient distortions on the differences between the real and measured orientation of fibers was investigated by computer simulations. In addition, the potential of the b-matrix Spatial Distribution in DTI (BSD-DTI) technique in correcting such kind of errors was demonstrated experimentally. The simulations revealed that the diffusion gradient inhomogeneity, if not corrected, leads to the erroneous indication of the fiber direction. The average and maximum deviations were about 1° and 15°, respectively. Remarkably, the deviation between the real and measured orientation of fibers is directionally dependent, what was confirmed in MRI measurement. The deviation errors can be effectively corrected by preceding the DTI measurement with the BSD-DTI calibration.

Matrix Metalloproteinase-9-Generated COOH-, but Not NH2-Terminal Fragments of Serum Amyloid A1 Retain Potentiating Activity in Neutrophil Migration to CXCL8, With Loss of Direct Chemotactic and Cytokine-Inducing Capacity.

Serum amyloid A1 (SAA1) is a prototypic acute phase protein, induced to extremely high levels by physical insults, including inflammation and infection. Human SAA and its NH2-terminal part have been studied extensively in the context of amyloidosis. By contrast, little is known about COOH-terminal fragments of SAA. Intact SAA1 chemoattracts leukocytes via the G protein-coupled receptor formyl peptide receptor like 1/formyl peptide receptor 2 (FPR2). In addition to direct leukocyte activation, SAA1 induces chemokine production by signaling through toll-like receptor 2. We recently discovered that these induced chemokines synergize with intact SAA1 to chemoattract leukocytes in vitro and in vivo. Gelatinase B or matrix metalloproteinase-9 (MMP-9) is also induced by SAA1 during infection and inflammation and processes many substrates in the immune system. We demonstrate here that MMP-9 rapidly cleaves SAA1 at a known consensus sequence that is also present in gelatins. Processing of SAA1 by MMP-9 at an accessible loop between two alpha helices yielded predominantly three COOH-terminal fragments: SAA1(52-104), SAA1(57-104), and SAA1(58-104), with a relative molecular mass of 5,884.4, 5,327.3, and 5,256.3, respectively. To investigate the effect of proteolytic processing on the biological activity of SAA1, we chemically synthesized the COOH-terminal SAA fragments SAA1(52-104) and SAA1(58-104) and the complementary NH2-terminal peptide SAA1(1-51). In contrast to intact SAA1, the synthesized SAA1 peptides did not induce interleukin-8/CXCL8 in monocytes or fibroblasts. Moreover, these fragments possessed no direct chemotactic activity for neutrophils, as observed for intact SAA1. However, comparable to intact SAA1, SAA1(58-104) cooperated with CXCL8 in neutrophil activation and migration, whereas SAA1(1-51) lacked this potentiating activity. This cooperative interaction between the COOH-terminal SAA1 fragment and CXCL8 in neutrophil chemotaxis was mediated by FPR2. Hence, proteolytic cleavage of SAA1 by MMP-9 fine tunes the inflammatory capacity of this acute phase protein in that only the synergistic interactions with chemokines remain to prolong the duration of inflammation.

An improved error bound for linear complementarity problems for B-matrices.

A new error bound for the linear complementarity problem when the matrix involved is a B-matrix is presented, which improves the corresponding result in (Li et al. in Electron. J. Linear Algebra 31(1):476-484, 2016). In addition some sufficient conditions such that the new bound is sharper than that in (García-Esnaola and Peña in Appl. Math. Lett. 22(7):1071-1075, 2009) are provided.

Error bounds for linear complementarity problems of weakly chained diagonally dominant B-matrices.

In this paper, new error bounds for the linear complementarity problem are obtained when the involved matrix is a weakly chained diagonally dominant B-matrix. The proposed error bounds are better than some existing results. The advantages of the results obtained are illustrated by numerical examples.

Improving the accuracy of PGSE DTI experiments using the spatial distribution of b matrix.

A novel method for improving the accuracy of diffusion tensor imaging (DTI) is proposed. It takes into account the b matrix spatial variations, which can be easily determined using a simple anisotropic diffusion phantom. In opposite to standard numerical procedure of the b matrix calculation that requires the exact knowledge of amplitudes, shapes and time dependencies of diffusion gradients, the new method, which we call BSD-DTI (B-matrix spatial distribution in DTI), relies on direct measurements of its space-dependent components. The proposed technique was demonstrated on the Bruker Biospec 94/20USR system, using the spin echo diffusion sequence to image an isotropic water phantom and an anisotropic capillary phantom. The accuracy of the diffusion tensor determination was improved by an overall factor of about 8 for the isotropic water phantom.