Symmetric indefinite triangular factorization revealing the rank profile matrix

We present a novel recursive algorithm for reducing a symmetric matrix to a triangular factorization which reveals the rank profile matrix. That is, the algorithm computes a factorization $\mathbf{P}^T\mathbf{A}\mathbf{P} = \mathbf{L}\mathbf{D}\mathbf{L}^T$ where $\mathbf{P}$ is a permutation matrix, $\mathbf{L}$ is lower triangular with a unit diagonal and $\mathbf{D}$ is symmetric block diagonal with $1{\times}1$ and $2{\times}2$ antidiagonal blocks. The novel algorithm requires $O(n^2r^{\omega-2})$ arithmetic operations. Furthermore, experimental results demonstrate that our algorithm can even be slightly more than twice as fast as the state of the art unsymmetric Gaussian elimination in most cases, that is it achieves approximately the same computational speed. By adapting the pivoting strategy developed in the unsymmetric case, we show how to recover the rank profile matrix from the permutation matrix and the support of the block-diagonal matrix. There is an obstruction in characteristic $2$ for revealing the rank profile matrix which requires to relax the shape of the block diagonal by allowing the 2-dimensional blocks to have a non-zero bottom-right coefficient. This relaxed decomposition can then be transformed into a standard $\mathbf{P}\mathbf{L}\mathbf{D}\mathbf{L}^T\mathbf{P}^T$ decomposition at a negligible cost

On fast multiplication of a matrix by its transpose

We present a non-commutative algorithm for the multiplication of a 2x2-block-matrix by its transpose using 5 block products (3 recursive calls and 2 general products) over C or any finite field.We use geometric considerations on the space of bilinear forms describing 2x2 matrix products to obtain this algorithm and we show how to reduce the number of involved additions.The resulting algorithm for arbitrary dimensions is a reduction of multiplication of a matrix by its transpose to general matrix product, improving by a constant factor previously known reductions.Finally we propose schedules with low memory footprint that support a fast and memory efficient practical implementation over a finite field.To conclude, we show how to use our result in LDLT factorization.Comment: ISSAC 2020, Jul 2020, Kalamata, Greec

On fast multiplication of a matrix by its transpose

We present a non-commutative algorithm for the multiplication of a block-matrix by its transpose over C or any finite field using 5 recursive products. We use geometric considerations on the space of bilinear forms describing 2×2 matrix products to obtain this algorithm and we show how to reduce the number of involved additions. The resulting algorithm for arbitrary dimensions is a reduction of multiplication of a matrix by its transpose to general matrix product, improving by a constant factor previously known reductions. Finally we propose space and time efficient schedules that enable us to provide fast practical implementations for higher-dimensional matrix products

A systematic review on the use of quantitative imaging to detect cancer therapy adverse effects in normal-appearing brain tissue

Cancer therapy for both central nervous system (CNS) and non-CNS tumors has been previously associated with transient and long-term cognitive deterioration, commonly referred to as ‘chemo fog’. This therapy-related damage to otherwise normal-appearing brain tissue is reported using post-mortem neuropathological analysis. Although the literature on monitoring therapy effects on structural magnetic resonance imaging (MRI) is well established, such macroscopic structural changes appear relatively late and irreversible. Early quantitative MRI biomarkers of therapy-induced damage would potentially permit taking these treatment side effects into account, paving the way towards a more personalized treatment planning. This systematic review (PROSPERO number 224196) provides an overview of quantitative tomographic imaging methods, potentially identifying the adverse side effects of cancer therapy in normal-appearing brain tissue. Seventy studies were obtained from the MEDLINE and Web of Science databases. Studies reporting changes in normal-appearing brain tissue using MRI, PET, or SPECT quantitative biomarkers, related to radio-, chemo-, immuno-, or hormone therapy for any kind of solid, cystic, or liquid tumor were included. The main findings of the reviewed studies were summarized, providing also the risk of bias of each study assessed using a modified QUADAS-2 tool. For each imaging method, this review provides the methodological background, and the benefits and shortcomings of each method from the imaging perspective. Finally, a set of recommendations is proposed to support future research

Opposite Modulation of RAC1 by Mutations in TRIO Is Associated with Distinct, Domain-Specific Neurodevelopmental Disorders

The Rho-guanine nucleotide exchange factor (RhoGEF) TRIO acts as a key regulator of neuronal migration, axonal outgrowth, axon guidance, and synaptogenesis by activating the GTPase RAC1 and modulating actin cytoskeleton remodeling. Pathogenic variants in TRIO are associated with neurodevelopmental diseases, including intellectual disability (ID) and autism spectrum disorders (ASD). Here, we report the largest international cohort of 24 individuals with confirmed pathogenic missense or nonsense variants in TRIO. The nonsense mutations are spread along the TRIO sequence, and affected individuals show variable neurodevelopmental phenotypes. In contrast, missense variants cluster into two mutational hotspots in the TRIO sequence, one in the seventh spectrin repeat and one in the RAC1-activating GEFD1. Although all individuals in this cohort present with developmental delay and a neuro-behavioral phenotype, individuals with a pathogenic variant in the seventh spectrin repeat have a more severe ID associated with macrocephaly than do most individuals with GEFD1 variants, who display milder ID and microcephaly. Functional studies show that the spectrin and GEFD1 variants cause a TRIO-mediated hyper- or hypo-activation of RAC1, respectively, and we observe a striking correlation between RAC1 activation levels and the head size of the affected individuals. In addition, truncations in TRIO GEFD1 in the vertebrate model X. tropicalis induce defects that are concordant with the human phenotype. This work demonstrates distinct clinical and molecular disorders clustering in the GEFD1 and seventh spectrin repeat domains and highlights the importance of tight control of TRIO-RAC1 signaling in neuronal development.<br/

Distributional Patterns of Polychaetes Across the West Antarctic Based on DNA Barcoding and Particle Tracking Analyses

Recent genetic investigations have uncovered a high proportion of cryptic species within Antarctic polychaetes. It is likely that these evolved in isolation during periods of glaciation, and it is possible that cryptic populations would have remained geographically restricted from one another occupying different regions of Antarctica. By analysing the distributions of nine morphospecies, (six of which contained potential cryptic species), we find evidence for widespread distributions within the West Antarctic. Around 60% of the cryptic species exhibited sympatric distributions, and at least one cryptic clade was found to be widespread. Additional DNA barcodes from GenBank and morphological records extended the observed range of three species studied here, and indicate potential circum-Antarctic traits. Particle tracking analyses were used to model theoretical dispersal ranges of pelagic larvae. Data from these models suggest that the observed species distributions inferred from genetic similarity could have been established and maintained through the regional oceanographic currents, including the Antarctic Circumpolar Current (ACC) and its coastal counter current. Improved understanding of the distribution of Antarctic fauna is essential for predicting the impacts of environmental change and determining management strategies for the region.Copyright © 2017 Brasier, Harle, Wiklund, Jeffreys, Linse, Ruhl and Glover. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms

A Tri-Oceanic Perspective: DNA Barcoding Reveals Geographic Structure and Cryptic Diversity in Canadian Polychaetes

Although polychaetes are one of the dominant taxa in marine communities, their distributions and taxonomic diversity are poorly understood. Recent studies have shown that many species thought to have broad distributions are actually a complex of allied species. In Canada, 12% of polychaete species are thought to occur in Atlantic, Arctic, and Pacific Oceans, but the extent of gene flow among their populations has not been tested.Sequence variation in a segment of the mitochondrial cytochrome c oxidase I (COI) gene was employed to compare morphological versus molecular diversity estimates, to examine gene flow among populations of widespread species, and to explore connectivity patterns among Canada's three oceans. Analysis of 1876 specimens, representing 333 provisional species, revealed 40 times more sequence divergence between than within species (16.5% versus 0.38%). Genetic data suggest that one quarter of previously recognized species actually include two or more divergent lineages, indicating that richness in this region is currently underestimated. Few species with a tri-oceanic distribution showed genetic cohesion. Instead, large genetic breaks occur between Pacific and Atlantic-Arctic lineages, suggesting their long-term separation. High connectivity among Arctic and Atlantic regions and low connectivity with the Pacific further supports the conclusion that Canadian polychaetes are partitioned into two distinct faunas.Results of this study confirm that COI sequences are an effective tool for species identification in polychaetes, and suggest that DNA barcoding will aid the recognition of species overlooked by the current taxonomic system. The consistent geographic structuring within presumed widespread species suggests that historical range fragmentation during the Pleistocene ultimately increased Canadian polychaete diversity and that the coastal British Columbia fauna played a minor role in Arctic recolonization following deglaciation. This study highlights the value of DNA barcoding for providing rapid insights into species distributions and biogeographic patterns in understudied groups

Ebolavirus Is Internalized into Host Cells via Macropinocytosis in a Viral Glycoprotein-Dependent Manner

Ebolavirus (EBOV) is an enveloped, single-stranded, negative-sense RNA virus that causes severe hemorrhagic fever with mortality rates of up to 90% in humans and nonhuman primates. Previous studies suggest roles for clathrin- or caveolae-mediated endocytosis in EBOV entry; however, ebolavirus virions are long, filamentous particles that are larger than the plasma membrane invaginations that characterize clathrin- or caveolae-mediated endocytosis. The mechanism of EBOV entry remains, therefore, poorly understood. To better understand Ebolavirus entry, we carried out internalization studies with fluorescently labeled, biologically contained Ebolavirus and Ebolavirus-like particles (Ebola VLPs), both of which resemble authentic Ebolavirus in their morphology. We examined the mechanism of Ebolavirus internalization by real-time analysis of these fluorescently labeled Ebolavirus particles and found that their internalization was independent of clathrin- or caveolae-mediated endocytosis, but that they co-localized with sorting nexin (SNX) 5, a marker of macropinocytosis-specific endosomes (macropinosomes). Moreover, the internalization of Ebolavirus virions accelerated the uptake of a macropinocytosis-specific cargo, was associated with plasma membrane ruffling, and was dependent on cellular GTPases and kinases involved in macropinocytosis. A pseudotyped vesicular stomatitis virus possessing the Ebolavirus glycoprotein (GP) also co-localized with SNX5 and its internalization and infectivity were affected by macropinocytosis inhibitors. Taken together, our data suggest that Ebolavirus is internalized into cells by stimulating macropinocytosis in a GP-dependent manner. These findings provide new insights into the lifecycle of Ebolavirus and may aid in the development of therapeutics for Ebolavirus infection

The Open Brain Consent: Informing research participants and obtaining consent to share brain imaging data

Having the means to share research data openly is essential to modern science. For human research, a key aspect in this endeavor is obtaining consent from participants, not just to take part in a study, which is a basic ethical principle, but also to share their data with the scientific community. To ensure that the participants' privacy is respected, national and/or supranational regulations and laws are in place. It is, however, not always clear to researchers what the implications of those are, nor how to comply with them. The Open Brain Consent (https://open-brain-consent.readthedocs.io) is an international initiative that aims to provide researchers in the brain imaging community with information about data sharing options and tools. We present here a short history of this project and its latest developments, and share pointers to consent forms, including a template consent form that is compliant with the EU general data protection regulation. We also share pointers to an associated data user agreement that is not only useful in the EU context, but also for any researchers dealing with personal (clinical) data elsewhere

Finite field linear algebra subroutines

International audienceIn this paper we study different implementations of finite field arithmetic, essential foundation of computer algebra. We focus on Galois fields of word size cardinality at most, with any characteristic. Classical representations as machine integers, floating point numbers, polynomials and Zech logarithms are compared. Furthermore, very efficient implementations of finite field dot products, matrix-vector products and matrix-matrix products (namely the symbolic equivalent of level 1, 2 and 3 BLAS) are presented. Our implementations have many symbolic linear algebra applications: symbolic triangularization, system solving, exact determinant computation, matrix normal form are such examples