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SUMMARY To reach Earth’s surface, magma must ascend from the hot, ductile asthenosphere through cold and brittle rock in the lithosphere. It does so via fluid-filled fractures called dykes. While the continuum mechanics of ductile asthenosphere is well established, there has been little theoretical work on the cold and brittle regime where dyking and faulting occurs. Geodynamic models use plasticity to model fault-like behaviour; plasticity also shows promise for modelling dykes. Here we build on an existing model to develop a poro-viscoelastic–viscoplastic theory for two-phase flow across the lithosphere. Our theory addresses the deficiencies of previous work by incorporating (i) a hyperbolic yield surface, (ii) a plastic potential with control of dilatancy and (iii) a viscous regularization of plastic failure. We use analytical and numerical solutions to investigate the behaviour of this theory. Through idealized models and a comparison to linear elastic fracture mechanics, we demonstrate that this behaviour includes a continuum representation of dyking. Finally, we consider a model scenario reminiscent of continental rifting and demonstrate the consequences of dyke injection into the cold, upper lithosphere: a sharp reduction in the force required to rift. 

SPEX Left LU is a software package for exactly solving unsymmetric sparse linear systems. As a component of the sparse exact (SPEX) software package, SPEX Left LU can be applied to any input matrix, A , whose entries are integral, rational, or decimal, and provides a solution to the system \( Ax = b \) , which is either exact or accurate to user-specified precision. SPEX Left LU preorders the matrix A with a user-specified fill-reducing ordering and computes a left-looking LU factorization with the special property that each operation used to compute the L and U matrices is integral. Notable additional applications of this package include benchmarking the stability and accuracy of state-of-the-art linear solvers and determining whether singular-to-double-precision matrices are indeed singular. Computationally, this article evaluates the impact of several novel pivoting schemes in exact arithmetic, benchmarks the exact iterative solvers within Linbox, and benchmarks the accuracy of MATLAB sparse backslash. Most importantly, it is shown that SPEX Left LU outperforms the exact iterative solvers in run time on easy instances and in stability as the iterative solver fails on a sizeable subset of the tested (both easy and hard) instances. The SPEX Left LU package is written in ANSI C, comes with a MATLAB interface, and is distributed via GitHub, as a component of the SPEX software package, and as a component of SuiteSparse. 

ABSTRACT In the oligotrophic oceans, key autotrophs depend on “helper” bacteria to reduce oxidative stress from hydrogen peroxide (H 2 O 2 ) in the extracellular environment. H 2 O 2 is also a ubiquitous stressor in freshwaters, but the effects of H 2 O 2 on autotrophs and their interactions with bacteria are less well understood in freshwaters. Naturally occurring H 2 O 2 in freshwater systems is proposed to impact the proportion of microcystin-producing (toxic) and non-microcystin-producing (nontoxic) Microcystis in blooms, which influences toxin concentrations and human health impacts. However, how different strains of Microcystis respond to naturally occurring H 2 O 2 concentrations and the microbes responsible for H 2 O 2 decomposition in freshwater cyanobacterial blooms are unknown. To address these knowledge gaps, we used metagenomics and metatranscriptomics to track the presence and expression of genes for H 2 O 2 decomposition by microbes during a cyanobacterial bloom in western Lake Erie in the summer of 2014. katG encodes the key enzyme for decomposing extracellular H 2 O 2 but was absent in most Microcystis cells. katG transcript relative abundance was dominated by heterotrophic bacteria. In axenic Microcystis cultures, an H 2 O 2 scavenger (pyruvate) significantly improved growth rates of one toxic strain while other toxic and nontoxic strains were unaffected. These results indicate that heterotrophic bacteria play a key role in H 2 O 2 decomposition in Microcystis blooms and suggest that their activity may affect the fitness of some Microcystis strains and thus the strain composition of Microcystis blooms but not along a toxic versus nontoxic dichotomy. IMPORTANCE Cyanobacterial harmful algal blooms (CHABs) threaten freshwater ecosystems globally through the production of toxins. Toxin production by cyanobacterial species and strains during CHABs varies widely over time and space, but the ecological drivers of the succession of toxin-producing species remain unclear. Hydrogen peroxide (H 2 O 2 ) is ubiquitous in natural waters, inhibits microbial growth, and may determine the relative proportions of Microcystis strains during blooms. However, the mechanisms and organismal interactions involved in H 2 O 2 decomposition are unexplored in CHABs. This study shows that some strains of bloom-forming freshwater cyanobacteria benefit from detoxification of H 2 O 2 by associated heterotrophic bacteria, which may impact bloom development. 

To meet the growing need for extended or exact precision solvers, an efficient framework based on Integer-Preserving Gaussian Elimination (IPGE) has been recently developed, which includes dense/sparse LU/Cholesky factorizations and dense LU/Cholesky factorization updates for column and/or row replacement. This paper discusses our ongoing work developing the sparse LU/Cholesky column/row-replacement update and the sparse rank-l update/downdate. We first present some basic background for the exact factorization framework based on IPGE. Then we give our proposed algorithms along with some implementation and data-structure details. Finally, we provide some experimental results showcasing the performance of our update algorithms. Specifically, we show that updating these exact factorizations can typically be 10x to 100x faster than (re-)factorizing the matrices from scratch. 

Abstract Planktothrix agardhii dominates the cyanobacterial harmful algal bloom biomass in Sandusky Bay, Lake Erie (USA) from May until September. This filamentous cyanobacterium known parasites including the chytrid fungal species Rhizophydium sp. C02, which was previously isolated from this region. The purpose of our work has been to establish how parasitic interactions affect Planktothrix population dynamics during a bloom event. Samples analyzed from the 2015 to 2019 bloom seasons using quantitative PCR investigate the spatial and temporal prevalence of chytrid infections. Abiotic factors examined in lab include manipulating temperature (17–31°C), conductivity (0.226–1.225 mS/cm) and turbulence. Planktothrix-specific chytrids are present throughout the bloom period and are occasionally at high enough densities to exert parasitic pressure on their hosts. Temperatures above 27.1°C in lab can inhibit chytrid infection, indicating the presence of a possible upper thermal refuge for the host. Data suggest that chytrids can survive conductivity spikes in lab at levels three-fold above Sandusky Bay waters if given sufficient time (7–12 days), whereas increased turbulence in lab severely inhibits chytrid infections, perhaps due to disruption of chemical signaling. Overall, these data provide insights into the environmental conditions that inhibit chytrid infections during Planktothrix-dominated blooms in temperate waters.