Foundations of space-time finite element methods: polytopes, interpolation, and integration

The main purpose of this article is to facilitate the implementation of space-time finite element methods in four-dimensional space. In order to develop a finite element method in this setting, it is necessary to create a numerical foundation, or equivalently a numerical infrastructure. This foundation should include a collection of suitable elements (usually hypercubes, simplices, or closely related polytopes), numerical interpolation procedures (usually orthonormal polynomial bases), and numerical integration procedures (usually quadrature rules). It is well known that each of these areas has yet to be fully explored, and in the present article, we attempt to directly address this issue. We begin by developing a concrete, sequential procedure for constructing generic four-dimensional elements (4-polytopes). Thereafter, we review the key numerical properties of several canonical elements: the tesseract, tetrahedral prism, and pentatope. Here, we provide explicit expressions for orthonormal polynomial bases on these elements. Next, we construct fully symmetric quadrature rules with positive weights that are capable of exactly integrating high-degree polynomials, e.g. up to degree 17 on the tesseract. Finally, the quadrature rules are successfully tested using a set of canonical numerical experiments on polynomial and transcendental functions.Comment: 34 pages, 18 figure

Rare coding variants in ten genes confer substantial risk for schizophrenia

Rare coding variation has historically provided the most direct connections between gene function and disease pathogenesis. By meta-analysing the whole exomes of 24,248 schizophrenia cases and 97,322 controls, we implicate ultra-rare coding variants (URVs) in 10 genes as conferring substantial risk for schizophrenia (odds ratios of 3-50, PPeer reviewe

Ubiquitous molecular substrates for associative learning and activity-dependent neuronal facilitation.

Recent evidence suggests that many of the molecular cascades and substrates that contribute to learning-related forms of neuronal plasticity may be conserved across ostensibly disparate model systems. Notably, the facilitation of neuronal excitability and synaptic transmission that contribute to associative learning in Aplysia and Hermissenda, as well as associative LTP in hippocampal CA1 cells, all require (or are enhanced by) the convergence of a transient elevation in intracellular Ca2+ with transmitter binding to metabotropic cell-surface receptors. This temporal convergence of Ca2+ and G-protein-stimulated second-messenger cascades synergistically stimulates several classes of serine/threonine protein kinases, which in turn modulate receptor function or cell excitability through the phosphorylation of ion channels. We present a summary of the biophysical and molecular constituents of neuronal and synaptic facilitation in each of these three model systems. Although specific components of the underlying molecular cascades differ across these three systems, fundamental aspects of these cascades are widely conserved, leading to the conclusion that the conceptual semblance of these superficially disparate systems is far greater than is generally acknowledged. We suggest that the elucidation of mechanistic similarities between different systems will ultimately fulfill the goal of the model systems approach, that is, the description of critical and ubiquitous features of neuronal and synaptic events that contribute to memory induction

Schizophrenia-associated somatic copy-number variants from 12,834 cases reveal recurrent NRXN1 and ABCB11 disruptions

While germline copy-number variants (CNVs) contribute to schizophrenia (SCZ) risk, the contribution of somatic CNVs (sCNVs)—present in some but not all cells—remains unknown. We identified sCNVs using blood-derived genotype arrays from 12,834 SCZ cases and 11,648 controls, filtering sCNVs at loci recurrently mutated in clonal blood disorders. Likely early-developmental sCNVs were more common in cases (0.91%) than controls (0.51%, p = 2.68e−4), with recurrent somatic deletions of exons 1–5 of the NRXN1 gene in five SCZ cases. Hi-C maps revealed ectopic, allele-specific loops forming between a potential cryptic promoter and non-coding cis-regulatory elements upon 5′ deletions in NRXN1. We also observed recurrent intragenic deletions of ABCB11, encoding a transporter implicated in anti-psychotic response, in five treatment-resistant SCZ cases and showed that ABCB11 is specifically enriched in neurons forming mesocortical and mesolimbic dopaminergic projections. Our results indicate potential roles of sCNVs in SCZ risk

Emerging Challenges for Weed Management in Herbicide-Resistant Crops

Since weed management is such a critical component of agronomic crop production systems, herbicides are widely used to provide weed control to ensure that yields are maximized. In the last few years, herbicide-resistant (HR) crops, particularly those that are glyphosate-resistant, and more recently, those with dicamba (3,6-dichloro-2-methoxybenzoic acid) and 2,4-D (2,4-dichlorophenoxyacetic acid) resistance are changing the way many growers manage weeds. However, past reliance on glyphosate and mistakes made in stewardship of the glyphosate-resistant cropping system have directly led to the current weed resistance problems that now occur in many agronomic cropping systems, and new technologies must be well-stewarded. New herbicide-resistant trait technologies in soybean, such as dicamba-, 2,4-D-, and isoxaflutole- ((5-cyclopropyl-4-isoxazolyl)[2-(methylsulfonyl)-4-(trifluoromethyl)phenyl]methanone) resistance, are being combined with glyphosate- and glufosinate-resistance traits to manage herbicide-resistant weed populations. In cropping systems with glyphosate-resistant weed species, these new trait options may provide effective weed management tools, although there may be increased risk of off-target movement and susceptible plant damage with the use of some of these technologies. The use of diverse weed management practices to reduce the selection pressure for herbicide-resistant weed evolution is essential to preserve the utility of new traits. The use of herbicides with differing sites of action (SOAs), ideally in combination as mixtures, but also in rotation as part of a weed management program may slow the evolution of resistance in some cases. Increased selection pressure from the effects of some herbicide mixtures may lead to more cases of metabolic herbicide resistance. The most effective long-term approach for weed resistance management is the use of Integrated Weed Management (IWM) which may build the ecological complexity of the cropping system. Given the challenges in management of herbicide-resistant weeds, IWM will likely play a critical role in enhancing future food security for a growing global population