Exact vortex solutions in a CP^N Skyrme-Faddeev type model

We consider a four dimensional field theory with target space being CP^N which constitutes a generalization of the usual Skyrme-Faddeev model defined on CP^1. We show that it possesses an integrable sector presenting an infinite number of local conservation laws, which are associated to the hidden symmetries of the zero curvature representation of the theory in loop space. We construct an infinite class of exact solutions for that integrable submodel where the fields are meromorphic functions of the combinations (x^1+i x^2) and (x^3+x^0) of the Cartesian coordinates of four dimensional Minkowski space-time. Among those solutions we have static vortices and also vortices with waves traveling along them with the speed of light. The energy per unity of length of the vortices show an interesting and intricate interaction among the vortices and waves.Comment: 21 pages, plain latex, no figure

Teaching and Learning of Calculus

This survey focuses on the main trends in the field of calculus education. Despite their variety, the findings reveal a cornerstone issue that is strongly linked to the formalism of calculus concepts and to the difficulties it generates in the learning and teaching process. As a complement to the main text, an extended bibliography with some of the most important references on this topic is included. Since the diversity of the research in the field makes it difficult to produce an exhaustive state-of-the-art summary, the authors discuss recent developments that go beyond this survey and put forward new research questions

Current understanding of the human microbiome

Author Posting. © The Author(s), 2018. This is the author's version of the work. It is posted here by permission of Nature Publishing Group for personal use, not for redistribution. The definitive version was published in Nature Medicine 24 (2018): 392–400, doi:10.1038/nm.4517.Our understanding of the link between the human microbiome and disease, including obesity, inflammatory bowel disease, arthritis and autism, is rapidly expanding. Improvements in the throughput and accuracy of DNA sequencing of the genomes of microbial communities associated with human samples, complemented by analysis of transcriptomes, proteomes, metabolomes and immunomes, and mechanistic experiments in model systems, have vastly improved our ability to understand the structure and function of the microbiome in both diseased and healthy states. However, many challenges remain. In this Review, we focus on studies in humans to describe these challenges, and propose strategies that leverage existing knowledge to move rapidly from correlation to causation, and ultimately to translation.Many of the studies described here in our laboratories were supported by the NIH, NSF, DOE, and the Alfred P. Sloan Foundation.2018-10-1

Effects of macromolecular crowding on intracellular diffusion from a single particle perspective

Compared to biochemical reactions taking place in relatively well-defined aqueous solutions in vitro, the corresponding reactions happening in vivo occur in extremely complex environments containing only 60–70% water by volume, with the remainder consisting of an undefined array of bio-molecules. In a biological setting, such extremely complex and volume-occupied solution environments are termed ‘crowded’. Through a range of intermolecular forces and pseudo-forces, this complex background environment may cause biochemical reactions to behave differently to their in vitro counterparts. In this review, we seek to highlight how the complex background environment of the cell can affect the diffusion of substances within it. Engaging the subject from the perspective of a single particle’s motion, we place the focus of our review on two areas: (1) experimental procedures for conducting single particle tracking experiments within cells along with methods for extracting information from these experiments; (2) theoretical factors affecting the translational diffusion of single molecules within crowded two-dimensional membrane and three-dimensional solution environments. We conclude by discussing a number of recent publications relating to intracellular diffusion in light of the reviewed material

Negative feedback regulation of the ERK1/2 MAPK pathway

The extracellular signal-regulated kinase 1/2 (ERK1/2) mitogen-activated protein kinase (MAPK) signalling pathway regulates many cellular functions, including proliferation, differentiation, and transformation. To reliably convert external stimuli into specific cellular responses and to adapt to environmental circumstances, the pathway must be integrated into the overall signalling activity of the cell. Multiple mechanisms have evolved to perform this role. In this review, we will focus on negative feedback mechanisms and examine how they shape ERK1/2 MAPK signalling. We will first discuss the extensive number of negative feedback loops targeting the different components of the ERK1/2 MAPK cascade, specifically the direct posttranslational modification of pathway components by downstream protein kinases and the induction of de novo gene synthesis of specific pathway inhibitors. We will then evaluate how negative feedback modulates the spatiotemporal signalling dynamics of the ERK1/2 pathway regarding signalling amplitude and duration as well as subcellular localisation. Aberrant ERK1/2 activation results in deregulated proliferation and malignant transformation in model systems and is commonly observed in human tumours. Inhibition of the ERK1/2 pathway thus represents an attractive target for the treatment of malignant tumours with increased ERK1/2 activity. We will, therefore, discuss the effect of ERK1/2 MAPK feedback regulation on cancer treatment and how it contributes to reduced clinical efficacy of therapeutic agents and the development of drug resistance

PolyMorphine provides extended analgesic-like effects in mice with spared nerve injury

Morphine is a well-characterized and effective analgesic commonly used to provide pain relief to patients suffering from both acute and chronic pain conditions. Despite its widespread use and effectiveness, one of the major drawbacks of morphine is its relatively short half-life of approximately 4 h. This short half-life often necessitates multiple administrations of the drug each day, which may contribute to both dependence and tolerance to morphine. Here, we tested the analgesic properties of a new polymer form of morphine known as PolyMorphine. This polymer has monomeric units of morphine incorporated into a poly(anhydride-ester) backbone that has been shown to hydrolyze into free morphine in vitro. Using an animal model of chronic pain, the spared nerve injury surgery, we showed that PolyMorphine is able to block spared nerve injury-induced hypersensitivity in mice for up to 24-h post-administration. Free morphine was shown to only block spared nerve injury-induced hypersensitivity for up to 2-h post-injection. PolyMorphine was also shown to act through the mu opioid receptor due to the ability of naloxone (a mu opioid receptor antagonist) to block PolyMorphine-induced analgesia in spared nerve injury animals pretreated with PolyMorphine. Additionally, we observed that PolyMorphine causes similar locomotor and constipation side effects as free morphine. Finally, we investigated if PolyMorphine had any effects in a non-evoked pain assay, conditioned place preference. Pretreatment of spared nerve injury mice with PolyMorphine blocked the development of conditioned place preference for 2-methyl-6-(phenylethynyl)pyridine (MPEP), a short-lasting mGluR5 antagonist with analgesic-like properties. Free morphine does not block the development of preference for MPEP, suggesting that PolyMorphine has longer lasting analgesic effects compared to free morphine. Together, these data show that PolyMorphine has the potential to provide analgesia for significantly longer than free morphine while likely working through the same receptor

Identification of outliers in a one-way random effects model

mixed linear model, variance components, random effects, robust statistics, median, median absolute deviation,