Semilinear mixed problems on Hilbert complexes and their numerical approximation

Arnold, Falk, and Winther recently showed [Bull. Amer. Math. Soc. 47 (2010), 281-354] that linear, mixed variational problems, and their numerical approximation by mixed finite element methods, can be studied using the powerful, abstract language of Hilbert complexes. In another recent article [arXiv:1005.4455], we extended the Arnold-Falk-Winther framework by analyzing variational crimes (a la Strang) on Hilbert complexes. In particular, this gave a treatment of finite element exterior calculus on manifolds, generalizing techniques from surface finite element methods and recovering earlier a priori estimates for the Laplace-Beltrami operator on 2- and 3-surfaces, due to Dziuk [Lecture Notes in Math., vol. 1357 (1988), 142-155] and later Demlow [SIAM J. Numer. Anal., 47 (2009), 805-827], as special cases. In the present article, we extend the Hilbert complex framework in a second distinct direction: to the study of semilinear mixed problems. We do this, first, by introducing an operator-theoretic reformulation of the linear mixed problem, so that the semilinear problem can be expressed as an abstract Hammerstein equation. This allows us to obtain, for semilinear problems, a priori solution estimates and error estimates that reduce to the Arnold-Falk-Winther results in the linear case. We also consider the impact of variational crimes, extending the results of our previous article to these semilinear problems. As an immediate application, this new framework allows for mixed finite element methods to be applied to semilinear problems on surfaces.Comment: 22 pages; v2: major revision, particularly sharpening of error estimates in Section

Yang-Mills Interactions and Gravity in Terms of Clifford Algebra

A model of Yang-Mills interactions and gravity in terms of the Clifford algebra Cl(0,6) is presented. The gravity and Yang-Mills actions are formulated as different order terms in a generalized action. The feebleness of gravity as well as the smallness of the cosmological constant and theta terms are discussed at the classical level. The invariance groups, including the de Sitter and the Pati-Salam SU(4) subgroups, consist of gauge transformations from either side of an algebraic spinor. Upon symmetry breaking via the Higgs fields, the remaining symmetries are the Lorentz SO(1,3), color SU(3), electromagnetic U(1)_EM, and an additional U(1). The first generation leptons and quarks are identified with even and odd parts of spinor idempotent projections. There are still several shortcomings with the current model. Further research is needed to fully recover the standard model results.Comment: 20 pages, to appear in Advances in Applied Clifford Algebra

Ultrafast carrier relaxation in GaN, In_(0.05)Ga_(0.95)N and an In_(0.05)Ga_(0.95)/In_(0.15)Ga_(0.85)N Multiple Quantum Well

Room temperature, wavelength non-degenerate ultrafast pump/probe measurements were performed on GaN and InGaN epilayers and an InGaN multiple quantum well structure. Carrier relaxation dynamics were investigated as a function of excitation wavelength and intensity. Spectrally-resolved sub-picosecond relaxation due to carrier redistribution and QW capture was found to depend sensitively on the wavelength of pump excitation. Moreover, for pump intensities above a threshold of 100 microJ/cm2, all samples demonstrated an additional emission feature arising from stimulated emission (SE). SE is evidenced as accelerated relaxation (< 10 ps) in the pump-probe data, fundamentally altering the re-distribution of carriers. Once SE and carrier redistribution is completed, a slower relaxation of up to 1 ns for GaN and InGaN epilayers, and 660 ps for the MQW sample, indicates carrier recombination through spontaneous emission.Comment: submitted to Phys. Rev.

Advancing urban mental health research: from complexity science to actionable targets for intervention

Urbanisation and common mental disorders (CMDs; ie, depressive, anxiety, and substance use disorders) are increasing worldwide. In this Review, we discuss how urbanicity and risk of CMDs relate to each other and call for a complexity science approach to advance understanding of this interrelationship. We did an ecological analysis using data on urbanicity and CMD burden in 191 countries. We found a positive, non-linear relationship with a higher CMD prevalence in more urbanised countries, particularly for anxiety disorders. We also did a review of meta-analytic studies on the association between urban factors and CMD risk. We identified factors relating to the ambient, physical, and social urban environment and showed differences per diagnosis of CMDs. We argue that factors in the urban environment are likely to operate as a complex system and interact with each other and with individual city inhabitants (including their psychological and neurobiological characteristics) to shape mental health in an urban context. These interactions operate on various timescales and show feedback loop mechanisms, rendering system behaviour characterised by non-linearity that is hard to predict over time. We present a conceptual framework for future urban mental health research that uses a complexity science approach. We conclude by discussing how complexity science methodology (eg, network analyses, system-dynamic modelling, and agent-based modelling) could enable identification of actionable targets for treatment and policy, aimed at decreasing CMD burdens in an urban context

Origins of the Ambient Solar Wind: Implications for Space Weather

The Sun's outer atmosphere is heated to temperatures of millions of degrees, and solar plasma flows out into interplanetary space at supersonic speeds. This paper reviews our current understanding of these interrelated problems: coronal heating and the acceleration of the ambient solar wind. We also discuss where the community stands in its ability to forecast how variations in the solar wind (i.e., fast and slow wind streams) impact the Earth. Although the last few decades have seen significant progress in observations and modeling, we still do not have a complete understanding of the relevant physical processes, nor do we have a quantitatively precise census of which coronal structures contribute to specific types of solar wind. Fast streams are known to be connected to the central regions of large coronal holes. Slow streams, however, appear to come from a wide range of sources, including streamers, pseudostreamers, coronal loops, active regions, and coronal hole boundaries. Complicating our understanding even more is the fact that processes such as turbulence, stream-stream interactions, and Coulomb collisions can make it difficult to unambiguously map a parcel measured at 1 AU back down to its coronal source. We also review recent progress -- in theoretical modeling, observational data analysis, and forecasting techniques that sit at the interface between data and theory -- that gives us hope that the above problems are indeed solvable.Comment: Accepted for publication in Space Science Reviews. Special issue connected with a 2016 ISSI workshop on "The Scientific Foundations of Space Weather." 44 pages, 9 figure

Conjunctivitis in atopic dermatitis patients with and without dupilumab therapy - international eczema council survey and opinion.

Background: Conjunctivitis is common in patients with atopic dermatitis (AD) in general and a commonly reported adverse event in AD clinical trials with dupilumab. Objective: To survey opinions and experience about conjunctivitis occurring in AD, including those during dupilumab treatment in a group of AD experts from the International Eczema Council (IEC). Methods: Electronic survey and in-person discussion of management strategies. Results: Forty-six (53.5%) IEC members from 19 countries responded to the survey. Consensus was reached for several statements regarding diagnostic workup, referral and treatment. IEC members suggest that patients with AD should (i) routinely be asked about ocular complaints or symptoms, (ii) obtain information about the potential for conjunctivitis before starting dupilumab therapy and (iii) if indicated, be treated with dupilumab despite previous or current conjunctivitis. In cases of new-onset conjunctivitis, there was consensus that dupilumab treatment should be continued when possible, with appropriate referral to an ophthalmologist. Limitations: The study relies on expert opinion from dermatologists. Responses from few dermatologists without dupilumab access were not excluded from the survey. Conclusion: The IEC recommends that dermatologists address conjunctivitis in patients with AD, especially during treatment with dupilumab

Pancreatic β-cell signaling: toward better understanding of diabetes and its treatment

Pancreatic β-cells play a central role in the maintenance glucose homeostasis by secreting insulin, a key hormone that regulates blood glucose levels. Dysfunction of the β-cells and/or a decrease in the β-cell mass are associated closely with the pathogenesis and pathophysiology of diabetes mellitus, a major metabolic disease that is rapidly increasing worldwide. Clarification of the mechanisms of insulin secretion and β-cell fate provides a basis for the understanding of diabetes and its better treatment. In this review, we discuss cell signaling critical for the insulin secretory function based on our recent studies

Deficiency of Pkc1 activity affects glycerol metabolism in Saccharomyces cerevisiae

In pressProtein kinase C is apparently involved in the control of many cellular systems: the cell wall integrity pathway, the synthesis of ribosomes, the appropriated reallocation of transcription factors under specific stress conditions and also the regulation of N-glycosylation activity. All these observations suggest the existence of additional targets not yet identified. In the context of the control of carbon metabolism, previous data demonstrated that Pkc1 p might play a central role in the control of cellular growth and metabolism in yeast. In particular, it has been suggested that it might be involved in the derepression of genes under glucose-repression by driving an appropriated subcellular localization of transcriptional factors, such as Mig1 p. In this work, we show that pkc1∆ mutant is unable to grow on glycerol because it cannot perform the derepression of GUT1 gene that encodes for glycerol kinase. Additionally, active transport is also partially affected. Using this phenotype, we were able to isolate a new pkc1∆ revertant. We also isolated two transformants identified as the nuclear exportin Msn5 and the histone deacetylase Hos2 extragenic suppressors of this mutation. Based on these results, we postulate that Pkc1 p may be involved in the control of the cellular localization and/or regulation of the activity of nuclear proteins implicated in gene expression.Fundação Universidade Federal de Ouro Preto (FUFOP). Fundação de Amparo a Pesquisa do Estado de Minas Gerais (FAPEMIG) - CBS-1875/95. Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) - 300998/89-9 to R.L.B., 301255/01-6 to L.G.F

Meta-analysis identifies seven susceptibility loci involved in the atopic March

Eczema often precedes the development of asthma in a disease course called the a 'atopic march'. To unravel the genes underlying this characteristic pattern of allergic disease, we conduct a multi-stage genome-wide association study on infantile eczema followed by childhood asthma in 12 populations including 2,428 cases and 17,034 controls. Here we report two novel loci specific for the combined eczema plus asthma phenotype, which are associated with allergic disease for the first time; rs9357733 located in EFHC1 on chromosome 6p12.3 (OR 1.27; P=2.1 × 10 a'8) and rs993226 between TMTC2 and SLC6A15 on chromosome 12q21.3 (OR 1.58; P=5.3 × 10 a'9). Additional susceptibility loci identified