Well-Posedness for Semi-Relativistic Hartree Equations of Critical Type

We prove local and global well-posedness for semi-relativistic, nonlinear Schr\"odinger equations $i \partial_t u = \sqrt{-\Delta + m^2} u + F(u)$ with initial data in $H^s(\mathbb{R}^3)$, $s \geq 1/2$. Here $F(u)$ is a critical Hartree nonlinearity that corresponds to Coulomb or Yukawa type self-interactions. For focusing $F(u)$, which arise in the quantum theory of boson stars, we derive a sufficient condition for global-in-time existence in terms of a solitary wave ground state. Our proof of well-posedness does not rely on Strichartz type estimates, and it enables us to add external potentials of a general class.Comment: 18 pages; replaced with revised version; remark and reference on blow up adde

A Centre-Stable Manifold for the Focussing Cubic NLS in R1+3R^{1+3}

Consider the focussing cubic nonlinear Schr\"odinger equation in $R^3$: $$i\psi_t+\Delta\psi = -|\psi|^2 \psi.$$ It admits special solutions of the form $e^{it\alpha}\phi$, where $\phi$ is a Schwartz function and a positive ($\phi>0$) solution of $$-\Delta \phi + \alpha\phi = \phi^3.$$ The space of all such solutions, together with those obtained from them by rescaling and applying phase and Galilean coordinate changes, called standing waves, is the eight-dimensional manifold that consists of functions of the form $e^{i(v \cdot + \Gamma)} \phi(\cdot - y, \alpha)$. We prove that any solution starting sufficiently close to a standing wave in the $\Sigma = W^{1, 2}(R^3) \cap |x|^{-1}L^2(R^3)$ norm and situated on a certain codimension-one local Lipschitz manifold exists globally in time and converges to a point on the manifold of standing waves. Furthermore, we show that \mc N is invariant under the Hamiltonian flow, locally in time, and is a centre-stable manifold in the sense of Bates, Jones. The proof is based on the modulation method introduced by Soffer and Weinstein for the $L^2$-subcritical case and adapted by Schlag to the $L^2$-supercritical case. An important part of the proof is the Keel-Tao endpoint Strichartz estimate in $R^3$ for the nonselfadjoint Schr\"odinger operator obtained by linearizing around a standing wave solution.Comment: 56 page

Electromagnetic transition form factors and dilepton decay rates of nucleon resonances

Relativistic, kinematically complete phenomenological expressions for the dilepton decay rates of nucleon resonances with arbitrary spin and parity are derived in terms of the magnetic, electric, and Coulomb transition form factors. The dilepton decay rates of the nucleon resonances with masses below 2 GeV are estimated using the extended vector meson dominance model for the transition form factors. The model provides a unified description of the photo- and electroproduction data, the vector meson decays, and the dilepton decays of the nucleon resonances. The constraints on the transition form factors from the quark counting rules are taken into account. The parameters of the model are fixed by fitting the available photo- and electroproduction data and using results of the multichannel partial-wave analysis of the $\pi N$ scattering. Where experimental data are not available, predictions of the non-relativistic quark models are used as an input. The vector meson coupling constants of the magnetic, electric, and Coulomb types are determined. The dilepton widths and the dilepton spectra from decays of nucleon resonances with masses below 2 GeV are calculated.Comment: An error in the code is found and fixed. Numerical results for the spin-half nucleon resonances changed. A few misprints are removed from the text. 56 pages including 7 tables and 27 eps figures, REVTe

MRLocus: Identifying causal genes mediating a trait through Bayesian estimation of allelic heterogeneity

Expression quantitative trait loci (eQTL) studies are used to understand the regulatory function of non-coding genome-wide association study (GWAS) risk loci, but colocalization alone does not demonstrate a causal relationship of gene expression affecting a trait. Evidence for mediation, that perturbation of gene expression in a given tissue or developmental context will induce a change in the downstream GWAS trait, can be provided by two-sample Mendelian Randomization (MR). Here, we introduce a new statistical method, MRLocus, for Bayesian estimation of the gene-to-trait effect from eQTL and GWAS summary data for loci with evidence of allelic heterogeneity, that is, containing multiple causal variants. MRLocus makes use of a colocalization step applied to each nearly-LD-independent eQTL, followed by an MR analysis step across eQTLs. Additionally, our method involves estimation of the extent of allelic heterogeneity through a dispersion parameter, indicating variable mediation effects from each individual eQTL on the downstream trait. Our method is evaluated against other state-of-the-art methods for estimation of the gene-to-trait mediation effect, using an existing simulation framework. In simulation, MRLocus often has the highest accuracy among competing methods, and in each case provides more accurate estimation of uncertainty as assessed through interval coverage. MRLocus is then applied to five candidate causal genes for mediation of particular GWAS traits, where gene-to-trait effects are concordant with those previously reported. We find that MRLocus’s estimation of the causal effect across eQTLs within a locus provides useful information for determining how perturbation of gene expression or individual regulatory elements will affect downstream traits. The MRLocus method is implemented as an R package available at https://mikelove.github.io/ mrlocus

Measurement of the mass difference between top quark and antiquark in pp collisions at root s=8 TeV

Peer reviewe

Contemporary integrative taxonomy for sexually deprived protists: A case study of Trachelomonas (Euglenaceae) from western Ukraine

As many other protist groups, euglenophytes are prone to false identification based solely on morphology because of a limited amount of morphological features and cryptic speciation. One of the supposedly completely asexual groups within the freshwater phototrophic representatives of euglenophytes is Trachelomonas , capable of forming an inorganic shell around its cell (i.e., the lorica). The International Code of Nomenclature for algae, fungi, and plants regulates the taxonomy not only of flowering plants, but explicitly also of phototrophic protists, and provides powerful tools to resolve various taxonomic challenges. To exemplify some of the problems and potential solutions, a number of Trachelomonas strains were collected from the muddy, lake‐rich region of Dobrostany and cultivated under stable laboratory conditions. Being a type locality of 58 unclarified Trachelomonas names, this region in western Ukraine is of great taxonomic importance. Based on light and electron microscopy, and on RAxML and MrBayes phylogenetics using multiple loci and a representative taxon sample, a detailed description of investigated strains and their systematic placement is provided. Morphologically, the strains differed slightly but consistently in minute characters such as size, lorica shape and ornamentation. The presently most comprehensive molecular tree of the Euglenaceae indicated to the existence of at least five different species present in the newly investigated samples, although they were collected from localities in very close vicinity to each other and at the same date. Based on morphological comparisons with type illustrations of species validly described 100 or more years ago, biological material was used to epitypify three names of Trachelomonas , eternally linking morphology with reliable genetic information. This taxonomic application is one of the powerful methods to clarify ambiguous scientific names, which has particular importance in character‐poor protists such as the euglenophytes

Psychosocial Treatment of Children in Foster Care: A Review

A substantial number of children in foster care exhibit psychiatric difficulties. Recent epidemiologi-cal and historical trends in foster care, clinical findings about the adjustment of children in foster care, and adult outcomes are reviewed, followed by a description of current approaches to treatment and extant empirical support. Available interventions for these children can be categorized as either symptom-focused or systemic, with empirical support for specific methods ranging from scant to substantial. Even with treatment, behavioral and emotional problems often persist into adulthood, resulting in poor functional outcomes. We suggest that self-regulation may be an important mediat-ing factor in the appearance of emotional and behavioral disturbance in these children

Chronic neuropsychiatric sequelae of SARS‐CoV‐2: Protocol and methods from the Alzheimer's Association Global Consortium

Introduction Coronavirus disease 2019 (COVID-19) has caused >3.5 million deaths worldwide and affected >160 million people. At least twice as many have been infected but remained asymptomatic or minimally symptomatic. COVID-19 includes central nervous system manifestations mediated by inflammation and cerebrovascular, anoxic, and/or viral neurotoxicity mechanisms. More than one third of patients with COVID-19 develop neurologic problems during the acute phase of the illness, including loss of sense of smell or taste, seizures, and stroke. Damage or functional changes to the brain may result in chronic sequelae. The risk of incident cognitive and neuropsychiatric complications appears independent from the severity of the original pulmonary illness. It behooves the scientific and medical community to attempt to understand the molecular and/or systemic factors linking COVID-19 to neurologic illness, both short and long term. Methods This article describes what is known so far in terms of links among COVID-19, the brain, neurological symptoms, and Alzheimer's disease (AD) and related dementias. We focus on risk factors and possible molecular, inflammatory, and viral mechanisms underlying neurological injury. We also provide a comprehensive description of the Alzheimer's Association Consortium on Chronic Neuropsychiatric Sequelae of SARS-CoV-2 infection (CNS SC2) harmonized methodology to address these questions using a worldwide network of researchers and institutions. Results Successful harmonization of designs and methods was achieved through a consensus process initially fragmented by specific interest groups (epidemiology, clinical assessments, cognitive evaluation, biomarkers, and neuroimaging). Conclusions from subcommittees were presented to the whole group and discussed extensively. Presently data collection is ongoing at 19 sites in 12 countries representing Asia, Africa, the Americas, and Europe. Discussion The Alzheimer's Association Global Consortium harmonized methodology is proposed as a model to study long-term neurocognitive sequelae of SARS-CoV-2 infection

Global, regional, and national disability-adjusted life-years (DALYs) for 315 diseases and injuries and healthy life expectancy (HALE), 1990–2015: a systematic analysis for the Global Burden of Disease Study 2015

Background Healthy life expectancy (HALE) and disability-adjusted life-years (DALYs) provide summary measures of health across geographies and time that can inform assessments of epidemiological patterns and health system performance, help to prioritise investments in research and development, and monitor progress toward the Sustainable Development Goals (SDGs). We aimed to provide updated HALE and DALYs for geographies worldwide and evaluate how disease burden changes with development. Methods We used results from the Global Burden of Diseases, Injuries, and Risk Factors Study 2015 (GBD 2015) for all-cause mortality, cause-specific mortality, and non-fatal disease burden to derive HALE and DALYs by sex for 195 countries and territories from 1990 to 2015. We calculated DALYs by summing years of life lost (YLLs) and years of life lived with disability (YLDs) for each geography, age group, sex, and year. We estimated HALE using the Sullivan method, which draws from age-specific death rates and YLDs per capita. We then assessed how observed levels of DALYs and HALE differed from expected trends calculated with the Socio-demographic Index (SDI), a composite indicator constructed from measures of income per capita, average years of schooling, and total fertility rate. Findings Total global DALYs remained largely unchanged from 1990 to 2015, with decreases in communicable, neonatal, maternal, and nutritional (Group 1) disease DALYs offset by increased DALYs due to non-communicable diseases (NCDs). Much of this epidemiological transition was caused by changes in population growth and ageing, but it was accelerated by widespread improvements in SDI that also correlated strongly with the increasing importance of NCDs. Both total DALYs and age-standardised DALY rates due to most Group 1 causes significantly decreased by 2015, and although total burden climbed for the majority of NCDs, age-standardised DALY rates due to NCDs declined. Nonetheless, age-standardised DALY rates due to several high-burden NCDs (including osteoarthritis, drug use disorders, depression, diabetes, congenital birth defects, and skin, oral, and sense organ diseases) either increased or remained unchanged, leading to increases in their relative ranking in many geographies. From 2005 to 2015, HALE at birth increased by an average of 2·9 years (95% uncertainty interval 2·9–3·0) for men and 3·5 years (3·4–3·7) for women, while HALE at age 65 years improved by 0·85 years (0·78–0·92) and 1·2 years (1·1–1·3), respectively. Rising SDI was associated with consistently higher HALE and a somewhat smaller proportion of life spent with functional health loss; however, rising SDI was related to increases in total disability. Many countries and territories in central America and eastern sub-Saharan Africa had increasingly lower rates of disease burden than expected given their SDI. At the same time, a subset of geographies recorded a growing gap between observed and expected levels of DALYs, a trend driven mainly by rising burden due to war, interpersonal violence, and various NCDs. Interpretation Health is improving globally, but this means more populations are spending more time with functional health loss, an absolute expansion of morbidity. The proportion of life spent in ill health decreases somewhat with increasing SDI, a relative compression of morbidity, which supports continued efforts to elevate personal income, improve education, and limit fertility. Our analysis of DALYs and HALE and their relationship to SDI represents a robust framework on which to benchmark geography-specific health performance and SDG progress. Country-specific drivers of disease burden, particularly for causes with higher-than-expected DALYs, should inform financial and research investments, prevention efforts, health policies, and health system improvement initiatives for all countries along the development continuum. Funding Bill & Melinda Gates Foundation