A note on isoparametric polynomials

We show that any homogeneous polynomial solution of |\nabla F(x)|^2=m^2|x|^(2m-2), m>1, is either a radially symmetric polynomial F(x)=\pm |x|^m (for even m's) or it is a composition of a Chebychev polynomial and a Cartan-M\"unzner polynomial.Comment: 6 page

Chronic breathlessness and sleep problems: a population-based survey

ObjectivesThis study aimed to explore the relationship (presence and severity) between chronic breathlessness and sleep problems, independently of diagnoses and health service contact by surveying a large, representative sample of the general population.SettingAnalysis of the 2017 South Australian Health Omnibus Survey, an annual, cross-sectional, face-to-face, multistage, clustered area systematic sampling survey carried out in Spring 2017.Chronic breathlessness was self-reported using the ordinal modified Medical Research Council (mMRC; scores 0 (none) to 4 (housebound)) where breathlessness has been present for more than 3 of the previous 6 months. 'Sleep problems-ever' and 'sleep problem-current' were assessed dichotomously. Regression models were adjusted for age; sex and body mass index (BMI).Results2900 responses were available (mean age 48.2 years (SD=18.6); 51% were female; mean BMI 27. 1 (SD=5.9)). Prevalence was: 2.7% (n=78) sleep problems-past; 6.8% (n=198) sleep problems-current and breathlessness (mMRC 1-4) was 8.8% (n=254). Respondents with sleep problemspast were more likely to be breathless, older with a higher BMI and sleep problems-present also included a higher likelihood of being female.After adjusting for age, sex and BMI, respondents with chronic breathlessness had 1.9 (95% CI=1.0 to 3.5) times the odds of sleep problems-past and sleep problems-current (adjusted OR=2.3; 95% CI=1.6 to 3.3).ConclusionsThere is a strong association between the two prevalent conditions. Future work will seek to understand if there is a causal relationship using validated sleep assessment tools and whether better managing one condition improves the other

Chapter 6: Assessing Applicability of Medical Test Studies in Systematic Reviews

Use of medical tests should be guided by research evidence about the accuracy and utility of those tests in clinical care settings. Systematic reviews of the literature about medical tests must address applicability to real-world decision-making. Challenges for reviews include: (1) lack of clarity in key questions about the intended applicability of the review, (2) numerous studies in many populations and settings, (3) publications that provide too little information to assess applicability, (4) secular trends in prevalence and the spectrum of the condition for which the test is done, and (5) changes in the technology of the test itself. We describe principles for crafting reviews that meet these challenges and capture the key elements from the literature necessary to understand applicability

Use of a High-Density Protein Microarray to Identify Autoantibodies in Subjects with Type 2 Diabetes Mellitus and an HLA Background Associated with Reduced Insulin Secretion

New biomarkers for type 2 diabetes mellitus (T2DM) may aid diagnosis, drug development or clinical treatment. Evidence is increasing for the adaptive immune system's role in T2DM and suggests the presence of unidentified autoantibodies. While high-density protein microarrays have emerged as a useful technology to identify possible novel autoantigens in autoimmune diseases, its application in T2DM has lagged. In Pima Indians, the HLA haplotype (HLA-DRB1*02) is protective against T2DM and, when studied when they have normal glucose tolerance, subjects with this HLA haplotype have higher insulin secretion compared to those without the protective haplotype. Possible autoantibody biomarkers were identified using microarrays containing 9480 proteins in plasma from Pima Indians with T2DM without the protective haplotype (n = 7) compared with those with normal glucose regulation (NGR) with the protective haplotype (n = 11). A subsequent validation phase involving 45 cases and 45 controls, matched by age, sex and specimen storage time, evaluated 77 proteins. Eleven autoantigens had higher antibody signals among T2DM subjects with the lower insulin-secretion HLA background compared with NGR subjects with the higher insulin-secretion HLA background (p<0.05, adjusted for multiple comparisons). PPARG2 and UBE2M had lowest p-values (adjusted p = 0.023) while PPARG2 and RGS17 had highest case-to-control antibody signal ratios (1.7). A multi-protein classifier involving the 11 autoantigens had sensitivity, specificity, and area under the receiver operating characteristics curve of 0.73, 0.80, and 0.83 (95% CI 0.74-0.91, p = 3.4x10-8), respectively. This study identified 11 novel autoantigens which were associated with T2DM and an HLA background associated with reduced insulin secretion. While further studies are needed to distinguish whether these antibodies are associated with insulin secretion via the HLA background, T2DM more broadly, or a combination of the two, this study may aid the search for autoantibody biomarkers by narrowing the list of protein targets

Spectral weight transfer in a disorder-broadened Landau level

In the absence of disorder, the degeneracy of a Landau level (LL) is $N=BA/\phi_0$, where $B$ is the magnetic field, $A$ is the area of the sample and $\phi_0=h/e$ is the magnetic flux quantum. With disorder, localized states appear at the top and bottom of the broadened LL, while states in the center of the LL (the critical region) remain delocalized. This well-known phenomenology is sufficient to explain most aspects of the Integer Quantum Hall Effect (IQHE) [1]. One unnoticed issue is where the new states appear as the magnetic field is increased. Here we demonstrate that they appear predominantly inside the critical region. This leads to a certain ``spectral ordering'' of the localized states that explains the stripes observed in measurements of the local inverse compressibility [2-3], of two-terminal conductance [4], and of Hall and longitudinal resistances [5] without invoking interactions as done in previous work [6-8].Comment: 5 pages 3 figure

The temporal representation of experience in subjective mood

Humans refer to their mood state regularly in day-to-day as well as clinical interactions. Theoretical accounts suggest that when reporting on our mood we integrate over the history of our experiences; yet, the temporal structure of this integration remains unexamined. Here, we use a computational approach to quantitatively answer this question and show that early events exert a stronger influence on reported mood (a primacy weighting) compared to recent events. We show that a Primacy model accounts better for mood reports compared to a range of alternative temporal representations across random, consistent, or dynamic reward environments, different age groups, and in both healthy and depressed participants. Moreover, we find evidence for neural encoding of the Primacy, but not the Recency, model in frontal brain regions related to mood regulation. These findings hold implications for the timing of events in experimental or clinical settings and suggest new directions for individualized mood interventions

Target trial emulation: Do antimicrobials or gastrointestinal nutraceuticals prescribed at first presentation for acute diarrhoea cause a better clinical outcome in dogs under primary veterinary care in the UK?

Target trial emulation applies design principles from randomised controlled trials to the analysis of observational data for causal inference and is increasingly used within human epidemiology. Veterinary electronic clinical records represent a potentially valuable source of information to estimate real-world causal effects for companion animal species. This study employed the target trial framework to evaluate the usefulness on veterinary observational data. Acute diarrhoea in dogs was used as a clinical exemplar. Inclusion required dogs aged ≥ 3 months and < 10 years, presenting for veterinary primary care with acute diarrhoea during 2019. Treatment strategies were: 1. antimicrobial prescription compared to no antimicrobial prescription and 2. gastrointestinal nutraceutical prescription compared to no gastrointestinal nutraceutical prescription. The primary outcome was clinical resolution (defined as no revisit with ongoing diarrhoea within 30 days from the date of first presentation). Informed from a directed acyclic graph, data on the following covariates were collected: age, breed, bodyweight, insurance status, comorbidities, vomiting, reduced appetite, haematochezia, pyrexia, duration, additional treatment prescription and veterinary group. Inverse probability of treatment weighting was used to balance covariates between the treatment groups for each of the two target trials. The risk difference (RD) of 0.4% (95% CI -4.5% to 5.3%) was non-significant for clinical resolution in dogs treated with antimicrobials compared with dogs not treated with antimicrobials. The risk difference (RD) of 0.3% (95% CI -4.5% to 5.0%) was non-significant for clinical resolution in dogs treated with gastrointestinal nutraceuticals compared with dogs not treated with gastrointestinal nutraceuticals. This study successfully applied the target trial framework to veterinary observational data. The findings show that antimicrobial or gastrointestinal prescription at first presentation of acute diarrhoea in dogs causes no difference in clinical resolution. The findings support the recommendation for veterinary professionals to limit antimicrobial use for acute diarrhoea in dogs