On eigenvalues of the Schr\"odinger operator with a complex-valued polynomial potential

In this paper, we generalize a recent result of A. Eremenko and A. Gabrielov on irreducibility of the spectral discriminant for the Schr\"odinger equation with quartic potentials. We consider the eigenvalue problem with a complex-valued polynomial potential of arbitrary degree d and show that the spectral determinant of this problem is connected and irreducible. In other words, every eigenvalue can be reached from any other by analytic continuation. We also prove connectedness of the parameter spaces of the potentials that admit eigenfunctions satisfying k>2 boundary conditions, except for the case d is even and k=d/2. In the latter case, connected components of the parameter space are distinguished by the number of zeros of the eigenfunctions.Comment: 23 page

Health care resource use by patients before and after a diagnosis of chronic fatigue syndrome (CFS/ME): a clinical practice research datalink study

BACKGROUND: Our aim was to investigate patterns of health care resource use by patients before and after a diagnosis of CFS/ME, as recorded by Clinical Practice Research Datalink (CPRD) GP practices in the UK. METHODS: We used a case–control study design in which patients who had a first recorded diagnosis of CFS/ME during the period 01/01/2001 to 31/12/2013 were matched 1:1 with controls by age, sex, and GP practice. We compared rates of GP consultations, diagnostic tests, prescriptions, referrals, and symptoms between the two groups from 15 years (in adults) or 10 years (in children) before diagnosis to 10 years after diagnosis. RESULTS: Data were available for 6710 adult and 916 child (age <18 years) matched case–control pairs. Rates of GP consultations, diagnostic tests, prescriptions, referrals, and symptoms spiked dramatically in the year when a CFS/ME diagnosis was recorded. GP consultation rates were 50% higher in adult cases compared to controls 11–15 years before diagnosis (rate ratio (RR) 1.49 (95% CI 1.46, 1.52)) and 56% higher 6–10 years after diagnosis (RR 1.56 (1.54, 1.57)). In children, consultation rates in cases were 45% higher 6–10 years before diagnosis (RR 1.45 (1.40, 1.51)) and 62% higher 6–10 years after diagnosis (RR 1.62 (1.54, 1.70)). For adults and children, rates of tests, prescriptions, referrals, and symptoms were higher in cases compared to controls for up to 10 years before and after diagnosis. CONCLUSIONS: Adults and children with CFS/ME have greater health care needs than the rest of the population for at least ten years before their diagnosis, and these higher levels of health care resource use continue for at least ten years after diagnosis

On eigenvalues of the Schr\"odinger operator with an even complex-valued polynomial potential

In this paper, we generalize several results of the article "Analytic continuation of eigenvalues of a quartic oscillator" of A. Eremenko and A. Gabrielov. We consider a family of eigenvalue problems for a Schr\"odinger equation with even polynomial potentials of arbitrary degree d with complex coefficients, and k<(d+2)/2 boundary conditions. We show that the spectral determinant in this case consists of two components, containing even and odd eigenvalues respectively. In the case with k=(d+2)/2 boundary conditions, we show that the corresponding parameter space consists of infinitely many connected components

China’s rising hydropower demand challenges water sector

Demand for hydropower is increasing, yet the water footprints (WFs) of reservoirs and hydropower, and their contributions to water scarcity, are poorly understood. Here, we calculate reservoir WFs (freshwater that evaporates from reservoirs) and hydropower WFs (the WF of hydroelectricity) in China based on data from 875 representative reservoirs (209 with power plants). In 2010, the reservoir WF totaled 27.9 × 109 m3 (Gm3), or 22% of China’s total water consumption. Ignoring the reservoir WF seriously underestimates human water appropriation. The reservoir WF associated with industrial, domestic and agricultural WFs caused water scarcity in 6 of the 10 major Chinese river basins from 2 to 12 months annually. The hydropower WF was 6.6 Gm3 yr−1 or 3.6 m3 of water to produce a GJ (109 J) of electricity. Hydropower is a water intensive energy carrier. As a response to global climate change, the Chinese government has promoted a further increase in hydropower energy by 70% by 2020 compared to 2012. This energy policy imposes pressure on available freshwater resources and increases water scarcity. The water-energy nexus requires strategic and coordinated implementations of hydropower development among geographical regions, as well as trade-off analysis between rising energy demand and water use sustainability

Antenatal thyroid hormone therapy and antithyroid drug use in Norway from 2004 to 2018

Objective Thyroid disease during pregnancy is associated with adverse pregnancy outcomes and suboptimal fetal development. During the last decades, guidelines for diagnosing thyroid disease during pregnancy have changed considerably and there has been increased awareness. This study aimed to describe the prevalence of thyroid disease treatment over time among pregnant women in Norway. Design Nationwide register-based study. Methods We combined historical data from the Medical Birth Registry of Norway and the Norwegian Prescription Database, identifying pregnant women using thyroid therapy from 2004 to 2018. Results A total of 855,067 pregnancies were included in the analyses. The proportion of women using thyroid hormone replacement therapy during pregnancy increased from 1.46% (n  = 800) in 2004 to 3.57% (n  = 1940) in 2018. The proportion of women using antithyroid medications also increased from 0.04% (n  = 20) in 2004 to 0.10% (n  = 56). During these 15 years, the mean maternal age increased by 0.9 years. When adjusting for age, the risk for being on thyroid hormone replacement therapy during pregnancy increased by an average of 5% per year (odds ratio: 1.05, 95% CI: 1.05–1.05). Conclusion During the recent 15 years, there has been a substantial increase in the use of thyroid hormone therapy in Norwegian pregnant women. We speculate that this could be due to an increased awareness in combination with overdiagnosis because of inappropriate diagnostic criteria. To truly understand the possible causes and consequences of this development, further research is warranted.publishedVersio

Regulation of denitrification at the cellular level: a clue to the understanding of N2O emissions from soils

Denitrifying prokaryotes use NOx as terminal electron acceptors in response to oxygen depletion. The process emits a mixture of NO, N2O and N2, depending on the relative activity of the enzymes catalysing the stepwise reduction of NO3− to N2O and finally to N2. Cultured denitrifying prokaryotes show characteristic transient accumulation of NO2−, NO and N2O during transition from oxic to anoxic respiration, when tested under standardized conditions, but this character appears unrelated to phylogeny. Thus, although the denitrifying community of soils may differ in their propensity to emit N2O, it may be difficult to predict such characteristics by analysis of the community composition. A common feature of strains tested in our laboratory is that the relative amounts of N2O produced (N2O/(N2+N2O) product ratio) is correlated with acidity, apparently owing to interference with the assembly of the enzyme N2O reductase. The same phenomenon was demonstrated for soils and microbial communities extracted from soils. Liming could be a way to reduce N2O emissions, but needs verification by field experiments. More sophisticated ways to reduce emissions may emerge in the future as we learn more about the regulation of denitrification at the cellular level

Trends in the incidence of chronic fatigue syndrome and fibromyalgia in the UK, 2001-2013: a Clinical Practice Research Datalink study

Objective Trends in recorded diagnoses of chronic fatigue syndrome (CFS, also known as 'myalgic encephalomyelitis' (ME)) and fibromyalgia (FM) in the UK were last reported more than ten years ago, for the period 1990-2001. Our aim was to analyse trends in incident diagnoses of CFS/ME and FM for the period 2001-2013, and to investigate whether incidence might vary by index of multiple deprivation (IMD) score. Design Electronic health records cohort study. Setting NHS primary care practices in the UK. Participants Participants: Patients registered with general practices linked to the Clinical Practice Research Datalink (CPRD) primary care database from January 2001 to December 2013. Main outcome measure Incidence of CFS/ME, FM, post-viral fatigue syndrome (PVFS), and asthenia/debility. Results The overall annual incidence of recorded cases of CFS/ME was 14.8 (95% CI 14.5, 15.1) per 100,000 people. Overall annual incidence per 100,000 people for FM was 33.3 (32.8-33.8), for PVFS 12.2 (11.9, 12.5), and for asthenia/debility 7.0 (6.8, 7.2). Annual incidence rates for CFS/ME diagnoses decreased from 17.5 (16.1, 18.9) in 2001 to 12.6 (11.5, 13.8) in 2013 (annual percent change -2.8% (-3.6%, -2.0%)). Annual incidence rates for FM diagnoses decreased from 32.3 (30.4, 34.3) to 27.1 (25.5, 28.6) in 2007, then increased to 38.2 (36.3, 40.1) per 100,000 people in 2013. Overall annual incidence of recorded fatigue symptoms was 2246 (2242, 2250) per 100,000 people. Compared with the least deprived IMD quintile, incidence of CFS/ME in the most deprived quintile was 39% lower (incidence rate ratio (IRR) 0.61 (0.50, 0.75)), whereas rates of FM were 40% higher (IRR 1.40 (0.95, 2.06)). Conclusion These analyses suggest a gradual decline in recorded diagnoses of CFS/ME since 2001, and an increase in diagnoses of fibromyalgia, with opposing socioeconomic patterns of lower rates of CFS/ME diagnoses in the poorest areas compared with higher rates of FM diagnoses

Housing system and herd size interactions in Norwegian dairy herds; associations with performance and disease incidence

<p>Abstract</p> <p>Background</p> <p>According to the Norwegian animal welfare regulations, it has been forbidden to build new tie-stall barns since the end of 2004. Previous studies have shown that cow performance and health differ between housing systems. The interaction between housing system and herd size with respect to performance and disease incidence has not been evaluated.</p> <p>Methods</p> <p>Cow performance and health in 620 herds housed in free-stall barns were compared with in 192 herds housed in tie-stall barns based on a mail survey and data from the Norwegian Dairy Herd Recording and Cattle Health Systems. The housing systems herds were comparable with respect to herd size (15-55 cows). Associations between performance/disease incidence and housing system, herd size and year of building the cow barn were tested in general linear models, and values for fixed herd size of 20 and 50 cows were calculated. On the individual cow level mixed models were run to test the effect of among others housing system and herd size on test-day milk yield, and to evaluate lactation curves in different parities. All cows were of the Norwegian Red Breed.</p> <p>Results</p> <p>Average milk production per cow-year was 134 kg lower in free-stall herd than in tie-stall herds, but in the range 27-45 cows there was no significant difference in yields between the herd categories. In herds with less than 27 cows there were increasingly lower yields in free-stalls, particularly in first parity, whereas the yields were increasingly higher in free-stalls with more than 45 cows.</p> <p>In free-stalls fertility was better, calving interval shorter, and the incidence rate of teat injuries, ketosis, indigestions, anoestrus and cystic ovaries was lower than in tie-stalls. All of these factors were more favourable in estimated 50-cow herds as compared to 20-cow herds. In the larger herd category, bulk milk somatic cell counts were higher, and the incidence rate of mastitis (all cases) and all diseases was lower.</p> <p>Conclusion</p> <p>This study has shown that there is an interaction between housing system and herd size, and that performance and health is not universally better in small free-stalls than in tie-stalls.</p