Constraints on the energy spectrum of non-Hermitian models in open environments

Motivated by recent progress on non-Hermitian topological band theories, we study the energy spectrum of a generic two-band non-Hermitian Hamiltonian. We prove rigorously that the complex energy spectrum of such a non-Hermitian Hamiltonian is restricted to the lower complex plane, provided that the parameters of the Hamiltonian satisfy a certain constraint. Furthermore, we consider one specific scenario where such a non-Hermitian Hamiltonian can arise, namely a two-band model coupled to an environment, and show that this aforementioned constraint orignates from very general physical considerations. Our findings are relevant in the definition of the energy gap in non-Hermitian topological band theories and also have implications on simulations of such theories using quantum systems.Comment: 7 pages, 1 figur

Iodine content of dietary supplements available on the Norwegian market

Postponed access: the file will be accessible after 2022-05-18Background: Insufficient iodine intake has been reported in groups of the Norwegian population. This is of concern, as iodine is an essential nutrient required throughout life. With few dietary sources of iodine, supplementation is recommended for individuals with a low intake of milk, dairy products and/or lean fish. However, no study has analysed the iodine content in supplements on the Norwegian market. Since legislation allows for deviation from labelled values of iodine content in dietary supplements, the use of these supplements could result in inadequate or excessive intake of iodine. Aim: To analyse iodine content in dietary supplements available on the Norwegian market and compare the results to the labelled content. Methods: Iodine containing dietary supplements were collected from pharmacies, health food stores, grocery stores, and online fitness stores in Norway. Three batches of each supplement product were purchased to account for variation in iodine content. During homogenisation and sample preparation, four samples from each batch were collected. Therefore, iodine was determined in a total of 12 samples from each supplement product by Inductively Coupled Plasma Mass Spectrometry. Mean analysed iodine content in each product was compared with the labelled iodine content. Results: A total of 52 supplements were included in the study, and 58% of the supplements were within ±10% of complete accordance with labelled iodine content. The mean iodine content of all supplements was 150 μg/recommended dose ± 60 μg/recommended dose, with minimum and maximum iodine of 32 μg/recommended dose and 421 μg/recommended dose, respectively. Two products were below the lower tolerance limit of -20% of labelled iodine content and two products exceeded the upper tolerance limit of +45% of labelled iodine content recommended by the European Commission. None of the supplements had iodine content below the minimum allowed iodine content of 23 μg per recommended daily dose. Conclusion: Our findings shows that the iodine content of approximately 60% of the supplements included in this present study is in accordance with the iodine content labelled on the product. However, the analysed iodine content of all included supplements was at a safe level and are unlikely to be harmful for most consumers. Yet, the labelling information of a few products could cause incorrect use of supplements and may result in excess iodine intake.Masteroppgave for klinisk ernæringNUCLI395MAMD-NUCL

Presynaptic Calcium Signalling in Cerebellar Mossy Fibres

Whole-cell recordings were obtained from mossy fibre terminals in adult turtles in order to characterize the basic membrane properties. Calcium imaging of presynaptic calcium signals was carried out in order to analyse calcium dynamics and presynaptic GABA B inhibition. A tetrodotoxin (TTX)-sensitive fast Na+ spike faithfully followed repetitive depolarizing pulses with little change in spike duration or amplitude, while a strong outward rectification dominated responses to long-lasting depolarizations. High-threshold calcium spikes were uncovered following addition of potassium channel blockers. Calcium imaging using Calcium-Green dextran revealed a stimulus-evoked all-or-none TTX-sensitive calcium signal in simple and complex rosettes. All compartments of a complex rosette were activated during electrical activation of the mossy fibre, while individual simple and complex rosettes along an axon appeared to be isolated from one another in terms of calcium signalling. CGP55845 application showed that GABA B receptors mediated presynaptic inhibition of the calcium signal over the entire firing frequency range of mossy fibres. A paired-pulse depression of the calcium signal lasting more than 1 s affected burst firing in mossy fibres; this paired-pulse depression was reduced by GABA B antagonists. While our results indicated that a presynaptic rosette electrophysiologically functioned as a unit, topical GABA application showed that calcium signals in the branches of complex rosettes could be modulated locally, suggesting that cerebellar glomeruli may be dynamically sub-compartmentalized due to ongoing inhibition mediated by Golgi cells. This could provide a fine-grained control of mossy fibre-granule cell information transfer and synaptic plasticity within a mossy fibre rosette

Effects of prescribed forest burning on carabid beetles (Coleoptera: Carabidae): a case study in south-eastern Norway

The influence of prescribed burning on ground beetles was studied in a single 12 ha stand that was partially clear-cut, selectively-cut and retained (= standing forest), and was compared to an unburned stand in 2002 in SE Norway. Thirty-two species were collected using Barber pitfall traps. Carabids were more numerous and more diverse in the burned area, compared to the unburned forest. Overall abundance was highest in the selectively-cut treatment, followed by the clear-cut and standing forest. Species diversity tended to increase in the sequence unburned forest – burned standing forest – burned selectively-cut – burned clearcut. Species composition differed little between the burned treatments. Pterostichus adstrictus, a species associated with open habitats and which frequently colonizes burned areas, was the most abundant species collected. It was most common in the burned area, particularly in the selectively-cut treatment. Our results suggest that burning of a single stand may support some carabid species, even endangered ones, although larger forest fires are probablymore effective for conservation purposes

From Interpreter to Compiler and Virtual Machine: A Functional Derivation

We show how to derive a compiler and a virtual machine from a compositional interpreter. We first illustrate the derivation with two evaluation functions and two normalization functions. We obtain Krivine's machine, Felleisen et al.'s CEK machine, and a generalization of these machines performing strong normalization, which is new. We observe that several existing compilers and virtual machines--e.g., the Categorical Abstract Machine (CAM), Schmidt's VEC machine, and Leroy's Zinc abstract machine--are already in derived form and we present the corresponding interpreter for the CAM and the VEC machine. We also consider Hannan and Miller's CLS machine and Landin's SECD machine. We derived Krivine's machine via a call-by-name CPS transformation and the CEK machine via a call-by-value CPS transformation. These two derivations hold both for an evaluation function and for a normalization function. They provide a non-trivial illustration of Reynolds's warning about the evaluation order of a meta-language

Computation of local exchange coefficients in strongly interacting one-dimensional few-body systems: local density approximation and exact results

One-dimensional multi-component Fermi or Bose systems with strong zero-range interactions can be described in terms of local exchange coefficients and mapping the problem into a spin model is thus possible. For arbitrary external confining potentials the local exchanges are given by highly non-trivial geometric factors that depend solely on the geometry of the confinement through the single-particle eigenstates of the external potential. To obtain accurate effective Hamiltonians to describe such systems one needs to be able to compute these geometric factors with high precision which is difficult due to the computational complexity of the high-dimensional integrals involved. An approach using the local density approximation would therefore be a most welcome approximation due to its simplicity. Here we assess the accuracy of the local density approximation by going beyond the simple harmonic oscillator that has been the focus of previous studies and consider some double-wells of current experimental interest. We find that the local density approximation works quite well as long as the potentials resemble harmonic wells but break down for larger barriers. In order to explore the consequences of applying the local density approximation in a concrete setup we consider quantum state transfer in the effective spin models that one obtains. Here we find that even minute deviations in the local exchange coefficients between the exact and the local density approximation can induce large deviations in the fidelity of state transfer for four, five, and six particles.Comment: 12 pages, 7 figures, 1 table, final versio