An improvement of the Kolmogorov-Riesz compactness theorem

The purpose of this short note is to provide a new and very short proof of a result by Sudakov, offering an important improvement of the classical result by Kolmogorov-Riesz on compact subsets of Lebesgue spaces

Conditional expectations associated with quantum states

An extension of the conditional expectations (those under a given subalgebra of events and not the simple ones under a single event) from the classical to the quantum case is presented. In the classical case, the conditional expectations always exist; in the quantum case, however, they exist only if a certain weak compatibility criterion is satisfied. This compatibility criterion was introduced among others in a recent paper by the author. Then, state-independent conditional expectations and quantum Markov processes are studied. A classical Markov process is a probability measure, together with a system of random variables, satisfying the Markov property and can equivalently be described by a system of Markovian kernels (often forming a semigroup). This equivalence is partly extended to quantum probabilities. It is shown that a dynamical (semi)group can be derived from a given system of quantum observables satisfying the Markov property, and the group generators are studied. The results are presented in the framework of Jordan operator algebras, and a very general type of observables (including the usual real-valued observables or self-adjoint operators) is considered.Comment: 10 pages, the original publication is available at http://www.aip.or

Spatial and temporal distribution of incidence of acquired equine polyneuropathy in Norway and Sweden, 1995-2012

BACKGROUND: Acquired equine polyneuropathy (AEP) is an emerging disease in horses in Sweden, Norway and Finland since 1995. Affected horses show bilateral pelvic limb knuckling and weakness, sometimes progressing to recumbency and euthanasia. The aetiology is unknown but is thought to be non-infectious and non-genetic, though possibly toxic or toxico-infectious. The objectives of this study were to describe the spatial, temporal and spatio-temporal features of AEP in Norway and Sweden for the period of 1995 to 2012. Data from all documented case farms (n = 136) were used. Space-time interaction clustering of case farms was investigated with a retrospective space-time scan statistic with a space-time permutation model, the space-time K-function and the Jacquez k nearest neighbour (kNN) test. RESULTS: There was a clear seasonality in disease occurrence, as 123 case farms presented their first case from January to May. However, there was large variation in the number of case farms between years. Case farms were more numerous in certain regions. Despite the larger horse population in Sweden, 120 of the case farms were in Norway. Space-time clustering was supported by the K-function and partly by the space-time scan, but not by the Jacquez k nearest neighbour (kNN) test. CONCLUSIONS: The results suggest an aetiology for AEP where the exposure is not consistent in time, but varies during and between years, assuming that the incubation period does not vary greatly. The results further suggest that the exposure varies between regions as well. Two out of three different analytical methods supported spatio-temporal clustering of case farms, which rendered inconclusive results. The negative result in the kNN test might be explained by lack of power, which is due to the small number of outbreaks in relation to the size of the study area and length of the study period, and further by the low to moderate power of methods to detect space-time clustering when the background population is unknown. Further research is needed to study how management, meteorological variables and other factors with local or regional differences may explain outbreaks of AEP

A hierarchy of compatibility and comeasurability levels in quantum logics with unique conditional probabilities

In the quantum mechanical Hilbert space formalism, the probabilistic interpretation is a later ad-hoc add-on, more or less enforced by the experimental evidence, but not motivated by the mathematical model itself. A model involving a clear probabilistic interpretation from the very beginning is provided by the quantum logics with unique conditional probabilities. It includes the projection lattices in von Neumann algebras and here probability conditionalization becomes identical with the state transition of the Lueders - von Neumann measurement process. This motivates the definition of a hierarchy of five compatibility and comeasurability levels in the abstract setting of the quantum logics with unique conditional probabilities. Their meanings are: the absence of quantum interference or influence, the existence of a joint distribution, simultaneous measurability, and the independence of the final state after two successive measurements from the sequential order of these two measurements. A further level means that two elements of the quantum logic (events) belong to the same Boolean subalgebra. In the general case, the five compatibility and comeasurability levels appear to differ, but they all coincide in the common Hilbert space formalism of quantum mechanics, in von Neumann algebras, and in some other cases.Comment: 12 page

Simplified methods of assessing the impact of grid frequency dynamics upon generating plants

The frequency of the national electricity grid is affected by fluctuations in supply and demand, and so continually "judders" in an essentially unpredictable fashion around 50 Hz. At present such perturbations do not seemingly affect Nuclear Electric as most of their plant is run at more or less constant load, but they would like to be able to offer the national grid a mode of operation in which they "followed" the grid frequency: i.e., as the frequency rose above or fell below 50 Hz, the plant's output would be adjusted so as to tend to restore the frequency to 50 Hz. The aim is to maintain grid frequency within 0.2 Hz of its notional value. Such a mode of operation, however, would cause a certain amount of damage to plant components owing to the consequent continual changes in temperature and pressure within them. Nuclear Electric currently have complex computational models of how plants will behave under these conditions, which allows them to compute plant data (e.g., reactor temperatures) from given grid frequency data. One approach to damage assessment would require several years'-worth of real grid data to be fed into this model and the corresponding damage computed (via "cycle distributions" created by their damage experts). The results of this analysis would demonstrate one of three possibilities: the damage may be acceptable under all reasonable operating conditions; or it may be acceptable except in the case of an exceptional abrupt change in grid frequency (caused by power transmission line failure, or another power station suddenly going off-line, for instance), in which case some kind of backup supply (e.g., gas boilers) would be required; or it may simply be unacceptable. However, their current model runs in approximately real time, making it inappropriate for such a large amount of data: our problem was to suggest alternative approaches. Specifically, we were asked the following questions: - Can component damage be reliably estimated directly from cycle distributions of grid frequency? i.e., are there maps from frequency cycle distributions to plant parameter cycle distributions? - Can a simple model of plant dynamics be used to assess the potential for such maps? - What methods can be used to select representative samples of grid frequency behaviour? - What weightings should be applied to the selections? - Is it possible to construct a "cycle transform" (Fourier transform) which will capture the essential features of grid frequency and which can then be inverted to generate simulated frequency transients? We did not consider this last question, other than to say "probably not". We were supplied with data of the actual grid frequency measurements for the evening of 29/7/95, and the corresponding plant responses (obtained using Nuclear Electric's current computational model). A simplified nonlinear mathematical model of the plant was also provided. Two main approaches were considered: statistical prediction and analytical modelling via a reduction of the simplified plant model

A stability version of H\"older's inequality

We present a stability version of H\"older's inequality, incorporating an extra term that measures the deviation from equality. Applications are given.Comment: Journal of Mathematical Analysis and Applications, Volume 343, Issue 2, Pages 842-852. This version differs from the published one in that it contains a new reference, and a trivial improvement of Corollary 3.2. fo

Pasienttilfredshet i en avrusningsinstitusjon for pasienter med rusmiddelproblemer - en kvantitativ deskriptiv studie

Patient satisfaction in inpatient detoxification for substance use disorders - a quantitative descriptive study The primary purpose of the study is to discover important factors for patients at inpatient detoxification by studying patient satisfaction. Data were collected from a patient experience survey carried out from 2013-2015 at a detoxification unit in Norway. The study includes 185 responses (response rate 62 %). Data were analyzed with descriptive and inferential statistics. Significant associations were found between patients’ satisfaction and all the factors of the therapeutic relationship except respect and courtesy, support and motivation, which were non-significant in this study. Conversations with therapist showed the largest effect on patient satisfaction (effect size (ES) = 1.27), followed by conversations with doctor (ES = 0.78) and compassionate staff (ES = 0.52). The results suggest that the therapeutic relationship is associated with patient satisfaction in inpatient detoxification

Ensemble averaged entanglement of two-particle states in Fock space

Recent results, extending the Schmidt decomposition theorem to wavefunctions of identical particles, are reviewed. They are used to give a definition of reduced density operators in the case of two identical particles. Next, a method is discussed to calculate time averaged entanglement. It is applied to a pair of identical electrons in an otherwise empty band of the Hubbard model, and to a pair of bosons in the the Bose-Hubbard model with infinite range hopping. The effect of degeneracy of the spectrum of the Hamiltonian on the average entanglement is emphasised.Comment: 19 pages Latex, changed title, references added in the conclusion