On the similarity of Sturm-Liouville operators with non-Hermitian boundary conditions to self-adjoint and normal operators

We consider one-dimensional Schrödinger-type operators in a bounded interval with non-self-adjoint Robin-type boundary conditions. It is well known that such operators are generically conjugate to normal operators via a similarity transformation. Motivated by recent interests in quasi-Hermitian Hamiltonians in quantum mechanics, we study properties of the transformations and similar operators in detail. In the case of parity and time reversal boundary conditions, we establish closed integral-type formulae for the similarity transformations, derive a non-local self-adjoint operator similar to the Schrödinger operator and also find the associated “charge conjugation” operator, which plays the role of fundamental symmetry in a Krein-space reformulation of the problem.

Impact of measurement errors on the determination of the linear modulus of human meniscal attachments

For the development of meniscal substitutes and related finite element models it is necessary to know the mechanical properties of the meniscus and its attachments. Measurement errors can falsify the determination of material properties. Therefore the impact of metrological and geometrical measurement errors on the determination of the linear modulus of human meniscal attachments was investigated. After total differentiation the error of the force (+0.10%), attachment deformation (−0.16%), and fibre length (+0.11%) measurements almost annulled each other. The error of the cross-sectional area determination ranged from 0.00%, gathered from histological slides, up to 14.22%, obtained from digital calliper measurements. Hence, total measurement error ranged from +0.05% to −14.17%, predominantly affected by the cross-sectional area determination error. Further investigations revealed that the entire cross-section was significantly larger compared to the load-carrying collagen fibre area. This overestimation of the cross-section area led to an underestimation of the linear modulus of up to −36.7%. Additionally, the cross-sections of the collagen-fibre area of the attachments significantly varied up to +90% along their longitudinal axis. The resultant ratio between the collagen fibre area and the histologically determined cross-sectional area ranged between 0.61 for the posterolateral and 0.69 for the posteromedial ligament. The linear modulus of human meniscal attachments can be significantly underestimated due to the use of different methods and locations of cross-sectional area determination. Hence, it is suggested to assess the load carrying collagen fibre area histologically, or, alternatively, to use the correction factors proposed in this study.

VMC++ versus BEAMnrc: a comparison of simulated linear accelerator heads for photon beams

BEAMnrc, a code for simulating medical linear accelerators based on EGSnrc, has been bench-marked and used extensively in the scientific literature and is therefore often considered to be the gold standard for Monte Carlo simulations for radiotherapy applications. However, its long computation times make it too slow for the clinical routine and often even for research purposes without a large investment in computing resources. VMC++ is a much faster code thanks to the intensive use of variance reduction techniques and a much faster implementation of the condensed history technique for charged particle transport. A research version of this code is also capable of simulating the full head of linear accelerators operated in photon mode (excluding multileaf collimators, hard and dynamic wedges). In this work, a validation of the full head simulation at 6 and 18 MV is performed, simulating with VMC++ and BEAMnrc the addition of one head component at a time and comparing the resulting phase space files. For the comparison, photon and electron fluence, photon energy fluence, mean energy, and photon spectra are considered. The largest absolute differences are found in the energy fluences. For all the simulations of the different head components, a very good agreement (differences in energy fluences between VMC++ and BEAMnrc <1%) is obtained. Only a particular case at 6 MV shows a somewhat larger energy fluence difference of 1.4%. Dosimetrically, these phase space differences imply an agreement between both codes at the <1% level, making VMC++ head module suitable for full head simulations with considerable gain in efficiency and without loss of accuracy.

The coupling of non-linear supersymmetry to supergravity

We study the coupling of non-linear supersymmetry to supergravity. The goldstino nilpotent superfield of global supersymmetry coupled to supergravity is described by a geometric action of the chiral curvature superfield R subject to the constraint (R−λ)2=0 with an appropriate constant λ. This constraint can be found as the decoupling limit of the scalar partner of the goldstino in a class of f(R) supergravity theories.

Detection of urinary stones at reduced radiation exposure: a phantom study comparing computed radiography and a low-dose digital radiography linear slit scanning system

OBJECTIVE: In this experimental study we assessed the diagnostic performance of digital linear slit scanning radiography compared with computed radiography (CR) for the detection of urinary calculi in an anthropomorphic phantom imitating patients weighing approximately 58-88 kg. CONCLUSION: Compared with CR, linear slit scanning radiography is superior for the detection of urinary stones and may be used for pretreatment localization and follow-up at a lower patient exposure.

A meta-analysis of cambium phenology and growth: linear and non-linear patterns in conifers of the northern hemisphere

Background and Aims Ongoing global warming has been implicated in shifting phenological patterns such as the timing and duration of the growing season across a wide variety of ecosystems. Linear models are routinely used to extrapolate these observed shifts in phenology into the future and to estimate changes in associated ecosystem properties such as net primary productivity. Yet, in nature, linear relationships may be special cases. Biological processes frequently follow more complex, non-linear patterns according to limiting factors that generate shifts and discontinuities, or contain thresholds beyond which responses change abruptly. This study investigates to what extent cambium phenology is associated with xylem growth and differentiation across conifer species of the northern hemisphere. Methods Xylem cell production is compared with the periods of cambial activity and cell differentiation assessed on a weekly time scale on histological sections of cambium and wood tissue collected from the stems of nine species in Canada and Europe over 1–9 years per site from 1998 to 2011. Key Results The dynamics of xylogenesis were surprisingly homogeneous among conifer species, although dispersions from the average were obviously observed. Within the range analysed, the relationships between the phenological timings were linear, with several slopes showing values close to or not statistically different from 1. The relationships between the phenological timings and cell production were distinctly non-linear, and involved an exponential pattern. Conclusions The trees adjust their phenological timings according to linear patterns. Thus, shifts of one phenological phase are associated with synchronous and comparable shifts of the successive phases. However, small increases in the duration of xylogenesis could correspond to a substantial increase in cell production. The findings suggest that the length of the growing season and the resulting amount of growth could respond differently to changes in environmental conditions.

On degeneracy and invariances of random fields paths with applications in Gaussian process modelling

We study pathwise invariances and degeneracies of random fields with motivating applications in Gaussian process modelling. The key idea is that a number of structural properties one may wish to impose a priori on functions boil down to degeneracy properties under well-chosen linear operators. We first show in a second order set-up that almost sure degeneracy of random field paths under some class of linear operators defined in terms of signed measures can be controlled through the two first moments. A special focus is then put on the Gaussian case, where these results are revisited and extended to further linear operators thanks to state-of-the-art representations. Several degeneracy properties are tackled, including random fields with symmetric paths, centred paths, harmonic paths, or sparse paths. The proposed approach delivers a number of promising results and perspectives in Gaussian process modelling. In a first numerical experiment, it is shown that dedicated kernels can be used to infer an axis of symmetry. Our second numerical experiment deals with conditional simulations of a solution to the heat equation, and it is found that adapted kernels notably enable improved predictions of non-linear functionals of the field such as its maximum.

Comparison of monte carlo collimator transport methods for photon treatment planning in radiotherapy

The aim of this work was a Monte Carlo (MC) based investigation of the impact of different radiation transport methods in collimators of a linear accelerator on photon beam characteristics, dose distributions, and efficiency. Thereby it is investigated if it is possible to use different simplifications in the radiation transport for some clinical situations in order to save calculation time.

Self-assembly of focal point oligo-catechol ethylene glycol dendrons on titanium oxide surfaces: adsorption kinetics, surface characterization, and nonfouling properties

This work covers the synthesis of second-generation, ethylene glycol dendrons covalently linked to a surface anchor that contains two, three, or four catechol groups, the molecular assembly in aqueous buffer on titanium oxide surfaces, and the evaluation of the resistance of the monomolecular adlayers against nonspecific protein adsorption in contact with full blood serum. The results were compared to those of a linear poly(ethylene glycol) (PEG) analogue with the same molecular weight. The adsorption kinetics as well as resulting surface coverages were monitored by ex situ spectroscopic ellipsometry (VASE), in situ optical waveguide lightmode spectroscopy (OWLS), and quartz crystal microbalance with dissipation (QCM-D) investigations. The expected compositions of the macromolecular films were verified by X-ray photoelectron spectroscopy (XPS). The results of the adsorption study, performed in a high ionic strength ("cloud-point") buffer at room temperature, demonstrate that the adsorption kinetics increase with increasing number of catechol binding moieties and exceed the values found for the linear PEG analogue. This is attributed to the comparatively smaller and more confined molecular volume of the dendritic macromolecules in solution, the improved presentation of the catechol anchor, and/or their much lower cloud-point in the chosen buffer (close to room temperature). Interestingly, in terms of mechanistic aspects of "nonfouling" surface properties, the dendron films were found to be much stiffer and considerably less hydrated in comparison to the linear PEG brush surface, closer in their physicochemical properties to oligo(ethylene glycol) alkanethiol self-assembled monolayers than to conventional brush surfaces. Despite these differences, both types of polymer architectures at saturation coverage proved to be highly resistant toward protein adsorption. Although associated with higher synthesis costs, dendritic macromolecules are considered to be an attractive alternative to linear polymers for surface (bio)functionalization in view of their spontaneous formation of ultrathin, confluent, and nonfouling monolayers at room temperature and their outstanding ability to present functional ligands (coupled to the termini of the dendritic structure) at high surface densities.

A 13-year analysis from Switzerland of non-fatal sledging (sledding or tobogganing) injuries

INTRODUCTION: Winter sports have evolved from an upper class activity to a mass industry. Especially sledging regained popularity at the start of this century, with more and more winter sports resorts offering sledge runs. This study investigated the rates of sledging injuries over the last 13 years and analysed injury patterns specific for certain age groups, enabling us to make suggestions for preventive measures. METHODS: We present a retrospective analysis of prospectively collected data. From 1996/1997 to 2008/2009, all patients involved in sledging injuries were recorded upon admission to a Level III trauma centre. Injuries were classified into body regions according to the Abbreviated Injury Scale (AIS). The Injury Severity Score (ISS) was calculated. Patients were stratified into 7 age groups. Associations between age and injured body region were tested using the chi-squared test. The slope of the linear regression with 95% confidence intervals was calculated for the proportion of patients with different injured body regions and winter season. RESULTS: 4956 winter sports patients were recorded. 263 patients (5%) sustained sledging injuries. Sledging injury patients had a median age of 22 years (interquartile range [IQR] 14-38 years) and a median ISS of 4 (IQR 1-4). 136 (51.7%) were male. Injuries (AIS≥2) were most frequent to the lower extremities (n=91, 51.7% of all AIS≥2 injuries), followed by the upper extremities (n=48, 27.3%), the head (n=17, 9.7%), the spine (n=7, 4.0%). AIS≥2 injuries to different body regions varied from season to season, with no significant trends (p>0.19). However, the number of patients admitted with AIS≥2 injuries increased significantly over the seasons analysed (p=0.031), as did the number of patients with any kind of sledging injury (p=0.004). Mild head injuries were most frequent in the youngest age group (1-10 years old). Injuries to the lower extremities were more often seen in the age groups from 21 to 60 years (p<0.001). CONCLUSION: Mild head trauma was mainly found in very young sledgers, and injuries to the lower extremities were more frequent in adults. In accordance with the current literature, we suggest that sledging should be performed in designated, obstacle-free areas that are specially prepared, and that children should always be supervised by adults. The effect of routine use of helmets and other protective devices needs further evaluation, but it seems evident that these should be obligatory on official runs.

Exhaustion is associated with reduced habituation of free cortisol responses to repeated acute psychosocial stress

We investigated the association between exhaustion and the habituation of free cortisol responses to repeated stress exposure. The study comprised 25 healthy male subjects (38-59 years) who were confronted three times with the Trier Social Stress Test. Mean cortisol responses showed the well-known general habituation effect. A two-way interaction day by exhaustion (p<0.05) indicated that mean cortisol responses vary across stress sessions depending on the extent of exhaustion. Linear regression revealed a negative dose-response relationship between exhaustion and the degree of habituation (p<0.02). We identified 19 individuals showing a response habituation (negative slope) and 6 individuals showing a response sensitization over the three sessions (positive slope) with the latter reporting higher exhaustion scores. It might be hypothesized that impaired habituation to repeated exposure to the same stressor could reflect a state of increased vulnerability for allostatic load. Absence of normal habituation might be one potential mechanism how exhaustion relates to increased disease vulnerability.

The influence of muscle strength on the gait profile score (GPS) across different patients

BACKGROUND Muscle strength greatly influences gait kinematics. The question was whether this association is similar in different diseases. METHODS Data from instrumented gait analysis of 716 patients were retrospectively assessed. The effect of muscle strength on gait deviations, namely the gait profile score (GPS) was evaluated by means of generalised least square models. This was executed for seven different patient groups. The groups were formed according to the type of disease: orthopaedic/neurologic, uni-/bilateral affection, and flaccid/spastic muscles. RESULTS Muscle strength had a negative effect on GPS values, which did not significantly differ amongst the different patient groups. However, an offset of the GPS regression line was found, which was mostly dependent on the basic disease. Surprisingly, spastic patients, who have reduced strength and additionally spasticity in clinical examination, and flaccid neurologic patients showed the same offset. Patients with additional lack of trunk control (Tetraplegia) showed the largest offset. CONCLUSION Gait kinematics grossly depend on muscle strength. This was seen in patients with very different pathologies. Nevertheless, optimal correction of biomechanics and muscle strength may still not lead to a normal gait, especially in that of neurologic patients. The basic disease itself has an additional effect on gait deviations expressed as a GPS-offset of the linear regression line.