The Highly Oscillatory Behavior of Automorphic Distributions for SL(2)

Automorphic distributions for SL(2) arise as boundary values of modular forms and, in a more subtle manner, from Maass forms. In the case of modular forms of weight one or of Maass forms, the automorphic distributions have continuous first antiderivatives. We recall earlier results of one of us on the Holder continuity of these continuous functions and relate them to results of other authors; this involves a generalization of classical theorems on Fourier series by S. Bernstein and Hardy-Littlewood. We then show that the antiderivatives are non-differentiable at all irrational points, as well as all, or in certain cases, some rational points. We include graphs of several of these functions, which clearly display a high degree of oscillation. Our investigations are motivated in part by properties of "Riemann's nondifferentiable function", also known as "Weierstrass' function".Comment: 27 pages, 6 Figures; version 2 corrects misprints and updates reference

Paying Refugees to Leave

States are increasingly paying refugees to repatriate, hoping to decrease the number of refugees residing within their borders. Drawing on in-depth interviews from East Africa and data from Israeli Labour Statistics, I provide a description of such payment schemes and consider whether they are morally permissible. In doing so, I address two types of cases. In the first type of case, governments pay refugees to repatriate to high-risk countries, never coercing them into returning. I argue that such payments are permissible if refugees’ choices are voluntary and if states allow refugees to return to the host country in the event of an emergency. I then describe cases where states detain refugees, and non-governmental organisations provide their own payments to refugees wishing to repatriate. In such cases, non-governmental organisations are only permitted to provide payments if the funds are sufficient to ensure post-return safety and if providing payments does not reinforce the government’s detention policy

Module design and fault diagnosis in electric vehicle batteries

Systems integration issues, such as electrical and thermal design and management of full battery packs - often containing hundreds of cells - have been rarely explored in the academic literature. In this paper we discuss the design and construction of a 9 kWh battery pack for a motorsports application. The pack contained 504 lithium cells arranged into 2 sidepods, each containing 3 modules, with each module in a 12P7S configuration. This paper focuses particularly on testing the full battery pack and diagnosing subsequent problems related to cells being connected in parallel. We demonstrate how a full vehicle test can be used to identify malfunctioning strings of cells for further investigation. After individual cell testing it was concluded that a single high inter-cell contact resistance was causing currents to flow unevenly within the pack, leading to cells being unequally worked. This is supported by a Matlab/Simulink model of one battery module, including contact resistances. Over time the unequal current flowing through cells can lead to significant differences in cells' state of charge and open circuit voltages, large currents flowing between cells even when the load is disconnected, cells discharging and aging more quickly than others, and jeopardise capacity and lifetime of the pack

Predicting growth and curve progression in the individual patient with adolescent idiopathic scoliosis: design of a prospective longitudinal cohort study

<p>Abstract</p> <p>Background</p> <p>Scoliosis is present in 3-5% of the children in the adolescent age group, with a higher incidence in females. Treatment of adolescent idiopathic scoliosis is mainly dependent on the progression of the scoliotic curve. There is a close relationship between curve progression and rapid (spinal) growth of the patient during puberty. However, until present time no conclusive method was found for predicting the timing and magnitude of the pubertal growth spurt in total body height, or the curve progression of the idiopathic scoliosis.</p> <p>The goal of this study is to determine the predictive value of several maturity indicators that reflect growth or remaining growth potential, in order to predict timing of the peak growth velocity of total body height in the individual patient with adolescent idiopathic scoliosis. Furthermore, different parameters are evaluated for their correlation with curve progression in the individual scoliosis patient.</p> <p>Methods/design</p> <p>This prospective, longitudinal cohort study will be incorporated in the usual care of patients with adolescent idiopathic scoliosis. All new patients between 8 and 17 years with adolescent idiopathic scoliosis (Cobb angle >10 degrees) visiting the outpatient clinic of the University Medical Center Groningen are included in this study. Follow up will take place every 6 months. The present study will use a new ultra-low dose X-ray system which can make total body X-rays. Several maturity indicators are evaluated like different body length dimensions, secondary sexual characteristics, skeletal age in hand and wrist, skeletal age in the elbow, the Risser sign, the status of the triradiate cartilage, and EMG ratios of the paraspinal muscle activity.</p> <p>Correlations of all dimensions will be calculated in relationship to the timing of the pubertal growth spurt, and to the progression of the scoliotic curve. An algorithm will be made for the optimal treatment strategy in the individual patient with adolescent idiopathic scoliosis.</p> <p>Discussion</p> <p>This study will determine the value of many maturity indicators and will be useful as well for other clinicians treating children with disorders of growth. Since not all clinicians have access to the presented new 3D X-ray system or have the time to make EMG's, for example, all indicators will be correlated to the timing of the peak growth velocity of total body height and curve progression in idiopathic scoliosis. Therefore each clinician can chose which indicators can be used best in their practice.</p> <p>Trial registration number</p> <p>NTR2048</p

Neutrino Interferometry In Curved Spacetime

Gravitational lensing introduces the possibility of multiple (macroscopic) paths from an astrophysical neutrino source to a detector. Such a multiplicity of paths can allow for quantum mechanical interference to take place that is qualitatively different to neutrino oscillations in flat space. After an illustrative example clarifying some under-appreciated subtleties of the phase calculation, we derive the form of the quantum mechanical phase for a neutrino mass eigenstate propagating non-radially through a Schwarzschild metric. We subsequently determine the form of the interference pattern seen at a detector. We show that the neutrino signal from a supernova could exhibit the interference effects we discuss were it lensed by an object in a suitable mass range. We finally conclude, however, that -- given current neutrino detector technology -- the probability of such lensing occurring for a (neutrino-detectable) supernova is tiny in the immediate future.Comment: 25 pages, 1 .eps figure. Updated version -- with simplified notation -- accepted for publication in Phys.Rev.D. Extra author adde

Holder exponents of irregular signals and local fractional derivatives

It has been recognized recently that fractional calculus is useful for handling scaling structures and processes. We begin this survey by pointing out the relevance of the subject to physical situations. Then the essential definitions and formulae from fractional calculus are summarized and their immediate use in the study of scaling in physical systems is given. This is followed by a brief summary of classical results. The main theme of the review rests on the notion of local fractional derivatives. There is a direct connection between local fractional differentiability properties and the dimensions/ local Holder exponents of nowhere differentiable functions. It is argued that local fractional derivatives provide a powerful tool to analyse the pointwise behaviour of irregular signals and functions.Comment: 20 pages, Late

Genetic, Maternal and Placental Factors in the Association between Birth Weight and Physical Fitness: A Longitudinal Twin Study

Background Adult cardiorespiratory fitness and muscle strength are related to all-cause and cardiovascular mortality. Both are possibly related to birth weight, but it is unclear what the importance is of genetic, maternal and placental factors in these associations. Design Peak oxygen uptake and measures of strength, flexibility and balance were obtained yearly during adolescence (10–18 years) in 114 twin pairs in the Leuven Longitudinal Twin Study. Their birth weights had been collected prospectively within the East Flanders Prospective Twin Survey. Results We identified linear associations between birth weight and adolescent vertical jump (b = 1.96 cm per kg birth weight, P = 0.02), arm pull (b = 1.85 kg per kg birth weight P = 0.03) and flamingo balance (b = −1.82 attempts to stand one minute per kg birth weight, P = 0.03). Maximum oxygen uptake appeared to have a U-shaped association with birth weight (the smallest and largest children had the lowest uptake, P = 0.01), but this association was no longer significant after adjustment for parental BMI. Using the individual twin’s deviation from his own twin pair’s average birth weight, we found positive associations between birth weight and adolescent vertical jump (b = 3.49, P = 0.0007) and arm pull (b = 3.44, P = 0.02). Δ scores were calculated within the twin pairs as first born twin minus second born twin. Δ birth weight was associated with Δ vertical jump within MZ twin pairs only (b = 2.63, P = 0.009), which indicates importance of placental factors. Conclusions We found evidence for an association between adolescent physical performance (strength, balance and possibly peak oxygen uptake) and birth weight. The associations with vertical jump and arm pull were likely based on individual, more specifically placental (in the case of vertical jump) factors. Our results should be viewed as hypothesis-generating and need confirmation, but potentially support preventive strategies to optimize birth weight, for example via placental function, to target later fitness and health

Predicting the peak growth velocity in the individual child: validation of a new growth model

Predicting the peak growth velocity in an individual patient with adolescent idiopathic scoliosis is essential or determining the prognosis of the disorder and timing of the (surgical) treatment. Until the present time, no accurate method has been found to predict the timing and magnitude of the pubertal growth spurt in the individual child. A mathematical model was developed in which the partial individual growth velocity curve was linked to the generic growth velocity curve. The generic curve was shifted and stretched or shrunk, both along the age axis and the height velocity axis. The individual age and magnitude of the PGV were obtained from the new predicted complete growth velocity curve. Predictions were made using 2, 1.5, 1 and 0.5 years of the available longitudinal data of the individual child, starting at different ages. The predicted values of 210 boys and 162 girls were compared to the child’s own original values of the PGV. The individual differences were compared to differences obtained when using the generic growth velocity curve as a standard. Using 2 years of data as input for the model, all predictions of the age of the PGV in boys and girls were significantly better in comparison to using the generic values. Using only 0.5 years of data as input, the predictions with a starting age from 13 to 15.5 years in boys and from 9.5 to 14.5 years in girls were significantly better. Similar results were found for the predictions of the magnitude of the PGV. This model showed highly accurate results in predicting the individual age and magnitude of the PGV, which can be used in the treatment of patients with adolescent idiopathic scoliosis