A brief history of long memory: Hurst, Mandelbrot and the road to ARFIMA

Long memory plays an important role in many fields by determining the behaviour and predictability of systems; for instance, climate, hydrology, finance, networks and DNA sequencing. In particular, it is important to test if a process is exhibiting long memory since that impacts the accuracy and confidence with which one may predict future events on the basis of a small amount of historical data. A major force in the development and study of long memory was the late Benoit B. Mandelbrot. Here we discuss the original motivation of the development of long memory and Mandelbrot's influence on this fascinating field. We will also elucidate the sometimes contrasting approaches to long memory in different scientific communitiesComment: 40 page

First Experiments on Stochastic Cooling of Heavy Ion Beams at the ESR

At the experimental storage ring ESR of GSI, one half of the foreseen pick-up and kicker tanks are installed, the rest will follow in 1998. First experimental tests of the stochastic precooling system have been performed since April 1997. Longitudinal Palmer cooling was successfully demonstrated. E-folding cooling times of 8.6 seconds were determined with carbon beams. No significant dependence of the cooling time on the number of particles was observed during these first tests. This may be explained by a low signal to noise ratio of the signals obtained from the pick-ups in the present configuration. With heavy ions in higher charge states faster cooling times are expected. The experiments are an important step towards the realization of experiments with radioactive fragments, e.g. in order to measure nuclear masses or half-lives of stripped exotic ions

Research in Crops and Soils: A Progress Report

The Experiment Station Agronomy Farm, located 1 mile east of Brookings, is representative of a large area of land in eastern South Dakota. It consists of 160 acres, 150 of which are laid out in various soil and crop experiments. The soil, commonly called loam and classified as Barnes Loam, is in a good state of fertility. Results of the experiments on this farm will indicate what may be expected from similar soil management, cropping systems, and crop varieties on the same type of soil and under comparable climatic conditions. Numerous experiments are in progress on this farm. The information in this circular is a progress report on those experiments for which results can now be evaluated. Further results will be published at intervals as the experiments progress

Fast Stochastic Cooling of Heavy Ions at the ESR Storage Ring

Since the completion of the installation of pick-up and kicker tanks in the ESR, stochastic cooling in all phase space dimensions has been demonstrated with rather short cooling times. New RF components were added. The system is now ready for experiments with secondary beams. The momentum sensitivity of the pick-up electrodes was measured. The ability of the Palmer cooling system to cool beams with a maximum momentum spread of ± 0.7 % was demonstrated. After injecting an uncooled primary argon beam from the SIS synchrotron, e-folding cooling times of 0.86 s in the longitudinal phase plane and 1.6 s in the horizontal plane were measured with 5×106 injected particles. These values are close to theoretical expectations. In a first experiment with uranium, the shortest cooling times have been below 0.5 s in both the longitudinal and vertical phase planes. The system cools the complete injected beam without beam loss. An experiment with beam accumulation following stochastic precooling was performed successfully. The resulting equilibrium phase space densities are high enough to be followed by fast electron cooling of the stack

Efficient Bayesian inference for natural time series using ARFIMA processes

Many geophysical quantities, such as atmospheric temperature, water levels in rivers, and wind speeds, have shown evidence of long memory (LM). LM implies that these quantities experience non-trivial temporal memory, which potentially not only enhances their predictability, but also hampers the detection of externally forced trends. Thus, it is important to reliably identify whether or not a system exhibits LM. In this paper we present a modern and systematic approach to the inference of LM. We use the flexible autoregressive fractional integrated moving average (ARFIMA) model, which is widely used in time series analysis, and of increasing interest in climate science. Unlike most previous work on the inference of LM, which is frequentist in nature, we provide a systematic treatment of Bayesian inference. In particular, we provide a new approximate likelihood for efficient parameter inference, and show how nuisance parameters (e.g., short-memory effects) can be integrated over in order to focus on long-memory parameters and hypothesis testing more directly. We illustrate our new methodology on the Nile water level data and the central England temperature (CET) time series, with favorable comparison to the standard estimators. For CET we also extend our method to seasonal long memory

Stochastic Cooling at the ESR

Stochastic precooling at the ESR storage ring of GSI will be used mainly for experiments with stored radioactive fragment beams. They arrive from the fragment separator with momentum spreads and emittances for which electron cooling is too slow. The installation of components at the ESR is now complete and first commissioning experiments have been performed. Both longitudinal and transverse stochastic cooling have been demonstrated. The paper gives a short account of the system architecture, and of the response of quarter-wave plates and superelectrodes at intermediate energies. The preparation of fragment beams suitable for subsequent electron cooling is discussed for the case that a mixture of different ion species is present in the cooler ring. Results of commissioning and future prospects are presented

Systematic inference of the long-range dependence and heavy-tail distribution parameters of ARFIMA models

Long-Range Dependence (LRD) and heavy-tailed distributions are ubiquitous in natural and socio-economic data. Such data can be self-similar whereby both LRD and heavy-tailed distributions contribute to the self-similarity as measured by the Hurst exponent. Some methods widely used in the physical sciences separately estimate these two parameters, which can lead to estimation bias. Those which do simultaneous estimation are based on frequentist methods such as Whittle’s approximate maximum likelihood estimator. Here we present a new and systematic Bayesian framework for the simultaneous inference of the LRD and heavy-tailed distribution parameters of a parametric ARFIMA model with non-Gaussian innovations. As innovations we use the α-stable and t-distributions which have power law tails. Our algorithm also provides parameter uncertainty estimates. We test our algorithm using synthetic data, and also data from the Geostationary Operational Environmental Satellite system (GOES) solar X-ray time series. These tests show that our algorithm is able to accurately and robustly estimate the LRD and heavy-tailed distribution parameters

The effect of feedback during training sessions on learning pattern-recognition based prosthesis control

Human-machine interfaces have not yet advanced to enable intuitive control of multiple degrees of freedom as offered by modern myoelectric prosthetic hands. Pattern Recognition (PR) control has been proposed to make human-machine interfaces in myoelectric prosthetic hands more intuitive, but it requires the user to generate high-quality, i.e., consistent and separable, electromyogram (EMG) patterns. To generate such patterns, user training is required and has shown promising results. However, how different levels of feedback affect effectivity in training differently, has not been established yet. Furthermore, a correlation between qualities of the EMG patterns (the focus of training) and user performance has not been shown yet. In this study, 37 able-bodied participants (mean age 21 years, 19 males) were recruited and trained PR control over five days. Three levels of feedback were tested for their effectiveness: no external feedback, visual feedback and visual feedback with coaching. Training resulted in improved performance from pre-to post-test with no interaction effect of feedback. Feedback did however affect the quality of the EMG patterns where people who did not receive external feedback generated higher amplitude patterns. A weak correlation was found between a principal component, composed of EMG amplitude and pattern variability, and performance. Our results show that training is highly effective in improving PR control regardless of feedback and that none of the quality metrics correlate with performance. We discuss how different levels of feedback can be leveraged to improve PR control training

Should Hands Be Restricted When Measuring Able-Bodied Participants To Evaluate Machine Learning Controlled Prosthetic Hands?

OBJECTIVE: When evaluating methods for machine-learning controlled prosthetic hands, able-bodied participants are often recruited, for practical reasons, instead of participants with upper limb absence (ULA). However, able-bodied participants have been shown to often perform myoelectric control tasks better than participants with ULA. It has been suggested that this performance difference can be reduced by restricting the wrist and hand movements of able-bodied participants. However, the effect of such restrictions on the consistency and separability of the electromyogram's (EMG) features remains unknown. The present work investigates whether the EMG separability and consistency between unaffected and affected arms differ and whether they change after restricting the unaffected limb in persons with ULA. METHODS: Both arms of participants with unilateral ULA were compared in two conditions: with the unaffected hand and wrist restricted or not. Furthermore, it was tested if the effect of arm and restriction is influenced by arm posture (arm down, arm in front, or arm up). RESULTS: Fourteen participants (two women, age=53.4±4.05) with acquired transradial limb loss were recruited. We found that the unaffected limb generated more separated EMG than the affected limb. Furthermore, restricting the unaffected hand and wrist lowered the separability of the EMG when the arm was held down. CONCLUSION: Limb restriction is a viable method to make the EMG of able-bodied participants more similar to that of participants with ULA. SIGNIFICANCE: Future research that evaluates methods for machine learning controlled hands in able-bodied participants should restrict the participants' hand and wrist