Long memory estimation for complex-valued time series

Long memory has been observed for time series across a multitude of fields and the accurate estimation of such dependence, e.g. via the Hurst exponent, is crucial for the modelling and prediction of many dynamic systems of interest. Many physical processes (such as wind data), are more naturally expressed as a complex-valued time series to represent magnitude and phase information (wind speed and direction). With data collection ubiquitously unreliable, irregular sampling or missingness is also commonplace and can cause bias in a range of analysis tasks, including Hurst estimation. This article proposes a new Hurst exponent estimation technique for complex-valued persistent data sampled with potential irregularity. Our approach is justified through establishing attractive theoretical properties of a new complex-valued wavelet lifting transform, also introduced in this paper. We demonstrate the accuracy of the proposed estimation method through simulations across a range of sampling scenarios and complex- and real-valued persistent processes. For wind data, our method highlights that inclusion of the intrinsic correlations between the real and imaginary data, inherent in our complex-valued approach, can produce different persistence estimates than when using real-valued analysis. Such analysis could then support alternative modelling or policy decisions compared with conclusions based on real-valued estimation

The great work of Michael Senko as a part of a durable application model

This paper defines a language for expressing a durable semantic application model as major part of the specifications for business applications This language consists of the modeling constructs from Natural Language Modeling (NLM). It will be shown in this article how these modeling constructs constitute a hierarchy within any durable semantic application model

Variable-density k-space filling curves for accelerated Magnetic Resonance Imaging

Reducing scan times in magnetic resonance imaging (MRI) is essential for attaining high spatial resolution, which could aid in diagnosing certain pathologies, such as Alzheimer's disease. Methods to accelerate the time of segmented MR acquisitions commonly rely on simple sampling patterns such as straight lines, spirals or slight variations of these elementary shapes. However, such geometrical approaches do not take full advantage of the degrees of freedom offered by the hardware and cannot be easily adapted to fit an arbitrary sampling distribution. Here, we report the use of a versatile method inspired from stippling techniques that automatically generates optimized sampling patterns compatible with MR hardware constraints on maximum gradient amplitude and slew rate. These non-Cartesian sampling curves are designed to comply with key criteria for optimal sampling: a controlled distribution of samples and a locally uniform k-space coverage. Combining sampling efficiency with compressed sensing, the resulting sampling patterns allowed up to 20-fold reductions in MR scan time (compared to fully-sampled Cartesian acquisitions) for two-dimensional T * 2-weighted imaging without deterioration of image quality, as demonstrated by our experimental results at 7 Tesla on in vivo human brains for a high in-plane resolution of 390 µm. In comparison to existing non-Cartesian sampling strategies (spiral and radial), the proposed technique also yielded superior image quality. Since our method does not involve additional hardware, this approach offers a cost-free solution that has the potential to improve sampling efficiency in many MRI applications