In this paper, we consider the one-dimensional anharmonic oscillator, which represents well the anharmonic vibrations in diatomic molecules. For the description of the associate potential we use the Morse potential, which gives a good approximation of the experimentally observed vibrational modes of molecules and hence contributes to the realistic description of the spectrum of diatomic molecules. The generalized and Gaussian coherent states are thus constructed and compared in terms of the localization of the particle in those states. We apply these results to the example of the sodium chloride molecule, 1H35Cl.

The Internet of Things (IoT) has gained significant recognition to become a novel sensing paradigm to interact with the physical world in this Industry 4.0 era. The IoTs are being used in many diverse applications that are part of our life and is growing to become the global digital nervous systems. It is quite evident that in the near future, hundreds of millions of individuals and businesses with billions will have smart-sensors and advanced communication technology, and these things will expand the boundaries of current systems. This will result in a potential change in the way we work, learn, innovate, live and entertain. The heterogeneous smart sensors within the Internet of Things are indispensable parts, which capture the raw data from the physical world by being the first port of contact. Often the sensors within the IoT are deployed or installed in harsh environments. This inevitably means that the sensors are prone to failure, malfunction, rapid attrition, malicious attacks, theft and tampering. All of these conditions cause the sensors within the IoT to produce unusual and erroneous readings, often known as outliers. Much of the current research has been done in developing the sensor outlier and fault detection models exclusively for the Wireless Sensor Networks (WSN), and adequate research has not been done so far in the context of the IoT. Wireless sensor network’s operational framework differ greatly when compared to IoT’s operational framework, using some of the existing models developed for WSN cannot be used on IoT’s for detecting outliers and faults. Sensor faults and outlier detection is very crucial in the IoT to detect the high probability of erroneous reading or data corruption, thereby ensuring the quality of the data collected by sensors. The data collected by sensors are initially pre-processed to be transformed into information and when Artificially Intelligent (AI), Machine Learning (ML) models are further used by the IoT, the information is further processed into applications and processes. Any faulty, erroneous, corrupted sensor readings corrupt the trained models, which thereby produces abnormal processes or outliers that are significantly distinct from the normal behavioural processes of a system. In this paper, we present a comprehensive review of the detecting sensor faults, anomalies, outliers in the Internet of Things and the challenges. A comprehensive guideline to select an adequate outlier detection model for the sensors in the IoT context for various applications is discussed.

Circadian rhythms become less dominant and less regular with chronic-degenerative disease, such that to accurately assess these pathological conditions it is important to quantify not only periodic characteristics but also more irregular aspects of the corresponding time series. Novel data-adaptive techniques, such as singular spectrum analysis (SSA), allow for the decomposition of experimental time series, in a model-free way, into a trend, quasiperiodic components and noise fluctuations. We compared SSA with the traditional techniques of cosinor analysis and intradaily variability using 1-week continuous actigraphy data in young adults with acute insomnia and healthy age-matched controls. The findings suggest a small but significant delay in circadian components in the subjects with acute insomnia, i.e. a larger acrophase, and alterations in the day-to-day variability of acrophase and amplitude. The power of the ultradian components follows a fractal 1/f power law for controls, whereas for those with acute insomnia this power law breaks down because of an increased variability at the 90min time scale, reminiscent of Kleitman’s basic rest-activity (BRAC) cycles. This suggests that for healthy sleepers attention and activity can be sustained at whatever time scale required by circumstances, whereas for those with acute insomnia this capacity may be impaired and these individuals need to rest or switch activities in order to stay focused. Traditional methods of circadian rhythm analysis are unable to detect the more subtle effects of day-to-day variability and ultradian rhythm fragmentation at the specific 90min time scale.

For the first time, fractal analysis techniques are implemented to study the correlations present in sleep actigraphy for individuals suffering from acute insomnia with comparisons made against healthy subjects. Analysis was carried out for 21 healthy individuals with no diagnosed sleep disorders and 26 subjects diagnosed with acute insomnia during night-time hours. Detrended fluctuation analysis was applied in order to look for 1/f-fluctuations indicative of high complexity. The aim is to investigate whether complexity analysis can differentiate between people who sleep normally and people who suffer from acute insomnia. We hypothesize that the complexity will be higher in subjects who suffer from acute insomnia owing to increased night-time arousals. This hypothesis, although contrary to much of the literature surrounding complexity in physiology, was found to be correct-for our study. The complexity results for nearly all of the subjects fell within a 1/f-range, indicating the presence of underlying control mechanisms. The subjects with acute insomnia displayed significantly higher correlations, confirmed by significance testingpossibly a result of too much activity in the underlying regulatory systems. Moreover, we found a linear relationship between complexity and variability, both of which increased with the onset of insomnia. Complexity analysis is very promising and could prove to be a useful non-invasive identifier for people who suffer from sleep disorders such as insomnia.

The Morse potential one-dimensional quantum system is a realistic model for studying vibrations of atoms in a diatomic molecule. This system is very close to the harmonic oscillator one. We thus propose a construction of squeezed coherent states similar to the one of the harmonic oscillator using ladder operators. The properties of these states are analysed with respect to the localization in position, minimal Heisenberg uncertainty relation, the statistical properties and illustrated with examples using the finite number of states in a well-known diatomic molecule.This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to 'Coherent states: mathematical and physical aspects'.