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In the last century, several astronomical measurements have supported that a significant percentage (about 22%) of the total mass of the Universe, on galactic and extragalactic scales, is composed of a mysterious ”dark” matter (DM). DM does not interact with the electromagnetic force; in other words it does not reflect, absorb or emit light. It is possible that DM particles are weakly interacting massive particles (WIMPs) that can annihilate (or decay) into Standard Model (SM) particles, and modern very- high-energy (VHE; > 100 GeV) instruments such as imaging atmospheric Cherenkov telescopes (IACTs) can play an important role in constraining the main properties of such DM particles, by detecting these products. One of the most privileged targets where to look for DM signal are dwarf spheroidal galaxies (dSphs), as they are expected to be high DM-dominated objects with a clean, gas-free environment. Some dSphs could be considered as extended sources, considering the angular resolution of IACTs; their angu- lar resolution is adequate to detect extended emission from dSphs. For this reason, we performed an extended-source analysis, by taking into account in the unbinned maximum likelihood estimation both the energy and the angular extension dependency of observed events. The goal was to set more constrained upper limits on the velocity-averaged cross-section annihilation of WIMPs with VERITAS data. VERITAS is an array of four IACTs, able to detect γ-ray photons ranging between 100 GeV and 30 TeV. The results of this extended analysis were compared against the traditional spectral analysis. We found that a 2D analysis may lead to more constrained results, depending on the DM mass, channel, and source. Moreover, in this thesis, the results of a multi-instrument project are presented too. Its goal was to combine already published 20 dSphs data from five different experiments, such as Fermi-LAT, MAGIC, H.E.S.S., VERITAS and HAWC, in order to set upper limits on the WIMP annihilation cross-section in the widest mass range ever reported.
Background:
Childhood and adolescence are critical stages of life for mental health and well-being. Schools are a key setting for mental health promotion and illness prevention. One in five children and adolescents have a mental disorder, about half of mental disorders beginning before the age of 14. Beneficial and explainable artificial intelligence can replace current paper- based and online approaches to school mental health surveys. This can enhance data acquisition, interoperability, data driven analysis, trust and compliance. This paper presents a model for using chatbots for non-obtrusive data collection and supervised machine learning models for data analysis; and discusses ethical considerations pertaining to the use of these models.
Methods:
For data acquisition, the proposed model uses chatbots which interact with students. The conversation log acts as the source of raw data for the machine learning. Pre-processing of the data is automated by filtering for keywords and phrases.
Existing survey results, obtained through current paper-based data collection methods, are evaluated by domain experts (health professionals). These can be used to create a test dataset to validate the machine learning models. Supervised learning
can then be deployed to classify specific behaviour and mental health patterns.
Results:
We present a model that can be used to improve upon current paper-based data collection and manual data analysis methods. An open-source GitHub repository contains necessary tools and components of this model. Privacy is respected through
rigorous observance of confidentiality and data protection requirements. Critical reflection on these ethics and law aspects is included in the project.
Conclusions:
This model strengthens mental health surveillance in schools. The same tools and components could be applied to other public health data. Future extensions of this model could also incorporate unsupervised learning to find clusters and patterns
of unknown effects.
Scientific inquiry requires that we formulate not only what we know, but also what we do not know and by how much. In climate data analysis, this involves an accurate specification of measured quantities and a consequent analysis that consciously propagates the measurement errors at each step. The dissertation presents a thorough analytical method to quantify errors of measurement inherent in paleoclimate data. An additional focus are the uncertainties in assessing the coupling between different factors that influence the global mean temperature (GMT).
Paleoclimate studies critically rely on `proxy variables' that record climatic signals in natural archives. However, such proxy records inherently involve uncertainties in determining the age of the signal. We present a generic Bayesian approach to analytically determine the proxy record along with its associated uncertainty, resulting in a time-ordered sequence of correlated probability distributions rather than a precise time series. We further develop a recurrence based method to detect dynamical events from the proxy probability distributions. The methods are validated with synthetic examples and
demonstrated with real-world proxy records. The proxy estimation step reveals the interrelations between proxy variability and uncertainty. The recurrence analysis of the East Asian Summer Monsoon during the last 9000 years confirms the well-known `dry' events at 8200 and 4400 BP, plus an additional significantly dry event at 6900 BP.
We also analyze the network of dependencies surrounding GMT. We find an intricate, directed network with multiple links between the different factors at multiple time delays. We further uncover a significant feedback from the GMT to the El Niño Southern Oscillation at quasi-biennial timescales. The analysis highlights the need of a more nuanced formulation of influences between different climatic factors, as well as the limitations in trying to estimate such dependencies.
In the present work synchronization phenomena in complex dynamical systems exhibiting multiple time scales have been analyzed. Multiple time scales can be active in different manners. Three different systems have been analyzed with different methods from data analysis. The first system studied is a large heterogenous network of bursting neurons, that is a system with two predominant time scales, the fast firing of action potentials (spikes) and the burst of repetitive spikes followed by a quiescent phase. This system has been integrated numerically and analyzed with methods based on recurrence in phase space. An interesting result are the different transitions to synchrony found in the two distinct time scales. Moreover, an anomalous synchronization effect can be observed in the fast time scale, i.e. there is range of the coupling strength where desynchronization occurs. The second system analyzed, numerically as well as experimentally, is a pair of coupled CO₂ lasers in a chaotic bursting regime. This system is interesting due to its similarity with epidemic models. We explain the bursts by different time scales generated from unstable periodic orbits embedded in the chaotic attractor and perform a synchronization analysis of these different orbits utilizing the continuous wavelet transform. We find a diverse route to synchrony of these different observed time scales. The last system studied is a small network motif of limit cycle oscillators. Precisely, we have studied a hub motif, which serves as elementary building block for scale-free networks, a type of network found in many real world applications. These hubs are of special importance for communication and information transfer in complex networks. Here, a detailed study on the mechanism of synchronization in oscillatory networks with a broad frequency distribution has been carried out. In particular, we find a remote synchronization of nodes in the network which are not directly coupled. We also explain the responsible mechanism and its limitations and constraints. Further we derive an analytic expression for it and show that information transmission in pure phase oscillators, such as the Kuramoto type, is limited. In addition to the numerical and analytic analysis an experiment consisting of electrical circuits has been designed. The obtained results confirm the former findings.
Recurrence plots, a rather promising tool of data analysis, have been introduced by Eckman et al. in 1987. They visualise recurrences in phase space and give an overview about the system's dynamics. Two features have made the method rather popular. Firstly they are rather simple to compute and secondly they are putatively easy to interpret. However, the straightforward interpretation of recurrence plots for some systems yields rather surprising results. For example indications of low dimensional chaos have been reported for stock marked data, based on recurrence plots. In this work we exploit recurrences or ``naturally occurring analogues'' as they were termed by E. Lorenz, to obtain three key results. One of which is that the most striking structures which are found in recurrence plots are hinged to the correlation entropy and the correlation dimension of the underlying system. Even though an eventual embedding changes the structures in recurrence plots considerably these dynamical invariants can be estimated independently of the special parameters used for the computation. The second key result is that the attractor can be reconstructed from the recurrence plot. This means that it contains all topological information of the system under question in the limit of long time series. The graphical representation of the recurrences can also help to develop new algorithms and exploit specific structures. This feature has helped to obtain the third key result of this study. Based on recurrences to points which have the same ``recurrence structure'', it is possible to generate surrogates of the system which capture all relevant dynamical characteristics, such as entropies, dimensions and characteristic frequencies of the system. These so generated surrogates are shadowed by a trajectory of the system which starts at different initial conditions than the time series in question. They can be used then to test for complex synchronisation.
We present a novel approach for recovery of the directional connectivity of a small oscillator network by means of the phase dynamics reconstruction from multivariate time series data. The main idea is to use a triplet analysis instead of the traditional pairwise one. Our technique reveals an effective phase connectivity which is generally not equivalent to a structural one. We demonstrate that by comparing the coupling functions from all possible triplets of oscillators, we are able to achieve in the reconstruction a good separation between existing and non-existing connections, and thus reliably reproduce the network structure.
Pulsar wind nebulae (PWNe) are the most abundant TeV gamma-ray emitters in the Milky Way. The radiative emission of these objects is powered by fast-rotating pulsars, which donate parts of their rotational energy into winds of relativistic particles. This thesis presents an in-depth study of the detected population of PWNe at high energies. To outline general trends regarding their evolutionary behaviour, a time-dependent model is introduced and compared to the available data. In particular, this work presents two exceptional PWNe which protrude from the rest of the population, namely the Crab Nebula and N 157B. Both objects are driven by pulsars with extremely high rotational energy loss rates. Accordingly, they are often referred to as energetic twins. Modelling the non-thermal multi-wavelength emission of N157B gives access to specific properties of this object, like the magnetic field inside the nebula. Comparing the derived parameters to those of the Crab Nebula reveals large intrinsic differences between the two PWNe. Possible origins of these differences are discussed in context of the resembling pulsars.
Compared to the TeV gamma-ray regime, the number of detected PWNe is much smaller in the MeV-GeV gamma-ray range. In the latter range, the Crab Nebula stands out by the recent detection of gamma-ray flares. In general, the measured flux enhancements on short time scales of days to weeks were not expected in the theoretical understanding of PWNe. In this thesis, the variability of the Crab Nebula is analysed using data from the Fermi Large Area Telescope (Fermi-LAT). For the presented analysis, a new gamma-ray reconstruction method is used, providing a higher sensitivity and a lower energy threshold compared to previous analyses. The derived gamma-ray light curve of the Crab Nebula is investigated for flares and periodicity. The detected flares are analysed regarding their energy spectra, and their variety and commonalities are discussed. In addition, a dedicated analysis of the flare which occurred in March 2013 is performed. The derived short-term variability time scale is roughly 6h, implying a small region inside the Crab Nebula to be responsible for the enigmatic flares. The most promising theories explaining the origins of the flux eruptions and gamma-ray variability are discussed in detail.
In the technical part of this work, a new analysis framework is presented. The introduced software, called gammalib/ctools, is currently being developed for the future CTA observa- tory. The analysis framework is extensively tested using data from the H. E. S. S. experiment. To conduct proper data analysis in the likelihood framework of gammalib/ctools, a model describing the distribution of background events in H.E.S.S. data is presented. The software provides the infrastructure to combine data from several instruments in one analysis. To study the gamma-ray emitting PWN population, data from Fermi-LAT and H. E. S. S. are combined in the likelihood framework of gammalib/ctools. In particular, the spectral peak, which usually lies in the overlap energy regime between these two instruments, is determined with the presented analysis framework. The derived measurements are compared to the predictions from the time-dependent model. The combined analysis supports the conclusion of a diverse population of gamma-ray emitting PWNe.
In the presented thesis, the most advanced photon reconstruction technique of ground-based γ-ray astronomy is adapted to the H.E.S.S. 28 m telescope. The method is based on a semi-analytical model of electromagnetic particle showers in the atmosphere. The properties of cosmic γ-rays are reconstructed by comparing the camera image of the telescope with the Cherenkov emission that is expected from the shower model. To suppress the dominant background from charged cosmic rays, events are selected based on several criteria. The performance of the analysis is evaluated with simulated events. The method is then applied to two sources that are known to emit γ-rays. The first of these is the Crab Nebula, the standard candle of ground-based γ-ray astronomy. The results of this source confirm the expected performance of the reconstruction method, where the much lower energy threshold compared to H.E.S.S. I is of particular importance. A second analysis is performed on the region around the Galactic Centre. The analysis results emphasise the capabilities of the new telescope to measure γ-rays in an energy range that is interesting for both theoretical and experimental astrophysics. The presented analysis features the lowest energy threshold that has ever been reached in ground-based γ-ray astronomy, opening a new window to the precise measurement of the physical properties of time-variable sources at energies of several tens of GeV.
In a classical context, synchronization means adjustment of rhythms of self-sustained periodic oscillators due to their weak interaction. The history of synchronization goes back to the 17th century when the famous Dutch scientist Christiaan Huygens reported on his observation of synchronization of pendulum clocks: when two such clocks were put on a common support, their pendula moved in a perfect agreement. In rigorous terms, it means that due to coupling the clocks started to oscillate with identical frequencies and tightly related phases. Being, probably, the oldest scientifically studied nonlinear effect, synchronization was understood only in 1920-ies when E. V. Appleton and B. Van der Pol systematically - theoretically and experimentally - studied synchronization of triode generators. Since that the theory was well developed and found many applications. Nowadays it is well-known that certain systems, even rather simple ones, can exhibit chaotic behaviour. It means that their rhythms are irregular, and cannot be characterized only by one frequency. However, as is shown in the Habilitation work, one can extend the notion of phase for systems of this class as well and observe their synchronization, i.e., agreement of their (still irregular!) rhythms: due to very weak interaction there appear relations between the phases and average frequencies. This effect, called phase synchronization, was later confirmed in laboratory experiments of other scientific groups. Understanding of synchronization of irregular oscillators allowed us to address important problem of data analysis: how to reveal weak interaction between the systems if we cannot influence them, but can only passively observe, measuring some signals. This situation is very often encountered in biology, where synchronization phenomena appear on every level - from cells to macroscopic physiological systems; in normal states as well as in severe pathologies. With our methods we found that cardiovascular and respiratory systems in humans can adjust their rhythms; the strength of their interaction increases with maturation. Next, we used our algorithms to analyse brain activity of Parkinsonian patients. The results of this collaborative work with neuroscientists show that different brain areas synchronize just before the onset of pathological tremor. Morevoever, we succeeded in localization of brain areas responsible for tremor generation.
Phase Space Reconstruction is a method that allows to reconstruct the phase space of a system using only an one dimensional time series as input. It can be used for calculating Lyapunov-exponents and detecting chaos. It helps to understand complex dynamics and their behavior. And it can reproduce datasets which were not measured. There are many different methods which produce correct reconstructions such as time-delay, Hilbert-transformation, derivation and integration. The most used one is time-delay but all methods have special properties which are useful in different situations. Hence, every reconstruction method has some situations where it is the best choice. Looking at all these different methods the questions are: Why can all these different looking methods be used for the same purpose? Is there any connection between all these functions? The answer is found in the frequency domain : Performing a Fourier transformation all these methods getting a similar shape: Every presented reconstruction method can be described as a multiplication in the frequency domain with a frequency-depending reconstruction function. This structure is also known as a filter. From this point of view every reconstructed dimension can be seen as a filtered version of the measured time series. It contains the original data but applies just a new focus: Some parts are amplified and other parts are reduced. Furthermore I show, that not every function can be used for reconstruction. In the thesis three characteristics are identified, which are mandatory for the reconstruction function. Under consideration of these restrictions one gets a whole bunch of new reconstruction functions. So it is possible to reduce noise within the reconstruction process itself or to use some advantages of already known reconstructions methods while suppressing unwanted characteristics of it.