The reliability of statistics is essential for official statistics. With administrative data more often used instead of survey data, non-sampling errors become important factors in the accuracy of...Show moreThe reliability of statistics is essential for official statistics. With administrative data more often used instead of survey data, non-sampling errors become important factors in the accuracy of statistics. For domain statistics, such as yearly turnover of enterprises, classification errors occur. This study aims to measure the effect of classification errors on domain statistics, more specially, bias and variance due to classification errors. In this study, a new method was developed that applies a Gaussian mixture model, estimated by the EM algorithm, in short referred to as the EM method. Further another method was introduced that combined the EM method with bootstrapping, referred to as the combined method. Among them, the EM method only estimates bias, and the combined method is able to estimate both bias and variance. Together with a previously used bootstrap method, the three methods were tested in a simulation study and in a case study. The bias and variance estimates from the three methods were compared with their corresponding true values in different settings. The results showed that the bias estimates from the EM and the combined method were closer to the true values compared to the bootstrap method; The combined method had closer outputs on variance estimation than the bootstrap method. The EM and the combined method were equally accurate in estimating the true bias. These results suggest that the EM and the combined method estimated the bias and variance more accurately than the bootstrap method. In practice, the combined method is recommended since both the bias and the variance can be estimated. In a situation with a very large data set, where the variance is usually small and the bias is of most concern, the EM method may be preferred.Show less
Authentication of a communication channel usually requires that the parties meet physically; but there is one solution if it is enough to confirm the geographical location of a party: quantum...Show moreAuthentication of a communication channel usually requires that the parties meet physically; but there is one solution if it is enough to confirm the geographical location of a party: quantum position verification (QPV). This is based on quantum mechanics, the no-cloning theorem, and special relativity, the invariance of the speed of light. We shown an extension of a QPV protocol where quantum information is communicated via the polarization state of single photons including the effects of photon loss and polarization noise, and explore it by numerical simulations. Moreover, we have designed and implemented the first steps of a QPV demonstration using optical fibers. We have been able to calibrate the setup for horizontal and vertical polarization states where a visibility of approximately 0.85 has been measured.Show less
As the basic unit of chromatin, the form in which DNA is tightly packed in the nucleus of eukaryotic cells, the nucleosome forms a physical barrier during transcription of the DNA. Understanding...Show moreAs the basic unit of chromatin, the form in which DNA is tightly packed in the nucleus of eukaryotic cells, the nucleosome forms a physical barrier during transcription of the DNA. Understanding the energetic landscape of the nucleosome during transcription extends our knowledge on how the nucleosome affects gene expression. An in vitro study of the energetic landscape of native nucleosomes has never been done. To facilitate such a study, techniques need to be developed to mechanically unzip native chromatin. In this research, we developed techniques on DNA unzipping using magnetic tweezers that are needed for the localization of nucleosomes in chromatin unzipping. We investigated long-lifetime DNA tethering to improve reproducibility and experimental practicality, which is vital for tethers containing nucleosomes. Techniques of force barrier localization during DNA unzipping were developed that could be used on nucleosomes. Two-state equilibrium statistical mechanics models for DNA unzipping and overstretching were developed that are extendable to include more states. These techniques aim to facilitate experiments on native nucleosomes that shine light on their fundamental role in epigenetics.Show less
We consider the family of skew tent maps Tα,β : [0, 1] → [0, 1] defined by Tα,β(x) = ( αx + α+β−αβ β for x ∈ [0, 1 − 1 β ], β − βx for x ∈ [1 − 1 β , 1] with α, β > 1 and α + β ≥ αβ. By A....Show moreWe consider the family of skew tent maps Tα,β : [0, 1] → [0, 1] defined by Tα,β(x) = ( αx + α+β−αβ β for x ∈ [0, 1 − 1 β ], β − βx for x ∈ [1 − 1 β , 1] with α, β > 1 and α + β ≥ αβ. By A. Lasota and J.A. Yorke [LY73] we know that each skew tent map has a unique acim. We fix the parameter β and show that the measure-theoretic entropy of the skew tent maps, with respect to the unique acim, depends continuously on α on a part of the parameter domain. The stability of the acim under small perturbations plays an important role in showing this result. We also investigate the relation between the measure theoretic entropy and the topological entropy for skew tent maps.Show less
Many eukaryotic organisms exhibit patterns in their DNA code that facilitate the wrapping of DNA into nucleosomes. At the same time, nucleosomes have been found to affect both interspecies DNA...Show moreMany eukaryotic organisms exhibit patterns in their DNA code that facilitate the wrapping of DNA into nucleosomes. At the same time, nucleosomes have been found to affect both interspecies DNA sequence divergence and mutational patterns in many cancer types. In my thesis I will propose a simple model capable of qualitatively reproducing all these features in a simulation. The model consists of treating the DNA code as a dynamical variable, with each specific sequence representing a state of the system. The energy required to wrap this sequence into one or more nucleosomes is the energy associated with such a state. The behaviour of the DNA sequence can then be deduced using the laws of statistical mechanics. The model turned out capable of qualitatively reproducing experimental facts.Show less
Quantum machine learning is currently regarded as one of the most promising candidates for solving problems that appear out of reach using classical computers. Recently, a novel subfield of quantum...Show moreQuantum machine learning is currently regarded as one of the most promising candidates for solving problems that appear out of reach using classical computers. Recently, a novel subfield of quantum learning was opened up by Havlíček et al., who proposed a quantum learning algorithm which is closely related to support vector machines, yet which can be implemented on currently available quantum hardware. In this thesis, contribute to quantum machine learning by presenting new results on the capabilities of this algorithm, placing it in the perspectives of classical learning theory and quantum complexity. As the follow-up research which has since been published mainly focusses on details of experimental implementation, results in this direction are still lacking. Specifically, we compare the hyperplane (explicit) and kernel (implicit) formulations of the classifier algorithm, study its generalisation performance in the framework of statistical learning theory, and pin down the precise requirements for a quantum advantage using this algorithm. To this end, we apply the so-called representer theorem, known from the study of kernel methods in machine learning, to show training set optimality of the implicit formulation under regularised error measures. Furthermore, we show a tight upper bound on the fat shattering dimension of this type of quantum classifier, and discuss the implications for generalisation performance. Lastly, we carry out a complexity theoretic study showing that classical intractability of evaluating quantum kernels implies also the intractability of these quantum classifiers. We argue that despite this fact, we cannot claim that there exist problems which are hard to learn classically, but not quantumly, in the PAC learning sense, and subsequently describe the complexity theoretic requirements of quantum CLF learning to achieve quantum learning supremacy.Show less
Atomic force microscopy (AFM) is a versatile surface-sensitive technique. One of the main challenges is to expand these capabilities to also image the subsurface structure of the sample, for...Show moreAtomic force microscopy (AFM) is a versatile surface-sensitive technique. One of the main challenges is to expand these capabilities to also image the subsurface structure of the sample, for example by using ultrasound. Existing ultrasound methodologies often indicate the phase of the cantilever vibration as the most sensitive subsurface channel. Even if such techniques can be developed to their full potential, it remains a question how accurate and fast these methods can become. To get an idea on the possibilities, we measured the frequency stability, which is similar to the phase stability, of a cantilever in a home-built AFM. We started by making the optical detection system and tested it by measuring the thermomechanical peak of the cantilever. Then the piezo inside the cantilever holder was fixed to drive the cantilever. In AFM the resonance frequency changes due to the tip-sample interaction. However no resonator is perfect, and the resonance frequency will vary even when there is no sample at all. To characterize the smallest tip-sample interactions that can be measured, one needs to characterize the frequency stability of the cantilever without a sample. To do this we have tracked the resonance frequency using a phase-locked loop. The cantilever was driven at its resonance frequency for 2 hours. The stability of its resonance frequency was analysed using the Allan deviation. We saw that for time intervals up to 30 seconds the Allan deviation had a downwards slope of −1 2 which corresponds to white frequency modulation. The short time interval Allan deviation was lower in measurements using a PLL bandwidth of 1000Hz. From the data became clear that using a PLL bandwidth of 1000Hz instead of 100Hz, the resonance frequency was flatter in time but had spikes. The lower PLL bandwidths we used were not able to resolve these spikes, that are probably caused by the unshielded cables used in the setup. Earlier we already saw spikes in the individual photodiode signals caused by these unshielded cables. For intervals longer than 30 seconds this slope for the Allan deviation was +1 (corresponds to drift in resonance frequency). This can be attributed to environmental changes, for instance temperature fluctuations, that change the resonance frequency of the cantilever. The minimum Allan deviation was aroundd 10−6. This is 11mHz RMS deviation for the 11kHz cantilever. This is equivalent to a 0.18mdeg phase noise, which is already less than the phase-contrast caused by a 50nm gold particle buried 200nm in a soft polymer at 1MHz. The minimum Allan deviation we measured is still 3 orders of magnitude above values found in the literature for resonators with a comparable mass. Shielding cables might improve this.Show less
Holographic microscopy is used as a new technique for measuring the 3D position of colloids. In this thesis the advantages and disadvantages of holographic microscopy are brought to light. The...Show moreHolographic microscopy is used as a new technique for measuring the 3D position of colloids. In this thesis the advantages and disadvantages of holographic microscopy are brought to light. The distance between passive colloids and a glass substrate is measured, in order to investigate how to use hologaphic microscopy to get a trustful result. The technology is not well established yet for a physical conclusion, nevertheless, this research was very helpful in understanding the technique.Show less
In this thesis, the potential of Chemical Exchange Saturation Transfer to image brain metabolites is presented. The Bloch-McConnell equations are simulated and the optimal parameters are found to...Show moreIn this thesis, the potential of Chemical Exchange Saturation Transfer to image brain metabolites is presented. The Bloch-McConnell equations are simulated and the optimal parameters are found to be 3.5uT, tsat = 1s for glutamate and 3uT, tsat = 1.5s for creatine. Furthermore, multiple quantification methods, including MTR asymmetry, Lorentzian fits and spinlock fits are evaluated for quantifying CEST signal from glutamate and creatine. The quantification methods are tested on the Bloch-McConnell simulations, 2-pool phantoms, 3-pool phantoms and in vivo.Show less
The recent popularization of machine learning as a new paradigm in computer science provides interesting opportunities for explaining phenomena of collective motion in living systems, as for...Show moreThe recent popularization of machine learning as a new paradigm in computer science provides interesting opportunities for explaining phenomena of collective motion in living systems, as for example flocks of birds or schools of fish. In this thesis we develop a model for collective motion using multi-agent reinforcement learning with orientation-based rewards, a new type of reward system that has not yet been found in literature. While the developed model is in principle generally applicable to all forms of collective motion observed in nature, we use the language of the flocking behaviour of birds as a particular example to frame our model. The birds have the option to either fly into an instinctive direction or act based on a Viscek-type of interaction with their neighbors, and are rewarded maximally when the resulting direction of movement is some predetermined prefered direction. The model distinghuishes between leaders that instinctively move towards this direction and followers that do not. We show that collective motion into this prefered direction emerges from this model, but only with a minimum of 1.23 encounters with neighbours on average, of which a minimal fraction of 0.2 should be leaders, which on average roughly corresponds to at least one encounter with a leader every four timesteps. These lower bounds are rudimentary estimates, as the present study serves mainly as a proof of concept that collective motion can emerge from this new type of model. Additionally it is suggested that, using deep reinforcement learning, this model can be viewed as a reinforcement learning extension of the Vicsek model.Show less
Well isolated mechanical systems have the potential to be developed into systems for magnetic, accelerometric and gravitational sensing, as well as to investigate the limits of quantum theory. This...Show moreWell isolated mechanical systems have the potential to be developed into systems for magnetic, accelerometric and gravitational sensing, as well as to investigate the limits of quantum theory. This holds especially for mechanical resonators which consist of levitated nano- and microparticles, since an advantage of this type of system is the lack of clamping losses, potentially resulting in an extremely low energy dissipation. Here, a mechanical resonator is presented, where a magnetic microparticle is levitated in a cylindrical trap of a type I superconductor. SQUID detection has been used to measure the vibrational modes of the particle. The damping factors of the resonator have been analytically calculated, resulting in an expected quality factor Q of 10^11. The coupling and energy of the six translational and rotational rigid body modes of the particle have been simulated, based on analytical approximations. Experimentally, a resonance is detected with a damping time of 47 seconds and a Q of 2.2*10^4. These are promising first results, since this difference in damping and Q factor can be explained as the Earth's magnetic field was trapped inside the experiment. With these complications resolved, an extremely sensitive micromechanical resonator can be developed. This opens a new road in the investigation of the boundary between the quantum and classical regime and gravitational research.Show less
Oscillons, localized oscillating configurations in nonlinear field theories, have been known to exist since the mid 1990’s. Since then a lot of research has been done to understand these exotic...Show moreOscillons, localized oscillating configurations in nonlinear field theories, have been known to exist since the mid 1990’s. Since then a lot of research has been done to understand these exotic solutions. They can emerge under rather general conditions and have been found to exist in well-motivated physical models. Although they have been studied extensively in single-field models, not a lot is known about them in theories where fields interact. In this thesis I try to gain insights into the complicated questions surrounding multi-field oscillons. In the first chapters I start by reviewing what oscillons are in the context of single-field models. I also show why it is generally expected that oscillons might have an impact on early Universe cosmology. In the last chapters I tackle multi-field oscillons in the context of two coupled scalar fields. I manage to find stable oscillons in a model with a specific ”exchange” symmetry and find a criterion to assess their stability by extending the Vakhitov-Kolokolov criterion. Oscillons in this system can both exist in in-phase and out-of-phase configurations, highlighting an interesting characteristic of oscillons in multi-field theories. Finally, I analyse oscillons in more general models of scalar fields, showing the influence of a mass mismatch on the oscillon solution and discussing its influence on stability. I conclude with some expected differences between symmetric and asymmetric couplings between the fields that need to be tested in the future.Show less
Classical integrable theories fail to thermalize. This situation can be attributed to the presence of the extensive number of integrals of motion that preclude exploration of the phase space. The...Show moreClassical integrable theories fail to thermalize. This situation can be attributed to the presence of the extensive number of integrals of motion that preclude exploration of the phase space. The further question to ask is what happens in the quantum integrable case. The answer turns to be more sophisticated than in the classical case and may, in particular, depend on a) what one means by thermalization and b) which local observables are considered. The no-go condition presented in this thesis will help to clarify these conditions when thermalization is defined in a particular way. This no-go condition will be applied to several examples of quantum integrable models.Show less
We look for cosmic neutrinos originating in Gamma Ray bursts using public data from the IceCube collaboration. We allow for a time difference between a neutrino and GRB photon of up to 40 days to...Show moreWe look for cosmic neutrinos originating in Gamma Ray bursts using public data from the IceCube collaboration. We allow for a time difference between a neutrino and GRB photon of up to 40 days to probe possible Lorentz invariance violations. These violations might become visible if a neutrino has high enough energy and traveled a long enough distance before we observe it. We make use of pseudo experiments to simulate different possible neutrino realizations and see how well a signal can be discerned from background. We find slightly less neutrinos than expected from background in the IceCube data. A signal associated with more than 3% of the GRBs can be excluded at 98% confidence in the northern hemisphere, and at 70% confidence in the southern hemisphere. Under the assumption that the highest energy neutrinos that can be associated to a GRB are experiencing LIV induced time shifts we have derived an intrinsic time difference at emission between GRB neutrinos and photons of ∆tin = (4.49 ± 23.0) 10^4s, and a LIV scale of ELIV = (1.05 ± 0.85) 10^15GeV, while the probability of finding similar results from purely uncorrelated events is P = 54%.Show less
Master thesis | Statistical Science for the Life and Behavioural Sciences (MSc)
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A stricter global sulfur regulation by International Maritime Organization MARPOL Annex IV is effective as of the beginning of 2020, but there is no monitoring system on whether the ships actually...Show moreA stricter global sulfur regulation by International Maritime Organization MARPOL Annex IV is effective as of the beginning of 2020, but there is no monitoring system on whether the ships actually comply with the sulfur cap. The thesis devises a systematic approach to a prototype of a sulfur compliance monitoring system using the state-of-the-art TROPOspheric Monitoring Instrument(TROPOMI) which measures the atmospheric presence of trace gases. Oceanic geographical coordinates are classified by the similarity in the concentration level of trace gas with the k-means clustering method and adequate averaging techniques. The choice of hyperparameters and the final results are statistically formulated and verified. The subsequent longitudinal analysis on the temporal trends of trace gas emission suggests that the sulfur dioxide measurements of TROPOMI are dominated by measurement noise. The thesis concludes with the outcome that the nitrogen dioxide measurements of TROPOMI can be well-utilized to backtrack the maritime anthropogenic activities such as the regional shipping route, which indicates a possibility to be further developed as a global monitoring system for both land and maritime emission.Show less
The pairing symmetry of the superconducting material Strontium Ruthenate (Sr2RuO4), despite much research, has not been established. The experimental evidence until now points to a pairing symmetry...Show moreThe pairing symmetry of the superconducting material Strontium Ruthenate (Sr2RuO4), despite much research, has not been established. The experimental evidence until now points to a pairing symmetry compatible with the existence of superconducting domains. The boundaries of these domains are expected to act as Josephson junctions. Although bulk samples contain a random and non-predictable domain structure, mesoscopic samples feature a controllable configuration of the domains. The behavior of singly or doubly presupposed connected domain boundary is investigated by the electronic transport properties of mesoscopic samples of Sr2RuO4, in which the domain walls are pinned to the geometry. The characteristic critical current oscillations and Shapiro steps of the Josephson junction are established, as well as current switchable states due to in-plane (IP) fields.Show less
Localization of light and cavity modes play an important role in optics. In photonic crystals, localization occurs at defects to the periodicity of the structure. Recently, twist in a coreless...Show moreLocalization of light and cavity modes play an important role in optics. In photonic crystals, localization occurs at defects to the periodicity of the structure. Recently, twist in a coreless photonic crystal fibre was shown to confine an optical mode. In this project, the analogous system of a rotating two-dimensional photonic crystal has been investigated. Building upon previous work by Götte, Barnett and Padgett, a wave equation for a rotating photonic crystal is derived. Although no explicit solutions have been found yet, several solving procedures are proposed. In addition, the effect of elastic deformations resulting from rotation-induced centrifugal force is investigated theoretically. We report the emergence of localized modes in a circular Bragg deformed by rotation. The wavelength of these modes is found to be proportional to the magnitude of the deformations. The localized modes reported here present a first step towards highly tunable cavity devices.Show less
In this thesis we will demonstrates how to construct a counting mechanical metamate- rial that is based on bi-stable buckling beams by creating a material that can count to ten. By coupling...Show moreIn this thesis we will demonstrates how to construct a counting mechanical metamate- rial that is based on bi-stable buckling beams by creating a material that can count to ten. By coupling bistable buckling beams in a suitable geometry we can design mate- rials that when cyclically compressed between two critical strains. We show that when two adjacent buckled beams touch, there is a characteristic length scale - the inversion length - that determines which of two beams snaps through when compressed to the snapping strain. We experimentally and analytically work out the characteristic inver- sion distance length scale that determines the outcome of the battle of the buckling beams and show how to modify beam geometries to design counting behaviour for many beam materials.Show less
Adopting some key ideas of the AdS/CFT correspondence, such as the geometrization of the RG formalism and having an AdS background spacetime, mappings of the 1D and 2D Ising model onto a network...Show moreAdopting some key ideas of the AdS/CFT correspondence, such as the geometrization of the RG formalism and having an AdS background spacetime, mappings of the 1D and 2D Ising model onto a network model were developed. The mappings primarily serve to engineer a 2D phase transition into a higher dimensional tree network and show what holographic properties are obtained by merely invoking some conceptual ’ingredients’ from the holographic duality. The networks were studied by MC simulation of the Ising model and subsequent construction. This thesis then further reports on efforts to describe the network ensemble seeded off the Ising model independently, by a(n) (exponential) random graph model.Show less
The cytoskeleton gives a cell its main structure and rigidity. It plays a significant role during many (force sensitive) mechanical cues from outside the cell. The anisotropy of the cytoskeleton...Show moreThe cytoskeleton gives a cell its main structure and rigidity. It plays a significant role during many (force sensitive) mechanical cues from outside the cell. The anisotropy of the cytoskeleton has been shown to control the geometry and forces of adherent cells. Bases on the the shape of curved cell edge segments of single cells, the size of internal stresses and traction forces can be calculated. However, such methods have not yet been applied to clusters of cells. Here we introduce two methods to describe the mechanical equilibrium of cell doublets. Either in a discontinuous way, where both cells are treated separately, or continuous, where we do not differentiate between the cells and treat it as a single cell.Show less
