Browsing by master's degree program "Magisterprogrammet i teoretiska och beräkningsmetoder"

AMPA receptors (AMPARs) are the most numerous synaptic receptors in the hippocampus. Here they take one of the central roles in the expression of long-term potentiation (LTP), the molecular mechanism underlying learning and memory. They belong to the group of glutamate-gated ion channels and have a structure characterized by 4 discrete domains. While the functional roles of C-terminal (CTD), transmembrane (TMD) and ligand-binding (LBD) domains have largely been established, the regulatory capacity - if any - of the N-terminal domain (NTD) remains questionable. In this thesis we used molecular dynamics (MD) simulations to show directly for the first time that AMPA receptor NTD domain can respond to the pH of the surrounding medium. Specifically, we identified a pair of histidine residues in the NTD interface, which are capable of acting as pH sensors - upon acidification of the environment the two histidines become protonated and through electrostatic repulsion destabilize the NTD interface. If experimentally validated, this model could provide a mechanistic explanation of AMPAR clustering in synapses. Due to low affinity for glutamate under physiological conditions, it has been proposed that AMPARs form clusters right underneath glutamate release sites in order to produce sufficiently large postsynaptic depolarizations. Since the lumen of glutamate vesicles is acidic, the presynaptic glutamate release is coupled to transient acidification of the synaptic environment. In our model this acidification is detected by identified interface histidines, which upon protonation cause structural rearrangement of the NTD interface. This rearrangement could lead to formation of interactions either with other AMPARs or synaptic anchor proteins (such as PSD-95), resulting in AMPAR clustering underneath glutamate release sites.

Response Surface Models (RSM) are cheap, reduced complexity, and, usually, statistical models that are fit to the response of more complex models to approximate their outputs with higher computational efficiency. In atmospheric science, there has been a continuous push to reduce the amount of training data required to fit an RSM. With this reduction in costly data gathering, RSMs can be used more ad hoc and quickly adapted to new applications. However, with the decrease in diverse training data, the risk increases that the RSM is eventually used on inputs on which it cannot make a prediction. If there is no indication from the model that its outputs can no longer be trusted, trust in an entire RSM decreases. We present a framework for building prudent RSMs that always output predictions with confidence and uncertainty estimates. We show how confidence and uncertainty can be propagated through downstream analysis such that even predictions on inputs outside the training domain or in areas of high variance can be integrated. Specifically, we introduce the Icarus RSM architecture, which combines an out-of-distribution detector, a prediction model, and an uncertainty quantifier. Icarus-produced predictions and their uncertainties are conditioned on the confidence that the inputs come from the same distribution that the RSM was trained on. We put particular focus on exploring out-of-distribution detection, for which we conduct a broad literature review, design an intuitive evaluation procedure with three easily-visualisable toy examples, and suggest two methodological improvements. We also explore and evaluate popular prediction models and uncertainty quantifiers. We use the one-dimensional atmospheric chemistry transport model SOSAA as an example of a complex model for this thesis. We produce a dataset of model inputs and outputs from simulations of the atmospheric conditions along air parcel trajectories that arrived at the SMEAR II measurement station in Hyytiälä, Finland, in May 2018. We evaluate several prediction models and uncertainty quantification methods on this dataset and construct a proof-of-concept SOSAA RSM using the Icarus RSM architecture. The SOSAA RSM is built on pairwise-difference regression using random forests and an auto-associative out-of-distribution detector with a confidence scorer, which is trained with both the original training inputs and new synthetic out-of-distribution samples. We also design a graphical user interface to configure the SOSAA model and trial the SOSAA RSM. We provide recommendations for out-of-distribution detection, prediction models, and uncertainty quantification based on our exploration of these three systems. We also stress-test the proof-of-concept SOSAA RSM implementation to reveal its limitations for predicting model perturbation outputs and show directions for valuable future research. Finally, our experiments affirm the importance of reporting predictions alongside well-calibrated confidence scores and uncertainty levels so that the predictions can be used with confidence and certainty in scientific research applications.

Using quantum algorithms to carry out ML tasks is what is known as Quantum Machine Learning (QML) and the methods developed within this field have the potential to outperform their classical counterparts in solving certain learning problems. The development of the field is partly dependent on that of a functional quantum random access memory (QRAM), called for by some of the algorithms devised. Such a device would store data in a superposition and could then be queried when algorithms require it, similarly to its classical counterpart, allowing for efficient data access. Taking an axiomatic approach to QRAM, this thesis provides the main considerations, assumptions and results regarding QRAM and yields a QRAM handbook and comprehensive introduction to the literature pertaining to it.

Hiukkasfysiikan standardimalli kuvaa alkeishiukkasia ja niiden välisiä vuorovaikutuksia. Higgsin bosonin löydön (2012) jälkeen kaikki standardimallin ennustamat hiukkaset on havaittu. Standardimalli on hyvin tarkka teoria, mutta kaikkia havaittuja asioita ei voida kuitenkaan selittää standardimallin puitteissa. Supersymmetria on yksi houkutteleva tapa laajentaa standardimallia. Matalan energian supersymmetriaa ei kuitenkaan ole havaittu. Supersymmetria vaatii toimiakseen niin sanotun kahden Higgsin dubletin mallin. Tavallisessa standardimallissa on yksi Higgsin dublettikenttä. Higgsin dubletissa on kaksi kompleksista kenttää eli yhteensä neljä vapausastetta, joten voisi olettaa, että siitä syntyy neljä hiukkasta. Kolme vapausasteista kuitenkin sitoutuu välibosoneihin W+, W− ja Z, jolloin jäljelle jää yksi Higgsin bosoni. Kahden Higgsin dubletin malleissa dublettikenttiä on kaksi. Koska se lisää teoriaan yhden neljän vapausasteen dubletin, Higgsin hiukkasia on siinä kaiken kaikkiaan viisi: kolme sähköisesti neutraalia (h, H ja A) sekä kaksi sähköisesti varattua (H+ ja H−). Tässä työssä keskitytään varattujen Higgsin hiukkasten etsintään malliriippumattomasti. Tutkimuksessa käytetään LHC-kiihdyttimen (Large Hadron Collider, suuri hadronitörmäytin) CMS-ilmaisimen (Compact Muon Solenoid, kompakti myonisolenoidi) keräämää dataa. Sähkövarauksellisten Higgsin bosonien etsintä keskittyy lopputiloihin, joissa varattu Higgsin bosoni hajoaa hadroniseksi tau-leptoniksi (eli tau-leptoniksi, joka puolestaan hajoaa hadroneiksi) sekä taun neutriinoksi. Niin sanottu liipaisu on tapa suodattaa dataa tallennusvaiheessa, sillä dataa tulee törmäyksistä niin paljon, ettei kaiken tallentaminen ole mahdollista. Eri liipaisimet hyväksyvät törmäystapauksia eri kriteerien perusteella. Liipaisusta aiheutuu merkittäviä systemaattisia epävarmuuksia. Tässä työssä liipaisun epävarmuuksia pyritään pienentämään käyttämällä sellaisia liipaisimia, joiden epävarmuudet ovat pienempiä. Tätä varten analyysi on jaettava riippumattomiin osiin, joiden epävarmuudet käsitellään erikseen. Lopuksi osat yhdistetään tilastollisesti toisiinsa, jolloin kokonaisepävarmuuden oletetaan pienenevän. Tässä työssä tutkitaan, pieneneekö tämä epävarmuus ja kuinka paljon. Näitä menetelmiä käyttäen kykenimme löytämään pieniä parannuksia analyysin tarkkuuteen raskaiden varattujen Higgsin bosonien kohdalla. Lisäksi odotettu raja, jota suurempi varatun Higgsin hiukkasen tuotto tässä lopputilassa olisi havaittavissa, paranee yllättävästi. Tätä rajan paranemista tutkitaan liipaisua emuloimalla. Työ on tarkoitus sisällyttää koko Run2:n datasta julkaistaviin tuloksiin.

Low-frequency $1/$ noise is ubiquitous, found in all electronic devices and other diverse areas such as as music, economics and biological systems. Despite valiant efforts, the source of $1/f$ noise remains one of the oldest unsolved mysteries in modern physics after nearly 100 years since its initial discovery in 1925. In metallic conductors resistance $1/f$ noise is commonly attributed to diffusion of mobile defects that alter the scattering cross section experienced by the charge carriers. Models based on two-level tunneling systems (TLTS) are typically employed. However, a model based on the dynamics of mobile defects forming temporary clusters would naturally offer long-term correlations required by $1/f$ noise via the nearly limitless number of configurations among a group of defects. Resistance $1/f$ noise due to such motion of mobile defects was studied via Monte Carlo simulations of a simple resistor network resembling an atomic lattice. The defects migrate through the lattice via thermally activated hopping motion, causing fluctuations in the resistance due to varying scattering cross section. The power spectral density (PSD) $S(f)$ of the simulated resistance noise was then calculated and first compared to $S(f)=C/f^\alpha$ noise, where $C$ is a constant and $\alpha$ is ideally close to unity. The value of $\alpha$ was estimated via a linear fit of the noise PSD on a log-log scale. The resistor network was simulated with varying values of temperature, system size and the concentration of defects. The noise produced by the simulations did not yield pure $1/f^\alpha$ noise, instead the lowest frequencies displayed a white noise tail, changing to $1/f^\alpha$ noise between $10^{-4}$ to $10^{-2}$~Hz. In this way the spectrum of the simulated noise resembles a Lorentzian. The value of $\alpha$ was found to be the most sensitive to temperature $T$, which directly affects the motion of the defects. At high $T$ the value of $\alpha$ was closer to 1, whereas at low $T$ it was closer to $1,5$. Varying the size of the system was found to have little impact on $\alpha$ when the temperature and concentration of defects were kept fixed. Increasing the number of defects was found to have slightly more effect on $\alpha$ when the temperature and system size were kept fixed. The value of $\alpha$ was closer to unity when the concentration of defects was higher, but the effect was not nearly as pronounced compared to varying the temperature. In addition, the simulated noise was compared to a PSD of the form $S(f)\propto e^{-\sqrt{N}/T}1/f$, where $N$ is the size of the system, according to recent theoretical proceedings. The $1/f^\alpha$ part of the simulated noise was found to roughly follow the above equation, but the results remain inconclusive. Although the simple toy model did not produce pure $1/f^\alpha$ noise, the dynamics of the mobile defects do seem to have an effect on the noise PSD, yielding noise closer to $1/f$ when there are more interactions between the defects due to either higher mobility or higher concentration of defects. However, this is disregarding the white noise tail. Recent experimental research on high quality graphene employing more rigorous kinetic Monte Carlo simulations have displayed more promising results. This indicates that the dynamics of temporary cluster formation of mobile defects is relevant to understand $1/f$ noise in metallic conductors, offering an objective for future work.

First order electroweak phase transitions (EWPTs) are an attractive area of research. This is mainly due to two reasons. First, they contain aspects that could help to explain the observed baryon asymmetry. Secondly, strong first order PTs could produce gravitational waves (GWs) that could be detectable by the Laser Interferometer Space Antenna (LISA), a future space-based GW detector. However, the electroweak PT in the Standard Model (SM) is not a first order transition but a crossover. In so-called beyond the SM theories the first order transitions are possible. To investigate the possibility of an EWPT and the detection by LISA, we must be able to parametrise the nature of the PT accurately. We are interested in the calculation of the bubble nucleation rate because it can be used to estimate the properties of the possible GW signal, such as the duration of the PT. The nucleation rate essentially quantifies how likely it is for a point in space to tunnel from one phase to the other. The calculation can be done either using perturbation theory or simulations. Perturbative approaches however suffer from the so-called infrared problem and are not free of theoretical uncertainty. We need to perform a nonperturbative calculation so that we can determine the nucleation rate accurately and test the results of perturbation theory. In this thesis, we will explain the steps that go into a nonperturbative calculation of the bubble nucleation rate. We perform the calculation on the cubic anisotropy model, a theory with two scalar fields. This toy model is one of the simplest in which a radiatively induced transition occurs. We present preliminary results on the nucleation rate and compare it with the thin-wall approximation.

Astronomical observations suggest that the cores of neutron stars may have high enough baryon densities to contain quark matter (QM). The unavailability of lattice field theory makes perturbative computations important for understanding the thermodynamics of quantum chromodynamics at high baryon densities. The gluon self-energy contributes to many transport coefficients in QM, such as thermal conductivity and shear viscosity, through quark-quark scattering processes. The contribution of short-wavelength virtual gluons to the self-energy of soft, long-wavelength gluons, known as the hard-thermal-loop (HTL) self-energy, was recently computed at next-to-leading order (NLO) in perturbation theory. In this thesis, we complete the evaluation of the NLO self-energy of soft gluons in cold QM by computing the contribution from soft virtual gluons, known as the one-loop HTL-resummed self- energy. We use HTL effective theory, a reorganization of the perturbative series for soft gluons, within the imaginary-time formulation of thermal field theory. We present the result in terms of elementary functions and finite integrals that can be evaluated numerically. We show explicitly that the NLO self-energy is finite and gauge dependent. The NLO self-energy could be used to compute corrections to transport coefficients in cold QM, which may be relevant for neutron-star applications.

This thesis is aimed to explore the topic of surface diffusion on copper and iron surfaces, using an accelerated molecular dynamics (MD) method known as collective variable-driven hyperdynamics (CVHD). The thesis is divided into six main sections: Introduction, Theory, Methods, Simulations, Results and Conclusion. The introduction briefly explains the main interest behind the topic and why diffusion is a difficult subject for classical MD simulations. In the theory section, the physical description of diffusion in metals is explained, as well as the important quantities that can be determined from these types of simulations. The following section dives into the basics concerning the molecular dynamics simulations method. It also gives a description of the theoretical basis of collective variable-driven hyperdynamics and how it is implemented alongside molecular dynamics. The simulations section more technically explains the system building methodology, discusses key parameters and gives reasoning for the chosen values of these parameters. Since, both copper and iron systems have been simulated, both sets of systems are explained independently. The results section displays the results for the copper and iron systems separately. In both sets of systems, the obtained activation energy of the dominant diffusion mechanisms remain the main point of focus. Lastly, the results are dissected and summarized.

Bayesian networks (BN) are models that map the mutual dependencies and independencies between a set of variables. The structure of the model can be represented as a directed acyclic graph (DAG), which is a graph where the nodes represent variables and the directed edges between variables represent a dependency. BNs can be either constructed by using knowledge of the system or derived computationally from observational data. Traditionally, BN structure discovery from observational data has been done through heuristic algorithms, but advances in deep learning have made it possible to train neural networks for this task in a supervised manner. This thesis provides an overview of BN structure discovery and discusses the strengths and weaknesses of the emerging supervised paradigm. One supervised method, the EQ-model, that uses neural networks for structure discovery using equivariant models, is also explored in further detail with empirical tests. Through a process of hyperparameter optimisation and moving to online training, the performance of the EQ-model is increased. The EQ-model is still observed to underperform in comparison to a competing score-based model, NOTEARS, but offers convenient features, such as dramatically faster runtime, that compensate for the reduced performance. Several interesting lines of further study that could be used to further improve the performance of the EQ-model are also identified.

One of the main questions in nuclear astrophysics is whether deconfined quark matter exists inside neutron stars. In order to answer this, the equation of state (EoS) of cold and dense quark matter, which plays an essential role in finding the equation of state of strongly interacting matter (QCD matter) inside neutron stars, needs to be determined as accurately as possible [14, 25]. The equation of state, or the pressure, of cold and dense quark matter was evaluated to the full three-loop order in perturbation theory back in 1977 by Freedman and McLerran [9, 10] and recently the contributions of the soft momentum scale to the four-loop pressure were evaluated in [13, 14, 15]. What is missing from the full four-loop pressure is the contribution of the hard momentum scale μ. In this thesis we shall first evaluate the known result for one three-loop Feynman diagram contributing to the three-loop pressure. After this, we derive a new result for a fermionic four-loop master integral at zero temperature and finite quark chemical potentials, which directly contributes to the yet unknown hard sector of the four-loop pressure of cold and dense quark matter.