Browsing by master's degree program "Master's Programme in Theoretical and Computational Methods"

Resonant inelastic X-ray scattering (RIXS) is one of the most powerful synchrotron based methods for attaining information of the electronic structure of materials. Novel ultra-brilliant X-ray sources, X-ray free electron lasers (XFEL), offer new intriguing possibilities beyond the traditional synchrotron based techniques facilitating the transition of X-ray spectroscopic methods to the nonlinear intensity regime. Such nonlinear phenomena are well known in the optical energy range, less so in X-ray energies. The transition of RIXS to the nonlinear region could have significant impact on X-ray based materials research by enabling more accurate measurements of previously observed transitions, allowing the detection of weakly coupled transitions on dilute samples and possibly uncovering completely unforeseen information or working as a platform for novel intricate methods of the future. The nonlinear RIXS or stimulated RIXS (SRIXS) on XFEL has already been demonstrated in the simplest possible proof of concept case. In this work a comprehensive introduction to SRIXS is presented from a theoretical point of view starting from the very beginning, thus making it suitable for anyone with the basic understanding of quantum mechanics and spectroscopy. To start off, the principles of many body quantum mechanics are revised and the configuration interactions method for representing molecular states is introduced. No previous familiarity with X-ray matter interaction or RIXS is required as the molecular and interaction Hamiltonians are carefully derived, based on which a thorough analysis of the traditional RIXS theory is presented. In order to stay in touch with the real world, the basic experimental facts are recapped before moving on to SRIXS. First, an intuitive picture of the nonlinear process is presented shedding some light onto the term \textit{stimulated} while introducing basic terminology and some X-ray pulse schemes along with futuristic theoretical examples of SRIXS experiments. After this, a careful derivation of the Maxwell-Liouville-von Neumann theory up to quadrupole order is presented for the first time ever. Finally, the chapter is concluded with a short analysis of the experimental status quo on XFELs and some speculation on possible transition metal samples where SRIXS in its current state could be applied to observe quadrupole transitions advancing the field remarkably.

This thesis is about exploring descriptors for atmospheric molecular clusters. Descriptors are needed for applying machine learning methods for molecular systems. There is a collection of descriptors readily available in the DScribe-library developed in Aalto University for custom machine learning applications. The question of which descriptors to use is up to the user to decide. This study takes the first steps in integrating machine learning into existing procedure of configurational sampling that aims to find the optimal structure for any given molecular cluster of interest. The structure selection step forms a bottleneck in the configurational sampling procedure. A new structure selection method presented in this study uses k-means clustering to find structures that are similar to each other. The clustering results can be used to discard redundant structures more effectively than before which leaves fewer structures to be calculated with more expensive computations. Altogether that speeds up the configurational sampling procedure. To aid the selection of suitable descriptor for this application, a comparison of four descriptors available in DScribe is made. A procedure for structure selection by representing atmospheric clusters with descriptors and labeling them into groups with k-means was implemented. The performance of descriptors was compared with a custom score suitable for this application, and it was found that MBTR outperforms the other descriptors. This structure selection method will be utilized in the existing configurational sampling procedure for atmospheric molecular clusters but it is not restricted to that application.

When the standard model gauge group SU(3) × SU(2) × U(1) is extended with an extra U(1) symmetry, the resulting Abelian U(1) × U(1) symmetry introduces a new kinetic mixing term into the Lagrangian. Such double U(1) symmetries appear in various extensions of the standard model and have therefore long been of interest in theoretical physics. Recently this kinetic mixing has received attention as a model for dark matter. In this thesis, a systematic review of kinetic mixing and its physical implications is given, some of the dark matter candidates relying on kinetic mixing are considered, and experimental bounds for kinetic mixing dark matter are discussed. In particular, the process of diagonalizing the kinetic and mass terms of the Lagrangian with a suitable basis choice is discussed. A rotational ambiquity arises in the basis choice when both U(1) fields are massless, and it is shown how this can be addressed. BBN bounds for a model with a fermion in the dark sector are also given based on the most recent value of the effective number of neutrino species, and it is found that a significant portion of the FIMP regime is excluded by this constraint.

Sijoitusten markkinariskin suuruutta tarkastellaan usein riskimittojen avulla. Riskimitta on kuvaus mahdollisia tappioita kuvaavien satunnaismuuttujien joukosta reaalilukuihin. Riski- mittojen avulla erilaisten sijotusten riskillisyyttä pystytään vertailemaan helposti. Pankki- valvojat hyödyntävät riskimittoja pankkien vakavaraisuuden valvonnassa. Pisimpään ylei- sessä käytössä on ollut VaR (Value-at-Risk) niminen riskimitta. VaR kertoo suurimman tappion, joka koetaan jollain asetetulla luottamustasolla α eli se on tappiojakauman α- kvantiili. Baselin uusimassa ohjeistuksessa (Minimum capital requirements of market risk) odotettu vaje niminen riskimitta korvaa VaR-riskimitan pääomavaateen laskennassa. Odotet- tu vaje kertoo, mikä on tappion odotusarvo silloin, kun tappio on suurempi kuin VaR- riskimitan antama luku. Riskimittaa ollaan vaihtamassa, koska VaR ei ole teoreettisilta ominaisuuksiltaan yhtä hyvä kuin odotettu vaje. Tämä johtuu siitä, että VaR ei ole sub- additiivinen, mikä tarkoittaa sitä, että positioiden yhteenlaskettu riski voi olla joissain ta- pauksissa suurempi kuin yksittäisten positioiden riskien summa. Tämä johtaa siihen, että hajauttamattoman sijoitussalkun riski voi olla pienempi kuin hajautetun. Odotettu vaje-riskimitta ei kuitenkaan ole täysin ongelmaton, koska se ei ole konsistentisti pisteytyvä, mikä tarkoittaa, että sille ei ole olemassa pisteytysfunktiota, jonka avulla voi- taisiin verrata estimoituja ja toteutuneita arvoja konsistentisti. Lisäksi se, että odotetun vajeen suuruus riippuu kaikista häntään jäävistä tappioista, tekee siitä herkän hännässä olevien tappioiden virheille. Tämä ei ole kovin hyvä ominaisuus, koska tappiojakaumien häntien estimointiin liittyy paljon epävarmuutta. Koska riskien estimointiin liittyy epävarmuutta, sääntely velvoittaa pankkeja toteumates- taamaan regulatiivisen pääomavaateen laskennassa käytettyjä riskiestimaatteja. Toteuma- testaamisella tarkoitetaan prosessia, jossa estimoituja riskilukuja verrataan toteutuneisiin tappioihin. VaR-estimaattien toteumatestaus perustuu niiden päivien lukumäärälle tes- tausjaksolla, joina tappio ylittää VaR-estimaatin antaman tappiotason. Odotetulle vajeelle ei ole vielä olemassa yhtä vakiintuneita toteumatestausmenetelmiä kuin VaR-estimaateille. Tässä tutkielmassa esitellään kolme erilaista tapaa toteumatestata odotettu vaje estimaat- teja, nämä tavat esittelivät Kratz kollegoineen, Moldenhauer ja Pitera sekä Costanzino ja Curran. Menetelmissä tarkastellaan useamman VaR-tason yhtäaikaisia ylityksiä, suojatun position eli tappion ja riskiestimaatin erotuksen positiiviseen lukuun kumuloitu- vasti summautuvien havaintojen määrää ja VaR-ylityksien keskimääräistä suuruutta. Tutkielman laskennallisessa osuudessa tutkittiin antavatko VaR- ja odotettu vaje- toteumatestit samanlaisia tuloksia ja vaikuttaako riskin estimointiin käytetyn havainto- jakson pituus estimaattien suoriutumiseen toteumatesteissä. Laskelmissa havaittiin, että odotettu vaje- ja VaR-toteumatestit antoivat samanlaisia tuloksia. Markkinadatasta eri kokoisilla estimointi-ikkunoilla lasketut estimaatit saivat toteumatestissä erikokoisia tes- tisuureiden arvoja, ja hyväksyivät väärän mallin tai hylkäsivät oikean malli eri todennä- köisyyksillä. Kun käytettiin puhtaasti simuloitua dataa, eri kokoisilla estimointi-ikkunoilla laskettujen estimaattien tuloksissa ei ollut eroja. Näin voidaan päätellä, että testitulosten erot eri mittaisilla havaintojaksoilla laskettujen estimaattien välillä eivät johdu pelkästään havaintojen määrästä vaan myös laadusta.

Federated learning is a method to train a machine learning model on multiple remote datasets without the need to gather the data from the remote sites to a central location. In healthcare, gathering the data from different hospitals into a central location can be a difficult and time-consuming task, due to privacy concerns and regulations regarding the use of sensitive data, making federated learning an attractive alternative to more traditional methods. This thesis adapted an existing federated gradient boosting model and developed a new federated random forest model and applied them to mortality prediction in intensive care units. The results were then compared to the centralized counterparts of the models. The results showed that while the federated models did not perform as well as the centralized models on a similar sized dataset, the federated random forest model can achieve superior performance when trained on multiple hospitals' data compared to centralized models trained on a single hospital. In scenarios where the centralized models had data from multiple hospitals the federated models could not perform as well as the centralized models. It was also found that the performance of the centralized models could not be improved with further federated training. In addition to practical advantages such as possibility of parallel or asynchronous training without modifications to the algorithm, the federated random forest performed better in all scenarios compared to the federated gradient boosting. The performance of the federated random forest was also found to be more consistent over different scenarios than the performance of federated gradient boosting, which was highly dependent on factors such as the order with the hospitals were traversed.

Due to the unique properties of foams, they can be found in many different applications in a wide variety of fields. The study of foams is also useful for the many properties they share with other phenomena, like impurities in cooling metals, where the impurities coarsen similarly to bubbles in foams. For these and other reasons foams have been studied extensively for over a hundred years and continue being an interesting area of study today due to new insights in both experimental and theoretical work and new applications waiting to be used and realized in different industries. The most impactful early work in the study of the properties of foams was done in the late 1800s by Plateau. His work was extended in the early to mid-1900s by Lifshitz, Slyozov, Wagner and von Neumann and by many more authors in recent years. The early work was mostly experimental or theoretical in the sense of performing mathematical calculations on paper, while the modern methods of study have kept the experimental part -- with more refined methods of measurement of course -- but shifted towards the implementation of the theory as simulations instead of solving problems on paper. In the early 90s Durian proposed a new method for simulating the mechanics of wet foams, based on repulsive spring-like forces between neighboring bubbles. This model was later extended to allow for the coarsening of the foam, and a slightly changed version of this model has been implemented in the code presented in this thesis. As foams consist of a very large number of bubbles, it is important to be able to simulate sufficiently large systems to realistically study the physics of foams. Very large systems have traditionally been too slow to simulate on the individual bubble level in the past, but thanks to the popularity of computer games and the continuous demand for better graphics in games, the graphics processing units have become very powerful and can nowadays be used to do highly parallel general computing. In this thesis, a modified version of Durian's wet foam model that runs on the GPU is presented. The code has been implemented in modern C++ using Nvidia's CUDA on the GPU. Using this program first a typical two-dimensional foam is simulated with 100000 bubbles. It is found that the simulation code replicates the expected behaviour for this kind of foam. After this, a more detailed analysis is done of a novel phenomenon of the separation of liquid and gas phases in low gas fraction foams that arises only with sufficiently large system sizes. It is found that the phase separation causes the foam to evolve as would a foam of higher gas fraction until the phases have mixed back together. It is hypothesized that the reason causing the phase separation is related to uneven energy distribution in the foam, which itself is related to jamming and uneven distribution of the sizes of the bubbles in the foam.

Blurring is a common phenomenon during image formation due to various factors like motion between the camera and the object, or atmospheric turbulence, or when the camera fails to have the object in focus, which leads to degradation in the image formation process. This leads to the pixels interacting with the neighboring ones, and the captured image is blurry as a result. This interaction with the neighboring pixels, is the 'spread' which is represented by the Point Spread Function. Image deblurring has many applications, for example in Astronomy, medical imaging, where extracting the exact image required might not be possible due to various limiting factors, and what we get is a deformed image. In such cases, it is necessary to use an apt deblurring algorithm keeping all necessary factors like performance and time in mind. This thesis analyzes the performance of learning and analytical methods in Image deblurring Algorithm. Inverse problems would be discussed at first, and how ill posed inverse problems like image deblurring cannot be tackled by naive deconvolution. This is followed by looking at the need for regularization, and how it is necessary to control the fluctuations resulting from extreme sensitivity to noise. The Image reconstruction problem has the form of a convex variational problem, and its prior knowledge acting as the inequality constraints which creates a feasible region for the optimal solution. Interior point methods iterates over and over within this feasible region. This thesis uses the iRestNet Method, which uses the Forward Backward iterative approach for the Machine learning algorithm, and Total Variation approach implemented using the FlexBox tool for analytical method, which uses the Primal Dual approach. The performance is measured using SSIM indices for a range of kernels, the SSIM map is also analyzed for comparing the deblurring efficiency.

The Earth’s Bond albedo is the fraction of total reflected radiative flux emerging from the Earth’s Top of the Atmosphere (ToA) to the incident solar radiation. As such, it is a crucial component in modeling the Earth’s climate. This thesis presents a novel method for estimating the Earth’s Bond albedo, utilising the dynamical effects of Earth radiation pressure on satellite orbits that are directly related to the Bond albedo. Where current methods for estimating the outgoing reflected radiation are based on point measurements of the radiance reflected by the Earth taken in the proximity of the planet, the new method presented in this thesis makes use of the fact that Global Positioning Satellites (GPS) together view the entirety of the ToA surface. The theoretical groundwork is laid for this new method starting from the basic principles of light scattering, satellite dynamics, and Bayesian inference. The feasibility of the method is studied numerically using synthetic data generated from real measurements of GPS satellite orbital elements and the imaging data from the Earth Polychromatic Imaging Camera (EPIC) aboard the Deep Space Climate Observatory (DSCOVR) spacecraft. The numerical methods section introduces the methods used for forward modeling the ToA outgoing radiation, the Runge-Kutta method for integrating the satellite orbits and the virtual-observation Markov-chain Monte Carlo methods used for solving the inverse problem. The section also describes a simple clustering method used for classifying the ToA from EPIC images. The inverse problem was studied with very simple models for the ToA, the satellites, and the satellite dynamics. These initial results were promising as the inverse problem algorithm was able to accurately estimate the Bond albedo. Further study of the method is required to determine how the inverse problem algorithm works when more realism is added to the models.

In this thesis we model the term structure of zero-coupon bonds. Firstly, in the static setting by norm optimization Hilbert space techniques and starting from a set of benchmark fixed income instruments, we obtain a closed from expression for a smooth discount curve. Moving on to the dynamic setting, we describe the stochastic modeling of the fixed income market. Finally, we introduce the Heath-Jarrow-Morton (HJM) methodology. We derive the evolution of zero-coupon bond prices implied by the HJM methodology and prove the HJM drift condition for non arbitrage pricing in the fixed income market under a dynamic setting. Knowing the current discount curve is crucial for pricing and hedging fixed income securities as it is a basic input to the HJM valuation methodology. Starting from the non arbitrage prices of a set of benchmark fixed income instruments, we find a smooth discount curve which perfectly reproduces the current market quotes by minimizing a suitably defined norm related to the flatness of the forward curve. The regularity of the discount curve estimated makes it suitable for use as an input in the HJM methodlogy. This thesis includes a self-contained introduction to the mathematical modeling of the most commonly traded fixed income securities. In addition, we present the mathematical background necessary for modeling the fixed income market in a dynamic setting. Some familiarity with analysis, basic probability theory and functional analysis is assumed.

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.