Money laundering is the activity of securing proceeds from criminal acts by concealing their origins. It is a vast global problem, as it is essential for all types of crime where the goal is to make profit. Anti money ...

Hovedmålet for denne oppgaven er å undersøke og sammenlikne to symmetriske krypteringsalgoritmer, AES og Kalyna. I oppgaven presenteres AES og Kalynas funksjoner og sammenlikner AES og Kalynas forskjellige funksjoner i ...

Masteroppgaven handeler om den matematiske teorien bak Supersingular Isogeny Key Exchange, som er en post-kvante kryptografi. Vi går igjennom nøkkel resultatene innenfor supersingulære kurver, ekspansjons grafer og kvaternione ...

With the advent of Industry 4.0, Predictive Maintenance (PdM) has garnered a lot of interest, both academically and in the industry. This thesis will be developing and using machine learning methods for PdM, using real ...

Background: Markov chain Monte Carlo (MCMC) methods for deep learning are not commonly used because of the computationally heavy Metropolis-Hastings (MH) test. MCMC methods can give more information in its predictions than ...

The aim of this thesis is to examine some of the symmetries of the Klein quartic curve by describing the fixed points of the subgroups of its automorphism group, and some orbits of fixed points on the quartic curve and on ...

Normalizing flows is a promising avenue in both density estimation and variational inference, which promises models that can both generate new samples and evaluate the exact density, both with reasonable computational ...

The lattice of honest degrees has been studied extensively since the 1960's. The introduction of the Growth Theorem in the 1990's would give more clarity to proofs of the already known results, and make new results easier ...

Oppgaven tar for seg polyedrisk kombinatorikk, et tema der hovedmålet er å finne polyedriske representasjoner av kombinatoriske strukturer og optimeringsproblemer. Det er et rikt tema som kobler sammen områder som kombinatorikk ...

Building upon recent work by Binda, Park, and Østvær we construct a theory of motives with compact support in the setting of logarithmic algebraic geometry. Starting from the notion of finite logarithmic correspondences ...

While neural networks have been demonstrated to be highly successful in mathematical and statistical modelling of a comprehensive selection of problems, their application to inverse problems is not without complications. ...

In this master's thesis we derive a connection between filtration shifts and differentials in a spectral sequence. We assume that the spectral sequence comes from a Cartan-Eilenberg system, and we develop a framework to ...

For electric propulsion motors installed on marine vessels, the prevention of overheating is usually based on resistor temperature detector sensors. The monitoring system raises an alarm if the detected temperatures reach ...

Fairness is an inherently important aspect of decision-making in general, and with automated algorithms increasingly making decisions impacting our lives it is of paramount importance that the decisions they make be fair ...

Seifert manifolds play a crucial role in the classification of 3-manifolds, as they occupy six of the eight geometries proposed by Thurston. In this thesis we determine which Seifert manifolds can be given a smooth action ...

Statistical boosting is a powerful tool that has become increasingly more popular in recent years. It works very well in the high-dimensional data setting, and it has many beneficial properties, e.g., shrinkage, automated ...

This thesis is concerned with rationality questions of algebraic varieties, specifically questions regarding stable rationality over the complex numbers. We use the techniques related to the motivic volume introduced by ...

\textit{Isogeny graphs} are a type of graphs, where the vertices represent elliptic curves and the edges represent isogenies. I will examine some of the structures of these graphs in this thesis. It turns out that the ...

The main aim of the thesis is to study attractors for certain iterated function systems arising from quantum channels on finite dimensional C*-algebras. I will show the existence of attractors on the density operators by ...

Denne oppgaven har som mål å drøfte ikke-standard analyse som et alternative til tradisjonell undervisning i kalkulus på videregående skole og begynnende universitet. For å kunne drøfte denne problemstillingen, vil oppgaven ...

Certain polyhedral fans can be constructed from matroids, and these serve as the local model of tropical manifolds. Such matroidal fans satisfy a tropical version of Poincaré duality [JRS17]. In this thesis, we give ...

In this thesis we reproduce the results of Laca and Neshveyev for characterizing certain KMS states on Pimsner algebras. Before getting there, we build up the necessary theory using various sources, giving detailed proofs ...

Denne oppgaven tar for seg projeksjoner på vegger. Når man projiserer et bilde på en vegg, ønsker man at det ikke skal bli fordreid. Vi vil ta for oss hvordan punkter, linjer og flater blir projisert, og viser at avbildningene ...

The purpose of this thesis is to look at certain abelian groups and their reduced twisted group C*-algebras. We consider a class of quantum channels on these algebras, associated with normalised positive definite functions, ...

Datamaskinen har i det siste århundret drastisk endret måten vi forholder oss til matematiske og naturvitenskapelige problemer, da en datamaskin har en beregningskapasitet som vi før bare kunne drømme om. Som en følge av ...

Vi ser på Schoof's og Satoh's algoritmer for opptelling av rasjonale punkter på elliptiske kurver over endelige kropper. Relevant bakgrunn om elliptiske kurver og de p-adiske tallene. Kort om ECC (elliptic curve cryptography). ...

This master thesis will demonstrate how to price perpetual American options with linear programming. American options are used both for hedging and speculation, and being able to price derivatives, without creating arbitrage ...

In this thesis we implement and employ a simplex spline basis developed by Cohen, Lyche, and Riesenfeld for the space of C1 quadratic splines on the Powell–Sabin 12-split of a triangle. A matrix recursion is used for ...

Given a non-principal ultrafilter, we define and prove properties of ultralimits of measure spaces (including σ-algebras, filtrations and measures), random variables and discrete-time stochastic processes. Among other ...

The recent results on non-uniqueness of the Euler equations, all based on the theory developed in the papers by Camillo De Lellis and László Székelyhidi Jr., are believed to be connected to the theory of turbulent fluid ...

In this master thesis we will prove Dirichlet's theorem on primes in arithmetic progressions. The theorem states that there are an infinite number of primes in every primitive residue class modulo any positive number q, ...

A Heron triangle is a triangle with integer sides and integer area. A rational triangle is a triangle with rational sides and area. We will set out to prove van Luijks Theorem, that there exist infinitely many non-similar ...

In this thesis we begin by looking at polynomials of m n x n matrices invariant under simultaneous conjugation. Thereafter we connect the invariant polynomials to simple representations of noncommutative plane curves, ...

In this thesis, we consider the mod 2 homology of Q≥0S0 as an E∞ space and show the following. The homologies H*Q≥0S0 and H*C∞S0 are isomorphic as free commutative /2-algebras. The homology H*Q≥0S0 is generated as an ...

This thesis investigates cubic hypersurfaces and their Fano schemes. After introducing the Fano schemes through low-dimensional examples, we move on to investigate cubic fourfolds. For the cubic fourfolds, we give complete ...

In this thesis we give an introduction to the Minimal Model Program and the Morrison-Kawamata cone conjecture. We then present some known results on anticanonical hypersurfaces building up to the result proven by Kollár ...

In this thesis, we study what can be said about Fermat's Last Theorem using only elementary methods. We will study the work of Sophie Germain and Niels Henrik Abel, both who worked with Fermat’s Last Theorem in the early ...

In this thesis we consider sextactic points on plane algebraic curves and a 2-Hessian curve that identifies these points. This curve was first established by Cayley, and we prove that Cayley's 2-Hessian is wrong. Moreover, ...

The main goal of this thesis is to reproduce the article [SW16] by Sims and Williams, categorising the primitive ideal space of the class of Deaconu- Renault groupoid C*-algebras generated by N_0^k-actions. We go through ...

We consider the bidomain model of cardiac electrophysiology. Departing from a discrete cellular model we derive the bidomain equations by homogenization. Using two-scale convergence we provide a rigorous homogenization ...

Målet ved denne artikkelen er å analysere forholdet mellom vri- og flyttespill og symmetrigruppen. Vi skal se sammenhengen mellom gruppeteori og mange populære spill, spesielt når man vil løse spillene

In this thesis we study the construction of wavelets for the Cuntz--Krieger $C^{\ast}$-algebras as developed by M. Marcolli and A. Paolucci in [MP11]. We identify and correct some errors in the construction, as well as ...

In this thesis we will study the phase space, Ph(A), for an associative k-algebra A. The phase space can be considered as a noncommutative tangent bundle. We will derive algebraic notions of points, curves, tangent vectors ...

The study of generic quartic symmetroids in projective 3-space dates back to Cayley, but little is known about the special specimens. This thesis sets out to survey the possibilities in the non-generic case. We prove that ...

This thesis aims to study the risk measure Conditional Value-at-Risk and analyse an optimization problem of maximizing expected return subject to this risk measure. The analysis include performing Fourier-Motzkin eliminations ...

Denne oppgaven studerer Reed-Solomon-koder og ser på hvordan dekoding av disse kan relateres til å finne potenssumdekomposisjoner av polynomer, hvilket kan tolkes geometrisk som å finne et sekantplan til den rasjonale ...

In this thesis, we consider applications of directed algebraic topology in optimization theory, by representing directed graphs as directed topological spaces. We review the classical max-flow min-cut theorem and a ...

Målet med denne masteroppgaven er å se på teorien som ligger til grunn for en rangeringsmodell kalt Offense-Defense Modellen. Jeg skriver om matriseskaleringer og dobbeltstokastiske matriser som ender med Sinkhorn-Knopp ...

In their article, "Continuity of the Spectrum of a Field of Self-Adjoint Operators", Beckus and Bellissard discuss the following problem: Given a family of bounded, self-adjoint linear operators indexed by a parameter t ...

Parallellaksiomet er det eneste aksiomet der hyperbolsk geometri skiller seg fra euklidsk. Mens det i euklidsk geometri er en unik linje som går gjennom et gitt punkt og er parallell med en gitt linje, finnes det i hyperbolsk ...

Denne oppgaven er skrevet i faget MAT5930L, som er det siste faget i Lektorprogrammet ved UiO. Emnet er Euklids Elementer. Vi ser på noen av proposisjonene i de tre første bøkene av Elementer. Her fokuserer vi på hvordan ...

This thesis studies a relationship between solving optimal stopping problems and solving the weak variational inequalites. We prove a theorem that presents conditions under which the weak variatonal inequalities have a ...

En polytop er et legeme i det euklidske rom som avgrenses av et endelig antall hyperplan. Vi kan legge på ulike begrensninger på polytopene og få et ulikt utvalg polytoper. I denne avhandlingen ser vi på polytoper av ulik ...

A detailed study of computable iterations of Gödel-sentences, both in normal recursion and generalisations to other recursive theories.

In 1862, substituting for professor O. J. Broch, Ludvig Sylow gives the first lectures ever given on the field of Galois theory in Norway, at the University of Christiania. He lectures on, amongst other things, what he ...

Punktene på en elliptisk kurve danner en gruppe. Hvis vi kaller origo i gruppa for Q, er et n-torsjonspunkt et punkt P som er slik at nP=Q. Mengden n-torsjonspunkter danner en abelsk gruppe. Alle 3-torsjonspunktene på en ...

An examination of the abridged notation introduced by Salmon for plane geometry. Culminating in its use to prove the theorems of Brianchon and Pascal, Steiner's theorem on Pascal's Hexagon and Steiner's solution of the ...

The first part of the thesis concerns the problem of ranking in general. We take a closer look at the two ranking methods; Elo rating and Colley rating. The former is used to rate and rank chess players, whereas the latter ...