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1 
Families of Sets Without the Baire PropertyNyagahakwa, Venuste January 2017 (has links)
The family of sets with the Baire property of a topological space X, i.e., sets which differ from open sets by meager sets, has different nice properties, like being closed under countable unions and differences. On the other hand, the family of sets without the Baire property of X is, in general, not closed under finite unions and intersections. This thesis focuses on the algebraic settheoretic aspect of the families of sets without the Baire property which are not empty. It is composed of an introduction and five papers. In the first paper, we prove that the family of all subsets of ℝ of the form (C \ M) ∪ N, where C is a finite union of Vitali sets and M, N are meager, is closed under finite unions. It consists of sets without the Baire property and it is invariant under translations of ℝ. The results are extended to the space ℝn for n ≥ 2 and to products of ℝn with finite powers of the Sorgenfrey line. In the second paper, we suggest a way to build a countable decomposition <img src="http://www.divaportal.org/cgibin/mimetex.cgi?%5Ctiny%5Clbrace%5Ctext%20X_i%5Crbrace%20_%7Bi=1%7D%5E%5Cinfty" /> of a topological space X which has an open subset homeomorphic to (ℝn, τ), n ≥ 1, where τ is some admissible extension of the Euclidean topology, such that the union of each nonempty proper subfamily of <img src="http://www.divaportal.org/cgibin/mimetex.cgi?%5Ctiny%5Clbrace%5Ctext%20X_i%5Crbrace%20_%7Bi=1%7D%5E%5Cinfty" /> does not have the Baire property in X. In the case when X is a separable metrizable manifold of finite dimension, each element of <img src="http://www.divaportal.org/cgibin/mimetex.cgi?%5Ctiny%5Clbrace%5Ctext%20X_i%5Crbrace%20_%7Bi=1%7D%5E%5Cinfty" /> can be chosen dense and zerodimensional. In the third paper, we develop a theory of semigroups of sets with respect to the union of sets. The theory is applied to Vitali selectors of ℝ to construct diverse abelian semigroups of sets without the Baire property. It is shown that in the family of such semigroups there is no element which contains all others. This leads to a supersemigroup of sets without the Baire property which contains all these semigroups and which is invariant under translations of ℝ. All the considered semigroups are enlarged by the use of meager sets, and the construction is extended to Euclidean spaces ℝn for n ≥ 2. In the fourth paper, we consider the family V1(Q) of all finite unions of Vitali selectors of a topological group G having a countable dense subgroup Q. It is shown that the collection <img src="http://www.divaportal.org/cgibin/mimetex.cgi?%5Ctiny%5Clbrace%5Ctext%20G%20%5Csetminus%20%5Ctext%20U%20:%20%5Ctext%20U%20%5Cin%20%5C%20%5Cmathcal%7BV%7D_1(%5Ctext%7BQ%7D)%5Crbrace" /> is a base for a topology τ(Q) on G. The space (G, τ (Q)) is T1, not Hausdorff and hyperconnected. It is proved that if Q1 and Q2 are countable dense subgroups of G such that Q1 ⊆ Q2 and the factor group Q2/Q1 is infinite (resp. finite) then τ(Q1) <img src="http://www.divaportal.org/cgibin/mimetex.cgi?%5Ctiny%5Cnot%5Csubseteq" /> τ(Q2) (resp. τ (Q1) ⊆ τ (Q2)). Nevertheless, we prove that all spaces constructed in this manner are homeomorphic. In the fifth paper, we investigate the relationship (inclusion or equality) between the families of sets with the Baire property for different topologies on the same underlying set. We also present some applications of the local function defined by the Euclidean topology on R and the ideal of meager sets there.

2 
Inverse factorization in electronic structure theory : Analysis and parallelizationArtemov, Anton G. January 2019 (has links)
This licentiate thesis is a part of an effort to run large electronic structure calculations in modern computational environments with distributed memory. The ultimate goal is to model materials consisting of millions of atoms at the level of quantum mechanics. In particular, the thesis focuses on different aspects of a computational problem of inverse factorization of Hermitian positive definite matrices. The considered aspects are numerical properties of the algorithms and parallelization. Not only is an efficient and scalable computation of inverse factors necessary in order to be able to run large scale electronic computations based on the Hartree–Fock or Kohn–Sham approaches with the selfconsistent field procedure, but it can be applied more generally for preconditioner construction. Parallelization of algorithms with unknown load and data distributions requires a paradigm shift in programming. In this thesis we also discuss a few parallel programming models with focus on taskbased models, and, more specifically, the Chunks and Tasks model. / eSSENCE

3 
Implementing and testing possible hedging strategies to minimise value fluctuations in a defaulted portfolioNilsson, Gabriel January 2019 (has links)
A Central Counterparty (CCP) handles clearing between its members and can mutualise and reduce the counterparty and credit risk in a network. In the case of a clearing member defaulting on its obligations, the defaulted portfolio will be taken over by the CCP, which will attempt to close out the positions as quickly as possible. It is vital that the CCP minimises the losses they may suffer during the period between default and close out, the so called holding period. This thesis investigates and tests several potential hedging strategies to minimise value fluctuations during the holding period. These include neutralising the exposure to different risk factors, as well as finding the ideal hedging position using principal component analysis. The defaulted portfolio can contain different instruments, such as options, interest rate swaps and bonds, which requires different approaches to neutralise exposure. To determine the performance of the different strategies, backtesting was performed on historical data from the years 2001 to 2013, and the results were analysed in order to determine the effectiveness and potential costs of the hedging. The results show that significant reduction in value fluctuations can be achieved by employing these strategies, while not exceeding an affordable level of cost. Based on the findings, a function was created in Java that can recommend optimal hedging positions given a defaulted portfolio of any composition.

4 
Linearscaling recursive expansion of the FermiDirac operatorAndersson, Linnéa January 2019 (has links)
No description available.

5 
Nonlinear inverse geothermal problemsWokiyi, Dennis January 2017 (has links)
The inverse geothermal problem consist of estimating the temperature distribution below the earth’s surface using temperature and heatflux measurements on the earth’s surface. The problem is important since temperature governs a variety of the geological processes including formation of magmas, minerals, fosil fuels and also deformation of rocks. Mathematical this problem is formulated as a Cauchy problem for an nonlinear elliptic equation and since the thermal properties of the rocks depend strongly on the temperature, the problem is nonlinear. This problem is illposed in the sense that it does not satisfy atleast one of Hadamard’s definition of wellposedness. We formulated the problem as an illposed nonlinear operator equation which is defined in terms of solving a wellposed boundary problem. We demonstrate existence of a unique solution to this wellposed problem and give stability estimates in appropriate function spaces. We show that the operator equation is welldefined in appropriate function spaces. Since the problem is illposed, regularization is needed to stabilize computations. We demostrate that Tikhonov regularization can be implemented efficiently for solving the operator equation. The algorithm is based on having a code for solving a well posed problem related to the operator equation. In this study we demostrate that the algorithm works efficiently for 2D calculations but can also be modified to work for 3D calculations.

6 
Invasionanalysis of stagestructured populations in temporallyvarying environments / Invasionsanalys av stadiestrukturerade populationer i tidsvarierande miljöerBrändström, Samuel January 2018 (has links)
Climate change may cause epidemic threats as species spreading human diseases invades previously unpopulated areas. A species can establish in new areas if they fulfills an invasion criterion. Two common invasion criteria are the longterm exponential growthrate, r, and the basic reproduction number, R0, that measures the population's exponential growth in time and growth between generations respectively. Previous work have determined the longterm exponential growthrate of the mosquito Aedes aegypti, a vector spreading dengue, zika and yellow fever, in Europe. However, in epidemiology r is rarely used as invasion criterion, which makes their results difficult to communicate and interpret. A more commonly used invasion criterion is the basic reproduction number R0. From this number, public health receives information about highrisk areas where they can vaccinate the population and prevent the mosquitoes from establishing by reducing breeding habitats. Here we extend the previous work by developing a method to calculate R0 for Aedes aegypti and verify it by the results from previous studies. Using R0 as invasion criterion we then predict the global distribution of Aedes aegypti during different climate change scenarios in the 21st century. One related to high emissions of greenhouse gases, RCP8.5, and one to low emissions, RCP2.6. We predict that the distribution of Aedes aegypti will expand towards higher latitudes at great speed during the 21st century assuming the high emission scenario RCP8.5. Assuming the low emission scenario RCP2.6, the distribution will not reach higher latitudes at the end of the 21st century. In Europe, the distribution covered 1.8 % in the beginning of the 20th century and at the end of the 21st century the distribution will cover 10 % assuming RCP8.5 and 2.0 % assuming RCP2.6. This work underscores the importance of reducing global warming and to take other preventive actions to avoid major epidemic outbreaks. Since we also provide instructions and software to calculate both r and R0 for stagestructured models in periodic environments, we anticipate that this work will support more studies of this kind to better understand the epidemic threats from climate change.

7 
Estimating fuel consumption using regression and machine learning / Estimering av bränsleförbrukning med regression och maskininlärningEkström, Lukas January 2018 (has links)
This thesis focuses on investigating the usage of statistical models for estimating fuel consumption of heavy duty vehicles. Several statistical models are assessed, along with machine learning using artiﬁcial neural networks. Data recorded by sensors on board trucks in the EU describe the operational usage of the vehicle. The usage of this data for estimating the fuel consumption is assessed, and several variables originating from the operational data is modelled and tested as possible input parameters. The estimation model for real world fuel consumption uses 8 parameters describing the operational usage of the vehicles, and 8 parameters describing the vehicles themselves. The operational parameters describe the average speed, topography, variation of speed, idling, and more. This model has an average relative error of 5.75%, with a prediction error less than 11.14% for 95% of all tested vehicles. When only vehicle parameters are considered, it is possible to make predictions with an average relative error of 9.30%, with a prediction error less than 19.50% for 95% of all tested vehicles. Furthermore, a computer software called Vehicle Energy Consumption Calculation tool(VECTO) must be used to simulate the fuel consumption for all heavy duty vehicles, according to legislation by the EU. Running VECTO is a slow process, and this thesis also investigates how well statistical models can be used to quickly estimate the VECTO fuel consumption. The model estimates VECTO fuel consumption with an average relative error of 0.32%and with a prediction error less than 0.65% for 95% of all tested vehicles. / Denna rapport fokuserar på att undersöka användningen av statistiska modeller för att uppskatta bränsleförbrukningen hos tunga fordon. Flera statistiska modeller utvärderas, tillsammans med maskinlärning med artiﬁciella neurala nätverk. Data som registreras av sensorer ombord på Scanialastbilar i EU beskriver fordonets drift. Användningen av dessa data för att uppskatta bränsleförbrukningen undersöks och ﬂera variabler som kommer från operativa data modelleras och testas som möjliga inparametrar. Uppskattningsmodellen för den verkliga bränsleförbrukningen använder 8 parametrar som beskriver användningen av fordonet och 8 parametrar som beskriver själva fordonet. Bland annat beskrivs medelhastighet, topograﬁ, hastighetsvariation, andel tomgång. Denna modell har ett genomsnittligt relativfel på 5.75 %, med ett skattningsfel mindre än 11.14% för 95% av de de fordon som testats. Om endast fordonsparametrar beaktas som inparametrar är det möjligt att göra skattningar med ett genomsnittligt relativfel på 9.30 %, med ett skattningsfel mindre än 19.50% för 95% av de de fordon som testats. Ett datorprogram kallat VECTO måste användas för att simulera bränsleförbrukningen för alla tunga fordon enligt EUlagstiftning. Att köra VECTO är en tidskrävande process, och denna rapport undersöker också hur väl statistiska modeller kan användas för att snabbt uppskatta VECTObränsleförbrukningen. Modellen uppskattar VECTObränsleförbrukningen med ett genomsnittligt relativfel på 0.32% och med ett skattningsfel mindre än 0.65% för 95% av de de fordon som testats.

8 
Reverse Stress Test Optimization : A study on how to optimize an algorithm for reverse stress testingMarklund, Sarah January 2018 (has links)
In this thesis we investigate how to optimize an algorithm that determines a scenario multiplier for a reverse stress test with a method where predefined scenarios are scaled. The scenarios are composed by different risk factors that represents market events. A reverse stress test is used for risk estimation and explains for what market condition a given portfolio will lose a particular amount. In this study we consider a reverse stress test where the goal is to find for what scenario a clearing house become insolvent, that is when the clearing house's loss is equal to its resource pool. The goal with this work is to find a more efficient algorithm than the current bisection algorithm for finding the scenario multiplier in the reverse stress test. The algorithms that were examined were one bracketing algorithm (the falseposition algorithm) and two iterative algorithms (the NewtonRaphson and Halley's algorithms), which were implemented in MATLAB. A comparative study was made where the efficiency of the optimized algorithms were compared with the bisection algorithm. The algorithms were evaluated by comparing the running times and number of iterations needed to find the scenario multiplier in the reverse stress test. Other optimization strategies that were investigated were to reduce the number of scenarios in the predefined scenario matrix to decrease the running time and determine an appropriate initial multiplier to use in the iterative algorithms. The reduction of scenarios consisted of removing the scenarios that were multiples of other scenarios by comparing the risk factors in each scenario. We used Taylor approximation to simplify the loss function and thereby approximate an initial multiplier, which would reduce the manually input from the user. Furthermore, we investigated the running times and number of iterations needed to find the scenario multiplier when several initial multipliers were used in the iterative algorithms to increase the chance of finding a solution. The result shows that both the NewtonRaphson algorithm and Halley's algorithm are more efficient and need less iterations to find the scenario multiplier than the current bisection algorithm. Halley's algorithm is the most efficient, which is on average 200470% faster than the current algorithm depending on how many initial multipliers that are used (one, two or three), while the NewtonRaphson algorithm is on average 150300% faster than the current algorithm. Furthermore, the result shows that the falseposition algorithm is not efficient for this aim. The result from the reduction of scenarios shows that scenarios could be removed by this approach, where the real scenario obtained from performing a reverse stress test was never among the removed scenarios. Moreover, the initial multiplier approximation could be used when the scenario matrix contains a certain type of risk factors. Finally, this study shows that the current bisection algorithm can be optimized by the NewtonRaphson algorithm and Halley's algorithm.

9 
Vortex Formation in Free SpaceOlsson, Martin January 2018 (has links)
Aircraft trailing vortices is an inevitable side effect when an aircraft generates lift. The vortices represent a danger for following aircraft and forces large spacing between landing and take off at airports. Detailed knowledge about the dynamics of aircraft trailing vortices is therefore needed to increase airport capacity and aviation safety. In this thesis, an accurate numerical simulation of aircraft trailing vortices is performed. The vortices undergo an expected instability phenomena followed by a reconnection process. The reconnection process is studied in detail. During the reconnection, theoretically described structures can be observed.

10 
Numerical methods for the chemical master equationEngblom, Stefan January 2006 (has links)
The numerical solution of chemical reactions described at the mesoscale is the topic of this thesis. This description, the master equation of chemical reactions, is an accurate model of reactions where stochastic effects are crucial for explaining certain effects observed in real life. In particular, this general equation is needed when studying processes inside living cells where other macroscale models fail to reproduce the actual behavior of the system considered. The main contribution of the thesis is the numerical investigation of two different methods for obtaining numerical solutions of the master equation. The first method produces statistical quantities of the solution and is a generalization of a frequently used macroscale description. It is shown that the method is efficient while still being able to preserve stochastic effects. By contrast, the other method obtains the full solution of the master equation and gains efficiency by an accurate representation of the state space. The thesis contains necessary background material as well as directions for intended future research. An important conclusion of the thesis is that, depending on the setup of the problem, methods of highly different character are needed.

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