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- Qi, Xiaomin, 1987-
(författare)
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Fixed points, fractals, iterated function systems and generalized support vector machines
- 2016
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- In this thesis, fixed point theory is used to construct a fractal type sets and to solve data classification problem. Fixed point method, which is a beautiful mixture of analysis, topology, and geometry has been revealed as a very powerful and important tool in the study of nonlinear phenomena. The existence of fixed points is therefore of paramount importance in several areas of mathematics and other sciences. In particular, fixed points techniques have been applied in such diverse fields as biology, chemistry, economics, engineering, game theory and physics. In Chapter 2 of this thesis it is demonstrated how to define and construct a fractal type sets with the help of iterations of a finite family of generalized F-contraction mappings, a class of mappings more general than contraction mappings, defined in the context of b-metric space. This leads to a variety of results for iterated function system satisfying a different set of contractive conditions. The results unify, generalize and extend various results in the existing literature. In Chapter 3, the theory of support vector machine for linear and nonlinear classification of data and the notion of generalized support vector machine is considered. In the thesis it is also shown that the problem of generalized support vector machine can be considered in the framework of generalized variation inequalities and results on the existence of solutions are established.
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| 2. |
- Tumwesigye, Alex Behakanira, 1982-
(författare)
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On one-dimensional dynamical systems and commuting elements in non-commutative algebras
- 2016
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This thesis work is about commutativity which is a very important topic in mathematics, physics, engineering and many other fields. Two processes are said to be commutative if the order of "operation" of these processes does not matter. A typical example of two processes in real life that are not commutative is the process of opening the door and the process of going through the door. In mathematics, it is well known that matrix multiplication is not always commutative. Commutating operators play an essential role in mathematics, physics engineering and many other fields. A typical example of the importance of commutativity comes from signal processing. Signals pass through filters (often called operators on a Hilbert space by mathematicians) and commutativity of two operators corresponds to having the same result even when filters are interchanged. Many important relations in mathematics, physics and engineering are represented by operators satisfying a number of commutation relations.In chapter two of this thesis we treat commutativity of monomials of operatos satisfying certain commutation relations in relation to one-dimensional dynamical systems. We derive explicit conditions for commutativity of the said monomials in relation to the existence of periodic points of certain one-dimensional dynamical systems. In chapter three, we treat the crossed product algebra for the algebra of piecewise constant functions on given set, describe the commutant of this algebra of functions which happens to be the maximal commutative subalgebra of the crossed product containing this algebra. In chapter four, we give a characterization of the commutant for the algebra of piecewise constant functions on the real line, by comparing commutants for a non decreasing sequence of algebras.
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| 3. |
- Engström, Christopher, 1987-
(författare)
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PageRank in Evolving Networks and Applications of Graphs in Natural Language Processing and Biology
- 2016
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This thesis is dedicated to the use of graph based methods applied to ranking problems on the Web-graph and applications in natural language processing and biology.Chapter 2-4 of this thesis is about PageRank and its use in the ranking of home pages on the Internet for use in search engines. PageRank is based on the assumption that a web page should be high ranked if it is linked to by many other pages and/or by other important pages. This is modelled as the stationary distribution of a random walk on the Web-graph.Due to the large size and quick growth of the Internet it is important to be able to calculate this ranking very efficiently. One of the main topics of this thesis is how this can be made more efficiently, mainly by considering specific types of subgraphs and how PageRank can be calculated or updated for those type of graph structures. In particular we will consider the graph partitioned into strongly connected components and how this partitioning can be utilized.Chapter 5-7 is dedicated to graph based methods and their application to problems in Natural language processing. Specifically given a collection of texts (corpus) we will compare different clustering methods applied to Pharmacovigilance terms (5), graph based models for the identification of semantic relations between biomedical words (6) and modifications of CValue for the annotation of terms in a corpus.In Chapter 8-9 we look at biological networks and the application of graph centrality measures for the identification of cancer genes. Specifically in (8) we give a review over different centrality measures and their application to finding cancer genes in biological networks and in (9) we look at how well the centrality of vertices in the true network is preserved in networks generated from experimental data.
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| 4. |
- Lundengård, Karl, 1987-, et al.
(författare)
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Moment-matching multinomial lattices using Vandermonde matrices for option pricing
- 2016
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Ingår i: Stochastic and Data Analysis Methods and Applications in Statistics and Demography. - : ISAST. - 9786185180188 - 9786185180195 ; , s. 15-29
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Konferensbidrag (refereegranskat)abstract
- Lattice models are discretization methods that divide the life of a financial option into time steps of equal length and model the underlying asset movement at each time step. A financial option of American or European style can be evaluated conveniently via backward induction using a lattice model. The most common lattice models are the well-known binomial- and trinomial lattice models, although severalkinds of higher order models have also been examined in the literature. In the presentpaper we present an explicit scheme for creating a lattice model of arbitrary order and use the Vandermonde matrix to determine suitable parameters. Some selected models created using this scheme are examined with regard to their suitability for option pricing
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| 5. |
- Murara, Jean-Paul, 1978-
(författare)
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Asset Pricing Models with Stochastic Volatility
- 2016
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Asset pricing modeling is a wide range area of research in Financial Engineering. In this thesis, which consists of an introduction, three papers and appendices; we deal with asset pricing models with stochastic volatility. Here stochastic volatility modeling includes diffusion models and regime-switching models. Stochastic volatility models appear as a response to the weakness of the constant volatility models. In Paper A , we present a survey on popular diffusion models where the volatility is itself a random process and we present the techniques of pricing European options under each model. Comparing single factor stochastic volatility models to constant factor volatility models it seems evident that the stochastic volatility models represent nicely the movement of the asset price and its relations with changes in the risk. However, these models fail to explain the large independent fluctuations in the volatility levels and slope. We consider Chiarella and Ziveyi model, which is a subclass of the model presented in Christoffersen and in paper A, we also explain a multi-factor stochastic volatility model presented in Chiarella and Ziveyi. We review the first-order asymptotic expansion method for determining European option price in such model. Multiscale stochastic volatilities models can capture the smile and skew of volatilities and therefore describe more accurately the movements of the trading prices. In paper B, we provide experimental and numerical studies on investigating the accuracy of the approximation formulae given by this asymptotic expansion. We present also a procedure for calibrating the parameters produced by our first-order asymptotic approximation formulae. Our approximated option prices will be compared to the approximation obtained by Chiarella and Ziveyi. In paper C, we implement and analyze the Regime-Switching GARCH model using real NordPool Electricity spot data. We allow the model parameters to switch between a regular regime and a non-regular regime, which is justified by the so-called structural break behaviour of electricity price series. In splitting the two regimes we consider three criteria, namely the intercountry price di_erence criterion, the capacity/flow difference criterion and the spikes-in-Finland criterion. We study the correlation relationships among these criteria using the mean-square contingency coe_cient and the co-occurrence measure. We also estimate our model parameters and present empirical validity of the model.
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