Computationally Efficient Methods for MDL-Optimal Density Estimation and Data Clustering

The Minimum Description Length (MDL) principle is a general, well-founded theoretical formalization of statistical modeling. The most important notion of MDL is the stochastic complexity, which can be interpreted as the shortest description length of a given sample of data relative to a model class. The exact definition of the stochastic complexity has gone through several evolutionary steps. The latest instantation is based on the so-called Normalized Maximum Likelihood (NML) distribution which has been shown to possess several important theoretical properties. However, the applications of this modern version of the MDL have been quite rare because of computational complexity problems, i.e., for discrete data, the definition of NML involves an exponential sum, and in the case of continuous data, a multi-dimensional integral usually infeasible to evaluate or even approximate accurately. In this doctoral dissertation, we present mathematical techniques for computing NML efficiently for some model families involving discrete data. We also show how these techniques can be used to apply MDL in two practical applications: histogram density estimation and clustering of multi-dimensional data.

Using Mathematical Morphology for Geometric Music Retrieval

The usual task in music information retrieval (MIR) is to find occurrences of a monophonic query pattern within a music database, which can contain both monophonic and polyphonic content. The so-called query-by-humming systems are a famous instance of content-based MIR. In such a system, the user's hummed query is converted into symbolic form to perform search operations in a similarly encoded database. The symbolic representation (e.g., textual, MIDI or vector data) is typically a quantized and simplified version of the sampled audio data, yielding to faster search algorithms and space requirements that can be met in real-life situations. In this thesis, we investigate geometric approaches to MIR. We first study some musicological properties often needed in MIR algorithms, and then give a literature review on traditional (e.g., string-matching-based) MIR algorithms and novel techniques based on geometry. We also introduce some concepts from digital image processing, namely the mathematical morphology, which we will use to develop and implement four algorithms for geometric music retrieval. The symbolic representation in the case of our algorithms is a binary 2-D image. We use various morphological pre- and post-processing operations on the query and the database images to perform template matching / pattern recognition for the images. The algorithms are basically extensions to classic image correlation and hit-or-miss transformation techniques used widely in template matching applications. They aim to be a future extension to the retrieval engine of C-BRAHMS, which is a research project of the Department of Computer Science at University of Helsinki.

Modern techniques in detection, identification and quantification of bacteria and peptides from foods

Standards have been placed to regulate the microbial and preservative contents to assure that foods are safe to the consumer. In a case of a food-related disease outbreak, it is crucial to be able to detect and identify quickly and accurately the cause of the disease. In addition, for every day control of food microbial and preservative contents, the detection methods must be easily performed for numerous food samples. In this present study, quicker alternative methods were studied for identification of bacteria by DNA fingerprinting. A flow cytometry method was developed as an alternative to pulsed-field gel electrophoresis, the golden method . DNA fragment sizing by an ultrasensitive flow cytometer was able to discriminate species and strains in a reproducible and comparable manner to pulsed-field gel electrophoresis. This new method was hundreds times faster and 200,000 times more sensitive. Additionally, another DNA fingerprinting identification method was developed based on single-enzyme amplified fragment length polymorphism (SE-AFLP). This method allowed the differentiation of genera, species, and strains of pathogenic bacteria of Bacilli, Staphylococci, Yersinia, and Escherichia coli. These fingerprinting patterns obtained by SE-AFLP were simpler and easier to analyze than those by the traditional amplified fragment length polymorphism by double enzyme digestion. Nisin (E234) is added as a preservative to different types of foods, especially dairy products, around the world. Various detection methods exist for nisin, but they lack in sensitivity, speed or specificity. In this present study, a sensitive nisin-induced green fluorescent protein (GFPuv) bioassay was developed using the Lactococcus lactis two-component signal system NisRK and the nisin-inducible nisA promoter. The bioassay was extremely sensitive with detection limit of 10 pg/ml in culture supernatant. In addition, it was compatible for quantification from various food matrices, such as milk, salad dressings, processed cheese, liquid eggs, and canned tomatoes. Wine has good antimicrobial properties due to its alcohol concentration, low pH, and organic content and therefore often assumed to be microbially safe to consume. Another aim of this thesis was to study the microbiota of wines returned by customers complaining of food-poisoning symptoms. By partial 16S rRNA gene sequence analysis, ribotyping, and boar spermatozoa motility assay, it was identified that one of the wines contained a Bacillus simplex BAC91, which produced a heat-stable substance toxic to the mitochondria of sperm cells. The antibacterial activity of wine was tested on the vegetative cells and spores of B. simplex BAC91, B. cereus type strain ATCC 14579 and cereulide-producing B. cereus F4810/72. Although the vegetative cells and spores of B. simplex BAC91 were sensitive to the antimicrobial effects of wine, the spores of B. cereus strains ATCC 14579 and F4810/72 stayed viable for at least 4 months. According to these results, Bacillus spp., more specifically spores, can be a possible risk to the wine consumer.

Use of non-specific and specific interactions in the analysis of testosterone and related compounds by capillary electromigration techniques

Determination of testosterone and related compounds in body fluids is of utmost importance in doping control and the diagnosis of many diseases. Capillary electromigration techniques are a relatively new approach for steroid research. Owing to their electrical neutrality, however, separation of steroids by capillary electromigration techniques requires the use of charged electrolyte additives that interact with the steroids either specifically or non-specifically. The analysis of testosterone and related steroids by non-specific micellar electrokinetic chromatography (MEKC) was investigated in this study. The partial filling (PF) technique was employed, being suitable for detection by both ultraviolet spectrophotometry (UV) and electrospray ionization mass spectrometry (ESI-MS). Efficient, quantitative PF-MEKC UV methods for steroid standards were developed through the use of optimized pseudostationary phases comprising surfactants and cyclodextrins. PF-MEKC UV proved to be a more sensitive, efficient and repeatable method for the steroids than PF-MEKC ESI-MS. It was discovered that in PF-MEKC analyses of electrically neutral steroids, ESI-MS interfacing sets significant limitations not only on the chemistry affecting the ionization and detection processes, but also on the separation. The new PF-MEKC UV method was successfully employed in the determination of testosterone in male urine samples after microscale immunoaffinity solid-phase extraction (IA-SPE). The IA-SPE method, relying on specific interactions between testosterone and a recombinant anti-testosterone Fab fragment, is the first such method described for testosterone. Finally, new data for interactions between steroids and human and bovine serum albumins were obtained through the use of affinity capillary electrophoresis. A new algorithm for the calculation of association constants between proteins and neutral ligands is introduced.

Miniaturized mass spectrometric ionization techniques for environmental analysis and bioanalysis

Miniaturized mass spectrometric ionization techniques for environmental analysis and bioanalysis Novel miniaturized mass spectrometric ionization techniques based on atmospheric pressure chemical ionization (APCI) and atmospheric pressure photoionization (APPI) were studied and evaluated in the analysis of environmental samples and biosamples. The three analytical systems investigated here were gas chromatography-microchip atmospheric pressure chemical ionization-mass spectrometry (GC-µAPCI-MS) and gas chromatography-microchip atmospheric pressure photoionization-mass spectrometry (GC-µAPPI-MS), where sample pretreatment and chromatographic separation precede ionization, and desorption atmospheric pressure photoionization-mass spectrometry (DAPPI-MS), where the samples are analyzed either as such or after minimal pretreatment. The gas chromatography-microchip atmospheric pressure ionization-mass spectrometry (GC-µAPI-MS) instrumentations were used in the analysis of polychlorinated biphenyls (PCBs) in negative ion mode and 2-quinolinone-derived selective androgen receptor modulators (SARMs) in positive ion mode. The analytical characteristics (i.e., limits of detection, linear ranges, and repeatabilities) of the methods were evaluated with PCB standards and SARMs in urine. All methods showed good analytical characteristics and potential for quantitative environmental analysis or bioanalysis. Desorption and ionization mechanisms in DAPPI were studied. Desorption was found to be a thermal process, with the efficiency strongly depending on thermal conductivity of the sampling surface. Probably the size and polarity of the analyte also play a role. In positive ion mode, the ionization is dependent on the ionization energy and proton affinity of the analyte and the spray solvent, while in negative ion mode the ionization mechanism is determined by the electron affinity and gas-phase acidity of the analyte and the spray solvent. DAPPI-MS was tested in the fast screening analysis of environmental, food, and forensic samples, and the results demonstrated the feasibility of DAPPI-MS for rapid screening analysis of authentic samples.

Development of analytical techniques for studies on dispersion of actinides in the environment and characterization of environmental radioactive particles

Radioactive particles from three locations were investigated for elemental composition, oxidation states of matrix elements, and origin. Instrumental techniques applied to the task were scanning electron microscopy, X-ray and gamma-ray spectrometry, secondary ion mass spectrometry, and synchrotron radiation based microanalytical techniques comprising X-ray fluorescence spectrometry, X-ray fluorescence tomography, and X-ray absorption near-edge structure spectroscopy. Uranium-containing low activity particles collected from Irish Sea sediments were characterized in terms of composition and distribution of matrix elements and the oxidation states of uranium. Indications of the origin were obtained from the intensity ratios and the presence of thorium, uranium, and plutonium. Uranium in the particles was found to exist mostly as U(IV). Studies on plutonium particles from Runit Island (Marshall Islands) soil indicated that the samples were weapon fuel fragments originating from two separate detonations: a safety test and a low-yield test. The plutonium in the particles was found to be of similar age. The distribution and oxidation states of uranium and plutonium in the matrix of weapon fuel particles from Thule (Greenland) sediments were investigated. The variations in intensity ratios observed with different techniques indicated more than one origin. Uranium in particle matrixes was mostly U(IV), but plutonium existed in some particles mainly as Pu(IV), and in others mainly as oxidized Pu(VI). The results demonstrated that the various techniques were effectively applied in the characterization of environmental radioactive particles. An on-line method was developed for separating americium from environmental samples. The procedure utilizes extraction chromatography to separate americium from light lanthanides, and cation exchange to concentrate americium before the final separation in an ion chromatography column. The separated radiochemically pure americium fraction is measured by alpha spectrometry. The method was tested with certified sediment and soil samples and found to be applicable for the analysis of environmental samples containing a wide range of Am-241 activity. Proceeding from the on-line method developed for americium, a method was also developed for separating plutonium and americium. Plutonium is reduced to Pu(III), and separated together with Am(III) throughout the procedure. Pu(III) and Am(III) are eluted from the ion chromatography column as anionic dipicolinate and oxalate complexes, respectively, and measured by alpha spectrometry.

Development of Sample Pretreatment and Liquid Chromatographic Techniques for Antioxidative Compounds

In this study, novel methodologies for the determination of antioxidative compounds in herbs and beverages were developed. Antioxidants are compounds that can reduce, delay or inhibit oxidative events. They are a part of the human defense system and are obtained through the diet. Antioxidants are naturally present in several types of foods, e.g. in fruits, beverages, vegetables and herbs. Antioxidants can also be added to foods during manufacturing to suppress lipid oxidation and formation of free radicals under conditions of cooking or storage and to reduce the concentration of free radicals in vivo after food ingestion. There is growing interest in natural antioxidants, and effective compounds have already been identified from antioxidant classes such as carotenoids, essential oils, flavonoids and phenolic acids. The wide variety of sample matrices and analytes presents quite a challenge for the development of analytical techniques. Growing demands have been placed on sample pretreatment. In this study, three novel extraction techniques, namely supercritical fluid extraction (SFE), pressurised hot water extraction (PHWE) and dynamic sonication-assisted extraction (DSAE) were studied. SFE was used for the extraction of lycopene from tomato skins and PHWE was used in the extraction of phenolic compounds from sage. DSAE was applied to the extraction of phenolic acids from Lamiaceae herbs. In the development of extraction methodologies, the main parameters of the extraction were studied and the recoveries were compared to those achieved by conventional extraction techniques. In addition, the stability of lycopene was also followed under different storage conditions. For the separation of the antioxidative compounds in the extracts, liquid chromatographic methods (LC) were utilised. Two novel LC techniques, namely ultra performance liquid chromatography (UPLC) and comprehensive two-dimensional liquid chromatography (LCxLC) were studied and compared with conventional high performance liquid chromatography (HPLC) for the separation of antioxidants in beverages and Lamiaceae herbs. In LCxLC, the selection of LC mode, column dimensions and flow rates were studied and optimised to obtain efficient separation of the target compounds. In addition, the separation powers of HPLC, UPLC, HPLCxHPLC and HPLCxUPLC were compared. To exploit the benefits of an integrated system, in which sample preparation and final separation are performed in a closed unit, dynamic sonication-assisted extraction was coupled on-line to a liquid chromatograph via a solid-phase trap. The increased sensitivity was utilised in the extraction of phenolic acids from Lamiaceae herbs. The results were compared to those of achieved by the LCxLC system.

Mathematical models on the impact of noise and dyadic molecular structures on the properties of a cardiac myocyte

In cardiac myocytes (heart muscle cells), coupling of electric signal known as the action potential to contraction of the heart depends crucially on calcium-induced calcium release (CICR) in a microdomain known as the dyad. During CICR, the peak number of free calcium ions (Ca) present in the dyad is small, typically estimated to be within range 1-100. Since the free Ca ions mediate CICR, noise in Ca signaling due to the small number of free calcium ions influences Excitation-Contraction (EC) coupling gain. Noise in Ca signaling is only one noise type influencing cardiac myocytes, e.g., ion channels playing a central role in action potential propagation are stochastic machines, each of which gates more or less randomly, which produces gating noise present in membrane currents. How various noise sources influence macroscopic properties of a myocyte, how noise is attenuated and taken advantage of are largely open questions. In this thesis, the impact of noise on CICR, EC coupling and, more generally, macroscopic properties of a cardiac myocyte is investigated at multiple levels of detail using mathematical models. Complementarily to the investigation of the impact of noise on CICR, computationally-efficient yet spatially-detailed models of CICR are developed. The results of this thesis show that (1) gating noise due to the high-activity mode of L-type calcium channels playing a major role in CICR may induce early after-depolarizations associated with polymorphic tachycardia, which is a frequent precursor to sudden cardiac death in heart failure patients; (2) an increased level of voltage noise typically increases action potential duration and it skews distribution of action potential durations toward long durations in cardiac myocytes; and that (3) while a small number of Ca ions mediate CICR, Excitation-Contraction coupling is robust against this noise source, partly due to the shape of ryanodine receptor protein structures present in the cardiac dyad.

Mathematical Aspects of Financial Markets with Frictions

Frictions are factors that hinder trading of securities in financial markets. Typical frictions include limited market depth, transaction costs, lack of infinite divisibility of securities, and taxes. Conventional models used in mathematical finance often gloss over these issues, which affect almost all financial markets, by arguing that the impact of frictions is negligible and, consequently, the frictionless models are valid approximations. This dissertation consists of three research papers, which are related to the study of the validity of such approximations in two distinct modeling problems. Models of price dynamics that are based on diffusion processes, i.e., continuous strong Markov processes, are widely used in the frictionless scenario. The first paper establishes that diffusion models can indeed be understood as approximations of price dynamics in markets with frictions. This is achieved by introducing an agent-based model of a financial market where finitely many agents trade a financial security, the price of which evolves according to price impacts generated by trades. It is shown that, if the number of agents is large, then under certain assumptions the price process of security, which is a pure-jump process, can be approximated by a one-dimensional diffusion process. In a slightly extended model, in which agents may exhibit herd behavior, the approximating diffusion model turns out to be a stochastic volatility model. Finally, it is shown that when agents' tendency to herd is strong, logarithmic returns in the approximating stochastic volatility model are heavy-tailed. The remaining papers are related to no-arbitrage criteria and superhedging in continuous-time option pricing models under small-transaction-cost asymptotics. Guasoni, Rásonyi, and Schachermayer have recently shown that, in such a setting, any financial security admits no arbitrage opportunities and there exist no feasible superhedging strategies for European call and put options written on it, as long as its price process is continuous and has the so-called conditional full support (CFS) property. Motivated by this result, CFS is established for certain stochastic integrals and a subclass of Brownian semistationary processes in the two papers. As a consequence, a wide range of possibly non-Markovian local and stochastic volatility models have the CFS property.