Wiener process-a random process with continuous time-plays an important role in mathematics, physics or economy. It is often good to know whether it contains any deterministic part, e.g. drift or scale. However, it is nearly impossible either observe the whole trajectory of the process or preserve its full history. This thesis deals with a statistical analysis based on partial observations, namely passage times through some given barriers. We propose several statistical methods for testing hypotheses about drift or scale using these observations. As supporting methods, we consider the maximum likelihood theory, non-parametric test against a trend, and binomial test. For testing the value of scale in the model with no drift and constant scale we recommend maximum likelihood theory. We derive the estimate and related tests in the case of observing only three barriers. The simulation study suggested observing more barriers for testing monotony of scale in a model with linear drift, or testing monotone and convex/concave drift in a model with constant scale. 1

The Vienna Tonkünstler-Verein (1885-1929) was established for the sole purpose of providing extensive support to the music and musicians of Vienna. The society became renowned in Vienna for its outstanding performances of chamber music and counted among its members many of the city’s foremost musicians and composers. Johannes Brahms had a significant influence on the society as its honorary president and assisted in establishing its composition competitions, aimed at promoting and reviving under-developed chamber genres. Of particular interest to clarinetists is the Verein’s competition of 1896, which aspired to promote chamber music literature for wind instruments. Brahms’s recently completed chamber works for clarinet were clearly influential in fin-de-siècle Vienna; for of the twelve works chosen as finalists in the competition, ten included the clarinet in the chamber combination.The purpose of this document is to provide an English-language history of the Vienna Tonkünstler-Verein and a thorough account of its1896 competition based on my study of the society’s annual reports. In addition, this document will provide the first published account of the anonymous submissions for the 1896 competition. It is my hope that this paper will serve as a springboard for future endeavors aimed at uncovering the identities of the anonymous finalists for this competition.

Using recently popularized invertible neural network We predict future video frames from complex dynamic scenes. Our invertible linear embedding (ILE) demonstrates successful learning, prediction and latent state inference. In contrast to other approaches, ILE does not use any explicit reconstruction loss or simplistic pixel-space assumptions. Instead, it leverages invertibility to optimize the likelihood of image sequences exactly, albeit indirectly.Experiments and comparisons against state of the art methods over synthetic and natural image sequences demonstrate the robustness of our approach, and a discussion of future work explores the opportunities our method might provide to other fields in which the accurate analysis and forecasting of non-linear dynamic systems is essential.

Tato práce se zabývá možností využití vlnkové transformace v aplikacích, které se zabývají potlačením šumu. Především se jedná o oblast filtrace signálu EKG. Úkolem je zhodnotit vliv různých parametrů nastavení samotné filtrace a zjistit jaký vliv má různé nastavení prahování wavelet koeficientů. Výsledkem práce je také stanovení hodnot prahů, stanovení nejlepšího způsobu rozkladu signálu a volba rekonstrukčních bank filtrů. Text obsahuje výsledky Wienerovy filtrace, při které byly testovány různé banky rozkladových a rekonstrukčních filtrů.Všechny popsané filtrační metody byly testovány na reálných záznamech EKG s aditivním myopotenciálním šumem. Algoritmy byly realizovány v prostředí MATLAB.

The presence of acoustic noise in audio recordings is an ongoing issue that plagues many applications. This ambient background noise is difficult to reduce due to its unpredictable nature. Many single channel noise reduction techniques exist but are limited in that they may distort the desired speech signal due to overlapping spectral content of the speech and noise. It is therefore of interest to investigate the use of multichannel noise reduction algorithms to further attenuate noise while attempting to preserve the speech signal of interest. Specifically, this thesis looks to investigate the use of microphone arrays in conjunction with multichannel noise reduction algorithms to aid aiding in speaker identification. Recording a speaker in the presence of acoustic background noise ultimately limits the performance and confidence of speaker identification algorithms. In situations where it is impossible to control the noise environment where the speech sample is taken, noise reduction algorithms must be developed and applied to clean the speech signal in order to give speaker identification software a chance at a positive identification. Due to the limitations of single channel techniques, it is of interest to see if spatial information provided by microphone arrays can be exploited to aid in speaker identification. This thesis provides an exploration of several time domain multichannel noise reduction techniques including delay sum beamforming, multi-channel Wiener filtering, and Spatial-Temporal Prediction filtering. Each algorithm is prototyped and filter performance is evaluated using various simulations and experiments. A three-dimensional noise model is developed to simulate and compare the performance of the above methods and experimental results of three data collections are presented and analyzed. The algorithms are compared and recommendations are given for the use of each technique. Finally, ideas for future work are discussed to improve performance and implementation of these multichannel algorithms. Possible applications for this technology include audio surveillance, identity verification, video chatting, conference calling and sound source localization.

The aim of this work is to provide an introduction into the theory of infinite dimensional stochastic processes. The thesis contains the paper A class of infinite dimensional stochastic processes with unbounded diffusion written at Linköping University during 2012. The aim of that paper is to take results from the finite dimensional theory into the infinite dimensional case. This is done via the means of a coordinate representation. It is shown that for a certain kind of Dirichlet form with unbounded diffusion, we have properties such as closability, quasi-regularity, and existence of local first and second moment of the associated process. The starting chapters of this thesis contain the prerequisite theory for understanding the paper. It is my hope that any reader unfamiliar with the subject will find this thesis useful, as an introduction to the field of infinite dimensional processes.

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This short contribution shows the relevance of audiovisual sources for the history of 20th century music. It traces the role played by the violinist Fritz Kreisler (1875–1962) in shaping the widespread cliché of the “Viennese sound” via an examination of audiovisual sources. The sources stored in different online archives or social media portals play a key role, but the traceability of a given agent is not guaranteed. For this reason, controlled vocabularies and a digital tool which enable the addition of new metadata to already existing sources should be developed in the near future. This would enable researchers to trace agents, such as institutions and artists, and to connect them with places, repertoires and cultural topoi.

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