Inverse Problem for Fractional Brownian Motion with Discrete Data

The problem of recovering information from measurement data has already been studied for a long time. In the beginning, the methods were mostly empirical, but already towards the end of the sixties Backus and Gilbert started the development of mathematical methods for the interpretation of geophysical data. The problem of recovering information about a physical phenomenon from measurement data is an inverse problem. Throughout this work, the statistical inversion method is used to obtain a solution. Assuming that the measurement vector is a realization of fractional Brownian motion, the goal is to retrieve the amplitude and the Hurst parameter. We prove that under some conditions, the solution of the discretized problem coincides with the solution of the corresponding continuous problem as the number of observations tends to infinity. The measurement data is usually noisy, and we assume the data to be the sum of two vectors: the trend and the noise. Both vectors are supposed to be realizations of fractional Brownian motions, and the goal is to retrieve their parameters using the statistical inversion method. We prove a partial uniqueness of the solution. Moreover, with the support of numerical simulations, we show that in certain cases the solution is reliable and the reconstruction of the trend vector is quite accurate.

Dependence Logic: Investigations into Higher-Order Semantics Defined on Teams

This thesis is a study of a rather new logic called dependence logic and its closure under classical negation, team logic. In this thesis, dependence logic is investigated from several aspects. Some rules are presented for quantifier swapping in dependence logic and team logic. Such rules are among the basic tools one must be familiar with in order to gain the required intuition for using the logic for practical purposes. The thesis compares Ehrenfeucht-Fraïssé (EF) games of first order logic and dependence logic and defines a third EF game that characterises a mixed case where first order formulas are measured in the formula rank of dependence logic. The thesis contains detailed proofs of several translations between dependence logic, team logic, second order logic and its existential fragment. Translations are useful for showing relationships between the expressive powers of logics. Also, by inspecting the form of the translated formulas, one can see how an aspect of one logic can be expressed in the other logic. The thesis makes preliminary investigations into proof theory of dependence logic. Attempts focus on finding a complete proof system for a modest yet nontrivial fragment of dependence logic. A key problem is identified and addressed in adapting a known proof system of classical propositional logic to become a proof system for the fragment, namely that the rule of contraction is needed but is unsound in its unrestricted form. A proof system is suggested for the fragment and its completeness conjectured. Finally, the thesis investigates the very foundation of dependence logic. An alternative semantics called 1-semantics is suggested for the syntax of dependence logic. There are several key differences between 1-semantics and other semantics of dependence logic. 1-semantics is derived from first order semantics by a natural type shift. Therefore 1-semantics reflects an established semantics in a coherent manner. Negation in 1-semantics is a semantic operation and satisfies the law of excluded middle. A translation is provided from unrestricted formulas of existential second order logic into 1-semantics. Also game theoretic semantics are considerd in the light of 1-semantics.

On linear order and computation : The expressiveness of interactive computations on linear orders and computations indexed by ordinals

We solve the Dynamic Ehrenfeucht-Fra\"iss\'e Game on linear orders for both players, yielding a normal form for quantifier-rank equivalence classes of linear orders in first-order logic, infinitary logic, and generalized-infinitary logics with linearly ordered clocks. We show that Scott Sentences can be manipulated quickly, classified into local information, and consistency can be decided effectively in the length of the Scott Sentence. We describe a finite set of linked automata moving continuously on a linear order. Running them on ordinals, we compute the ordinal truth predicate and compute truth in the constructible universe of set-theory. Among the corollaries are a study of semi-models as efficient database of both model-theoretic and formulaic information, and a new proof of the atomicity of the Boolean algebra of sentences consistent with the theory of linear order -- i.e., that the finitely axiomatized theories of linear order are dense.

Locality and order-invariant logics

Malli on logiikassa käytetty abstraktio monille matemaattisille objekteille. Esimerkiksi verkot, ryhmät ja metriset avaruudet ovat malleja. Äärellisten mallien teoria on logiikan osa-alue, jossa tarkastellaan logiikkojen, formaalien kielten, ilmaisuvoimaa malleissa, joiden alkioiden lukumäärä on äärellinen. Rajoittuminen äärellisiin malleihin mahdollistaa tulosten soveltamisen teoreettisessa tietojenkäsittelytieteessä, jonka näkökulmasta logiikan kaavoja voidaan ajatella ohjelmina ja äärellisiä malleja niiden syötteinä. Lokaalisuus tarkoittaa logiikan kyvyttömyyttä erottaa toisistaan malleja, joiden paikalliset piirteet vastaavat toisiaan. Väitöskirjassa tarkastellaan useita lokaalisuuden muotoja ja niiden säilymistä logiikkoja yhdistellessä. Kehitettyjä työkaluja apuna käyttäen osoitetaan, että Gaifman- ja Hanf-lokaalisuudeksi kutsuttujen varianttien välissä on lokaalisuuskäsitteiden hierarkia, jonka eri tasot voidaan erottaa toisistaan kasvavaa dimensiota olevissa hiloissa. Toisaalta osoitetaan, että lokaalisuuskäsitteet eivät eroa toisistaan, kun rajoitutaan tarkastelemaan äärellisiä puita. Järjestysinvariantit logiikat ovat kieliä, joissa on käytössä sisäänrakennettu järjestysrelaatio, mutta sitä on käytettävä siten, etteivät kaavojen ilmaisemat asiat riipu valitusta järjestyksestä. Määritelmää voi motivoida tietojenkäsittelyn näkökulmasta: vaikka ohjelman syötteen tietojen järjestyksellä ei olisi odotetun tuloksen kannalta merkitystä, on syöte tietokoneen muistissa aina jossakin järjestyksessä, jota ohjelma voi laskennassaan hyödyntää. Väitöskirjassa tutkitaan minkälaisia lokaalisuuden muotoja järjestysinvariantit ensimmäisen kertaluvun predikaattilogiikan laajennukset yksipaikkaisilla kvanttoreilla voivat toteuttaa. Tuloksia sovelletaan tarkastelemalla, milloin sisäänrakennettu järjestys lisää logiikan ilmaisuvoimaa äärellisissä puissa.

State Agent, Identity and the "New World Order" : Reconstructing Polish Defence Identity after the Cold War Era

National identity signifies and makes state s defence- and foreign policy behaviour meaningful. National consciousness is narrated into existence by narratives upon one s own exceptionalism and Otherness of the other nations. While national identity may be understood merely as a self-image of a nation, defence identity refers to the borders of Otherness and issues that have been considered as worth defending for. As national identities and all the world order models are human constructions, they may be changed by the human efforts as well; states and nations may deliberately promote communitarian or even cosmopolitan equality and tolerance without borders of Otherness. The main research question of the thesis is: How does Poland constitute herself as a nation and a state agent in the current world order and to what extent have contextual foreign and defence policy interactions changed the Polish defence identity during the post-Cold War era? The main empirical argument of the thesis is: Poland is a narrated idea of a Christian Catholic nation-state, which the Polish State, the Catholic Church of Poland, the Armed Forces of Poland as well as a majority of the Polish nation share. Polish defence identity has been almost impenetrable to contextual foreign and defence policy interactions during the post-Cold War era. While Christian religious ontology binds corporate Poland together, allowing her to survive any number of military and political catastrophes, it simultaneously brings her closer to the USA, raises tensions in the infidel EU-context, and restrains corporate Poland s pursuit of communitarian, or even cosmopolitan, global equality and tolerance. It is not the case that corporate Poland s foreign and defence policy orientation is instinctively Atlanticist by nature, as has been argued. Rather, it has been the State s rational project to overcome a habituated and reified fear of becoming geopolitically sandwiched between Russian and German Others by leaning on the USA; among the Polish nation, support for the USA has been declining since 2004. It is not corporate Poland either that has turned into a constructive European , as has been argued, but rather the Polish nation that has, at least partly, managed to emancipate itself from its habituation to a betrayal by Europe narrative, since it favours the EU as much as it favours NATO. It seems that in the Polish case a truly common European CFSP vis-à-vis Russia may offer a solution that will emancipate the Polish State from its habituated EU-sceptic role identity and corporate Poland from its narrated borders of Otherness towards Russia and Germany, but even then one cannot be sure whether any other perspective than the Polish one on a common stand towards Russia would satisfy the Poles themselves.

Clinical aspects of exhaled nitric oxide in adults : Associations with atopy, bronchial hyperresponsiveness, smoking and chronic obstruction

Measurement of fractional exhaled nitric oxide (FENO) has proven useful in assessment of patients with respiratory symptoms, especially in predicting steroid response. The objective of these studies was to clarify issues relevant for the clinical use of FENO. The influence of allergic sensitization per se on FENO in healthy asymptomatic subjects was studied, the association between airway inflammation and bronchial hyperresponsiveness (BHR) in steroid-naive subjects with symptoms suggesting asthma was examined, as well as the possible difference in this association between atopic and nonatopic subjects. Influence of smoking on FENO was compared between atopic and nonatopic steroid-naive asthmatics and healthy subjects. The short-term repeatability of FENO in COPD patients was examined in order to assess whether the degree of chronic obstruction influences the repeatability. For these purposes, we studied a random sample of 248 citizens of Helsinki, 227 army conscripts with current symptoms suggesting asthma, 19 COPD patients, and 39 healthy subjects. FENO measurement, spirometry and bronchodilatation test, structured interview. skin prick tests, and histamine and exercise challenges were performed. Among healthy subjects with no signs of airway diseases, median FENO was similar in skin prick test-positive and –negative subjects, and the upper normal limit of FENO was 30 ppb. In atopic and nonatopic subjects with symptoms suggesting asthma, FENO associated with severity of exercise- or histamine-induced BHR only in atopic patients. FENO in smokers with steroid-naive asthma was significantly higher than in healthy smokers and nonsmokers. Among atopic asthmatics, FENO was significantly lower in smokers than in nonsmokers, whereas no difference appeared among nonatopic asthmatics. The 24-h repeatability of FENO was equally good in COPD patients as in healthy subjects. These findings indicate that allergic sensitization per se does not influence FENO, supporting the view that elevated FENO indicates NO-producing airway inflammation, and that same reference range can be applied to both skin prick test-positive and -negative subjects. The significant correlation between FENO and degree of BHR only in atopic steroid-naive subjects with current asthmatic symptoms supports the view that pathogenesis of BHR in atopic asthma is strongly involved in NO-producing airway inflammation, whereas in development of BHR in nonatopic asthma other mechanisms may dominate. Attenuation of FENO only in atopic but not in nonatopic smokers with steroid-naive asthma may result from differences in mechanisms of FENO formation as well as in sensitivity of these mechanisms to smoking in atopic and nonatopic asthma. The results suggest, however, that in young adult smokers, FENO measurement may prove useful in assessment of airway inflammation. The short-term repeatability of FENO in COPD patients with moderate to very severe disease and in healthy subjects was equally good.

Future chemistry teachers use of knowledge dimensions and high-order cognitive skills in pre-laboratory concept maps

This poster describes a pilot case study, which aim is to study how future chemistry teachers use knowledge dimensions and high-order cognitive skills (HOCS) in their pre-laboratory concept maps to support chemistry laboratory work. The research data consisted of 168 pre-laboratory concept maps that 29 students constructed as a part of their chemistry laboratory studies. Concept maps were analyzed by using a theory based content analysis through Anderson & Krathwohls' learning taxonomy (2001). This study implicates that novice concept mapper students use all knowledge dimensions and applying, analyzing and evaluating HOCS to support the pre-laboratory work.

Word order and tonal shape in the production of focus in short Finnish utterances

This paper presents results from a study on the production of Finnish prosody. The effect of word order and the tonal shape in the production of Finnish prosody was studied as produced by 8 native Finnish speakers. Predictions formulated with regard to results from an earlier study pertaining to the perception of promi- nence were tested. These predictions had to do with the tonal shape of the utterances in the form of a flat hat pattern and the effect of word order on the so called top-line declination within an adver- bial phrase in the utterances. The results from the experiment give support to the following claims: the temporal domain of prosodic focus is the whole utterance, word order reversal from unmarked to marked has an effect on the production of prosody, and the pro- duction of the tonal aspects of focus in Finnish follows a basic flat hat pattern. That is the prominence of a word can be produced by an f 0 rise or a fall, depending on the location of the word in an utterance. The basic accentual shape of a Finnish word is then not a pointed rise/fall hat shape as claimed before since it can vary depending on the syllable structure and the position within an ut- terance.

Sensitivity of wetland methane emissions to model assumptions: application and model testing against site observations

Abstract. Methane emissions from natural wetlands and rice paddies constitute a large proportion of atmospheric methane, but the magnitude and year-to-year variation of these methane sources is still unpredictable. Here we describe and evaluate the integration of a methane biogeochemical model (CLM4Me; Riley et al., 2011) into the Community Land Model 4.0 (CLM4CN) in order to better explain spatial and temporal variations in methane emissions. We test new functions for soil pH and redox potential that impact microbial methane production in soils. We also constrain aerenchyma in plants in always-inundated areas in order to better represent wetland vegetation. Satellite inundated fraction is explicitly prescribed in the model because there are large differences between simulated fractional inundation and satellite observations. A rice paddy module is also incorporated into the model, where the fraction of land used for rice production is explicitly prescribed. The model is evaluated at the site level with vegetation cover and water table prescribed from measurements. Explicit site level evaluations of simulated methane emissions are quite different than evaluating the grid cell averaged emissions against available measurements. Using a baseline set of parameter values, our model-estimated average global wetland emissions for the period 1993–2004 were 256 Tg CH4 yr−1, and rice paddy emissions in the year 2000 were 42 Tg CH4 yr−1. Tropical wetlands contributed 201 Tg CH4 yr−1, or 78 % of the global wetland flux. Northern latitude (>50 N) systems contributed 12 Tg CH4 yr−1. We expect this latter number may be an underestimate due to the low high-latitude inundated area captured by satellites and unrealistically low high-latitude productivity and soil carbon predicted by CLM4. Sensitivity analysis showed a large range (150–346 Tg CH4 yr−1) in predicted global methane emissions. The large range was sensitive to: (1) the amount of methane transported through aerenchyma, (2) soil pH (± 100 Tg CH4 yr−1), and (3) redox inhibition (± 45 Tg CH4 yr−1).