Noncommutative Gravitation as a Gauge Theory of Twisted Poincaré Symmetry

Gravitaation kvanttiteorian muotoilu on ollut teoreettisten fyysikkojen tavoitteena kvanttimekaniikan synnystä lähtien. Kvanttimekaniikan soveltaminen korkean energian ilmiöihin yleisen suhteellisuusteorian viitekehyksessä johtaa aika-avaruuden koordinaattien operatiiviseen ei-kommutoivuuteen. Ei-kommutoivia aika-avaruuden geometrioita tavataan myös avointen säikeiden säieteorioiden tietyillä matalan energian rajoilla. Ei-kommutoivan aika-avaruuden gravitaatioteoria voisi olla yhteensopiva kvanttimekaniikan kanssa ja se voisi mahdollistaa erittäin lyhyiden etäisyyksien ja korkeiden energioiden prosessien ei-lokaaliksi uskotun fysiikan kuvauksen, sekä tuottaa yleisen suhteellisuusteorian kanssa yhtenevän teorian pitkillä etäisyyksillä. Tässä työssä tarkastelen gravitaatiota Poincarén symmetrian mittakenttäteoriana ja pyrin yleistämään tämän näkemyksen ei-kommutoiviin aika-avaruuksiin. Ensin esittelen Poincarén symmetrian keskeisen roolin relativistisessa fysiikassa ja sen kuinka klassinen gravitaatioteoria johdetaan Poincarén symmetrian mittakenttäteoriana kommutoivassa aika-avaruudessa. Jatkan esittelemällä ei-kommutoivan aika-avaruuden ja kvanttikenttäteorian muotoilun ei-kommutoivassa aika-avaruudessa. Mittasymmetrioiden lokaalin luonteen vuoksi tarkastelen huolellisesti mittakenttäteorioiden muotoilua ei-kommutoivassa aika-avaruudessa. Erityistä huomiota kiinnitetään näiden teorioiden vääristyneeseen Poincarén symmetriaan, joka on ei-kommutoivan aika-avaruuden omaama uudentyyppinen kvanttisymmetria. Seuraavaksi tarkastelen ei-kommutoivan gravitaatioteorian muotoilun ongelmia ja niihin kirjallisuudessa esitettyjä ratkaisuehdotuksia. Selitän kuinka kaikissa tähänastisissa lähestymistavoissa epäonnistutaan muotoilla kovarianssi yleisten koordinaattimunnosten suhteen, joka on yleisen suhteellisuusteorian kulmakivi. Lopuksi tutkin mahdollisuutta yleistää vääristynyt Poincarén symmetria lokaaliksi mittasymmetriaksi --- gravitaation ei-kommutoivan mittakenttäteorian saavuttamisen toivossa. Osoitan, että tällaista yleistystä ei voida saavuttaa vääristämällä Poincarén symmetriaa kovariantilla twist-elementillä. Näin ollen ei-kommutoivan gravitaation ja vääristyneen Poincarén symmetrian tutkimuksessa tulee jatkossa keskittyä muihin lähestymistapoihin.

Location and scale mixtures of Gaussians with flexible tail behaviour: Properties, inference and application to multivariate clustering

The family of location and scale mixtures of Gaussians has the ability to generate a number of flexible distributional forms. The family nests as particular cases several important asymmetric distributions like the Generalized Hyperbolic distribution. The Generalized Hyperbolic distribution in turn nests many other well known distributions such as the Normal Inverse Gaussian. In a multivariate setting, an extension of the standard location and scale mixture concept is proposed into a so called multiple scaled framework which has the advantage of allowing different tail and skewness behaviours in each dimension with arbitrary correlation between dimensions. Estimation of the parameters is provided via an EM algorithm and extended to cover the case of mixtures of such multiple scaled distributions for application to clustering. Assessments on simulated and real data confirm the gain in degrees of freedom and flexibility in modelling data of varying tail behaviour and directional shape.

A new family of multivariate heavy-tailed distributions with variable marginal amounts of tailweight: Application to robust clustering

We propose a family of multivariate heavy-tailed distributions that allow variable marginal amounts of tailweight. The originality comes from introducing multidimensional instead of univariate scale variables for the mixture of scaled Gaussian family of distributions. In contrast to most existing approaches, the derived distributions can account for a variety of shapes and have a simple tractable form with a closed-form probability density function whatever the dimension. We examine a number of properties of these distributions and illustrate them in the particular case of Pearson type VII and t tails. For these latter cases, we provide maximum likelihood estimation of the parameters and illustrate their modelling flexibility on simulated and real data clustering examples.

Random vibration of a second order non-linear elastic system

A method is presented for obtaining, approximately, the response covariance and probability distribution of a non-linear oscillator under a Gaussian excitation. The method has similarities with the hierarchy closure and the equivalent linearization approaches, but is different. A Gaussianization technique is used to arrive at the output autocorrelation and the input-output cross-correlation. This along with an energy equivalence criterion is used to estimate the response distribution function. The method is applicable in both the transient and steady state response analysis under either stationary or non-stationary excitations. Good comparison has been observed between the predicted and the exact steady state probability distribution of a Duffing oscillator under a white noise input.

Nitrous oxide emissions from selected natural and managed northern ecosystems

Microbial activity in soils is the main source of nitrous oxide (N2O) to the atmosphere. Nitrous oxide is a strong greenhouse gas in the troposphere and participates in ozone destructive reactions in the stratosphere. The constant increase in the atmospheric concentration, as well as uncertainties in the known sources and sinks of N2O underline the need to better understand the processes and pathways of N2O in terrestrial ecosystems. This study aimed at quantifying N2O emissions from soils in northern Europe and at investigating the processes and pathways of N2O from agricultural and forest ecosystems. Emissions were measured in forest ecosystems, agricultural soils and a landfill, using the soil gradient, chamber and eddy covariance methods. Processes responsible for N2O production, and the pathways of N2O from the soil to the atmosphere, were studied in the laboratory and in the field. These ecosystems were chosen for their potential importance to the national and global budget of N2O. Laboratory experiments with boreal agricultural soils revealed that N2O production increases drastically with soil moisture content, and that the contribution of the nitrification and denitrification processes to N2O emissions depends on soil type. Laboratory study with beech (Fagus sylvatica) seedlings demonstrated that trees can serve as conduits for N2O from the soil to the atmosphere. If this mechanism is important in forest ecosystems, the current emission estimates from forest soils may underestimate the total N2O emissions from forest ecosystems. Further field and laboratory studies are needed to evaluate the importance of this mechanism in forest ecosystems. The emissions of N2O from northern forest ecosystems and a municipal landfill were highly variable in time and space. The emissions of N2O from boreal upland forest soil were among the smallest reported in the world. Despite the low emission rates, the soil gradient method revealed a clear seasonal variation in N2O production. The organic topsoil was responsible for most of the N2O production and consumption in this forest soil. Emissions from the municipal landfill were one to two orders of magnitude higher than those from agricultural soils, which are the most important source of N2O to the atmosphere. Due to their small areal coverage, landfills only contribute minimally to national N2O emissions in Finland. The eddy covariance technique was demonstrated to be useful for measuring ecosystem-scale emissions of N2O in forest and landfill ecosystems. Overall, more measurements and integration between different measurement techniques are needed to capture the large variability in N2O emissions from natural and managed northern ecosystems.

Carbon balance and component CO2 fluxes in boreal Scots pine stands

The forest vegetation takes up atmospheric carbon dioxide (CO2) in photosynthesis. Part of the fixed carbon is released back into the atmosphere during plant respiration but a substantial part is stored as plant biomass, especially in the stems of trees. Carbon also accumulates in the soil as litter and via the roots. CO2 is released into the atmosphere from these carbon stocks in the decomposition of dead biomass. Carbon balance of a forest stand is the difference between the CO2 uptake and CO2 efflux. This study quantifies and analyses the dynamics of carbon balance and component CO2 fluxes in four Southern Finnish Scots pine stands that covered the typical economic rotation time of 80 years. The study was based on direct flux measurements with chambers and eddy covariance (EC), and modelling of component CO2 fluxes. The net CO2 exchange of the stand was partitioned into component fluxes: photosynthesis of trees and ground vegetation, respiration of tree foliage and stems, and CO2 efflux from the soil. The relationships between the component fluxes and the environmental factors (light, temperature, atmospheric CO2, air humidity and soil moisture) were studied with mathematical modelling. The annual CO2 balance varied from a source of about 400 g C/m2 at a recently clearcut site to net CO2 uptake of 200 300 g C/m2 in a middle-aged (40-year-old) and a mature (75-year-old) stand. A 12-year-old sapling site was at the turning point from source to a sink of CO2. In the middle-aged stand, photosynthetic production was dominated by trees. Under closed pine canopies, ground vegetation accounted for 10 20% of stand photosynthesis whereas at the open sites the proportion and also the absolute photosynthesis of ground vegetation was much higher. The aboveground respiration was dominated by tree foliage which accounted for one third of the ecosystem respiration. Rate of wood respiration was in the order of 10% of total ecosystem respiration. CO2 efflux from the soil dominated the ecosystem respiratory fluxes in all phases of stand development. Instantaneous and delayed responses to the environmental driving factors could predict well within-year variability in photosynthetic production: In the short term and during the growing season photosynthesis follows primarily light while the seasonal variation is more strongly connected to temperature. The temperature relationship of the annual cycle of photosynthesis was found to be almost equal in the southern boreal zone and at the timberline in the northern boreal zone. The respiratory fluxes showed instantaneous and seasonal temperature relationships but they could also be connected to photosynthesis at an annual timescale.

A Kalman filter based strategy for linear structural system identification based on multiple static and dynamic test data

The problem of identification of stiffness, mass and damping properties of linear structural systems, based on multiple sets of measurement data originating from static and dynamic tests is considered. A strategy, within the framework of Kalman filter based dynamic state estimation, is proposed to tackle this problem. The static tests consists of measurement of response of the structure to slowly moving loads, and to static loads whose magnitude are varied incrementally; the dynamic tests involve measurement of a few elements of the frequency response function (FRF) matrix. These measurements are taken to be contaminated by additive Gaussian noise. An artificial independent variable τ, that simultaneously parameterizes the point of application of the moving load, the magnitude of the incrementally varied static load and the driving frequency in the FRFs, is introduced. The state vector is taken to consist of system parameters to be identified. The fact that these parameters are independent of the variable τ is taken to constitute the set of ‘process’ equations. The measurement equations are derived based on the mechanics of the problem and, quantities, such as displacements and/or strains, are taken to be measured. A recursive algorithm that employs a linearization strategy based on Neumann’s expansion of structural static and dynamic stiffness matrices, and, which provides posterior estimates of the mean and covariance of the unknown system parameters, is developed. The satisfactory performance of the proposed approach is illustrated by considering the problem of the identification of the dynamic properties of an inhomogeneous beam and the axial rigidities of members of a truss structure.

Geometry-free stochastic analysis of BDS triple frequency signals

The paper presents a geometry-free approach to assess the variation of covariance matrices of undifferenced triple frequency GNSS measurements and its impact on positioning solutions. Four independent geometryfree/ ionosphere-free (GFIF) models formed from original triple-frequency code and phase signals allow for effective computation of variance-covariance matrices using real data. Variance Component Estimation (VCE) algorithms are implemented to obtain the covariance matrices for three pseudorange and three carrier-phase signals epoch-by-epoch. Covariance results from the triple frequency Beidou System (BDS) and GPS data sets demonstrate that the estimated standard deviation varies in consistence with the amplitude of actual GFIF error time series. The single point positioning (SPP) results from BDS ionosphere-free measurements at four MGEX stations demonstrate an improvement of up to about 50% in Up direction relative to the results based on a mean square statistics. Additionally, a more extensive SPP analysis at 95 global MGEX stations based on GPS ionosphere-free measurements shows an average improvement of about 10% relative to the traditional results. This finding provides a preliminary confirmation that adequate consideration of the variation of covariance leads to the improvement of GNSS state solutions.

Stationary processes for object detection and non-rigid structure-from-motion

Stationary processes are random variables whose value is a signal and whose distribution is invariant to translation in the domain of the signal. They are intimately connected to convolution, and therefore to the Fourier transform, since the covariance matrix of a stationary process is a Toeplitz matrix, and Toeplitz matrices are the expression of convolution as a linear operator. This thesis utilises this connection in the study of i) efficient training algorithms for object detection and ii) trajectory-based non-rigid structure-from-motion.

Modelling of solute transport in a mild heterogeneous porous medium using stochastic finite element method: Effects of random source conditions

Randomness in the source condition other than the heterogeneity in the system parameters can also be a major source of uncertainty in the concentration field. Hence, a more general form of the problem formulation is necessary to consider randomness in both source condition and system parameters. When the source varies with time, the unsteady problem, can be solved using the unit response function. In the case of random system parameters, the response function becomes a random function and depends on the randomness in the system parameters. In the present study, the source is modelled as a random discrete process with either a fixed interval or a random interval (the Poisson process). In this study, an attempt is made to assess the relative effects of various types of source uncertainties on the probabilistic behaviour of the concentration in a porous medium while the system parameters are also modelled as random fields. Analytical expressions of mean and covariance of concentration due to random discrete source are derived in terms of mean and covariance of unit response function. The probabilistic behaviour of the random response function is obtained by using a perturbation-based stochastic finite element method (SFEM), which performs well for mild heterogeneity. The proposed method is applied for analysing both the 1-D as well as the 3-D solute transport problems. The results obtained with SFEM are compared with the Monte Carlo simulation for 1-D problems.

Exploiting ground-based measurements of the Global Positioning System for numerical weather prediction

Data assimilation provides an initial atmospheric state, called the analysis, for Numerical Weather Prediction (NWP). This analysis consists of pressure, temperature, wind, and humidity on a three-dimensional NWP model grid. Data assimilation blends meteorological observations with the NWP model in a statistically optimal way. The objective of this thesis is to describe methodological development carried out in order to allow data assimilation of ground-based measurements of the Global Positioning System (GPS) into the High Resolution Limited Area Model (HIRLAM) NWP system. Geodetic processing produces observations of tropospheric delay. These observations can be processed either for vertical columns at each GPS receiver station, or for the individual propagation paths of the microwave signals. These alternative processing methods result in Zenith Total Delay (ZTD) and Slant Delay (SD) observations, respectively. ZTD and SD observations are of use in the analysis of atmospheric humidity. A method is introduced for estimation of the horizontal error covariance of ZTD observations. The method makes use of observation minus model background (OmB) sequences of ZTD and conventional observations. It is demonstrated that the ZTD observation error covariance is relatively large in station separations shorter than 200 km, but non-zero covariances also appear at considerably larger station separations. The relatively low density of radiosonde observing stations limits the ability of the proposed estimation method to resolve the shortest length-scales of error covariance. SD observations are shown to contain a statistically significant signal on the asymmetry of the atmospheric humidity field. However, the asymmetric component of SD is found to be nearly always smaller than the standard deviation of the SD observation error. SD observation modelling is described in detail, and other issues relating to SD data assimilation are also discussed. These include the determination of error statistics, the tuning of observation quality control and allowing the taking into account of local observation error correlation. The experiments made show that the data assimilation system is able to retrieve the asymmetric information content of hypothetical SD observations at a single receiver station. Moreover, the impact of real SD observations on humidity analysis is comparable to that of other observing systems.

Testing against changing correlation

A test for time-varying correlation is developed within the framework of a dynamic conditional score (DCS) model for both Gaussian and Student t-distributions. The test may be interpreted as a Lagrange multiplier test and modified to allow for the estimation of models for time-varying volatility in the individual series. Unlike standard moment-based tests, the score-based test statistic includes information on the level of correlation under the null hypothesis and local power arguments indicate the benefits of doing so. A simulation study shows that the performance of the score-based test is strong relative to existing tests across a range of data generating processes. An application to the Hong Kong and South Korean equity markets shows that the new test reveals changes in correlation that are not detected by the standard moment-based test.

Turbulent vertical fluxes and air quality measured in urban air in Helsinki

There is a growing need to understand the exchange processes of momentum, heat and mass between an urban surface and the atmosphere as they affect our quality of life. Understanding the source/sink strengths as well as the mixing mechanisms of air pollutants is particularly important due to their effects on human health and climate. This work aims to improve our understanding of these surface-atmosphere interactions based on the analysis of measurements carried out in Helsinki, Finland. The vertical exchange of momentum, heat, carbon dioxide (CO2) and aerosol particle number was measured with the eddy covariance technique at the urban measurement station SMEAR III, where the concentrations of ultrafine, accumulation mode and coarse particle numbers, nitrogen oxides (NOx), carbon monoxide (CO), ozone (O3) and sulphur dioxide (SO2) were also measured. These measurements were carried out over varying measurement periods between 2004 and 2008. In addition, black carbon mass concentration was measured at the Helsinki Metropolitan Area Council site during three campaigns in 1996-2005. Thus, the analyzed dataset covered far, the most comprehensive long-term measurements of turbulent fluxes reported in the literature from urban areas. Moreover, simultaneously measured urban air pollution concentrations and turbulent fluxes were examined for the first time. The complex measurement surrounding enabled us to study the effect of different urban covers on the exchange processes from a single point of measurement. The sensible and latent heat fluxes closely followed the intensity of solar radiation, and the sensible heat flux always exceeded the latent heat flux due to anthropogenic heat emissions and the conversion of solar radiation to direct heat in urban structures. This urban heat island effect was most evident during winter nights. The effect of land use cover was seen as increased sensible heat fluxes in more built-up areas than in areas with high vegetation cover. Both aerosol particle and CO2 exchanges were largely affected by road traffic, and the highest diurnal fluxes reached 109 m-2 s-1 and 20 µmol m-2 s-1, respectively, in the direction of the road. Local road traffic had the greatest effect on ultrafine particle concentrations, whereas meteorological variables were more important for accumulation mode and coarse particle concentrations. The measurement surroundings of the SMEAR III station served as a source for both particles and CO2, except in summer, when the vegetation uptake of CO2 exceeded the anthropogenic sources in the vegetation sector in daytime, and we observed a downward median flux of 8 µmol m-2 s-1. This work improved our understanding of the interactions between an urban surface and the atmosphere in a city located at high latitudes in a semi-continental climate. The results can be utilised in urban planning, as the fraction of vegetation cover and vehicular activity were found to be the major environmental drivers affecting most of the exchange processes. However, in order to understand these exchange and mixing processes on a city scale, more measurements above various urban surfaces accompanied by numerical modelling are required.

Single-Symbol ML Decodable Precoded DSTBCs for Cooperative Networks

Single-symbol maximum likelihood (ML) decodable distributed orthogonal space-time block codes (DOST- BCs) have been introduced recently for cooperative networks and an upper-bound on the maximal rate of such codes along with code constructions has been presented. In this paper, we introduce a new class of distributed space-time block codes (DSTBCs) called semi-orthogonal precoded distributed single-symbol decodable space-time block codes (Semi-SSD-PDSTBCs) wherein, the source performs preceding on the information symbols before transmitting it to all the relays. A set of necessary and sufficient conditions on the relay matrices for the existence of semi-SSD- PDSTBCs is proved. It is shown that the DOSTBCs are a special case of semi-SSD-PDSTBCs. A subset of semi-SSD-PDSTBCs having diagonal covariance matrix at the destination is studied and an upper bound on the maximal rate of such codes is derived. The bounds obtained are approximately twice larger than that of the DOSTBCs. A systematic construction of Semi- SSD-PDSTBCs is presented when the number of relays K ges 4 and the constructed codes are shown to have higher rates than that of DOSTBCs.

Modelling boreal forest CO2 exchange and seasonality

Man-induced climate change has raised the need to predict the future climate and its feedback to vegetation. These are studied with global climate models; to ensure the reliability of these predictions, it is important to have a biosphere description that is based upon the latest scientific knowledge. This work concentrates on the modelling of the CO2 exchange of the boreal coniferous forest, studying also the factors controlling its growing season and how these can be used in modelling. In addition, the modelling of CO2 gas exchange at several scales was studied. A canopy-level CO2 gas exchange model was developed based on the biochemical photosynthesis model. This model was first parameterized using CO2 exchange data obtained by eddy covariance (EC) measurements from a Scots pine forest at Sodankylä. The results were compared with a semi-empirical model that was also parameterized using EC measurements. Both of the models gave satisfactory results. The biochemical canopy-level model was further parameterized at three other coniferous forest sites located in Finland and Sweden. At all the sites, the two most important biochemical model parameters showed seasonal behaviour, i.e., their temperature responses changed according to the season. Modelling results were improved when these changeover dates were related to temperature indices. During summer-time the values of the biochemical model parameters were similar at all the four sites. Different control factors for CO2 gas exchange were studied at the four coniferous forests, including how well these factors can be used to predict the initiation and cessation of the CO2 uptake. Temperature indices, atmospheric CO2 concentration, surface albedo and chlorophyll fluorescence (CF) were all found to be useful and have predictive power. In addition, a detailed simulation study of leaf stomata in order to separate physical and biochemical processes was performed. The simulation study brought to light the relative contribution and importance of the physical transport processes. The results of this work can be used in improving CO2 gas exchange models in boreal coniferous forests. The meteorological and biological variables that represent the seasonal cycle were studied, and a method for incorporating this cycle into a biochemical canopy-level model was introduced.