Integral Transformations of Volterra Gaussian Processes

We study integral representations of Gaussian processes with a pre-specified law in terms of other Gaussian processes. The dissertation consists of an introduction and of four research articles. In the introduction, we provide an overview about Volterra Gaussian processes in general, and fractional Brownian motion in particular. In the first article, we derive a finite interval integral transformation, which changes fractional Brownian motion with a given Hurst index into fractional Brownian motion with an other Hurst index. Based on this transformation, we construct a prelimit which formally converges to an analogous, infinite interval integral transformation. In the second article, we prove this convergence rigorously and show that the infinite interval transformation is a direct consequence of the finite interval transformation. In the third article, we consider general Volterra Gaussian processes. We derive measure-preserving transformations of these processes and their inherently related bridges. Also, as a related result, we obtain a Fourier-Laguerre series expansion for the first Wiener chaos of a Gaussian martingale. In the fourth article, we derive a class of ergodic transformations of self-similar Volterra Gaussian processes.

Plant guard cell anion channel SLAC1 regulates stomatal closure

Plants are rooted to their growth place; therefore it is important that they react adequately to changes in environmental conditions. Stomatal pores, which are formed of a pair of guard cells in leaf epidermis, regulate plant gas-exchange. Importantly, guard cells protect the plant from desiccation in drought conditions by reducing the aperture of the stomatal pore. They serve also as the first barrier against the major air pollutant ozone, but the behaviour of guard cells during ozone exposure has not been sufficiently addressed. Aperture of the stomatal pore is regulated by the influx and efflux of osmotically active ions via ion channels and transporters across the guard cell membrane, however the molecular identity of guard cell plasma membrane anion channel has remained unknown. In the frame of this study, guard cell behaviour during ozone exposure was studied using the newly constructed Arabidopsis whole-rosette gas-exchange system. Ozone induced a Rapid Transient Decrease (RTD) in stomatal conductance within 10 min from the start of exposure, which was followed by a recovery in the conductance within the next 40 min. The decrease in stomatal conductance was dependent on the applied ozone concentration. Three minutes of ozone exposure was sufficient to induce RTD and further ozone application during the closure-recovery process had no effect on RTD, demonstrating that the whole process is programmed within the first three minutes. To address the molecular components responsible for RTD, the ozone response was measured in 59 different Arabidopsis mutants involved in guard cell signalling. Four of the tested mutants slac1 (originally rcd3), ost1, abi1-1 and abi2-1 lacked RTD completely. As the ozone sensitive mutant slac1 lacked RTD, the next aim of this study was to identify and characterize SLAC1. SLAC1 was shown to be a central regulator in response to all major factors regulating guard cell aperture: CO2, light/darkness transitions, ozone, relative air humidity, ABA, NO, H2O2, and extracellular Ca2+. It encodes the first guard cell plasma membrane slow type anion channel to be identified at the molecular level. Interestingly, the rapid type anion conductance was intact in slac1 mutant plants. For activation, SLAC1 needs to be phosphorylated. Protein kinase OST1 was shown to phosphorylate several amino acids in the N-terminal tail of SLAC1, Ser120 was one of its main targets, which led to SLAC1 activation. The lack of RTD in type 2C protein phosphatase mutants abi1-1 and abi2-1, suggests that these proteins have a regulatory role in ozoneinduced activation of the slow type anion channel.

Epithelial sodium channel in airway epithelium of the newborn infant : Implications for postnatal pulmonary adaptation

The aim of the present thesis was to study the role of the epithelial sodium channel (ENaC) in clearance of fetal lung fluid in the newborn infant by measurement of airway epithelial expression of ENaC, of nasal transepithelial potential difference (N-PD), and of lung compliance (LC). In addition, the effect of postnatal dexamethasone on airway epithelial ENaC expression was measured in preterm infants with bronchopulmonary dysplasia (BPD). The patient population was formed of selected term newborn infants born in the Department of Obstetrics (Studies II-IV) and selected preterm newborn infants treated in the neonatal intensive care unit of the Hospital for Children and Adolescents (Studies I and IV) of the Helsinki University Central Hospital in Finland. A small population of preterm infants suffering from BPD was included in Study I. Studies I, III, and IV included airway epithelial measurement of ENaC and in Studies II and III, measurement of N-PD and LC. In Study I, ENaC expression analyses were performed in the Research Institute of the Hospital for Sick Children in Toronto, Ontario, Canada. In the following studies, analyses were performed in the Scientific Laboratory of the Hospital for Children and Adolescents. N-PD and LC measurements were performed at bedside in these hospitals. In term newborn infants, the percentage of amiloride-sensitive N-PD, a surrogate for ENaC activity, measured during the first 4 postnatal hours correlates positively with LC measured 1 to 2 days postnatally. Preterm infants with BPD had, after a therapeutic dose of dexamethasone, higher airway epithelial ENaC expression than before treatment. These patients were subsequently weaned from mechanical ventilation, probably as a result of the clearance of extra fluid from the alveolar spaces. In addition, we found that in preterm infants ENaC expression increases with gestational age (GA). In preterm infants, ENaC expression in the airway epithelium was lower than in term newborn infants. During the early postnatal period in those born both preterm and term airway epithelial βENaC expression decreased significantly. Term newborn infants delivered vaginally had a significantly smaller airway epithelial expression of αENaC after the first postnatal day than did those delivered by cesarean section. The functional studies showed no difference in N-PD between infants delivered vaginally and by cesarean section. We therefore conclude that the low airway epithelial expression of ENaC in the preterm infant and the correlation of N-PD with LC in the term infant indicate a role for ENaC in the pathogenesis of perinatal pulmonary adaptation and neonatal respiratory distress. Because dexamethasone raised ENaC expression in preterm infants with BPD, and infants were subsequently weaned from ventilator therapy, we suggest that studies on the treatment of respiratory distress in the preterm infant should include the induction of ENaC activity.

Ion channel gene variants predisposing to severe human ventricular arrhythmias

Congenital long QT syndrome (LQTS) with an estimated prevalence of 1:2000-1:10 000 manifests with prolonged QT interval on electrocardiogram and risk for ventricular arrhythmias and sudden death. Several ion channel genes and hundreds of mutations in these genes have been identified to underlie the disorder. In Finland, four LQTS founder mutations of potassium channel genes account for up to 40-70% of genetic spectrum of LQTS. Acquired LQTS has similar clinical manifestations, but often arises from usage of QT-prolonging medication or electrolyte disturbances. A prolonged QT interval is associated with increased morbidity and mortality not only in clinical LQTS but also in patients with ischemic heart disease and in the general population. The principal aim of this study was to estimate the actual prevalence of LQTS founder mutations in Finland and to calculate their effect on QT interval in the Finnish background population. Using a large population-based sample of over 6000 Finnish individuals from the Health 2000 Survey, we identified LQTS founder mutations KCNQ1 G589D (n=8), KCNQ1 IVS7-2A>G (n=1), KCNH2 L552S (n=2), and KCNH2 R176W (n=16) in 27 study participants. This resulted in a weighted prevalence estimate of 0.4% for LQTS in Finland. Using a linear regression model, the founder mutations resulted in a 22- to 50-ms prolongation of the age-, sex-, and heart rate-adjusted QT interval. Collectively, these data suggest that one of 250 individuals in Finland may be genetically predisposed to ventricular arrhythmias arising from the four LQTS founder mutations. A KCNE1 D85N minor allele with a frequency of 1.4% was associated with a 10-ms prolongation in adjusted QT interval and could thus identify individuals at increased risk of ventricular arrhythmias at the population level. In addition, the previously reported associations of KCNH2 K897T, KCNH2 rs3807375, and NOS1AP rs2880058 with QT interval duration were confirmed in the present study. In a separate study, LQTS founder mutations were identified in a subgroup of acquired LQTS, providing further evidence that congenital LQTS gene mutations may underlie acquired LQTS. Catecholaminergic polymorphic ventricular tachycardia (CPVT) is characterized by exercise-induced ventricular arrhythmias in a structurally normal heart and results from defects in the cardiac Ca2+ signaling proteins, mainly ryanodine receptor type 2 (RyR2). In a patient population of typical CPVT, RyR2 mutations were identifiable in 25% (4/16) of patients, implying that noncoding variants or other genes are involved in CPVT pathogenesis. A 1.1 kb RyR2 exon 3 deletion was identified in two patients independently, suggesting that this region may provide a new target for RyR2-related molecular genetic studies. Two novel RyR2 mutations showing a gain-of-function defect in vitro were identified in three victims of sudden cardiac death. Extended pedigree analyses revealed some surviving mutation carriers with mild structural abnormalities of the heart and resting ventricular arrhythmias suggesting that not all RyR2 mutations lead to a typical CPVT phenotype, underscoring the relevance of tailored risk stratification of a RyR2 mutation carrier.

Non-Gaussian Cosmological Perturbations from Hybrid Inflation and Preheating

This thesis consists of four research papers and an introduction providing some background. The structure in the universe is generally considered to originate from quantum fluctuations in the very early universe. The standard lore of cosmology states that the primordial perturbations are almost scale-invariant, adiabatic, and Gaussian. A snapshot of the structure from the time when the universe became transparent can be seen in the cosmic microwave background (CMB). For a long time mainly the power spectrum of the CMB temperature fluctuations has been used to obtain observational constraints, especially on deviations from scale-invariance and pure adiabacity. Non-Gaussian perturbations provide a novel and very promising way to test theoretical predictions. They probe beyond the power spectrum, or two point correlator, since non-Gaussianity involves higher order statistics. The thesis concentrates on the non-Gaussian perturbations arising in several situations involving two scalar fields, namely, hybrid inflation and various forms of preheating. First we go through some basic concepts -- such as the cosmological inflation, reheating and preheating, and the role of scalar fields during inflation -- which are necessary for the understanding of the research papers. We also review the standard linear cosmological perturbation theory. The second order perturbation theory formalism for two scalar fields is developed. We explain what is meant by non-Gaussian perturbations, and discuss some difficulties in parametrisation and observation. In particular, we concentrate on the nonlinearity parameter. The prospects of observing non-Gaussianity are briefly discussed. We apply the formalism and calculate the evolution of the second order curvature perturbation during hybrid inflation. We estimate the amount of non-Gaussianity in the model and find that there is a possibility for an observational effect. The non-Gaussianity arising in preheating is also studied. We find that the level produced by the simplest model of instant preheating is insignificant, whereas standard preheating with parametric resonance as well as tachyonic preheating are prone to easily saturate and even exceed the observational limits. We also mention other approaches to the study of primordial non-Gaussianities, which differ from the perturbation theory method chosen in the thesis work.

Measurement of the top quark mass in the dilepton channel using mT2 at CDF

We present measurements of the top quark mass using the \mT2, a variable related to the transverse mass in events with two missing particles. We use the template method applied to t\tbar dilepton events produced in p\pbar collisions at Fermilab's Tevatron and collected by the CDF detector. From a data sample corresponding to an integrated luminosity of 3.4 \invfb, we select 236 t\tbar candidate events. Using the \mT2 distribution, we measure the top quark mass to be M_{Top} = 168.0^{+4.8}_{-4.0} $\pm$ {2.9} GeV/c^{2}. By combining the \mT2 with the reconstructed top mass distributions based on a neutrino weighting method, we measure M_{top}=169.3 $\pm$ 2.7 $\pm$ 3.2 GeV/c^{2}. This is the first application of the \mT2 variable in a mass measurement at a hadron collider.

Search for the associated production of the standard-model Higgs boson in the all-hadronic channel

"We report on a search for the standard-model Higgs boson in pp collisions at s=1.96 TeV using an integrated luminosity of 2.0 fb(-1). We look for production of the Higgs boson decaying to a pair of bottom quarks in association with a vector boson V (W or Z) decaying to quarks, resulting in a four-jet final state. Two of the jets are required to have secondary vertices consistent with B-hadron decays. We set the first 95% confidence level upper limit on the VH production cross section with V(-> qq/qq('))H(-> bb) decay for Higgs boson masses of 100-150 GeV/c(2) using data from run II at the Fermilab Tevatron. For m(H)=120 GeV/c(2), we exclude cross sections larger than 38 times the standard-model prediction."

Search for new physics in the μμ+e/μ+E̸T channel with a low-pT lepton threshold at the Collider Detector at Fermilab

A search for new physics using three-lepton (trilepton) data collected with the CDF II detector and corresponding to an integrated luminosity of 976 pb-1 is presented. The standard model predicts a low rate of trilepton events, which makes some supersymmetric processes, such as chargino-neutralino production, measurable in this channel. The mu+mu+l signature is investigated, where l is an electron or a muon, with the additional requirement of large missing transverse energy. In this analysis, the lepton transverse momenta with respect to the beam direction (pT) are as low as 5 GeV/c, a selection that improves the sensitivity to particles which are light as well as to ones which result in leptonically decaying tau leptons. At the same time, this low-p_T selection presents additional challenges due to the non-negligible heavy-quark background at low lepton momenta. This background is measured with an innovative technique using experimental data. Several dimuon and trilepton control regions are investigated, and good agreement between experimental results and standard-model predictions is observed. In the signal region, we observe one three-muon event and expect 0.4+/-0.1 mu+mu+l events

Inclusive Search for Standard Model Higgs Boson Production in the WW Decay Channel using the CDF II Detector

We present a search for standard model (SM) Higgs boson production using ppbar collision data at sqrt(s) = 1.96 TeV, collected with the CDF II detector and corresponding to an integrated luminosity of 4.8 fb-1. We search for Higgs bosons produced in all processes with a significant production rate and decaying to two W bosons. We find no evidence for SM Higgs boson production and place upper limits at the 95% confidence level on the SM production cross section (sigma(H)) for values of the Higgs boson mass (m_H) in the range from 110 to 200 GeV. These limits are the most stringent for m_H > 130 GeV and are 1.29 above the predicted value of sigma(H) for mH = 165 GeV.

Measurement of the top pair production cross section in the dilepton decay channel in pp̅ collisions at √s=1.96 TeV

A measurement of the $\ttbar$ production cross section in $\ppbar$ collisions at $\sqrt{{\rm s}}$ = 1.96 TeV using events with two leptons, missing transverse energy, and jets is reported. The data were collected with the CDF II Detector. The result in a data sample corresponding to an integrated luminosity 2.8 fb$^{-1}$ is: $\sigma_{\ttbar}$ = 6.27 $\pm$ 0.73(stat) $\pm$ 0.63(syst) $\pm$ 0.39(lum) pb. for an assumed top mass of 175 GeV/$c^{2}$.

Measurement of the top quark mass in the dilepton channel using mT2 at CDF

We present measurements of the top quark mass using the \mT2, a variable related to the transverse mass in events with two missing particles. We use the template method applied to t\tbar dilepton events produced in p\pbar collisions at Fermilab's Tevatron and collected by the CDF detector. From a data sample corresponding to an integrated luminosity of 3.4 \invfb, we select 236 t\tbar candidate events. Using the \mT2 distribution, we measure the top quark mass to be M_{Top} = 168.0^{+4.8}_{-4.0} $\pm$ {2.9} GeV/c^{2}. By combining the \mT2 with the reconstructed top mass distributions based on a neutrino weighting method, we measure M_{top}=169.3 $\pm$ 2.7 $\pm$ 3.2 GeV/c^{2}. This is the first application of the \mT2 variable in a mass measurement at a hadron collider.

Search for the associated production of the standard-model Higgs boson in the all-hadronic channel

"We report on a search for the standard-model Higgs boson in pp collisions at s=1.96 TeV using an integrated luminosity of 2.0 fb(-1). We look for production of the Higgs boson decaying to a pair of bottom quarks in association with a vector boson V (W or Z) decaying to quarks, resulting in a four-jet final state. Two of the jets are required to have secondary vertices consistent with B-hadron decays. We set the first 95% confidence level upper limit on the VH production cross section with V(-> qq/qq('))H(-> bb) decay for Higgs boson masses of 100-150 GeV/c(2) using data from run II at the Fermilab Tevatron. For m(H)=120 GeV/c(2), we exclude cross sections larger than 38 times the standard-model prediction."

Top Quark Mass Measurement in the lepton+jets Channel Using a Matrix Element Method and in situ Jet Energy Calibration

A precision measurement of the top quark mass m_t is obtained using a sample of ttbar events from ppbar collisions at the Fermilab Tevatron with the CDF II detector. Selected events require an electron or muon, large missing transverse energy, and exactly four high-energy jets, at least one of which is tagged as coming from a b quark. A likelihood is calculated using a matrix element method with quasi-Monte Carlo integration taking into account finite detector resolution and jet mass effects. The event likelihood is a function of m_t and a parameter DJES to calibrate the jet energy scale /in situ/. Using a total of 1087 events, a value of m_t = 173.0 +/- 1.2 GeV/c^2 is measured.