Renormalization methods in KAM theory

It is well known that an integrable (in the sense of Arnold-Jost) Hamiltonian system gives rise to quasi-periodic motion with trajectories running on invariant tori. These tori foliate the whole phase space. If we perturb an integrable system, the Kolmogorow-Arnold-Moser (KAM) theorem states that, provided some non-degeneracy condition and that the perturbation is sufficiently small, most of the invariant tori carrying quasi-periodic motion persist, getting only slightly deformed. The measure of the persisting invariant tori is large together with the inverse of the size of the perturbation. In the first part of the thesis we shall use a Renormalization Group (RG) scheme in order to prove the classical KAM result in the case of a non analytic perturbation (the latter will only be assumed to have continuous derivatives up to a sufficiently large order). We shall proceed by solving a sequence of problems in which theperturbations are analytic approximations of the original one. We will finally show that the approximate solutions will converge to a differentiable solution of our original problem. In the second part we will use an RG scheme using continuous scales, so that instead of solving an iterative equation as in the classical RG KAM, we will end up solving a partial differential equation. This will allow us to reduce the complications of treating a sequence of iterative equations to the use of the Banach fixed point theorem in a suitable Banach space.

Modeling Asymmetries in Financial Data with Multiplicative Error Models

This thesis addresses modeling of financial time series, especially stock market returns and daily price ranges. Modeling data of this kind can be approached with so-called multiplicative error models (MEM). These models nest several well known time series models such as GARCH, ACD and CARR models. They are able to capture many well established features of financial time series including volatility clustering and leptokurtosis. In contrast to these phenomena, different kinds of asymmetries have received relatively little attention in the existing literature. In this thesis asymmetries arise from various sources. They are observed in both conditional and unconditional distributions, for variables with non-negative values and for variables that have values on the real line. In the multivariate context asymmetries can be observed in the marginal distributions as well as in the relationships of the variables modeled. New methods for all these cases are proposed. Chapter 2 considers GARCH models and modeling of returns of two stock market indices. The chapter introduces the so-called generalized hyperbolic (GH) GARCH model to account for asymmetries in both conditional and unconditional distribution. In particular, two special cases of the GARCH-GH model which describe the data most accurately are proposed. They are found to improve the fit of the model when compared to symmetric GARCH models. The advantages of accounting for asymmetries are also observed through Value-at-Risk applications. Both theoretical and empirical contributions are provided in Chapter 3 of the thesis. In this chapter the so-called mixture conditional autoregressive range (MCARR) model is introduced, examined and applied to daily price ranges of the Hang Seng Index. The conditions for the strict and weak stationarity of the model as well as an expression for the autocorrelation function are obtained by writing the MCARR model as a first order autoregressive process with random coefficients. The chapter also introduces inverse gamma (IG) distribution to CARR models. The advantages of CARR-IG and MCARR-IG specifications over conventional CARR models are found in the empirical application both in- and out-of-sample. Chapter 4 discusses the simultaneous modeling of absolute returns and daily price ranges. In this part of the thesis a vector multiplicative error model (VMEM) with asymmetric Gumbel copula is found to provide substantial benefits over the existing VMEM models based on elliptical copulas. The proposed specification is able to capture the highly asymmetric dependence of the modeled variables thereby improving the performance of the model considerably. The economic significance of the results obtained is established when the information content of the volatility forecasts derived is examined.

Spectral Tuning and Adaptation to Different Light Environments of Mysid Visual Pigments

In the present thesis, questions of spectral tuning, the relation of spectral and thermal properties of visual pigments, and evolutionary adaptation to different light environments were addressed using a group of small crustaceans of the genus Mysis as a model. The study was based on microspectrophotometric measurements of visual pigment absorbance spectra, electrophysiological measurements of spectral sensitivities of dark-adapted eyes, and sequencing of the opsin gene retrieved through PCR. The spectral properties were related to the spectral transmission of the respective light environments, as well as to the phylogentic histories of the species. The photoactivation energy (Ea) was estimated from temperature effects on spectral sensitivity in the long-wavelength range, and calculations were made for optimal quantum catch and optimal signal-to-noise ratio in the different light environments. The opsin amino acid sequences of spectrally characterized individuals were compared to find candidate residues for spectral tuning. The general purpose was to clarify to what extent and on what time scale adaptive evolution has driven the functional properties of (mysid) visual pigments towards optimal performance in different light environments. An ultimate goal was to find the molecular mechanisms underlying the spectral tuning and to understand the balance between evolutionary adaptation and molecular constraints. The totally consistent segregation of absorption maxima (λmax) into (shorter-wavelength) marine and (longer-wavelength) freshwater populations suggests that truly adaptive evolution is involved in tuning the visual pigment for optimal performance, driven by selection for high absolute visual sensitivity. On the other hand, the similarity in λmax and opsin sequence between several populations of freshwater M. relicta in spectrally different lakes highlights the limits to adaptation set by evolutionary history and time. A strong inverse correlation between Ea and λmax was found among all visual pigments studied in these respects, including those of M. relicta and 10 species of vertebrate pigments, and this was used to infer thermal noise. The conceptual signal-to-noise ratios thus calculated for pigments with different λmax in the Baltic Sea and Lake Pääjärvi light environments supported the notion that spectral adaptation works towards maximizing the signal-to-noise ratio rather than quantum catch as such. Judged by the shape of absorbance spectra, the visual pigments of all populations of M. relicta and M. salemaai used exclusively the A2 chromophore (3, 4-dehydroretinal). A comparison of amino acid substitutions between M. relicta and M. salemaai indicated that mysid shrimps have a small number of readily available tuning sites to shift between a shorter - and a longer -wavelength opsin. However, phylogenetic history seems to have prevented marine M. relicta from converting back to the (presumably) ancestral opsin form, and thus the more recent reinvention of marine spectral sensitivity has been accomplished by some other novel mechanism, yet to be found

Comparison and integration of MEG and fMRI

MEG directly measures the neuronal events and has greater temporal resolution than fMRI, which has limited temporal resolution mainly due to the larger timescale of the hemodynamic response. On the other hand fMRI has advantages in spatial resolution, while the localization results with MEG can be ambiguous due to the non-uniqueness of the electromagnetic inverse problem. Thus, these methods could provide complementary information and could be used to create both spatially and temporally accurate models of brain function. We investigated the degree of overlap, revealed by the two imaging methods, in areas involved in sensory or motor processing in healthy subjects and neurosurgical patients. Furthermore, we used the spatial information from fMRI to construct a spatiotemporal model of the MEG data in order to investigate the sensorimotor system and to create a spatiotemporal model of its function. We compared the localization results from the MEG and fMRI with invasive electrophysiological cortical mapping. We used a recently introduced method, contextual clustering, for hypothesis testing of fMRI data and assessed the the effect of neighbourhood information use on the reproducibility of fMRI results. Using MEG, we identified the ipsilateral primary sensorimotor cortex (SMI) as a novel source area contributing to the somatosensory evoked fields (SEF) to median nerve stimulation. Using combined MEG and fMRI measurements we found that two separate areas in the lateral fissure may be the generators for the SEF responses from the secondary somatosensory cortex region. The two imaging methods indicated activation in corresponding locations. By using complementary information from MEG and fMRI we established a spatiotemporal model of somatosensory cortical processing. This spatiotemporal model of cerebral activity was in good agreement with results from several studies using invasive electrophysiological measurements and with anatomical studies in monkey and man concerning the connections between somatosensory areas. In neurosurgical patients, the MEG dipole model turned out to be more reliable than fMRI in the identification of the central sulcus. This was due to prominent activation in non-primary areas in fMRI, which in some cases led to erroneous or ambiguous localization of the central sulcus.

Electrocardiographic repolarization variables in detecting myocardial infarction and ischemic injury : From body surface potential mapping to a single lead

The aim of the studies was to improve the diagnostic capability of electrocardiography (ECG) in detecting myocardial ischemic injury with a future goal of an automatic screening and monitoring method for ischemic heart disease. The method of choice was body surface potential mapping (BSPM), containing numerous leads, with intention to find the optimal recording sites and optimal ECG variables for ischemia and myocardial infarction (MI) diagnostics. The studies included 144 patients with prior MI, 79 patients with evolving ischemia, 42 patients with left ventricular hypertrophy (LVH), and 84 healthy controls. Study I examined the depolarization wave in prior MI with respect to MI location. Studies II-V examined the depolarization and repolarization waves in prior MI detection with respect to the Minnesota code, Q-wave status, and study V also with respect to MI location. In study VI the depolarization and repolarization variables were examined in 79 patients in the face of evolving myocardial ischemia and ischemic injury. When analyzed from a single lead at any recording site the results revealed superiority of the repolarization variables over the depolarization variables and over the conventional 12-lead ECG methods, both in the detection of prior MI and evolving ischemic injury. The QT integral, covering both depolarization and repolarization, appeared indifferent to the Q-wave status, the time elapsed from MI, or the MI or ischemia location. In the face of evolving ischemic injury the performance of the QT integral was not hampered even by underlying LVH. The examined depolarization and repolarization variables were effective when recorded in a single site, in contrast to the conventional 12-lead ECG criteria. The inverse spatial correlation of the depolarization and depolarization waves in myocardial ischemia and injury could be reduced into the QT integral variable recorded in a single site on the left flank. In conclusion, the QT integral variable, detectable in a single lead, with optimal recording site on the left flank, was able to detect prior MI and evolving ischemic injury more effectively than the conventional ECG markers. The QT integral, in a single-lead or a small number of leads, offers potential for automated screening of ischemic heart disease, acute ischemia monitoring and therapeutic decision-guiding as well as risk stratification.

Electromagnetic signatures of lightning near the HF frequency band

The dissertation deals with remote narrowband measurements of the electromagnetic radiation emitted by lightning flashes. A lightning flash consists of a number of sub-processes. The return stroke, which transfers electrical charge from the thundercloud to to the ground, is electromagnetically an impulsive wideband process; that is, it emits radiation at most frequencies in the electromagnetic spectrum, but its duration is only some tens of microseconds. Before and after the return stroke, multiple sub-processes redistribute electrical charges within the thundercloud. These sub-processes can last for tens to hundreds of milliseconds, many orders of magnitude longer than the return stroke. Each sub-process causes radiation with specific time-domain characteristics, having maxima at different frequencies. Thus, if the radiation is measured at a single narrow frequency band, it is difficult to identify the sub-processes, and some sub-processes can be missed altogether. However, narrowband detectors are simple to design and miniaturize. In particular, near the High Frequency band (High Frequency, 3 MHz to 30 MHz), ordinary shortwave radios can, in principle, be used as detectors. This dissertation utilizes a prototype detector which is essentially a handheld AM radio receiver. Measurements were made in Scandinavia, and several independent data sources were used to identify lightning sub-processes, as well as the distance to each individual flash. It is shown that multiple sub-processes radiate strongly near the HF band. The return stroke usually radiates intensely, but it cannot be reliably identified from the time-domain signal alone. This means that a narrowband measurement is best used to characterize the energy of the radiation integrated over the whole flash, without attempting to identify individual processes. The dissertation analyzes the conditions under which this integrated energy can be used to estimate the distance to the flash. It is shown that flash-by-flash variations are large, but the integrated energy is very sensitive to changes in the distance, dropping as approximately the inverse cube root of the distance. Flashes can, in principle, be detected at distances of more than 100 km, but since the ground conductivity can vary, ranging accuracy drops dramatically at distances larger than 20 km. These limitations mean that individual flashes cannot be ranged accurately using a single narrowband detector, and the useful range is limited to 30 kilometers at the most. Nevertheless, simple statistical corrections are developed, which enable an accurate estimate of the distance to the closest edge of an active storm cell, as well as the approach speed. The results of the dissertation could therefore have practical applications in real-time short-range lightning detection and warning systems.

Multiwavelength studies of regolith effects in planetary remote sensing

A large proportion of our knowledge about the surfaces of atmosphereless solar-system bodies is obtained through remote-sensing measurements. The measurements can be carried out either as ground-based telescopic observations or space-based observations from orbiting spacecraft. In both cases, the measurement geometry normally varies during the observations due to the orbital motion of the target body, the spacecraft, etc.. As a result, the data are acquired over a variety of viewing and illumination angles. Surfaces of planetary bodies are usually covered with a layer of loose, broken-up rock material called the regolith whose physical properties affect the directional dependence of remote-sensed measurements. It is of utmost importance for correct interpretation of the remote-sensed data to understand the processes behind this alteration. In the thesis, the multi-angular effects that the physical properties of the regolith have on remote-sensing measurements are studied in two regimes of electromagnetic radiation, visible to near infrared and soft X-rays. These effects are here termed generally the regolith effects in remote sensing. Although the physical mechanisms that are important in these regions are largely different, notable similarities arise in the methodology that is used in the study of the regolith effects, including the characterization of the regolith both in experimental studies and in numerical simulations. Several novel experimental setups have been constructed for the thesis. Alongside the experimental work, theoretical modelling has been carried out, and results from both approaches are presented. Modelling of the directional behaviour of light scattered from a regolith is utilized to obtain shape and spin-state information of several asteroids from telescopic observations and to assess the surface roughness and single-scattering properties of lunar maria from spacecraft observations. One of the main conclusions is that the azimuthal direction is an important factor in detailed studies of planetary surfaces. In addition, even a single parameter, such as porosity, can alter the light scattering properties of a regolith significantly. Surface roughness of the regolith is found to alter the elemental fluorescence line ratios of a surface obtained through planetary soft X-ray spectrometry. The results presented in the thesis are among the first to report this phenomenon. Regolith effects need to be taken into account in the analysis of remote-sensed data, providing opportunities for retrieving physical parameters of the surface through inverse methods.

The effects of marriage partners' socio-economic positions on the risk of divorce in Finland

Väitöskirjatutkimuksen tavoitteena oli selvittää, miten aviopuolisoiden sosioekonominen asema vaikuttaa avioeroriskiin Suomessa. Tutkimuksessa käytettiin Tilastokeskuksen rekistereistä koottua aineistoa, joka koskee suomalaisten ensimmäisiä avioliittoja vuoden 1990 lopussa ja avioeroja vuosina 1991−93. Väitöskirjaan sisältyy kolme osatutkimusta. Ensimmäinen osatutkimus käsitteli avioeroriskin vaihtelua aviopuolisoiden sosioekonomisen aseman eri osatekijöiden (koulutusaste, sosiaaliryhmä, pääasiallinen toiminta, tulotaso, asunnon omistaminen ja asumisahtaus) mukaan. Kaiken kaikkiaan avioeroriski oli sitä pienempi, mitä paremmassa taloudellisessa ja sosiaalisessa asemassa aviopuolisot olivat. Esimerkiksi miehen ja vaimon korkea koulutusaste, toimihenkilöammatti, työssäkäynti (etenkin verrattuna työttömyyteen) sekä omistusasunnossa asuminen liittyivät pienentyneeseen avioeroriskiin. Vaimon sosioekonomisen aseman yhteys avioeroriskiin oli paljolti samanlainen kuin miehen aseman yhteys. Huomattavin poikkeus tähän oli, että vaimon suuret tulot lisäsivät avioeroriskiä, vaikka miehen suurilla tuloilla oli päinvastainen vaikutus. Lisäksi kotitaloustyötä pääasiallisena toimintanaan tekevillä naisilla (pääasiallisen toiminnan luokka ”muut”) oli vielä pienempi avioeroriski kuin työssäkäyvillä naisilla. Toisessa osatutkimuksessa keskityttiin aviomiehen ja vaimon aseman yhdistettyyn vaikutukseen. Selviä viitteitä siitä, että puolisoiden koulutustasojen erilaisuus lisäisi eroriskiä, ei saatu. Pareilla, joissa molemmilla oli enintään perusasteen koulutus, oli kuitenkin odotettua pienempi avioeroriski. Eroriski oli suhteellisen alhainen pareilla, joissa vaimo oli työssäkäyvä tai kotitaloustyötä tekevä ja aviomies työssäkäyvä. Eroriskiä kasvatti se, että aviomies, vaimo tai molemmat puolisot olivat työttömiä. Vaimon korkea tulotaso lisäsi eroriskiä miehen kaikilla tulotasoilla mutta erityisen voimakkaasti silloin, kun miehen tulotaso oli alhainen. Kolmanneksi selvitettiin, vaikuttaako puolisoiden sosioekonominen asema avioeroriskiin eri tavalla riippuen siitä, kauanko avioliitto on kestänyt. Tällöin havaittiin, että vähän koulutettujen ja työntekijäammateissa toimivien puolisoiden suuri eroriski rajoittuu paljolti nuorimpiin avioliittoihin. Sen sijaan esim. puolisoiden työttömyys, vaimon korkea tulotaso ja vuokra-asunnossa asuminen kasvattivat eroriskiä riippumatta siitä, kuinka kauan avioliitto oli kestänyt. Kaiken kaikkiaan eroriski oli siis sitä pienempi, mitä paremmassa taloudellisessa ja sosiaalisessa asemassa puolisot olivat. Vaimon taloudellisilla ja sosiaalisilla resursseilla näyttää kuitenkin olevan myös joitakin avioeroriskiä lisääviä vaikutuksia.

Parathyroid hormone as an outcome indicator in old age

Serum parathyroid hormone (PTH) and vitamin D are the major regulators of extracellular calcium homeostasis. The inverse association between PTH and vitamin D and the common age-related elevation of the PTH concentration are well known phenomena. However, the confounding or modifying factors of this relationship and their impact on the response of PTH levels to vitamin D supplementation need further investigation. Clinical conditions such as primary hyperparathyroidism (PHPT), renal failure and vitamin D deficiency, characterized by an elevation of the PTH concentration, have been associated with impaired long-term health outcomes. Curative treatments for these conditions have also been shown to decreases PTH concentration and attenuate some of the adverse health effects. In PHPT it has also been commonly held that hypercalcaemia, the other hallmark of the disease, is the key mediator of the adverse health outcomes. In chronic kidney disease the systemic vascular disease has been proposed to have the most important impact on general health. Some evidence also indicates that vitamin D may have significant extraskeletal actions. However, the frank elevation of PTH concentration seen in advanced PHPT and in end-stage renal failure have also been suggested to be at least partly causally related to an increased risk of death as well as cognitive dysfunction. However, the exact mechanisms have remained unclear. Furthermore, the predictive value of elevated PTH in unselected older populations has been less well studied. The studies presented in this thesis investigated the impact of age and mobility on the responses of PTH levels to vitamin D deficiency and supplementation. Furthermore, the predictive value of PTH for long-term survival and cognitive decline was addressed in an unselected population of older people. The hypothesis was that age and chronic immobility are related to a persistently blunted elevation of PTH concentration, even in the presence of chronic vitamin D deficiency, and to attenuated responses of PTH to vitamin D supplementation. It was also further hypothesized that a slightly elevated or even high-normal PTH concentration is an independent indicator of an increased risk of death and cognitive decline in the general aged population. The data of this thesis are based on three samples: a meta-analysis of published vitamin D supplementation trials, a randomized placebo controlled six-month vitamin D supplementation trial, and a longitudinal prospective cohort study on a general aged population. Based on a PubMed search, a meta-analysis of 52 clinical trials with 6 290 adult participants was performed to evaluate the impact of age and immobility on the responses of PTH to 25-OHD levels and vitamin D supplementation. A total of 218 chronically immobile, very old inpatients were also enrolled into a vitamin D supplementation trial. Mortality data for these patients was also collected after a two-year follow-up. Finally, data from the Helsinki Aging Study, which followed three random age cohorts (75, 80 and 85 years) until death in almost all subjects, was used to evaluate the predictive value of PTH for long-term survival and cognitive decline. This series of studies demonstrated that in older people without overt renal failure or severe hypercalcaemia, serum 25-OHD and PTH were closely associated, but this relationship was also affected by age and immobility. Furthermore, a substantial proportion of old chronically bedridden patients did not respond to vitamin D deficiency by elevating PTH, and the effect of a high-dose (1200 IU/d) six-month cholecalciferol supplementation on the PTH concentration was minor. This study demonstrated longitudinally for the first time that the blunted PTH also persisted over time. Even a subtle elevation of PTH to high-normal levels predicted impaired long-term health outcomes. Slightly elevated PTH concentrations indicated an increased risk of clinically significant cognitive decline and death during the last years of life in a general aged population. This association was also independent of serum ionized calcium (Ca2+) and the estimated glomerular filtration rate (GFR). A slightly elevated PTH also indicated impaired two-year survival during the terminal years of frail elderly subjects independently of Ca2+, GFR, and of 25-OHD levels. The interplay between PTH and vitamin D in the regulation of calcium homeostasis is more complex than has been generally considered. In addition to muskuloskeletal health parathyroid hormone is also related to the maintenance of other important domains of health in old age. Higher PTH concentrations, even within conventional laboratory reference ranges, seem to be an independent indicator of an increased risk of all-cause and of cardiovascular mortality, independently of established cardiovascular risk factors, disturbances in mineral metabolism, and renal failure. Limited and inconsistent evidence supports the role of vitamin D deficiency-related lack of neuroprotective effects over the causal association between PTH and impaired cognitive functions. However, the causality of these associations remains unclear. The clinical implications of the observed relationships remain to be elucidated by future studies interfering with PTH concentrations, especially by long-term interventions to reduce PTH.

Search for Higgs bosons predicted in two-Higgs-doublet models via decays to tau lepton pairs in 1.96 TeV proton-antiproton collisions

We present the results of a search for Higgs bosons predicted in two-Higgs-doublet models, in the case where the Higgs bosons decay to tau lepton pairs, using 1.8 inverse fb of integrated luminosity of proton-antiproton collisions recorded by the CDF II experiment at the Fermilab Tevatron. Studying the observed mass distribution in events where one or both tau leptons decay leptonically, no evidence for a Higgs boson signal is observed. The result is used to infer exclusion limits in the two-dimensional parameter space of tan beta versus m(A).

Search for Higgs bosons predicted in two-Higgs-doublet models via decays to tau lepton pairs in 1.96 TeV proton-antiproton collisions

We present the results of a search for Higgs bosons predicted in two-Higgs-doublet models, in the case where the Higgs bosons decay to tau lepton pairs, using 1.8 inverse fb of integrated luminosity of proton-antiproton collisions recorded by the CDF II experiment at the Fermilab Tevatron. Studying the observed mass distribution in events where one or both tau leptons decay leptonically, no evidence for a Higgs boson signal is observed. The result is used to infer exclusion limits in the two-dimensional parameter space of tan beta versus m(A).

Diffractive W and Z production at the Fermilab Tevatron

We report on a measurement of the fraction of events with a W or Z boson produced diffractively in antiproton-proton collisions at a center of mass energy of 1.96 TeV, using data from 0.6 inverse femtobarns of integrated luminosity collected with the CDF-II detector equipped with a Roman-pot spectrometer that detects the antiproton (pbar) from pbar+p --> pbar+[X+W/Z]. We find that (0.97 +/- 0.11)% of Ws and (0.85 +/- 0.22)% of Zs are produced diffractively in a region of (anti)proton fractional momentum loss (\xi) of 0.03-1t p+[X+W/Z]+pbar, and on exclusive Z production, pbar+p-->pbar+Z+p. No signal is seen above background for these processes, and comparisons are made with expectations.

Search for standard model Higgs boson production in association with a W boson using a neural network discriminant at CDF

We present a search for standard model Higgs boson production in association with a W boson in proton-antiproton collisions at a center of mass energy of 1.96 TeV. The search employs data collected with the CDF II detector that correspond to an integrated luminosity of approximately 1.9 inverse fb. We select events consistent with a signature of a single charged lepton, missing transverse energy, and two jets. Jets corresponding to bottom quarks are identified with a secondary vertex tagging method, a jet probability tagging method, and a neural network filter. We use kinematic information in an artificial neural network to improve discrimination between signal and background compared to previous analyses. The observed number of events and the neural network output distributions are consistent with the standard model background expectations, and we set 95% confidence level upper limits on the production cross section times branching fraction ranging from 1.2 to 1.1 pb or 7.5 to 102 times the standard model expectation for Higgs boson masses from 110 to $150 GeV/c^2, respectively.

First Observation of Vector Boson Pairs in a Hadronic Final State at the Tevatron Collider

We present the first observation in hadronic collisions of the electroweak production of vector boson pairs (VV, V=W, Z) where one boson decays to a dijet final state. The data correspond to 3.5  fb-1 of integrated luminosity of pp̅ collisions at √s=1.96  TeV collected by the CDF II detector at the Fermilab Tevatron. We observe 1516±239(stat)±144(syst) diboson candidate events and measure a cross section σ(pp̅ →VV+X) of 18.0±2.8(stat)±2.4(syst)±1.1(lumi)  pb, in agreement with the expectations of the standard model.

First Observation of Vector Boson Pairs in a Hadronic Final State at the Tevatron Collider

We present the first observation in hadronic collisions of the electroweak production of vector boson pairs (VV, V=W,Z) where one boson decays to a dijet final state . The data correspond to 3.5 inverse femtobarns of integrated luminosity of ppbar collisions at sqrt(s)=1.96 TeV collected by the CDFII detector at the Fermilab Tevatron. We observe 1516+/-239(stat)+/-144(syst) diboson candidate events and measure a cross section sigma(ppbar->VV+X) of 18.0+/-2.8(stat)+/-2.4(syst)+/-1.1(lumi) pb, in agreement with the expectations of the standard model.