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.

AndroMedia - Towards a Context-aware Mobile Music Recommender

Portable music players have made it possible to listen to a personal collection of music in almost every situation, and they are often used during some activity to provide a stimulating audio environment. Studies have demonstrated the effects of music on the human body and mind, indicating that selecting music according to situation can, besides making the situation more enjoyable, also make humans perform better. For example, music can boost performance during physical exercises, alleviate stress and positively affect learning. We believe that people intuitively select different types of music for different situations. Based on this hypothesis, we propose a portable music player, AndroMedia, designed to provide personalised music recommendations using the user’s current context and listening habits together with other user’s situational listening patterns. We have developed a prototype that consists of a central server and a PDA client. The client uses Bluetooth sensors to acquire context information and logs user interaction to infer implicit user feedback. The user interface also allows the user to give explicit feedback. Large user interface elements facilitate touch-based usage in busy environments. The prototype provides the necessary framework for using the collected information together with other user’s listening history in a context- enhanced collaborative filtering algorithm to generate context-sensitive recommendations. The current implementation is limited to using traditional collaborative filtering algorithms. We outline the techniques required to create context-aware recommendations and present a survey on mobile context-aware music recommenders found in literature. As opposed to the explored systems, AndroMedia utilises other users’ listening habits when suggesting tunes, and does not require any laborious set up processes.

Modeling ecological and evolutionary processes in spatially structured populations

Many species inhabit fragmented landscapes, resulting either from anthropogenic or from natural processes. The ecological and evolutionary dynamics of spatially structured populations are affected by a complex interplay between endogenous and exogenous factors. The metapopulation approach, simplifying the landscape to a discrete set of patches of breeding habitat surrounded by unsuitable matrix, has become a widely applied paradigm for the study of species inhabiting highly fragmented landscapes. In this thesis, I focus on the construction of biologically realistic models and their parameterization with empirical data, with the general objective of understanding how the interactions between individuals and their spatially structured environment affect ecological and evolutionary processes in fragmented landscapes. I study two hierarchically structured model systems, which are the Glanville fritillary butterfly in the Åland Islands, and a system of two interacting aphid species in the Tvärminne archipelago, both being located in South-Western Finland. The interesting and challenging feature of both study systems is that the population dynamics occur over multiple spatial scales that are linked by various processes. My main emphasis is in the development of mathematical and statistical methodologies. For the Glanville fritillary case study, I first build a Bayesian framework for the estimation of death rates and capture probabilities from mark-recapture data, with the novelty of accounting for variation among individuals in capture probabilities and survival. I then characterize the dispersal phase of the butterflies by deriving a mathematical approximation of a diffusion-based movement model applied to a network of patches. I use the movement model as a building block to construct an individual-based evolutionary model for the Glanville fritillary butterfly metapopulation. I parameterize the evolutionary model using a pattern-oriented approach, and use it to study how the landscape structure affects the evolution of dispersal. For the aphid case study, I develop a Bayesian model of hierarchical multi-scale metapopulation dynamics, where the observed extinction and colonization rates are decomposed into intrinsic rates operating specifically at each spatial scale. In summary, I show how analytical approaches, hierarchical Bayesian methods and individual-based simulations can be used individually or in combination to tackle complex problems from many different viewpoints. In particular, hierarchical Bayesian methods provide a useful tool for decomposing ecological complexity into more tractable components.

Below-ground processes in meadow soil under elevated ozone and carbon dioxide : - Greenhouse gas fluxes, N cycling and microbial communities

This thesis focuses on how elevated CO2 and/or O3 affect the below-ground processes in semi-natural vegetation, with an emphasis on greenhouse gases, N cycling and microbial communities. Meadow mesocosms mimicking lowland hay meadows in Jokioinen, SW Finland, were enclosed in open-top chambers and exposed to ambient and elevated levels of O3 (40-50 ppb) and/or CO2 (+100 ppm) for three consecutive growing season, while chamberless plots were used as chamber controls. Chemical and microbiological analyses as well as laboratory incubations of the mesocosm soils under different treatments were used to study the effects of O3 and/or CO2. Artificially constructed mesocosms were also compared with natural meadows with regards to GHG fluxes and soil characteristics. In addition to research conducted at the ecosystem level (i.e. the mesocosm study), soil microbial communities were also examined in a pot experiment with monocultures of individual species. By comparing mesocosms with similar natural plant assemblage, it was possible to demonstrate that artificial mesocosms simulated natural habitats, even though some differences were found in the CH4 oxidation rate, soil mineral N, and total C and N concentrations in the soil. After three growing seasons of fumigations, the fluxes of N2O, CH4, and CO2 were decreased in the NF+O3 treatment, and the soil NH4+-N and mineral N concentrations were lower in the NF+O3 treatment than in the NF control treatment. The mesocosm soil microbial communities were affected negatively by the NF+O3 treatment, as the total, bacterial, actinobacterial, and fungal PLFA biomasses as well as the fungal:bacterial biomass ratio decreased under elevated O3. In the pot survey, O3 decreased the total, bacterial, actinobacterial, and mycorrhizal PLFA biomasses in the bulk soil and affected the microbial community structure in the rhizosphere of L. pratensis, whereas the bulk soil and rhizosphere of the other monoculture, A. capillaris, remained unaffected by O3. Elevated CO2 caused only minor and insignificant changes in the GHG fluxes, N cycling, and the microbial community structure. In the present study, the below-ground processes were modified after three years of moderate O3 enhancement. A tentative conclusion is that a decrease in N availability may have feedback effects on plant growth and competition and affect the N cycling of the whole meadow ecosystem. Ecosystem level changes occur slowly, and multiplication of the responses might be expected in the long run.

Behavioural, population, and genetic processes affecting metapopulation dynamics of the Glanville fritillary butterfly

In my thesis I have been studying the effects of population fragmentation and extinction-recolonization dynamics on genetic and evolutionary processes in the Glanville fritillary butterfly (Melitaea cinxia). By conducting crosses within and among newly-colonized populations and using several fitness measures, I found a strong decrease in fitness following colonization by a few related individuals, and a strong negative relationship between parental relatedness and offspring fitness. Thereafter, I was interested in determining the number and relatedness of individuals colonizing new populations, which I did using a set of microsatellites I had previously developed for this species. Additionally, I am interested in the evolution of key life-history traits. By following the lifetime reproductive success of males emerging at different times in a semi-natural setup, I demonstrated that protandry is adaptive in males, and I was able to rule out, for M. cinxia, alternative incidental hypotheses evoked to explain the evolution of protandry in insects. Finally, in work I did together with Prof. Hanna Kokko, I am proposing bet-hedging as a new mechanism that could explain the evolution of polyandry in M. cinxia.

Aerosol Particle Formation: Meteorological and Synoptic Processes behind the Event

Aerosol particles in the atmosphere are known to significantly influence ecosystems, to change air quality and to exert negative health effects. Atmospheric aerosols influence climate through cooling of the atmosphere and the underlying surface by scattering of sunlight, through warming of the atmosphere by absorbing sun light and thermal radiation emitted by the Earth surface and through their acting as cloud condensation nuclei. Aerosols are emitted from both natural and anthropogenic sources. Depending on their size, they can be transported over significant distances, while undergoing considerable changes in their composition and physical properties. Their lifetime in the atmosphere varies from a few hours to a week. New particle formation is a result of gas-to-particle conversion. Once formed, atmospheric aerosol particles may grow due to condensation or coagulation, or be removed by deposition processes. In this thesis we describe analyses of air masses, meteorological parameters and synoptic situations to reveal conditions favourable for new particle formation in the atmosphere. We studied the concentration of ultrafine particles in different types of air masses, and the role of atmospheric fronts and cloudiness in the formation of atmospheric aerosol particles. The dominant role of Arctic and Polar air masses causing new particle formation was clearly observed at Hyytiälä, Southern Finland, during all seasons, as well as at other measurement stations in Scandinavia. In all seasons and on multi-year average, Arctic and North Atlantic areas were the sources of nucleation mode particles. In contrast, concentrations of accumulation mode particles and condensation sink values in Hyytiälä were highest in continental air masses, arriving at Hyytiälä from Eastern Europe and Central Russia. The most favourable situation for new particle formation during all seasons was cold air advection after cold-front passages. Such a period could last a few days until the next front reached Hyytiälä. The frequency of aerosol particle formation relates to the frequency of low-cloud-amount days in Hyytiälä. Cloudiness of less than 5 octas is one of the factors favouring new particle formation. Cloudiness above 4 octas appears to be an important factor that prevents particle growth, due to the decrease of solar radiation, which is one of the important meteorological parameters in atmospheric particle formation and growth. Keywords: Atmospheric aerosols, particle formation, air mass, atmospheric front, cloudiness

Investigations of planetary boundary layer processes and particle formation in the atmosphere of planet Mars

The planet Mars is the Earth's neighbour in the Solar System. Planetary research stems from a fundamental need to explore our surroundings, typical for mankind. Manned missions to Mars are already being planned, and understanding the environment to which the astronauts would be exposed is of utmost importance for a successful mission. Information of the Martian environment given by models is already now used in designing the landers and orbiters sent to the red planet. In particular, studies of the Martian atmosphere are crucial for instrument design, entry, descent and landing system design, landing site selection, and aerobraking calculations. Research of planetary atmospheres can also contribute to atmospheric studies of the Earth via model testing and development of parameterizations: even after decades of modeling the Earth's atmosphere, we are still far from perfect weather predictions. On a global level, Mars has also been experiencing climate change. The aerosol effect is one of the largest unknowns in the present terrestrial climate change studies, and the role of aerosol particles in any climate is fundamental: studies of climate variations on another planet can help us better understand our own global change. In this thesis I have used an atmospheric column model for Mars to study the behaviour of the lowest layer of the atmosphere, the planetary boundary layer (PBL), and I have developed nucleation (particle formation) models for Martian conditions. The models were also coupled to study, for example, fog formation in the PBL. The PBL is perhaps the most significant part of the atmosphere for landers and humans, since we live in it and experience its state, for example, as gusty winds, nightfrost, and fogs. However, PBL modelling in weather prediction models is still a difficult task. Mars hosts a variety of cloud types, mainly composed of water ice particles, but also CO2 ice clouds form in the very cold polar night and at high altitudes elsewhere. Nucleation is the first step in particle formation, and always includes a phase transition. Cloud crystals on Mars form from vapour to ice on ubiquitous, suspended dust particles. Clouds on Mars have a small radiative effect in the present climate, but it may have been more important in the past. This thesis represents an attempt to model the Martian atmosphere at the smallest scales with high resolution. The models used and developed during the course of the research are useful tools for developing and testing parameterizations for larger-scale models all the way up to global climate models, since the small-scale models can describe processes that in the large-scale models are reduced to subgrid (not explicitly resolved) scale.

Dynamical processes in the stratosphere and upper troposphere and their influence on the distribution of trace gases in the polar atmosphere

Transport plays an important role in the distribution of long-lived gases such as ozone and water vapour in the atmosphere. Understanding of observed variability in these gases as well as prediction of the future changes depends therefore on our knowledge of the relevant atmospheric dynamics. This dissertation studies certain dynamical processes in the stratosphere and upper troposphere which influence the distribution of ozone and water vapour in the atmosphere. The planetary waves that originate in the troposphere drive the stratospheric circulation. They influence both the meridional transport of substances as well as parameters of the polar vortices. In turn, temperatures inside the polar vortices influence abundance of the Polar Stratospheric Clouds (PSC) and therefore the chemical ozone destruction. Wave forcing of the stratospheric circulation is not uniform during winter. The November-December averaged stratospheric eddy heat flux shows a significant anticorrelation with the January-February averaged eddy heat flux in the midlatitude stratosphere and troposphere. These intraseasonal variations are attributable to the internal stratospheric vacillations. In the period 1979-2002, the wave forcing exhibited a negative trend which was confined to the second half of winter only. In the period 1958-2002, area, strength and longevity of the Arctic polar vortices do not exhibit significant long-term changes while the area with temperatures lower than the threshold temperature for PSC formation shows statistically significant increase. However, the Arctic vortex parameters show significant decadal changes which are mirrored in the ozone variability. Monthly ozone tendencies in the Northern Hemisphere show significant correlations (|r|=0.7) with proxies of the stratospheric circulation. In the Antarctic, the springtime vortex in the lower stratosphere shows statistically significant trends in temperature, longevity and strength (but not in area) in the period 1979-2001. Analysis of the ozone and water vapour vertical distributions in the Arctic UTLS shows that layering below and above the tropopause is often associated with poleward Rossby wave-breaking. These observations together with calculations of cross-tropopause fluxes emphasize the importance of poleward Rossby wave breaking for the stratosphere-troposphere exchange in the Arctic.

Ultrastructure of Biofilms Formed by Bacteria from Industrial Processes

Microorganisms exist predominantly as sessile multispecies communities in natural habitats. Most bacterial species can form these matrix-enclosed microbial communities called biofilms. Biofilms occur in a wide range of environments, on every surface with sufficient moisture and nutrients, also on surfaces in industrial settings and engineered water systems. This unwanted biofilm formation on equipment surfaces is called biofouling. Biofouling can significantly decrease equipment performance and lifetime and cause contamination and impaired quality of the industrial product. In this thesis we studied bacterial adherence to abiotic surfaces by using coupons of stainless steel coated or not coated with fluoropolymer or diamond like carbon (DLC). As model organisms we used bacterial isolates from paper machines (Meiothermus silvanus, Pseudoxanthomonas taiwanensis and Deinococcus geothermalis) and also well characterised species isolated from medical implants (Staphylococcus epidermidis). We found that coating of steel surface with these materials reduced its tendency towards biofouling: Fluoropolymer and DLC coatings repelled all four biofilm formers on steel. We found great differences between bacterial species in their preference of surfaces to adhere as well as their ultrastructural details, like number and thickness of adhesion organelles they expressed. These details responded differently towards the different surfaces they adhered to. We further found that biofilms of D. geothermalis formed on titanium dioxide coated coupons of glass, steel and titanium, were effectively removed by photocatalytic action in response to irradiation at 360 nm. However, on non-coated glass or steel surfaces irradiation had no detectable effect on the amount of bacterial biomass. We showed that the adhesion organelles of bacteria on illuminated TiO2 coated coupons were complety destroyed whereas on non-coated coupons they looked intact when observed by microscope. Stainless steel is the most widely used material for industrial process equipments and surfaces. The results in this thesis showed that stainless steel is prone to biofouling by phylogenetically distant bacterial species and that coating of the steel may offer a tool for reduced biofouling of industrial equipment. Photocatalysis, on the other hand, is a potential technique for biofilm removal from surfaces in locations where high level of hygiene is required. Our study of natural biofilms on barley kernel surfaces showed that also there the microbes possessed adhesion organelles visible with electronmicroscope both before and after steeping. The microbial community of dry barley kernels turned into a dense biofilm covered with slimy extracellular polymeric substance (EPS) in the kernels after steeping in water. Steeping is the first step in malting. We also presented evidence showing that certain strains of Lactobacillus plantarum and Wickerhamomyces anomalus, when used as starter cultures in the steeping water, could enter the barley kernel and colonise the tissues of the barley kernel. By use of a starter culture it was possible to reduce the extensive production of EPS, which resulted in a faster filtration of the mash.

Designing a blended learning model for primary school language learning

In Finland, there is a desperate need for flexible, reliable and functional multi-e-learning settings for pupils aged 11-13. Southern Finland has several ongoing e-learning projects, but none that develop a multiple setting, with learning and teaching occurring between more than two schools. In 2006, internet connections were not broadband and data transfer was mainly audio data. Connections and technical problems occurred, which were an obstacle to multi-e-learning. Internet connections today enable web-based learning in major parts of
Lapland and by 2015, broadband will reach even the remotest villages up north. Therefore, it is important to research the possibilities of multi-e-learning and to build collaborative, learner-centred, versatile network models for primary school-aged pupils. The resulting model will facilitate distance learning to extend education to rural, sparsely populated areas, and it will give a model of using mobile devices in language portfolios. This will promote regional equality and prevent exclusion. Working with portfolios provides the opportunity to develop mobility from a pedagogical point of view. It is important to study the pros and cons of mobile devices in producing artefacts on portfolios in e-learning and language learning settings.
The current study represents a design-based research approach. The design research approach includes two important aspects concerning the current research: ‘a teacher as researcher’ aspect, which means there is the possibility to be strongly involved in developing processes and an obstacle-aspect, which means that problems while developing, are seen as a
promoter in evolving the designed model, as apposed to negative results.

Designing a blended learning model for primary school language learning

In Finland, there is a desperate need for flexible, reliable and functional multi-e-learning settings for pupils aged 11-13. Southern Finland has several ongoing e-learning projects, but none that develop a multiple setting, with learning and teaching occurring between more than two schools. In 2006, internet connections were not broadband and data transfer was mainly audio data. Connections and technical problems occurred, which were an obstacle to multi-e-learning. Internet connections today enable web-based learning in major parts of Lapland and by 2015, broadband will reach even the remotest villages up north. Therefore, it is important to research the possibilities of multi-e-learning and to build collaborative, learner-centred, versatile network models for primary school-aged pupils. The resulting model will facilitate distance learning to extend education to rural, sparsely populated areas, and it will give a model of using mobile devices in language portfolios. This will promote regional equality and prevent exclusion. Working with portfolios provides the opportunity to develop mobility from a pedagogical point of view. It is important to study the pros and cons of mobile devices in producing artefacts on portfolios in e-learning and language learning settings. The current study represents a design-based research approach. The design research approach includes two important aspects concerning the current research: ‘a teacher as researcher’ aspect, which means there is the possibility to be strongly involved in developing processes and an obstacle-aspect, which means that problems while developing, are seen as a promoter in evolving the designed model, as apposed to negative results.

Perspectives on knowledge creating inquiry in higher education

Higher education is faced with the challenge of strengthening students competencies for the constantly evolving technology-mediated practices of knowledge work. The knowledge creation approach to learning (Paavola et al., 2004; Hakkarainen et al., 2004) provides a theoretical tool to address learning and teaching organized around complex problems and the development of shared knowledge objects, such as reports, products, and new practices. As in professional work practices, it appears necessary to design sufficient open-endedness and complexity for students teamwork in order to generate unpredictable and both practically and epistemologically challenging situations. The studies of the thesis examine what kinds of practices are observed when student teams engage in knowledge creating inquiry processes, how the students themselves perceive the process, and how to facilitate inquiry with technology-mediation, tutoring, and pedagogical models. Overall, 20 student teams collaboration processes and productions were investigated in detail. This collaboration took place in teams or small groups of 3-6 students from multiple domain backgrounds. Two pedagogical models were employed to provide heuristic guidance for the inquiry processes: the progressive inquiry model and the distributed project model. Design-based research methodology was employed in combination with case study as the research design. Database materials from the courses virtual learning environment constituted the main body of data, with additional data from students self-reflections and student and teacher interviews. Study I examined the role of technology mediation and tutoring in directing students knowledge production in a progressive inquiry process. The research investigated how the scale of scaffolding related to the nature of knowledge produced and the deepening of the question explanation process. In Study II, the metaskills of knowledge-creating inquiry were explored as a challenge for higher education: metaskills refers to the individual, collective, and object-centered aspects of monitoring collaborative inquiry. Study III examined the design of two courses and how the elaboration of shared objects unfolded based on the two pedagogical models. Study IV examined how the arranged concept-development project for external customers promoted practices of distributed, partially virtual, project work, and how the students coped with the knowledge creation challenge. Overall, important indicators of knowledge creating inquiry were the following: new versions of knowledge objects and artifacts demonstrated a deepening inquiry process; and the various productions were co-created through iterations of negotiations, drafting, and versioning by the team members. Students faced challenges of establishing a collective commitment, devising practices to co-author and advance their reports, dealing with confusion, and managing culturally diverse teams. The progressive inquiry model, together with tutoring and technology, facilitated asking questions, generating explanations, and refocusing lines of inquiry. The involvement of the customers was observed to provide a strong motivation for the teams. On the evidence, providing team-specific guidance, exposing students to models of scientific argumentation and expert work practices, and furnishing templates for the intended products appear to be fruitful ways to enhance inquiry processes. At the institutional level, educators do well to explore ways of developing collaboration with external customers, public organizations or companies, and between educational units in order to enhance educational practices of knowledge creating inquiry.

Canopy processes, fluxes and microclimate in a pine forest

Interaction between forests and the atmosphere occurs by radiative and turbulent transport. The fluxes of energy and mass between surface and the atmosphere directly influence the properties of the lower atmosphere and in longer time scales the global climate. Boreal forest ecosystems are central in the global climate system, and its responses to human activities, because they are significant sources and sinks of greenhouse gases and of aerosol particles. The aim of the present work was to improve our understanding on the existing interplay between biologically active canopy, microenvironment and turbulent flow and quantify. In specific, the aim was to quantify the contribution of different canopy layers to whole forest fluxes. For this purpose, long-term micrometeorological and ecological measurements made in a Scots pine (Pinus sylvestris) forest at SMEAR II research station in Southern Finland were used. The properties of turbulent flow are strongly modified by the interaction between the canopy elements: momentum is efficiently absorbed in the upper layers of the canopy, mean wind speed and turbulence intensities decrease rapidly towards the forest floor and power spectra is modulated by spectral short-cut . In the relative open forest, diabatic stability above the canopy explained much of the changes in velocity statistics within the canopy except in strongly stable stratification. Large eddies, ranging from tens to hundred meters in size, were responsible for the major fraction of turbulent transport between a forest and the atmosphere. Because of this, the eddy-covariance (EC) method proved to be successful for measuring energy and mass exchange inside a forest canopy with exception of strongly stable conditions. Vertical variations of within canopy microclimate, light attenuation in particular, affect strongly the assimilation and transpiration rates. According to model simulations, assimilation rate decreases with height more rapidly than stomatal conductance (gs) and transpiration and, consequently, the vertical source-sink distributions for carbon dioxide (CO2) and water vapor (H2O) diverge. Upscaling from a shoot scale to canopy scale was found to be sensitive to chosen stomatal control description. The upscaled canopy level CO2 fluxes can vary as much as 15 % and H2O fluxes 30 % even if the gs models are calibrated against same leaf-level dataset. A pine forest has distinct overstory and understory layers, which both contribute significantly to canopy scale fluxes. The forest floor vegetation and soil accounted between 18 and 25 % of evapotranspiration and between 10 and 20 % of sensible heat exchange. Forest floor was also an important deposition surface for aerosol particles; between 10 and 35 % of dry deposition of particles within size range 10 30 nm occurred there. Because of the northern latitudes, seasonal cycle of climatic factors strongly influence the surface fluxes. Besides the seasonal constraints, partitioning of available energy to sensible and latent heat depends, through stomatal control, on the physiological state of the vegetation. In spring, available energy is consumed mainly as sensible heat and latent heat flux peaked about two months later, in July August. On the other hand, annual evapotranspiration remains rather stable over range of environmental conditions and thus any increase of accumulated radiation affects primarily the sensible heat exchange. Finally, autumn temperature had strong effect on ecosystem respiration but its influence on photosynthetic CO2 uptake was restricted by low radiation levels. Therefore, the projected autumn warming in the coming decades will presumably reduce the positive effects of earlier spring recovery in terms of carbon uptake potential of boreal forests.

Searching the inclusive ℓγE̸T+b-quark signature for radiative top quark decay and non-standard-model processes

In a search for new phenomena in a signature suppressed in the standard model of elementary particles (SM), we compare the inclusive production of events containing a lepton, a photon, significant transverse momentum imbalance (MET), and a jet identified as containing a b-quark, to SM predictions. The search uses data produced in proton-antiproton collisions at 1.96 TeV corresponding to 1.9 fb-1 of integrated luminosity taken with the CDF detector at the Fermilab Tevatron. We find 28 lepton+photon+MET+b events versus an expectation of 31.0+4.1/-3.5 events. If we further require events to contain at least three jets and large total transverse energy, simulations predict that the largest SM source is top-quark pair production with an additional radiated photon, ttbar+photon. In the data we observe 16 ttbar+photon candidate events versus an expectation from SM sources of 11.2+2.3/-2.1. Assuming the difference between the observed number and the predicted non-top-quark total is due to SM top quark production, we estimate the ttg cross section to be 0.15 +- 0.08 pb.