Analysing local algorithms in location-aware quasi-unit-disk graphs

A local algorithm with local horizon r is a distributed algorithm that runs in r synchronous communication rounds; here r is a constant that does not depend on the size of the network. As a consequence, the output of a node in a local algorithm only depends on the input within r hops from the node. We give tight bounds on the local horizon for a class of local algorithms for combinatorial problems on unit-disk graphs (UDGs). Most of our bounds are due to a refined analysis of existing approaches, while others are obtained by suggesting new algorithms. The algorithms we consider are based on network decompositions guided by a rectangular tiling of the plane. The algorithms are applied to matching, independent set, graph colouring, vertex cover, and dominating set. We also study local algorithms on quasi-UDGs, which are a popular generalisation of UDGs, aimed at more realistic modelling of communication between the network nodes. Analysing the local algorithms on quasi-UDGs allows one to assume that the nodes know their coordinates only approximately, up to an additive error. Despite the localisation error, the quality of the solution to problems on quasi-UDGs remains the same as for the case of UDGs with perfect location awareness. We analyse the increase in the local horizon that comes along with moving from UDGs to quasi-UDGs.

Novel insights on functions of myotilin/palladin family members

Poikkijuovaisen luuranko- ja sydänlihaksen supistumisyksikkö, sarkomeeri, koostuu tarkoin järjestyneistä aktiini- ja myosiinisäikeistä. Rakenne eroaa muista solutyypeistä, joissa aktiinisäikeistö muovautuu jatkuvasti ja sen järjestyminen säätelee solun muotoa, solujakautumista, soluliikettä ja solunsisäisten organellien kuljetusta. Myotilin, palladin ja myopalladin kuuluvat proteiiniperheeseen, jonka yhteispiirteenä ovat immunoglobuliinin kaltaiset (Igl) domeenit. Proteiinit liittyvät aktiinitukirankaan ja niiden arvellaan toimivan solutukirangan rakenne-elementteinä ja säätelijöinä. Myotilinia ja myopalladinia ilmennetään poikkijuovaisessa lihaksessa. Sen sijaan palladinin eri silmukointimuotoja tavataan monissa kudostyypeissä kuten hermostossa, ja eri muodoilla saattaa olla solutyypistä riippuvia tehtäviä. Poikkijuovaisessa lihaksessa kaikki perheen jäsenet sijaitsevat aktiinisäikeitä yhdistävässä Z-levyssä ja ne sitovat Z-levyn rakenneproteiinia, -aktiniinia. Myotilingeenin pistemutaatiot johtavat periytyviin lihastauteihin, kun taas palladinin mutaatioiden on kuvattu liittyvän periytyvään haimasyöpään ja lisääntyneeseen sydäninfarktin riskiin. Tässä tutkimuksessa selvitettin myotilinin ja pallainin toimintaa. Kokeissa löydettiin uusia palladinin 90-92kDa alatyyppiin sitoutuvia proteiineja. Yksi niistä on aktiinidynamiikkaa säätelevä profilin. Profilinilla on kahdenlaisia tehtäviä; se edesauttaa aktiinisäikeiden muodostumista, mutta se voi myös eristää yksittäisiä aktiinimolekyylejä ja edistää säikeiden hajoamista. Solutasolla palladinin ja profilinin sijainti on yhtenevä runsaasti aktiinia sisältävillä solujen reuna-alueilla. Palladinin ja profilinin sidos on heikko ja hyvin dynaaminen, joka sopii palladinin tehtävään aktiinisäideiden muodostumisen koordinoijana. Toinen palladinin sitoutumiskumppani on aktiinisäikeitä yhteensitova -aktiniini. -Aktiniini liittää solutukirangan solukalvon proteiineihin ja ankkuroi solunsisäisiä viestintämolekyylejä. Sitoutumista välittävä alue on hyvin samankaltainen palladinissa ja myotilinissa. Luurankolihaksen liiallinen toistuva venytys muuttaa Z-levyjen rakennetta ja muotoa. Prosessin aikana syntyy uusia aktiinifilamenttejä sisältäviä tiivistymiä ja lopulta uusia sarkomeereja. Löydöstemme perusteella myotilinin uudelleenjärjestyminen noudattaa aktiinin muutoksia. Tämä viittaa siihen, että myotilin liittää yhteen uudismuodostuvia aktiinisäikeitä ja vakauttaa niitä. Myotilin saattaa myös ankkuroida viesti- tai rakennemolekyylejä, joiden tehtävänä on edesauttaa Z-levyjen uudismuodostusta. Tulostemme perusteella arvelemme, että myotilin toimii Z-levyjen rakenteen vakaajana ja aktiinisäikeiden säätelijänä. Palladinin puute johtaa sikiöaikaiseen kuolemaan hiirillä, mutta myotilinin puutoksella ei ole samanlaisia vaikutuksia. Tuotettujen myotilin poistogeenisten hiirten todetiin syntyvän ja kehittyvän normaalisti eikä niillä esiintynyt rakenteellisia tai toiminnallisia häiriöitä. Toisaalta aiemmissa kokeissa, joissa hiirille on siirretty ihmisen lihastautia aikaansaava myotilingeeni, nähdään samankaltaisia kuin sairailla ihmisillä. Näin ollen muuntunut myotilin näyttä olevan lihaksen toiminnalle haitallisempi kuin myotilinin puute. Myotilinin ja palladinin yhteisvaikutusta selvittääksemme risteytimme myotilin poistegeenisen hiiren ja hiirilinjan, joka ilmentää puutteellisesti palladinin 200 kDa muotoa. Puutteellisesti 200 kDa palladinia ilmentävien hiirten sydänlihaksessa todettiin vähäisiä hienorakenteen muutoksia, mutta risteytetyillä hiirillä tavattiin rakenteellisia ja toiminnallisia muutoksia myös luurankolihaksessa. Tulosten perusteella voidaan todeta, että palladinin 200 kDa muoto säätelee sydänlihassolujen rakennetta. Luurankolihaksessa sen sijaan myotilinilla ja palladinilla näyttäisi olevan päällekkäisiä tehtäviä.

Composition operators on vector-valued BMOA and related function spaces

A composition operator is a linear operator between spaces of analytic or harmonic functions on the unit disk, which precomposes a function with a fixed self-map of the disk. A fundamental problem is to relate properties of a composition operator to the function-theoretic properties of the self-map. During the recent decades these operators have been very actively studied in connection with various function spaces. The study of composition operators lies in the intersection of two central fields of mathematical analysis; function theory and operator theory. This thesis consists of four research articles and an overview. In the first three articles the weak compactness of composition operators is studied on certain vector-valued function spaces. A vector-valued function takes its values in some complex Banach space. In the first and third article sufficient conditions are given for a composition operator to be weakly compact on different versions of vector-valued BMOA spaces. In the second article characterizations are given for the weak compactness of a composition operator on harmonic Hardy spaces and spaces of Cauchy transforms, provided the functions take values in a reflexive Banach space. Composition operators are also considered on certain weak versions of the above function spaces. In addition, the relationship of different vector-valued function spaces is analyzed. In the fourth article weighted composition operators are studied on the scalar-valued BMOA space and its subspace VMOA. A weighted composition operator is obtained by first applying a composition operator and then a pointwise multiplier. A complete characterization is given for the boundedness and compactness of a weighted composition operator on BMOA and VMOA. Moreover, the essential norm of a weighted composition operator on VMOA is estimated. These results generalize many previously known results about composition operators and pointwise multipliers on these spaces.

Aspects of atomic decompositions and Bergman projections

The concept of an atomic decomposition was introduced by Coifman and Rochberg (1980) for weighted Bergman spaces on the unit disk. By the Riemann mapping theorem, functions in every simply connected domain in the complex plane have an atomic decomposition. However, a decomposition resulting from a conformal mapping of the unit disk tends to be very implicit and often lacks a clear connection to the geometry of the domain that it has been mapped into. The lattice of points, where the atoms of the decomposition are evaluated, usually follows the geometry of the original domain, but after mapping the domain into another this connection is easily lost and the layout of points becomes seemingly random. In the first article we construct an atomic decomposition directly on a weighted Bergman space on a class of regulated, simply connected domains. The construction uses the geometric properties of the regulated domain, but does not explicitly involve any conformal Riemann map from the unit disk. It is known that the Bergman projection is not bounded on the space L-infinity of bounded measurable functions. Taskinen (2004) introduced the locally convex spaces LV-infinity consisting of measurable and HV-infinity of analytic functions on the unit disk with the latter being a closed subspace of the former. They have the property that the Bergman projection is continuous from LV-infinity onto HV-infinity and, in some sense, the space HV-infinity is the smallest possible substitute to the space H-infinity of analytic functions. In the second article we extend the above result to a smoothly bounded strictly pseudoconvex domain. Here the related reproducing kernels are usually not known explicitly, and thus the proof of continuity of the Bergman projection is based on generalised Forelli-Rudin estimates instead of integral representations. The minimality of the space LV-infinity is shown by using peaking functions first constructed by Bell (1981). Taskinen (2003) showed that on the unit disk the space HV-infinity admits an atomic decomposition. This result is generalised in the third article by constructing an atomic decomposition for the space HV-infinity on a smoothly bounded strictly pseudoconvex domain. In this case every function can be presented as a linear combination of atoms such that the coefficient sequence belongs to a suitable Köthe co-echelon space.

Methicillin-resistant Staphylococcus aureus in Finland: recent changes in the epidemiology, long-term facility aspects, and phenotypic and molecular detection of isolates

Staphylococcus aureus is one of the most important bacteria that cause disease in humans, and methicillin-resistant S. aureus (MRSA) has become the most commonly identified antibiotic-resistant pathogen in many parts of the world. MRSA rates have been stable for many years in the Nordic countries and the Netherlands with a low MRSA prevalence in Europe, but in the recent decades, MRSA rates have increased in those low-prevalence countries as well. MRSA has been established as a major hospital pathogen, but has also been found increasingly in long-term facilities (LTF) and in communities of persons with no connections to the health-care setting. In Finland, the annual number of MRSA isolates reported to the National Infectious Disease Register (NIDR) has constantly increased, especially outside the Helsinki metropolitan area. Molecular typing has revealed numerous outbreak strains of MRSA, some of which have previously been associated with community acquisition. In this work, data on MRSA cases notified to the NIDR and on MRSA strain types identified with pulsed-field gel electrophoresis (PFGE), multilocus sequence typing (MLST), and staphylococcal cassette chromosome mec (SCCmec) typing at the National Reference Laboratory (NRL) in Finland from 1997 to 2004 were analyzed. An increasing trend in MRSA incidence in Finland from 1997 to 2004 was shown. In addition, non-multi-drug resistant (NMDR) MRSA isolates, especially those resistant only to methicillin/oxacillin, showed an emerging trend. The predominant MRSA strains changed over time and place, but two internationally spread epidemic strains of MRSA, FIN-16 and FIN-21, were related to the increase detected most recently. Those strains were also one cause of the strikingly increasing invasive MRSA findings. The rise of MRSA strains with SCCmec types IV or V, possible community-acquired MRSA was also detected. With questionnaires, the diagnostic methods used for MRSA identification in Finnish microbiology laboratories and the number of MRSA screening specimens studied were reviewed. Surveys, which focused on the MRSA situation in long-term facilities in 2001 and on the background information of MRSA-positive persons in 2001-2003, were also carried out. The rates of MRSA and screening practices varied widely across geographic regions. Part of the NMDR MRSA strains could remain undetected in some laboratories because of insufficient diagnostic techniques used. The increasing proportion of elderly population carrying MRSA suggests that MRSA is an emerging problem in Finnish long-term facilities. Among the patients, 50% of the specimens were taken on a clinical basis, 43% on a screening basis after exposure to MRSA, 3% on a screening basis because of hospital contact abroad, and 4% for other reasons. In response to an outbreak of MRSA possessing a new genotype that occurred in a health care ward and in an associated nursing home of a small municipality in Northern Finland in autumn 2003, a point-prevalence survey was performed six months later. In the same study, the molecular epidemiology of MRSA and methicillin-sensitive S. aureus (MSSA) strains were also assessed, the results to the national strain collection compared, and the difficulties of MRSA screening with low-level oxacillin-resistant isolates encountered. The original MRSA outbreak in LTF, which consisted of isolates possessing a nationally new PFGE profile (FIN-22) and internationally rare MLST type (ST-27), was confined. Another previously unrecognized MRSA strain was found with additional screening, possibly indicating that current routine MRSA screening methods may be insufficiently sensitive for strains possessing low-level oxacillin resistance. Most of the MSSA strains found were genotypically related to the epidemic MRSA strains, but only a few of them had received the SCCmec element, and all those strains possessed the new SCCmec type V. In the second largest nursing home in Finland, the colonization of S. aureus and MRSA, and the role of screening sites along with broth enrichment culture on the sensitivity to detect S. aureus were studied. Combining the use of enrichment broth and perineal swabbing, in addition to nostrils and skin lesions swabbing, may be an alternative for throat swabs in the nursing home setting, especially when residents are uncooperative. Finally, in order to evaluate adequate phenotypic and genotypic methods needed for reliable laboratory diagnostics of MRSA, oxacillin disk diffusion and MIC tests to the cefoxitin disk diffusion method at both +35°C and +30°C, both with or without an addition of sodium chloride (NaCl) to the Müller Hinton test medium, and in-house PCR to two commercial molecular methods (the GenoType® MRSA test and the EVIGENETM MRSA Detection test) with different bacterial species in addition to S. aureus were compared. The cefoxitin disk diffusion method was superior to that of oxacillin disk diffusion and to the MIC tests in predicting mecA-mediated resistance in S. aureus when incubating at +35°C with or without the addition of NaCl to the test medium. Both the Geno Type® MRSA and EVIGENETM MRSA Detection tests are usable, accurate, cost-effective, and sufficiently fast methods for rapid MRSA confirmation from a pure culture.

Interactions and turnover of the muscular dystrophy protein myotilin

The striated muscle sarcomere is a force generating and transducing unit as well as an important sensor of extracellular cues and a coordinator of cellular signals. The borders of individual sarcomeres are formed by the Z-disks. The Z-disk component myotilin interacts with Z-disk core structural proteins and with regulators of signaling cascades. Missense mutations in the gene encoding myotilin cause dominantly inherited muscle disorders, myotilinopathies, by an unknown mechanism. In this thesis the functions of myotilin were further characterized to clarify the molecular biological basis and the pathogenetic mechanisms of inherited muscle disorders, mainly caused by mutated myotilin. Myotilin has an important function in the assembly and maintenance of the Z-disks probably through its actin-organizing properties. Our results show that the Ig-domains of myotilin are needed for both binding and bundling actin and define the Ig domains as actin-binding modules. The disease-causing mutations appear not to change the interplay between actin and myotilin. Interactions between Z-disk proteins regulate muscle functions and disruption of these interactions results in muscle disorders. Mutations in Z-disk components myotilin, ZASP/Cypher and FATZ-2 (calsarcin-1/myozenin-2) are associated with myopathies. We showed that proteins from the myotilin and FATZ families interact via a novel and unique type of class III PDZ binding motif with the PDZ domains of ZASP and other Enigma family members and that the interactions can be modulated by phosphorylation. The morphological findings typical of myotilinopathies include Z-disk alterations and aggregation of dense filamentous material. The causes and mechanisms of protein aggregation in myotilinopathy patients are unknown, but impaired degradation might explain in part the abnormal protein accumulation. We showed that myotilin is degraded by the calcium-dependent, non-lysosomal cysteine protease calpain and by the proteasome pathway, and that wild type and mutant myotilin differ in their sensitivity to degradation. These studies identify the first functional difference between mutated and wild type myotilin. Furthermore, if degradation of myotilin is disturbed, it accumulates in cells in a manner resembling that seen in myotilinopathy patients. Based on the results, we propose a model where mutant myotilin escapes proteolytic breakdown and forms protein aggregates, leading to disruption of myofibrils and muscular dystrophy. In conclusion, the main results of this study demonstrate that myotilin is a Z-disk structural protein interacting with several Z-disk components. The turnover of myotilin is regulated by calpain and the ubiquitin proteasome system and mutations in myotilin seem to affect the degradation of myotilin, leading to protein accumulations in cells. These findings are important for understanding myotilin-linked muscle diseases and designing treatments for these disorders.

Molecular line and continuum studies of the early stages of star formation

New stars form in dense interstellar clouds of gas and dust called molecular clouds. The actual sites where the process of star formation takes place are the dense clumps and cores deeply embedded in molecular clouds. The details of the star formation process are complex and not completely understood. Thus, determining the physical and chemical properties of molecular cloud cores is necessary for a better understanding of how stars are formed. Some of the main features of the origin of low-mass stars, like the Sun, are already relatively well-known, though many details of the process are still under debate. The mechanism through which high-mass stars form, on the other hand, is poorly understood. Although it is likely that the formation of high-mass stars shares many properties similar to those of low-mass stars, the very first steps of the evolutionary sequence are unclear. Observational studies of star formation are carried out particularly at infrared, submillimetre, millimetre, and radio wavelengths. Much of our knowledge about the early stages of star formation in our Milky Way galaxy is obtained through molecular spectral line and dust continuum observations. The continuum emission of cold dust is one of the best tracers of the column density of molecular hydrogen, the main constituent of molecular clouds. Consequently, dust continuum observations provide a powerful tool to map large portions across molecular clouds, and to identify the dense star-forming sites within them. Molecular line observations, on the other hand, provide information on the gas kinematics and temperature. Together, these two observational tools provide an efficient way to study the dense interstellar gas and the associated dust that form new stars. The properties of highly obscured young stars can be further examined through radio continuum observations at centimetre wavelengths. For example, radio continuum emission carries useful information on conditions in the protostar+disk interaction region where protostellar jets are launched. In this PhD thesis, we study the physical and chemical properties of dense clumps and cores in both low- and high-mass star-forming regions. The sources are mainly studied in a statistical sense, but also in more detail. In this way, we are able to examine the general characteristics of the early stages of star formation, cloud properties on large scales (such as fragmentation), and some of the initial conditions of the collapse process that leads to the formation of a star. The studies presented in this thesis are mainly based on molecular line and dust continuum observations. These are combined with archival observations at infrared wavelengths in order to study the protostellar content of the cloud cores. In addition, centimetre radio continuum emission from young stellar objects (YSOs; i.e., protostars and pre-main sequence stars) is studied in this thesis to determine their evolutionary stages. The main results of this thesis are as follows: i) filamentary and sheet-like molecular cloud structures, such as infrared dark clouds (IRDCs), are likely to be caused by supersonic turbulence but their fragmentation at the scale of cores could be due to gravo-thermal instability; ii) the core evolution in the Orion B9 star-forming region appears to be dynamic and the role played by slow ambipolar diffusion in the formation and collapse of the cores may not be significant; iii) the study of the R CrA star-forming region suggests that the centimetre radio emission properties of a YSO are likely to change with its evolutionary stage; iv) the IRDC G304.74+01.32 contains candidate high-mass starless cores which may represent the very first steps of high-mass star and star cluster formation; v) SiO outflow signatures are seen in several high-mass star-forming regions which suggest that high-mass stars form in a similar way as their low-mass counterparts, i.e., via disk accretion. The results presented in this thesis provide constraints on the initial conditions and early stages of both low- and high-mass star formation. In particular, this thesis presents several observational results on the early stages of clustered star formation, which is the dominant mode of star formation in our Galaxy.

Enzymatic cross-linking of β-casein and its impact on digestibility and allergenicity

Protein modification via enzymatic cross-linking is an attractive way for altering food structure so as to create products with increased quality and nutritional value. These modifications are expected to affect not only the structure and physico-chemical properties of proteins but also their physiological characteristics, such as digestibility in the GI-tract and allergenicity. Protein cross-linking enzymes such as transglutaminases are currently commercially available, but also other types of cross-linking enzymes are being explored intensively. In this study, enzymatic cross-linking of β-casein, the most abundant bovine milk protein, was studied. Enzymatic cross-linking reactions were performed by fungal Trichoderma reesei tyrosinase (TrTyr) and the performance of the enzyme was compared to that of transglutaminase from Streptoverticillium mobaraense (Tgase). Enzymatic cross-linking reactions were followed by different analytical techniques, such as size exclusion chromatography -Ultra violet/Visible multi angle light scattering (SEC-UV/Vis-MALLS), phosphorus nuclear magnetic resonance spectroscopy (31P-NMR), atomic force (AFM) and matrix-assisted laser desorption/ionisation-time of flight mass spectrometry (MALDI-TOF MS). The research results showed that in both cases cross-linking of β-casein resulted in the formation of high molecular mass (MM ca. 1 350 kg mol-1), disk-shaped nanoparticles when the highest enzyme dosage and longest incubation times were used. According to SEC-UV/Vis-MALLS data, commercial β-casein was cross-linked almost completely when TrTyr and Tgase were used as cross-linking enzymes. In the case of TrTyr, high degree of cross-linking was confirmed by 31P-NMR where it was shown that 91 % of the tyrosine side-chains were involved in the cross-linking. The impact of enzymatic cross-linking of β-casein on in vitro digestibility by pepsin was followed by various analytical techniques. The research results demonstrated that enzymatically cross-linked β-casein was stable under the acidic conditions present in the stomach. Furthermore, it was found that cross-linked β-casein was more resistant to pepsin digestion when compared to that of non modified β-casein. The effects of enzymatic cross-linking of β-casein on allergenicity were also studied by different biochemical test methods. On the basis of the research results, enzymatic cross-linking decreased allergenicity of native β-casein by 14 % when cross-linked by TrTyr and by 6 % after treatment by Tgase. It can be concluded that in addition to the basic understanding of the reaction mechanism of TrTyr on protein matrix, the research results obtained in this study can have high impact on various applications like food, cosmetic, medical, textile and packing sectors.

Planar subgraphs without low-degree nodes

We study the following problem: given a geometric graph G and an integer k, determine if G has a planar spanning subgraph (with the original embedding and straight-line edges) such that all nodes have degree at least k. If G is a unit disk graph, the problem is trivial to solve for k = 1. We show that even the slightest deviation from the trivial case (e.g., quasi unit disk graphs or k = 1) leads to NP-hard problems.

Water quality estimation by optical remote sensing in boreal lakes

In lake-rich regions, the gathering of information about water quality is challenging because only a small proportion of the lakes can be assessed each year by conventional methods. One of the techniques for improving the spatial and temporal representativeness of lake monitoring is remote sensing from satellites and aircrafts. The experimental material included detailed optical measurements in 11 lakes, air- and spaceborne remote sensing measurements with concurrent field sampling, automatic raft measurements and a national dataset of routine water quality measurements from over 1100 lakes. The analyses of the spatially high-resolution airborne remote sensing data from eutrophic and mesotrophic lakes showed that one or a few discrete water quality observations using conventional monitoring can yield a clear over- or underestimation of the overall water quality in a lake. The use of TM-type satellite instruments in addition to routine monitoring results substantially increases the number of lakes for which water quality information can be obtained. The preliminary results indicated that coloured dissolved organic matter (CDOM) can be estimated with TM-type satellite instruments, which could possibly be utilised as an aid in estimating the role of lakes in global carbon budgets. Based on the results of reflectance modelling and experimental data, MERIS satellite instrument has optimal or near-optimal channels for the estimation of turbidity, chlorophyll a and CDOM in Finnish lakes. MERIS images with a 300 m spatial resolution can provide water quality information in different parts of large and medium-sized lakes, and in filling in the gaps resulting from conventional monitoring. Algorithms that would not require simultaneous field data for algorithm training would increase the amount of remote sensing-based information available for lake monitoring. The MERIS Boreal Lakes processor, trained with the optical data and concentration ranges provided by this study, enabled turbidity estimations with good accuracy without the need for algorithm correction with field measurements, while chlorophyll a and CDOM estimations require further development of the processor. The accuracy of interpreting chlorophyll a via semi empirical algorithms can be improved by classifying lakes prior to interpretation according to their CDOM level and trophic status. Optical modelling indicated that the spectral diffuse attenuation coefficient can be estimated with reasonable accuracy from the measured water quality concentrations. This provides more detailed information on light attenuation from routine monitoring measurements than is available through the Secchi disk transparency. The results of this study improve the interpretation of lake water quality by remote sensing and encourage the use of remote sensing in lake monitoring.