Radiative transfer, interception and scattering in coniferous forests : models and applications for production ecology and remote sensing

This work develops methods to account for shoot structure in models of coniferous canopy radiative transfer. Shoot structure, as it varies along the light gradient inside canopy, affects the efficiency of light interception per unit needle area, foliage biomass, or foliage nitrogen. The clumping of needles in the shoot volume also causes a notable amount of multiple scattering of light within coniferous shoots. The effect of shoot structure on light interception is treated in the context of canopy level photosynthesis and resource use models, and the phenomenon of within-shoot multiple scattering in the context of physical canopy reflectance models for remote sensing purposes. Light interception. A method for estimating the amount of PAR (Photosynthetically Active Radiation) intercepted by a conifer shoot is presented. The method combines modelling of the directional distribution of radiation above canopy, fish-eye photographs taken at shoot locations to measure canopy gap fraction, and geometrical measurements of shoot orientation and structure. Data on light availability, shoot and needle structure and nitrogen content has been collected from canopies of Pacific silver fir (Abies amabilis (Dougl.) Forbes) and Norway spruce (Picea abies (L.) Karst.). Shoot structure acclimated to light gradient inside canopy so that more shaded shoots have better light interception efficiency. Light interception efficiency of shoots varied about two-fold per needle area, about four-fold per needle dry mass, and about five-fold per nitrogen content. Comparison of fertilized and control stands of Norway spruce indicated that light interception efficiency is not greatly affected by fertilization. Light scattering. Structure of coniferous shoots gives rise to multiple scattering of light between the needles of the shoot. Using geometric models of shoots, multiple scattering was studied by photon tracing simulations. Based on simulation results, the dependence of the scattering coefficient of shoot from the scattering coefficient of needles is shown to follow a simple one-parameter model. The single parameter, termed the recollision probability, describes the level of clumping of the needles in the shoot, is wavelength independent, and can be connected to previously used clumping indices. By using the recollision probability to correct for the within-shoot multiple scattering, canopy radiative transfer models which have used leaves as basic elements can use shoots as basic elements, and thus be applied for coniferous forests. Preliminary testing of this approach seems to explain, at least partially, why coniferous forests appear darker than broadleaved forests in satellite data.

On the Geometry of Infinite-Dimensional Grassmannian Manifolds and Gauge Theory

This PhD Thesis is about certain infinite-dimensional Grassmannian manifolds that arise naturally in geometry, representation theory and mathematical physics. From the physics point of view one encounters these infinite-dimensional manifolds when trying to understand the second quantization of fermions. The many particle Hilbert space of the second quantized fermions is called the fermionic Fock space. A typical element of the fermionic Fock space can be thought to be a linear combination of the configurations m particles and n anti-particles . Geometrically the fermionic Fock space can be constructed as holomorphic sections of a certain (dual)determinant line bundle lying over the so called restricted Grassmannian manifold, which is a typical example of an infinite-dimensional Grassmannian manifold one encounters in QFT. The construction should be compared with its well-known finite-dimensional analogue, where one realizes an exterior power of a finite-dimensional vector space as the space of holomorphic sections of a determinant line bundle lying over a finite-dimensional Grassmannian manifold. The connection with infinite-dimensional representation theory stems from the fact that the restricted Grassmannian manifold is an infinite-dimensional homogeneous (Kähler) manifold, i.e. it is of the form G/H where G is a certain infinite-dimensional Lie group and H its subgroup. A central extension of G acts on the total space of the dual determinant line bundle and also on the space its holomorphic sections; thus G admits a (projective) representation on the fermionic Fock space. This construction also induces the so called basic representation for loop groups (of compact groups), which in turn are vitally important in string theory / conformal field theory. The Thesis consists of three chapters: the first chapter is an introduction to the backround material and the other two chapters are individually written research articles. The first article deals in a new way with the well-known question in Yang-Mills theory, when can one lift the action of the gauge transformation group on the space of connection one forms to the total space of the Fock bundle in a compatible way with the second quantized Dirac operator. In general there is an obstruction to this (called the Mickelsson-Faddeev anomaly) and various geometric interpretations for this anomaly, using such things as group extensions and bundle gerbes, have been given earlier. In this work we give a new geometric interpretation for the Faddeev-Mickelsson anomaly in terms of differentiable gerbes (certain sheaves of categories) and central extensions of Lie groupoids. The second research article deals with the question how to define a Dirac-like operator on the restricted Grassmannian manifold, which is an infinite-dimensional space and hence not in the landscape of standard Dirac operator theory. The construction relies heavily on infinite-dimensional representation theory and one of the most technically demanding challenges is to be able to introduce proper normal orderings for certain infinite sums of operators in such a way that all divergences will disappear and the infinite sum will make sense as a well-defined operator acting on a suitable Hilbert space of spinors. This research article was motivated by a more extensive ongoing project to construct twisted K-theory classes in Yang-Mills theory via a Dirac-like operator on the restricted Grassmannian manifold.

Finitary Abstract Elementary Classes

The research in model theory has extended from the study of elementary classes to non-elementary classes, i.e. to classes which are not completely axiomatizable in elementary logic. The main theme has been the attempt to generalize tools from elementary stability theory to cover more applications arising in other branches of mathematics. In this doctoral thesis we introduce finitary abstract elementary classes, a non-elementary framework of model theory. These classes are a special case of abstract elementary classes (AEC), introduced by Saharon Shelah in the 1980's. We have collected a set of properties for classes of structures, which enable us to develop a 'geometric' approach to stability theory, including an independence calculus, in a very general framework. The thesis studies AEC's with amalgamation, joint embedding, arbitrarily large models, countable Löwenheim-Skolem number and finite character. The novel idea is the property of finite character, which enables the use of a notion of a weak type instead of the usual Galois type. Notions of simplicity, superstability, Lascar strong type, primary model and U-rank are inroduced for finitary classes. A categoricity transfer result is proved for simple, tame finitary classes: categoricity in any uncountable cardinal transfers upwards and to all cardinals above the Hanf number. Unlike the previous categoricity transfer results of equal generality the theorem does not assume the categoricity cardinal being a successor. The thesis consists of three independent papers. All three papers are joint work with Tapani Hyttinen.

Optimisation Problems in Wireless Sensor Networks : Local Algorithms and Local Graphs

This thesis studies optimisation problems related to modern large-scale distributed systems, such as wireless sensor networks and wireless ad-hoc networks. The concrete tasks that we use as motivating examples are the following: (i) maximising the lifetime of a battery-powered wireless sensor network, (ii) maximising the capacity of a wireless communication network, and (iii) minimising the number of sensors in a surveillance application. A sensor node consumes energy both when it is transmitting or forwarding data, and when it is performing measurements. Hence task (i), lifetime maximisation, can be approached from two different perspectives. First, we can seek for optimal data flows that make the most out of the energy resources available in the network; such optimisation problems are examples of so-called max-min linear programs. Second, we can conserve energy by putting redundant sensors into sleep mode; we arrive at the sleep scheduling problem, in which the objective is to find an optimal schedule that determines when each sensor node is asleep and when it is awake. In a wireless network simultaneous radio transmissions may interfere with each other. Task (ii), capacity maximisation, therefore gives rise to another scheduling problem, the activity scheduling problem, in which the objective is to find a minimum-length conflict-free schedule that satisfies the data transmission requirements of all wireless communication links. Task (iii), minimising the number of sensors, is related to the classical graph problem of finding a minimum dominating set. However, if we are not only interested in detecting an intruder but also locating the intruder, it is not sufficient to solve the dominating set problem; formulations such as minimum-size identifying codes and locating dominating codes are more appropriate. This thesis presents approximation algorithms for each of these optimisation problems, i.e., for max-min linear programs, sleep scheduling, activity scheduling, identifying codes, and locating dominating codes. Two complementary approaches are taken. The main focus is on local algorithms, which are constant-time distributed algorithms. The contributions include local approximation algorithms for max-min linear programs, sleep scheduling, and activity scheduling. In the case of max-min linear programs, tight upper and lower bounds are proved for the best possible approximation ratio that can be achieved by any local algorithm. The second approach is the study of centralised polynomial-time algorithms in local graphs these are geometric graphs whose structure exhibits spatial locality. Among other contributions, it is shown that while identifying codes and locating dominating codes are hard to approximate in general graphs, they admit a polynomial-time approximation scheme in local graphs.

Hormone therapy in elderly women; a comparative study with alendronate of the effects on bone, cardiovascular risk factors, periodontal conditions and quality of life

Thirty percent of 70-year-old women have osteoporosis; after age of 80 its prevalence is up to 70%. Postmenopausal women with osteoporosis seem to be at an increased risk for cardiovascular events, and deterioration of oral health, as shown by attachment loss of teeth, which is proportional to the severity of osteoporosis. Osteoporosis can be treated with many different medication, e.g. estrogen and alendronate. We randomized 90 elderly osteoporotic women (65-80 years of age) to receive hormone therapy (HT)(2mg E2+NETA), 10mg alendronate, and their combination for two years and compared their effects on bone mineral density (BMD) and turnover, two surrogate markers of the risk of cardiovascular diseases, C-reactive protein (CRP) and E-selectin, as well as oral health. The effect of HT on health-related quality of life (HRQoL) was studied in the population-based cohort of 1663 postmenopausal women (mean age 68 yr) (585 estrogen users and 1078 non-users). BMD was measured with dual-energy X-ray absorptiometry (DXA) at 0, 12 and 24 months. Urinary N-telopeptide (NTX) of type I collagen, a marker of bone resorption, and serum aminoterminal propeptide of human type I procollagen (PINP), a marker of bone formation, were measured every six months of treatment. Serum CRP and E-selectin, were measured at 0, 6, and 12 months. Dental, and periodontal conditions, and gingival crevicular fluid (GCF) matrix metalloproteinase (MMP)-8 levels were studied to evaluate the oral health status and for the mouth symptoms a structured questionnaire was used. The HRQoL was measured with 15D questionnaire. Lumbar spine BMD increased similarly in all treatment groups (6.8-8.4% and 9.1-11.2%). Only HT increased femoral neck BMD at both 12 (4.9%) and 24 months (5.8%), at the latter time point the HT group differed significantly from the other groups. HT reduced bone marker levels of NTX and PINP significantly less than other two groups.Oral HT significantly increased serum CRP level by 76.5% at 6 and by 47.1% (NS) at 12 months, and decreased serum E-selectin level by 24.3% and 30.0%. Alendronate had no effect on these surrogate markers. Alendronate caused a decrease in the resting salivary flow rate and tended to increase GCF MMP-8 levels. Otherwise, there was no effect on the parameters of oral health. HT improved the HRQoL of elderly women significantly on the dimensions of usual activities, vitality and sexual activity, but the overall improvement in HRQoL was neither statistically significant nor clinically important. In conclusion, bisphosphonates might be the first option to start the treatment of postmenopausal osteoporosis in the old age.

Specific language impairment in pre-adolescence, adolescence, and adulthood with special emphasis on health-related quality of life

This clinical study focused on effects of childhood specific language impairment (SLI) on daily functioning in late life. SLI is a neurobiological disorder with genetic predisposition and manifests as poor language production or comprehension or both in a child with age-level non-verbal intelligence and no other known cause for deficient language development. The prevalence rate of around 7% puts it among the most prevalent developmental disorders in childhood. Negative long-term effects, such as problems in learning and behavior, are frequent. In follow-up studies the focus has seldom been on self-perception of daily functioning and participation, which are considered important in the International Classification of Functioning, Disability, and Health (ICF). To investigate the self-perceived aspects of everyday functioning in individuals with childhood receptive SLI compared with age- and gender-matched control populations, the 15D, 16D, and 17D health-related quality of life (HRQoL) questionnaires were applied. These generic questionnaires include 15, 16, and 17 dimensions, respectively, and give both a single index score and a profile with values on each dimension. Information on different life domains (rehabilitation, education, employment etc.) from each age-group was collected with separate questionnaires. The study groups comprised adults, adolescents (12-16 years), and pre-adolescents (8-11 years) who had received a diagnosis of receptive SLI and had been examined, usually before school age, at the Department of Phoniatrics of Helsinki University Central Hospital, where children with language deficits caused by various etiologies are examined and treated by a multidisciplinary team. The adult respondents included 33 subjects with a mean age of 34 years. Measured with 15D, the subjects perceived their HRQoL to be nearly as good as that of their controls, but on the dimensions of speech, usual activities, mental functioning, and distress they were significantly worse off. They significantly more often lived with their parents (19%) or were pensioned (26%) than the adult Finnish population on average. Adults with self-perceived problems in finding words and in remembering instructions, manifestations of persistent language impairment, showed inferior every day functioning to the rest of the study group. Of the adolescents and pre-adolescents, 48 and 51, respectively, responded. The majority in both groups had received special education or extra educational support at school. They all had attended speech therapy at some point; at the time of the study only one adolescent, but every third pre-adolescent still received speech therapy. The 16D score of the adolescent or the 17D score of the pre-adolescents did not differ from that of their controls. The 16D profiles differed on some dimensions; subjects were significantly worse off on the dimension of mental functioning, but better off on the dimension of vitality than controls. Of the 17D dimensions, the study group was significantly worse off on speech, whereas the control group reported significantly more problems in sleeping. Of the childhood performance measures investigated, low verbal intelligence quotient (VIQ), which is often considered to reflect receptive language impairment, was in adults subjects significantly associated with some of the self-perceived problems, such as problems in usual activities and mental functioning. The 15D, 16D, and 17D questionnaires served well in measuring self-perceived HRQoL. Such standardized measures with population values are especially important in confirming with the ICF guidelines. In the future these questionnaires could perhaps be used on a more individual level in follow-up of children in clinics, and even in special schools and classes, to detect those children at greatest risk of negative long-term effects and perhaps diminished well-being regarding daily functioning and participation.

Accuracy of absorbed dose in external photon beam radiotherapy : what level is sufficient and how to approach it?

Radiation therapy (RT) plays currently significant role in curative treatments of several cancers. External beam RT is carried out mostly by using megavoltage beams of linear accelerators. Tumor eradication and normal tissue complications correlate to dose absorbed in tissues. Normally this dependence is steep and it is crucial that actual dose within patient accurately correspond to the planned dose. All factors in a RT procedure contain uncertainties requiring strict quality assurance. From hospital physicist´s point of a view, technical quality control (QC), dose calculations and methods for verification of correct treatment location are the most important subjects. Most important factor in technical QC is the verification that radiation production of an accelerator, called output, is within narrow acceptable limits. The output measurements are carried out according to a locally chosen dosimetric QC program defining measurement time interval and action levels. Dose calculation algorithms need to be configured for the accelerators by using measured beam data. The uncertainty of such data sets limits for best achievable calculation accuracy. All these dosimetric measurements require good experience, are workful, take up resources needed for treatments and are prone to several random and systematic sources of errors. Appropriate verification of treatment location is more important in intensity modulated radiation therapy (IMRT) than in conventional RT. This is due to steep dose gradients produced within or close to healthy tissues locating only a few millimetres from the targeted volume. The thesis was concentrated in investigation of the quality of dosimetric measurements, the efficacy of dosimetric QC programs, the verification of measured beam data and the effect of positional errors on the dose received by the major salivary glands in head and neck IMRT. A method was developed for the estimation of the effect of the use of different dosimetric QC programs on the overall uncertainty of dose. Data were provided to facilitate the choice of a sufficient QC program. The method takes into account local output stability and reproducibility of the dosimetric QC measurements. A method based on the model fitting of the results of the QC measurements was proposed for the estimation of both of these factors. The reduction of random measurement errors and optimization of QC procedure were also investigated. A method and suggestions were presented for these purposes. The accuracy of beam data was evaluated in Finnish RT centres. Sufficient accuracy level was estimated for the beam data. A method based on the use of reference beam data was developed for the QC of beam data. Dosimetric and geometric accuracy requirements were evaluated for head and neck IMRT when function of the major salivary glands is intended to be spared. These criteria are based on the dose response obtained for the glands. Random measurement errors could be reduced enabling lowering of action levels and prolongation of measurement time interval from 1 month to even 6 months simultaneously maintaining dose accuracy. The combined effect of the proposed methods, suggestions and criteria was found to facilitate the avoidance of maximal dose errors of up to even about 8 %. In addition, their use may make the strictest recommended overall dose accuracy level of 3 % (1SD) achievable.

Biovalta, toiseus ja naisten toimijuus hedelmöityshoidoissa

Biopower, Otherness and Women's Agency in Assisted Reproduction. This sociological study analyses how, why and with what kind of consequences assisted reproductive technologies (ART) have become the primary technology for governing infertility in Finland both on the level of individuals and society. The phenomenon is construed as one the strategies of the Focaultian biopower since ART are political techniques of the beginning of life par excellence, as they are used to prepare the bodies of certain types of women to create certain kind of life, i.e. certain kind of children. Moreover, ART are interpreted to be gendered control techniques with which the pure, and at the same time prevailing, social order symbolised by a female body is maintained by naming and excluding otherness, unsuitable mother candidates and children. Finally, it is considered how the agency, subjectivity, of women experiencing infertility and seeking treatment appears in the prevailing context of ART. The introduction of IVF-based reproductive technologies to Finland and the treatment practices of the early 1990s have been studied on the basis of a clinic questionnaire, medical doctor interviews and articles of the Medical Journal Duodecim from 1969 to 2000. Opinions on the method of the treatment providers were studied by conducting a theme interview with fertilisation doctors in 1993. Experiences of women who have received treatment or experienced infertility were studied by means of a survey in 1994 and by analysing the content of messages in an online discussion forum in 2000. On the basis of the medical doctor interviews, significant criterion for choosing mother candidates turned out to be her vitality and her mental and physical health, which are considered prerequisites for a vitality of the child to be born. The hierarchies concerning children became evident. While people normally make their children on their own, this is what people experiencing infertility are trying to do as well. In the era of ART, the primary child is genetically the parents' own child, a secondary option for Finnish parents is a genetically Finnish child conceived by donated Finnish gametes or embryos and the last option is an adopted child of foreign origin. Women's agency mainly appears in their way of using ART as a technology of the self for self-control on one's own nature, which helps them to prepare their bodies in order to become pregnant in co-operation with a fertilisation doctor. Women's creative free agency exceeding governance appeared as a distinctive use of language with which they created shared meaning for their infertility experience, their own individual and group identity and distinctive reality. ART are very political techniques as they have a possibility to change the methods of having children and to shape life. Therefore, further sociological research on them is important and needed. Key words: practises of assisted reproduction, women's agency, biopower, vital politics of the beginning of life, otherness

Knowledge through Discussion : An Interpretation of Epistemology in Plato's Meno

According to Meno s paradox we cannot inquire into what we do not know because we do not know what we are inquiring into. There are many ways to interpret the paradox but the central issue about our ability to reach truth is a profound one. In the dialogue Meno, Plato presents the paradox and an outline of a solution which enables us to reach knowledge (epistēmē) through philosophical discussion. During the last century Meno has often been considered transitional between Socratic thinking and Plato s own philosophy, and thus the dialogue has not been adequately interpreted as an integrated whole. Therefore the distinctive epistemology of the dialogue has not gained due notice. In this thesis the dialogue is analysed as an integrated whole and the philosophical interpretation also takes into account its dramatic features. The thesis emphasises the role of language and definitions in acquiring knowledge. Among the results concerning these subjects is a new interpretation of Socrates s defintion of shape (schēma). The theory of anamnēsis all learning is recollection in the Meno is argued to answer the paradox philosophically although Plato s presentation also contains playful and ironic elements. The background of the way Plato presents his case is that he appreciated the fact that no argument can plausibly demonstrate that argumentation is able to reach truth. In the Meno, Plato makes the earliest explicit distinction between knowledge and true belief in the history of Western philosophy. He also gives a definition of knowledge which is the basis of the so called classical definition of knowledge as justified true belief. In the Meno, true beliefs become knowledge when someone ties them down by reasoning about the explanation. The analysis of the epistemology of the dialogue from this perspective gives an interpretation which integrates the central concepts of the epistemology in the dialogue elenchos, anamnēsis and hypothetical inquiry into a unified whole which contains a plausible argument according to which the ignorant can reach knowledge through discussion. The conception that emerges by such an analysis is interesting both from the point of view of current interests and that of the history of philosophy. The method of knowledge acquisition in the Meno can, for example, be seen as a predecessor of modern scientific methods. The Meno is the earliest Greek mathematical text that has survived in its original form. The analysis presented in the thesis of the geometric passages in the dialogue provides new results both concerning Socrates s geometry lesson with the slave and the example presenting the hypothetical method. Concerning the latter, a new interpretation is presented. Keywords: anamnēsis, epistēmē, knowledge, Meno s paradox, Plato

The Role of Abduction in Self-Similarity

Based on the Aristotelian criterion referred to as 'abductio', Peirce suggests a method of hypothetical inference, which operates in a different way than the deductive and inductive methods. “Abduction is nothing but guessing” (Peirce, 7.219). This principle is of extreme value for the study of our understanding of mathematical self-similarity in both of its typical presentations: relative or absolute. For the first case, abduction incarnates the quantitative/qualitative relationships of a self-similar object or process; for the second case, abduction makes understandable the statistical treatment of self-similarity, 'guessing' the continuity of geometric features to the infinity through the use of a systematic stereotype (for instance, the assumption that the general shape of the Sierpiński triangle continuates identically into its particular shapes). The metaphor coined by Peirce, of an exact map containig itself the same exact map (a map of itself), is not only the most important precedent of Mandelbrot’s problem of measuring the boundaries of a continuous irregular surface with a logarithmic ruler, but also still being a useful abstraction for the conceptualisation of relative and absolute self-similarity, and its mechanisms of implementation. It is useful, also, for explaining some of the most basic geometric ontologies as mental constructions: in the notion of infinite convergence of points in the corners of a triangle, or the intuition for defining two parallel straight lines as two lines in a plane that 'never' intersect.

Porsastuotannon tuottavuuskehitys sikatilinpäätöstiloilla vuosina 2003–2008

Tutkimuksessa mitataan porsastuotannon tuottavuuden kehitystä ProAgrian sikatilinpäätöstiloilla vuosina 2003–2008. Tuottavuutta mitataan Fisher-tuottavuusindeksillä, joka dekomponoidaan tekniseen, allokatiiviseen ja skaalatehokkuuteen sekä teknologiseen kehitykseen ja hintavaikutukseen. Koko aineistosta aggregoidulla tuottavuusindeksillä mitattuna tuottavuus kasvoi viidessä vuodessa yhteensä 14,3 % vuotuisen kasvun ollessa 2,7 %. Tuottajien keskimääräinen tuottavuusindeksi antaa lähes saman tuloksen: sen mukaan tuottavuus kasvaa yhteensä 14,7 %, mikä tekee 2,8 % vuodessa. Skaalatehokkuuden paraneminen havaitaan merkittävimmäksi tuottavuuskasvun lähteeksi. Skaalatehokkuus paranee aggregoidusti mitattuna 1,6 % vuodessa ja tiloilla keskimäärin 2,1 % vuodessa. Teknisen tehokkuuden koheneminen on toinen tuottavuuskasvua edistävä tekijä tutkimusjaksolla. Molemmilla mittaustavoilla nousu on keskimäärin 1,4 % vuodessa. Allokatiivinen tehokkuus laskee hieman: aggregoidusti mitattuna 0,1 % ja keskimäärin 0,4 % vuodessa. Teknologinen kehitys tutkimusjaksolla on lievästi negatiivista, keskimäärin -0,1 % vuodessa. Vuosittaiset vaihtelut ovat kuitenkin voimakkaita. Hintojen muutokset eivät juuri ole vaikuttaneet tuottavuuden tasoon, sillä hintavaikutuksen vuotuiset muutokset jäävät jokaisena vuonna alle puoleen prosenttiin ja keskimääräinen vuotuinen muutos on -0,1 %. Keskeinen tuottavuuskasvua edistänyt tekijä näyttää olleen tilakoon kasvu, joka on parantanut rakenteellista tehokkuutta. Teknologisen kehityksen jääminen negatiiviseksi kuitenkin tarkoittaa, että paras havaittu tuottavuuden taso ei ole noussut lainkaan.

Hyperfine effects in the nuclear magnetic resonance of paramagnetic molecules

Paramagnetic, or open-shell, systems are often encountered in the context of metalloproteins, and they are also an essential part of molecular magnets. Nuclear magnetic resonance (NMR) spectroscopy is a powerful tool for chemical structure elucidation, but for paramagnetic molecules it is substantially more complicated than in the diamagnetic case. Before the present work, the theory of NMR of paramagnetic molecules was limited to spin-1/2 systems and it did not include relativistic corrections to the hyperfine effects. It also was not systematically expandable. --- The theory was first expanded by including hyperfine contributions up to the fourth power in the fine structure constant α. It was then reformulated and its scope widened to allow any spin state in any spatial symmetry. This involved including zero-field splitting effects. In both stages the theory was implemented into a separate analysis program. The different levels of theory were tested by demonstrative density functional calculations on molecules selected to showcase the relative strength of new NMR shielding terms. The theory was also tested in a joint experimental and computational effort to confirm assignment of 11 B signals. The new terms were found to be significant and comparable with the terms in the earlier levels of theory. The leading-order magnetic-field dependence of shielding in paramagnetic systems was formulated. The theory is now systematically expandable, allowing for higher-order field dependence and relativistic contributions. The prevailing experimental view of pseudocontact shift was found to be significantly incomplete, as it only includes specific geometric dependence, which is not present in most of the new terms introduced here. The computational uncertainty in density functional calculations of the Fermi contact hyperfine constant and zero-field splitting tensor sets a limit for quantitative prediction of paramagnetic shielding for now.

Optimisation problems in wireless sensor networks

This thesis studies optimisation problems related to modern large-scale distributed systems, such as wireless sensor networks and wireless ad-hoc networks. The concrete tasks that we use as motivating examples are the following: (i) maximising the lifetime of a battery-powered wireless sensor network, (ii) maximising the capacity of a wireless communication network, and (iii) minimising the number of sensors in a surveillance application. A sensor node consumes energy both when it is transmitting or forwarding data, and when it is performing measurements. Hence task (i), lifetime maximisation, can be approached from two different perspectives. First, we can seek for optimal data flows that make the most out of the energy resources available in the network; such optimisation problems are examples of so-called max-min linear programs. Second, we can conserve energy by putting redundant sensors into sleep mode; we arrive at the sleep scheduling problem, in which the objective is to find an optimal schedule that determines when each sensor node is asleep and when it is awake. In a wireless network simultaneous radio transmissions may interfere with each other. Task (ii), capacity maximisation, therefore gives rise to another scheduling problem, the activity scheduling problem, in which the objective is to find a minimum-length conflict-free schedule that satisfies the data transmission requirements of all wireless communication links. Task (iii), minimising the number of sensors, is related to the classical graph problem of finding a minimum dominating set. However, if we are not only interested in detecting an intruder but also locating the intruder, it is not sufficient to solve the dominating set problem; formulations such as minimum-size identifying codes and locating–dominating codes are more appropriate. This thesis presents approximation algorithms for each of these optimisation problems, i.e., for max-min linear programs, sleep scheduling, activity scheduling, identifying codes, and locating–dominating codes. Two complementary approaches are taken. The main focus is on local algorithms, which are constant-time distributed algorithms. The contributions include local approximation algorithms for max-min linear programs, sleep scheduling, and activity scheduling. In the case of max-min linear programs, tight upper and lower bounds are proved for the best possible approximation ratio that can be achieved by any local algorithm. The second approach is the study of centralised polynomial-time algorithms in local graphs – these are geometric graphs whose structure exhibits spatial locality. Among other contributions, it is shown that while identifying codes and locating–dominating codes are hard to approximate in general graphs, they admit a polynomial-time approximation scheme in local graphs.

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.

A maximal operator, Carleson's embedding, and tent spaces for vector-valued functions

This thesis is concerned with the area of vector-valued Harmonic Analysis, where the central theme is to determine how results from classical Harmonic Analysis generalize to functions with values in an infinite dimensional Banach space. The work consists of three articles and an introduction. The first article studies the Rademacher maximal function that was originally defined by T. Hytönen, A. McIntosh and P. Portal in 2008 in order to prove a vector-valued version of Carleson's embedding theorem. The boundedness of the corresponding maximal operator on Lebesgue-(Bochner) -spaces defines the RMF-property of the range space. It is shown that the RMF-property is equivalent to a weak type inequality, which does not depend for instance on the integrability exponent, hence providing more flexibility for the RMF-property. The second article, which is written in collaboration with T. Hytönen, studies a vector-valued Carleson's embedding theorem with respect to filtrations. An earlier proof of the dyadic version assumed that the range space satisfies a certain geometric type condition, which this article shows to be also necessary. The third article deals with a vector-valued generalizations of tent spaces, originally defined by R. R. Coifman, Y. Meyer and E. M. Stein in the 80's, and concerns especially the ones related to square functions. A natural assumption on the range space is then the UMD-property. The main result is an atomic decomposition for tent spaces with integrability exponent one. In order to suit the stochastic integrals appearing in the vector-valued formulation, the proof is based on a geometric lemma for cones and differs essentially from the classical proof. Vector-valued tent spaces have also found applications in functional calculi for bisectorial operators. In the introduction these three themes come together when studying paraproduct operators for vector-valued functions. The Rademacher maximal function and Carleson's embedding theorem were applied already by Hytönen, McIntosh and Portal in order to prove boundedness for the dyadic paraproduct operator on Lebesgue-Bochner -spaces assuming that the range space satisfies both UMD- and RMF-properties. Whether UMD implies RMF is thus an interesting question. Tent spaces, on the other hand, provide a method to study continuous time paraproduct operators, although the RMF-property is not yet understood in the framework of tent spaces.