Bayesian statistical analysis of bacterial diversity

Bacteria play an important role in many ecological systems. The molecular characterization of bacteria using either cultivation-dependent or cultivation-independent methods reveals the large scale of bacterial diversity in natural communities, and the vastness of subpopulations within a species or genus. Understanding how bacterial diversity varies across different environments and also within populations should provide insights into many important questions of bacterial evolution and population dynamics. This thesis presents novel statistical methods for analyzing bacterial diversity using widely employed molecular fingerprinting techniques. The first objective of this thesis was to develop Bayesian clustering models to identify bacterial population structures. Bacterial isolates were identified using multilous sequence typing (MLST), and Bayesian clustering models were used to explore the evolutionary relationships among isolates. Our method involves the inference of genetic population structures via an unsupervised clustering framework where the dependence between loci is represented using graphical models. The population dynamics that generate such a population stratification were investigated using a stochastic model, in which homologous recombination between subpopulations can be quantified within a gene flow network. The second part of the thesis focuses on cluster analysis of community compositional data produced by two different cultivation-independent analyses: terminal restriction fragment length polymorphism (T-RFLP) analysis, and fatty acid methyl ester (FAME) analysis. The cluster analysis aims to group bacterial communities that are similar in composition, which is an important step for understanding the overall influences of environmental and ecological perturbations on bacterial diversity. A common feature of T-RFLP and FAME data is zero-inflation, which indicates that the observation of a zero value is much more frequent than would be expected, for example, from a Poisson distribution in the discrete case, or a Gaussian distribution in the continuous case. We provided two strategies for modeling zero-inflation in the clustering framework, which were validated by both synthetic and empirical complex data sets. We show in the thesis that our model that takes into account dependencies between loci in MLST data can produce better clustering results than those methods which assume independent loci. Furthermore, computer algorithms that are efficient in analyzing large scale data were adopted for meeting the increasing computational need. Our method that detects homologous recombination in subpopulations may provide a theoretical criterion for defining bacterial species. The clustering of bacterial community data include T-RFLP and FAME provides an initial effort for discovering the evolutionary dynamics that structure and maintain bacterial diversity in the natural environment.

Elements of Volatility at High Frequency

Volatility is central in options pricing and risk management. It reflects the uncertainty of investors and the inherent instability of the economy. Time series methods are among the most widely applied scientific methods to analyze and predict volatility. Very frequently sampled data contain much valuable information about the different elements of volatility and may ultimately reveal the reasons for time varying volatility. The use of such ultra-high-frequency data is common to all three essays of the dissertation. The dissertation belongs to the field of financial econometrics. The first essay uses wavelet methods to study the time-varying behavior of scaling laws and long-memory in the five-minute volatility series of Nokia on the Helsinki Stock Exchange around the burst of the IT-bubble. The essay is motivated by earlier findings which suggest that different scaling laws may apply to intraday time-scales and to larger time-scales, implying that the so-called annualized volatility depends on the data sampling frequency. The empirical results confirm the appearance of time varying long-memory and different scaling laws that, for a significant part, can be attributed to investor irrationality and to an intraday volatility periodicity called the New York effect. The findings have potentially important consequences for options pricing and risk management that commonly assume constant memory and scaling. The second essay investigates modelling the duration between trades in stock markets. Durations convoy information about investor intentions and provide an alternative view at volatility. Generalizations of standard autoregressive conditional duration (ACD) models are developed to meet needs observed in previous applications of the standard models. According to the empirical results based on data of actively traded stocks on the New York Stock Exchange and the Helsinki Stock Exchange the proposed generalization clearly outperforms the standard models and also performs well in comparison to another recently proposed alternative to the standard models. The distribution used to derive the generalization may also prove valuable in other areas of risk management. The third essay studies empirically the effect of decimalization on volatility and market microstructure noise. Decimalization refers to the change from fractional pricing to decimal pricing and it was carried out on the New York Stock Exchange in January, 2001. The methods used here are more accurate than in the earlier studies and put more weight on market microstructure. The main result is that decimalization decreased observed volatility by reducing noise variance especially for the highly active stocks. The results help risk management and market mechanism designing.

Phytoplankton ecology of subarctic lakes in Finnish Lapland

Climate is warming and it is especially seen in arctic areas, where the warming trend is expected to be greatest. Arctic freshwater ecosystems, which are a very characteristic feature of the arctic landscape, are especially sensitive to climate change. They could be used as early warning systems, but more information about the ecosystem functioning and responses are needed for proper interpretation of the observations. Phytoplankton species and assemblages could be especially suitable for climate-related studies, since they have short generation times and react rapidly to changes in the environment. In addition, phytoplankton provides a good tool for lake classifications, since different species have different requirements and tolerance ranges for various environmental factors. The use of biological indicators is especially useful in arctic areas, were many of the chemical factors commonly fall under the detection limit and therefore do not provide much information about the environment. This work brings new information about species distribution and dynamics of arctic freshwater phytoplankton in relation to environmental factors. The phytoplankton of lakes in Finnish Lapland and other European high-altitude or high-latitude areas were compared. Most lakes were oligotrophic and dominated by flagellated species belonging to chrysophytes, cryptophytes and dinoflagellates. In Finnish Lapland cryptophytes were of less importance, whereas desmids had high species richness in many of the lakes. In Pan-European scale, geographical and catchment-related factors were explaining most of the differences in species distributions between different districts, whereas lake water chemistry (especially conductivity, SiO2 and pH) was most important regionally. Seasonal and interannual variation of phytoplankton was studied in subarctic Lake Saanajärvi. Characteristic phytoplankton species in this oligotrophic, dimictic lake belonged mainly to chrysophytes and diatoms. The maximum phytoplankton biomass in Lake Saanajärvi occurs during autumn, while spring biomass is very low. During years with heavy snow cover the lake suffers from pH drop caused by melt waters, but the effects of this acid pulse are restricted to surface layers and last for a relatively short period. In addition to some chemical parameters (mainly Ca and nutrients), length of the mixing cycle and physical factors such as lake water temperature and thermal stability of water column had major impact on phytoplankton dynamics. During a year with long and strong thermal stability, the phytoplankton community developed towards an equilibrium state, with heavy dominance of only a few taxa for a longer period of time. During a year with higher windiness and less thermal stability, the species composition was more diverse and species with different functional strategies were able to occur simultaneously. The results of this work indicate that although arctic lakes in general share many common features concerning their catchment and water chemistry, large differences in biological features can be found even in a relatively small area. Most likely the lakes with very different algal flora do not respond in a similar way to differences in the environmental factors, and more information about specific arctic lake types is needed. The results also show considerable year to year differences in phytoplankton species distribution and dynamics, and these changes are most likely linked to climatic factors.

Kesämökkikäynnin virkistysarvon määrittäminen matkakustannusmenetelmällä

Tämän tutkielman tarkoituksena on määrittää kesämökkikäynnin virkistysarvo. Aihetta ei ole aikaisemmin tutkittu, vaikka kesämökkeily on merkittävä osa suomalaista elämää. Kesämökkikäynnin virkistysarvo tarkoittaa hyötyä, jonka yksilö saa kesämökillä virkistäytymisestä. Virkistäytyminen kesämökillä pitää sisällään kaiken kesämökillä ja sen ympäristössä tapahtuvan harrastamisen ja rentoutumisen. Koska ympäristö on tärkeässä osassa mökillä virkistäytymisessä, tässä tutkielmassa on lisäksi tarkoitus tutkia, kuinka mökkiympäristön ominaisuudet vaikuttavat virkistysarvoon. Tarkasteltavina ympäristön ominaisuuksina ovat virkistäytymisen estävät leväkukinnot ja mökin rannattomuus. Koska mökkeily toisaalta myös kuormittaa ympäristöä, tutkielmassa tutkitaan myös, kuinka sähköistys, ympäristöä kuormittava kesämökin ominaisuus, vaikuttaa virkistysarvoon. Virkistysarvo on markkinaton hyöty, joten sen määrittämiseen on käytettävä jotain markkinattomien hyödykkeiden arvottamismenetelmää. Tässä työssä arvottaminen tapahtuu matkakustannusmenetelmällä, jota käytetään yleisesti ympäristön tarjoamien virkistyspalveluiden taloudelliseen arvottamiseen. Kesämökkikäyntien kysyntää kuvaava matkakustannusmallin ekonometrinen mallintaminen suoritetaan negatiivisella binomimallilla. Tutkielman tulosten mukaan noin neljän päivän pituinen käynti sähköistetyllä kesämökillä, jossa on ranta eivätkä levät häiritse virkistäytymistä, tuottaa 167-205 euron suuruisen virkistyshyödyn. Virkistäytymisen estävät leväkukinnot laskevat arvoa 40 prosentilla ja mökin rannattomuus 45 prosentilla. Käynti sähköistetyllä mökillä tuottaa 3-5 prosenttia korkeamman virkistyshyödyn kuin käynti sähköistämättömällä mökillä. Suomessa kesän aikana tehtävien mökkikäyntien yhteenlaskettu virkistyshyöty on 430-530 miljoonaa, jos mökillä on ranta, jossa levistä ei ole haittaa. Häiritsevät leväkukinnot laskevat yhteenlaskettua virkistyshyötyä 30 miljoonalla ja rannattomuus 10-20 miljoonalla. Sähköistys nostaa yhteenlaskettua virkistyshyötyä 20-30 miljoonalla eurolla.

Univariate, bivariate, and multivariate methods in corpus-based lexicography : A study of synonymy

In this dissertation, I present an overall methodological framework for studying linguistic alternations, focusing specifically on lexical variation in denoting a single meaning, that is, synonymy. As the practical example, I employ the synonymous set of the four most common Finnish verbs denoting THINK, namely ajatella, miettiä, pohtia and harkita ‘think, reflect, ponder, consider’. As a continuation to previous work, I describe in considerable detail the extension of statistical methods from dichotomous linguistic settings (e.g., Gries 2003; Bresnan et al. 2007) to polytomous ones, that is, concerning more than two possible alternative outcomes. The applied statistical methods are arranged into a succession of stages with increasing complexity, proceeding from univariate via bivariate to multivariate techniques in the end. As the central multivariate method, I argue for the use of polytomous logistic regression and demonstrate its practical implementation to the studied phenomenon, thus extending the work by Bresnan et al. (2007), who applied simple (binary) logistic regression to a dichotomous structural alternation in English. The results of the various statistical analyses confirm that a wide range of contextual features across different categories are indeed associated with the use and selection of the selected think lexemes; however, a substantial part of these features are not exemplified in current Finnish lexicographical descriptions. The multivariate analysis results indicate that the semantic classifications of syntactic argument types are on the average the most distinctive feature category, followed by overall semantic characterizations of the verb chains, and then syntactic argument types alone, with morphological features pertaining to the verb chain and extra-linguistic features relegated to the last position. In terms of overall performance of the multivariate analysis and modeling, the prediction accuracy seems to reach a ceiling at a Recall rate of roughly two-thirds of the sentences in the research corpus. The analysis of these results suggests a limit to what can be explained and determined within the immediate sentential context and applying the conventional descriptive and analytical apparatus based on currently available linguistic theories and models. The results also support Bresnan’s (2007) and others’ (e.g., Bod et al. 2003) probabilistic view of the relationship between linguistic usage and the underlying linguistic system, in which only a minority of linguistic choices are categorical, given the known context – represented as a feature cluster – that can be analytically grasped and identified. Instead, most contexts exhibit degrees of variation as to their outcomes, resulting in proportionate choices over longer stretches of usage in texts or speech.

Kilpailukykyvaltion koululainsäädännön rakentuminen : Suomen eduskunta ja 1990-luvun koulutuspoliittinen käänne

Finnish education policy, educational legislation and the entire education system changed significantly during the 1990s as part of a general restructuring of public administration. There has been a clear divergence from the former tradition of a system of regulation, founded on detailed legislation and the principle of equality. The new governance, which is based more on individual choice, efficiency and evaluation, emphasizes that the development of a high standard of education is a necessity in the light of global competition. This study explores the legislative process regarding education policy in the Finnish Parliament during the 1990s, and highlights in particular how the international discourse on education policies was restructured in the context of Finnish legislation. The research material consists of all the public parliamentary documents relating to education, including government proposals, minutes from the discussions in the chamber and archive material (final protocols, reports and statements) for the Committee for Education and Culture. The discourse on the process of drafting and passing education legislation is modelled on three interrelated policy technologies (market, management and performance), which are understood here as mechanisms connecting general political ideas to normative legislation. The changes in the regulation of education were part of a general public administration reform instigated during the mid 1980s. The research results will prove that during the left-right coalition cabinet of PM Harri Holkeri, new policy technologies affected the parliamentary discourse on education policy. This was particularly influenced by a change in the preconditions for the management of education that was created as a result of the numerous demands to deregulate and delegate decision-making authority to the local and school levels while rendering the whole education system more effective. At the turn of the decade, market-type mechanisms were more indirectly manifested in the forms of individuality and freedom of choice, which were reflected, for example, in proposals to “lower the hurdles” by separating general from vocational secondary education with a view to encouraging students to select courses from other educational establishments, in addition to relaxing the requirements for establishing private schools and abolishing a hundred-year-old strict national catchment-area system. Later, in the course of the 1990s, after the subjects, players, and methods of evaluation had been more precisely defined, evaluation based on performance would result in the active measurement of the attainment of set objectives. In the spring of 1991, from the outset of PM Esko Aho's right-centre coalition cabinet, the education budget suffered cutbacks as a result of a global recession and this influenced the legislative work of, and discourses in, parliament. Representatives of the parties in power regarded the recession solely as an external factor that was remote from the political arena. In their view, the education system should rise to the challenge by ensuring the efficient and innovative use of the resources available and by developing new forms of indicators for evaluating results. Representatives of the opposition opposed the cabinet’s standpoint as a result of the recession, criticized the measures taken by pointing out the harmful effect of constantly cutting the budget and argued that the government had made political capital out of the recession by using it as an opportunity to give more room to market, management and performance technologies within the Finnish education system. Criticism of the new education policy became even stronger during PM Paavo Lipponen's first “rainbow” coalition cabinet with critical views being expressed not only from the opposition but also from representatives within the government. Representatives from the left demanded legislative restrictions and the instigation of measures to relieve the presumed negative effects of market, management and performance in the name of educational equality. The new management by results steering method within the university sector and the introduction of commercial education services in compulsory education were fiercely criticized. The argument over “setting outer limits” including, for example, the demands for more detailed legislation and earmarked state subsidies was characteristic of Parliament’s legislative discourse in the latter part of the 1990s. Keywords: education policy, education legislation, Parliament of Finland

On the Rademacher maximal function

Tools known as maximal functions are frequently used in harmonic analysis when studying local behaviour of functions. Typically they measure the suprema of local averages of non-negative functions. It is essential that the size (more precisely, the L^p-norm) of the maximal function is comparable to the size of the original function. When dealing with families of operators between Banach spaces we are often forced to replace the uniform bound with the larger R-bound. Hence such a replacement is also needed in the maximal function for functions taking values in spaces of operators. More specifically, the suprema of norms of local averages (i.e. their uniform bound in the operator norm) has to be replaced by their R-bound. This procedure gives us the Rademacher maximal function, which was introduced by Hytönen, McIntosh and Portal in order to prove a certain vector-valued Carleson's embedding theorem. They noticed that the sizes of an operator-valued function and its Rademacher maximal function are comparable for many common range spaces, but not for all. Certain requirements on the type and cotype of the spaces involved are necessary for this comparability, henceforth referred to as the “RMF-property”. It was shown, that other objects and parameters appearing in the definition, such as the domain of functions and the exponent p of the norm, make no difference to this. After a short introduction to randomized norms and geometry in Banach spaces we study the Rademacher maximal function on Euclidean spaces. The requirements on the type and cotype are considered, providing examples of spaces without RMF. L^p-spaces are shown to have RMF not only for p greater or equal to 2 (when it is trivial) but also for 1 < p < 2. A dyadic version of Carleson's embedding theorem is proven for scalar- and operator-valued functions. As the analysis with dyadic cubes can be generalized to filtrations on sigma-finite measure spaces, we consider the Rademacher maximal function in this case as well. It turns out that the RMF-property is independent of the filtration and the underlying measure space and that it is enough to consider very simple ones known as Haar filtrations. Scalar- and operator-valued analogues of Carleson's embedding theorem are also provided. With the RMF-property proven independent of the underlying measure space, we can use probabilistic notions and formulate it for martingales. Following a similar result for UMD-spaces, a weak type inequality is shown to be (necessary and) sufficient for the RMF-property. The RMF-property is also studied using concave functions giving yet another proof of its independence from various parameters.

The Macroeconomic Effects of Fiscal Policy in a Small Open Economy under a Flexible Exchange Rate Regime

This licentiate's thesis analyzes the macroeconomic effects of fiscal policy in a small open economy under a flexible exchange rate regime, assuming that the government spends exclusively on domestically produced goods. The motivation for this research comes from the observation that the literature on the new open economy macroeconomics (NOEM) has focused almost exclusively on two-country global models and the analyses of the effects of fiscal policy on small economies are almost completely ignored. This thesis aims at filling in the gap in the NOEM literature and illustrates how the macroeconomic effects of fiscal policy in a small open economy depend on the specification of preferences. The research method is to present two theoretical model that are extensions to the model contained in the Appendix to Obstfeld and Rogoff (1995). The first model analyzes the macroeconomic effects of fiscal policy, making use of a model that exploits the idea of modelling private and government consumption as substitutes in private utility. The model offers intuitive predictions on how the effects of fiscal policy depend on the marginal rate of substitution between private and government consumption. The findings illustrate that the higher the substitutability between private and government consumption, (i) the bigger is the crowding out effect on private consumption (ii) and the smaller is the positive effect on output. The welfare analysis shows that the less fiscal policy decreases welfare the higher is the marginal rate of substitution between private and government consumption. The second model of this thesis studies how the macroeconomic effects of fiscal policy depend on the elasticity of substitution between traded and nontraded goods. This model reveals that this elasticity a key variable to explain the exchange rate, current account and output response to a permanent rise in government spending. Finally, the model demonstrates that temporary changes in government spending are an effective stabilization tool when used wisely and timely in response to undesired fluctuations in output. Undesired fluctuations in output can be perfectly offset by an opposite change in government spending without causing any side-effects.

The effects of the 2004 reduction in the price of alcohol on alcohol-related harm in Finland : A natural experiment based on register data

Changes in alcohol pricing have been documented as inversely associated with changes in consumption and alcohol-related problems. Evidence of the association between price changes and health problems is nevertheless patchy and is based to a large extent on cross-sectional state-level data, or time series of such cross-sectional analyses. Natural experimental studies have been called for. There was a substantial reduction in the price of alcohol in Finland in 2004 due to a reduction in alcohol taxes of one third, on average, and the abolition of duty-free allowances for travellers from the EU. These changes in the Finnish alcohol policy could be considered a natural experiment, which offered a good opportunity to study what happens with regard to alcohol-related problems when prices go down. The present study investigated the effects of this reduction in alcohol prices on (1) alcohol-related and all-cause mortality, and mortality due to cardiovascular diseases, (2) alcohol-related morbidity in terms of hospitalisation, (3) socioeconomic differentials in alcohol-related mortality, and (4) small-area differences in interpersonal violence in the Helsinki Metropolitan area. Differential trends in alcohol-related mortality prior to the price reduction were also analysed. A variety of population-based register data was used in the study. Time-series intervention analysis modelling was applied to monthly aggregations of deaths and hospitalisation for the period 1996-2006. These and other mortality analyses were carried out for men and women aged 15 years and over. Socioeconomic differentials in alcohol-related mortality were assessed on a before/after basis, mortality being followed up in 2001-2003 (before the price reduction) and 2004-2005 (after). Alcohol-related mortality was defined in all the studies on mortality on the basis of information on both underlying and contributory causes of death. Hospitalisation related to alcohol meant that there was a reference to alcohol in the primary diagnosis. Data on interpersonal violence was gathered from 86 administrative small-areas in the Helsinki Metropolitan area and was also assessed on a before/after basis followed up in 2002-2003 and 2004-2005. The statistical methods employed to analyse these data sets included time-series analysis, and Poisson and linear regression. The results of the study indicate that alcohol-related deaths increased substantially among men aged 40-69 years and among women aged 50-69 after the price reduction when trends and seasonal variation were taken into account. The increase was mainly attributable to chronic causes, particularly liver diseases. Mortality due to cardiovascular diseases and all-cause mortality, on the other hand, decreased considerably among the-over-69-year-olds. The increase in alcohol-related mortality in absolute terms among the 30-59-year-olds was largest among the unemployed and early-age pensioners, and those with a low level of education, social class or income. The relative differences in change between the education and social class subgroups were small. The employed and those under the age of 35 did not suffer from increased alcohol-related mortality in the two years following the price reduction. The gap between the age and education groups, which was substantial in the 1980s, thus further broadened. With regard to alcohol-related hospitalisation, there was an increase in both chronic and acute causes among men under the age of 70, and among women in the 50-69-year age group when trends and seasonal variation were taken into account. Alcohol dependence and other alcohol-related mental and behavioural disorders were the largest category in both the total number of chronic hospitalisation and in the increase. There was no increase in the rate of interpersonal violence in the Helsinki Metropolitan area, and even a decrease in domestic violence. There was a significant relationship between the measures of social disadvantage on the area level and interpersonal violence, although the differences in the effects of the price reduction between the different areas were small. The findings of the present study suggest that that a reduction in alcohol prices may lead to a substantial increase in alcohol-related mortality and morbidity. However, large population group differences were observed regarding responsiveness to the price changes. In particular, the less privileged, such as the unemployed, were most sensitive. In contrast, at least in the Finnish context, the younger generations and the employed do not appear to be adversely affected, and those in the older age groups may even benefit from cheaper alcohol in terms of decreased rates of CVD mortality. The results also suggest that reductions in alcohol prices do not necessarily affect interpersonal violence. The population group differences in the effects of the price changes on alcohol-related harm should be acknowledged, and therefore the policy actions should focus on the population subgroups that are primarily responsive to the price reduction.

Essays on the Linkages Between Financial Markets, and Risk Asymmetries (summary section only)

During the last few decades there have been far going financial market deregulation, technical development, advances in information technology, and standardization of legislation between countries. As a result, one can expect that financial markets have grown more interlinked. The proper understanding of the cross-market linkages has implications for investment and risk management, diversification, asset pricing, and regulation. The purpose of this research is to assess the degree of price, return, and volatility linkages between both geographic markets and asset categories within one country, Finland. Another purpose is to analyze risk asymmetries, i.e., the tendency of equity risk to be higher after negative events than after positive events of equal magnitude. The analysis is conducted both with respect to total risk (volatility), and systematic risk (beta). The thesis consists of an introductory part and four essays. The first essay studies to which extent international stock prices comove. The degree of comovements is low, indicating benefits from international diversification. The second essay examines the degree to which the Finnish market is linked to the “world market”. The total risk is divided into two parts, one relating to world factors, and one relating to domestic factors. The impact of world factors has increased over time. After 1993, when foreign investors were allowed to freely invest in Finnish assets, the risk level has been higher than previously. This was also the case during the economic recession in the beginning of the 1990’s. The third essay focuses on the stock, bond, and money markets in Finland. According to a trading model, the degree of volatility linkages should be strong. However, the results contradict this. The linkages are surprisingly weak, even negative. The stock market is the most independent, while the money market is affected by events on the two other markets. The fourth essay concentrates on volatility and beta asymmetries. Contrary to many international studies there are only few cases of risk asymmetries. When they occur, they tend to be driven by the market-wide component rather than the portfolio specific element.

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.