An axiomatization of the nucleolus of the assignment game

[cat] En el domini dels jocs bilaterals d’assignació, es presenta una axiomàtica del nucleolus com l´unica solució que compleix les propietats de consistència respecte del joc derivat definit per Owen (1992) i monotonia de les queixes dels sectors respecte de la seva cardinalitat. Com a conseqüència obtenim una caracterització geomètrica del nucleolus mitjançant una propietat de bisecció més forta que la que satisfan els punts del kernel (Maschler et al, 1979).

A note on the coincidence between Stackelberg and Nash equilibria in a differential game between government and firms

[cat] A Navas i Marín Solano es va demostrar la coincidència entre els equilibris de Nash i de Stackelberg per a una versi´o modificada del joc diferencial proposat por Lancaster (1973). Amb l’objectiu d’obtenir una solució interior, es van imposar restriccions importants sobre el valors dels paràmetres del model. En aquest treball estenem aquest resultat, en el límit en que la taxa de descompte és igual a zero, eliminant les restriccions i considerant totes les solucions possibles.

The maximun and the addition of assigment games

[cat] En el context dels mercats a dues bandes, considerem, en primer lloc, que els jugadors poden escollir on dur a terme les seves transaccions. Mostrem que el joc corresponent a aquesta situació, que es representa pel màxim d’un conjunt finit de jocs d’assignació, pot ser un joc no equilibrat. Aleshores proporcionem condicions per a l’equilibri del joc i, per aquest cas, analitzem algunes propietats del core del joc. En segon lloc, considerem que els jugadors poden fer transaccions en diversos mercats simultàniament i, llavors, sumar els guanys obtinguts. El joc corresponent, representat per la suma d’un conjunt finit de jocs d’assignació, és equilibrat. A més a més, sota certes condicions, la suma dels cores dels dos jocs d’assignació coincideix amb el core del joc suma.

Exposure to superfluous information reduces cooperation and increases antisocial punishment in reputation-based interactions

Human cooperation is often based on reputation gained from previous interactions with third parties. Such reputation can be built on generous or punitive actions, and both, one's own reputation and the reputation of others have been shown to influence decision making in experimental games that control for confounding variables. Here we test how reputation-based cooperation and punishment react to disruption of the cognitive processing in different kinds of helping games with observers. Saying a few superfluous words before each interaction was used to possibly interfere with working memory. In a first set of experiments, where reputation could only be based on generosity, the disruption reduced the frequency of cooperation and lowered mean final payoffs. In a second set of experiments where reputation could only be based on punishment, the disruption increased the frequency of antisocial punishment (i.e. of punishing those who helped) and reduced the frequency of punishing defectors. Our findings suggest that working memory can easily be constraining in reputation-based interactions within experimental games, even if these games are based on a few simple rules with a visual display that provides all the information the subjects need to play the strategies predicted from current theory. Our findings also highlight a weakness of experimental games, namely that they can be very sensitive to environmental variation and that quantitative conclusions about antisocial punishment or other behavioral strategies can easily be misleading.

Conformity, upstream reciprocity and social diversity: secondary mechanisms for the evolution of cooperation

Cooperation is ubiquitous in nature: genes cooperate in genomes, cells in muti- cellular organims, and individuals in societies. In humans, division of labor and trade are key elements of most known societies, where social life is regulated by- moral systems specifying rights and duties often enforced by third party punish¬ment. Over the last decades, several primary mechanisms, such as kin selection, direct and indirect reciprocity, have been advanced to explain the evolution of cooperation from a naturalistic approach. In this thesis, I focus on the study of three secondary mechanisms which, although insufficient to allow for the evo¬lution of cooperation, have been hypothesized to further promote it when they are linked to proper primary mechanisms: conformity (the tendency to imitate common behaviors), upstream reciprocity (the tendency to help somebody once help has been received from somebody else) and social diversity (heterogeneous social contexts). I make use of mathematical and computational models in the formal framework of evolutionary game theory in order to investigate the theoret¬ical conditions under which conformity, upstream reciprocity and social diversity are able to raise the levels of cooperation attained in evolving populations. - La coopération est ubiquitaire dans la nature: les gènes coopèrent dans les génomes, les cellules dans les organismes muticellulaires, et les organismes dans les sociétés. Chez les humains, la division du travail et le commerce sont des éléments centraux de la plupart des sociétés connues, où la vie sociale est régie par des systèmes moraux établissant des droits et des devoirs, souvent renforcés par la punition. Au cours des dernières décennies, plusieurs mécanismes pri¬maires, tels que la sélection de parentèle et les réciprocités directe et indirecte, ont été avancés pour expliquer l'évolution de la coopération d'un point de vue nat¬uraliste. Dans cette thèse, nous nous concentrons sur l'étude de trois mécanismes secondaires qui, bien qu'insuffisants pour permettre l'évolution de la coopération, sont capables de la promouvoir davantage s'ils sont liés aux mécanismes primaires appropriés: la conformité (tendance à imiter des comportements en commun), la 'réciprocité en amont' (tendance à aider quelqu'un après avoir reçu l'aide de quelqu'un d'autre) et la diversité sociale (contextes sociaux hétérogènes). Nous faisons usage de modèles mathématiques et informatiques dans le cadre formel de la théorie des jeux évolutionnaires afin d'examiner les conditions théoriques dans lesquelles la conformité, la 'réciprocité en amont' et la diversité sociale sont capables d'élever le niveau de coopération des populations en évolution.

A general theory of rank testing

This paper develops an approach to rank testing that nests all existing rank tests andsimplifies their asymptotics. The approach is based on the fact that implicit in every ranktest there are estimators of the null spaces of the matrix in question. The approach yieldsmany new insights about the behavior of rank testing statistics under the null as well as localand global alternatives in both the standard and the cointegration setting. The approach alsosuggests many new rank tests based on alternative estimates of the null spaces as well as thenew fixed-b theory. A brief Monte Carlo study illustrates the results.

Risk and global change : developing scientific methods for advocacy and awareness raising

Les catastrophes sont souvent perçues comme des événements rapides et aléatoires. Si les déclencheurs peuvent être soudains, les catastrophes, elles, sont le résultat d'une accumulation des conséquences d'actions et de décisions inappropriées ainsi que du changement global. Pour modifier cette perception du risque, des outils de sensibilisation sont nécessaires. Des méthodes quantitatives ont été développées et ont permis d'identifier la distribution et les facteurs sous- jacents du risque.¦Le risque de catastrophes résulte de l'intersection entre aléas, exposition et vulnérabilité. La fréquence et l'intensité des aléas peuvent être influencées par le changement climatique ou le déclin des écosystèmes, la croissance démographique augmente l'exposition, alors que l'évolution du niveau de développement affecte la vulnérabilité. Chacune de ses composantes pouvant changer, le risque est dynamique et doit être réévalué périodiquement par les gouvernements, les assurances ou les agences de développement. Au niveau global, ces analyses sont souvent effectuées à l'aide de base de données sur les pertes enregistrées. Nos résultats montrent que celles-ci sont susceptibles d'être biaisées notamment par l'amélioration de l'accès à l'information. Elles ne sont pas exhaustives et ne donnent pas d'information sur l'exposition, l'intensité ou la vulnérabilité. Une nouvelle approche, indépendante des pertes reportées, est donc nécessaire.¦Les recherches présentées ici ont été mandatées par les Nations Unies et par des agences oeuvrant dans le développement et l'environnement (PNUD, l'UNISDR, la GTZ, le PNUE ou l'UICN). Ces organismes avaient besoin d'une évaluation quantitative sur les facteurs sous-jacents du risque, afin de sensibiliser les décideurs et pour la priorisation des projets de réduction des risques de désastres.¦La méthode est basée sur les systèmes d'information géographique, la télédétection, les bases de données et l'analyse statistique. Une importante quantité de données (1,7 Tb) et plusieurs milliers d'heures de calculs ont été nécessaires. Un modèle de risque global a été élaboré pour révéler la distribution des aléas, de l'exposition et des risques, ainsi que pour l'identification des facteurs de risque sous- jacent de plusieurs aléas (inondations, cyclones tropicaux, séismes et glissements de terrain). Deux indexes de risque multiples ont été générés pour comparer les pays. Les résultats incluent une évaluation du rôle de l'intensité de l'aléa, de l'exposition, de la pauvreté, de la gouvernance dans la configuration et les tendances du risque. Il apparaît que les facteurs de vulnérabilité changent en fonction du type d'aléa, et contrairement à l'exposition, leur poids décroît quand l'intensité augmente.¦Au niveau local, la méthode a été testée pour mettre en évidence l'influence du changement climatique et du déclin des écosystèmes sur l'aléa. Dans le nord du Pakistan, la déforestation induit une augmentation de la susceptibilité des glissements de terrain. Les recherches menées au Pérou (à base d'imagerie satellitaire et de collecte de données au sol) révèlent un retrait glaciaire rapide et donnent une évaluation du volume de glace restante ainsi que des scénarios sur l'évolution possible.¦Ces résultats ont été présentés à des publics différents, notamment en face de 160 gouvernements. Les résultats et les données générées sont accessibles en ligne (http://preview.grid.unep.ch). La méthode est flexible et facilement transposable à des échelles et problématiques différentes, offrant de bonnes perspectives pour l'adaptation à d'autres domaines de recherche.¦La caractérisation du risque au niveau global et l'identification du rôle des écosystèmes dans le risque de catastrophe est en plein développement. Ces recherches ont révélés de nombreux défis, certains ont été résolus, d'autres sont restés des limitations. Cependant, il apparaît clairement que le niveau de développement configure line grande partie des risques de catastrophes. La dynamique du risque est gouvernée principalement par le changement global.¦Disasters are often perceived as fast and random events. If the triggers may be sudden, disasters are the result of an accumulation of actions, consequences from inappropriate decisions and from global change. To modify this perception of risk, advocacy tools are needed. Quantitative methods have been developed to identify the distribution and the underlying factors of risk.¦Disaster risk is resulting from the intersection of hazards, exposure and vulnerability. The frequency and intensity of hazards can be influenced by climate change or by the decline of ecosystems. Population growth increases the exposure, while changes in the level of development affect the vulnerability. Given that each of its components may change, the risk is dynamic and should be reviewed periodically by governments, insurance companies or development agencies. At the global level, these analyses are often performed using databases on reported losses. Our results show that these are likely to be biased in particular by improvements in access to information. International losses databases are not exhaustive and do not give information on exposure, the intensity or vulnerability. A new approach, independent of reported losses, is necessary.¦The researches presented here have been mandated by the United Nations and agencies working in the development and the environment (UNDP, UNISDR, GTZ, UNEP and IUCN). These organizations needed a quantitative assessment of the underlying factors of risk, to raise awareness amongst policymakers and to prioritize disaster risk reduction projects.¦The method is based on geographic information systems, remote sensing, databases and statistical analysis. It required a large amount of data (1.7 Tb of data on both the physical environment and socio-economic parameters) and several thousand hours of processing were necessary. A comprehensive risk model was developed to reveal the distribution of hazards, exposure and risk, and to identify underlying risk factors. These were performed for several hazards (e.g. floods, tropical cyclones, earthquakes and landslides). Two different multiple risk indexes were generated to compare countries. The results include an evaluation of the role of the intensity of the hazard, exposure, poverty, governance in the pattern and trends of risk. It appears that the vulnerability factors change depending on the type of hazard, and contrary to the exposure, their weight decreases as the intensity increases.¦Locally, the method was tested to highlight the influence of climate change and the ecosystems decline on the hazard. In northern Pakistan, deforestation exacerbates the susceptibility of landslides. Researches in Peru (based on satellite imagery and ground data collection) revealed a rapid glacier retreat and give an assessment of the remaining ice volume as well as scenarios of possible evolution.¦These results were presented to different audiences, including in front of 160 governments. The results and data generated are made available online through an open source SDI (http://preview.grid.unep.ch). The method is flexible and easily transferable to different scales and issues, with good prospects for adaptation to other research areas. The risk characterization at a global level and identifying the role of ecosystems in disaster risk is booming. These researches have revealed many challenges, some were resolved, while others remained limitations. However, it is clear that the level of development, and more over, unsustainable development, configures a large part of disaster risk and that the dynamics of risk is primarily governed by global change.

A geometric chracterization of the nucleolus of the assignment game

Maschler et al. (1979) caracteritzen geomètricament la intersecció del kernel i del core en els jocs cooperatius, demostrant que les distribucions que pertanyen a ambdós conjunts es troben en el punt mig d’un cert rang de negociació entre parelles de jugadors. En el cas dels jocs d’assignació, aquesta caracterització vol dir que el kernel només conté aquells elements del core on el màxim que un jugador pot transferir a una parella òptima és igual al màxim que aquesta parella li pot transferir, sense sortir-se’n del core. En aquest treball demostrem que el nucleolus d’un joc d’assignació queda caracteritzat si requerim que aquesta propietat de bisecció es compleixi no només per parelles, sinó també per coalicions entre sectors aparellades òptimament.

A geometric chracterization of the nucleolus of the assignment game

Maschler et al. (1979) caracteritzen geomètricament la intersecció del kernel i del core en els jocs cooperatius, demostrant que les distribucions que pertanyen a ambdós conjunts es troben en el punt mig d’un cert rang de negociació entre parelles de jugadors. En el cas dels jocs d’assignació, aquesta caracterització vol dir que el kernel només conté aquells elements del core on el màxim que un jugador pot transferir a una parella òptima és igual al màxim que aquesta parella li pot transferir, sense sortir-se’n del core. En aquest treball demostrem que el nucleolus d’un joc d’assignació queda caracteritzat si requerim que aquesta propietat de bisecció es compleixi no només per parelles, sinó també per coalicions entre sectors aparellades òptimament.

Coopetitive advantage – How firms create and appropriate value by collaborating with their competitors

Collaboration between competing firms (coopetition) has emerged as an important issue forn business practice in many industries. Extant literature has examined coopetition on many levels of analysis, but lacks clarity in distinguishing it explicitly from cooperation between noncompeting organizations. Because of this, the performance implications of coopetition from the perspective of an individual firm are still ambiguous – some research suggests positive results whereas other studies suggest detrimental outcomes. The aim in this dissertation is to narrow these gaps by exploring how firms create and appropriate value through collaboration with their competitors. The dissertation is divided into two parts. The first part comprises an overview of the relevant literature, as well as the conclusions of the whole study, and the second part includes six research publications. Both qualitative and quantitative methodologies are utilized. The results suggest that coopetition embodies the distinctive logic of value creation and appropriation from the perspective of an individual firm, and thus differs in terms of performance implications from cooperation between non-competitors. The distinction comes from the fact that competitors have somewhat similar understanding, capabilities and interest related to certain markets, which is potentially both challenging and beneficial in terms of the individual firm’s competitiveness. It appears from the findings that there are distinctive firm-external and firm-specific factors affecting the success of a coopetition strategy. This study makes three main contributions. First, on the conceptual level it shows the distinction between coopetition and cooperation between non-rivals as a collaborative inter-organizational relationship. Secondly, it sets out a framework and propositions that enhance understanding of how value is created and appropriated in coopetition from the perspective of an individual firm. Thirdly, it offers empirical evidence of how coopetition affects firms’ innovation and market performance, and identifies the focal internal and external factors involved. In general terms, the thesis adds to our knowledge of how a firm can successfully utilize a coopetition strategy in its pursuit of improved performance.

Spontaneous Focusing on Quantitative Relations and the Development of Rational Number Conceptual Knowledge

The aim of the present set of studies was to explore primary school children’s Spontaneous Focusing On quantitative Relations (SFOR) and its role in the development of rational number conceptual knowledge. The specific goals were to determine if it was possible to identify a spontaneous quantitative focusing tendency that indexes children’s tendency to recognize and utilize quantitative relations in non-explicitly mathematical situations and to determine if this tendency has an impact on the development of rational number conceptual knowledge in late primary school. To this end, we report on six original empirical studies that measure SFOR in children ages five to thirteen years and the development of rational number conceptual knowledge in ten- to thirteen-year-olds. SFOR measures were developed to determine if there are substantial differences in SFOR that are not explained by the ability to use quantitative relations. A measure of children’s conceptual knowledge of the magnitude representations of rational numbers and the density of rational numbers is utilized to capture the process of conceptual change with rational numbers in late primary school students. Finally, SFOR tendency was examined in relation to the development of rational number conceptual knowledge in these students. Study I concerned the first attempts to measure individual differences in children’s spontaneous recognition and use of quantitative relations in 86 Finnish children from the ages of five to seven years. Results revealed that there were substantial inter-individual differences in the spontaneous recognition and use of quantitative relations in these tasks. This was particularly true for the oldest group of participants, who were in grade one (roughly seven years old). However, the study did not control for ability to solve the tasks using quantitative relations, so it was not clear if these differences were due to ability or SFOR. Study II more deeply investigated the nature of the two tasks reported in Study I, through the use of a stimulated-recall procedure examining children’s verbalizations of how they interpreted the tasks. Results reveal that participants were able to verbalize reasoning about their quantitative relational responses, but not their responses based on exact number. Furthermore, participants’ non-mathematical responses revealed a variety of other aspects, beyond quantitative relations and exact number, which participants focused on in completing the tasks. These results suggest that exact number may be more easily perceived than quantitative relations. As well, these tasks were revealed to contain both mathematical and non-mathematical aspects which were interpreted by the participants as relevant. Study III investigated individual differences in SFOR 84 children, ages five to nine, from the US and is the first to report on the connection between SFOR and other mathematical abilities. The cross-sectional data revealed that there were individual differences in SFOR. Importantly, these differences were not entirely explained by the ability to solve the tasks using quantitative relations, suggesting that SFOR is partially independent from the ability to use quantitative relations. In other words, the lack of use of quantitative relations on the SFOR tasks was not solely due to participants being unable to solve the tasks using quantitative relations, but due to a lack of the spontaneous attention to the quantitative relations in the tasks. Furthermore, SFOR tendency was found to be related to arithmetic fluency among these participants. This is the first evidence to suggest that SFOR may be a partially distinct aspect of children’s existing mathematical competences. Study IV presented a follow-up study of the first graders who participated in Studies I and II, examining SFOR tendency as a predictor of their conceptual knowledge of fraction magnitudes in fourth grade. Results revealed that first graders’ SFOR tendency was a unique predictor of fraction conceptual knowledge in fourth grade, even after controlling for general mathematical skills. These results are the first to suggest that SFOR tendency may play a role in the development of rational number conceptual knowledge. Study V presents a longitudinal study of the development of 263 Finnish students’ rational number conceptual knowledge over a one year period. During this time participants completed a measure of conceptual knowledge of the magnitude representations and the density of rational numbers at three time points. First, a Latent Profile Analysis indicated that a four-class model, differentiating between those participants with high magnitude comparison and density knowledge, was the most appropriate. A Latent Transition Analysis reveal that few students display sustained conceptual change with density concepts, though conceptual change with magnitude representations is present in this group. Overall, this study indicated that there were severe deficiencies in conceptual knowledge of rational numbers, especially concepts of density. The longitudinal Study VI presented a synthesis of the previous studies in order to specifically detail the role of SFOR tendency in the development of rational number conceptual knowledge. Thus, the same participants from Study V completed a measure of SFOR, along with the rational number test, including a fourth time point. Results reveal that SFOR tendency was a predictor of rational number conceptual knowledge after two school years, even after taking into consideration prior rational number knowledge (through the use of residualized SFOR scores), arithmetic fluency, and non-verbal intelligence. Furthermore, those participants with higher-than-expected SFOR scores improved significantly more on magnitude representation and density concepts over the four time points. These results indicate that SFOR tendency is a strong predictor of rational number conceptual development in late primary school children. The results of the six studies reveal that within children’s existing mathematical competences there can be identified a spontaneous quantitative focusing tendency named spontaneous focusing on quantitative relations. Furthermore, this tendency is found to play a role in the development of rational number conceptual knowledge in primary school children. Results suggest that conceptual change with the magnitude representations and density of rational numbers is rare among this group of students. However, those children who are more likely to notice and use quantitative relations in situations that are not explicitly mathematical seem to have an advantage in the development of rational number conceptual knowledge. It may be that these students gain quantitative more and qualitatively better self-initiated deliberate practice with quantitative relations in everyday situations due to an increased SFOR tendency. This suggests that it may be important to promote this type of mathematical activity in teaching rational numbers. Furthermore, these results suggest that there may be a series of spontaneous quantitative focusing tendencies that have an impact on mathematical development throughout the learning trajectory.

Bone properties and skeletal maturity in adolescent males, as assessed by quantitative ultrasound

ABSTRACT Background: Previous studies have implied that weight-bearing, intense and prolonged physical activities optimize bone accretion during the grow^ing years. The majority of past inquiries have used dual-energy X-ray absorptiometry (DXA) to examine bone strength and hand-wrist radiography to determine skeletal maturity in children. Recently, quantitative ultrasound (QUS) technologies have been developed to examine bone properties and skeletal maturity in a safe, noninvasive and cost-effective manner. Objective: The purpose of this study was to compare bone properties and skeletal maturity in competitive male child and adolescent athletes with minimallyactive, age-matched controls, using QUS technology. >. Methods: In total, 224 males were included in the study. The 115 pre-pubertal boys aged 10-12 years consisted of control, minimally-active children (n=34), soccer players (n=26), gymnasts (n=25) and hockey players (n=30). In addition, the 109 late-pubertal boys aged 14-16 years consisted of control, minimally-active adolescents (n=31), soccer players (n=30), gymnasts (n=17) and hockey players (n=31). The athletic groups were elite level players that predominantly trained year-round. Physical activity, nutrition and sports participation were assessed with various questionnaires. Anthropometries, such as height, weight and relative body fat percentage (BF%) were assessed using standard measures. Skeletal strength and age were evaluated using bone QUS. Lastly, salivary testosterone (sT) concentration was measured using Radioimmunoassay (RIA). Results: Within each age group, there were no significant differences between the activity groups in age and pubertal stage. An age effect was apparent in all variables, as expected. A sport effect was noted in all physical characteristics: the child and adolescent gymnasts were shorter and lighter than other sports groups. Adiposity was greater in the controls and in the hockey players. All child subjects were pubertal stage (fanner) I or II, while adolescent subjects were pubertal stage IV or V. There were no differences in daily energy and mineral intakes between sports groups. In both age groups, gymnasts had a higher training volume than other athletic groups. Bone speed of sound (50s) was higher in adolescents compared with the children. Gymnasts had signifieantly higher radial 50S than controls, hockey and soccer players in both age cohorts. Hockey athletes also had higher radial 50S than controls and soccer players in the child and adolescent groups, respectiyely. Child gymnasts and soccer players had greater tibial 50S compared with the hockey players and control groups. Likewise, adolescent gymnasts and soccer players had higher tibial SoS compared with the control group. No interaction was apparent between age and type of activity in any of the bone measures. » Lastly, maturity as assessed by sT and secondary sex characteristics (Tanner stage) was not different between sports group within each age group. Despite the similarity in chronological age, androgen levels and sexual maturity, differences between activity groups were noted in skeletal maturity. In the younger group, hockey players had the highest bone age while the soccer players had the lowest bone age. In the adolescent group, gymnasts and hockey players were characterized by higher skeletal maturity compared with controls. An interaction between the age and sport type effects was apparent in skeletal maturity, reflecting the fact that among the children, the soccer players were significantly less mature than the rest of the groups, while in the adolescents, the controls were the least skeletally mature. Summary and Conclusions: In summary, radial and tibial SOS are enhanced by the unique loading pattern in each sport (i.e, upper and lower extremities in gymnastics, lower extremities in soccer), with no cumulative effect between childhood and adolescence. That is, the effect of sport participation on bone SOS was apparent already among the young athletes. Enhanced bone properties among athletes of specific sports suggest that participation in these sports can improve bone strength and potential bone health.

Diatoms as indicators of lake trophic status

Relationships between surface sediment diatom assemblages and lake trophic status were studied in 50 Canadian Precambrian Shield lakes in the Muskoka-Haliburton and southern Ontario regions. The purpose of this study was to develop mathematical regression models to infer lake trophic status from diatom assemblage data. To achieve this goal, however, additional investigations dealing with the evaluation of lake trophic status and the autecological features of key diatom species were carried out. Because a unifying index and classification for lake trophic status was not available, a new multiple index was developed in this study, by the computation of the physical, chemical and biological data from 85 south Ontario lakes. By using the new trophic parameter, the lake trophic level (TL) was determined: TL = 1.37 In[1 +(TP x Chl-a / SD)], where, TP=total phosphorus, Chl-a=chlorophyll-a and SD=Secchi depth. The boundaries between 7 lake trophic categories (Ultra-oligotrophic lakes: 0-0.24; Oligotrophic lakes: 0.241-1.8; Oligomesotrophic lakes: 1.813.0; Mesotrophic lakes: 3.01-4.20; Mesoeutrophic lakes: 4.21-5.4; Eutrophic lakes: 5.41-10 and Hyper-eutrophic lakes: above 10) were established. The new trophic parameter was more convenient for management of water quality, communication to the public and comparison with other lake trophic status indices than many of the previously published indices because the TL index attempts to Increase understanding of the characteristics of lakes and their comprehensive trophic states. It is more reasonable and clear for a unifying determination of true trophic states of lakes. Diatom specIes autecology analysis was central to this thesis. However, the autecological relationship of diatom species and lake trophic status had not previously been well documented. Based on the investigation of the diatom composition and variety of species abundance in 30 study lakes, the distribution optima of diatom species were determined. These determinations were based on a quantitative method called "weighted average" (Charles 1985). On this basis, the diatom species were classified into five trophic categories (oligotrophic, oligomesotrophic, mesotrophic, mesoeutrophic and eutrophic species groups). The resulting diatom trophic status autecological features were used in the regressIon analysis between diatom assemblages and lake trophic status. When the TL trophic level values of the 30 lakes were regressed against their fi ve corresponding diatom trophic groups, the two mathematical equations for expressing the assumed linear relationship between the diatom assemblages composition were determined by (1) uSIng a single regression technique: Trophic level of lake (TL) = 2.643 - 7.575 log (Index D) (r = 0.88 r2 = 0.77 P = 0.0001; n = 30) Where, Index D = (0% + OM% + M%)/(E% + ME% + M%); 4 (2) uSIng a' multiple regressIon technique: TL=4.285-0.076 0%- 0.055 OM% - 0.026 M% + 0.033 ME% + 0.065 E% (r=0.89, r2=0.792, P=O.OOOl, n=30) There was a significant correlation between measured and diatom inferred trophic levels both by single and multiple regressIon methods (P < 0.0001, n=20), when both models were applied to another 20 test lakes. Their correlation coefficients (r2 ) were also statistically significant (r2 >0.68, n=20). As such, the two transfer function models between diatoms and lake trophic status were validated. The two models obtained as noted above were developed using one group of lakes and then tested using an entirely different group of lakes. This study indicated that diatom assemblages are sensitive to lake trophic status. As indicators of lake trophic status, diatoms are especially useful in situations where no local trophic information is available and in studies of the paleotrophic history of lakes. Diatom autecological information was used to develop a theory assessing water quality and lake trophic status.

Investigation of molecular polarizabilities and derivatives in halomethanes

The research undertaken was to obtain absolute Raman intensities for the symmetric stretching vibrations of the methyl halides, CH3X with (X=F, CI, Br), by experiment and theory. The intensities were experimentally measured using the Ar+ ion gas laser as excitation source, a Spex 14018 double monochromator and a RCA C-31034 photomultiplier tube as detector. These intensities arise from changes in the derivative of the polarizability (8 a'), with respect to vibration along a normal coordinate (8qi). It was intended that these derivatives obtained with respect to normal coordinates would be converted to derivatives with respect to internal coordinates, for a quantitative comparison with theory. Theoretical numerical polarizability derivatives for the stretching vibrations are obtained using the following procedure. A vibration was simulated in the molecule by increasi.ng and decreasing the respective bond by the amount ±o.oosA for the C-H bonds and ±o.oIA for the C-X (X=F, CI, Br) bond. The derivative was obtained by taking the difference in the polarizability for the equilibrium geometry and the geometry when a particular bond is changed. This difference, when divided by the amount of change in each bond and the number of bonds present results in the derivative of the polarizability with respect to internal coordinate i.e., !1u/!1r. These derivatives were obtained by two methods: I} ab initio molecular orbital calculation and 2} theory of atoms in molecules (AIM) analysis. Due to errors in the experimental setup only a qualitative analysis of the results was undertaken relative to the theory. Theoretically it is predicted that the symmetric carbonhalogen stretch vibrations are more intense than the respective carbon-hydrogen stretch, but only for the methyl chloride and bromide. The carbon fluorine stretch is less intense than the carbon-hydrogen stretch, a fact which is attributed to the small size and high electronegativity of the fluorine atom. The experimental observations are seen to agree qualitatively with the theory results. It is hoped that when the experiment is repeated, a quantitative comparison can be made. The analysis by the theory of atoms in molecules, along with providing polarizabilities and polarizability derivatives, gives additional information outlined below. The theory provides a pictorial description of the main factors contributing to the molecular polarizability and polarizability derivative. These contributions are from the charge transfer and atomic dipole terms i.e., transfer of charge from one atom to another and the reorganization of atomic electronic charge distribution due to presence of an electric field. The linear relationship between polarizability and molecular volume was also observed.