| 1. |
- Andrén, Lina J., 1980-
(författare)
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On Latin squares and avoidable arrays
- 2010
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This thesis consists of the four papers listed below and a survey of the research area. I Lina J. Andrén: Avoiding (m, m, m)-arrays of order n = 2k II Lina J. Andrén: Avoidability of random arrays III Lina J. Andr´en: Avoidability by Latin squares of arrays with even order IV Lina J. Andrén, Carl Johan Casselgren and Lars-Daniel Öhman: Avoiding arrays of odd order by Latin squares Papers I, III and IV are all concerned with a conjecture by Häggkvist saying that there is a constant c such that for any positive integer n, if m ≤ cn, then for every n × n array A of subsets of {1, . . . , n} such that no cell contains a set of size greater than m, and none of the elements 1, . . . , n belongs to more than m of the sets in any row or any column of A, there is a Latin square L on the symbols 1, . . . , n such that there is no cell in L that contains a symbol that belongs to the set in the corresponding cell of A. Such a Latin square is said to avoid A. In Paper I, the conjecture is proved in the special case of order n = 2k . Paper III improves on the techniques of Paper I, expanding the proof to cover all arrays of even order. Finally, in Paper IV, similar methods are used together with a recoloring theorem to prove the conjecture for all orders. Paper II considers another aspect of the problem by asking to what extent way a deterministic result concerning the existence of Latin squares that avoid certain arrays can be used when the sets in the array are assigned randomly.
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| 2. |
- Ehn, Micael
(författare)
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Modeling Specialization and Division of Labor in Cultural Evolution
- 2011
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Division of labor and division of knowledge are so important and common in society today that it is difficult to imagine a functional society where everyone knows the same things and performs the same tasks. In such a society everyone grows, or gathers, and prepares their own food, makes their own tools, builds their own house, and so on. Cultural evolution is the field of research that studies the creation and diffusion of ideas and societies. It is very uncommon for these studies to take into account the effects of specialization. This thesis will show that specialization is of great importance to cultural evolution. The thesis is divided into two parts: The first is an introduction to studies of specialization and division of labor. The thesis begins with an interdisciplinary survey of the research on division of labor and specialization, including both theoretic and empirical studies. Next is an introduction to modeling specialization and division of labor. This includes a general framework and a number of basic models of different aspects of specialization and division of labor. Part two consists of four papers. The first paper studies the interaction between specialization and cultural cumulation. The second and third papers examine cultural cumulation, specifically the circumstances under which cultural knowledge increases and how cultural knowledge is distributed in the population. The last paper is a mathematical model of how specialization of knowledge (i.e. higher education) leads to social stratification.
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| 3. |
- Ehn, Micael, 1983-
(författare)
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On the causes and effects of specialization : A mathematical approach
- 2009
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Division of labor and division of knowledge are so important andcommon in society today that it is almost impossible to imagine asociety where everyone knows the same things and perform the sametasks. This would be a society where everyone grows, or gathers, andprepares their own food, makes their own tools, builds their ownhouse, and so on. Cultural evolution is the field of research that studies the creationand diffusion of ideas and societies. It is very uncommon for thesestudies to take into account the effects of specialization. Thisthesis will show that specialization is of great importance tocultural evolution. The thesis is divided into three parts: one introduction and two papers. The introduction covers the mathematical models used byeconomists to study the relation between the market and division oflabor. The first paper is an interdisciplinary survey of the researchon division of labor and specialization, including both theoretic andempirical studies. The second paper is a mathematical model of howspecialization of knowledge (i.e. higher education) leads to socialstratification. The model is tested against statistical data fromseveral countries and found to be a good predictor of the differencesin income between people of high and low education.
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| 4. |
- Funcke, Alexander, 1982-
(författare)
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Mathematical models of social norms and petty corruption
- 2015
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Corruption is a problem all around the world, but the extent of the problem varies between countries and situations. In this thesis, I focus on how corruption levels can change when they are culturally determined. For this reason, I study the dynamics of the cultural underpinnings: social norms and conventions.The dissertation consists of six papers. In the first paper, I expand a common definition of social norms. The aim of the extension is to capture the fact that the scope of a social norm may be larger than just a single specific situation. I introduce a similarity measure and develop a mathematical model according to which all situations' social norms are interconnected, and affect each other, but those situations that are most similar and most recent have the greatest normative effect on a current situation. Given this model I test the effect of bringing about norm change by temporarily dismantling institutions and then reestablishing them.In the second paper, I show in a mathematical model how it is possible to design fine and reward mechanisms that make it superfluous for individuals to form beliefs about how others will act. Through this mechanism, it should be possible to circumvent the problem that norm change typically will be successful only if it is synchronized across a large part of the population.In the third paper, I and my co-authors, first conducted a survey. The results of which demonstrate that there is a general tendency among people to consider themselves to be less prone to corrupt behavior than the average person. Such an "everyone-is-better-than-average" effect is a well-established phenomenon in social psychology but not previously demonstrated in the corruption domain. We then show in a mathematical model that such systematic biases in estimation of own versus others' corruption make it more difficult to achieve norm change in the direction of less corruption.In the fourth and fifth paper we again consider the "everyone-is-better-than-average" effect and see how in certain value based groups the effect can be reversed. This changes the insight from the third paper slightly.The last paper considers a classic question of how a collective can succeed in collective action when it is risky to be among the first individuals to act. I and my co-author investigate how the collective can benefit from access to a set of signal acts that signal an individual's level of commitment to the collective cause. The problem is modeled as a threshold model where an individual's inclination to conduct a specific act depends on the previous commitment level in the population.
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| 5. |
- Ingre, Michael, 1965-
(författare)
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P-hacking in academic research : a critical review of the job strain model and of the association between night work and breast cancer in women
- 2017
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- P-hacking can be described as a more or less deliberate, explorative approach to data analysis with a flexible/opportunistic search space and the reporting of primarily statistically significant findings. This leads to inflated type-1 error rates and to bias in reported estimates in the scientific literature.This thesis aims to describe how p-hacking can be manifested in academic research and to illustrate how bias due to p-hacking is expected to affect the veracity of published findings using two specific examples from the literature. This thesis also argues that when evaluating published findings in the current academic environment, we should assume a priori that biases due to p-hacking and publication bias are present.The thesis used Monte Carlo simulations and systematic reviews of the literature in two specific fields: the proposed associations between exposure to night work and breast cancer in women, and between job strain and coronary heart disease.A general model and mathematical framework to predict expected bias from p-hacking was developed, and can be used for a priori defined protected inferences of any published finding, under explicit assumptions of various levels of p-hacking. The model indicated a close to 100% chance of demonstrating a false positive association in larger studies, but also showed that even minimal p-hacking results in substantial bias in estimates.The literature review identified large flexibility in the analytical process, allowing for the final model to be picked from a large pool of available models, with an implied search space of thousands of estimates. Some of the specific observations made here could be used to argue evidence for high risk of p-hacking and publication bias in the reviewed literature:None of the 17 reviewed studies on job strain and coronary heart disease reported the proper estimate of the job strain interaction (chapter 6) and our analysis showed that the proper estimate would not have been statistically significant in any of the studies (chapter 7).One study described a data driven approach with an implied search space of at least 502 models, where adjusting for confounding did not reduce the strength of the association, as would be expected, but instead increased its strength so it fell above the threshold for statistical significance (chapter 5).One study was based on a speculative and marginally significant estimate after arbitrarily restricting the analysis to a subgroup, when estimates on the full group were available and indicated a non-significant association (chapter 5).Statistical power analyses on research into night work and breast cancer indicated that statistically significant findings were over-represented in the literature (p≈.001) suggesting the presence of bias from p-hacking or selective publishing of significant findings (chapter 5).The findings also suggest that previously reported estimates in meta-analyses was likely to represent prevailing bias in the two fields reviewed here. A bias-adjusted meta-analysis on the job strain model and coronary heart disease with a total of 462,220 subjects and 6,836 CHD events indicated no support for the job strain interaction (RR=1.00; 95% CI: 0.88--1.14). In addition, it did not show an increased risk due to high job demand (RR=1.03; 95% CI: 0.97--1.11) but it did confirm previously reported risks due to low job control (RR=1.11; 95% CI: 1.03--1.20).
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| 6. |
- Jansson, Fredrik, 1981-
(författare)
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Modelling Two-Person Interactions Within and Between Cultural Groups
- 2013
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- The groups with which we associate influence our actions. This is often the case even when they are not deliberately organised but rather based on social categories, such as sex and skin colour, or cultural homogeneity, such as common language or customs. Group membership can cause widespread phenomena such as ingroup favouritism, polarisation of opinion and competition. Previous experiments have shown that these effects can be triggered by even completely arbitrary distinctions between groups. This thesis uses mathematical models to investigate under what circumstances these phenomena can arise.Using a game theoretical approach, the first three papers address the evolution of ingroup favouritism. Previous models have focused on the prisoners’ dilemma, interactions where the socially optimal behaviour is to co-operate, but where it is in the individual’s self-interest not to. The results presented here suggest that co-ordination problems may have been more important than those of co-operation in the evolution of an ingroup bias. In particular, this applies to common goals that require trust. It is also demonstrated in a behavioural experiment that such trust is most common within groups, but that it can emerge between groups through group reputation.The fourth paper focuses on a model on how cultural groups in contact can develop common norms, rather than polarise into different norm groups, by assuming a confirmation bias. The model is empirically tested on demographic and linguistic data from Mauritian Creole, a natural language developed from the mixing of parent languages.In the fifth paper, the group is defined by common preferences (e.g. for pop songs), which are transmitted in a random copying model. The competitive success of the groups, with respect to their size, is recorded on a toplist, the turnover rate of which is derived.In the final paper, people match up in pairs between groups according to their preferences, and all stable matchings are found under a specific assumption of bounded rationality, when people’s individual behaviour may be affected by the consequences for fellow group members.
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| 7. |
- Lundgren, Robin, 1977-
(författare)
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Convergence of Option Rewards
- 2010
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This thesis consists of an introduction and five articles devoted to optimal stopping problems of American type options. In article A, we get general convergence results for the American option rewards for multivariate Markov price processes. These results are used to prove convergence of tree approximations presented in papers A, B, C and E.In article B, we study the problem of optimal reselling for European options. The problem can be transformed to the problem of exercising an American option with two underlying assets. An approximative binomial-trinomial tree algorithm for the reselling model is constructed. In article C, we continue our study of optimal reselling of European options and give the complete solution of the approximation problem. In the article D, we consider general knockout options of American type. A Monte-Carlo method is used to study structure of optimal stopping domains generated by combinations of different pay-off functions and knockout domains.In article E the American option with knock out domains is considered. In order to show convergence of the reward functional the problem is reformulated in such a way that the convergence results in paper A can be applied.
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| 8. |
- Lundgren, Robin, 1977-
(författare)
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Optimal Stopping and Convergence of Option Rewards
- 2009
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This thesis is based on two articles devoted to optimal stopping problems of American type options. In article A, we study the problem of optimal reselling for European options. The problem can be transformed to the problem of exercising an American option with two underlying. An approximate binomial-trinomial tree algorithm for the reselling model is constructed. In article B, we get general convergence results for the American option rewards for multivariate Markov price processes. These results are used to prove convergence of tree approximations presented in papers A and B.
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| 9. |
- Pham, Lan Anh, 1991-
(författare)
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On avoiding and completing colorings
- 2019
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- All of my papers are related to the problem of avoiding and completing an edge precoloring of a graph. In more detail, given a graph G and a partial proper edge precoloring φ of G and a list assignment L for every non-colored edge of G, can we extend φ to a proper edge coloring of G which avoids L? In Paper I, G is the d-dimensional hypercube graph Qd, a partial proper edge precoloring φ and a list assignment L must satisfy certain sparsity conditions. Paper II still deals with the hypercube graph Qd, but the list assignment L for every edge of Qd is an empty set and φ must be a partial proper edge precoloring of at most d-1 edges. In Paper III, G is a (d,s)-edge colorable graph; that is G has a proper d-edge coloring, where every edge is contained in at least s-1 2-colored 4-cycles, L must satisfy certain sparsity conditions and we do not have a partial proper edge precoloring φ on edges of G. The problem in Paper III is also considered in Paper IV and Paper V, but here G can be seen as the complete 3-uniform 3-partite hypergraph K3n,n,n, where n is a power of two in paper IV and n is an even number in paper V.
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| 10. |
- Ryve, Andreas, 1973-
(författare)
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Approaching Mathematical Discourse : Two analytical frameworks and their relation to problem solving interactions
- 2006
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- The driving force of conducting the two studies presented in this thesis is to examine ways that conceptual understanding and problem solving could be part of mathematics teaching, and through that, part of students' mathematical knowledge. The specific aims of the thesis are: 1) to characterize the classroom discourse of two, apparently similar, problem solving courses in teacher education and 2) to discuss the possibilities of developing two analytical approaches - the communicational approach to cognition and the dialogical approach - used for studying mathematical discourse. The two aims are elaborated on by means of data collected through audiotaped recordings and field notes from observations of problem-solving activities in engineering and teacher education. In relation to the first aim, the analysis of the classroom discourse within the two courses makes it clear that both courses displayed different kinds of discourse that could be broadly categorized in terms of: subject-oriented, didactically oriented, and problem solving oriented discourses. However, the comparisons between the two courses reveal a marked difference in the distribution of these categories of discourse. It is suggested that the introduction of explicit conceptual frameworks in teaching is of crucial importance for the topical focus of the classroom discourse, and for prospective teachers' opportunity to engage in mathematical productive discourse. The analyses of the two approaches for studying mathematical discourse reveal that the two frameworks can be further developed and the study also indicates ways in which such development can be achieved using a theory of contextualization and theories of mathematical learning. Finally, the thesis discusses theoretical and practical implications of the results, foregrounding issues of importance for the research on mathematical discourse, and for teachers and teacher educators involved in designing instructions for mathematical problem solving.
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