| 1. |
- Gerlee, Philip, 1980, et al.
(författare)
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Scientific Models : Red Atoms, White Lies and Black Boxes in a Yellow Book
- 2016
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Bok (övrigt vetenskapligt/konstnärligt)abstract
- A zebrafish, the hull of a miniature ship, a mathematical equation and a food chain - what do these things have in common? They are examples of models used by scientists to isolate and study particular aspects of the world around us. This book begins by introducing the concept of a scientific model from an intuitive perspective, drawing parallels to mental models and artistic representations. It then recounts the history of modelling from the 16th century up until the present day. The iterative process of model building is described and discussed in the context of complex models with high predictive accuracy versus simpler models that provide more of a conceptual understanding. To illustrate the diversity of opinions within the scientific community, we also present the results of an interview study, in which ten scientists from different disciplines describe their views on modelling and how models feature in their work. Lastly, it includes a number of worked examples that span different modelling approaches and techniques. It provides a comprehensive introduction to scientific models and shows how models are constructed and used in modern science. It also addresses the approach to, and the culture surrounding modelling in different scientific disciplines. It serves as an inspiration for model building and also facilitates interdisciplinary collaborations by showing how models are used in different scientific fields. The book is aimed primarily at students in the sciences and engineering, as well as students at teacher training colleges but will also appeal to interested readers wanting to get an overview of scientific modelling in general and different modelling approaches in particular.
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| 2. |
- Gerlee, Philip, 1980, et al.
(författare)
-
Scientific Models
- 2016
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Bok (övrigt vetenskapligt/konstnärligt)abstract
- A zebrafish, the hull of a miniature ship, a mathematical equation and a food chain - what do these things have in common? They are examples of models used by scientists to isolate and study particular aspects of the world around us. This book begins by introducing the concept of a scientific model from an intuitive perspective, drawing parallels to mental models and artistic representations. It then recounts the history of modelling from the 16th century up until the present day. The iterative process of model building is described and discussed in the context of complex models with high predictive accuracy versus simpler models that provide more of a conceptual understanding. To illustrate the diversity of opinions within the scientific community, we also present the results of an interview study, in which ten scientists from different disciplines describe their views on modelling and how models feature in their work. Lastly, it includes a number of worked examples that span different modelling approaches and techniques. It provides a comprehensive introduction to scientific models and shows how models are constructed and used in modern science. It also addresses the approach to, and the culture surrounding modelling in different scientific disciplines. It serves as an inspiration for model building and also facilitates interdisciplinary collaborations by showing how models are used in different scientific fields. The book is aimed primarily at students in the sciences and engineering, as well as students at teacher training colleges but will also appeal to interested readers wanting to get an overview of scientific modelling in general and different modelling approaches in particular.
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| 3. |
- Thunberg, Hans, 1956-, et al.
(författare)
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The Widening Gap — A Swedish Perspective
- 2008
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Ingår i: Mathematics Education Research Journal. - 1033-2170 .- 2211-050X. ; 20:2, s. 38-56
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Tidskriftsartikel (refereegranskat)abstract
- Transition problems from secondary to tertiary level in mathematics have been arecurrent issue in Sweden. This paper summarises the development during the lastdecades. Results from two recent research studies that illuminate the transitionproblem are presented. The first one, based on empirical data from a major Swedishtechnical university, characterises the widening gap, in content and in approach,between secondary school and first year university courses. The second study dealswith students’ encounters with mathematical proof and is based on a largeinvestigation at another main Swedish university. We discuss the influence on thecurrent transition problems of school reforms and of the great expansion of highereducation in Sweden during the last 10 – 15 years in view of the results from theresearch studies.
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| 4. |
- Bergqvist, Tomas, 1962-, et al.
(författare)
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Upper secondary students’ task reasoning
- 2008
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Ingår i: International Journal of Mathematical Education in Science and Technology. - : Informa UK Limited. - 0020-739X .- 1464-5211. ; 39:1
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Tidskriftsartikel (refereegranskat)abstract
- Upper secondary students’ task solving reasoning was analysed, with a focus on grounds for different strategy choices and implementations. The results indicate that mathematically well-founded considerations were rare. The dominating reasoning types were algorithmic reasoning, where students tried to remember a suitable algorithm, sometimes in a random way, and guided reasoning, where progress was possible only when essentially all important strategy choices were made by the interviewer.
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| 5. |
- Pejlare, Johanna, 1976
(författare)
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On Axioms and Images in the History of Mathematics
- 2007
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This dissertation deals with aspects of axiomatization, intuition and visualization in the history of mathematics. Particular focus is put on the end of the 19th century, before David Hilbert's (1862–1943) work on the axiomatization of Euclidean geometry. The thesis consists of three papers. In the first paper the Swedish mathematician Torsten Brodén (1857–1931) and his work on the foundations of Euclidean geometry from 1890 and 1912, is studied. A thorough analysis of his foundational work is made as well as an investigation into his general view on science and mathematics. Furthermore, his thoughts on geometry and its nature and what consequences his view has for how he proceeds in developing the axiomatic system, is studied. In the second paper different aspects of visualizations in mathematics are investigated. In particular, it is argued that the meaning of a visualization is not revealed by the visualization and that a visualization can be problematic to a person if this person, due to a limited knowledge or limited experience, has a simplified view of what the picture represents. A historical study considers the discussion on the role of intuition in mathematics which followed in the wake of Karl Weierstrass' (1815–1897) construction of a nowhere differentiable function in 1872. In the third paper certain aspects of the thinking of the two scientists Felix Klein (1849–1925) and Heinrich Hertz (1857–1894) are studied. It is investigated how Klein and Hertz related to the idea of naïve images and visual thinking shortly before the development of modern axiomatics. Klein in several of his writings emphasized his belief that intuition plays an important part in mathematics. Hertz argued that we form images in our mind when we experience the world, but these images may contain elements that do not exist in nature.
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| 6. |
- Bergwall, Andreas, 1972-
(författare)
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On a generality framework for proving tasks
- 2015
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Ingår i: Proceedings of the Ninth Congress of the European Society for Research in Mathematics Education. - Prague : Charles University in Prague, Faculty of Education and ERME. - 9788072908448 ; , s. 86-92
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Konferensbidrag (refereegranskat)abstract
- In this paper I present an analytic framework for generality in textbook proving tasks that involve functions. The framework is discussed in relation to results obtained when analysing tasks in integral calculus. The results show that the frameworks’ categories are easily distinguishable if the functions are explicitly described. The results are also promising regarding the possibility to clarify differences between textbooks. The analysed sections exemplify that there is not necessarily a correlation between the number of general proving tasks and the opportunities for students to engage in reasoning about arbitrary functions. Limitations and possible refinements of the framework are also discussed.
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| 7. |
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| 8. |
- Höök, Mikael, 1982-, et al.
(författare)
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Descriptive and predictive growth curves in energy system analysis
- 2011
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Ingår i: Natural Resources Research. - : Springer Science and Business Media LLC. - 1520-7439 .- 1573-8981. ; 20:2, s. 103-116
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Tidskriftsartikel (refereegranskat)abstract
- This study reviews a variety of growth curve models and the theoretical frameworks that lay behind them. In many systems, growth patterns are, or must, ultimately be subjected to some form of limitation. A number of curve models have been developed to describe and predict such behaviours. Symmetric growth curves have frequently been used for forecasting fossil fuel production, but others have expressed a need for more flexible and asymmetric models. A number of examples show differences and applications of various growth curve models. It is concluded that these growth curve models can be utilised as forecasting tools, but are do not necessarily provide better predictions than any other method. Consequently, growth curve models and other forecasting methods should be used together to provide a triangulated forecast. Furthermore, the growth curve methodology offers a simple tool for resource management to determine what might happen to future production if resource availability poses a problem. In the light of peak oil and the awareness of natural resources as a basis for the continued well-being of society and mankind, resource management should be an important factor in future social planning.
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| 9. |
- Jansson, Fredrik
(författare)
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What games support the evolution of an ingroup bias?
- 2015
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Ingår i: Journal of Theoretical Biology. - : Elsevier BV. - 0022-5193 .- 1095-8541. ; 373, s. 100-110
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Tidskriftsartikel (refereegranskat)abstract
- There is an increasing wealth of models trying to explain the evolution of group discrimination and an ingroup bias. This paper sets out to systematically investigate the most fundamental assumption in these models: in what kind of situations do the interactions take place? What strategic structures - games - support the evolution of an ingroup bias? More specifically, the aim here is to find the prerequisites for when a bias also with respect to minimal groups - arbitrarily defined groups void of group-specific qualities - is selected for, and which cannot be ascribed to kin selection.Through analyses and simulations of minimal models of two-person games, this paper indicates that only some games are conducive to the evolution of ingroup favouritism. In particular, this class does not contain the prisoners׳ dilemma, but it does contain anti-co-ordination and co-ordination games. Contrasting to the prisoners׳ dilemma, these are games where it is not a matter of whether to behave altruistically, but rather one of predicting what the other person will be doing, and where I would benefit from you knowing my intentions.In anti-co-ordination games, on average, not only will agents discriminate between groups, but also in such a way that their choices maximise the sum of the available payoffs towards the ingroup more often than towards the outgroup. And in co-ordination games, even if agents do manage to co-ordinate with the whole population, they are more likely to co-ordinate on the socially optimal equilibrium within their group. Simulations show that this occurs most often in games where there is a component of risk-taking, and thus trust, involved. A typical such game is the stag hunt or assurance game.
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| 10. |
- Smolla, Marco, et al.
(författare)
-
Underappreciated features of cultural evolution
- 2021
-
Ingår i: Proceedings of the Royal Society of London. Biological Sciences. - : The Royal Society. - 0962-8452 .- 1471-2954 .- 0962-8436 .- 1471-2970. ; 376:1828
-
Tidskriftsartikel (refereegranskat)abstract
- Cultural evolution theory has long been inspired by evolutionary biology. Conceptual analogies between biological and cultural evolution have led to the adoption of a range of formal theoretical approaches from population dynamics and genetics. However, this has resulted in a research programme with a strong focus on cultural transmission. Here, we contrast biological with cultural evolution, and highlight aspects of cultural evolution that have not received sufficient attention previously. We outline possible implications for evolutionary dynamics and argue that not taking them into account will limit our understanding of cultural systems. We propose twelve key questions for future research, among which are calls to improve our understanding of the combinatorial properties of cultural innovation, and the role of development and life history in cultural dynamics. Finally, we discuss how this vibrant research field can make progress by embracing its multidisciplinary nature.
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| 11. |
- Eriksson, Urban, Lektor i fysik med inriktning mot fysikdidaktik, 1968-
(författare)
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Disciplinary discernment : reading the sky in astronomy education
- 2019
-
Ingår i: Physical review physics education research. - : American Physical Society. - 2469-9896. ; 15:1
-
Tidskriftsartikel (refereegranskat)abstract
- This theoretical paper introduces a new way to view and characterize learning astronomy. It describes a framework, based on results from empirical data, analyzed through standard qualitative research method- ology, in which a theoretical model for a vital competency of learning astronomy is proposed: reading the sky, a broad description under with various skills and competencies are included. This model takes into account not only disciplinary knowledge but also disciplinary discernment and extrapolating three dimensionality. Together, these constitute the foundation for the competency referred to as reading the sky. In this paper, these competencies are described and discussed and merged to form a new framework vital for learning astronomy to better match the challenges students face when entering the discipline of astronomy.
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| 12. |
- Lundberg, Anna L.V. 1967
(författare)
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Encountering Proportional Reasoning During a Single Algebra Lesson: A Microgenetic Analysis
- 2022
-
Ingår i: International Electronic Journal of Mathematics Education. - Eastbourne, United Kingdom : Modestum Publishing Ltd. - 1306-3030. ; 17:1
-
Tidskriftsartikel (refereegranskat)abstract
- This case study explores how 12-13-year-old students encounter proportional reasoning while working with geometric patterning tasks using concrete materials. The focus is on the students’ use of spontaneous concepts when first dealing with such patterns in the context of collaborative work. Based on video recordings of a single lesson, a microgenetic analysis was performed to identify students’ learning trajectories, starting with students familiarizing themselves with pattern structure, followed by engagement in proportional reasoning, and ending with students perceiving a new technique to handle a situation where proportional reasoning did not suffice. While some student groups were able to move along the whole trajectory, most groups, when facing challenges, regressed to simpler techniques. The results provide new insights into students’ learning trajectories, which can be used to support students’ progress in the context of student-teacher interaction.
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| 13. |
- Jansson, Fredrik, et al.
(författare)
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Modelling cultural systems and selective filters
- 2021
-
Ingår i: Philosophical Transactions of the Royal Society of London. Biological Sciences. - : The Royal Society. - 0962-8436 .- 1471-2970. ; 376:1828
-
Tidskriftsartikel (refereegranskat)abstract
- A specific goal of the field of cultural evolution is to understand how processes of transmission and selection at the individual level lead to population-wide patterns of cultural diversity and change. Models of cultural evolution have typically assumed that traits are independent of one another and essentially exchangeable. But culture has a structure: traits bear relationships to one another that affect the transmission and selection process itself. Here we introduce a modelling framework to explore the effect of cultural structure on the process of learning. Through simulations, we find that introducing this simple structure changes the cultural dynamics. Based on a basic filtering mechanism for parsing these relationships, more elaborate cultural filters emerge. In a mostly incompatible cultural domain of traits, these filters organise culture into mostly (but not fully) consistent and stable systems. Incompatible domains produce small homogeneous cultures, while more compatibility increases size, diversity, and group divergence. When individuals copy based on a trait's features (here, its compatibility relationships) they produce more homogeneous cultures than when they copy based on the agent carrying the cultural trait. We discuss the implications of considering cultural systems and filters in the dynamics of cultural change.
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| 14. |
- Sorooshian, Shahryar, 1980, et al.
(författare)
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Performance of the decision-making trial and evaluation laboratory
- 2023
-
Ingår i: AIMS Mathematics. - : American Institute of Mathematical Sciences (AIMS). - 2473-6988. ; 8:3, s. 7490-7514
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Tidskriftsartikel (refereegranskat)abstract
- Multiple attribute decision-making (MADM) techniques constitute a practical approach for solving complex problems involving multiple and often conflicting criteria. Decision-making trial and evaluation laboratory (DEMATEL) is a popular MADM technique with both admirers and critics. This study presents a comprehensive review of DEMATEL through bibliometric analysis using the Scopus database. This article examined 3,521 papers published in journals, conferences or books between 1981 and 2023. We examined a few parameters for commenting on the performance of the technique. Among them are research outputs, the network of DEMATEL users, implementation subject areas, research zones, financing opportunities and publication hosts and their impact trends. We conclude from the findings of this study that the DEMATEL is capable of dealing with modern problem-solving in future environments. Although the growth of new MADMs is obvious, based on the gathered data, we forecast that more than 776 documents will be published in 2025 using DEMATEL for problem-solving. This expanding tendency will continue in the future. As distinct MADMs have diverse constraints, foundations, computing complexity and standpoints, which result in different performances, outmoded low-performance MADM techniques must be reported by researchers to continue this paper’s objective to minimize ambiguity among decision-makers and practitioners. To facilitate such a comparison in the future, a quantitative performance coefficient was also developed here.
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| 15. |
- Hamon, Thierry, et al.
(författare)
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Combining Compositionality and Pagerank for the Identification of Semantic Relations between Biomedical Words
- 2012
-
Ingår i: BioNLP. - 9781937284206 - 1937284204 ; , s. 109-117
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Konferensbidrag (refereegranskat)abstract
- The acquisition of semantic resources and relations is an important task for several applications, such as query expansion, information retrieval and extraction, machine translation. However, their validity should also be computed and indicated, especially for automatic systems and applications. We exploit the compositionality based methods for the acquisition of synonymy relations and of indicators of these synonyms. We then apply pagerank-derived algorithm to the obtained semantic graph in order to filter out the acquired synonyms. Evaluation performed with two independent experts indicates that the quality of synonyms is systematically improved by 10 to 15% after their filtering.
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| 16. |
- Pejlare, Johanna, 1976, et al.
(författare)
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Programming to learn mathematics - exploring student teachers' instrumental genesis
- 2022
-
Ingår i: The relation between mathematics education research and teachers' professional development. - Göteborg : Swedish Society for Research in Mathematics Education. - 1651-3274. - 9789198402452 ; 16, s. 69-79
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Konferensbidrag (refereegranskat)abstract
- Programming is now a prescribed part of the curriculum in mathematics in both primary and secondary school in Sweden, as in many other countries. Teacher training must thus prepare students for the challenges of teaching mathematics with programming. We explore how student teachers see their own training in programming in relation to mathematics and what opportunities to learn mathematics they believe that programming can offer pupils in school. An instrumental approach is used to analyse observations and a questionnaire on secondary school student teacher’ experience of a programming lab, where they investigate Riemann sums with programming. We find that students feel challenged by both the programming and the mathematical content, and that they see the challenges as useful, both for themselves and for their future pupils.
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| 17. |
- Sorooshian, Shahryar, 1980, et al.
(författare)
-
Expedited analytical hierarchical process for multicriteria decision making
- 2022
-
Ingår i: ICIC Express Letters. - 1881-803X. ; 16:2, s. 145-151
-
Tidskriftsartikel (refereegranskat)abstract
- In this study, a procedure to overcome analytical hierarchical process (AHP) limitations was developed and tested, and a tool created via pairwise comparison chart and weighted sum method hybridization was introduced. In addition, a multicriteria decision-making software was selected to validate the constructed hybrid decision-making tool. The software was formulated based on an established decision-making technique. Data for the comparison analysis were obtained from an ongoing research, and output from the comparison analysis provided evidence for the accuracy of the constructed tool. The proposed hybridized method aligned with AHP reasoning but demonstrated a faster process; hence, it was called ‘expedited AHP’.
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| 18. |
- Pejlare, Johanna, 1976
(författare)
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Infinite sums and the calculation of ?, as presented by the Swedish mathematician Anders Gabriel Duhre in the early 18th century
- 2019
-
Ingår i: Proceedings of the Eighth European Summer University on History and Epistemology in Mathematics Education ESU 8. - Oslo : Oslo Metropolitan University Storbyuniversitetet. - 2535-6984 .- 2535-6992. - 9788283642117
-
Konferensbidrag (refereegranskat)abstract
- Anders Gabriel Duhre, an important mathematician and mathematics educator in Sweden during the 18th century, contributed with two textbooks in mathematics, one in algebra and one in geometry. Among others, he treats infinitesimals based on Nieuwentijts’ theories from Analysis infinitorum and infinite sums based on Wallis’ method of induction from Arithmetica infinitorum. Based on these results, Duhre develops an ingenious method to determine the area enclosed by curves by constructing a corresponding curve. He applies his method to the circle in order to find an expression of ? as an infinite series. The series he finds is a modified version of the Gregory-Leibniz’ series. In the present paper we consider in detail Duhre’s presentation in order to further investigate the influence upon him as well as his influence on the Swedish mathematical society of his time.
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| 19. |
- Sjögren, Jörgen, et al.
(författare)
-
Concept Formation and Concept Grounding
- 2014
-
Ingår i: Philosophia. - : Springer Science+Business Media B.V.. - 0048-3893 .- 1574-9274. ; 42:3, s. 827-839
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Tidskriftsartikel (refereegranskat)abstract
- Recently Carrie S. Jenkins formulated an epistemology of mathematics, or rather arithmetic, respecting apriorism, empiricism, and realism. Central is an idea of concept grounding. The adequacy of this idea has been questioned e.g. concerning the grounding of the mathematically central concept of set (or class), and of composite concepts. In this paper we present a view of concept formation in mathematics, based on ideas from Carnap, leading to modifications of Jenkins’s epistemology that may solve some problematic issues with her ideas. But we also present some further problems with her view, concerning the role of proof for mathematical knowledge.
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| 20. |
- Pejlare, Johanna, 1976, et al.
(författare)
-
On the relations between geometry and algebra in Gestrinius' edition of Euclid's Elements
- 2016
-
Ingår i: Radford, L., Furinghetti, F., & Hausberger, T. (Eds.) (2016). Proceedings of the 2016 ICME Satellite Meeting of the International Study Group on the Relations Between the History and Pedagogy of Mathematics. Montpellier, France: IREM de Montpellier.. - 2909916510 ; , s. 513-523
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Konferensbidrag (refereegranskat)abstract
- In 1637 the Swedish mathematician Martinus Erici Gestrinius contributed with a commented edition of Euclid’s Elements. In this article we analyse the relationship between geometry and algebra in Gestrinius’ Elements, as presented in Book II. Of particular interest are Propositions 4, 5, and 6, dealing with straight lines cut into equal and unequal parts, and the three kinds of quadratic equations Gestrinius associates with them. We argue that Gestrinius followed Clavius translation of the Elements, but was influenced by Ramus to include algebra.
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| 21. |
- Ögren, Magnus, 1977-, et al.
(författare)
-
There’s more to the multimedia effect than meets the eye : is seeing pictures believing?
- 2017
-
Ingår i: Instructional science. - : Springer Netherlands. - 0020-4277 .- 1573-1952. ; 45:2, s. 263-287
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Tidskriftsartikel (refereegranskat)abstract
- Textbooks in applied mathematics often use graphs to explain the meaning of formulae, even though their benefit is still not fully explored. To test processes underlying this assumed multimedia effect we collected performance scores, eye movements, and think-aloud protocols from students solving problems in vector calculus with and without graphs. Results showed no overall multimedia effect, but instead an effect to confirm statements that were accompanied by graphs, irrespective of whether these statements were true or false. Eye movement and verbal data shed light on this surprising finding. Students looked proportionally less at the text and the problem statement when a graph was present. Moreover, they experienced more mental effort with the graph, as indicated by more silent pauses in thinking aloud. Hence, students actively processed the graphs. This, however, was not sufficient. Further analysis revealed that the more students looked at the statement, the better they performed. Thus, in the multimedia condition the graph drew students’ attention and cognitive capacities away from focusing on the statement. A good alternative strategy in the multimedia condition was to frequently look between graph and problem statement, and thus to integrate their information. In conclusion, graphs influence where students look and what they process, and may even mislead them into believing accompanying information. Thus, teachers and textbook designers should be very critical on when to use graphs and carefully consider how the graphs are integrated with other parts of the problem.
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| 22. |
- Wang, Siyang, et al.
(författare)
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CONVERGENCE OF FINITE DIFFERENCE METHODS FOR THE WAVE EQUATION IN TWO SPACE DIMENSIONS
- 2018
-
Ingår i: Mathematics of Computation. - : American Mathematical Society (AMS). - 0025-5718 .- 1088-6842. ; 87:314, s. 2737-2763
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Tidskriftsartikel (refereegranskat)abstract
- When using a finite difference method to solve an initial-boundary-value problem, the truncation error is often of lower order at a few grid points near boundaries than in the interior. Normal mode analysis is a powerful tool to analyze the effect of the large truncation error near boundaries on the overall convergence rate, and has been used in many research works for different equations. However, existing work only concerns problems in one space dimension. In this paper, we extend the analysis to problems in two space dimensions. The two dimensional analysis is based on a diagonalization procedure that decomposes a two dimensional problem to many one dimensional problems of the same type. We present a general framework of analyzing convergence for such one dimensional problems, and explain how to obtain the result for the corresponding two dimensional problem. In particular, we consider two kinds of truncation errors in two space dimensions: the truncation error along an entire boundary, and the truncation error localized at a few grid points close to a corner of the computational domain. The accuracy analysis is in a general framework, here applied to the second order wave equation. Numerical experiments corroborate our accuracy analysis.
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| 23. |
- Hammar Chiriac, Eva, 1961-
(författare)
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Group work is not one, but a great many processes – Understanding group work dynamics
- 2012
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Ingår i: Encyclopedia of Mathematics Research. - New York : Nova Science Publishers, Inc. - 9781613242285 ; , s. 153-167
-
Bokkapitel (övrigt vetenskapligt/konstnärligt)abstract
- This book discusses current research developments in the field of mathematics. Topics presented include exceptional groups, symmetric spaces and applications; LIE group analysis; graph groupoids and corresponding representations; fuzzy logic in molecular computing; closed-loop optimal fuzzy reasoning; nozzle design optimisation; a branch-and-price algorithm for the stochastic generalised assignment problem; parametric dual regularisation in a linear-convex mathematical programming and fast multilevel algorithms for diverse application in computational biology and bioinformatics.
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| 24. |
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| 25. |
- Mamontov, Eugen, 1955
(författare)
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Ordinary differential equation system for population of individuals and the corresponding probabilistic model
- 2008
-
Ingår i: Mathl. Computer Modelling. - : Elsevier BV. - 0895-7177.
-
Tidskriftsartikel (refereegranskat)abstract
- The key model for particle populations in statistical mechanics is the Bogolyubov–Born– Green–Kirkwood–Yvon (BBGKY) equation chain. It is derived mainly from the Hamilton ordinary differential equation (ODE) system for the vectors of the particle states in the particle position-momentum phase space. Many problems beyond physics or chemistry, for instance, in the living-matter sciences (biology, medicine, ecology, and scoiology) make it necessary to extend the notion of a particle to an individual, or active particle. This challenge is met by the generalized kinetic theory. It implements the extension by extending the phase space from the space of the position-momentum vectors to more rich spaces formed by the state vectors with the entries which need not be limited to the entries of the position and momentum: they include other scalar variables (e.g., those associated with modelling homeorhesis or other features inherent to the individuals). One can assume that the dynamics of the state vector in the extended space, i.e. the states of the individuals (rather than common particles) is also described by an ODE system. The latter, however, need not be the Hamilton one. The question is how one can derive the analogue of the BBGKY paradigm for the new settings. The present work proposes an answer to this question. It applies a very limited number of carefully selected tools of probability theory and common statistical mechanics. It in particular uses the well-known feature that the maximum number of the individuals which can mutually interact simultaneously is bounded by a fixed value of a few units. The present approach results in the finite system of equations for the reduced many-individual distribution functions thereby eliminating the so-called closure problem inevitable in the BBGKY theory. The thermodynamic-limit assumption is not needed either. The system includes consistently derived terms of all of the basic types known in kinetic theory, in particular, both the “mean-field” and scattering-integral terms, and admits the kinetic equation of the form allowing a direct chemical-reaction reading. The present approach can deal with Hamilton’s equation systems which are nonmonogenic and not treated in statistical mechanics. The proposed modelling suggests the basis of the generalized kinetic theory and may serve as the stochastic mechanics of population of individuals.
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| 26. |
- Liljekvist, Yvonne, 1967-, et al.
(författare)
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Multi-theoretical approach when researching mathematics teachers’ professional development in self-organized online groups
- 2019
-
Ingår i: Proceedings of the Eleventh Congress of the European Society for Research in Mathematics Education (CERME11) ⟨hal-02418200⟩.
-
Konferensbidrag (refereegranskat)abstract
- Teachers worldwide are using social media as a professional development resource. In studying social media as ‘a place’ for teachers’ professional development, we investigated large Facebook groups with themes connected to teaching and learning in compulsory schools. The interaction in these groups was analysed within the framework of systemic functional grammar. In order to reveal knowledge known and shared by teachers as a community, we have also used Shulman’s (1987) framework. Most posts received responses and this response is in line with the expected response pattern. The speech functions ‘Questions’ and ‘Offers’ were most common. Further, most posts addressed subject specific knowledge. The multi-theoretical approach used when researching mathematics teachers’ professional development in self-organized online groups showed that these large Facebook groups facilitated professional learning.
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| 27. |
- Smolla, Marco, et al.
(författare)
-
Underappreciated features of cultural evolution
- 2024
-
Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- Cultural evolution theory has long been inspired by evolutionary biology. Conceptual analogies between biological and cultural evolution have led to the adoption of a range of formal theoretical approaches from population dynamics and genetics. However, this has resulted in a research programme with a strong focus on cultural transmission. Here, we contrast biological with cultural evolution, and highlight aspects of cultural evolution that have not received sufficient attention previously. We outline possible implications for evolutionary dynamics and argue that not taking them into account will limit our understanding of cultural systems. We propose twelve key questions for future research, among which are calls to improve our understanding of the combinatorial properties of cultural innovation, and the role of development and life history in cultural dynamics. Finally, we discuss how this vibrant research field can make progress by embracing its multidisciplinary nature.
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| 28. |
- Wedman, Lotta, 1975-
(författare)
-
Views on concept in the framework of Three worlds of mathematics : A concept analysis
- 2018
-
Ingår i: Perspectives on professional development of mathematics teachers. - Göteborg, Sweden. - 1651-3274. - 9789198402421 ; , s. 121-130
-
Konferensbidrag (refereegranskat)abstract
- There are examples of conceptual incoherencies within the field of mathematics education. In this paper, a concept analysis of the notion concept in Tall’s framework of Three worlds of mathematics is conducted. In the first phase of the study, an analysing tool is constructed from a literature review in philosophy and cognitive science. This tool makes two distinctions. One distinction is between views considering concepts as abstract and views considering concepts as mental. The other distinction is between views considering concepts as intersubjective and views considering concepts as subjective. Preliminary results show that different views on concept are mixed in the framework of Three worlds of mathematics.
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| 29. |
- Pejlare, Johanna, 1976, et al.
(författare)
-
Writing the History of Mathematics: Interpretations of the Mathematics of the Past and Its Relation to theMathematics of Today
- 2021
-
Ingår i: Handbook of the Mathematics of the Arts and Sciences. - Cham : Springer International Publishing. - 9783319706580 ; , s. 2395-2420
-
Bokkapitel (övrigt vetenskapligt/konstnärligt)abstract
- In the present chapter, interpretations of the mathematics of the past are problematized, based on examples such as archeological artifacts, as well as written sources from the ancient Egyptian, Babylonian, and Greek civilizations. The distinction between history and heritage is considered in relation to Euler’s function concept, Cauchy’s sum theorem, and the Unguru debate. Also, the distinction between the historical past and the practical past, as well as the distinction between the historical and the nonhistorical relations to the past, are made concrete based on Torricelli’s result on an infinitely long solid from the seventeenth century. Two complementary but different ways of analyzing the mathematics of the past are the synchronic and diachronic perspectives, which may be useful, for instance, regarding the history of school mathematics. Furthermore, recapitulation, or the belief that students’ conceptual development in mathematics is paralleled to the historical epistemology of mathematics, is problematized emphasizing the important role of culture.
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| 30. |
- Berndtsson, Bo, 1950
(författare)
-
Probability measures associated to geodesics in the space of kähler metrics
- 2018
-
Ingår i: Springer Proceedings in Mathematics and Statistics. - Cham : Springer International Publishing. - 2194-1017 .- 2194-1009. ; 269, s. 395-419
-
Konferensbidrag (refereegranskat)abstract
- We associate certain probability measures on R to geodesics in the space HL of positively curved metrics on a line bundle L, and to geodesics in the finite dimensional symmetric space of hermitian norms on H0(X, kL). We prove that the measures associated to the finite dimensional spaces converge weakly to the measures related to geodesics in HL as k goes to infinity. The convergence of second order moments implies a recent result of Chen and Sun on geodesic distances in the respective spaces, while the convergence of first order moments gives convergence of Donaldson’s Z-functional to the Aubin–Yau energy. We also include a result on approximation of infinite dimensional geodesics by Bergman kernels which generalizes work of Phong and Sturm.
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| 31. |
- Jansson, Fredrik, et al.
(författare)
-
Cultural Systems
- 2024
-
Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- Many cultural phenomena cannot be understood by studying traits in isolation. Instead, they are embedded in webs of relations, layered with rich social meaning, and sequentially acquired and evaluated, \emph{filtered}, in light of previously acquired traits. Incorporating multiple traits and their relations is needed to understand the organization, dynamics, and emergent products of cultural evolution. We argue that a systems approach offers the potential for: (i) a more thorough understanding of the source and character of emergent phenomena, crucial for understanding the origin and historical development of culture; (ii) an increased scope of cultural evolution, whereby faithful transmission, self-organization and filtering of culture can be accounted for by systems dynamics without the need for strong assumptions about innate machinery; and (iii) a more robust theoretical connection between cultural evolution and processes of development as they are studied in developmental psychology and related fields.
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| 32. |
- Jansson, Fredrik, et al.
(författare)
-
Modelling cultural systems and selective filters
- 2024
-
Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- A specific goal of the field of cultural evolution is to understand how processes of transmission and selection at the individual level lead to population-wide patterns of cultural diversity and change. Models of cultural evolution have typically assumed that traits are independent of one another and essentially exchangeable. But culture has a structure: traits bear relationships to one another that affect the transmission and selection process itself. Here we introduce a modelling framework to explore the effect of cultural structure on the process of learning. Through simulations, we find that introducing this simple structure changes the cultural dynamics. Based on a basic filtering mechanism for parsing these relationships, more elaborate cultural filters emerge. In a mostly incompatible cultural domain of traits, these filters organise culture into mostly (but not fully) consistent and stable systems. Incompatible domains produce small homogeneous cultures, while more compatibility increases size, diversity, and group divergence. When individuals copy based on a trait's features (here, its compatibility relationships) they produce more homogeneous cultures than when they copy based on the agent carrying the cultural trait. We discuss the implications of considering cultural systems and filters in the dynamics of cultural change.
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| 33. |
- Jansson, Fredrik, et al.
(författare)
-
Modelling Cultural Systems and Selective Filters
- 2022
-
Konferensbidrag (refereegranskat)abstract
- IntroductionCultural traits are embedded in webs of relations and sequentially acquired and evaluated – filtered – in light of previously acquired traits. Incorporating multiple traits and their relations is needed to understand the organisation, dynamics, and emergent products of cultural evolution.ApproachWe introduce a modelling framework of individual filtering of interdependent traits and explore the effects on cultural transmission and emergent phenomena, through mathematical treatment and simulations.FindingsSequential acquisition of compatible traits leads to culturally evolved filters. These organise culture into mostly consistent and stable systems. Depending on the structure of trait relations, they modulate rates of cultural change, exhibit path dependence and punctuated equilibria, and can generate convergent transmission, clustering and polarisation.DiscussionA systems view of culture can give a fuller understanding of the source and character of emergent phenomena. It increases the scope of cultural evolution, whereby faithful transmission, self-organisation and filters can be accounted for by systems dynamics without strong assumptions on innate machinery.
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| 34. |
- Geli, Patricia
(författare)
-
Modeling the Mechanism of Postantibiotic Effect and Determining Implications for Dosing Regimens
- 2009
-
Ingår i: Journal of Mathematical Biology. - : Springer Science and Business Media LLC. - 0303-6812 .- 1432-1416. ; 59:5, s. 1416-1432
-
Tidskriftsartikel (refereegranskat)abstract
- A stochastic model is proposed to explain one possible underlying mechanism of the postantibiotic effect (PAE). This phenomenon, of continued inhibition of bacterial growth after removal of the antibiotic drug, is of high relevance in the context of optimizing dosing regimens. One clinical implication of long PAE lies in the possibility of increasing intervals between drug administrations. The model describes the dynamics of synthesis, saturation and removal of penicillin binding proteins (PBPs). High fractions of saturated PBPs are in the model associated with a lower growth capacity of bacteria. An analytical solution for the bivariate probability of saturated and unsaturated PBPs is used as a basis to explore optimal antibiotic dosing regimens. Our finding that longer PAEs do not necessarily promote for increased intervals between doses, might help for our understanding of data provided from earlier PAE studies and for the determination of the clinical relevance of PAE in future studies.
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| 35. |
- Strömberg, Ann-Brith, 1961, et al.
(författare)
-
Mixed-Integer Linear Optimization: Primal–Dual Relations and Dual Subgradient and Cutting-Plane Methods
- 2020
-
Ingår i: Numerical Nonsmooth Optimization: State of the Art Algorithms. - Cham : Springer International Publishing. ; , s. 499-547, s. 499-547
-
Bokkapitel (övrigt vetenskapligt/konstnärligt)abstract
- This chapter presents several solution methodologies for mixed-integer linear optimization, stated as mixed-binary optimization problems, by means of Lagrangian duals, subgradient optimization, cutting-planes, and recovery of primal solutions. It covers Lagrangian duality theory for mixed-binary linear optimization, a problem framework for which ultimate success—in most cases—is hard to accomplish, since strong duality cannot be inferred. First, a simple conditional subgradient optimization method for solving the dual problem is presented. Then, we show how ergodic sequences of Lagrangian subproblem solutions can be computed and used to recover mixed-binary primal solutions. We establish that the ergodic sequences accumulate at solutions to a convexified version of the original mixed-binary optimization problem. We also present a cutting-plane approach to the Lagrangian dual, which amounts to solving the convexified problem by Dantzig–Wolfe decomposition, as well as a two-phase method that benefits from the advantages of both subgradient optimization and Dantzig–Wolfe decomposition. Finally, we describe how the Lagrangian dual approach can be used to find near optimal solutions to mixed-binary optimization problems by utilizing the ergodic sequences in a Lagrangian heuristic, to construct a core problem, as well as to guide the branching in a branch-and-bound method. The chapter is concluded with a section comprising notes, references, historical downturns, and reading tips.
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| 36. |
- Arnlind, Joakim, et al.
(författare)
-
Construction of n-Lie algebras and n-ary Hom-Nambu-Lie algebras
- 2011
-
Ingår i: Journal of Mathematical Physics. - : AIP Publishing. - 0022-2488 .- 1089-7658. ; 52:12, s. 123502-
-
Tidskriftsartikel (refereegranskat)abstract
- As n-ary operations, generalizing Lie and Poisson algebras, arise in many different physical contexts, it is interesting to study general ways of constructing explicit realizations of such multilinear structures. Generically, they describe the dynamics of a physical system, and there is a need of understanding their quantization. Hom-Nambu-Lie algebras provide a framework that might be an appropriate setting in which n-Lie algebras (n-ary Nambu-Lie algebras) can be deformed, and their quantization studied. We present a procedure to construct (n + 1)-ary Hom-Nambu-Lie algebras from n-ary Hom-Nambu-Lie algebras equipped with a generalized trace function. It turns out that the implications of the compatibility conditions, that are necessary for this construction, can be understood in terms of the kernel of the trace function and the range of the twisting maps. Furthermore, we investigate the possibility of defining (n + k)-Lie algebras from n-Lie algebras and a k-form satisfying certain conditions. (C) 2011 American Institute of Physics. [doi:10.1063/1.3653197]
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| 37. |
- van Bommel, Jorryt, 1974-, et al.
(författare)
-
Five minutes : Young students' understanding of time
- 2023
-
Ingår i: Proceedings of the Thirteenth Congress of the European Society for Research in Mathematics Education (CERME13). - Budapest : ERME. - 9789637031045
-
Konferensbidrag (refereegranskat)abstract
- The focus of this paper is on young students’ understanding of time which is hardly studied. In the presented study, Swedish 6-year-olds first worked on a task about estimating time and after that they posed their own tasks about time. The research questions concern what aspects of time come to light when 6-year-olds (1) estimate the time needed for specific activities and (2) pose tasks related to time When estimating time, the arguments given by the students were based on previous experiences, personal situations, and emotions. Sometimes more than one of these were used in the same line of argumentation. The tasks posed by the students were related to estimation of a set time, estimation of a time given a specific activity, using a timer, point-of-time, and time as a context. Our study suggests estimation and measurement of time as a suitable content to enlarge students’ understanding of time in addition to the more common focus on ‘telling the time’.
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| 38. |
- Doverborg, Elisabet, 1947, et al.
(författare)
-
Children's experience of shape in space
- 2001
-
Ingår i: For the learning of mathematics. ; 21:3, s. 32-38
-
Tidskriftsartikel (refereegranskat)abstract
- From a developmental educational perspective on children's learning an exploratory qualitative study has been carried out in the area of shape in space, which is considered to be one aspect of basic mathematics. The main idea is that shape is viewed as an aspect of children's everyday life. The work with six year old children is followed and described in a group named “the variational learning group”. The concept “variational” describes the teacher's strategies, that is, they are using the variation of children's own experience in their teaching. In this group the innovations take place, both in terms of how the content is dealt with and how the teachers work on children's learning. The children are here exposed to the surrounding world where shapes are reflected upon, discussed, examined and created in 2D flat shapes and 3D solid shapes. The children's learning about shapes in this group is also evaluated and compared with children's learning in a more traditional preschool class, here named “the reference group”. The differences between the two groups in children's abilities to imagine and draw a 3D cube and a house are obvious. The children did not significantly improve their skills in conceptualizing 3D on their own after 16 months. This means that the way a content is dealt with and the approach to learning makes a great difference.
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| 39. |
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| 40. |
- Mamontov, Eugen, 1955
(författare)
-
Homeorhesis and evolutionary properties of living systems: From ordinary differential equations to the active-particle generalized kinetics theory
- 2006
-
Ingår i: 10th Evolutionary Biology Meeting at Marseilles, 20-22 September 2006, Marseilles, France.
-
Konferensbidrag (refereegranskat)abstract
- Advanced generalized-kinetic-theory (GKT) models for biological systems are developed for populations of active (or living) particles [1]-[5]. These particles are described with both the stochastic variables common in kinetic theory (such as time, the particle random location and velocity) and the stochastic variables related to the internal states of an active particle. Evolution of these states represents biological, ecological, or social properties of the particle behavior. Paper [6] analyzes a number of the well-known statistical-mechanics approaches and shows that the active-particle GKT (APGKT) is the only treatment capable of modelling living systems. Work [2] summarizes the significance of the notion of an active particle in kinetic models. This notion draws attention to the features distinguishing living matter from nonliving matter. They are discussed by many authors (e.g., [7]-[15], [1]-[3], [6], [16]-[18]). Work [11] considers a lot of differences between living and nonliving matters, and the limitations of the modelling approaches developed for nonliving matter. Work [6] mainly focuses on the comparison of a few theoretical mechanics treatments in terms of the key living-matter properties formulated in [15]. One of the necessary properties of the evolution of living systems is homeorhesis. It is, loosely speaking, a peculiar qualitative and quantitative insensitivity of a living system to the exogenous signals acting on it. The earlier notion, homeostasis, was introduced by W. B. Cannon in 1926 who discussed the phenomenon in detail later [7]. Homeorhesis introduced by C. H. Waddington [8, p. 32] generalizes homeostasis and is well known in biology [8], [9], [12]. It is an inherent part of mathematical models for oncogeny (e.g., [16]-[18], [6, Appendix]). Homeorhesis is also discussed in [3, Section 4] in connection with APGKT. Homeorhesis is documented in ecology (e.g., [11], [13, the left column on p. 675]) where it is one of the key notions of the strong Gaia theory, a version of the Gaia theory (e.g., [14, Chapter 8]). The strong Gaia theory “states that the planet with its life, a single living system, is regulated in certain aspects by that life” [14, p. 124]. The very origin of the name “Gaia” is related to homeorhesis or homeostasis [14, p. 118]. These notions are also used in psychology and sociology. If evolution of a system is not homeorhetic, the system can not be living. Work [6, Appendix] derives a preliminary mathematical formulation of homeorhesis in terms of the simplest dynamical systems, i.e. ordinary differential equations (ODEs). The present work complements, extended, and further specify the approach of [6, Appendix]. The work comprises the two main parts. The first part develops the sufficient conditions for ODE systems to describe homeorhesis, and suggests a fairly general structure of the ODE model. It regards homeorhesis as piecewise homeostasis. The model can be specified in different ways depending on specific systems and specific purposes of the analysis. An example of the specification is also noted (the PhasTraM nonlinear reaction-diffusion model for hyperplastic oncogeny [16]-[18]). The second part of the work discusses implementation of the above homeorhesis ODE model in terms of a special version [3] of APGKT (see above). The key feature of this version is that the components of a living population need not be discrete: the subdivision into the components is described with a general, continuous-discrete probability distribution (see also [6]). This enables certain properties of living matter noted in [15]. Moreover, the corresponding APGKT model presents a system of, firstly, a generalized kinetic equation for the conditional distribution function conditioned by the internal states of the population and, secondly, Ito's stochastic differential equations for these states. This treatement employs the results on nonstationary invariant diffusion stochastic processes [19]. The second part of the work also stresses that APGKT is substantially more important for the living-matter analysis than in the case of nonliving matter. One of the reasons is certain limitations in experimental sampling of the living-system modes presented with stochastic processes. A few directions for future research are suggested as well. REFERENCES: [1] Bellomo, N., Bellouquid, A. and Delitala, M., 2004, Mathematical topics on the modelling complex multicellular systems and tumor immune cells competition, Math. Models Methods Appl. Sci., 14, 1683-1733. [2] Bellomo, N., 2006, New hot Paper Comments, Essential Science Indicators, http://www.esi-topics.com/nhp/2006 /may- 06-NicolaBellomo.html. [3] Willander, M., Mamontov, E. and Chiragwandi, Z., 2004, Modelling living fluids with the subdivision into the components in terms of probability distributions, Math. Models Methods Appl. Sci. 14, 1495-1520. [4] Bellomo, N. and Maini, P.K., 2005, Preface and the Special Issue “Multiscale Cancer Modelling-A New Frontier in Applied Mathematics”, Math. Models Methods Appl. Sci., 15, iii-viii. [5] De Angelis, E. and Delitala, M., 2006, Modelling complex systems in applied sciences: Methods and tools of the mathematical kinetic theory for active particles. Mathl Comput. Modelling, 43, 1310-1328. [6] Mamontov, E., Psiuk-Maksymowicz, K. and Koptioug, A., 2006, Stochastic mechanics in the context of the properties of living systems, Mathl Comput. Modelling, Article in Press, 13 pp. [7] Cannon, W.B., 1932, The Wisdom of the Body (New York: Norton). [8] Waddington, C.H., 1957, The Strategy of the Genes. A Discussion of Some Aspects of Theoretical Biology (London, George Allen and Unwin). [9] Waddington, C.H., 1968, Towards a theoretical biology, Nature, 218, 525-527. [10] Cotnoir, P.-A., 1981, La compétence environnementale: Une affaire d’adaptation. Séminaire en écologie behaviorale, Univeristé du Québec, Montralé. Available online at: http://pac.cam.org/culture.doc . [11] O’Neill, R.V., DeAngelis, D.L., Waide, J.B. and Allen, T.F.H., 1986, A Hierarchical Concept of Ecosystems, Princeton: Princeton Univ. Press). [12] Sauvant, D., 1992, La modélisation systémique en nutrition, Reprod. Nutr. Dev., 32, 217-230. [13] Christensen, N.L., Bartuska, A.M., Brown, J.H., Carpenter, S., D'Antonio, C., Francis, R., Franklin, J.F., MacMahon, J.A., Noss, R.F., Parsons, D.J., Peterson, C.H., Turner, M.G. and Woodmansee, R.G., 1996, The Report of the Ecological Society of America Committee on the Scientific Basis for Ecosystem Management, Ecological Applications, 6, 665-691. Available online at: http://www.esa.org/pao/esaPositions/Papers/ReportOfSBEM.php. [14] Margulis, L., 1998, Symbiotic Planet. A New Look at Evolution (Amherst: Sciencewriters). [15] Hartwell, L.H., Hopfield, J.J., Leibler, S. and Murray, A.W., 1999, From molecular to modular cell biology, Nature, 402, C47-C52. [16] Mamontov, E., Koptioug, A.V. and Psiuk-Maksymowicz, K., 2006, The minimal, phase-transition model for the cell- number maintenance by the hyperplasia-extended homeorhesis, Acta Biotheoretica, 54, 44 pp., (no. 2, May-June, accepted). [17] Psiuk-Maksymowicz, K. and Mamontov, E., 2005, The time-slices method for rapid solving the Cauchy problem for nonlinear reaction-diffusion equations in the competition of homeorhesis with genotoxically activated hyperplasia, In: European Conference on Mathematical and Theoretical Biology - ECMTB05 (July 18-22, 2005) Book of Abstracts, Vol.1 (Dresden: Center for Information Services and High Performance Computing, Dresden Univ. Technol.), p. 429 (http://www.ecmtb05.org/). [18] Psiuk-Maksymowicz, K. and Mamontov, E., 2006, The homeorhesis-based modelling and fast numerical analysis for oncogenic hyperplasia under radiation therapy, submitted. [19] Mamontov, E., 2005, Nonstationary invariant distributions and the hydrodynamic-style generalization of the Kolmogorov-forward/Fokker-Planck equation, Appl. Math. Lett. 18 (9) 976-982.
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| 41. |
- Gerken, Jan, 1991, et al.
(författare)
-
Equivariance versus augmentation for spherical images
- 2022
-
Ingår i: Proceedings of Machine Learning Resaerch. ; , s. 7404-7421
-
Konferensbidrag (refereegranskat)abstract
- We analyze the role of rotational equivariance in convolutional neural networks (CNNs) applied to spherical images. We compare the performance of the group equivariant networks known as S2CNNs and standard non-equivariant CNNs trained with an increasing amount of data augmentation. The chosen architectures can be considered baseline references for the respective design paradigms. Our models are trained and evaluated on single or multiple items from the MNIST- or FashionMNIST dataset projected onto the sphere. For the task of image classification, which is inherently rotationally invariant, we find that by considerably increasing the amount of data augmentation and the size of the networks, it is possible for the standard CNNs to reach at least the same performance as the equivariant network. In contrast, for the inherently equivariant task of semantic segmentation, the non-equivariant networks are consistently outperformed by the equivariant networks with significantly fewer parameters. We also analyze and compare the inference latency and training times of the different networks, enabling detailed tradeoff considerations between equivariant architectures and data augmentation for practical problems.
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| 42. |
- Mamontov, Eugen, 1955, et al.
(författare)
-
What stochastic mechanics are relevant to the study of living systems?
- 2005
-
Ingår i: Proceedings of the Latvian Academy of Sciences. Section B: Natural, Exact and Applied Sciences. - Riga, Latvia : Latvian Academy of Sciences. - 1407-009X. ; 59:6, s. 255-262
-
Tidskriftsartikel (refereegranskat)abstract
- Biologists have identified many features of living systems which cannot be studied by application of fundamental statistical mechanics (FSM). The present work focuses on some of these features. By discussing all the basic approaches of FSM, the work formulates the extension of the kinetic-theory paradigm (based on the reduced one-particle distribution function) that possesses all the considered properties of the living systems. This extension appears to be a model within the generalized-kinetic theory developed by N. Bellomo and his co-authors. In connection with this model, the work also stresses some other features necessary for making the model relevant to living systems. An example is discussed, which is a generalized kinetic equation coupled with the probability-density equation which represents the varying component content of a living system. The work also suggests directions for future research.
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| 43. |
- Tapani, Sofia, 1982
(författare)
-
Stochastic modelling and analysis of early mouse development
- 2011
-
Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- The aim of this thesis is to model and describe dynamical events for biological cells using statistical and mathematical tools. The thesis includes five papers that all relate to stochastic modelling of cells. In order to understand the development and patterning of the early mammalian embryo, stochastic modelling has become a more important tool than ever. It allows for studying the processes that mediate the transition from pluripotency of the embryonic cells to their differentiation. It is still unclear whether the positions of cells determine their future fates. One alternative possibility is that cells are pre-specified at random positions and then sort according to a already set fate. Mouse embryonic cells are thought to be equivalent in their developmental properties until approaching the eight-cell stage. Some biological studies show, in comparison, that patterning can be present already at sperm entry and in the pronuclei migration. We investigate in Paper I the dynamics of the pronuclei migration by analysing their trajectories and find that not only do the pronuclei follow a noise corrupted path towards the centre of the egg but they also have some attraction to each other which affects their dynamics. Continuing in Paper II and III, we use these results to model this behaviour with a coupled stochastic differential equation model. This enables us to simulate distributions that describe the meeting plane between pronuclei which in turn can be related to the orientation of the first cleavage of the egg. Our results show that adding randomness in sperm entry point is different from the randomness added through the environment of the egg. We are also able to show that data sets with normal eggs and eggs treated with an actin growth inhibitor give rise to considerably different model dynamics, suggesting that the treatment is affecting the migration in an invasive way. Altering the pronuclei dynamics can alter the polarity of the egg and may transfer into the later axis-formation process. Invasiveness of experimental procedures is a difficult issue to handle. The alternative to invasive procedures is not appealing since it means that important developmental features may not be discovered because of individual variability and noise, leading to guesswork of the underlying mechanisms. The embryonic cells are easily affected by treatments performed to make the measuring, made by hand, easier or by the light exposure of the microscope. Treatments as such are used for example for producing flourescent proteins in membranes or slowing processes down. Paper IV and Paper V serve to analyse how light induced stress affects yeast cells and we employ a method for analysing the noisy non-stationary time series, which are a result of the yeast experiments, using wavelet decomposition.
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| 44. |
- Winberg, Mikael, 1963-
(författare)
-
Motivation for Learning Science and Mathematics: Identifying Personal and Environmental Factors
- 2011
-
Konferensbidrag (refereegranskat)abstract
- Several theories in motivation research aim at explaining or predicting the emotional experiences and behavior of students in academic situations as well as the quality of learning outcomes. However, there are still ambiguities regarding the mechanisms of motivation, how motivation can be influenced, and what effects motivation has on learning. As a first step to examine the role of situational and personal variables involved in some of the most influential motivation theories, their relative ability to predict student behavior, emotional experiences and learning outcomes were investigated by PLS analysis of questionnaire data from 658 upper secondary school students. As to outcomes, results show that experiences of anxiety, on one hand, are orthogonal to perceived degree of learning, enjoyment, and motivated behavior, on the other. Major predictors of anxiety emotions were; Attributions, pertaining to the perceived degree of control over outcomes; the nature of relations to peers; and whether the students perceived that the goal of the lesson was understanding or ‘production’. The degree of learning, motivated behavior, and enjoyment were, in descending order, predicted by students’ achievement goals and motivation type, the teacher’s engagement, character of feedback, autonomy support and the level of teacher demands on students. To some extent, students’ epistemological beliefs regarding the complexity of knowledge also predicted these types of outcomes.
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| 45. |
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| 46. |
- Jansson, Fredrik, et al.
(författare)
-
Democratic revolutions as institutional innovation diffusion : rapid adoption and survival of democracy
- 2013
-
Ingår i: Technological forecasting & social change. - New York : Elsevier BV. - 0040-1625 .- 1873-5509. ; 80:8, s. 1546-1556
-
Tidskriftsartikel (refereegranskat)abstract
- Recent ‘democratic revolutions’ in Islamic countries call for a re-consideration of transitions to and from democracy. Transitions to democracy have often been considered the outcome of socio-economic modernization and therefore slow and incremental processes. But as a recent study has made clear, in the last century, transitions to democracy have mainly occurred through rapid leaps rather than slow and incremental steps. Here, we therefore apply an innovation and systems perspective and consider transitions to democracy as processes of institutional, and therefore systemic, innovation adoption. We show that transitions to democracy starting before 1900 lasted for an average of 50 years and a median of 56 years, while transitions originating later took an average of 4.6 years and a median of 1.7 years. However, our results indicate that the survival time of democratic regimes is longer in cases where the transition periods have also been longer, suggesting that patience paid in previous democratizations. We identify a critical ‘consolidation-preparing’ transition period of 12 years. Our results also show that in cases where the transitions have not been made directly from autocracy to democracy, there are no main institutional paths towards democracy. Instead, democracy seems reachable from a variety of directions. This is in line with the analogy of diffusion of innovations at the nation systems level, for which assumptions are that potential adopter systems may vary in susceptibility over time. The adoption of the institutions of democracy therefore corresponds to the adoption of a new political communications standard for a nation, in this case the innovation of involving in principle all adult citizens on an equal basis.
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| 47. |
- Bergwall, Andreas, 1972-
(författare)
-
Conceptualizing reasoning-and-proving opportunities in textbook expositions : Cases from secondary calculus
- 2017
-
Ingår i: Proceedings of the Tenth Congress of the European Society for Research in Mathematics Education (CERME10, February 1-5, 2017). - Dublin, Ireland : European Society for Research in Mathematics Education. - 9781873769737 ; , s. 91-98
-
Konferensbidrag (refereegranskat)abstract
- Several recent textbook studies focus on opportunities to learn reasoning-and-proving. They typically investigate the extent to which justifications are general proofs and what opportunities exist for learning important elements of mathematical reasoning. In this paper, I discuss how a particular analytical framework for this might be refined. Based on an in-depth analysis of certain textbook passages in upper secondary calculus textbooks, I make an account for analytical issues encountered during this process and identify aspects of reasoning-and-proving in textbooks that might be missed unless the framework is refined. Among them there are characterizations of generality, use of different representations, logical and mathematical structure, and ordering of material and student activities. Finally, implications beyond textbook research are discussed.
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| 48. |
- Bergwall, Andreas, 1972-
(författare)
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Topic-specific characteristics of proof-related reasoning
- 2023
-
Ingår i: International Journal of Mathematical Education in Science and Technology. - : Taylor & Francis. - 0020-739X .- 1464-5211.
-
Tidskriftsartikel (refereegranskat)abstract
- Students’ difficulties with proofs are well documented. To remedy this, it is often recommended that reasoning and proving be focused on in all grades and content areas of school mathematics. However, proofs continue to have a marginal place in many classrooms, or are only given explicit attention in courses in Euclidean geometry. Geometry is also the most common topic for educational research on reasoning and proving. This paper compares what four other topics in secondary school mathematics – logarithms, primitive functions, definite integrals, and combinatorics – can offer in terms of opportunities to learn proof. The types and natures of reasoning in expository sections and students’ tasks in 11 Swedish and Finnish textbooks are analysed in search of similarities and differences between these topics. The results are accounted for with special focus on opportunities for reasoning about general cases. Finally, the findings are discussed in relation to mathematical aspects of the four analysed topics.
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| 49. |
- Liljekvist, Yvonne, 1967-, et al.
(författare)
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Professional Learning Communities in a Web 2.0 World : Rethinking the Conditions for Professional Development
- 2017
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Ingår i: Teacher Empowerment Toward Professional Development and Practices. - Singapore, Singapore : Springer. - 9789811041501 ; , s. 269-280
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Bokkapitel (refereegranskat)abstract
- The new technologies, in particular social media in Web 2.0, enable rapid change in people’s behaviour, which needs to be considered in research on teacher empowerment and teacher professional development and growth. In this chapter we discuss how teachers in an informal, yet structured, way use social media to expand their professional learning communities beyond the local school context in Sweden. This is an example of how a new behaviour is emerging among teachers that changes the opportunities and the frames for professional development and growth. Through teachers’ engagement in social media, such as Facebook, extended professional learning communities arise and teachers’ professional development and growth become evident. Global levels influence local levels: teachers from different schools engage in structured discussions related to everyday practice, such as issues of learning goals in pre-school or topics related to a specific course in upper secondary school. The teachers’ arena for professional development and growth has changed, which means that the context of teacher empowerment is rapidly changing too. Consequently, the chapter includes theoretical reflections on professional learning communities in a Web 2.0 world and how this phenomenon may affect our approach to enhancing teachers’ professional development.
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- Nyström, Peter, 1959, et al.
(författare)
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Hur samstämmiga är svenska styrdokument och nationella prov med ramverk och uppgifter i TIMSS Advanced 2015?
- 2016
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- TIMSS Advanced (Trends in Mathematics and Science Study ) är en internationell studie som undersöker gymnasieelevers kunskaper i avancerad matematik och fysik. TIMSS Advanced har genomförts tre gånger, 1995, 2008 och 2015, och Sverige har deltagit varje gång. I 2015 års studie deltog svenska elever i årskurs 3 på naturvetenskaps- och teknikprogrammet som slutfört eller håller på att slutföra kursen matematik 4 respektive fysik 2. Studien ger möjlighet att analysera förändringar i motsvarande elevgruppers kunskaper över tid inom dessa områden, men också möjlighet att jämföra svenska resultat med resultat från andra länder. TIMSS Advanced 2015 har genomförts av Skolverket i samarbete med Nationellt Centrum för Matematikutbildning (NCM) vid Göteborgs universitet. Skolverket har sammanställt en nationell huvudrapport med resultaten från TIMSS Advanced 2015. En viktig utgångspunkt för tolkning och analys av resultaten är att veta i vilken utsträckning svenska elever fått möjlighet att lära sig det som prövas i TIMSS Advanced. I denna rapport analyseras därför samstämmigheten mellan TIMSS Advanced 2015 och svenska ämnesplaner, nationella prov och bedömningsstöd. Mot bakgrund av ämnenas kopplingar mellan varandra genomförs också en analys som särskilt fokuserar på inslaget av matematik i fysikuppgifterna.
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