| 1. |
- 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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| 2. |
- 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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| 3. |
- 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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| 4. |
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| 5. |
- Mamontov, Eugen, 1955
(författare)
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Ordinary differential equation system for population of individuals and the corresponding probabilistic model
- 2008
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Ingår i: Mathl. Computer Modelling. - : Elsevier BV. - 0895-7177.
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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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| 6. |
- Geli, Patricia
(författare)
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Modeling the Mechanism of Postantibiotic Effect and Determining Implications for Dosing Regimens
- 2009
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Ingår i: Journal of Mathematical Biology. - : Springer Science and Business Media LLC. - 0303-6812 .- 1432-1416. ; 59:5, s. 1416-1432
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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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| 7. |
- Doverborg, Elisabet, 1947, et al.
(författare)
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Children's experience of shape in space
- 2001
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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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| 8. |
- Mamontov, Eugen, 1955
(författare)
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Homeorhesis and evolutionary properties of living systems: From ordinary differential equations to the active-particle generalized kinetics theory
- 2006
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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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| 9. |
- Mamontov, Eugen, 1955, et al.
(författare)
-
What stochastic mechanics are relevant to the study of living systems?
- 2005
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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
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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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| 10. |
- Andersson, Fredrik K., et al.
(författare)
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The mathematics of internet search engines
- 2008
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Ingår i: Acta Applicandae Mathematicae - An International Survey Journal on Applying Mathematics and Mathematical Applications. - : Springer. - 0167-8019 .- 1572-9036. ; 104:2, s. 211-242
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Tidskriftsartikel (refereegranskat)abstract
- This article presents a survey of techniques for ranking results in search engines, with emphasis on link-based ranking methods and the PageRank algorithm. The problem of selecting, in relation to a user search query, the most relevant documents from an unstructured source such as the WWW is discussed in detail. The need for extending classical information retrieval techniques such as boolean searching and vector space models with link-based ranking methods is demonstrated. The PageRank algorithm is introduced, and its numerical and spectral properties are discussed. The article concludes with an alternative means of computing PageRank, along with some example applications of this new method.
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| 11. |
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| 12. |
- Bråting, Kajsa, 1975-, et al.
(författare)
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Visualizations in Mathematics
- 2008
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Ingår i: Erkenntnis. - : Springer Science and Business Media LLC. - 0165-0106 .- 1572-8420. ; 68:3, s. 345-358
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we discuss visualizations in mathematics from a historical and didactical perspective. We consider historical debates from the 17th and 19th centuries regarding the role of intuition and visualizations in mathematics. We also consider the problem of what a visualization in mathematical learning can achieve. In an empirical study we investigate what mathematical conclusions university students made on the basis of a visualization. We emphasize that a visualization in mathematics should always be considered in its proper context.
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| 13. |
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| 14. |
- Andrews, Paul, 1954-
(författare)
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Comparative studies of mathematics teachers’ observable learning objectives : validating low inference codes
- 2009
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Ingår i: Educational Studies in Mathematics. - : Springer Science and Business Media LLC. - 0013-1954 .- 1573-0816. ; 71:2, s. 97-122
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Tidskriftsartikel (refereegranskat)abstract
- Videotape is an increasingly used tool in cross-national studies of mathematics teaching. However, the means by which videotaped lessons are coded and analysed remains an underdeveloped area with scholars adopting substantially different approaches to the task. In this paper we present an approach based on generic descriptors of mathematics learning objectives. Exploiting live observations in five European countries, the descriptors were developed in a bottom-up recursive manner for application to videotaped lessons from four of these countries, Belgium (Flanders), England, Hungary and Spain. The analyses showed not only that the descriptors were consistently operationalised but also that they facilitated the identification of both similarities and differences in the ways in which teachers conceptualise and present mathematics that resonated with the available literature. In so doing we make both methodological and theoretical contributions to comparative mathematics research in general and debates concerning the national mathematics teaching script in particular.
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| 15. |
- Bråting, Kajsa, 1975-
(författare)
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Studies in the Conceptual Development of Mathematical Analysis
- 2009
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This dissertation deals with the development of mathematical concepts from a historical and didactical perspective. In particular, the development of concepts in mathematical analysis during the 19th century is considered. The thesis consists of a summary and three papers. In the first paper we investigate the Swedish mathematician E.G. Björling's contribution to uniform convergence in connection with Cauchy's sum theorem from 1821. In connection to Björling's convergence theory we discuss some modern interpretations of Cauchy's expression x=1/n. We also consider Björling's convergence conditions in view of Grattan-Guinness distinction between history and heritage. In the second paper we study visualizations in mathematics from historical and didactical perspectives. We consider some historical debates regarding the role of intuition and visual thinking in mathematics. We also consider the problem of what a visualization in mathematics can achieve in learning situations. In an empirical study we investigate what mathematical conclusions university students made on the basis of a visualization. In the third paper we consider Cauchy's theorem on power series expansions of complex valued functions on the basis of a paper written by E.G. Björling in 1852. We discuss Björling's, Lamarle's and Cauchy's different conditions for expanding a complex valued function in a power seris. In the third paper we also discuss the problem of the ambiguites of fundamental concpets that existed during the mid-19th century. We argue that Cauchy's and Lamarle's proofs of Cauchy's theorem on power series expansions of complex valued functions are correct on the basis of their own definitions of the fundamental concepts involved.
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| 16. |
- Brattström, Gudrun
(författare)
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Leonardo da Pisa : Inger Christensen och Fibonacci
- 2008
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Ingår i: Lyrikvännen. - 0460-0762. ; 55:6, s. 33-38
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Tidskriftsartikel (populärvet., debatt m.m.)abstract
- Den danska poeten Inger Christensen byggde sin diktsamling Alfabet på Fibonaccis talserie. Artikeln är en kort historisk essä över Fibonacci, och beskriver även hur talserien är konstruerad.
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| 17. |
- Brandell, Gerd, et al.
(författare)
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Gender and Mathematics: recent development from a Swedish perspective
- 2007
-
Ingår i: ZDM. - : Springer Science and Business Media LLC. - 1863-9690 .- 1863-9704. ; 39:3, s. 235-250
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Tidskriftsartikel (refereegranskat)abstract
- A fairly large study of attitudes towards mathematics among Swedish students at secondary level was conducted during 2001–2004. A newly developed instrument was used that was designed to capture gender stereotyped attitudes among students related to various aspects of mathematics in education and future life. The new scale and its development are described with reference to the original Australian studies. The scale builds on the Fennema–Sherman attitude scale “Mathematics as a male domain” but allows mathematics to be viewed as female, male or gender neutral, reflecting a different societal and educational situation than in the seventies when attitudes towards mathematics as a male domain were first investigated. The Swedish study shows that mathematics is perceived as gendered, mostly as a male domain, by large minorities of students at secondary level. However, the results are complex, with clear differences in responses from female and male students. Furthermore, mathematics is also viewed as female in some aspects. A comparison with Australian data shows that Swedish students are less inclined to view mathematics as a female domain than Australian students of the same age. The relevance of the study is related to the lack of equity in mathematics in education and as a professional field in the Swedish society, documented by earlier research.
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| 18. |
- Bergqvist, Ewa, 1971-
(författare)
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A verbal factor in the PISA 2003 mathematics items : Tentative analyses
- 2009
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Ingår i: Proceedings of the 33rd Conference of the International Group for the Psychology of Mathematics Education. - Thessaloniki, Greece : PME. - 9789602436523 ; , s. 145-152
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Konferensbidrag (refereegranskat)abstract
- This study uses a statistical method to identify verbal items among mathematical items from PISA 2003. The verbal items are preliminary analysed and compared to the non-verbal items concerning number of text lines, response types, cognitive level, and competences measured. The results show that the verbal items, to a higher percentage than the non-verbal items, measures the reproduction competency, are straightforward, and of open constructed-response type. These results and proposed further analyses are discussed.
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| 19. |
- Österholm, Magnus, 1976-
(författare)
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Kan vi separera läsning från matematikämnet?
- 2009
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Ingår i: Dyslexi. - Stockholm : Svenska Dyslexiföreningen. - 1401-2480. ; 14:3, s. 18-21
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Tidskriftsartikel (populärvet., debatt m.m.)abstract
- För uppgifter som man använder i undervisning eller prov i matematik så vill man i första hand utveckla eller testa kunskaper i matematik och inte elevernas läsförmåga. Om undervisning i matematik bygger mycket på läsning så verkar det finnas större risk att elever som har svårigheter med läsning också kommer få svårigheter med matematikämnet. En tanke kan därför vara att man vill separera läsning från matematikämnet, för att på så sätt undvika dessa potentiella problem. Mitt syfte med denna artikel är att analysera vissa aspekter av relationer mellan läsning och matematik, för att på detta sätt se om och hur en sådan separering kan göras.
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| 20. |
- Österholm, Magnus, 1976-
(författare)
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Theories of epistemological beliefs and communication : A unifying attempt
- 2009
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Ingår i: Proceedings of the 33rd Conference of the International Group for the Psychology of Mathematics Education. - 9789602436523 ; , s. 4-257-4-264
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Konferensbidrag (refereegranskat)abstract
- In order to develop more detailed knowledge about possible effects of beliefs in mathematics education, it is suggested that we look more in-depth at more general types of theories. In particular, the study of relations between epistemological beliefs and communication is put forward as a good starting point in this endeavor. Theories of the constructs of epistemological beliefs and communication are analyzed in order to try to create a coherent theoretical foundation for the study of relations between the two constructs. Although some contradictions between theories are found, a type of unification is suggested, building on the theories of epistemological resources and discursive psychology.
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| 21. |
- Mamontov, Eugen, 1955
(författare)
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Modelling homeorhesis by ordinary differential equations
- 2007
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Ingår i: Mathl Comput. Modelling. - : Elsevier BV. - 0895-7177. ; 45:5-6, s. 694-707
-
Tidskriftsartikel (refereegranskat)abstract
- Homeorhesis is a necessary feature of any living system. If a system does not perform homeorhesis, it is nonliving. The present work develops the sufficient conditions for the ODE model to describe homeorhesis and suggests the structure of the model. The proposed homeorhesis model is fairly general. It treats homeorhesis as piecewise homeostasis. The model can be specified in different ways depending on the specific system and specific purposes of this analysis. An example of the specification is the PhasTraM model, the homeorhesis-aware nonlinear reaction–diffusion model for hyperplastic oncogeny in the previous works of the author. The qualitative agreement of the developed homeorhesis model with the living-system experimental results is noted. The work also shows that the basic mathematical models (such as the active-particle generalized kinetic theory) are substantially more important for the living-matter studies than in the case of nonliving matter. A few directions for future research are suggested as well.
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| 22. |
- Görnerup, Olof, 1977
(författare)
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Inference of Hierarchical Structure in Complex Systems
- 2008
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Hierarchical organization is a central property of complex systems. It is even argued that a system is required to be hierarchical in order to evolve complexity within reasonable time. A hierarchy of a system is defined as the set of self-contained levels at which the system operates and can be described on. Given a dynamical system there are only specific levels that are valid. This thesis mainly concerns the definition and inference of such levels. Paper I describes an algorithm for finding hierarchical levels in stochastic processes. The method systematically explores the set of possible partitions of a process' state space and statistically determines which of the partitions that impose closed dynamics. It is applicable to moderately sized systems. In Paper II an alternative approach that applies to linear dynamical systems is presented. In this case the spectral properties of the matrix that defines a system's dynamics is utilized, which allows for analysis of large systems (with on the order of thousand states). The specification and analysis of an algorithm that is based on the results in Paper II is presented in Paper III. Paper IV applies the spectral method and a complementary agglomeration method to infer aggregated dynamics in a Markov model of codon substitutions in DNA. The standard genetic code is identified as a projection that gives the hierarchical level of amino acid substitutions. Further, higher order amino acid groups that are relatively conserved under substitutions are found to define other levels of dynamics. Paper V and VI relate hierarchical organization to primordial evolution in a conceptual model that is based on the RNA world hypothesis. A well-stirred system of processes that catalyze the production of other processes is shown to successively build higher levels of organization from simple and general-purpose components by autocatalysis.
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| 23. |
- Cortas Nordlander, Maria, et al.
(författare)
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Influence of Student’s Attitudes and Beliefs on the Ability of Solving Mathematical Problems with Irrelevant Information
- 2009
-
Ingår i: Beliefs and attitudes in mathematics education. - Rotterdam : Sense Publishers. - 9789087907228 - 9789087907211 ; , s. 165-178
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Bokkapitel (övrigt vetenskapligt/konstnärligt)abstract
- A limited quantitative survey has been performed in order to study how attitudes, beliefs and feelings of students may influence the ability of solving text-based mathematical problems containing irrelevant information. The survey is also analyzing their capability of scrutinizing texts and sorting out relevant information.The students took a written test with text-based problems of different amount of irrelevant information. The capability of understanding such problems was investigated versus degree of mathematical maturity and gender. Obtained results indicate a noticeable correlation between the occurrence of irrelevant information and the ability of solving the problems. Furthermore, attitudes, beliefs, and the degree of mathematical maturity, expressed in terms of age, have a clear influence on the results. On the other hand, this study has not revealed any significant difference between genders as regards the capability of solving text-based problems with irrelevant information.
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| 24. |
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| 25. |
- Khrennikov, Andrei
(författare)
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On the problem of hidden variables for quantum field theory
- 2006
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Ingår i: NUOVO CIMENTO DELLA SOCIETA ITALIANA DI FISICA B-GENERAL. - : DELLA SOCIETA ITALIANA DI FISICA. - 0369-3554. ; 121, s. 505-521
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Tidskriftsartikel (refereegranskat)abstract
- We propose a solution of the problem of hidden variables for quantum field theory
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| 26. |
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| 27. |
- Nilsson, Per, 1967-
(författare)
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Elever resonerar om sannolikhet
- 2009
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Ingår i: Matematikdidaktiska frågor. - Göteborg : Livréna AB. - 9789185143115
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Bokkapitel (populärvet., debatt m.m.)abstract
- Kapitlet beskriver en studie om hur elever utan erfarenhet av undervisning i sannolikhet kan resonera om och hantera experimentella situationer som kräver förståelse av slump och sannolikhet. Samtidigt vill jag synliggöra den potential som ryms inom ramen för barns lust att upptäcka och förstå aktiviteter som fångar deras genuina intresse. Inledningsvis ges en kort bakgrunden till studien. Den följs av en diskussion av begreppen slump och sannolikhet. Jag beskriver utförligt de tärningsspel jag använt för att generera empiriskt material i studien. Därefter presenteras och karaktäriseras några av de resonemang om sannolikheter som elevernas handlingar visade prov på när de spelade. Hur elever förstår och utvecklar begrepp betraktas utifrån det sätt på vilket elevernas förståelse varierar med deras tolkningar av spelsituationerna. Som avslutning diskuterar jag hur olika aspekter av studien bidrar med idéer till att utveckla undervisning i matematik i allmänhet och i sannolikhet i synnerhet.
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| 28. |
- Nyman, Peter, 1971-
(författare)
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A Symbolic Classical Computer Language for Simulation of Quantum Algorithms
- 2009
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Ingår i: Lecture Notes in Computer Science. - Berlin / Heidelberg : Springer. - 0302-9743 .- 1611-3349. - 9783642008337 ; 5494, s. 158-173
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Tidskriftsartikel (refereegranskat)abstract
- Quantum computing is an extremely promising research combining theoretical and experimental quantum physics, mathematics, quantum information theory and computer science. Classical simulation of quantum computations will cover part of the gap between the theoretical mathematical formulation of quantum mechanics and the realization of quantum computers. One of the most important problems in “quantum computer science” is the development of new symbolic languages for quantum computing and the adaptation of existing symbolic languages for classical computing to quantum algorithms. The present paper is devoted to the adaptation of the Mathematica symbolic language to known quantum algorithms and corresponding simulation on the classical computer. Concretely we shall represent in the Mathematica symbolic language Simon’s algorithm, the Deutsch-Josza algorithm, Grover’s algorithm, Shor’s algorithm and quantum error-correcting codes. We shall see that the same framework can be used for all these algorithms. This framework will contain the characteristic property of the symbolic language representation of quantum computing and it will be a straightforward matter to include this framework in future algorithms.
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| 29. |
- Nyman, Peter
(författare)
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Simulation of Quantum Algorithms on a Symbolic Computer
- 2007
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Ingår i: Quantum Theory. - : Melville, New York. ; , s. 383-389
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- This paper is a presentation of how to implement quantum algorithms (namely, Shor's algorithm ) on a classical computer by using the well-known Mathematica package. It will give us a lucid connection between mathematical formulation of quantum mechanics and computational methods.
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| 30. |
- Schalley, Andrea C.
(författare)
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Das mathematische Weltbild der Maya
- 2000
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Bok (refereegranskat)abstract
- In acht Kapiteln zu Schriftsystem, religiösem Weltbild, Zahlensystem, Kalendersystem, Arithmetik und Astronomie bringt das Buch eine Gesamtdarstellung des mathematisch-astronomischen Wissens der Maya nach aktuellem Erkenntnisstand.
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| 31. |
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| 32. |
- Mamontov, Eugen, 1955, et al.
(författare)
-
Managing panic-stricken crowds: The need in quantitative models for social dynamics
- 2007
-
Ingår i: Abstract Booklet, The 8th Annual Conference of the European Sociological Association.
-
Konferensbidrag (refereegranskat)abstract
- Panics typically occur during disaster or social crisis. Panics in crowds in public sites (airports, hospitals, supermarkets, office buildings, air- or sea-liners, trains, stadiums, downtown areas, etc.) often cause stampedes leading to injuries or deaths. How can we best organize public events at existing sites in order to prevent the tragic outcomes? How can one design new public sites to avoid the consequences of panic? What methods and tools can be applied? These questions determine the focus of the present work. Obviously, experimental approaches are inapplicable. Intuitive problem solving does not assure specific and consistent solutions. Therefore, the work concentrates on the non-intuitive, model-based approaches. Evaluation of the model-based solutions involves quantitative characteristics, e.g., the time of the evacuation, the probability for individuals to get injured, the concentration of oxygen, etc. Subsequently, any suitable model must be quantitative. Moreover, the behaviour of crowds develops continuously in both space and time. Thus, the models must also be space-time continuous. The work analyzes these and other features of the models for social dynamics and emphasizes the key differences from the dynamical models in the natural sciences studying nonliving matter. The related application aspects and directions for future research are also discussed.
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| 33. |
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| 34. |
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| 35. |
- Cortas Nordlander, Maria, et al.
(författare)
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A Study of Students’ Ability to Solve Text-Based Mathematical Problems with Irrelevant or Superfluous Information
- 2008
-
Ingår i: Mathematical Views, MAVI 14.
-
Konferensbidrag (refereegranskat)abstract
- A limited quantitative survey has been performed in order to study the capability of students to solve text-based mathematical problems containing irrelevant or superfluous information, as well as their ability to scrutinize text and sort out the relevant information. The students took a written test with text-based problems of different amount of irrelevant or superfluous information. The capability of understanding such problems was investigated versus degree of maturity and gender. Obtained results indicate a noticeable correlation between the occurrence of irrelevant or superfluous information and ability of solving the problems. Furthermore, the results show that the degree of maturity, expressed in terms of age, has a clear influence on the results. This study has not revealed any significant difference between genders as regards ability of sorting out the relevant information.
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| 36. |
- Mouwitz, Lars, 1949
(författare)
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Matematik och bildning : berättelse, gräns, tystnad : Mathematics and Liberal Education: narrative, limit, tacitness
- 2006
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Mathemathics and Liberal Education – narrative, limit, tacitness is a study of mathematics as a special human endeavour to grasp and understand the world. Mathematics is seen as a cultural activity related to other cultural phenomena as music, art and literature, but also as a very efficient modelling tool for science, economy and social organisation. The concept of Bildung includes many aspects, but one of the most significant is to handle the double perspective of including both connections and limitations between different kinds of human understanding, in this case with mathematics in focus. To explore this double perspective the study has its focus mainly on the mathematical language. A language has a special territory of objects, structures and relations possible to name and handle. Therefore it will also define a certain kind of tacitness, an area not expressible in that very language. A typical example is the notation of a chess game. The mathematical language with its very specified vocabulary certainly also has a somewhat similar kind of tacitness. The research question is to identify and discuss aspects of human activities, which reasonably should be called “mathematical”, that the mathematics language could not articulate. The purpose is to show the necessity of a manifoldness of understanding, also in mathematical activities. Focus is on pure mathematics and mathematical modelling as two kinds of successful mathematical narratives with great scientific and societal impact. The study is on a meta-mathematical level with origin and base in the Department of Skill and Technology at the Royal Institute of Technology, and the empirical material is gathered mostly at three Dialogue Seminars at the Royal Dramatic Theatre, Stockholm. The approach is broad, including humanistic, philosophical and artistic perspectives. Skilled representatives from other fields than mathematics have in many cases contributed, in rich analogical and metaphorical dialogues, to qualify the research question.
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| 37. |
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| 38. |
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| 39. |
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| 40. |
- Österholm, Magnus, 1976-
(författare)
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A reading comprehension perspective on problem solving
- 2006
-
Ingår i: Developing and researching quality in mathematics teaching and learning : proceedings of MADIF 5 : the 5th Swedish Mathematics Education Research Seminar, Malmö, January 24-25, 2006. - Linköping : Svensk förening för matematikdidaktisk forskning (SMDF). - 9197393444 ; , s. 136-145
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Konferensbidrag (refereegranskat)abstract
- The purpose of this paper is to discuss the bi-directional relationship between reading comprehension and problem solving, i.e. how reading comprehension can affect and become an integral part of problem solving, and how it can be affected by the mathematical text content or by the mathematical situation when the text is read. Based on theories of reading comprehension and a literature review it is found that the relationship under study is complex and that the reading process can affect as well as act as an integral part of the problem solving process but also that not much research has focused on this relationship.
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| 41. |
- Österholm, Magnus, 1976-
(författare)
-
Characterizing reading comprehension of mathematical texts
- 2006
-
Ingår i: Educational Studies in Mathematics. - : Springer Science and Business Media LLC. - 0013-1954 .- 1573-0816. ; 63:3, s. 325-346
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Tidskriftsartikel (refereegranskat)abstract
- This study compares reading comprehension of three different texts: two mathematical texts and one historical text. The two mathematical texts both present basic concepts of group theory, but one does it using mathematical symbols and the other only uses natural language. A total of 95 upper secondary and university students read one of the mathematical texts and the historical text. Before reading the texts, a test of prior knowledge for both mathematics and history was given and after reading each text, a test of reading comprehension was given. The results reveal a similarity in reading comprehension between the mathematical text without symbols and the historical text, and also a difference in reading comprehension between the two mathematical texts. This result suggests that mathematics in itself is not the most dominant aspect affecting the reading comprehension process, but the use of symbols in the text is a more relevant factor. Although the university students had studied more mathematics courses than the upper secondary students, there was only a small and insignificant difference between these groups regarding reading comprehension of the mathematical text with symbols. This finding suggests that there is a need for more explicit teaching of reading comprehension for texts including symbols.
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| 42. |
- Österholm, Magnus
(författare)
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Do students need to learn how to use their mathematics textbooks? : The case of reading comprehension
- 2008
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Ingår i: Nordisk matematikkdidaktikk. - Mölndal : Nordisk matematikkdidaktikk. - 1104-2176. ; 13:3, s. 53-73
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Tidskriftsartikel (refereegranskat)abstract
- The main question discussed in this paper is whether students need to learn how to read mathematical texts. I describe and analyze the results from different types of studies about mathematical texts; studies about properties of mathematical texts, about the reading of mathematical tasks, and about the reading of mathematical expository texts. These studies show that students seem to develop special reading strategies for mathematical texts that are not desirable. It has not been possible to find clear evidence for the need of a specific ”mathematical reading ability”. However, there is still a need to focus more on reading in mathematics teaching since students seem to develop the non-desirable reading strategies.
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| 43. |
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| 44. |
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| 45. |
- Österholm, Magnus, 1976-
(författare)
-
Läsförståelsens roll inom matematikutbildning
- 2009. - 1
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Ingår i: Matematikdidaktiska frågor. - Göteborg : Nationellt centrum för matematikutbildning (NCM), Göteborgs universitet. - 9789185143115 ; , s. 154-165
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Bokkapitel (populärvet., debatt m.m.)abstract
- Denna artikel beskriver undersökningar kring hur universitetsstudenter och skolelever läser olika typer av texter. Frågor jag vill besvara är hur man bör förhålla sig till läsning inom matematikutbildning och om man behöver behandla läsförståelse som en del av undervisning inom matematik. I artikeln behandlar jag undersökningar kring läsning av uppgiftstexter samt undersökningar kring läsning av förklarande texter. Därefter jämför jag dessa olika typer av lässituationer och noterar då vissa likheter mellan lässtrategier som elever använder sig av i de olika situationerna. Bland annat noterar jag att texter som innehåller symboler tycks aktivera en speciell lässtrategi hos elever. Denna strategi verkar handla om att fokusera på symboler och andra typer av nyckelord i texten, vilket resulterar i en sämre läsförståelse. En slutsats är därför att det finns behov av att behandla läsning i matematikundervisning eftersom elever på egen hand tenderar att utveckla bristfälliga lässtrategier. Jag diskuterar också förslag på hur man kan göra detta. Som avslutning i artikeln diskuterar jag även hur resultaten om läsning kan ses i relation till andra forskningsresultat.
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| 46. |
- Österholm, Magnus, 1976-
(författare)
-
Metacognition and reading - criteria for comprehension of mathematics texts
- 2006
-
Ingår i: Proceedings of the 30th conference of the International group for the psychology of mathematics education. - Prague : The International Group for the Psychology of Mathematics Education. ; , s. 289-296
-
Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- This study uses categories of comprehension criteria to examine students’ reasons for stating that they do, or do not, understand a given mathematics text. Nine student teachers were individually interviewed, where they read a text and commented on their comprehension, in particular, why they felt they did, or did not, understand the text. The students had some difficulties commenting on their comprehension in this manner, something that can be due to that much of comprehension monitoring, when criteria for comprehension are used, might be operating at an unconscious cognitive level. Some specific aspects of mathematics texts are examined, such as the symbolic language and conceptual and procedural understanding.
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| 47. |
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| 48. |
- Otani, Hiroki, et al.
(författare)
-
Morphometric study on the characteristic external features of normal and abnormal human embryos
- 2008
-
Ingår i: Congenit Anom Kyoto. - : Wiley. ; 48:1, s. 18-28
-
Tidskriftsartikel (refereegranskat)abstract
- The embryonic period is characterized by organogenesis and accompanying dynamic changes in external features. The measurement of human embryos has been limited to whole body dimensions, such as crown-rump length. More detailed measurements would add quantitative information about these characteristic events and provide a better understanding of normal and abnormal embryonic development. In the present study, we defined axes, landmarks, and measurements for human embryos, and measured 250 externally normal human embryos at Carnegie stages 14-23 (6.5-29.3 mm in crown-rump length, approximately 5-8 weeks of estimated ovulation age) that were fixed in Bouin's solution and preserved in 10% formalin solution. The axes, landmarks, and measurements defined for human embryos are corresponding to those in human and primate fetuses. The whole body, head, face, and extremities were measured using a scale attached to a dissecting microscope. Axial length, head height plus ear-shoulder length plus trunk height, was designated as a new measurement of the whole body, which is comparable with crown-rump length. Approximate standards of these measurements were obtained. The ratios of some measurements to trunk height and between the different parts were also obtained, and several different developmental patterns were recognized. The reproducibility of each measurement was evaluated by measuring 50 specimens three times each at intervals of one or two months. As a pilot study for the application of the proposed measurements, 84 human embryos with external anomalies, including holoprosencephaly, anomalies of extremities, and pharyngeal arch anomalies, were measured using the same method, and a few tendencies characteristic to holoprosencephaly were noticed.
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| 49. |
- Mamontov, Eugen, 1955, et al.
(författare)
-
The minimal, phase-transition model for the cell-number maintenance by the hyperplasia-extended homeorhesis
- 2006
-
Ingår i: Acta Biotheoretica. - : Springer Science and Business Media LLC. - 0001-5342 .- 1572-8358. ; 54:2, s. 61-101
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Tidskriftsartikel (refereegranskat)abstract
- Oncogenic hyperplasia is the first and inevitable stage of formation of a (solid) tumor. This stage is also the core of many other proliferative diseases. The present work proposes the first minimal model that combines homeorhesis with oncogenic hyperplasia where the latter is regarded as a genotoxically activated homeorhetic dysfunction. This dysfunction is specified as the transitions of the fluid of cells from a fluid, homeorhetic state to a solid, hyperplastic-tumor state, and back. The key part of the model is a nonlinear reaction-diffusion equation (RDE) where the biochemical-reaction rate is generalized to the one in the well-known Schlögl physical theory of the non-equilibrium phase transitions. A rigorous analysis of the stability and qualitative aspects of the model, where possible, are presented in detail. This is related to the spatially homogeneous case, i.e. when the above RDE is reduced to a nonlinear ordinary differential equation. The mentioned genotoxic activation is treated as a prevention of the quiescent G0-stage of the cell cycle implemented with the threshold mechanism that employs the critical concentration of the cellular fluid and the nonquiescent-cell-duplication time. The continuous tumor morphogeny is described by a time-space-dependent cellular-fluid concentration. There are no sharp boundaries (i.e. no concentration jumps exist) between the domains of the homeorhesis- and tumor-cell populations. No presumption on the shape of a tumor is used. To estimate a tumor in specific quantities, the model provides the time-dependent tumor locus, volume, and boundary that also points out the tumor shape and size. The above features are indispensable in the quantitative development of antiproliferative drugs or therapies and strategies to prevent oncogenic hyperplasia in cancer and other proliferative diseases. The work proposes an analytical-numerical method for solving the aforementioned RDE. A few topics for future research are suggested.
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| 50. |
- Nordebo, Sven, et al.
(författare)
-
Estimation of Parameters of an Inhomogeneous Dielectric Layer
- 2009
-
Ingår i: <em>Mathematical Modeling of Wave phenomena.</em>. - Melville, New York : American Institute of Physics. - 9780735406438 ; , s. 94-103
-
Konferensbidrag (refereegranskat)abstract
- This paper presents a general framework for sensitivity analysis for fewparameter inverse problems using the Fisher information and the Cram´er-Rao bound. In particular, the one-dimensional inverse problem of estimating the dispersive parameters of an inhomogeneous dielectric layer with linear spatial variation is studied. The analysis technique is particularly well-suited for inverse problems using few parameters, and it is anticipated that the framework may be used as a basis for extensive numerical investigations and physical interpretations. The ill-posedness of the inverse problem can be explicitely quantified by using the Fisher information analysis. As an example, the sensitivity analysis is used together with asymptotic theory to show that the inverse problem becomes extremely ill-posed when the linear spatial variation vanishes.
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