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Sökning: AMNE:(NATURAL SCIENCES Mathematics)

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51.
  • 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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52.
  • 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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53.
  • 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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54.
  • 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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55.
  • Benn, J., et al. (författare)
  • Currents and Finite Elements as Tools for Shape Space
  • 2019
  • Ingår i: Journal of Mathematical Imaging and Vision. - : Springer Science and Business Media LLC. - 0924-9907 .- 1573-7683. ; 61:8, s. 1197-1220
  • Tidskriftsartikel (refereegranskat)abstract
    • The nonlinear spaces of shapes (unparameterized immersed curves or submanifolds) are of interest for many applications in image analysis, such as the identification of shapes that are similar modulo the action of some group. In this paper, we study a general representation of shapes as currents, which are based on linear spaces and are suitable for numerical discretization, being robust to noise. We develop the theory of currents for shape spaces by considering both the analytic and numerical aspects of the problem. In particular, we study the analytical properties of the current map and the norm that it induces on shapes. We determine the conditions under which the current determines the shape. We then provide a finite element-based discretization of the currents that is a practical computational tool for shapes. Finally, we demonstrate this approach on a variety of examples.
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56.
  • 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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57.
  • Xia, Jiacheng, 1991 (författare)
  • Vector-valued Eisenstein series of congruence types and their products
  • 2019
  • Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
    • Historically, Kohnen and Zagier connected modular forms with period polynomials, and as a consequence of this association concluded that the products of at most two Eisenstein series span all spaces of classical modular forms of level 1. Later Borisov and Gunnells among other authors extended the result to higher levels. We consider this problem for vector-valued modular forms, establish the framework of congruence types and obtain the structure of the space of vector-valued Eisenstein series using tools from representation theory. Based on this development and historic results, we show that the space of vector-valued modular forms of certain weights and any congruence type can be spanned by the invariant vectors of that type tensor at most two Eisenstein series.
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58.
  • Casarino, V., et al. (författare)
  • On the variation operator for the Ornstein-Uhlenbeck semigroup in dimension one
  • 2024
  • Ingår i: Annali Di Matematica Pura Ed Applicata. - 0373-3114 .- 1618-1891. ; 203:1, s. 205-219
  • Tidskriftsartikel (refereegranskat)abstract
    • Consider the variation seminorm of the Ornstein-Uhlenbeck semigroup Ht in dimension one, taken with respect to t. We show that this seminorm defines an operator of weak type (1, 1) for the relevant Gaussian measure. The analogous Lp estimates for 1 < p < 8 were already known.
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59.
  • Eriksson, Kimmo, 1967-, et al. (författare)
  • Biases for acquiring information individually rather than socially
  • 2009
  • Ingår i: Journal of Evolutionary Psychology. - 0737-4828. ; 7:4, s. 309-329
  • Tidskriftsartikel (refereegranskat)abstract
    • We discuss theoretical and empirical arguments for a human bias to acquire information individually rather than socially. In particular, we argue that when other people can be observed, information collection is a public good and hence some of the individual variation in the choice between individual and social learning can be explained by variation in social value orientation. We conducted two experimental studies, based on the game Explore & Collect, to test the predictions that (1) socially and individually acquired information of equal objective value are treated differently, and (2) prosocial subjects tend to spend more effort than selfish subjects on individual acquiring of information. Both predictions were supported.
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60.
  • Johnson, Tomas, 1979-, et al. (författare)
  • On a computer-aided approach to the computation of Abelian integrals
  • 2011
  • Ingår i: BIT Numerical Mathematics. - : Springer Science and Business Media LLC. - 0006-3835 .- 1572-9125. ; 51:3, s. 653-667
  • Tidskriftsartikel (refereegranskat)abstract
    • An accurate method to compute enclosures of Abelian integrals is developed. This allows for an accurate description of the phase portraits of planar polynomial systems that are perturbations of Hamiltonian systems. As an example, it is applied to the study of bifurcations of limit cycles arising from a cubic perturbation of an elliptic Hamiltonian of degree four.
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