| 1. |
- Gyllingberg, Linnéa, et al.
(författare)
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Finding analytical approximations for discrete, stochastic, individual-based models of ecology
- 2023
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Ingår i: Mathematical Biosciences. - : Elsevier. - 0025-5564 .- 1879-3134. ; 365
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Tidskriftsartikel (refereegranskat)abstract
- Discrete time, spatially extended models play an important role in ecology, modelling population dynamics of species ranging from micro-organisms to birds. An important question is how ’bottom up’, individual-based models can be approximated by ’top down’ models of dynamics. Here, we study a class of spatially explicit individual-based models with contest competition: where species compete for space in local cells and then disperse to nearby cells. We start by describing simulations of the model, which exhibit large-scale discrete oscillations and characterize these oscillations by measuring spatial correlations. We then develop two new approximate descriptions of the resulting spatial population dynamics. The first is based on local interactions of the individuals and allows us to give a difference equation approximation of the system over small dispersal distances. The second approximates the long-range interactions of the individual-based model. These approximations capture demographic stochasticity from the individual-based model and show that dispersal stabilizes population dynamics. We calculate extinction probability for the individual-based model and show convergence between the local approximation and the non-spatial global approximation of the individual-based model as dispersal distance and population size simultaneously tend to infinity. Our results provide new approximate analytical descriptions of a complex bottom-up model and deepen understanding of spatial population dynamics.
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| 2. |
- Liu, Hong, et al.
(författare)
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On the maximum number of integer colourings with forbidden monochromatic sums
- 2021
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Ingår i: The Electronic Journal of Combinatorics. - : The Electronic Journal of Combinatorics. - 1097-1440 .- 1077-8926. ; 28:1
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Tidskriftsartikel (refereegranskat)abstract
- Let f(n, r) denote the maximum number of colourings of A ⊆ {1, …, n} with r colours such that each colour class is sum-free. Here, a sum is a subset {x, y, z} such that x + y = z. We show that f(n, 2) = 2⌈n/2⌉, and describe the extremal subsets. Further, using linear optimisation, we asymptotically determine the logarithm of f(n, r) for r ≤ 5. Similar results were obtained by Hán and Jiménez in the setting of finite abelian groups.
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| 3. |
- Prodinger, Helmut
(författare)
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Counting ternary trees according to the number of middle edges and factorizing into (3 / 2) -ary trees
- 2022
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Ingår i: Asian-European Journal of Mathematics. - : World Scientific Publishing. - 1793-5571 .- 1793-7183. ; 15:11
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Tidskriftsartikel (refereegranskat)abstract
- The sequence A120986 in the Encyclopedia of Integer Sequences counts ternary trees according to the number of edges (equivalently nodes) and the number of middle edges. Using a certain substitution, the underlying cubic equation can be factored. This leads to an extension of the concept of (3/2)-ary trees, introduced by Knuth in his christmas lecture from 2014.
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| 4. |
- Brännström, Åke, 1975-, et al.
(författare)
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Rigorous conditions for food-web intervality in high-dimensional trophic niche spaces
- 2011
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Ingår i: Journal of Mathematical Biology. - : Springerlink. - 0303-6812 .- 1432-1416. ; 63:3, s. 575-592
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Tidskriftsartikel (refereegranskat)abstract
- Food webs represent trophic (feeding) interactions in ecosystems. Since the late 1970s, it has been recognized that food-webs have a surprisingly close relationship to interval graphs. One interpretation of food-web intervality is that trophic niche space is low-dimensional, meaning that the trophic character of a species can be expressed by a single or at most a few quantitative traits. In a companion paper we demonstrated, by simulating a minimal food-web model, that food webs are also expected to be interval when niche-space is high-dimensional. Here we characterize the fundamental mechanisms underlying this phenomenon by proving a set of rigorous conditions for food-web intervality in high-dimensional niche spaces. Our results apply to a large class of food-web models, including the special case previously studied numerically.
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| 5. |
- Engström, Christian, et al.
(författare)
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Homogenization of the Maxwell equations using Floquet-Bloch decomposition
- 2003
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Ingår i: Mathematical and numerical waves 2003. - Berlin, Heidelberg : Springer. - 9783642558566 - 354040127X ; , s. 412-416
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Konferensbidrag (refereegranskat)abstract
- Using Bloch waves to represent the full solution of the Maxwell equations inperiodic media, we study the limit process where the material's period becomes much smaller than the wavelenght. it is seen that effective material parameters can be extracted and explicity represented in terms of the non-vanishing Bloch waves, providing an alternative means of homogenization.
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| 6. |
- Engström, Christian
(författare)
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Inverse bounds of two-component composites
- 2007
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Ingår i: SIAM Journal on Applied Mathematics. - : Society for Industrial and Applied Mathematics. - 0036-1399 .- 1095-712X. ; 68:3, s. 666-679
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Tidskriftsartikel (refereegranskat)abstract
- A method is presented for estimating microstructural parameters from permittivity measurements of two-component composites. This structural information is described by a particular positive measure in the Stieltjes integral representation of the effective permittivity. The dependence on the geometrical structure can be reduced to the problem of calculating the moments of the measure. We present a method that uses measurement data at a set of distinct frequencies or temperatures to calculate bounds on several moments. These inverse bounds are improved when the volume fraction is known or the material is isotropic. Composites with known geometrical structure illustrate the method.
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| 7. |
- Engström, Christian, et al.
(författare)
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Numerical methods for homogenization of Maxwell's equations
- 2004
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Ingår i: URSI 2004 International Symposium on Electromagnetic Theory. - : Pisa University Press. - 8884922526 - 9788884922526 ; , s. 987-989
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Konferensbidrag (refereegranskat)abstract
- When the wavelength is much larger than the typical scale of the microstructure in a material, it is possible to define effective or homogenized material coefficients. Two numerical methods for the determination of the homogenized coefficients are compared. Numerical examples, where extreme properties of the effective material are achieved in the two dimensional case, are presented.
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| 8. |
- Engström, Christian
(författare)
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On the spectrum of a holomorphic operator-valued function with applications to absorptive photonic crystals
- 2010
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Ingår i: Mathematical Models and Methods in Applied Sciences. - : World Scientific. - 0218-2025. ; 20:8, s. 1319-1341
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Tidskriftsartikel (refereegranskat)abstract
- We study electromagnetic wave propagation in a periodic and frequency dependent material characterized by a space- and frequency-dependent complex-valued permittivity. The spectral parameter relates to the time-frequency, leading to spectral analysis of a holomorphic operator-valued function. We apply the Floquet transform and show for a fixed quasi-momentum that the resulting family of spectral problems has a spectrum consisting of at most countably many isolated eigenvalues of finite multiplicity. These eigenvalues depend continuously on the quasi-momentum and no nonzero real eigenvalue exists when the material is absorptive. Moreover, we reformulate the special case of a rational operator-valued function in terms of a polynomial operator pencil and study two-component dispersive and absorptive crystals in detail.
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| 9. |
- Engström, Christian, et al.
(författare)
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On the spectrum of an operator pencil with applications to wave propagation in periodic and frequency dependent materials
- 2009
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Ingår i: SIAM Journal on Applied Mathematics. - : Society for Industrial & Applied Mathematics (SIAM). - 0036-1399 .- 1095-712X. ; 70:1, s. 231-247
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Tidskriftsartikel (refereegranskat)abstract
- We study wave propagation in periodic and frequency dependent materials when the medium in a frequency interval is characterized by a real-valued permittivity. The spectral parameter relates to the quasi momentum, which leads to spectral analysis of a quadratic operator pencil where frequency is a parameter. We show that the underlying operator has a discrete spectrum, where the eigenvalues are symmetrically placed with respect to the real and imaginary axis. Moreover, we discretize the operator pencil with finite elements and use a Krylov space method to compute eigenvalues of the resulting large sparse matrix pencil.
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| 10. |
- 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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