| 1. |
- Lundow, Per Håkan, et al.
(författare)
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EXACT AND APPROXIMATE COMPRESSION OF TRANSFER MATRICES FOR GRAPH HOMOMORPHISMS
- 2008
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Ingår i: LMS Journal of Computation and Mathematics. - : Cambridge University Press. - 1461-1570. ; 11, s. 1-14
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Tidskriftsartikel (refereegranskat)abstract
- The aim of this paper is to extend the previous work on transfer matrix compression in the case of graph homomorphisms. For H-homomorphisms of lattice-like graphs we demonstrate how the automorphisms of H, as well as those of the underlying lattice, can be used to reduce the size of the relevant transfer matrices. As applications of this method we give currently best known bounds for the number of 4- and 5-colourings of the square grid, and the number of 3- and 4-colourings of the three-dimensional cubic lattice. Finally, we also discuss approximate compression of transfer matrices.
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| 2. |
- Pilotto, Francesca, et al.
(författare)
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Late Holocene anthropogenic landscape change in northwestern Europe impacted insect biodiversity as much as climate change did after the last Ice Age
- 2022
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Ingår i: Proceedings of the Royal Society of London. Biological Sciences. - : Royal Society Publishing. - 0962-8452 .- 1471-2954. ; 289:1977
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Tidskriftsartikel (refereegranskat)abstract
- Since the last Ice Age (ca 115 000–11 700 years ago), the geographical ranges of most plants and animals have shifted, expanded or contracted. Understanding the timing, geographical patterns and drivers of past changes in insect communities is essential for evaluating the biodiversity implications of future climate changes, yet our knowledge of long-term patterns is limited. We applied a network modelling approach to the recent fossil record of northwestern European beetles to investigate how their taxonomic and trait composition changed during the past 16 000 years. We found two major changes in beetle faunas 4000–3500 and 10 000–9500 years ago, coinciding with periods of human population growth in the Late Holocene and climate warming in the Early Holocene. Our results demonstrate that humans have affected insect biodiversity since at least the introduction of agropastoralism, with landscape-scale effects that can be observed at sites away from areas of direct human impact.
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| 3. |
- Gerken, Jan, 1991, et al.
(författare)
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Equivariance versus augmentation for spherical images
- 2022
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Ingår i: Proceedings of Machine Learning Resaerch. ; 162, s. 7404-7421
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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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| 4. |
- Berg, André, et al.
(författare)
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Lie-Trotter Splitting for the Nonlinear Stochastic Manakov System
- 2021
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Ingår i: Journal of Scientific Computing. - : Springer Science and Business Media LLC. - 0885-7474 .- 1573-7691. ; 88:1
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Tidskriftsartikel (refereegranskat)abstract
- This article analyses the convergence of the Lie-Trotter splitting scheme for the stochastic Manakov equation, a system arising in the study of pulse propagation in randomly birefringent optical fibers. First, we prove that the strong order of the numerical approximation is 1/2 if the nonlinear term in the system is globally Lipschitz. Then, we show that the splitting scheme has convergence order 1/2 in probability and almost sure order 1/2- in the case of a cubic nonlinearity. We provide several numerical experiments illustrating the aforementioned results and the efficiency of the Lie-Trotter splitting scheme. Finally, we numerically investigate the possible blowup of solutions for some power-law nonlinearities.
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| 5. |
- Dmytryshyn, Andrii, 1986-, et al.
(författare)
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Miniversal deformations of matrices of bilinear forms
- 2012
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Ingår i: Linear Algebra and its Applications. - : Elsevier. - 0024-3795 .- 1873-1856. ; 436:7, s. 2670-2700
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Tidskriftsartikel (refereegranskat)abstract
- Arnold [V.I. Arnold, On matrices depending on parameters, Russian Math. Surveys 26 (2) (1971) 29–43] constructed miniversal deformations of square complex matrices under similarity; that is, a simple normal form to which not only a given square matrix A but all matrices B close to it can be reduced by similarity transformations that smoothly depend on the entries of B. We construct miniversal deformations of matrices under congruence.
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| 6. |
- Galindo-Prieto, Beatriz, et al.
(författare)
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A new approach for variable influence on projection (VIP) in O2PLS models
- 2017
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Ingår i: Chemometrics and Intelligent Laboratory Systems. - : Elsevier. - 0169-7439 .- 1873-3239. ; 160, s. 110-124
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Tidskriftsartikel (refereegranskat)abstract
- A novel variable influence on projection approach for O2PLS® models, named VIPO2PLS, is presented in this paper. VIPO2PLS is a model-based method for judging the importance of variables. Its cornerstone is the 2-way formalism of the O2PLS models; i.e. the use of both predictive and orthogonal normalized loadings of the two modelled data matrices, and also a new weighting system based on the sum of squares of both data blocks (X, Y). The VIPO2PLS algorithm has been tested in one synthetic data set and two real cases, and the outcomes have been compared to the PLS-VIP, VIPOPLS, and i-PLS methods. The purpose is to achieve a sharper and enhanced model interpretation of O2PLS models by using the new VIPO2PLS method for assessing the importance of both X- and Y- variables.
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| 7. |
- Berg, André, 1990-
(författare)
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Numerical analysis and simulation of stochastic partial differential equations with white noise dispersion
- 2023
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This doctoral thesis provides a comprehensive numerical analysis and exploration of several stochastic partial differential equations (SPDEs). More specifically, this thesis investigates time integrators for SPDEs with white noise dispersion. The thesis begins by examining the stochastic nonlinear Schrödinger equation with white noise dispersion (SNLSE), see Paper 1. The investigation probes the performance of different numerical integrators for this equation, focusing on their convergences, L2-norm preservation, and computational efficiency. Further, this thesis thoroughly investigates a conjecture on the critical exponent of the SNLSE, related to a phenomenon known as blowup, through numerical means. The thesis then introduces and studies exponential integrators for the stochastic Manakov equation (SME) by presenting two new time integrators - the explicit and symmetric exponential integrators - and analyzing their convergence properties, see Paper 2. Notably, this study highlights the flexibility and efficiency of these integrators compared to traditional schemes. The narrative then turns to the Lie-Trotter splitting integrator for the SME, see Paper 3, comparing its performance to existing time integrators. Theoretical proofs for convergence in various senses, alongside extensive numerical experiments, shed light on the efficacy of the proposed numerical scheme. The thesis also deep dives into the critical exponents of the SME, proposing a conjecture regarding blowup conditions for this SPDE.Lastly, the focus shifts to the stochastic generalized Benjamin-Bona-Mahony equation, see Paper 4. The study introduces and numerically assesses four novel exponential integrators for this equation. A primary finding here is the superior performance of the symmetric exponential integrator. This thesis also offers a succinct and novel method to depict the order of convergence in probability.
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| 8. |
- Lindh, Magnus, 1973-
(författare)
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Evolution of Plants : a mathematical perspective
- 2016
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- The Earth harbors around 300 000 plant species. The rich and complex environment provided by plants is considered a key factor for the extraordinary diversity of the terrestrial fauna by, for example, providing food and shelter. This thesis contributes to the understanding of these questions by investigating how the interplay of physiology, demography, and evolution gives rise to variation and diversity in fundamental plant traits. This will help us answer questions such as: How has this amazing diversity of plant species emerged? Which mechanisms maintain diversity? How are plant strategies and plant diversity influenced by variations in the environment?A plant faces multiple problems to survive and reproduce successfully. These problems can be modeled by considering traits, trade-offs and a fitness measure. For example: How to maximize growth rate, while maximizing structural stability? I will investigate four plant models in order to understand the function of plants, and mechanisms promoting diversity. Paper I: We study how annual plants with and without growth constraints should optimize their flowering time when productivity or season length changes. With a dynamic ontogenetic growth model and optimal control theory we prove that a bang-bang reproductive control is optimal under constrained growth and constant mortality rate. We find that growth constraints can flip the direction of optimal phenological response for increasing productivity. The reason is that the growth rate of vegetative mass saturates at high productivity and therefore it is better to flower earlier and take advantage of a longer reproductive period. If season length extends equally both in the beginning and the end of the season, growth constraints control the direction of the optimal response as well. Our theory can help explaining phenological patterns along productivity gradients, and can be linked to empirical observations made on a calendar scale.Paper II: We introduce a new measure of tree crown-rise efficiency based on the loss of biomass of the tree during growth. The more mass the tree looses during growth, the less crown-rise efficient it is. Top-heavy shapes loose more biomass than bottom-heavy shapes. Light-use efficiency is defined as the mean light assimilation of the leaves in the crown times the ratio of leaf mass and total mass. We then study the trade-off between light-use efficiency to crown-rise efficiency for tree crown shapes. We assume that the total tree mass is constant, and a constant vertical light gradient represent the shading from a surrounding forest. We find large differences in crown shapes at intermediate vertical light gradient, when both self-shading and mean-field shading are important, suggesting light-use vs crown-rise efficiency as a new trade-off that can explain tree diversity. Our crown-rise efficiency measure could easily be integrated into existing forest models.Paper III: We extend an evolutionary tree crown model, where trees with different heights compete for light, with drought-induced mortality rates depending on ground-water availability and the depth of an optional taproot. The model does not include competition for ground water. Our model explains how ground-water availability can shape plant communities, when taproot and non-taproot strategies can coexist, and when only one of these strategies can persist. We investigate how emerging plant diversity varies with water table depth, soil water gradient and drought-induced mortality rate. The taproot enables plants to reach deep water, thus reducing mortality, but also carries a construction cost, thus inducing a trade-off. We find that taproots maintain plant diversity under increasing drought mortality, and that taproots evolve when groundwater is accessible at low depths. There are no viable strategies at high drought mortality and deep water table. Red Queen evolutionary dynamics appear at intermediate drought mortality in mixed communities with and without taproots, as the community never reaches a final evolutionarily stable composition.Paper IV: We extend a size-structured plant model, with self-shading and two evolving traits, crown top-heaviness and crown width-to-height ratio. The model allows us to identify salient trade-offs for the crown shape. The most important trade-off for top-heaviness is light-use efficiency vs crownrise efficiency, and the most important trade-off for width-to-height ratio is self-shading vs branch costs. We find that when the two traits coevolve; the outcome is a single common evolutionarily stable strategy (ESS), far away from the highest net primary production (NPP). When only sun angle is decreasing with increasing latitude both the crown width-to-height ratio and crown top-heaviness decrease. However, when light response in addition to the sun angle decreases with increasing latitude, the crown width-to-height ratio is nearly invariant of latitude except at low site productivity when the ratio decreases with latitude. Top-heaviness is always decreasing with increasing latitude. Finally, we find that crown top-heaviness increases with the NPP or leaf-area index (LAI) at ESS, but crown width-to-height ratio is maximal at an intermediate NPP or LAI.
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| 9. |
- Bayisa, Fekadu, et al.
(författare)
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Regularised Semi-parametric Composite Likelihood Intensity Modelling of a Swedish Spatial Ambulance Call Point Pattern
- 2023
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Ingår i: Journal of Agricultural Biological and Environmental Statistics. - : Springer. - 1085-7117 .- 1537-2693. ; 28, s. 664-83
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Tidskriftsartikel (refereegranskat)abstract
- Motivated by the development of optimal dispatching strategies for prehospital resources, we model the spatial distribution of ambulance call events in the Swedish municipality Skelleftea during 2014-2018 in order to identify important spatial covariates and discern hotspot regions. Our large-scale multivariate data point pattern of call events consists of spatial locations and marks containing the associated priority levels and sex labels. The covariates used are related to road network coverage, population density, and socio-economic status. For each marginal point pattern, we model the associated intensity function by means of a log-linear function of the covariates and their interaction terms, in combination with lasso-like elastic-net regularized composite/Poisson process likelihood estimation. This enables variable selection and collinearity adjustment as well as reduction of variance inflation from overfitting and bias from underfitting. To incorporate mobility adjustment, reflecting people's movement patterns, we also include a nonparametric (kernel) intensity estimate as an additional covariate. The kernel intensity estimation performed here exploits a new heuristic bandwidth selection algorithm. We discover that hotspot regions occur along dense parts of the road network. A mean absolute error evaluation of the fitted model indicates that it is suitable for designing prehospital resource dispatching strategies. Supplementary materials accompanying this paper appear online.
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| 10. |
- Berg, André, et al.
(författare)
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APPROXIMATED EXPONENTIAL INTEGRATORS FOR THE STOCHASTIC MANAKOV EQUATION
- 2023
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Ingår i: Journal of Computational Dynamics. - : American Institute of Mathematical Sciences (AIMS). - 2158-2491 .- 2158-2505. ; 10:2, s. 323-344
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Tidskriftsartikel (refereegranskat)abstract
- . This article presents and analyzes an approximated exponential integrator for the (inhomogeneous) stochastic Manakov system. This system of SPDE occurs in the study of pulse propagation in randomly birefringent optical fibers. For a globally Lipschitz-continuous nonlinearity, we prove that the strong order of the time integrator is 1/2. This is then used to prove that the approximated exponential integrator has convergence order 1/2 in probability and almost sure order 1/2-, in the case of the cubic nonlinear coupling which is relevant in optical fibers. Finally, we present several numerical experiments in order to support our theoretical findings and to illustrate the efficiency of the approximated exponential integrator as well as a modified version of it.
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