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- Balehowsky, Tracey, et al.
(author)
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Shape analysis via gradient flows on diffeomorphism groups
- 2023
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In: Nonlinearity. - : IOP Publishing. - 1361-6544 .- 0951-7715. ; 36:2, s. 862-877
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Journal article (peer-reviewed)abstract
- We study a Riemannian gradient flow on Sobolev diffeomorphisms for the problem of image registration. The energy functional quantifies the effect of transforming a template to a target, while also penalizing non-isometric deformations. The main result is well-posedness of the flow. We also give a geometric description of the gradient in terms of the momentum map.
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| 3. |
- Hanstorp, Dag, 1960, et al.
(author)
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A versatile system for optical manipulation experiments
- 2017
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In: Proceedings of SPIE - The International Society for Optical Engineering. SPIE Nanoscience + Engineering, 2017, San Diego, California, United States. - : SPIE. - 0277-786X .- 1996-756X. - 9781510611528
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Conference paper (peer-reviewed)abstract
- Downloading of the abstract is permitted for personal use only. In this paper a versatile experimental system for optical levitation is presented. Microscopic liquid droplets are produced on demand from piezo-electrically driven dispensers. The charge of the droplets is controlled by applying an electric field on the piezo-dispenser head. The dispenser releases droplets into a vertically focused laser beam. The size and position in 3 dimensions of trapped droplets are measured using two orthogonally placed high speed cameras. Alternatively, the vertical position is determined by imaging scattered light onto a position sensitive detector. The charge of a trapped droplets is determined by recording its motion when an electric field is applied, and the charge can be altered by exposing the droplet to a radioactive source or UV light. Further, spectroscopic information of the trapped droplet is obtained by imaging the droplet on the entrance slit of a spectrometer. Finally, the trapping cell can be evacuated, allowing investigations of droplet dynamics in vacuum. The system is utilized to study a variety of physical phenomena, and three pilot experiments are given in this paper. First, a system used to control and measure the charge of the droplet is presented. Second, it is demonstrated how particles can be made to rotate and spin by trapping them using optical vortices. Finally, the Raman spectra of trapped glycerol droplets are obtained and analyzed. The long term goal of this work is to create a system where interactions of droplets with the surrounding medium or with other droplets can be studied with full control of all physical variables.
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| 4. |
- Karlsson, Carl-Joar, et al.
(author)
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Decisions and disease: a mechanism for the evolution of cooperation
- 2020
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In: Scientific Reports. - : Springer Science and Business Media LLC. - 2045-2322. ; 10:1
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Journal article (peer-reviewed)abstract
- In numerous contexts, individuals may decide whether they take actions to mitigate the spread of disease, or not. Mitigating the spread of disease requires an individual to change their routine behaviours to benefit others, resulting in a 'disease dilemma' similar to the seminal prisoner's dilemma. In the classical prisoner's dilemma, evolutionary game dynamics predict that all individuals evolve to 'defect.' We have discovered that when the rate of cooperation within a population is directly linked to the rate of spread of the disease, cooperation evolves under certain conditions. For diseases which do not confer immunity to recovered individuals, if the time scale at which individuals receive accurate information regarding the disease is sufficiently rapid compared to the time scale at which the disease spreads, then cooperation emerges. Moreover, in the limit as mitigation measures become increasingly effective, the disease can be controlled; the number of infections tends to zero. It has been suggested that disease spreading models may also describe social and group dynamics, indicating that this mechanism for the evolution of cooperation may also apply in those contexts.
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- Karlsson, Carl-Joar, 1995
(author)
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Game theory and applications
- 2021
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Licentiate thesis (other academic/artistic)abstract
- Individual-level interactions and decisions spread though populations and change the collective-level dynamics in an intricate way. Nevertheless, game theory is well suited for the unification of these viewpoints. This thesis introduces the works The strength of diversity and Decisions and disease: a mechanism for the evolution of cooperation, which show that games have broad applications in population dynamics modeling. In The strength of diversity we calculate the equilibrium strategies of the so-called game of teams. The game of teams is an individual-level competition between teams, and a team's strategy in this context is a distribution of strength over the team members. It turns out that the equilibrium strategies are flat distributions or 'alternating' flat distributions whenever there exists equilibrium strategies. In Decisions and disease: a mechanism for the evolution of cooperation we combine the classic SIR and SIS models from epidemiology with the prisoner's dilemma game. The transmission rate is computed as the average over defecting and cooperating individuals, and the individuals are subjected to a replicator equation that takes into account the portion of infectious members of the population. We compute the steady state solutions and interpret the results.
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| 6. |
- Karlsson, Carl-Joar, 1995
(author)
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Shapes and games
- 2024
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Doctoral thesis (other academic/artistic)abstract
- This thesis summarizes the four articles “Decisions and disease”, “Diversity strengthens competing teams”, “Shape analysis via gradient flows on diffeomorphism groups” and “Team game adaptive dynamics”. Each article has a different context, but the mathematical aims are unified as we prove optimality of solutions or well-posedness of dynamics. Moreover, the modelling perspective is central to each investigation. In “Decisions and disease” we combine the classic SIR and SIS models from epidemiology with the prisoner’s dilemma game. Here, the steady state solutions are interpreted in terms of cooperation during a pandemic. Another game is studied in “Diversity strengthens competing teams”, namely the so-called Game of Teams, for which all Nash equilibria are found. The optimal solutions, i.e., the Nash equilibria, are characterized by teams with maximal diversity in the sense that the successful teams have as different members as possible. Gradient flows are explored next, with a focus on an efficient method for image matching. We prove well-posedness of a gradient flow that is regularized by the deformation of the Riemannian metric of the manifold which the images are defined on. Lastly, the adaptive dynamics framework is applied to the Game of Teams. This model of evolution pushes the strategies of the game in the direction of the selection gradient. We have analyzed the well-posedness of the adaptive dynamics equations and answered questions about the stationary solutions, that is which solutions that do not display any dynamics despite the selection pressure that the selection gradient forces on them. It is found that the stationary solutions agree with the Nash equilibria.
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| 7. |
- Rowlett, Julie, 1978, et al.
(author)
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Diversity strengthens competing teams
- 2022
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In: Royal Society Open Science. - : The Royal Society. - 2054-5703. ; 9:8
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Journal article (peer-reviewed)abstract
- How does the composition of a collection of individuals affect its outcome in competition with other collections of individuals? Assuming that individuals can be different, we develop a model to interpolate between individual-level interactions and collective-level consequences. Rooted in theoretical mathematics, the model is not constrained to any specific context. Potential applications include research, education, sports, politics, ecology, agriculture, algorithms and finance. Our first main contribution is a game theoretic model that interpolates between the internal composition of an ensemble of individuals and the repercussions for the ensemble as a whole in competition with others. The second main contribution is the rigorous identification of all equilibrium points and strategies. These equilibria suggest a mechanistic underpinning for biological and physical systems to tend towards increasing diversity due to the strength it imparts to the system in competition with others.
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