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- Eriksson, Olivia, 1971-
(författare)
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Simplicity within Complexity : Understanding dynamics of cellular networks by model reduction
- 2008
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Cellular networks composed of interactions between genes, proteins and metabolites, determines the behavioural repertoire of the cell. Recent developments in high-throughput experimental techniques and computational methods allow static descriptions of these networks on a genome scale. There are also several dynamical mathematical models characterizing small subnetworks of the cell such as a signaling cascade or cell division. These networks exhibit a considerable complexity, and mathematical analysis are therefore essential in order to uncover the underlying dynamical core driving the systems. A core description can reveal the relative functional contributions of the various molecular interactions and goes to the heart of what kind of computations biological circuits perform. Partially successful methodologies toward this end includes bifurcation analysis, which only considers a small number of dimensions, and large-scale computer simulations. In this thesis we explore a third route utilizing the inherent biological structure and dynamics of the network as a tool for model simplification. Using the well studied cell cycle, as a model system, we observe that the this network can be divided into dynamical modules displaying a switch-like behaviour. This allows a transformation into a piecewise linear system with delay, the subsequent use of tools from linear systems theory and finally a core dynamical description. Analytical expressions capturing important cell cycle features such as cell mass, as well as necessary constraints for cell cycle oscillations, are thereby retrieved. Finally we use the dynamical core together with large-scale simulations in order to study the balance between robustness and sensitivity. It appears that biological features such as switches, modularity and robustness provide a means to reformulate intractable mathematical problems into solvable ones, as biology appears to suggest a path of simplicity within the realm of mathematical complexity.
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| 2. |
- Li, Yibei, 1993-
(författare)
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Dynamic Optimization for Agent-Based Systems and Inverse Optimal Control
- 2019
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This dissertation is concerned with three problems within the field of optimization for agent--based systems. Firstly, the inverse optimal control problem is investigated for the single-agent system. Given a dynamic process, the goal is to recover the quadratic cost function from the observation of optimal control sequences. Such estimation could then help us develop a better understanding of the physical system and reproduce a similar optimal controller in other applications. Next, problems of optimization over networked systems are considered. A novel differential game approach is proposed for the optimal intrinsic formation control of multi-agent systems. As for the credit scoring problem, an optimal filtering framework is utilized to recursively improve the scoring accuracy based on dynamic network information.In paper A, the problem of finite horizon inverse optimal control problem is investigated, where the linear quadratic (LQ) cost function is required to be estimated from the optimal feedback controller. Although the infinite-horizon inverse LQ problem is well-studied with numerous results, the finite-horizon case is still an open problem. To the best of our knowledge, we propose the first complete result of the necessary and sufficient condition for the existence of corresponding LQ cost functions. Under feasible cases, the analytic expression of the whole solution space is derived and the equivalence of weighting matrices is discussed. For infeasible problems, an infinite dimensional convex problem is formulated to obtain a best-fit approximate solution with minimal control residual, where the optimality condition is solved under a static quadratic programming framework to facilitate the computation.In paper B, the optimal formation control problem of a multi-agent system is studied. The foraging behavior of N agents is modeled as a finite-horizon non-cooperative differential game under local information, and its Nash equilibrium is studied. The collaborative swarming behaviour derived from non-cooperative individual actions also sheds new light on understanding such phenomenon in the nature. The proposed framework has a tutorial meaning since a systematic approach for formation control is proposed, where the desired formation can be obtained by only intrinsically adjusting individual costs and network topology. In contrast to most of the existing methodologies based on regulating formation errors to the pre-defined pattern, the proposed method does not need to involve any information of the desired pattern beforehand. We refer to this type of formation control as intrinsic formation control. Patterns of regular polygons, antipodal formations and Platonic solids can be achieved as Nash equilibria of the game while inter-agent collisions are naturally avoided.Paper C considers the credit scoring problem by incorporating dynamic network information, where the advantages of such incorporation are investigated in two scenarios. Firstly, when the scoring publishment is merely individual--dependent, an optimal Bayesian filter is designed for risk prediction, where network observations are utilized to provide a reference for the bank on future financial decisions. Furthermore, a recursive Bayes estimator is proposed to improve the accuracy of score publishment by incorporating the dynamic network topology as well. It is shown that under the proposed evolution framework, the designed estimator has a higher precision than all the efficient estimators, and the mean square errors are strictly smaller than the Cramér-Rao lower bound for clients within a certain range of scores.
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