Perturbation and approximation methods for linear operators with applications to train control, water resource management and evolution of physical systems. Linear equations are used to solve practical problems. In realistic problems the equations and their solutions depend on parameters obtained by measurement of physical quantities and on data derived from observations and experiments. Changes to the values of the key parameters will lead to changes in the solutions. This project will devel ....Perturbation and approximation methods for linear operators with applications to train control, water resource management and evolution of physical systems. Linear equations are used to solve practical problems. In realistic problems the equations and their solutions depend on parameters obtained by measurement of physical quantities and on data derived from observations and experiments. Changes to the values of the key parameters will lead to changes in the solutions. This project will develop methods to better understand the relationships between the key parameters and the solutions and will apply the new insights to practical problems such as the minimization of fuel consumption in trains, optimal resource management in water supply systems and the evolution of physical systems.Read moreRead less
New Analytical Perspectives on the Algorithmic Complexity of the Hamiltonian Cycle Problem. Hamiltonian Cycle Problem (HCP), known - in the complexity theory of
algorithms -to be NP-hard is proposed for study, from three innovative,
separate (yet related) analytical perspectives: singularly perturbed
(controlled) Markov chains, that links the HCP with systems and control
theories; parametric nonconvex optimization, that links HCP with fast
interior point methods of modern optimization an ....New Analytical Perspectives on the Algorithmic Complexity of the Hamiltonian Cycle Problem. Hamiltonian Cycle Problem (HCP), known - in the complexity theory of
algorithms -to be NP-hard is proposed for study, from three innovative,
separate (yet related) analytical perspectives: singularly perturbed
(controlled) Markov chains, that links the HCP with systems and control
theories; parametric nonconvex optimization, that links HCP with fast
interior point methods of modern optimization and the spectral approach
based on a novel adaptation of Ihara-Selberg trace formula for regular
graphs. Our mathematical approach to this archetypal complex problem of graph
theory and discrete optimization promises to enhance the fundamental
understanding - and ultimate "managibility" - of the underlying
difficulty of HCP.
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