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Modelling Protein Target-Search in Human Chromosomes
Umeå University, Faculty of Science and Technology, Department of Physics.
(English)Manuscript (preprint) (Other academic)
National Category
Other Physics Topics
Identifiers
URN: urn:nbn:se:umu:diva-164023OAI: oai:DiVA.org:umu-164023DiVA, id: diva2:1360539
Available from: 2019-10-14 Created: 2019-10-14 Last updated: 2019-10-16
In thesis
1. My first-passage: target search in physics and biology
Open this publication in new window or tab >>My first-passage: target search in physics and biology
2019 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Random walks and diffusing particles have been a corner stone in modelling the random motion of a varying quantity with applications spanning over many research fields. And in most of the applications one can ask a question related to when something happened for the first time. That is, a first-passage problem. Typical examples include chemical reactions which can not happen until the constituents meet for the first time, a neuron firing when a fluctuating voltage exceeds a threshold value and the triggering of buy/sell orders of a stock option. The applications are many, which is why first-passage problems have attracted researchers for a long time, and will keep doing so. In this thesis we analyse first-passage problems analytically.

A stochastic system can always be simulated, so why bother with analytical solutions? Well, there are many system where the first passage is improbable in a reasonable time. Simulating those systems with high precision is hard to do efficiently. But evaluating an analytical expression happens in a heart beat. The only problem is that the first-passage problem is tricky to solve as soon as you take a small step away from the trivial ones. Consequently, many first-passage problems are still unsolved.

In this thesis, we derive approximate solutions to first-passage related problems for a random walker and a diffusing particle bounded in a potential, which the current methods are unable to handle. We also study a continuous-time random walker on a network and solve the corresponding first-passage problem exactly in way that has not been done before. These results give access to a new set of analytical tools that can be used to solve a broad class of first-passage problems.

Place, publisher, year, edition, pages
Umeå: Umeå universitet, 2019. p. 55
Keywords
first-passage, mean first-passage time, mean first-arrival time, random walk, diffusion, zero-crossing, persistence, survival probability, network, resetting
National Category
Other Physics Topics
Research subject
Theoretical Physics
Identifiers
urn:nbn:se:umu:diva-164025 (URN)978-91-7855-109-5 (ISBN)
Public defence
2019-11-08, N410, Naturvetarhuset, Umeå, 09:00 (English)
Opponent
Supervisors
Available from: 2019-10-17 Created: 2019-10-14 Last updated: 2019-10-16Bibliographically approved

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Nyberg, Markus

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