The version in the Kent Academic Repository may differ from the final published version. Users are advised to check http://kar.kent.ac.uk for the status of the paper. Users should always cite the published version of record. EnquiriesFor any further enquiries regarding the licence status of this document, please contact: researchsupport@kent.ac.uk If you believe this document infringes copyright then please contact the KAR admin team with the take-down information provided at http://kar.kent.ac.uk/contact.html We present three models of how transcription factors (TFs) bind to their specific binding sites on the DNA: a model based on statistical physics, a Markov-chain model and a computational simulation. Citation for published versionComparison of these models suggests that the effect of non-specific binding can be significant. We also investigate possible mechanisms for cooperativity. The simulation model suggests that direct interactions between TFs are unlikely to be the main source of cooperativity between specific binding sites, because such interactions tend to lead to the formation of clusters on the DNA with undesirable side-effects.
Received (?? ?? 2011) Revised (Day Month Year)Purpose-In recent years Monte-Carlo sampling methods, such as Monte Carlo tree search, have achieved tremendous success in model free reinforcement learning. A combination of the so called upper confidence bounds policy to preserve the "exploration vs. exploitation" balance to select actions for sample evaluations together with massive computing power to store and to update dynamically a rather large pre-evaluated game tree lead to the development of software that has beaten the top human player in the game of Go on a 9 by 9 board. Much effort in the current research is devoted to widening the range of applicability of the Monte-Carlo sampling methodology to partially observable Markov decision processes with non-immediate payoffs. The main challenge introduced by randomness and incomplete information is to deal with the action evaluation at the chance nodes due to drastic differences in the possible payoffs the same action could lead to. The aim of this article is to establish a version of a theorem that originated from population genetics and has been later adopted in evolutionary computation theory that will lead to novel Monte-Carlo sampling algorithms that provably increase the AI potential. Due to space limitations the actual algorithms themselves will be presented in the sequel papers, however, the current paper provides a solid mathematical foundation for the development of such algorithms and explains why they are so promising. Design/Methodology/Approach-In the current paper we set up a mathematical framework, state and prove a version of a Geiringer-like theorem that is very well-suited for the development of Mote-Carlo sampling algorithms to cope with randomness and incomplete information to make decisions. From the framework it will be clear that such algorithm increase what seems like a limited sample of rollouts exponentially in size by exploiting the symmetry within the state space at little or no additional * EPSRC EP/D003/05/1 "Amorphous Computing" and EPSRC EP/I009809/1 "Evolutionary Approximation Algorithms for Optimization: Algorithm Design and Complexity Analysis" Grants. computational cost. Appropriate notions of recombination (or crossover) and schemata are introduced to stay inline with the traditional evolutionary computation terminology. The main theorem is proved using the methodology developed in the PhD thesis of the first author, however the general case of nonhomologous recombination presents additional challenges that have been overcome thanks to a lovely application of the classical and elementary tool known as the "Markov inequality" together with the lumping quotients of Markov chains techniques developed and successfully applied by the authors in the previous research for different purposes. This methodology will be mildly extended to establish the main result of the current article. In addition to establishing the Geiringer-like theorem for Monte Carlo sampling, which is the central objective of this paper, we also strengthen the...
Purpose-A variety of phenomena such as world wide web, social or business networks, interactions are modelled by various kinds of networks (such as the scale free or preferential attachment networks). However, due to the model-specific requirements one may want to rewire the network to optimize the communication among the various nodes while not overloading the number of channels (i.e. preserving the number of edges). The purpose of this paper is to present a formal framework for this problem and to examine a family of local search strategies to cope with it. Design/methodology/approach-This is mostly theoretical work. The authors use rigorous mathematical framework to setup the model and then we prove some interesting theorems about it which pertain to various local search algorithms that work by rerouting the network. Findings-This paper proves that in cases when every pair of nodes is sampled with non-zero probability then the algorithm is ergodic in the sense that it samples every possible network on the specified set of nodes and having a specified number of edges with nonzero probability. Incidentally, the ergodicity result led to the construction of a class of algorithms for sampling graphs with a specified number of edges over a specified set of nodes uniformly at random and opened some other challenging and important questions for future considerations. Originality/value-The measure-theoretic framework presented in the current paper is original and rather general. It allows one to obtain new points of view on the problem.
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