3,579 research outputs found

    Sharp benefit-to-cost rules for the evolution of cooperation on regular graphs

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    We study two of the simple rules on finite graphs under the death-birth updating and the imitation updating discovered by Ohtsuki, Hauert, Lieberman and Nowak [Nature 441 (2006) 502-505]. Each rule specifies a payoff-ratio cutoff point for the magnitude of fixation probabilities of the underlying evolutionary game between cooperators and defectors. We view the Markov chains associated with the two updating mechanisms as voter model perturbations. Then we present a first-order approximation for fixation probabilities of general voter model perturbations on finite graphs subject to small perturbation in terms of the voter model fixation probabilities. In the context of regular graphs, we obtain algebraically explicit first-order approximations for the fixation probabilities of cooperators distributed as certain uniform distributions. These approximations lead to a rigorous proof that both of the rules of Ohtsuki et al. are valid and are sharp.Comment: Published in at http://dx.doi.org/10.1214/12-AAP849 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

    Complete Issue 20, 1999

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    Trend-based analysis of a population model of the AKAP scaffold protein

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    We formalise a continuous-time Markov chain with multi-dimensional discrete state space model of the AKAP scaffold protein as a crosstalk mediator between two biochemical signalling pathways. The analysis by temporal properties of the AKAP model requires reasoning about whether the counts of individuals of the same type (species) are increasing or decreasing. For this purpose we propose the concept of stochastic trends based on formulating the probabilities of transitions that increase (resp. decrease) the counts of individuals of the same type, and express these probabilities as formulae such that the state space of the model is not altered. We define a number of stochastic trend formulae (e.g. weakly increasing, strictly increasing, weakly decreasing, etc.) and use them to extend the set of state formulae of Continuous Stochastic Logic. We show how stochastic trends can be implemented in a guarded-command style specification language for transition systems. We illustrate the application of stochastic trends with numerous small examples and then we analyse the AKAP model in order to characterise and show causality and pulsating behaviours in this biochemical system

    On the Properties of Language Classes Defined by Bounded Reaction Automata

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    Reaction automata are a formal model that has been introduced to investigate the computing powers of interactive behaviors of biochemical reactions([14]). Reaction automata are language acceptors with multiset rewriting mechanism whose basic frameworks are based on reaction systems introduced in [4]. In this paper we continue the investigation of reaction automata with a focus on the formal language theoretic properties of subclasses of reaction automata, called linearbounded reaction automata (LRAs) and exponentially-bounded reaction automata (ERAs). Besides LRAs, we newly introduce an extended model (denoted by lambda-LRAs) by allowing lambda-moves in the accepting process of reaction, and investigate the closure properties of language classes accepted by both LRAs and lambda-LRAs. Further, we establish new relationships of language classes accepted by LRAs and by ERAs with the Chomsky hierarchy. The main results include the following : (i) the class of languages accepted by lambda-LRAs forms an AFL with additional closure properties, (ii) any recursively enumerable language can be expressed as a homomorphic image of a language accepted by an LRA, (iii) the class of languages accepted by ERAs coincides with the class of context-sensitive languages.Comment: 23 pages with 3 figure

    Bipolar Quantum Logic Gates and Quantum Cellular Combinatorics – A Logical Extension to Quantum Entanglement

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    Based on bipolar dynamic logic (BDL) and bipolar quantum linear algebra (BQLA) this work introduces bipolar quantum logic gates and quantum cellular combinatorics with a logical interpretation to quantum entanglement. It is shown that: 1) BDL leads to logically definable causality and generic particle-antiparticle bipolar quantum entanglement; 2) BQLA makes composite atom-atom bipolar quantum entanglement reachable. Certain logical equivalence is identified between the new interpretation and established ones. A logical reversibility theorem is presented for ubiquitous quantum computing. Physical reversibility is briefly discussed. It is shown that a bipolar matrix can be either a modular generalization of a quantum logic gate matrix or a cellular connectivity matrix. Based on this observation, a scalable graph theory of quantum cellular combinatorics is proposed. It is contended that this work constitutes an equilibrium-based logical extension to Bohr’s particle-wave complementarity principle, Bohm’s wave function and Bell’s theorem. In the meantime, it is suggested that the result may also serve as a resolution, rather than a falsification, to the EPR paradox and, therefore, a equilibrium-based logical unification of local realism and quantum non-locality

    Complexity of Model Testing for Dynamical Systems with Toric Steady States

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    In this paper we investigate the complexity of model selection and model testing for dynamical systems with toric steady states. Such systems frequently arise in the study of chemical reaction networks. We do this by formulating these tasks as a constrained optimization problem in Euclidean space. This optimization problem is known as a Euclidean distance problem; the complexity of solving this problem is measured by an invariant called the Euclidean distance (ED) degree. We determine closed-form expressions for the ED degree of the steady states of several families of chemical reaction networks with toric steady states and arbitrarily many reactions. To illustrate the utility of this work we show how the ED degree can be used as a tool for estimating the computational cost of solving the model testing and model selection problems

    Stochastic models and numerical algorithms for a class of regulatory gene networks

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    Regulatory gene networks contain generic modules like those involving feedback loops, which are essential for the regulation of many biological functions. We consider a class of self-regulated genes which are the building blocks of many regulatory gene networks, and study the steady state distributions of the associated Gillespie algorithm by providing efficient numerical algorithms. We also study a regulatory gene network of interest in synthetic biology and in gene therapy, using mean-field models with time delays. Convergence of the related time-nonhomogeneous Markov chain is established for a class of linear catalytic networks with feedback loop
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