3,579 research outputs found
Sharp benefit-to-cost rules for the evolution of cooperation on regular graphs
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
Trend-based analysis of a population model of the AKAP scaffold protein
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
Systems approaches to modelling pathways and networks.
Peer reviewedPreprin
On the Properties of Language Classes Defined by Bounded Reaction Automata
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
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
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
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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