Approximate Bisimulations for Sodium Channel Dynamics

Abstract. This paper shows that, in the context of the Iyer et al. 67-variable cardiac myocycte model (IMW), it is possible to replace the detailed 13-state continuous-time MDP model of the sodium-channel dy-namics, with a much simpler Hodgkin-Huxley (HH)-like two-state sodium-channel model, while only incurring a bounded approximation error. The technical basis for this result is the construction of an approximate bisim-ulation between the HH and IMW channel models, both of which are input-controlled (voltage in this case) continuous-time Markov chains. The construction of the appropriate approximate bisimulation, as well as the overall result regarding the behavior of this modified IMW model, in-volves: (1) The identification of the voltage-dependent parameters of the m and h gates in the HH-type channel, based on the observations of the IMW channel. (2) Proving that the distance between observations of the two channels never exceeds a given error. (3) Exploring the sensitivity of the overall IMW model to the HH-type sodium-channel approximation. Our extensive simulation results experimentally validate our findings, for varying IMW-type input stimuli

Computing Probabilistic Bisimilarity Distances

Behavioural equivalences like probabilistic bisimilarity rely on the transition probabilities and, as a result, are sensitive to minuscule changes of those probabilities. Such behavioural equivalences are not robust, as first observed by Giacalone, Jou and Smolka. Probabilistic bisimilarity distances, a robust quantitative generalization of probabilistic bisimilarity, capture the similarity of the behaviour of states of a probabilistic model. The smaller the distance, the more alike the states behave. In particular, states are probabilistic bisimilar if and only if the distance between them is zero. In this dissertation, we focus on algorithms to compute probabilistic bisimilarity distances for two probabilistic models: labelled Markov chains and probabilistic automata. In the late nineties, Desharnais, Gupta, Jagadeesan and Panangaden defined probabilistic bisimilarity distances on the states of a labelled Markov chain. This provided a quantitative generalization of probabilistic bisimilarity, which was introduced by Larsen and Skou a decade earlier. Several algorithms to approximate and compute these probabilistic bisimilarity distances have been put forward. In this dissertation, we correct and generalize some of these policy iteration algorithms. Moreover, we develop several new algorithms which have better performance in practice and can handle much larger systems. Similarly, Deng, Chothia, Palamidessi and Pang presented probabilistic bisimilarity distances on the states of a probabilistic automaton. This provided a robust quantitative generalization of probabilistic bisimilarity introduced by Segala and Lynch. Although the complexity of computing probabilistic bisimilarity distances for probabilistic automata has already been studied and shown to be in NP coNP and PPAD, we are not aware of any practical algorithms to compute those distances. In this dissertation, we provide several key results that may prove to be useful for the development of algorithms to compute probabilistic bisimilarity distances for probabilistic automata. In particular, we present a polynomial time algorithm that decides distance one. Furthermore, we give an alternative characterization of the probabilistic bisimilarity distances as a basis for a policy iteration algorithm

Computer Aided Verification

This open access two-volume set LNCS 10980 and 10981 constitutes the refereed proceedings of the 30th International Conference on Computer Aided Verification, CAV 2018, held in Oxford, UK, in July 2018. The 52 full and 13 tool papers presented together with 3 invited papers and 2 tutorials were carefully reviewed and selected from 215 submissions. The papers cover a wide range of topics and techniques, from algorithmic and logical foundations of verification to practical applications in distributed, networked, cyber-physical, and autonomous systems. They are organized in topical sections on model checking, program analysis using polyhedra, synthesis, learning, runtime verification, hybrid and timed systems, tools, probabilistic systems, static analysis, theory and security, SAT, SMT and decisions procedures, concurrency, and CPS, hardware, industrial applications

Computer Aided Verification

This open access two-volume set LNCS 10980 and 10981 constitutes the refereed proceedings of the 30th International Conference on Computer Aided Verification, CAV 2018, held in Oxford, UK, in July 2018. The 52 full and 13 tool papers presented together with 3 invited papers and 2 tutorials were carefully reviewed and selected from 215 submissions. The papers cover a wide range of topics and techniques, from algorithmic and logical foundations of verification to practical applications in distributed, networked, cyber-physical, and autonomous systems. They are organized in topical sections on model checking, program analysis using polyhedra, synthesis, learning, runtime verification, hybrid and timed systems, tools, probabilistic systems, static analysis, theory and security, SAT, SMT and decisions procedures, concurrency, and CPS, hardware, industrial applications

Renewable Energy

Renewable Energy is energy generated from natural resources - such as sunlight, wind, rain, tides and geothermal heat - which are naturally replenished. In 2008, about 18% of global final energy consumption came from renewables, with 13% coming from traditional biomass, such as wood burning. Hydroelectricity was the next largest renewable source, providing 3% (15% of global electricity generation), followed by solar hot water/heating, which contributed with 1.3%. Modern technologies, such as geothermal energy, wind power, solar power, and ocean energy together provided some 0.8% of final energy consumption. The book provides a forum for dissemination and exchange of up - to - date scientific information on theoretical, generic and applied areas of knowledge. The topics deal with new devices and circuits for energy systems, photovoltaic and solar thermal, wind energy systems, tidal and wave energy, fuel cell systems, bio energy and geo-energy, sustainable energy resources and systems, energy storage systems, energy market management and economics, off-grid isolated energy systems, energy in transportation systems, energy resources for portable electronics, intelligent energy power transmission, distribution and inter - connectors, energy efficient utilization, environmental issues, energy harvesting, nanotechnology in energy, policy issues on renewable energy, building design, power electronics in energy conversion, new materials for energy resources, and RF and magnetic field energy devices