Extended Differential Aggregations in Process Algebra for Performance and Biology

We study aggregations for ordinary differential equations induced by fluid semantics for Markovian process algebra which can capture the dynamics of performance models and chemical reaction networks. Whilst previous work has required perfect symmetry for exact aggregation, we present approximate fluid lumpability, which makes nearby processes perfectly symmetric after a perturbation of their parameters. We prove that small perturbations yield nearby differential trajectories. Numerically, we show that many heterogeneous processes can be aggregated with negligible errors.Comment: In Proceedings QAPL 2014, arXiv:1406.156

Tautomeric mutation: A quantum spin modelling

A quantum spin model representing tautomeric mutation is proposed for any DNA molecule. Based on this model, the quantum mechanical calculations for mutational rate and complementarity restoring repair rate in the replication processes are carried out. A possible application to a real biological system is discussed.Comment: 7 pages (no figures

A split-and-perturb decomposition of number-conserving cellular automata

This paper concerns $d$-dimensional cellular automata with the von Neumann neighborhood that conserve the sum of the states of all their cells. These automata, called number-conserving or density-conserving cellular automata, are of particular interest to mathematicians, computer scientists and physicists, as they can serve as models of physical phenomena obeying some conservation law. We propose a new approach to study such cellular automata that works in any dimension $d$ and for any set of states $Q$. Essentially, the local rule of a cellular automaton is decomposed into two parts: a split function and a perturbation. This decomposition is unique and, moreover, the set of all possible split functions has a very simple structure, while the set of all perturbations forms a linear space and is therefore very easy to describe in terms of its basis. We show how this approach allows to find all number-conserving cellular automata in many cases of $d$ and $Q$. In particular, we find all three-dimensional number-conserving CAs with three states, which until now was beyond the capabilities of computers

Spatio-temporal modelling of wave formation in an excitable chemical medium based on a revised FitzHugh-Nagumo model

The wavefront profile and the propagation velocity of waves in an experimentally observed Belousov-Zhabotinskii reaction are analyzed and a revised FitzHumgh-Nagumo(FHN) model of these systems is identified. The ratio between the excitation period and the recovery period, for a solitary wave are studied, and included within the model. Averaged travelling velocities at different spatial positions are shown to be consistent under the same experimental conditions. The relationship between the propagation velocity and the curvature of the wavefront are also studied to deduce the diffusion coefficient in the model, which is a function of the curvature of the wavefront and not a constant. The application of the identified model is demonstrated on real experimental data and validated using multi-step ahead predictions

Modelling of Diesel fuel properties through its surrogates using Perturbed-Chain, Statistical Associating Fluid Theory

The Perturbed-Chain, Statistical Associating Fluid Theory equation of state is utilised to model the effect of pressure and temperature on the density, volatility and viscosity of four Diesel surrogates; these calculated properties are then compared to the properties of several Diesel fuels. Perturbed-Chain, Statistical Associating Fluid Theory calculations are performed using different sources for the pure component parameters. One source utilises literature values obtained from fitting vapour pressure and saturated liquid density data or from correlations based on these parameters. The second source utilises a group contribution method based on the chemical structure of each compound. Both modelling methods deliver similar estimations for surrogate density and volatility that are in close agreement with experimental results obtained at ambient pressure. Surrogate viscosity is calculated using the entropy scaling model with a new mixing rule for calculating mixture model parameters. The closest match of the surrogates to Diesel fuel properties provides mean deviations of 1.7% in density, 2.9% in volatility and 8.3% in viscosity. The Perturbed-Chain, Statistical Associating Fluid Theory results are compared to calculations using the Peng–Robinson equation of state; the greater performance of the Perturbed-Chain, Statistical Associating Fluid Theory approach for calculating fluid properties is demonstrated. Finally, an eight-component surrogate, with properties at high pressure and temperature predicted with the group contribution Perturbed-Chain, Statistical Associating Fluid Theory method, yields the best match for Diesel properties with a combined mean absolute deviation of 7.1% from experimental data found in the literature for conditions up to 373°K and 500 MPa. These results demonstrate the predictive capability of a state-of-the-art equation of state for Diesel fuels at extreme engine operating conditions

Can Computer Algebra be Liberated from its Algebraic Yoke ?

So far, the scope of computer algebra has been needlessly restricted to exact algebraic methods. Its possible extension to approximate analytical methods is discussed. The entangled roles of functional analysis and symbolic programming, especially the functional and transformational paradigms, are put forward. In the future, algebraic algorithms could constitute the core of extended symbolic manipulation systems including primitives for symbolic approximations.Comment: 8 pages, 2-column presentation, 2 figure

Excitable Delaunay triangulations

In an excitable Delaunay triangulation every node takes three states (resting, excited and refractory) and updates its state in discrete time depending on a ratio of excited neighbours. All nodes update their states in parallel. By varying excitability of nodes we produce a range of phenomena, including reflection of excitation wave from edge of triangulation, backfire of excitation, branching clusters of excitation and localized excitation domains. Our findings contribute to studies of propagating perturbations and waves in non-crystalline substrates

Towards generalized measures grasping CA dynamics

In this paper we conceive Lyapunov exponents, measuring the rate of separation between two initially close configurations, and Jacobians, expressing the sensitivity of a CA's transition function to its inputs, for cellular automata (CA) based upon irregular tessellations of the n-dimensional Euclidean space. Further, we establish a relationship between both that enables us to derive a mean-field approximation of the upper bound of an irregular CA's maximum Lyapunov exponent. The soundness and usability of these measures is illustrated for a family of 2-state irregular totalistic CA