Designing heteroclinic and excitable networks in phase space using two populations of coupled cells

We give a constructive method for realizing an arbitrary directed graph (with no one-cycles) as a heteroclinic or an excitable dynamic network in the phase space of a system of coupled cells of two types. In each case, the system is expressed as a system of first order differential equations. One of the cell types (the $p$-cells) interacts by mutual inhibition and classifies which vertex (state) we are currently close to, while the other cell type (the $y$-cells) excites the $p$-cells selectively and becomes active only when there is a transition between vertices. We exhibit open sets of parameter values such that these dynamical networks exist and demonstrate via numerical simulation that they can be attractors for suitably chosen parameters

Evaluation of stochastic effects on biomolecular networks using the generalised Nyquist stability criterion

Abstract—Stochastic differential equations are now commonly used to model biomolecular networks in systems biology, and much recent research has been devoted to the development of methods to analyse their stability properties. Stability analysis of such systems may be performed using the Laplace transform, which requires the calculation of the exponential matrix involving time symbolically. However, the calculation of the symbolic exponential matrix is not feasible for problems of even moderate size, as the required computation time increases exponentially with the matrix order. To address this issue, we present a novel method for approximating the Laplace transform which does not require the exponential matrix to be calculated explicitly. The calculation time associated with the proposed method does not increase exponentially with the size of the system, and the approximation error is shown to be of the same order as existing methods. Using this approximation method, we show how a straightforward application of the generalized Nyquist stability criterion provides necessary and sufficient conditions for the stability of stochastic biomolecular networks. The usefulness and computational efficiency of the proposed method is illustrated through its application to the problem of analysing a model for limit-cycle oscillations in cAMP during aggregation of Dictyostelium cells

Robustness analysis of magnetic torquer controlled spacecraft attitude dynamics

This paper describes a systematic approach to the robustness analysis of linear periodically time-varying (LPTV) systems. The method uses the technique known as Lifting to transform the original time-varying uncertain system into linear fractional transformation (LFT) form. The stability and performance robustness of the system to structured parametric uncertainty can then be analysed non-conservatively using the structured singular value μ. The method is applied to analyse the stability robustness of an attitude control law for a spacecraft controlled by magnetic torquer bars, whose linearised dynamics can naturally be written in linear periodically time-varying form. The proposed method allows maximum allowable levels of uncertainty, as well as worst-case uncertainty combinations to be computed. The destabilising effect of these uncertain parameter combinations is verified in time-domain simulations

Sochi 2014 Winter Olympics and the Controversy of the Russian Propaganda Laws: is the IOC Buckling Under the Pressure of its own Incoherence in Thought?

The Sochi Winter Olympics were a triumph in the eyes of Russia and the International Olympic Committee (IOC). Yet, a controversy around the introduction of anti-propaganda laws in Russia that had been criticised for being discriminatory marred the efforts of the IOC to fulfil its self proclaimed aspiration of ‘encouraging the harmonious development of man’. This article discusses the controversy utilising a legally pluralist approach to sports governance, and providing a critical reading of the practices of neoliberal globalisation that marked the issue of sexuality at the Sochi games. The paper argues that the legal influence of the IOC on domestic and international legal norms is contradictory and inconsistent. This, when considered alongside the aspirations of the IOC is significantly problematic and demonstrates the importance of investigating the underlying power structures of this influential international governing body

Stochastic noise and synchronisation during Dictyostelium aggregation make cAMP oscillations robust

The molecular network, which underlies the oscillations in the concentration of adenosine 3′, 5′-cyclic monophosphate (cAMP) during the aggregation phase of starvation-induced development in Dictyostelium discoideum, achieves remarkable levels of robust performance in the face of environmental variations and cellular heterogeneity. However, the reasons for this robustness remain poorly understood. Tools and concepts from the field of control engineering provide powerful methods for uncovering the mechanisms underlying the robustness of these types of biological systems. Using such methods, two important factors contributing to the robustness of cAMP oscillations in Dictyostelium are revealed. First, stochastic fluctuations in the molecular interactions of the intracellular network, arising from random or directional noise and biological sources, play an important role in preserving stable oscillations in the face of variations in the kinetics of the network. Second, synchronisation of the aggregating cells through the diffusion of extracellular cAMP appears to be a key factor in ensuring robustness to cell-to-cell variations of the oscillatory waves of cAMP observed in Dictyostelium cell cultures. The conclusions have important general implications for the robustness of oscillating biomolecular networks (whether seen at organism, cell, or intracellular levels and including circadian clocks or Ca2+ oscillations, etc.), and suggest that such analysis can be conducted more reliably by using models including stochastic simulations, even in the case where molecular concentrations are very high

The use of simulation in chemical process control learning and the development of PISim

PISim is a new piece of software for process control teaching and learning. The software allows control structures to be designed on a piping and instrumentation diagram and, as the structure is created, the software automatically spawns device mimics representing the real physical HMIs that operators would see. These can be placed on a control panel and a simulation of the process can be operated using the student’s control scheme. The use of PISim in an introductory control class at Strathclyde University is described and student feedback is presented

Resonance bifurcations of robust heteroclinic networks

Robust heteroclinic cycles are known to change stability in resonance bifurcations, which occur when an algebraic condition on the eigenvalues of the system is satisfied and which typically result in the creation or destruction of a long-period periodic orbit. Resonance bifurcations for heteroclinic networks are more complicated because different subcycles in the network can undergo resonance at different parameter values, but have, until now, not been systematically studied. In this article we present the first investigation of resonance bifurcations in heteroclinic networks. Specifically, we study two heteroclinic networks in $\R^4$ and consider the dynamics that occurs as various subcycles in each network change stability. The two cases are distinguished by whether or not one of the equilibria in the network has real or complex contracting eigenvalues. We construct two-dimensional Poincare return maps and use these to investigate the dynamics of trajectories near the network. At least one equilibrium solution in each network has a two-dimensional unstable manifold, and we use the technique developed in [18] to keep track of all trajectories within these manifolds. In the case with real eigenvalues, we show that the asymptotically stable network loses stability first when one of two distinguished cycles in the network goes through resonance and two or six periodic orbits appear. In the complex case, we show that an infinite number of stable and unstable periodic orbits are created at resonance, and these may coexist with a chaotic attractor. There is a further resonance, for which the eigenvalue combination is a property of the entire network, after which the periodic orbits which originated from the individual resonances may interact. We illustrate some of our results with a numerical example.Comment: 46 pages, 20 figures. Supplementary material (two animated gifs) can be found on http://www.maths.leeds.ac.uk/~alastair/papers/KPR_res_net_abs.htm