Simulation and inference algorithms for stochastic biochemical reaction networks: from basic concepts to state-of-the-art

Stochasticity is a key characteristic of intracellular processes such as gene regulation and chemical signalling. Therefore, characterising stochastic effects in biochemical systems is essential to understand the complex dynamics of living things. Mathematical idealisations of biochemically reacting systems must be able to capture stochastic phenomena. While robust theory exists to describe such stochastic models, the computational challenges in exploring these models can be a significant burden in practice since realistic models are analytically intractable. Determining the expected behaviour and variability of a stochastic biochemical reaction network requires many probabilistic simulations of its evolution. Using a biochemical reaction network model to assist in the interpretation of time course data from a biological experiment is an even greater challenge due to the intractability of the likelihood function for determining observation probabilities. These computational challenges have been subjects of active research for over four decades. In this review, we present an accessible discussion of the major historical developments and state-of-the-art computational techniques relevant to simulation and inference problems for stochastic biochemical reaction network models. Detailed algorithms for particularly important methods are described and complemented with MATLAB implementations. As a result, this review provides a practical and accessible introduction to computational methods for stochastic models within the life sciences community

Topological Groupoids

A groupoid is a set G in which a single valued product ab is defined for every pair of elements a, b ε G. If G is a groupoid and at the same time a Hausdorff topological space, and, moreover, the multiplication in the groupoid G is continuous in the topological space G, then G is called a topological groupoid. Our aim in this dissertation is two-fold: (1) to study topological groupoids for their own sake; (2) to investigate the relation of certain topological properties to associativity. We note, in relation to the first motif, that many authors have dealt with non-associative algebraic structures, i.e. Albert [1]*, Frink [4], Garrison [5], Etherington [2], Hausmann and Ore [7], and Stein [22]

Factors affecting the operation of laser-triggered gas switch (LTGS) with multi-electrode spark gap

Multi-electrode spark switches can be used for switching applications at elevated voltages or for command triggering. Symmetrical field graded electrodes allow the electrical stress across individual gaps to be controlled, thus maximising the hold off voltage and reducing switch pre-fire. The paper considers some aspects of multielectrode switch design and their influence on switching behavior. Non-symmetrical, uni-directional electrode topologies can be employed with advantages over traditional symmetrical design. The choice of working gas and gas pressure can influence switching performance in terms of delay-time and jitter. Transient analysis of switch characteristics has been undertaken in order to understand multi-electrode switching

Isolated Effects of Footwear Structure and Cushioning on Running Mechanics in Habitual Mid/Forefoot Runners

The true differences between barefoot and shod running are difficult to directly compare 2 because of the concomitant change to a mid/forefoot footfall pattern that typically occurs 3 during barefoot running. The purpose of this study was to compare isolated effects of footwear 4 structure and cushioning on running mechanics in habitual mid/forefoot runners running shod 5 (SHOD), barefoot (BF), and barefoot on a foam surface (BF+FOAM). Ten habitually shod 6 mid/forefoot runners were recruited (male=8, female=2). Repeated measures ANOVA 7 (α=0.05) revealed differences between conditions for only vertical peak active force, contact 8 time, negative and total ankle joint work, and peak dorsiflexion angle. Post hoc tests revealed 9 that BF+FOAM resulted in smaller vertical active peak magnitude and instantaneous vertical 10 loading rate than SHOD. SHOD resulted in lower total ankle joint work than BF and 11 BF+FOAM. BF+FOAM resulted in lower negative ankle joint work than either BF or SHOD. 12 Contact time was shorter with BF than BF+FOAM or SHOD. Peak dorsiflexion angle was 13 smaller in SHOD than BF. No other differences in sagittal joint kinematics, kinetics, or ground 14 reaction forces were observed. These overall similarities in running mechanics between SHOD 15 and BF+FOAM question the effects of footwear structure on habituated mid/forefoot running 16 described previously

P6_5 The Flash and Quantum Tunneling

The Flash, a popular DC Comics superhero, is regarded as the fastest human alive. He has the power to run faster than light and phase through solid objects while doing so. Since his power to run faster than light is disputed by Einstein's Theory of Special Relativity, for this article we will assume that he is able to achieve a maximum velocity of 0:99 c . Given the high kinetic energy, in this paper we look at the possibility of him quantum tunneling through a solid object such as a wall

Rapid Bayesian inference for expensive stochastic models

Almost all fields of science rely upon statistical inference to estimate unknown parameters in theoretical and computational models. While the performance of modern computer hardware continues to grow, the computational requirements for the simulation of models are growing even faster. This is largely due to the increase in model complexity, often including stochastic dynamics, that is necessary to describe and characterize phenomena observed using modern, high resolution, experimental techniques. Such models are rarely analytically tractable, meaning that extremely large numbers of stochastic simulations are required for parameter inference. In such cases, parameter inference can be practically impossible. In this work, we present new computational Bayesian techniques that accelerate inference for expensive stochastic models by using computationally inexpensive approximations to inform feasible regions in parameter space, and through learning transforms that adjust the biased approximate inferences to closer represent the correct inferences under the expensive stochastic model. Using topical examples from ecology and cell biology, we demonstrate a speed improvement of an order of magnitude without any loss in accuracy. This represents a substantial improvement over current state-of-the-art methods for Bayesian computations when appropriate model approximations are available