If a semiflexible polymer confined to a narrow channel bends around by 180°, the polymer is said to exhibit a hairpin. The equilibrium extension statistics of the confined polymer are well understood when hairpins are vanishingly rare or when they are plentiful. Here, we analyze the extension statistics in the intermediate situation via experiments with DNA coated by the protein RecA, which enhances the stiffness of the DNA molecule by approximately one order of magnitude. We find that the extension distribution is highly non-Gaussian, in good agreement with Monte-Carlo simulations of confined discrete wormlike chains. We develop a simple model that qualitatively explains the form of the extension distribution. The model shows that the tail of the distribution at short extensions is determined by conformations with one hairpin.

Spiking Neural Network (SNN) simulations require internal variables -such as the membrane voltages of individual neurons and their synaptic inputs -to be updated on a sub-millisecond resolution. As a result, a single second of simulation time requires many thousands of update calculations per neuron. Furthermore, increases in the scale of SNN models have, accordingly, led to manyfold increases in the runtime of SNN simulations. Existing solutions to this problem of scale include high performance CPU based simulators capable of multithreaded execution ("CPU parallelism"). More recent GPU based simulators have emerged, which aim to utilise GPU parallelism for SNN execution. We have identified several key speedups, which give GPU based simulators up to an order of magnitude performance increase over CPU based simulators on several benchmarks. We present the Spike simulator with three key optimisations: timestep grouping, active synapse grouping, and delay insensitivity. Combined, these optimisations massively increase the speed of executing a SNN simulation and produce a simulator which is, on a single machine, faster than currently available simulators.

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Theoretical results for the extension of a polymer confined to a channel are usually derived in the limit of infinite contour length. But experimental studies and simulations of DNA molecules confined to nanochannels are not necessarily in this asymptotic limit. We calculate the statistics of the span and the end-to-end distance of a semiflexible polymer of finite length in the extended de Gennes regime, exploiting the fact that the problem can be mapped to a one-dimensional weakly self-avoiding random walk. The results thus obtained compare favourably with pruned-enriched Rosenbluth method (PERM) simulations of a three-dimensional discrete wormlike chain model of DNA confined in a nanochannel. We discuss the implications for experimental studies of linear λ-DNA confined to nanochannels at the high ionic strengths used in many experiments.

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