Accelerating Parallel Tempering: Quantile Tempering Algorithm (QuanTA)

Using MCMC to sample from a target distribution, $\pi(x)$ on a $d$-dimensional state space can be a difficult and computationally expensive problem. Particularly when the target exhibits multimodality, then the traditional methods can fail to explore the entire state space and this results in a bias sample output. Methods to overcome this issue include the parallel tempering algorithm which utilises an augmented state space approach to help the Markov chain traverse regions of low probability density and reach other modes. This method suffers from the curse of dimensionality which dramatically slows the transfer of mixing information from the auxiliary targets to the target of interest as $d \rightarrow \infty$. This paper introduces a novel prototype algorithm, QuanTA, that uses a Gaussian motivated transformation in an attempt to accelerate the mixing through the temperature schedule of a parallel tempering algorithm. This new algorithm is accompanied by a comprehensive theoretical analysis quantifying the improved efficiency and scalability of the approach; concluding that under weak regularity conditions the new approach gives accelerated mixing through the temperature schedule. Empirical evidence of the effectiveness of this new algorithm is illustrated on canonical examples

When leaseholders are landlords: Edwards v Kumarasamy [2016] UKSC 40; [2016] 3 W.L.R. 310

The course of social changes can often be traced in the evolution of case law. The recent decision of the Supreme Court in Edwards v Kumarasamy is a good example. Here landlord and tenant law has had to get to grips with how far a landlord should be under an obligation to repair, where the landlord is himself a leaseholder, and not primarily liable for repairs. This scenario has arisen due to the revival of the ‘buy-to-let’ property market, and because properties which are affordable – both to the buyer and the renter – will often be leasehold flats. In allowing the landlord’s appeal, the Supreme Court has clarified the extent of the immediate landlord’s repairing obligations towards the tenant, and rejected some rather unorthodox views expressed by the Court of Appeal

Weight-Preserving Simulated Tempering

Simulated tempering is popular method of allowing MCMC algorithms to move between modes of a multimodal target density {\pi}. One problem with simulated tempering for multimodal targets is that the weights of the various modes change for different inverse-temperature values, sometimes dramatically so. In this paper, we provide a fix to overcome this problem, by adjusting the mode weights to be preserved (i.e., constant) over different inverse-temperature settings. We then apply simulated tempering algorithms to multimodal targets using our mode weight correction. We present simulations in which our weight-preserving algorithm mixes between modes much more successfully than traditional tempering algorithms. We also prove a diffusion limit for an version of our algorithm, which shows that under appropriate assumptions, our algorithm mixes in time O(d [log d]^2)

Forcing boundary-layer transition on an inverted airfoil in ground effect and at varying incidence

Presented at 34th AIAA Applied Aerodynamics ConferenceThe influence of the laminar boundary-layer state on a wing operating in ground effect at Re = 6 × 10 has been investigated using experiments with a model that provides two-dimensional flow and computations with a panel-method code. The effect of a boundary-layer trip placed at varying distances from the leading edge was observed at various incidences in terms of on-surface characteristics, including pressure measurements, flow visualisation and hot-film anemometry, and off-surface characteristics with LDA surveys below and behind the wing. The act of forcing transition led to downforce being reduced and drag increased, moreover, it altered almost all aspects of the wing’s aerodynamic characteristics, with the effect becoming greater as the trip was placed closer to the leading edge. These aspects include the replacement of a laminar separation bubble with trailing-edge separation, a thicker boundary layer, and a thicker wake with greater velocity deficit. The importance of considering laminar phenomena for wings operating in ground effect has been show

Optical influence of oil droplets on cone photoreceptor sensitivity

Oil droplets are spherical organelles found in the cone photoreceptors of vertebrates. They are generally assumed to focus incident light into the outer segment, and thereby improve light catch because of the droplets' spherical lens-like shape. However, using full-wave optical simulations of physiologically realistic cone photoreceptors from birds, frogs and turtles we find that pigmented oil droplets actually drastically reduce the transmission of light into the outer segment integrated across the full visible wavelength range of each species. Only transparent oil droplets improve light catch into the outer segments, and any enhancement is critically dependent on the refractive index, diameter of the oil droplet, and diameter and length of the outer segment. Furthermore, oil droplets are not the only optical elements found in cone inner segments. The ellipsoid, a dense aggregation of mitochondria situated immediately prior to the oil droplet, mitigates the loss of light at oil droplet surface. We describe a framework for integrating these optical phenomena into simple models of receptor sensitivity and the relevance of these observations to evolutionary appearance and loss of oil droplets is discussed.</jats:p