On the cardinality and complexity of the set of codings for self-similar sets with positive Lebesgue measure

Let λ1,…,λn be real numbers in (0,1) and p1,…,pn be points in Rd. Consider the collection of maps fj:Rd→Rd given by fj(x)=λjx+(1−λj)pj. It is a well known result that there exists a unique nonempty compact set Λ⊂Rd satisfying Λ=∪nj=1fj(Λ). Each x∈Λ has at least one coding, that is a sequence (ϵi)∞i=1 ∈{1,…,n}N that satisfies limN→∞fϵ1…fϵN(0)=x. We study the size and complexity of the set of codings of a generic x∈Λ when Λ has positive Lebesgue measure. In particular, we show that under certain natural conditions almost every x∈Λ has a continuum of codings. We also show that almost every x∈Λ has a universal coding. Our work makes no assumptions on the existence of holes in Λ and improves upon existing results when it is assumed Λ contains no holes.

Mesh adaptation on the sphere using optimal transport and the numerical solution of a Monge-Ampère type equation

An equation of Monge-Ampère type has, for the first time, been solved numerically on the surface of the sphere in order to generate optimally transported (OT) meshes, equidistributed with respect to a monitor function. Optimal transport generates meshes that keep the same connectivity as the original mesh, making them suitable for r-adaptive simulations, in which the equations of motion can be solved in a moving frame of reference in order to avoid mapping the solution between old and new meshes and to avoid load balancing problems on parallel computers. The semi-implicit solution of the Monge-Ampère type equation involves a new linearisation of the Hessian term, and exponential maps are used to map from old to new meshes on the sphere. The determinant of the Hessian is evaluated as the change in volume between old and new mesh cells, rather than using numerical approximations to the gradients. OT meshes are generated to compare with centroidal Voronoi tesselations on the sphere and are found to have advantages and disadvantages; OT equidistribution is more accurate, the number of iterations to convergence is independent of the mesh size, face skewness is reduced and the connectivity does not change. However anisotropy is higher and the OT meshes are non-orthogonal. It is shown that optimal transport on the sphere leads to meshes that do not tangle. However, tangling can be introduced by numerical errors in calculating the gradient of the mesh potential. Methods for alleviating this problem are explored. Finally, OT meshes are generated using observed precipitation as a monitor function, in order to demonstrate the potential power of the technique.

Connecting climate model projections of global temperature change with the real world

Current state-of-the-art global climate models produce different values for Earth’s mean temperature. When comparing simulations with each other and with observations it is standard practice to compare temperature anomalies with respect to a reference period. It is not always appreciated that the choice of reference period can affect conclusions, both about the skill of simulations of past climate, and about the magnitude of expected future changes in climate. For example, observed global temperatures over the past decade are towards the lower end of the range of CMIP5 simulations irrespective of what reference period is used, but exactly where they lie in the model distribution varies with the choice of reference period. Additionally, we demonstrate that projections of when particular temperature levels are reached, for example 2K above ‘pre-industrial’, change by up to a decade depending on the choice of reference period. In this article we discuss some of the key issues that arise when using anomalies relative to a reference period to generate climate projections. We highlight that there is no perfect choice of reference period. When evaluating models against observations, a long reference period should generally be used, but how long depends on the quality of the observations available. The IPCC AR5 choice to use a 1986-2005 reference period for future global temperature projections was reasonable, but a case-by-case approach is needed for different purposes and when assessing projections of different climate variables. Finally, we recommend that any studies that involve the use of a reference period should explicitly examine the robustness of the conclusions to alternative choices.

The impact of location and type on the performance of Low-Voltage network connected Battery Energy Storage Systems

This paper assesses the impact of the location and configuration of Battery Energy Storage Systems (BESS) on Low-Voltage (LV) feeders. BESS are now being deployed on LV networks by Distribution Network Operators (DNOs) as an alternative to conventional reinforcement (e.g. upgrading cables and transformers) in response to increased electricity demand from new technologies such as electric vehicles. By storing energy during periods of low demand and then releasing that energy at times of high demand, the peak demand of a given LV substation on the grid can be reduced therefore mitigating or at least delaying the need for replacement and upgrade. However, existing research into this application of BESS tends to evaluate the aggregated impact of such systems at the substation level and does not systematically consider the impact of the location and configuration of BESS on the voltage profiles, losses and utilisation within a given feeder. In this paper, four configurations of BESS are considered: single-phase, unlinked three-phase, linked three-phase without storage for phase-balancing only, and linked three-phase with storage. These four configurations are then assessed based on models of two real LV networks. In each case, the impact of the BESS is systematically evaluated at every node in the LV network using Matlab linked with OpenDSS. The location and configuration of a BESS is shown to be critical when seeking the best overall network impact or when considering specific impacts on voltage, losses, or utilisation separately. Furthermore, the paper also demonstrates that phase-balancing without energy storage can provide much of the gains on unbalanced networks compared to systems with energy storage.

Differential interaction of estrogen receptor and thyroid hormone receptor isoforms on the rat oxytocin receptor promoter leads to differences in transcriptional regulation

Both the estrogen receptor (ER) and thyroid hormone receptor (TR) are members of the nuclear receptor superfamily. Two isoforms of the ER, alpha and beta, exist. The TRalpha and beta isoforms are products of two distinct genes that are further differentially spliced to give TRalpha1 and alpha2, TRbeta1 and beta2. The TRs have been shown to interfere with ER-mediated transcription from both the consensus estrogen response element (ERE) and the rat preproenkephalin (PPE) promoter, possibly by competing with ER binding to the ERE or by squelching coactivators essential for ER-mediated transcription. The rat oxytocin receptor (OTR) gene is thought to be involved in several facets of reproductive and affiliative behaviors. 17beta-Estradiol-bound ERs upregulate the OTR gene in the ventromedial hypothalamus, a region critical for the induction of lordosis behavior in several species. We investigated the effects of the ligand-binding TR isoforms on the ER-mediated transcription from a physiological promoter of a behaviorally relevant gene such as the OTR. Only ERalpha could induce the OTR gene in two cell lines tested, the CV-1 and the SK-N-BE2C neuroblastoma cell lines. ERbeta was incapable of inducing the gene in either cell line. ERalpha is therefore not equivalent to ERbeta on this physiological promoter. Indeed, in the neural cell line, ERbeta can inhibit ERalpha-mediated induction from the OTR promoter. While the TRalpha1 isoform inhibited ERalpha-mediated induction in the neural cell line, the TRbeta1 isoform stimulated induction, thus demonstrating isoform specificity in the interaction. The use of a DNA-binding mutant, the TR P box mutant, showed that inhibition of ERalpha-mediated induction of the rat OTR gene promoter by the TRalpha1 isoform does not require DNA-binding ability. SRC-1 overexpression relieved TRalpha1-mediated inhibition in both cell lines, suggesting that squelching for coactivators is an important molecular mechanism in TRalpha-mediated inhibition. Such interactions between TR and ER isoforms on the rat OTR promoter provide a mechanism to achieve neuroendocrine integration.

Isoform specificity for oestrogen receptor and thyroid hormone receptor genes and their interactions on the NR2D gene promoter

Oestrogens are critical for the display of lordosis behaviour and, in recent years, have also been shown to be involved in synaptic plasticity. In the brain, the regulation of ionotropic glutamate receptors has consequences for excitatory neurotransmission. Oestrogen regulation of the N-methyl-d-aspartate receptor subunit 2D (NR2D) has generated considerable interest as a possible molecular mechanism by which synaptic plasticity can be modulated. Since more than one isoform of the oestrogen receptor (ER) exists in mammals, it is possible that oestrogen regulation via the ERalpha and ERbeta isoforms on the NR2D oestrogen response element (ERE) is not equivalent. In the kidney fibroblast (CV1) cell line, we show that in response to 17beta-oestradiol, only ERalpha, not ERbeta, could upregulate transcription from the ERE which is in the 3' untranslated region of the NR2D gene. When this ERE is in the 5' position, neither ERalpha nor ERbeta showed transactivation capacity. Thyroid hormone receptor (TR) modulation of ER mediated induction has been shown for other ER target genes, such as the preproenkephalin and oxytocin receptor genes. Since the various TR isoforms exhibit distinct roles, we hypothesized that TR modulation of ER induction may also be isoform specific. This is indeed the case. The TRalpha1 isoform stimulated ERalpha mediated induction from the 3'-ERE whereas the TRbeta1 isoform inhibited this induction. This study shows that isoforms of both the ER and TR have different transactivation properties. Such flexible regulation and crosstalk by nuclear receptor isoforms leads to different transcriptional outcomes and the combinatorial logic may aid neuroendocrine integration.