The chain rule for F\mathcal F-differentiation

Let $X$ be a perfect, compact subset of the complex plane, and let $D^{(1)}(X)$ denote the (complex) algebra of continuously complex-differentiable functions on $X$. Then $D^{(1)}(X)$ is a normed algebra of functions but, in some cases, fails to be a Banach function algebra. Bland and the second author investigated the completion of the algebra $D^{(1)}(X)$, for certain sets $X$ and collections $\mathcal{F}$ of paths in $X$, by considering $\mathcal{F}$-differentiable functions on $X$. In this paper, we investigate composition, the chain rule, and the quotient rule for this notion of differentiability. We give an example where the chain rule fails, and give a number of sufficient conditions for the chain rule to hold. Where the chain rule holds, we observe that the Fa\'a di Bruno formula for higher derivatives is valid, and this allows us to give some results on homomorphisms between certain algebras of $\mathcal{F}$-differentiable functions.Comment: 12 pages, submitte

Abstract Swiss Cheese Space and the Classicalisation of Swiss Cheeses

Swiss cheese sets are compact subsets of the complex plane obtained by deleting a sequence of open disks from a closed disk. Such sets have provided numerous counterexamples in the theory of uniform algebras. In this paper, we introduce a topological space whose elements are what we call "abstract Swiss cheeses". Working within this topological space, we show how to prove the existence of "classical" Swiss cheese sets (as discussed in a paper of Feinstein and Heath from 2010) with various desired properties. We first give a new proof of the Feinstein-Heath classicalisation theorem. We then consider when it is possible to "classicalise" a Swiss cheese while leaving disks which lie outside a given region unchanged. We also consider sets obtained by deleting a sequence of open disks from a closed annulus, and we obtain an analogue of the Feinstein-Heath theorem for these sets. We then discuss regularity for certain uniform algebras. We conclude with an application of these techniques to obtain a classical Swiss cheese set which has the same properties as a non-classical example of O'Farrell (1979).Comment: To appear in the Journal of Mathematical Analysis and Application

The Histone 3'-Terminal Stem-Loop-Binding Protein Enhances Translation through a Functional and Physical Interaction with Eukaryotic Initiation Factor 4G (eIF4G) and eIF3

Metazoan cell cycle-regulated histone mRNAs are unique cellular mRNAs in that they terminate in a highly conserved stem-loop structure instead of a poly(A) tail. Not only is the stem-loop structure necessary for 3'-end formation but it regulates the stability and translational efficiency of histone mRNAs. The histone stem-loop structure is recognized by the stem-loop-binding protein (SLBP), which is required for the regulation of mRNA processing and turnover. In this study, we show that SLBP is required for the translation of mRNAs containing the histone stem-loop structure. Moreover, we show that the translation of mRNAs ending in the histone stem-loop is stimulated in Saccharomyces cerevisiae cells expressing mammalian SLBP. The translational function of SLBP genetically required eukaryotic initiation factor 4E (eIF4E), eIF4G, and eIF3, and expressed SLBP coisolated with S. cerevisiae initiation factor complexes that bound the 5' cap in a manner dependent on eIF4G and eIF3. Furthermore, eIF4G coimmunoprecipitated with endogenous SLBP in mammalian cell extracts and recombinant SLBP and eIF4G coisolated. These data indicate that SLBP stimulates the translation of histone mRNAs through a functional interaction with both the mRNA stem-loop and the 5' cap that is mediated by eIF4G and eIF3

The Brown-dwarf Atmosphere Monitoring (BAM) Project II: Multi-epoch monitoring of extremely cool brown dwarfs

With the discovery of Y dwarfs by the WISE mission, the population of field brown dwarfs now extends to objects with temperatures comparable to those of Solar System planets. To investigate the atmospheres of these newly identified brown dwarfs, we have conducted a pilot study monitoring an initial sample of three late T-dwarfs (T6.5, T8 and T8.5) and one Y-dwarf (Y0) for infrared photometric variability at multiple epochs. With J-band imaging, each target was observed for a period of 1.0h to 4.5h per epoch, which covers a significant fraction of the expected rotational period. These measurements represent the first photometric monitoring for these targets. For three of the four targets (2M1047, Ross 458C and WISE0458), multi-epoch monitoring was performed, with the time span between epochs ranging from a few hours to ~2 years. During the first epoch, the T8.5 target WISE0458 exhibited variations with a remarkable min-to-max amplitude of 13%, while the second epoch light curve taken ~2 years later did not note any variability to a 3% upper limit. With an effective temperature of ~600 K, WISE0458 is the coldest variable brown dwarf published to-date, and combined with its high and variable amplitude makes it a fascinating target for detailed follow-up. The three remaining targets showed no significant variations, with a photometric precision between 0.8% and 20.0%, depending on the target brightness. Combining the new results with previous multi-epoch observations of brown dwarfs with spectral types of T5 or later, the currently identified variables have locations on the colour-colour diagram better matched by theoretical models incorporating cloud opacities rather than cloud-free atmospheres. This preliminary result requires further study to determine if there is a definitive link between variability among late-T dwarfs and their location on the colour-colour diagram.Comment: 9 pages, 6 figures, 3 tables, accepted for publication in MNRA

Phase transitions in the classical simulability of open quantum systems

We introduce a Langevin unravelling of the density matrix evolution of an open quantum system over matrix product states, which we term the time-dependent variational principle-Langevin equation. This allows the study of entanglement dynamics as a function of both temperature and coupling to the environment. As the strength of coupling to and temperature of the environment is increased, we find a transition where the entanglement of the individual trajectories saturates, permitting a classical simulation of the system for all times. This is the Hamiltonian open system counterpart of the saturation in entanglement found in random circuits with projective or weak measurements. If a system is open, there is a limit to the advantage in simulating its behaviour on a quantum computer, even when that evolution harbours important quantum effects. Moreover, if a quantum simulator is in this phase, it cannot simulate with quantum advantage

The aging male: investigation, treatment and monitoring of late-onset hypogonadism in males

Androgen deficiency in the aging male has become a topic of increasing interest and debate throughout the world. The demographics clearly demonstrate the increasing percentage of the population that is in the older age groups. The data also support the concept that testosterone falls progressively with age and that a significant percentage of men over the age of 60 years have serum testosterone levels that are below the lower limits of young adults (age 20-30 years) men. The principal questions raised by these observations are whether older hypogonadal men will benefit from testosterone treatment and what will be the risks associated with such intervention. The past decade has brought evidence of benefit of androgen treatment on multiple target organs of hypogonadal men and recent studies show short-term beneficial effects of testosterone in older men that are similar to those in younger men. Long-term data on the effects of testosterone treatment in the older population are limited and specific risk data on the prostate and cardiovascular systems are needed. Answers to key questions of functional benefits that may retard frailty of the elderly are not yet available. The recommendations described below were prepared for the International Society of Andrology (ISA) and the International Society for the Study of the Aging Male (ISSAM) following a panel discussion with active participation from the audience sponsored by the ISA on the topic at the 4th ISSAM Congress in Prague in February 2004.peer-reviewe

Cannabis and depression: A twin model approach to co-morbidity

Cannabis use disorder (CUD) co-occurs with major depressive disorder (MDD) more frequently than would be expected by chance. However, studies to date have not produced a clear understanding of the mechanisms underlying this co-morbidity. Genetically informative studies can add valuable insight to this problem, as they allow the evaluation of competing models of co-morbidity. This study uses data from the Australian Twin Registry to compare 13 co-morbidity twin models initially proposed by Neale and Kendler (Am J Hum Genet 57:935–953, 1995). The analysis sample comprised 2410 male and female monozygotic and dizygotic twins (average age 32) who were assessed on CUD and MDD using the SSAGA-OZ interview. Data were analyzed in OpenMx. Of the 13 different co-morbidity models, two fit equally well: CUD causes MDD and Random Multiformity of CUD. Both fit substantially better than the Correlated Liabilities model. Although the current study cannot differentiate between them statistically, these models, in combination, suggest that CUD risk factors may causally influence the risk to develop MDD, but only when risk for CUD is high

Shedding some light on Thismia rodwayi F. Muell. (fairy lanterns) in Tasmania: distribution, habitat and conservation status

Thismia rodwayi is a seldom-seen, subterranean plant that occurs in Tasmania, the eastern states of the Australian mainland and New Zealand. Surveys for the species were prompted by a new record from Archers Sugarloaf near Meander in Tasmania's central north. Several new populations of the species were subsequently discovered in wet eucalypt forests dominated by Eucalyptus obliqua, E. regnans, E. delegatensis or E. viminalis, with an understorey dominated by Pomaderris apetala, Bedfordia salicina and/or Olearia argophylla. The species is now known from the Meander, Glen Huon, Little Denison River, Mount Field, Mount Wellington and Ben Lomond areas. Analysis of current information suggests that the listing of T. rodwayi under Schedule 5 (Rare) of the Tasmanian Threatened Species Protection Act 1995 is appropriate

Enlargement of Cavernous Haemangioma Associated with Exogenous Administration of Oestrogens

A cavernous haemangioma of the liver which enlarged rapidly while the patient was receiving exogenous oestrogens is reported. A dramatic decrease in the size of the tumour was produced by ligating the right hepatic artery and portal vein. The literature on large haemangiomas of the liver is reviewed.S. Afr. Med. J., 48, 695 (1974)

An L Band Spectrum of the Coldest Brown Dwarf

The coldest brown dwarf, WISE 0855, is the closest known planetary-mass, free-floating object and has a temperature nearly as cold as the solar system gas giants. Like Jupiter, it is predicted to have an atmosphere rich in methane, water, and ammonia, with clouds of volatile ices. WISE 0855 is faint at near-infrared wavelengths and emits almost all its energy in the mid-infrared. Skemer et al. 2016 presented a spectrum of WISE 0855 from 4.5-5.1 micron (M band), revealing water vapor features. Here, we present a spectrum of WISE 0855 in L band, from 3.4-4.14 micron. We present a set of atmosphere models that include a range of compositions (metallicities and C/O ratios) and water ice clouds. Methane absorption is clearly present in the spectrum. The mid-infrared color can be better matched with a methane abundance that is depleted relative to solar abundance. We find that there is evidence for water ice clouds in the M band spectrum, and we find a lack of phosphine spectral features in both the L and M band spectra. We suggest that a deep continuum opacity source may be obscuring the near-infrared flux, possibly a deep phosphorous-bearing cloud, ammonium dihyrogen phosphate. Observations of WISE 0855 provide critical constraints for cold planetary atmospheres, bridging the temperature range between the long-studied solar system planets and accessible exoplanets. JWST will soon revolutionize our understanding of cold brown dwarfs with high-precision spectroscopy across the infrared, allowing us to study their compositions and cloud properties, and to infer their atmospheric dynamics and formation processes.Comment: 19 pages, 21 figures. Accepted for publication in Ap