The monic integer transfinite diameter

We study the problem of finding nonconstant monic integer polynomials, normalized by their degree, with small supremum on an interval I. The monic integer transfinite diameter t_M(I) is defined as the infimum of all such supremums. We show that if I has length 1 then t_M(I) = 1/2. We make three general conjectures relating to the value of t_M(I) for intervals I of length less that 4. We also conjecture a value for t_M([0, b]) where 0 < b < 1. We give some partial results, as well as computational evidence, to support these conjectures. We define two functions that measure properties of the lengths of intervals I with t_M(I) on either side of t. Upper and lower bounds are given for these functions. We also consider the problem of determining t_M(I) when I is a Farey interval. We prove that a conjecture of Borwein, Pinner and Pritsker concerning this value is true for an infinite family of Farey intervals.Comment: 32 pages, 5 figure

On univoque Pisot numbers

We study Pisot numbers $\beta \in (1, 2)$ which are univoque, i.e., such that there exists only one representation of 1 as $1 = \sum_{n \geq 1} s_n\beta^{-n}$, with $s_n \in \{0, 1\}$. We prove in particular that there exists a smallest univoque Pisot number, which has degree 14. Furthermore we give the smallest limit point of the set of univoque Pisot numbers.Comment: Accepted by Mathematics of COmputatio

Amino acids precursors in lunar finds

The consistent pattern is discussed of amino acids found in lunar dust from Apollo missions. The evidence indicates that compounds yielding amino acids were implanted into the surface of the moon by the solar wind, and the kind and amounts of amino acids found on the moon are closely similar to those found in meteorites. It is concluded that there is a common cosmochemical pattern for the moom and meteorites, and this offers evidence of a common course of cosmochemical reactions for carbon

Computing Garsia Entropy for Bernoulli Convolutions with Algebraic Parameters

We introduce a parameter space containing all algebraic integers $\beta\in(1,2]$ that are not Pisot or Salem numbers, and a sequence of increasing piecewise continuous function on this parameter space which gives a lower bound for the Garsia entropy of the Bernoulli convolution $\nu_{\beta}$. This allows us to show that $\mathrm{dim}_\mathrm{H} (\nu_{\beta})=1$ for all $\beta$ with representations in certain open regions of the parameter space.Comment: 21 pages, 2 figures, 5 table

Use of “Entertainment” Chimpanzees in Commercials Distorts Public Perception Regarding Their Conservation Status

Chimpanzees (Pan troglodytes) are often used in movies, commercials and print advertisements with the intention of eliciting a humorous response from audiences. The portrayal of chimpanzees in unnatural, human-like situations may have a negative effect on the public's understanding of their endangered status in the wild while making them appear as suitable pets. Alternatively, media content that elicits a positive emotional response toward chimpanzees may increase the public's commitment to chimpanzee conservation. To test these competing hypotheses, participants (n = 165) watched a series of commercials in an experiment framed as a marketing study. Imbedded within the same series of commercials was one of three chimpanzee videos. Participants either watched 1) a chimpanzee conservation commercial, 2) commercials containing “entertainment” chimpanzees or 3) control footage of the natural behavior of wild chimpanzees. Results from a post-viewing questionnaire reveal that participants who watched the conservation message understood that chimpanzees were endangered and unsuitable as pets at higher levels than those viewing the control footage. Meanwhile participants watching commercials with entertainment chimpanzees showed a decrease in understanding relative to those watching the control footage. In addition, when participants were given the opportunity to donate part of their earnings from the experiment to a conservation charity, donations were least frequent in the group watching commercials with entertainment chimpanzees. Control questions show that participants did not detect the purpose of the study. These results firmly support the hypothesis that use of entertainment chimpanzees in the popular media negatively distorts the public's perception and hinders chimpanzee conservation efforts

Analytic calculation of radio emission from parametrized extensive air showers:A tool to extract shower parameters

The radio intensity and polarization footprint of a cosmic-ray induced extensive air shower is determined by the time-dependent structure of the current distribution residing in the plasma cloud at the shower front. In turn, the time dependence of the integrated charge-current distribution in the plasma cloud, the longitudinal shower structure, is determined by interesting physics which one would like to extract, such as the location and multiplicity of the primary cosmic-ray collision or the values of electric fields in the atmosphere during thunderstorms. To extract the structure of a shower from its footprint requires solving a complicated inverse problem. For this purposewe have developed a code that semianalytically calculates the radio footprint of an extensive air shower given an arbitrary longitudinal structure. This code can be used in an optimization procedure to extract the optimal longitudinal shower structure given a radio footprint. On the basis of air-shower universality we propose a simple parametrization of the structure of the plasma cloud. This parametrization is based on the results of Monte Carlo shower simulations. Deriving the parametrization also teaches which aspects of the plasma cloud are important for understanding the features seen in the radio-emission footprint. The calculated radio footprints are compared with microscopic CoREAS simulations

A classification of (some)Pisot-Cyclotomic numbers

Abstract A complete classification of degree 2, 3 and degree 4 Pisot-Cyclotomic numbers is given. Some examples of higher degrees are also given. Pisot-Cyclotomic numbers have applications to quasicrystals and quasilattices

Evidence for an abundant old population of Galactic ultra long period magnetars and implications for fast radio bursts

Two recent discoveries, namely PSR J0901-4046 and GLEAM-X J162759.5-523504.3 (hereafter GLEAM-X J1627), have corroborated an extant population of radio-loud periodic sources with long periods (76 s and 1091 s respectively) whose emission can hardly be explained by rotation losses. We argue that GLEAM-X J1627 is a highly-magnetized object consistent with a magnetar (an ultra long period magnetar - ULPM), and demonstrate it is unlikely to be either a magnetically or a rotationally-powered white dwarf. By studying these sources together with previously detected objects, we find there are at least a handful of promising candidates for Galactic ULPMs. The detections of these objects imply a substantial number, $N \gtrsim 13000$ and $N \gtrsim 500$ for PSR J0901--4046 like and GLEAM-X J1627 like objects, respectively, within our Galaxy. These source densities, as well as cooling age limits from non-detection of thermal X-rays, Galactic offsets, timing stability and dipole spindown limits, all imply the ULPM candidates are substantially older than confirmed Galactic magnetars and that their formation channel is a common one. Their existence implies widespread survival of magnetar-like fields for several Myr, distinct from the inferred behaviour in confirmed Galactic magnetars. ULPMs may also constitute a second class of FRB progenitors which could naturally exhibit very long periodic activity windows. Finally, we show that existing radio campaigns are biased against detecting objects like these and discuss strategies for future radio and X-ray surveys to identify more such objects. We estimate that ${\cal O}(100)$ more such objects should be detected with SKA-MID and DSA-2000.Comment: 22 pages, 10 figures. Published in MNRA

'A light in a very dark place' : The role of a voluntary organisation providing support for those affected by encephalitis

Voluntary organisations are seen as contributing to the ‘democratisation’ of health and social care. Little, however, is written about their role and this paper, by focusing on the work of The Encephalitis Society, provides insights into the challenges facing voluntary organisations as they manage twin roles as service providers and advocates, of people with neurological disorders. Two studies are presented: a review conducted by the Society, focusing on patient’s experiences of neurological services; and an external evaluation of the Society’s current provision. The first, based on a postal survey of its members affected by encephalitis (n = 339), illustrates the Society’s advocacy role. The survey provided support for the Association of British Neurologists’ recommendation for nationally agreed standards of care. The second study, a postal survey of recent contacts (n = 76) and in-depth telephone interviews (n = 22), illustrates the Society’s value role as a service provider and supports its role in helping rehabilitate affected individuals and their families. These studies provided the Society with information for policy and service development. Importantly, providing the basis of informed action and partnership with stakeholders and informing the organisation’s sense of purpose, in the changing context of welfare provision in the UK