On the upper regularity dimensions of measures

We study the \emph{upper regularity dimension} which describes the extremal local scaling behaviour of a measure and effectively quantifies the notion of \emph{doubling}. We conduct a thorough study of the upper regularity dimension, including its relationship with other concepts such as the Assouad dimension, the upper local dimension, the $L^q$-spectrum and weak tangent measures. We also compute the upper regularity dimension explicitly in a number of important contexts including self-similar measures, self-affine measures, and measures on sequences.Comment: 22 pages, 4 figures. We corrected an error in Theorem 2.2 and provided a new example concerning weak tangent measures. Minor corrections were added in section 3.6.1, not changing any results. To appear in Indiana Univ. Math.

NICMOS Photometry of the Unusual Dwarf Planet Haumea and its Satellites

We present here Hubble Space Telescope NICMOS F110W and F160W observations of Haumea, and its two satellites Hi'iaka and Namaka. From the measured (F110W-F160W) colors of –1.208 ± 0.004, –1.48 ± 0.06, and –1.4 ± 0.2 mag for each object, respectively, we infer that the 1.6 μm water-ice absorption feature depths on Hi'iaka and Namaka are at least as deep as that of Haumea. The light curve of Haumea is detected in both filters, and we find that the infrared color is bluer by ~2%-3% at the phase of the red spot. These observations suggest that the satellites of Haumea were formed from the collision that produced the Haumea collisional family

The Hubble Wide Field Camera 3 Test of Surfaces in the Outer Solar System: The Compositional Classes of the Kuiper Belt

We present the first results of the Hubble Wide Field Camera 3 Test of Surfaces in the Outer Solar System (H/WTSOSS). The purpose of this survey was to measure the surface properties of a large number of Kuiper belt objects and attempt to infer compositional and dynamical correlations. We find that the Centaurs and the low-perihelion scattered disk and resonant objects exhibit virtually identical bifurcated optical colour distributions and make up two well defined groups of object. Both groups have highly correlated optical and NIR colours which are well described by a pair of two component mixture models that have different red components, but share a common neutral component. The small, $H_{606}\gtrsim5.6$ high-perihelion excited objects are entirely consistent with being drawn from the two branches of the mixing model suggesting that the colour bifurcation of the Centaurs is apparent in all small excited objects. On the other hand, objects larger than $H_{606}\sim5.6$ are not consistent with the mixing model, suggesting some evolutionary process avoided by the smaller objects. The existence of a bifurcation amongst all excited populations argues that the two separate classes of object existed in the primordial disk before the excited Kuiper belt was populated. The cold classical objects exhibit a different type of surface which has colours that are consistent with being drawn from the red branch of the mixing model, but with much higher albedos.Comment: Accepted to the Astrophysical Journal. 49 Pages, 15 Figure

An evolutionarily stable joining policy for group foragers

For foragers that exploit patchily distributed resources that are challenging to locate, detecting discoveries made by others with a view to joining them and sharing the patch may often be an attractive tactic, and such behavior has been observed across many taxa. If, as will commonly be true, the time taken to join another individual on a patch increases with the distance to that patch, then we would expect foragers to be selective in accepting joining opportunities: preferentially joining nearby discoveries. If competition occurs on patches, then the profitability of joining (and of not joining) will be influenced by the strategies adopted by others. Here we present a series of models designed to illuminate the evolutionarily stable joining strategy. We confirm rigorously the previous suggestion that there should be a critical joining distance, with all joining opportunities within that distance being accepted and all others being declined. Further, we predict that this distance should be unaffected by the total availability of food in the environment, but should increase with decreasing density of other foragers, increasing speed of movement towards joining opportunities, increased difficulty in finding undiscovered food patches, and decreasing speed with which discovered patches can be harvested. We are further able to make predictions as to how fully discovered patches should be exploited before being abandoned as unprofitable, with discovered patches being more heavily exploited when patches are hard to find: patches can be searched for remaining food more quickly, forager density is low, and foragers are relatively slow in traveling to discovered patches

Water ice in the Kuiper belt

We examine a large collection of low-resolution near-infrared spectra of Kuiper Belt objects (KBOs) and centaurs in an attempt to understand the presence of water ice in the Kuiper Belt. We find that water ice on the surface of these objects occurs in three separate manners: (1) Haumea family members uniquely show surfaces of nearly pure water ice, presumably a consequence of the fragmentation of the icy mantle of a larger differentiated proto-Haumea; (2) large objects with absolute magnitudes of H < 3 (and a limited number to H = 4.5) have surface coverings of water ice—perhaps mixed with ammonia—that appears to be related to possibly ancient cryovolcanism on these large objects; and (3) smaller KBOs and centaurs which are neither Haumea family members nor cold-classical KBOs appear to divide into two families (which we refer to as "neutral" and "red"), each of which is a mixture of a common nearly neutral component and either a slightly red or very red component that also includes water ice. A model suggesting that the difference between neutral and red objects due to formation in an early compact solar system either inside or outside, respectively, of the ~20 AU methanol evaporation line is supported by the observation that methanol is only detected on the reddest objects, which are those which would be expected to have the most of the methanol containing mixture

On the Assouad dimension of self-similar sets with overlaps

It is known that, unlike the Hausdorff dimension, the Assouad dimension of a self-similar set can exceed the similarity dimension if there are overlaps in the construction. Our main result is the following precise dichotomy for self-similar sets in the line: either the \emph{weak separation property} is satisfied, in which case the Hausdorff and Assouad dimensions coincide; or the \emph{weak separation property} is not satisfied, in which case the Assouad dimension is maximal (equal to one). In the first case we prove that the self-similar set is Ahlfors regular, and in the second case we use the fact that if the \emph{weak separation property} is not satisfied, one can approximate the identity arbitrarily well in the group generated by the similarity mappings, and this allows us to build a \emph{weak tangent} that contains an interval. We also obtain results in higher dimensions and provide illustrative examples showing that the `equality/maximal' dichotomy does not extend to this setting.Comment: 24 pages, 2 figure

The Mass, Orbit, and Tidal Evolution of the Quaoar-Weywot System

Here we present new adaptive optics observations of the Quaoar-Weywot system. With these new observations we determine an improved system orbit. Due to a 0.39 day alias that exists in available observations, four possible orbital solutions are available with periods of $\sim11.6$, $\sim12.0$, $\sim12.4$, and $\sim12.8$ days. From the possible orbital solutions, system masses of $1.3-1.5\pm0.1\times10^{21}$ kg are found. These observations provide an updated density for Quaoar of 2.7-5.0{g cm^{-3}}. In all cases, Weywot's orbit is eccentric, with possible values $\sim0.13-0.16$. We present a reanalysis of the tidal orbital evolution of the Quoaor-Weywot system. We have found that Weywot has probably evolved to a state of synchronous rotation, and have likely preserved their initial inclinations over the age of the Solar system. We find that for plausible values of the effective tidal dissipation factor tides produce a very slow evolution of Weywot's eccentricity and semi-major axis. Accordingly, it appears that Weywot's eccentricity likely did not tidally evolve to its current value from an initially circular orbit. Rather, it seems that some other mechanism has raised its eccentricity post-formation, or Weywot formed with a non-negligible eccentricity.Comment: Accepted to Icarus, Nov. 8 201

Modulation of individual components of gastric motor response to duodenal glucose

AIM: To evaluate individual components of the antro-pyloro-duodenal (APD) motor response to graded small intestinal glucose infusions in healthy humans. METHODS: APD manometry was performed in 15 healthy subjects (12 male; 40 ± 5 years, body mass index 26.5 ± 1.6 kg/m2) during four 20-min intraduodenal infusions of glucose at 0, 0.5, 1.0 and 1.5 kcal/min, in a randomised double-blinded fashion. Glucose solutions were infused at a rate of 1 mL/min and separated by 40-min “wash-out” period. Data are mean ± SE. Inferential analyses are repeated measure analysis of variance with Bonferroni post-hoc testing. RESULTS: At 0 kcal/min frequency of pressure waves were: antrum (7.5 ± 1.8 waves/20 min) and isolated pyloric pressure waves (IPPWs) (8.0 ± 2.3 waves/20 min) with pyloric tone (0.0 ± 0.9 mmHg). Intraduodenal glucose infusion acutely increased IPPW frequency (P < 0.001) and pyloric tone (P = 0.015), and decreased antral wave frequency (P = 0.007) in a dose-dependent fashion. A threshold for stimulation was observed at 1.0 kcal/min for pyloric phasic pressure waves (P = 0.002) and 1.5 kcal/min for pyloric tone and antral contractility. CONCLUSION: There is hierarchy for the activation of gastrointestinal motor responses to duodenal glucose infusion. An increase in IPPWs is the first response observed.Adam M Deane, Laura K Besanko, Carly M Burgstad, Marianne J Chapman, Michael Horowitz, Robert JL Frase

Obituary: Arthur Cruickshank 1932 - 2011. A native Gondwanan, who studied the former continent's fossil tetrapods

Dr Arthur Richard Ivor Cruickshank died on 4th December 2011, aged 79, in the Borders General Hospital, Melrose, Scotland. Arthur Cruickshank was part of the post-war generation of palaeontologists who laid the foundations on which today’s researchers build. Appropriately for someone from an expatriate Scots family living in Kenya, much of his work was on the extinct reptiles of the great southern palaeocontinent of Gondwana