Carryless Arithmetic Mod 10

We investigate what arithmetic would look like if carry digits into other digit position were ignored, so that 9 + 4 = 3, 5 + 5 = 0, 9 X 4 = 6, 5 X 4 = 0, and so on. For example, the primes are now 21, 23, 25, 27, 29, 41, 43, 45, 47, ... .Comment: 7 pages. To the memory of Martin Gardner (October 21, 1914 -- May 22, 2010). Revised version (with a number of small improvements), July 7 201

On Asymmetric Coverings and Covering Numbers

An asymmetric covering D(n,R) is a collection of special subsets S of an n-set such that every subset T of the n-set is contained in at least one special S with |S| - |T| <= R. In this paper we compute the smallest size of any D(n,1) for n <= 8. We also investigate ``continuous'' and ``banded'' versions of the problem. The latter involves the classical covering numbers C(n,k,k-1), and we determine the following new values: C(10,5,4) = 51, C(11,7,6,) =84, C(12,8,7) = 126, C(13,9,8)= 185 and C(14,10,9) = 259. We also find the number of nonisomorphic minimal covering designs in several cases.Comment: 11 page

“Don’t Jobs Change?” Substitution of Professionals by Support Staff in Public Libraries, 1997-2007

poster abstractAmong MLS-level librarians, there is substantial anecdotal prevalence of the idea that administrators of public libraries seek to reduce costs by replacing MLS librarians with support staff. The migration of tasks such as copy and original cataloging and reference services to support staff has been well-documented. This study used national data from the Public Libraries Survey, from 1997 and 2007, to test this substitution hypothesis. Data indicates that for this time period, the utilization of MLS librarians as a percent of total library staffs did not diminish overall. Relative to population served, libraries did not reduce MLS positions but did increase support staffing. This has implications for understanding the 2008-2013 period of reduced public resources, and for the staffing of public libraries in the longer term

Polarization-resolved second-harmonic-generation optical coherence tomography in collagen

We describe a novel imaging technique, second-harmonic-generation optical coherence tomography (SHOCT). This technique combines the spatial resolution and depth penetration of optical coherence tomography (OCT) with the molecular sensitivity of second-harmonic-generation spectroscopy. As a consequence of the coherent detection required for OCT, polarization-resolved images arise naturally. We demonstrate this new technique on a skin sample from the belly of Icelandic salmon, acquiring polarization-resolved SHOCT and OCT images simultaneously

Timing of the 2008 Outburst of SAX J1808.4-3658 with XMM-Newton: A Stable Orbital Period Derivative over Ten Years

We report on a timing analysis performed on a 62-ks long XMM-Newton observation of the accreting millisecond pulsar SAX J1808.4-3658 during the latest X-ray outburst that started on September 21, 2008. By connecting the time of arrivals of the pulses observed during the XMM observation, we derived the best-fit orbital solution and a best-fit value of the spin period for the 2008 outburst. Comparing this new set of orbital parameters and, in particular, the value of the time of ascending-node passage with the orbital parameters derived for the previous four X-ray outbursts of SAX J1808.4-3658 observed by the PCA on board RXTE, we find an updated value of the orbital period derivative, which turns out to be $\dot P_{\rm orb} = (3.89 \pm 0.15) \times 10^{-12}$ s/s. This new value of the orbital period derivative agrees with the previously reported value, demonstrating that the orbital period derivative in this source has remained stable over the past ten years. Although this timespan is not sufficient yet for confirming the secular evolution of the system, we again propose an explanation of this behavior in terms of a highly non-conservative mass transfer in this system, where the accreted mass (as derived from the X-ray luminosity during outbursts) accounts for a mere 1% of the mass lost by the companion.Comment: 4 pages, 3 figures. Final version, including editing corrections, to appear on A&A Letter

Age differences in the use of serving size information on food labels: numeracy or attention?

ObjectiveThe ability to use serving size information on food labels is important for managing age-related chronic conditions such as diabetes, obesity and cancer. Past research suggests that older adults are at risk for failing to accurately use this portion of the food label due to numeracy skills. However, the extent to which older adults pay attention to serving size information on packages is unclear. We compared the effects of numeracy and attention on age differences in accurate use of serving size information while individuals evaluated product healthfulness.DesignAccuracy and attention were assessed across two tasks in which participants compared nutrition labels of two products to determine which was more healthful if they were to consume the entire package. Participants' eye movements were monitored as a measure of attention while they compared two products presented side-by-side on a computer screen. Numeracy as well as food label habits and nutrition knowledge were assessed using questionnaires.SettingSacramento area, California, USA, 2013-2014.SubjectsStratified sample of 358 adults, aged 20-78 years.ResultsAccuracy declined with age among those older adults who paid less attention to serving size information. Although numeracy, nutrition knowledge and self-reported food label use supported accuracy, these factors did not influence age differences in accuracy.ConclusionsThe data suggest that older adults are less accurate than younger adults in their use of serving size information. Age differences appear to be more related to lack of attention to serving size information than to numeracy skills

The Yellowstone Permutation

Define a sequence of positive integers by the rule that a(n) = n for 1 <= n = 4, a(n) is the smallest number not already in the sequence which has a common factor with a(n-2) and is relatively prime to a(n-1). We show that this is a permutation of the positive integers. The remarkable graph of this sequence consists of runs of alternating even and odd numbers, interrupted by small downward spikes followed by large upward spikes, suggesting the eruption of geysers in Yellowstone National Park. On a larger scale the points appear to lie on infinitely many distinct curves. There are several unanswered questions concerning the locations of these spikes and the equations for these curves.Comment: 10 pages, 6 figures. Mar 7 2015: mostly stylistic change

Spectral triangulation molecular contrast optical coherence tomography with indocyanine green as the contrast agent

We report a new molecular contrast optical coherence tomography (MCOCT) implementation that profiles the contrast agent distribution in a sample by measuring the agent's spectral differential absorption. The method, spectra triangulation MCOCT, can effectively suppress contributions from spectrally dependent scatterings from the sample without a priori knowledge of the scattering properties. We demonstrate molecular imaging with this new MCOCT modality by mapping the distribution of indocyanine green, a FDA-approved infrared red dye, within a stage 54 Xenopus laevis