A Tale of Two Fractals: The Hofstadter Butterfly and The Integral Apollonian Gaskets

This paper unveils a mapping between a quantum fractal that describes a physical phenomena, and an abstract geometrical fractal. The quantum fractal is the Hofstadter butterfly discovered in 1976 in an iconic condensed matter problem of electrons moving in a two-dimensional lattice in a transverse magnetic field. The geometric fractal is the integer Apollonian gasket characterized in terms of a 300 BC problem of mutually tangent circles. Both of these fractals are made up of integers. In the Hofstadter butterfly, these integers encode the topological quantum numbers of quantum Hall conductivity. In the Apollonian gaskets an infinite number of mutually tangent circles are nested inside each other, where each circle has integer curvature. The mapping between these two fractals reveals a hidden threefold symmetry embedded in the kaleidoscopic images that describe the asymptotic scaling properties of the butterfly. This paper also serves as a mini review of these fractals, emphasizing their hierarchical aspects in terms of Farey fractions

Erratum:Molecular-scale thermoelectricity: as simple as 'ABC' (Nanoscale Adv. (2020) 2 (5329–5334) DOI: 10.1039/D0NA00772B)

The authors regret that the name of one of the authors (Troy L. R. Bennett) was shown incorrectly in the original article. The corrected author list is as shown above. The Royal Society of Chemistry apologises for these errors and any consequent inconvenience to authors and readers.</p

Seasonal size variation in the predatory cladoceran Bythotrephes cederstroemii in Lake Michigan

1.  Dry weight, body length and spine length were measured for the exotic cladoceran Bythotrephes cederstroemii collected from offshore and inshore stations in southeastern Lake Michigan. Average dry weight of each developmental stage exhibited seasonal variation by a factor of more than 5. 2.  Mean dry weight of Bythotrephes was closely correlated with water temperature. Contrary to the inverse relationship between water temperature and body size frequently observed for other invertebrates, the dry weight of Bythotrephes increased at higher ambient temperatures. 3.  No significant correlation was observed between abundances of major zooplankton taxa and the dry weight of Bythotrephes . An indirect effect of temperature on prey consumption may cause seasonal variation in dry weight of Bythotrephes in Lake Michigan. 4.  Distances between adjacent pairs of barbs, added to the caudal spine with each moult, are significantly shorter in Bythotrephes which produce resting eggs. Less material investment in the exoskeleton of sexually reproducing females was observed in favour of growth and reproduction.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/74641/1/j.1365-2427.1994.tb00842.x.pd

Identification of novel collagen breakdown products by human osteoclasts in vitro and in vivo

Bone resorption involves dissolution of minerals and enzymatic degradation of bone matrix. The primary enzyme is cathepsin K but other proteases including matrix metalloproteinases are involved. Some cathepsin K cleavage products have been partially identified, including cross-linked telopeptides of type I collagen. Here, we aimed to characterize the entire complement of bone breakdown products resulting from osteoclast action under controlled conditions in vitro. We analyzed extracellular media from human osteoclasts cultured on dentin substrates, using untargeted liquid chromatography mass spectrometry. We discovered 22 breakdown products resulting from osteoclastic action. These products were peptide fragment sequences that mapped to various collagen proteins present in bone and dentin. Nine peptide fragments mapped exclusively to collagen I alpha-1 chain (COL1A1), the most abundant protein in bone. We subsequently detected 21 of the fragment products, initially observed in vitro, in human serum and/or urine. Consistent positive correlations were observed between the COL1A1-specific peptide fragments and established bone biochemical markers in serum and urine. Ten urine fragments and two serum fragments markedly increased (p 2) in urine from patients with bone metastasis (24 out of 112) among a lung cancer cohort. The range of collagen peptide fragments we discovered as a direct result of osteoclast activity indicates a complexity of bone resorption pathways not previously known, extending beyond the known proteolytic cleavage events in bone collagen proteins. Monitoring biofluid concentrations of these novel bone markers has the potential to capture multiple pathways of bone resorption activity beyond the existing assays based on cathepsin K

The Atacama Cosmology Telescope: A Catalog of >4000 Sunyaev–Zel’dovich Galaxy Clusters

We present a catalog of 4195 optically confirmed Sunyaev–Zel'dovich (SZ) selected galaxy clusters detected with signal-to-noise ratio >4 in 13,211 deg2 of sky surveyed by the Atacama Cosmology Telescope (ACT). Cluster candidates were selected by applying a multifrequency matched filter to 98 and 150 GHz maps constructed from ACT observations obtained from 2008 to 2018 and confirmed using deep, wide-area optical surveys. The clusters span the redshift range 0.04 1 clusters, and a total of 868 systems are new discoveries. Assuming an SZ signal versus mass-scaling relation calibrated from X-ray observations, the sample has a 90% completeness mass limit of M500c > 3.8 × 1014 M⊙, evaluated at z = 0.5, for clusters detected at signal-to-noise ratio >5 in maps filtered at an angular scale of 2farcm4. The survey has a large overlap with deep optical weak-lensing surveys that are being used to calibrate the SZ signal mass-scaling relation, such as the Dark Energy Survey (4566 deg2), the Hyper Suprime-Cam Subaru Strategic Program (469 deg2), and the Kilo Degree Survey (825 deg2). We highlight some noteworthy objects in the sample, including potentially projected systems, clusters with strong lensing features, clusters with active central galaxies or star formation, and systems of multiple clusters that may be physically associated. The cluster catalog will be a useful resource for future cosmological analyses and studying the evolution of the intracluster medium and galaxies in massive clusters over the past 10 Gyr

Female Entrepreneurial Networks and Networking Activity in Technology-based Ventures:An Exploratory Study

The ability to develop and manage effective networks is a crucial entrepreneurial competence for venture establishment and growth. Relatively little attention has been paid to the network development and networking activities of female entrepreneurs in general, and even less to such activities in technology-based ventures.The limited existing evidence suggests that female entrepreneurs may develop different approaches to network development and participation to that of their male counterparts.This article presents findings from exploratory, qualitative research conducted in Northern Ireland, which focused on the nature and dynamics of female entrepreneurial networks in traditionally male-dominated science, engineering and technology-based ventures. Drawing upon information-rich evidence from 18 in-depth interviews with the lead female entrepreneurs of technology-based ventures, insights are presented into the nature and dynamics of female entrepreneurial networks and networking at different stages of the business life cycle

Effects of sleep deprivation on neural functioning: an integrative review

Sleep deprivation has a broad variety of effects on human performance and neural functioning that manifest themselves at different levels of description. On a macroscopic level, sleep deprivation mainly affects executive functions, especially in novel tasks. Macroscopic and mesoscopic effects of sleep deprivation on brain activity include reduced cortical responsiveness to incoming stimuli, reflecting reduced attention. On a microscopic level, sleep deprivation is associated with increased levels of adenosine, a neuromodulator that has a general inhibitory effect on neural activity. The inhibition of cholinergic nuclei appears particularly relevant, as the associated decrease in cortical acetylcholine seems to cause effects of sleep deprivation on macroscopic brain activity. In general, however, the relationships between the neural effects of sleep deprivation across observation scales are poorly understood and uncovering these relationships should be a primary target in future research

Curvature-bias corrections using a pseudomass method

Momentum measurements for very high momentum charged particles, such as muons from electroweak vector boson decays, are particularly susceptible to charge-dependent curvature biases that arise from misalignments of tracking detectors. Low momentum charged particles used in alignment procedures have limited sensitivity to coherent displacements of such detectors, and therefore are unable to fully constrain these misalignments to the precision necessary for studies of electroweak physics. Additional approaches are therefore required to understand and correct for these effects. In this paper the curvature biases present at the LHCb detector are studied using the pseudomass method in proton-proton collision data recorded at centre of mass energy √s = 13 TeV during 2016, 2017 and 2018. The biases are determined using Z → μ+μ- decays in intervals defined by the data-taking period, magnet polarity and muon direction. Correcting for these biases, which are typically at the 10-4 GeV-1 level, improves the Z → μ+μ- mass resolution by roughly 18% and eliminates several pathological trends in the kinematic-dependence of the mean dimuon invariant mass