The Asymptotic distribution of circles in the orbits of Kleinian groups

Let P be a locally finite circle packing in the plane invariant under a non-elementary Kleinian group Gamma and with finitely many Gamma-orbits. When Gamma is geometrically finite, we construct an explicit Borel measure on the plane which describes the asymptotic distribution of small circles in P, assuming that either the critical exponent of Gamma is strictly bigger than 1 or P does not contain an infinite bouquet of tangent circles glued at a parabolic fixed point of Gamma. Our construction also works for P invariant under a geometrically infinite group Gamma, provided Gamma admits a finite Bowen-Margulis-Sullivan measure and the Gamma-skinning size of P is finite. Some concrete circle packings to which our result applies include Apollonian circle packings, Sierpinski curves, Schottky dances, etc.Comment: 31 pages, 8 figures. Final version. To appear in Inventiones Mat

Functional and molecular analysis of proprioceptive sensory neuron excitability in mice

Neurons located in dorsal root ganglia (DRG) are crucial for transmitting peripheral sensations such as proprioception, touch, temperature, and nociception to the spinal cord before propagating these signals to higher brain structures. To date, difficulty in identifying modality-specific DRG neurons has limited our ability to study specific populations in detail. As the calcium-binding protein parvalbumin (PV) is a neurochemical marker for proprioceptive DRG cells we used a transgenic mouse line expressing green fluorescent protein (GFP) in PV positive DRGs, to study the functional and molecular properties of putative proprioceptive neurons. Immunolabeled DRGs showed a 100% overlap between GFP positive (GFP+) and PV positive cells, confirming the PVeGFP mouse accurately labeled PV neurons. Targeted patch-clamp recording from isolated GFP+ and GFP negative (GFP−) neurons showed the passive membrane properties of the two groups were similar, however, their active properties differed markedly. All GFP+ neurons fired a single spike in response to sustained current injection and their action potentials (APs) had faster rise times, lower thresholds and shorter half widths. A hyperpolarization-activated current (Ih) was observed in all GFP+ neurons but was infrequently noted in the GFP− population (100% vs. 11%). For GFP+ neurons, Ih activation rates varied markedly, suggesting differences in the underlying hyperpolarization-activated cyclic nucleotide-gated channel (HCN) subunit expression responsible for the current kinetics. Furthermore, quantitative polymerase chain reaction (qPCR) showed the HCN subunits 2, 1, and 4 mRNA (in that order) was more abundant in GFP+ neurons, while HCN 3 was more highly expressed in GFP− neurons. Likewise, immunolabeling confirmed HCN 1, 2, and 4 protein expression in GFP+ neurons. In summary, certain functional properties of GFP+ and GFP− cells differ markedly, providing evidence for modality-specific signaling between the two groups. However, the GFP+ DRG population demonstrates considerable internal heterogeneity when hyperpolarization-activated cyclic nucleotide-gated channel (HCN channel) properties and subunit expression are considered. We propose this heterogeneity reflects the existence of different peripheral receptors such as tendon organs, muscle spindles or mechanoreceptors in the putative proprioceptive neuron population

Research needs for optimising wastewater-based epidemiology monitoring for public health protection

Wastewater-based epidemiology (WBE) is an unobtrusive method used to observe patterns in illicit drug use, poliovirus, and severe acute respiratory syndrome coronavirus-2 (SARS-CoV-2). The pandemic and need for surveillance measures have led to the rapid acceleration of WBE research and development globally. With the infrastructure available to monitor SARS-CoV-2 from wastewater in 58 countries globally, there is potential to expand targets and applications for public health protection, such as other viral pathogens, antimicrobial resistance (AMR), pharmaceutical consumption, or exposure to chemical pollutants. Some applications have been explored in academic research but are not used to inform public health decision-making. We reflect on the current knowledge of WBE for these applications and identify barriers and opportunities for expanding beyond SARS-CoV-2. This paper critically reviews the applications of WBE for public health and identifies the important research gaps for WBE to be a useful tool in public health. It considers possible uses for pathogenic viruses, AMR, and chemicals. It summarises the current evidence on the following: (1) the presence of markers in stool and urine; (2) environmental factors influencing persistence of markers in wastewater; (3) methods for sample collection and storage; (4) prospective methods for detection and quantification; (5) reducing uncertainties; and (6) further considerations for public health use

Design of linear and star-shaped macromolecular organic semiconductors for photonic applications

P.J.S. and A.L.K. thank the EPSRC for funding under Grants EP/R03480X/1, EP/P02744X/2, and EP/N009908/2.One of the most desirable and advantageous attributes of organic materials chemistry is the ability to tune the molecular structure to achieve targeted physical properties. This can be performed to achieve specific values for the ionization potential or electron affinity of the material, the absorption and emission characteristics, charge transport properties, phase behavior, solubility, processability, and many other properties, which in turn can help push the limits of performance in organic semiconductor devices. A striking example is the ability to make subtle structural changes to a conjugated macromolecule to vary the absorption and emission properties of a generic chemical structure. In this Account, we demonstrate that target properties for specific photonic applications can be achieved from different types of semiconductor structures, namely, monodisperse star-shaped molecules, complex linear macromolecules, and conjugated polymers. The most appropriate material for any single application inevitably demands consideration of a trade-off of various properties; in this Account, we focus on applications such as organic lasers, electrogenerated chemiluminescence, hybrid light emitting diodes, and visible light communications. In terms of synthesis, atom and step economies are also important. The star-shaped structures consist of a core unit with 3 or 4 functional connection points, to which can be attached conjugated oligomers of varying length and composition. This strategy follows a convergent synthetic pathway and allows the isolation of target macromolecules in good yield, high purity, and absolute reproducibility. It is a versatile approach, providing a wide choice of constituent molecular units and therefore varying properties, while the products share many of the desirable attributes of polymers. Constructing linear conjugated macromolecules with multifunctionality can lead to complex synthetic routes and lower atom and step economies, inferior processability, and lower thermal or chemical stability, but these materials can be designed to provide a range of different targeted physical properties. Conventional conjugated polymers, as the third type of structure, often feature so-called “champion” properties. The synthetic challenge is mainly concerned with monomer synthesis, but the final polymerization sequence can be hard to control, leading to variable molecular weights and polydispersities and some degree of inconsistency in the properties of the same material between different synthetic batches. If a champion characteristic persists between samples, then the variation of other properties between batches can be tolerable, depending on the target application. In the case of polymers, we have chosen to study PPV-type polymers with bulky side groups that provide protection of their conjugated backbone from π–π stacking interactions. These polymers exhibit high photoluminescence quantum yields (PLQYs) in films and short radiative lifetimes and are an important benchmark to monodisperse star-shaped systems in terms of different absorption/emission regions. This Account therefore outlines the advantages and special features of monodisperse star-shaped macromolecules for photonic applications but also considers the two alternative classes of materials and highlights the pros and cons of each class of conjugated structure.Publisher PDFPeer reviewe

Quantum Kinetic Theory V: Quantum kinetic master equation for mutual interaction of condensate and noncondensate

A detailed quantum kinetic master equation is developed which couples the kinetics of a trapped condensate to the vapor of non-condensed particles. This generalizes previous work which treated the vapor as being undepleted.Comment: RevTeX, 26 pages and 5 eps figure

Terrestrial and submarine evidence for the extent and timing of the Last Glacial Maximum and the onset of deglaciation on the maritime-Antarctic and sub-Antarctic islands

This paper is the maritime and sub–Antarctic contribution to the Scientific Committee for Antarctic Research (SCAR) Past Antarctic Ice Sheet Dynamics (PAIS) community Antarctic Ice Sheet reconstruction. The overarching aim for all sectors of Antarctica was to reconstruct the Last Glacial Maximum (LGM) ice sheet extent and thickness, and map the subsequent deglaciation in a series of 5000 year time slices. However, our review of the literature found surprisingly few high quality chronological constraints on changing glacier extents on these timescales in the maritime and sub–Antarctic sector. Therefore, in this paper we focus on an assessment of the terrestrial and offshore evidence for the LGM ice extent, establishing minimum ages for the onset of deglaciation, and separating evidence of deglaciation from LGM limits from those associated with later Holocene glacier fluctuations. Evidence included geomorphological descriptions of glacial landscapes, radiocarbon dated basal peat and lake sediment deposits, cosmogenic isotope ages of glacial features and molecular biological data. We propose a classification of the glacial history of the maritime and sub–Antarctic islands based on this assembled evidence. These include: (Type I) islands which accumulated little or no LGM ice; (Type II) islands with a limited LGM ice extent but evidence of extensive earlier continental shelf glaciations; (Type III) seamounts and volcanoes unlikely to have accumulated significant LGM ice cover; (Type IV) islands on shallow shelves with both terrestrial and submarine evidence of LGM (and/or earlier) ice expansion; (Type V) Islands north of the Antarctic Polar Front with terrestrial evidence of LGM ice expansion; and (Type VI) islands with no data. Finally, we review the climatological and geomorphological settings that separate the glaciological history of the islands within this classification scheme

Ultra-wide coverage VLC system with alignment-free receiver

In this work we present an ultra-wide coverage visible light communication (VLC) system based on a mechanical beam steering system at the transmitter terminal and a fluorescent optical concentrator at the receiver. The transmitter and receiver full field of view (FFOV) are 100° and 120°, respectively. The coverage area of the transmitter system at 2m is 12.5m2 and a data link of 300Mbps has been achieved at this range.Postprin