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In this paper, a discrete Markov chain model is developed to describe the inventory at a bike share station. The uniqueness of solutions is first studied. Then the model calibration is considered by investigating a constrained optimization problem. Numerical simulations involving real data are conducted to demonstrate the model effectiveness as well. 

Key Points The “stable” warm late Pliocene ∼3.3–3.1 million years ago was a time of climate transition, especially in the southern hemisphere Ocean temperatures and ice sheets evolved asynchronously 3.3–2.4 Ma during the onset and intensification of Northern Hemisphere Glaciation Climate variability evolved in complex, non‐uniform ways, most strongly expressed in northern mid‐latitude sea‐surface temperature records 

Abstract We describe updated scientific goals for the wide-field, millimeter-wave survey that will be produced by the Simons Observatory (SO). Significant upgrades to the 6-meter SO Large Aperture Telescope (LAT) are expected to be complete by 2028, and will include a doubled mapping speed with 30,000 new detectors and an automated data reduction pipeline. In addition, a new photovoltaic array will supply most of the observatory's power. The LAT survey will cover about 60% of the sky at a regular observing cadence, with five times the angular resolution and ten times the map depth of thePlancksatellite. The science goals are to: (1) determine the physical conditions in the early universe and constrain the existence of new light particles; (2) measure the integrated distribution of mass, electron pressure, and electron momentum in the late-time universe, and, in combination with optical surveys, determine the neutrino mass and the effects of dark energy via tomographic measurements of the growth of structure at redshifts z ≲ 3; (3) measure the distribution of electron density and pressure around galaxy groups and clusters, and calibrate the effects of energy input from galaxy formation on the surrounding environment; (4) produce a sample of more than 30,000 galaxy clusters, and more than 100,000 extragalactic millimeter sources, including regularly sampled AGN light-curves, to study these sources and their emission physics; (5) measure the polarized emission from magnetically aligned dust grains in our Galaxy, to study the properties of dust and the role of magnetic fields in star formation; (6) constrain asteroid regoliths, search for Trans-Neptunian Objects, and either detect or eliminate large portions of the phase space in the search for Planet 9; and (7) provide a powerful new window into the transient universe on time scales of minutes to years, concurrent with observations from the Vera C. Rubin Observatory of overlapping sky. 

Strain-sensitive Ba x Sr 1− x TiO 3 perovskite systems are widely used because of their superior nonlinear dielectric behaviors. In this research, new heterostructures including paraelectric Ba 0.5 Sr 0.5 TiO 3 (BSTO) and ferroelectric BaTiO 3 (BTO) materials were epitaxially fabricated on flexible muscovite substrate. Through simple bending, the application of mechanical force can regulate the dielectric constant of BSTO from −77 to 36% and the channel current of BTO-based ferroelectric field effect transistor by two orders. The detailed mechanism was studied through the exploration of phase transition and determination of band structure. In addition, the phase-field simulations were implemented to provide theoretical support. This research opens a new avenue for mechanically controllable components based on high-quality oxide heteroepitaxy. 

ABSTRACT We present a detection of the splashback feature around galaxy clusters selected using the Sunyaev–Zel’dovich (SZ) signal. Recent measurements of the splashback feature around optically selected galaxy clusters have found that the splashback radius, rsp, is smaller than predicted by N-body simulations. A possible explanation for this discrepancy is that rsp inferred from the observed radial distribution of galaxies is affected by selection effects related to the optical cluster-finding algorithms. We test this possibility by measuring the splashback feature in clusters selected via the SZ effect in data from the South Pole Telescope SZ survey and the Atacama Cosmology Telescope Polarimeter survey. The measurement is accomplished by correlating these cluster samples with galaxies detected in the Dark Energy Survey Year 3 data. The SZ observable used to select clusters in this analysis is expected to have a tighter correlation with halo mass and to be more immune to projection effects and aperture-induced biases, potentially ameliorating causes of systematic error for optically selected clusters. We find that the measured rsp for SZ-selected clusters is consistent with the expectations from simulations, although the small number of SZ-selected clusters makes a precise comparison difficult. In agreement with previous work, when using optically selected redMaPPer clusters with similar mass and redshift distributions, rsp is ∼2σ smaller than in the simulations. These results motivate detailed investigations of selection biases in optically selected cluster catalogues and exploration of the splashback feature around larger samples of SZ-selected clusters. Additionally, we investigate trends in the galaxy profile and splashback feature as a function of galaxy colour, finding that blue galaxies have profiles close to a power law with no discernible splashback feature, which is consistent with them being on their first infall into the cluster.