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  1. We initiate the study of federated reinforcement learning under environmental heterogeneity by considering a policy evaluation problem. Our setup involves agents interacting with environments that share the same state and action space but differ in their reward functions and state transition kernels. Assuming agents can communicate via a central server, we ask: Does exchanging information expedite the process of evaluating a common policy? To answer this question, we provide the first comprehensive finite-time analysis of a federated temporal difference (TD) learning algorithm with linear function approximation, while accounting for Markovian sampling, heterogeneity in the agents' environments, and multiple local updates to save communication. Our analysis crucially relies on several novel ingredients: (i) deriving perturbation bounds on TD fixed points as a function of the heterogeneity in the agents' underlying Markov decision processes (MDPs); (ii) introducing a virtual MDP to closely approximate the dynamics of the federated TD algorithm; and (iii) using the virtual MDP to make explicit connections to federated optimization. Putting these pieces together, we rigorously prove that in a low-heterogeneity regime, exchanging model estimates leads to linear convergence speedups in the number of agents. 
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  2. We consider Shimura varieties for orthogonal or spin groups acting on hermitian symmetric domains of type IV. We give regular $p$ -adic integral models for these varieties over odd primes $p$ at which the level subgroup is the connected stabilizer of a vertex lattice in the orthogonal space. Our construction is obtained by combining results of Kisin and the first author with an explicit presentation and resolution of a corresponding local model. 
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  3. null (Ed.)
    Let $(G,\unicode[STIX]{x1D707})$ be a pair of a reductive group $G$ over the $p$ -adic integers and a minuscule cocharacter $\unicode[STIX]{x1D707}$ of $G$ defined over an unramified extension. We introduce and study ‘ $(G,\unicode[STIX]{x1D707})$ -displays’ which generalize Zink’s Witt vector displays. We use these to define certain Rapoport–Zink formal schemes purely group theoretically, i.e. without $p$ -divisible groups. 
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  4. An integrated urban transportation system usually consists of multiple transport modes that have complementary characteristics of capacities, speeds, and costs, facilitating smooth passenger transfers according to planned schedules. However, such an integration is not designed to operate under disruptive events, e.g., a signal failure at a subway station or a breakdown of a bus, which have rippling effects on passenger demand and significantly increase delays. To address these disruptive events, current solutions mainly rely on a substitute service to transport passengers from and to affected areas using adhoc schedules. To fully utilize heterogeneous transportation systems under disruptive events, we design a service called eRoute based on a hierarchical receding horizon control framework to automatically reroute, reschedule, and reallocate multi-mode transportation systems based on real-time and predicted demand and supply. Focusing on an integration of subway and bus, we implement and evaluate eRoute with large datasets including (i) a bus system with 13,000 buses, (ii) a subway system with 127 subway stations, (iii) an automatic fare collection system with a total of 16,840 readers and 8 million card users from a metropolitan city. The data-driven evaluation results show that our solution improves the ratio of served passengers (RSP) by up to 11.5 times and reduces the average traveling time by up to 82.1% compared with existing solutions. 
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  5. Abstract The global network of gravitational-wave observatories now includes five detectors, namely LIGO Hanford, LIGO Livingston, Virgo, KAGRA, and GEO 600. These detectors collected data during their third observing run, O3, composed of three phases: O3a starting in 2019 April and lasting six months, O3b starting in 2019 November and lasting five months, and O3GK starting in 2020 April and lasting two weeks. In this paper we describe these data and various other science products that can be freely accessed through the Gravitational Wave Open Science Center at https://gwosc.org . The main data set, consisting of the gravitational-wave strain time series that contains the astrophysical signals, is released together with supporting data useful for their analysis and documentation, tutorials, as well as analysis software packages. 
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    Free, publicly-accessible full text available July 28, 2024
  6. Abstract We use 47 gravitational wave sources from the Third LIGO–Virgo–Kamioka Gravitational Wave Detector Gravitational Wave Transient Catalog (GWTC–3) to estimate the Hubble parameter H ( z ), including its current value, the Hubble constant H 0 . Each gravitational wave (GW) signal provides the luminosity distance to the source, and we estimate the corresponding redshift using two methods: the redshifted masses and a galaxy catalog. Using the binary black hole (BBH) redshifted masses, we simultaneously infer the source mass distribution and H ( z ). The source mass distribution displays a peak around 34 M ⊙ , followed by a drop-off. Assuming this mass scale does not evolve with the redshift results in a H ( z ) measurement, yielding H 0 = 68 − 8 + 12 km s − 1 Mpc − 1 (68% credible interval) when combined with the H 0 measurement from GW170817 and its electromagnetic counterpart. This represents an improvement of 17% with respect to the H 0 estimate from GWTC–1. The second method associates each GW event with its probable host galaxy in the catalog GLADE+ , statistically marginalizing over the redshifts of each event’s potential hosts. Assuming a fixed BBH population, we estimate a value of H 0 = 68 − 6 + 8 km s − 1 Mpc − 1 with the galaxy catalog method, an improvement of 42% with respect to our GWTC–1 result and 20% with respect to recent H 0 studies using GWTC–2 events. However, we show that this result is strongly impacted by assumptions about the BBH source mass distribution; the only event which is not strongly impacted by such assumptions (and is thus informative about H 0 ) is the well-localized event GW190814. 
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    Free, publicly-accessible full text available June 1, 2024
  7. Abstract We present the results of a model-based search for continuous gravitational waves from the low-mass X-ray binary Scorpius X-1 using LIGO detector data from the third observing run of Advanced LIGO and Advanced Virgo. This is a semicoherent search that uses details of the signal model to coherently combine data separated by less than a specified coherence time, which can be adjusted to balance sensitivity with computing cost. The search covered a range of gravitational-wave frequencies from 25 to 1600 Hz, as well as ranges in orbital speed, frequency, and phase determined from observational constraints. No significant detection candidates were found, and upper limits were set as a function of frequency. The most stringent limits, between 100 and 200 Hz, correspond to an amplitude h 0 of about 10 −25 when marginalized isotropically over the unknown inclination angle of the neutron star’s rotation axis, or less than 4 × 10 −26 assuming the optimal orientation. The sensitivity of this search is now probing amplitudes predicted by models of torque balance equilibrium. For the usual conservative model assuming accretion at the surface of the neutron star, our isotropically marginalized upper limits are close to the predicted amplitude from about 70 to 100 Hz; the limits assuming that the neutron star spin is aligned with the most likely orbital angular momentum are below the conservative torque balance predictions from 40 to 200 Hz. Assuming a broader range of accretion models, our direct limits on gravitational-wave amplitude delve into the relevant parameter space over a wide range of frequencies, to 500 Hz or more. 
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