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1. The Absolute Age of NGC 3201 Derived from Detached Eclipsing Binaries and the Hess Diagram

   https://doi.org/10.3847/1538-4357/ad59a9  

   Ying, Jiaqi_Martin; Chaboyer, Brian; Du, Wenxin (July 2024, The Astrophysical Journal)

   Abstract We estimate the absolute age of the globular cluster NGC 3201 using 10,000 sets of theoretical isochrones constructed through Monte Carlo simulation using the Dartmouth Stellar Evolution Program. These isochrones take into consideration the uncertainty introduced by the choice of stellar evolution parameters. We fit isochrones with three detached eclipsing binaries and obtained an age independent of distance. We also fit isochrones with differential reddening corrected Hubble Space Telescope photometry data utilizing two different Hess diagram-based fitting methods. Results from three different methods analyzing two different types of data agree to within 1σ, and we find the absolute age of NGC 3201 = 11.85 ± 0.74 Gyr. We also perform a variable importance analysis to study the uncertainty contribution from individual parameters, and we find the distance is the dominant source of uncertainty in photometry-based analysis, while total metallicity, helium abundance,α-element abundance, mixing length, and treatment of helium diffusion are an important source of uncertainties for all three methods. 

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2. Algorithm and Hardware Co-Design for FPGA Acceleration of Hamiltonian Monte Carlo Based No-U-Turn Sampler

   Wang, Y.; Li, P. (July 2021, The 32nd IEEE International Conference on Application-specific Systems, Architectures and Processors)

   null (Ed.)

   Monte Carlo (MC) methods are widely used in many research areas such as physical simulation, statistical analysis, and machine learning. Application of MC methods requires drawing fast mixing samples from a given probability distribution. Among existing sampling methods, the Hamiltonian Monte Carlo (HMC) utilizes gradient information during Hamiltonian simulation and can produce fast mixing samples at the highest efficiency. However, without carefully chosen simulation parameters for a specific problem, HMC generally suffers from simulation locality and computation waste. As a result, the No-U-Turn Sampler (NUTS) has been proposed to automatically tune these parameters during simulation and is the current state-of-the-art sampling algorithm. However, application of NUTS requires frequent gradient calculation of a given distribution and high-volume vector processing, especially for large-scale problems, leading to drawing an expensively large number of samples and a desire of hardware acceleration. While some hardware acceleration works have been proposed for traditional Markov Chain Monte Carlo (MCMC) and HMC methods, there is no existing work targeting hardware acceleration of the NUTS algorithm. In this paper, we present the first NUTS accelerator on FPGA while addressing the high complexity of this state-of-the-art algorithm. Our hardware and algorithm co-optimizations include an incremental resampling technique which leads to a more memory efficient architecture and pipeline optimization for multi-chain sampling to maximize the throughput. We also explore three levels of parallelism in the NUTS accelerator to further boost performance. Compared with optimized C++ NUTS package: RSTAN, our NUTS accelerator can reach a maximum speedup of 50.6X and an energy improvement of 189.7X. 

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3. Quasi-Monte Carlo Quasi-Newton in Variational Bayes

   Liu, Sifan; Owen, Art B. (January 2021, Journal of machine learning research)

   Many machine learning problems optimize an objective that must be measured with noise. The primary method is a first order stochastic gradient descent using one or more Monte Carlo (MC) samples at each step. There are settings where ill-conditioning makes second order methods such as limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) more effective. We study the use of randomized quasi-Monte Carlo (RQMC) sampling for such problems. When MC sampling has a root mean squared error (RMSE) of O(n−1/2) then RQMC has an RMSE of o(n−1/2) that can be close to O(n−3/2) in favorable settings. We prove that improved sampling accuracy translates directly to improved optimization. In our empirical investigations for variational Bayes, using RQMC with stochastic quasi-Newton method greatly speeds up the optimization, and sometimes finds a better parameter value than MC does. 

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4. Accelerating the estimation of collisionless energetic particle confinement statistics in stellarators using multifidelity Monte Carlo

   https://doi.org/10.1088/1741-4326/ac4777  

   Law, Frederick; Cerfon, Antoine; Peherstorfer, Benjamin (May 2022, Nuclear Fusion)

   Abstract In the design of stellarators, energetic particle confinement is a critical point of concern which remains challenging to study from a numerical point of view. Standard Monte Carlo (MC) analyses are highly expensive because a large number of particle trajectories need to be integrated over long time scales, and small time steps must be taken to accurately capture the features of the wide variety of trajectories. Even when they are based on guiding center trajectories, as opposed to full-orbit trajectories, these standard MC studies are too expensive to be included in most stellarator optimization codes. We present the first multifidelity Monte Carlo (MFMC) scheme for accelerating the estimation of energetic particle confinement in stellarators. Our approach relies on a two-level hierarchy, in which a guiding center model serves as the high-fidelity model, and a data-driven linear interpolant is leveraged as the low-fidelity surrogate model. We apply MFMC to the study of energetic particle confinement in a four-period quasi-helically symmetric stellarator, assessing various metrics of confinement. Stemming from the very high computational efficiency of our surrogate model as well as its sufficient correlation to the high-fidelity model, we obtain speedups of up to 10 with MFMC compared to standard MC. 

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5. Random Sampling-and-Averaging Techniques for Single-Photon Arrival-Time Detections in Quantum Applications: Theoretical Analysis and Realization Methodology

   https://doi.org/10.1109/TCSI.2021.3135833  

   Wu, Tony; Yang, Ruoman; Hsueh, Tzu-Chien (January 2022, IEEE Transactions on Circuits and Systems I: Regular Papers)

   Zhao, Weisheng (Ed.)

   A random sampling-and-averaging (RSA) technique based on stochastic Monte Carlo methods is described in this paper for enhancing the accuracy of single-photon arrival-time measurements down to sub-picosecond ranges in emerging quantum applications. The theoretical variances of both synchronous and asynchronous RSA techniques are presented in the mathematical formats and experimentally verified by the Monte Carlo simulations. Meanwhile, the methodology of converting the mathematical models into an almost all-digital low-power integrated-circuit is elaborated by a circuit-level example with the instruction of setting circuit parameters. Along with the superior measurement resolution, scalable dynamic ranges, high linearity, high noise immunity, and low power/area consumption, the primary limitation of the RSA techniques has also been addressed for the forthcoming conversion-rate enhancement techniques. 

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