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Stochastic Intensity for Minimal Repairs in Heterogeneous Populations
Cha, Ji Hwan,Finkelstein, Maxim Cambridge University Press 2011 Journal of applied probability Vol.48 No.3
<P>In this note we revisit the discussion on minimal repair in heterogeneous populations in Finkelstein (2004). We consider the corresponding stochastic intensities (intensity processes) for items in heterogeneous populations given available information on their operational history, i.e. the failure (repair) times and the time since the last failure (repair). Based on the improved definitions, the setup of Finkelstein (2004) is modified and the main results are corrected in accordance with the updating procedure for the conditional frailty distribution.</P>
Results for Burn-in of Systems Under External Shocks
Ji Hwan Cha,Finkelstein, Maxim IEEE 2013 IEEE transactions on reliability Vol.62 No.4
<P>Recently, Cha and Finkelstein (IEEE Transactions on Reliability, 2011) have proposed and studied the new burn-in procedures for systems operating in an environment with shocks. The systems were characterized by the strength, which in this context is the capability of the system to survive a shock of a given magnitude. That work implicitly assumed that the impacts of environmental shocks on a system in field usage are statistically independent. However, in reality, each subsequent survived shock updates the distribution of the system's strength, introducing certain dependence, and this was overlooked in the original paper. In the current paper, we develop the new stochastic approach, and modify the failure model of Cha and Finkelstein (IEEE Transactions on Reliability, 2011) accordingly to account for the described statistical dependence. We obtain rather general results that, most importantly, justify practical application of shocks of the controlled magnitude as a new method of burn-in. Specifically, we show that the probability of failure under an environmental shock is decreasing with time, and with the controlled magnitude of the burn-in shock. We also discuss the corresponding optimization problems.</P>
Diffusion Encoding Methods in MRI: Perspectives and Challenges
Alan Finkelstein,Xiaozhi Cao,Congyu Liao,Giovanni Schifitto,Jianhui Zhong 대한자기공명의과학회 2022 Investigative Magnetic Resonance Imaging Vol.26 No.4
Diffusion MRI (dMRI) is an important imaging modality that is used extensively to diagnose and monitor diseases. dMRI measures random motion of water molecules and helps elucidate microstructural properties of tissues. Optimal diffusion encoding paradigms have been developed to reduce acquisition time, minimize artifacts, and acquire high fidelity data needed for advanced modeling of tissue properties. To further probe microstructural properties, joint diffusion-relaxometry and diffusion weighted MR fingerprinting have garnered interest. A thorough knowledge of different diffusion encoding methods is essential to accurately encode diffusion in MR experiments. Here, we review fundamental physics of diffusion encoding methods, their associated challenges, and how to address them. Advanced diffusion acquisition methods are also discussed.
Song, Mimi,Finkelstein, Steven L.,Ashby, Matthew L. N.,Grazian, A.,Lu, Yu,Papovich, Casey,Salmon, Brett,Somerville, Rachel S.,Dickinson, Mark,Duncan, K.,Faber, Sandy M.,Fazio, Giovanni G.,Ferguson, He American Astronomical Society 2016 The Astrophysical Journal Vol.825 No.1
<P>We present galaxy stellar mass functions (GSMFs) at z = 4-8 from a rest-frame ultraviolet (UV) selected sample of similar to 4500 galaxies, found via photometric redshifts over an area of similar to 280 arcmin(2) in the Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey (CANDELS)/Great Observatories Origins Deep Survey (GOODS) fields and the Hubble Ultra Deep Field. The deepest Spitzer/IRAC data to date and the relatively large volume allow us to place a better constraint at both the low- and high-mass ends of the GSMFs compared to previous space-based studies from pre-CANDELS observations. Supplemented by a stacking analysis, we find a linear correlation between the rest-frame UV absolute magnitude at 1500 angstrom (M-UV) and logarithmic stellar mass (log M-*) that holds for galaxies with log(M-*/M-circle dot) less than or similar to 10. We use simulations to validate our method of measuring the slope of the log M-*-M-UV relation, finding that the bias is minimized with a hybrid technique combining photometry of individual bright galaxies with stacked photometry for faint galaxies. The resultant measured slopes do not significantly evolve over z = 4-8, while the normalization of the trend exhibits a weak evolution toward lower masses at higher redshift. We combine the log M-*-M-UV distribution with observed rest-frame UV luminosity functions at each redshift to derive the GSMFs, finding that the low-mass-end slope becomes steeper with increasing redshift from alpha = -1.55(-0.07)(+0.08) at z = 4 to alpha = -2.25(-0.35)(+0.72) at z = 8. The inferred stellar mass density, when integrated over M-* = 10(8)-10(13) M-circle dot, increases by a factor of 10(-2)(+30) between z = 7 and z = 4 and is in good agreement with the time integral of the cosmic star formation rate density.</P>
Stochastic Modeling for Environmental Stress Screening
Cha, Ji Hwan,Finkelstein, Maxim Cambridge University Press 2014 Journal of applied probability Vol.51 No.2
<P>Environmental stress screening (ESS) of manufactured items is used to reduce the occurrence of future failures that are caused by latent defects by eliminating the items with these defects. Some practical descriptions of the relevant ESS procedures can be found in the literature; however, the appropriate stochastic modeling and the corresponding thorough analysis have not been reported. In this paper we develop a stochastic model for the ESS, analyze the effect of this operation on the population characteristics of the screened items, and also consider the relevant optimization issues.</P>