• Journal of Korean Society of Transportation
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• v.27 no.2
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• pp.157-168
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• 2009

The random utility theory and the multinomial logit model (including a more recent variant--the mixed multinomial logit) derived from it have constituted a back bone for theoretical and empirical analyses of various travel demand features including mode choice. In their empirical applications, however, it is customary to specify random utilities which are linear in modal attributes such as time and cost, and in socio-economic variables. The linearity helps easy derivation of important information such as value of travel time savings by calculating marginal rate of substitution between time and cost. In this paper the author focuses on the very linearity of the random utilities. Taking into account the fact that the mode chooser is also labour supplier, commodity consumer as well as leisure-seeker, the author sets up a maximization model of the traveller, which encompasses various economic activities of the traveller. The author derive from the model the indifference curve defined on the space of modal attributes, time and cost and investigate under what conditions the random utility of the traveller becomes linear. It turns out that there exist the conditions under which the random utility is really linear in modal attributes, but the property does not hold when the traveller has a corner solution on the space of modal attributes, or when the primary utility function of the traveller is directly affected by labour provided and/or the travel time itself. As a corollary of the analysis, a random utility is suggested, approximated up to the second order of the variables involved for empirical studies of the field.

• Progress in Medical Physics
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• v.23 no.4
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• pp.317-325
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• 2012

The Varian PORTALVISION (Varian Medical Systems, US) shows significant overresponses as the off-center distance increases compared to the predicted dose. In order to correct the dose discrepancy, the off-axis correction is applied to VARIAN iX linear accelerators. The portal dose for $38{\times}28cm^2$ open field is acquired for 6 MV, 15 MV photon beams and also are predicted by PDIP algorithm under the same condition of the portal dose acquisition. The off-axis correction is applied by modifying the $40{\times}40cm^2$ diagonal beam profile data which is used for the beam profile calibration. The ratios between predicted dose and measured dose is modeled as a function of off-axis distance with the $4^{th}$ polynomial and is applied to the $40{\times}40cm^2$ diagonal beam profile data as the weight to correct measured dose by EPID detector. The discrepancy between measured dose and predicted dose is reduced from $4.17{\pm}2.76$ CU to $0.18{\pm}0.8$ CU for 6 MV photon beam and from $3.23{\pm}2.59$ CU to $0.04{\pm}0.85$ CU for 15 MV photon beam. The passing rate of gamma analysis for the pyramid fluence patten with the 4%, 4 mm criteria is improved from 98.7% to 99.1% for 6 MV photon beam, from 99.8% to 99.9% for 15 MV photon beam. IMRT QA is also performed for randomly selected Head and Neck and Prostate IMRT plans after applying the off-axis correction. The gamma passing rare is improved by 3% on average, for Head and Neck cases: $94.7{\pm}3.2%$ to $98.2{\pm}1.4%$, for Prostate cases: $95.5{\pm}2.6%$, $98.4{\pm}1.8%$. The gamma analysis criteria is 3%, 3 mm with 10% threshold. It is considered that the off-axis correction might be an effective and easily adaptable means for correcting the discrepancy between measured dose and predicted dose for IMRT QA using EPID in clinic.