Wataru Komatsubara | Searcharxiv

arXiv2024

Active Adaptive Experimental Design for Treatment Effect Estimation with Covariate Choices

This study designs an adaptive experiment for efficiently estimating average treatment effects (ATEs). In each round of our adaptive experiment, an experimenter sequentially samples an experimental unit, assigns a treatment, and observes the corresponding outcome immediately. At the end of the experiment, the experimenter estimates an ATE using the gathered samples. The objective is to estimate the ATE with a smaller asymptotic variance. Existing studies have designed experiments that adaptively optimize the propensity score (treatment-assignment probability). As a generalization of such an approach, we propose optimizing the covariate density as well as the propensity score. First, we derive the efficient covariate density and propensity score that minimize the semiparametric efficiency bound and find that optimizing both covariate density and propensity score minimizes the semiparametric efficiency bound more effectively than optimizing only the propensity score. Next, we design an adaptive experiment using the efficient covariate density and propensity score sequentially estimated during the experiment. Lastly, we propose an ATE estimator whose asymptotic variance aligns with the minimized semiparametric efficiency bound.

stat.ME↗

arXiv2022

Critical Power for Temporal-Pulse Collapse in Third-Harmonic Generation

The self-trapping critical power of light propagation is one of the key physical quantities characterizing nonlinear-beam propagation. Above the critical power, the spatial and temporal profiles of the beam deviate from its original shapes. Therefore, the critical power is considered an important indicator in nonlinear optical phenomena, such as filamentation and laser processing. However, although the concept of the critical power has been established for fundamental waves, it remains unclear if the power-dependent phenomena can also be observed in harmonic generation because of the complex interplay of nonlinear-propagation effects and ionization-plasma effects. In this study, we find the critical power for the third-harmonic generation; the criterion for whether or not temporal-pulse collapse occurs in the third-harmonic generation is determined only by the incident power. Experiments show that a certain incident power exists, at which the third-harmonic power exerts a specific dependence, independent of the focusing conditions. This incident power is approximately six times lower than the self-trapping critical power of the fundamental pulse, which indicates that it is unique to the third-harmonic generation. Numerical calculations reveal that at this incident power, the third-harmonic pulse begins to collapse temporally. Furthermore, the numerical calculations reproduce the experimental results without the nonlinear effects of the fundamental pulse, dispersion effect, and ionization-plasma effects. This shows that the pulse collapse is due to the interference effects from the third-order nonlinear term, which disappears after long-distance propagation due to phase mismatch, and higher-order nonlinear terms. This study demonstrates the existence of the critical power for harmonic pulses and show that higher-order nonlinear effects on the harmonics can yield a universal phenomenon.

physics.optics↗