In order to exhume the buried signatures of "missing planetary caustics" in the KMTNet data, we conducted a systematic anomaly search to the residuals from point-source point-lens fits, based on a modified version of the KMTNet EventFinder algorithm. This search reveals the lowest mass-ratio planetary caustic to date in the microlensing event OGLE-2019-BLG-1053, for which the planetary signal had not been noticed before. The planetary system has a planet-host mass ratio of q = (1.25±0.13)×10 −5 . A Bayesian analysis yields estimates of the mass of the host star, M host = 0.61 +0.29 −0.24 M , the mass of its planet, M planet = 2.48 +1.19 −0.98 M ⊕ , the projected planet-host separation, a ⊥ = 3.4 +0.5 −0.5 au, and the lens distance of D L = 6.8 +0.6 −0.9 kpc. The discovery of this very low mass-ratio planet illustrates the utility of our method and opens a new window for a large and homogeneous sample to study the microlensing planet-host mass-ratio function down to q ∼ 10 −5 .

We report the analysis of OGLE-2019-BLG-0960, which contains the smallest mass-ratio microlensing planet found to date (q = 1.2–1.6 × 10−5 at 1σ). Although there is substantial uncertainty in the satellite parallax measured by Spitzer, the measurement of the annual parallax effect combined with the finite source effect allows us to determine the mass of the host star (M L = 0.3–0.6 M ⊙), the mass of its planet (m p = 1.4–3.1 M ⊕), the projected separation between the host and planet (a ⊥ = 1.2–2.3 au), and the distance to the lens system (D L = 0.6–1.2 kpc). The lens is plausibly the blend, which could be checked with adaptive optics observations. As the smallest planet clearly below the break in the mass-ratio function, it demonstrates that current experiments are powerful enough to robustly measure the slope of the mass-ratio function below that break. We find that the cross-section for detecting small planets is maximized for planets with separations just outside of the boundary for resonant caustics and that sensitivity to such planets can be maximized by intensively monitoring events whenever they are magnified by a factor A > 5. Finally, an empirical investigation demonstrates that most planets showing a degeneracy between (s > 1) and (s < 1) solutions are not in the regime ( ∣ log s ∣ ≫ 0 ) for which the “close”/“wide” degeneracy was derived. This investigation suggests that there is a link between the “close”/“wide” and “inner/outer” degeneracies and also that the symmetry in the lens equation goes much deeper than symmetries uncovered for the limiting cases.

Periodical cicadas are known for unusually long and prime-numbered life cycles (13 and 17 years) for insects. To explain the evolution of prime-numbered reproductive intervals (life cycles), the hybridization hypothesis claims that prime numbers greatly reduce the chance of hybridization with other life cycles. We investigate the hybridization hypothesis using a simulation model. This model is a deterministic, discrete population model with three parameters: larval survival per year, clutch size, and emergence success. Reproductive intervals from 10 years to 20 years compete for survival in the simulations. The model makes three key assumptions: a Mendelian genetic system, random mating among broods of different life-cycle lengths, and integer population sizes. Longer life cycles have larger clutch sizes but suffer higher total mortality than shorter life cycles. Our results show that (1) nonprime-numbered reproductive intervals disappear rapidly in comparison to the selection among the various prime-numbered life cycles, (2) the selection of prime-numbered intervals happens only when populations are at the verge of extinction, and (3) the 13- and 17-year prime phenotypes evolve under certain conditions of the model and may coexist. The hybridization hypothesis is discussed in light of other hypotheses for the evolution of periodical cicada life cycles.

Periodical cicadas are well known for their prime-numbered life cycles (17 and 13 years) and their mass periodical emergences. The origination and persistence of prime-numbered cycles are explained by the hybridization hypothesis on the basis of their lower likelihood of hybridization with other cycles. Recently, we showed by using an integer-based numerical model that prime-numbered cycles are indeed selected for among 10-to 20-year cycles. Here, we develop a real-number-based model to investigate the factors affecting the selection of prime-numbered cycles. We include an Allee effect in our model, such that a critical population size is set as an extinction threshold. We compare the real-number models with and without the Allee effect. The results show that in the presence of an Allee effect, prime-numbered life cycles are most likely to persist and to be selected under a wide range of extinction thresholds.extinction thresholds ͉ hybridization ͉ Magicicada ͉ predator satiation

An aerial image mask inspection system for extreme ultraviolet lithography (EUVL) is developed. This system consists of microscopes using the same wavelength of light as is used for the exposure and produces a magnified image of defects on a mask. Using this microscope, amplitude defects on finished masks and phase defects on glass substrates are observed. A phase defect was formed by a multilayer coated on a line pattern with 5 nm high and 90 nm wide on a glass substrate. Although the defect detected is made beforehand, it is detected by reflection of the light which penetrated the multilayer. These results show that it is possible to detect the internal reflectivity distribution without depending on surface perturbations. We tried to observe “pit defects”, but it was not possible to observe these at this time. The pit defects, such as scratches on glass substrates may not become defects depending on the process of formation of the multilayer.

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A defect inspection technique on an extreme ultraviolet lithography mask is described. There are two kinds of defects, amplitude defects and phase defects due to the multilayer coating. The technique utilizes a microscope using the same 13.5 nm wavelength as the light used for exposure, and producing a magnified image of defects on a mask. Using this microscope, amplitude defects on practical masks and phase defects are observed. A phase defect was formed by a multilayer coated on a line pattern with a height of 5 nm and width of 90 nm on a glass substrate. Although the detected defect is made beforehand, it is detected by reflection of the light which penetrated inside of a multilayer. These results show that it is possible to detect the internal reflectivity distribution, without depending on surface perturbations.

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