Hodge ideals and spectrum of isolated hypersurface singularities

We introduce Hodge ideal spectrum for isolated hypersurface singularities to see the difference between the Hodge ideals and the microlocal $V$-filtration modulo the Jacobian ideal. Via the Tjurina subspectrum, we can compare the Hodge ideal spectrum with the Steenbrink spectrum which can be defined by the microlocal $V$-filtration. As a consequence of a formula of Mustata and Popa, these two spectra coincide in the weighted homogeneous case. We prove sufficient conditions for their coincidence and non-coincidence in some non-weighted-homogeneous cases where the defining function is semi-weighted-homogeneous or with non-degenerate Newton boundary in most cases. We also show that the convenience condition can be avoided in a formula of Zhang for the non-degenerate case, and present an example where the Hodge ideals are not weakly decreasing even modulo the Jacobian ideal.Comment: 29 page

Spectrum of non-degenerate functions with simplicial Newton polyhedra

We prove a simple formula for the spectrum of non-degenerate functions of 3 variables with simplicial convenient Newton polyhedra (which does not hold in the non-simplicial case) generalizing a picture of Arnold in the 2 variable case. Combining this with Steenbrink's conjecture on a refinement of Yomdin's formula (proved long ago), we can deduce a formula for the spectrum of certain non-isolated surface singularities with simplicial non-degenerate Newton boundaries.Comment: 17 page

Fabrication of a spherical inclusion phantom for validation of magnetic resonance-based magnetic susceptibility imaging

© 2019 Kim et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.Fabrication of a spherical multi-compartment MRI phantom is demonstrated that can be used to validate magnetic resonance (MR)-based susceptibility imaging reconstruction. The phantom consists of a 10 cm diameter gelatin sphere that encloses multiple smaller gelatin spheres doped with different concentrations of paramagnetic contrast agents. Compared to previous multi-compartment phantoms with cylindrical geometry, the phantom provides the following benefits: (1) no compartmental barrier materials are used that can introduce signal voids and spurious phase; (2) compartmental geometry is reproducible; (3) spherical susceptibility boundaries possess a ground-truth analytical phase solution for easy experimental validation; (4) spherical geometry of the overall phantom eliminates background phase due to air-phantom boundary in any scan orientation. The susceptibility of individual compartments can be controlled independently by doping. During fabrication, formalin crosslinking and water-proof surface coating effectively blocked water diffusion between the compartments to preserve the phantom’s integrity. The spherical shapes were realized by molding the inner gel compartments in acrylic spherical shells, 3 cm in diameter, and constructing the whole phantom inside a larger acrylic shell. From gradient echo images obtained at 3T, we verified that the phantom produced phase images in agreement with the theoretical prediction. Factors that limit the agreement include: air bubbles trapped at the gel interfaces, imperfect magnet shimming, and the susceptibility of external materials such as the phantom support hardware. The phantom images were used to validate publicly available codes for quantitative susceptibility mapping. We believe that the proposed phantom can provide a useful testbed for validation of MR phase imaging and MR-based magnetic susceptibility reconstructio

Clinical Study A Comparison of Clinical Outcomes of Dislocated Intraocular Lens Fixation between In Situ Refixation and Conventional Exchange Technique Combined with Vitrectomy

. Purpose. To evaluate surgical efficacy of in situ refixation technique for dislocated posterior chamber intraocular lens (PCIOL). Methods. This was a single-center retrospective case series. 34 patients (34 eyes) who underwent sclera fixation for dislocated IOLs combined with vitrectomy were studied. Of 34 eyes, 17 eyes underwent IOL exchange and the other 17 eyes underwent in situ refixation. Results. Mean follow-up period was 6 months. Mean logMAR best corrected visual acuity (BCVA) was not significantly different between the groups 6 months after surgery (0.10 ± 0.03 in the IOL exchange group and 0.10 ± 0.05 in the refixation group; = 0.065). Surgically induced astigmatism (SIA) was significantly lower in the refixation group (0.79 ± 0.41) than in the IOL exchange group (1.29 ± 0.46) ( = 0.004) at 3 months, which persisted to 6 months (1.13 ± 0.18 in the IOL exchange group and 0.74 ± 0.11 in the refixation group; = 0.006). Postoperative complications occurred in 3 eyes in the IOL exchange group (17.6%) and 2 eyes in the refixation group (11.8%). However, all of the patients were well managed without additional surgery. Conclusion. The in situ refixation technique should be preferentially considered if surgery is indicated since it seemed to produce a sustained less SIA compared to IOL exchange

Stimulated penetrating keratoplasty using real-time virtual intraoperative surgical optical coherence tomography

An intraoperative surgical microscope is an essential tool in a neuro-or ophthalmological surgical environment. Yet, it has an inherent limitation to classify subsurface information because it only provides the surface images. To compensate for and assist in this problem, combining the surgical microscope with optical coherence tomography (OCT) has been adapted. We developed a real-time virtual intraoperative surgical OCT (VISOCT) system by adapting a spectral-domain OCT scanner with a commercial surgical microscope. Thanks to our custommade beam splitting and image display subsystems, the OCT images and microscopic images are simultaneously visualized through an ocular lens or the eyepiece of the microscope. This improvement helps surgeons to focus on the operation without distraction to view OCT images on another separate display. Moreover, displaying the OCT live images on the eyepiece helps surgeon's depth perception during the surgeries. Finally, we successfully processed stimulated penetrating keratoplasty in live rabbits. We believe that these technical achievements are crucial to enhance the usability of the VISOCT system in a real surgical operating condition.open0

A Mixed-effects Height-Diameter Model for Pinus densiflora Trees in Gangwon Province, Korea

A new mixed-effects model was developed that predicts individual-tree total height for Pinus densiflora trees in Gangwon province as a function of individual-tree diameter (cm). The mixed-effects model contains two random-effects parameters. Maximum likelihood estimation was used to fit the model to 560 height-diameter observations of individual trees measured throughout Gwangwon province in 2007 as part of the National Forest Inventory Program in Korea. The new model is an improvement over fixed effects models because it can be calibrated to a local area, such as an inventory plot or individual stand. The new model also appears to be an improvement over the Forest Resources Evaluation and Prediction Program for the ten calibration trees used in this study. An example is provided that describes how to estimate the random-effects parameters using ten calibration trees