Motivic Milnor fiber of a quasi-ordinary hypersurface

Let f : (Cd+1, 0) -> (C, 0) be a germ of complex analytic function such that its zero level defines an irreducible germ of quasi-ordinary hypersurface (S, 0) subset of (Cd+1, 0). We describe the motivic Igusa zeta function, the motivic Milnor fibre and the Hodge-Steenbrink spectrum of f at 0 in terms of topological invariants of (S, 0) subset of (Cd+1, 0)

Log canonical thresholds of quasi-ordinary hypersurface singularities

The log canonical thresholds of irreducible quasi-ordinary hypersurface singularities are computed, using an explicit list of pole candidates for the motivic zeta function found by the last two authors

Motivic Milnor fiber of a quasi-ordinary hypersurface

Let $f$ be a germ of complex analytic function at $({\mathbf{C}}^{d+1}, 0)$ such that its zero level defines an irreducible germ of quasi-ordinary hypersurface $(S,0)$. We describe the motivic Igusa zeta function, the motivic Milnor fibre and the Hodge-Steenbrink spectrum of $f$ at 0 in terms of topological invariants of the quasi-ordinary hypersurface $(S,0)$

The monodromy conjecture for plane meromorphic germs

International audienceA notion of Milnor fibration for meromorphic functions and the corresponding concepts of monodromy and monodromy zeta function have been introduced in [GZLM1]. In this article we define the topological zeta function for meromorphic germs and we study its poles in the plane case. We show that the poles do not behave as in the holomorphic case but still do satisfy a generalization of the monodromy conjecture

Long-term changes in corneal structure and tear inflammatory mediators after orthokeratology and LASIK

PURPOSE: To monitor changes in corneal structure and level of inflammatory mediators in tears of myopic patients following orthokeratology (OK) and laser in situ keratomileusis (LASIK). METHODS: Sixty-two myopic subjects were analyzed in this prospective study. Thirty-two had worn Paragon CRT contact lenses and 30 underwent standard LASIK. Thirty-two control subjects were also recruited. Pachometry and corneal topography were performed 12 months after both interventions. Tears were collected and assayed using ELISA for IL-6, IL-8, matrix metalloproteinase-9 (MMP-9), and epidermal growth factor (EGF). RESULTS: Corneal power decreased in the central area and increased in the paracentral area. Simultaneously, there was a central corneal thinning with mid-peripheral thickening for OK. No changes were observed for LASIK. In comparison with controls, IL-6, IL-8, MMP-9, and EGF levels were increased significantly for OK (P < 0.01). Only MMP-9 (P < 0.01) and EGF (P < 0.01) were increased for LASIK. Pro-inflammatory response was found to be associated with the degree of myopia in the OK group. The MMP-9 and EGF upregulation was linked to the presence of iron deposition in both groups, whereas increased levels of EGF were connected with the presence of myopic regression after LASIK. CONCLUSIONS: Both interventions involved important tissue reshaping. The physical presence of a reverse geometry contact lens caused certain markers to change significantly in comparison with no lens wear or LASIK in the long-term response. MMP-9 was significantly higher in tears of subjects presenting iron deposition after OK or LASIK, and EGF levels seemed to play an important role in postoperative refractive outcomes after LASIK.Supported by National Grant PI081380 from Instituto de Salud Carlos III, Spain, awarded to the Ocular Surface and Contact Lens Research Group GI-1750

On the precisión of the nucleator

Abstract The nucleator is a design unbiased method of local stereology for estimating the volume of a bounded object. The only information required lies in the intersection of the object with an isotropic random ray emanating from a fixed point (called the pivotal point) associated with the object. For instance, the volume of a neuron can be estimated from a random ray emanating from its nucleolus. The nucleator is extensively used in biosciences because it is efficient and easy to apply. The estimator variance can be reduced by increasing the number of rays. In an earlier paper a systematic sampling design was proposed, and theoretical variance predictors were derived, for the corresponding volume estimator. Being the only variance predictors hitherto available for the nucleator, our basic goal was to check their statistical performance by means of Monte Carlo resampling on computer reconstructions of real objects. As a plus, the empirical distribution of the volume estimator revealed statistical properties of practical relevance

On the precision of the isotropic Cavalieri design

ABSTRACT: The isotropic Cavalieri design is based on a isotropically oriented set of parallel systematic sections a constant distance apart. Its advantage over the ordinary Cavalieri design is twofold - first, besides volume it allows the unbiased estimation of surface area, and second, the error variance predictor for the volume estimator is much simpler, involving only the surface area of the object, and the distance between sections. In an earlier paper, the two hemispheres of a rat brain were arranged perpendicular to each other before sectioning, aiming at reducing the error variance with respect to other arrangements (such as the aligned one) by exploiting an intuitively plausible antithetic effect. Because the total surface area of the objects is unchanged under any arrangements, however, the error variance predictor for the volume estimator does not depend on object shape, which looks intriguing. Using reconstructions of the mentioned hemispheres, we dilucidate the aparent paradox by means of automatic Monte Carlo replications of the relevant volume estimates under the antithetic and the aligned arrangements.The authors acknowledge financial support from the Spanish project AYA2015-66357-R (MINECO/FEDER)

Upcoming Special Issue: “Artificial Intelligence, Data Science and E-health in Vision Research and Clinical Activity”

[Excerpt] Over the past 13 years Journal of Optometry has published a significant amount of scientific and clinical information covered in over 450 manuscripts published with Original Articles and Review Articles representing over 76% of all the documents making the journal rank high in the international databases.1,2 Considering the emerging technological advances applied to visual sciences the Journal will publish a Special Issue to include novel scientific contributions and novel applications of different branches of artificial intelligence, data science and other approaches to digitalization of vision science research and clinical activity. From basic visual function testing of visual acuity or contrast sensitivity3 to complex screening and diagnostic tools including visual field evaluation technology4 is about to change the paradigm of applying screening testing in flexible, portable and self-used platforms. This has the potential of expanding the capability of the population to self-screen their vision, receive warning messages to visit a clinician and potentially promote early diagnosis. This is also an opportunity to obtain massive amounts of data that might improve our understanding of visual science and vision health provision around the World. [...]- (undefined