Hermitian symmetric polynomials and CR complexity

Properties of Hermitian forms are used to investigate several natural questions from CR Geometry. To each Hermitian symmetric polynomial we assign a Hermitian form. We study how the signature pairs of two Hermitian forms behave under the polynomial product. We show, except for three trivial cases, that every signature pair can be obtained from the product of two indefinite forms. We provide several new applications to the complexity theory of rational mappings between hyperquadrics, including a stability result about the existence of non-trivial rational mappings from a sphere to a hyperquadric with a given signature pair.Comment: 19 pages, latex, fixed typos, to appear in Journal of Geometric Analysi

Obstructions to embeddability into hyperquadrics and explicit examples

We give series of explicit examples of Levi-nondegenerate real-analytic hypersurfaces in complex spaces that are not transversally holomorphically embeddable into hyperquadrics of any dimension. For this, we construct invariants attached to a given hypersurface that serve as obstructions to embeddability. We further study the embeddability problem for real-analytic submanifolds of higher codimension and answer a question by Forstneri\v{c}.Comment: Revised version, appendix and references adde

The experience of visual art for people living with mild-to-moderate vision loss

Background: Visual art can enhance wellbeing and quality-of-life; however, the experience of visual art for people with mild-to-moderate vision loss has not been examined. Methods: Eight participants (6 females, 2 males; Mean age = 81 years, SD = 7.9, range 70–91 years; 4 with mild vision loss and 4 with moderate vision loss based on binocular visual acuity) completed a mixed-methods study comprising: a semi-structured interview on visual art experience; an eye examination; and questionnaires about visual functioning and quality-of-life. Results: Various themes were identified: visual perception of art (e.g. altered colours, visual distortions, etc.), viewing conditions, elements of art, personal preference, deriving meaning, appreciation of art, impact of impaired visual perception, and social aspects of art. Conclusions: The overall experience of art is influenced by how an individual sees, perceives, and makes meaning from art. Even mild vision loss can impair this experience and impact emotional and social wellbeing.</p

The aspherical explosion of the Type IIP SN 2017gmr

Type IIP supernovae (SNe IIP), which represent the most common class of core-collapse (CC) SNe, show a rapid increase in continuum polarization just after entering the tail phase. This feature can be explained by a highly asymmetric helium core, which is exposed when the hydrogen envelope becomes transparent. Here we report the case of an SN IIP (SN 2017gmr) that shows an unusually early rise of the polarization, 30 d before the start of the tail phase. This implies that SN 2017gmr is an SN IIP that has very extended asphericity. The asymmetries are not confined to the helium core, but reach out to a significant part of the outer hydrogen envelope, hence clearly indicating a marked intrinsic diversity in the aspherical structure of CC explosions. These observations provide new constraints on the explosion mechanism, where viable models must be able to produce such extended deviations from spherical symmetry, and account for the observed geometrical diversity

Discriminating early-stage diabetic retinopathy with subjective and objective perimetry

Introduction: To prevent progression of early-stage diabetic retinopathy, we need functional tests that can distinguish multiple levels of neural damage before classical vasculopathy. To that end, we compared multifocal pupillographic objective perimetry (mfPOP), and two types of subjective automated perimetry (SAP), in persons with type 2 diabetes (PwT2D) with either no retinopathy (noDR) or mild to-moderate non-proliferative retinopathy (mmDR). Methods: Both eyes were assessed by two mfPOP test methods that present stimuli within either the central ±15° (OFA15) or ±30° (OFA30), each producing per-region sensitivities and response delays. The SAP tests were 24-2 Short Wavelength Automated Perimetry and 24-2 Matrix perimetry. Results: Five of eight mfPOP global indices were significantly different between noDR and mmDR eyes, but none of the equivalent measures differed for SAP. Per-region mfPOP identified significant hypersensitivity and longer delays in the peripheral visual field, verifying earlier findings. Diagnostic power for discrimination of noDR vs. mmDR, and normal controls vs. PwT2D, was much higher for mfPOP than SAP. The mfPOP per-region delays provided the best discrimination. The presence of localized rather than global changes in delay ruled out iris neuropathy as a major factor. Discussion: mfPOP response delays may provide new surrogate endpoints for studies of interventions for early-stage diabetic eye damage.</p