Cone In Space Research Articles

Об изменении кривизны конформно-плоской метрики при преобразовании Лежандра

Известно, что теория конформно-плоских ри-мановых метрик тесно связана с псевдоевклидовой геометрией, что обусловлено существованием канонического изометрического вложения конформно-плоской метрики в изотропный конус псевдоевклидова пространства. Впервые этот факт был замечен X. Бринкманном, а позднее использован в работах Н. Кюипера. Геометрия однородных римановых многообразий с конформноплоской римановой метрикой изучалась в работах А.Д. Алексеевского и Б.Н. Кимельфельда, в которых дана их классификация. В неоднородном случае подобной классификации не существует, поэтому при исследовании конформноплоских римановых многообразий используются ограничения различного типа: либо на размерность многообразия, либо на топологическое строение, либо на различные типы кривизны римано-вого многообразия с конформно-плоской метрикой. В последнем случае хорошо известны теоремы об однородных римановых многообразиях с конформно-плоской метрикой ограниченной одномерной кривизны, полученные В.В. Славским и Е.Д. Родионовым. В данной работе исследуется поведение одномерной кривизны и кривизны Риччи при преобразовании Лежандра конформноплоской римановой метрики.DOI 10.14258/izvasu(2018)4-16

Cone Photoreceptor Cell Segmentation and Diameter Measurement on Adaptive Optics Images Using Circularly Constrained Active Contour Model.

PurposeCone photoreceptor cells can be noninvasively imaged in the living human eye by using nonconfocal adaptive optics scanning ophthalmoscopy split detection. Existing metrics, such as cone density and spacing, are based on simplifying cone photoreceptors to single points. The purposes of this study were to introduce a computer-aided approach for segmentation of cone photoreceptors, to apply this technique to create a normal database of cone diameters, and to demonstrate its use in the context of existing metrics.MethodsCone photoreceptor segmentation is achieved through a circularly constrained active contour model (CCACM). Circular templates and image gradients attract active contours toward cone photoreceptor boundaries. Automated segmentation from in vivo human subject data was compared to ground truth established by manual segmentation. Cone diameters computed from curated data (automated segmentation followed by manual removal of errors) were compared with histology and published data.ResultsOverall, there was good agreement between automated and manual segmentations and between diameter measurements (n = 5191 cones) and published histologic data across retinal eccentricities ranging from 1.35 to 6.35 mm (temporal). Interestingly, cone diameter was correlated to both cone density and cone spacing (negatively and positively, respectively; P < 0.01 for both). Application of the proposed automated segmentation to images from a patient with late-onset retinal degeneration revealed the presence of enlarged cones above individual reticular pseudodrusen (average 23.0% increase, P < 0.05).ConclusionsCCACM can accurately segment cone photoreceptors on split detection images across a range of eccentricities. Metrics derived from this automated segmentation of adaptive optics retinal images can provide new insights into retinal diseases.

Superconformal blocks from Wilson lines with loop corrections

We compute the mathcal{N}=1 superconformal blocks from the networks of open Wilson lines in the osp(1|2) Chern-Simons theory in the expansion of large central charge c. We first reproduce the 1/c correction of conformal weight from an open Wilson line by adopting the regularization prescription developed in our previous works. We then obtain the closed form expressions of superconformal blocks including 1/c corrections, which were not available before. We also examine heavy operators corresponding to supersymmetric conical spaces, and the geometry is quantized by utilizing the coadjoint orbits of the super Virasoro group. Superconformal blocks involving these operators are also examined.

High-resolution imaging of photoreceptors in healthy human eyes using an adaptive optics retinal camera.

To determine the effects of age on perifoveal cone density in healthy subjects using adaptive optics. Healthy subjects of various ages were imaged using an adaptive optics retinal camera (RTX-1® Imagine Eyes, Orsay, France). All patients underwent a comprehensive ophthalmologic examination and retinal imaging using spectral-domain optical coherence tomography (Spectralis®, Heidelberg Engineering, Heidelberg, Germany). Cone density together with cone spacing and cone mosaic packing were measured in the nasal and temporal area 450 µm from the fovea. A multivariate analysis was performed to determine which of the following parameters were related to a decrease in cone density: age, axial length, central macular thickness, and retrofoveal choroidal thickness. One hundred and sixty-seven eyes of 101 subjects aged 6-78 years were studied. Perifoveal cone density significantly decreased with age (R2 = 0.17, p<0.01). Inversely, cone spacing increased with age (R2=0.18, p<0.01). There was no change in the cone packing mosaic (p>0.05). The mean coefficient of variation between fellow eyes was 3.9%. Age and axial length were related to a cone density decrease, while choroidal and retinal thicknesses did not affect cone metrics in healthy subjects. A moderate perifoveal cone loss occurs with age. The precise consequences of these findings on visual function should be investigated. In addition to a better understanding of normal retinal anatomy, these results could act as a comparative database for further studies on normal and diseased retinas.

Relationship Between Foveal Cone Structure and Visual Acuity Measured With Adaptive Optics Scanning Laser Ophthalmoscopy in Retinal Degeneration.

PurposeTo evaluate foveal function in patients with inherited retinal degenerations (IRD) by measuring visual acuity (VA) after correction of higher-order aberrations.MethodsAdaptive optics scanning laser ophthalmoscopy (AOSLO) was used to image cones in 4 healthy subjects and 15 patients with IRD. The 840-nm scanning laser delivered an “E” optotype to measure AOSLO-mediated VA (AOSLO-VA). Cone spacing was measured at the preferred retinal locus by two independent graders and the percentage of cones below the average density of 47 age-similar healthy subjects was computed. Cone spacing was correlated with best-corrected VA measured with the Early Treatment of Diabetic Retinopathy Study protocol (ETDRS-VA), AOSLO-VA, and foveal sensitivity.ResultsETDRS-VA significantly correlated with AOSLO-VA (ρ = 0.79, 95% confidence interval [CI] 0.5–0.9). Cone spacing correlated with AOSLO-VA (ρ = 0.54, 95% CI 0.02–0.7), and negatively correlated with ETDRS letters read (ρ = −0.64, 95% CI −0.8 to −0.2). AOSLO-VA remained ≥20/20 until cones decreased to 40.2% (CI 31.1–45.5) below normal. Similarly, ETDRS-VA remained ≥20/20 until cones were 42.0% (95% CI 36.5–46.1) below normal. Cone spacing z scores negatively correlated with foveal sensitivity (ρ = −0.79, 95% CI −0.9 to −0.4) and foveal sensitivity was ≥35 dB until cones were 43.1% (95% CI 39.3–46.6) below average.ConclusionsVA and foveal cone spacing were weakly correlated until cones were reduced by 40% to 43% below normal. The relationship suggests that VA is an insensitive measure of foveal cone survival; cone spacing may be a more sensitive measure of cone loss.

Lattice-valued convergence associated with CNS spaces

In this paper, in the context of meet continuous quantale, we present a notion of conical topological lattice-valued convergence space, which provides the theory of lattice-valued convergence associated with such conical neighborhood spaces.

Distribution of cone density, spacing and arrangement in adult healthy retinas with adaptive optics flood illumination.

The aim of this article is to analyse cone density, spacing and arrangement using an adaptive optics flood illumination retina camera (rtx1™) on a healthy population. Cone density, cone spacing and packing arrangements were measured on the right retinas of 109 subjects at 2°, 3°, 4°, 5° and 6° of eccentricity along 4 meridians. The effects of eccentricity, meridian, axial length, spherical equivalent, gender and age were evaluated. Cone density decreased on average from 28 884 ± 3 692 cones/mm2, at 2° of eccentricity, to 15 843 ± 1 598 cones/mm2 at 6°. A strong inter-individual variation, especially at 2°, was observed. No important difference of cone density was observed between the nasal and temporal meridians or between the superior and inferior meridians. However, the horizontal and vertical meridians differed by around 14% (T-test, p<0.0001). Cone density, expressed in units of area, decreased as a function of axial length (r2 = 0.60), but remained constant (r2 = 0.05) when cone density is expressed in terms of visual angle supporting the hypothesis that the retina is stretched during the elongation of the eyeball. Gender did not modify the cone distribution. Cone density was slightly modified by age but only at 2°. The older group showed a smaller density (7%). Cone spacing increased from 6,49 ± 0,42 μm to 8,72 ± 0,45 μm respectively between 2° and 6° of eccentricity. The mosaic of the retina is mainly triangularly arranged (i.e. cells with 5 to 7 neighbors) from 2° to 6°. Around half of the cells had 6 neighbors.

Early Patterns of Macular Degeneration in ABCA4-Associated Retinopathy

PurposeTo describe the earliest features of ABCA4-associated retinopathy.DesignCase series.ParticipantsChildren with a clinical and molecular diagnosis of ABCA4-associated retinopathy without evidence of macular atrophy.MethodsThe retinal phenotype was characterized by color fundus photography, OCT, fundus autofluorescence (FAF) imaging, electroretinography, and in 2 patients, adaptive optics scanning laser ophthalmoscopy (AOSLO). Sequencing of the ABCA4 gene was performed in all patients.Main Outcome MeasuresVisual acuity, OCT, FAF, electroretinography, and AOSLO results.ResultsEight children with ABCA4-associated retinopathy without macular atrophy were identified. Biallelic variants in ABCA4 were identified in all patients. Four children were asymptomatic, and 4 reported loss of VA. Patients were young (median age, 8.5 years; interquartile range, 6.8 years) with good visual acuity (median, 0.155 logarithm of the minimum angle of resolution [logMAR]; interquartile range, 0.29 logMAR). At presentation, the macula appeared normal (n = 3), had a subtly altered foveal reflex (n = 4), or demonstrated manifest fine yellow dots (n = 1). Fundus autofluorescence identified hyperautofluorescent dots in the central macula in 3 patients, 2 of whom showed a normal fundus appearance. Only 1 child had widespread hyperautofluorescent retinal flecks at presentation. OCT imaging identified hyperreflectivity at the base of the outer nuclear layer in all 8 patients. Where loss of outer nuclear volume was evident, this appeared to occur preferentially at a perifoveal locus. Longitudinal split-detector AOSLO imaging in 2 individuals confirmed that the greatest change in cone spacing occurred in the perifoveal, and not foveolar, photoreceptors. Electroretinography showed a reduced B-wave–to–A-wave ratio in 3 of 5 patients tested; in 2 children, recordings clearly showed electronegative results.ConclusionsIn childhood-onset ABCA4-associated retinopathy, the earliest stages of macular atrophy involve the parafovea and spare the foveola. In some cases, these changes are predated by tiny, foveal, yellow, hyperautofluorescent dots. Hyperreflectivity at the base of the outer nuclear layer, previously described as thickening of the external limiting membrane, is likely to represent a structural change at the level of the foveal cone nuclei. Electroretinography suggests that the initial site of retinal dysfunction may occur after phototransduction.

Los exilios políticos y la dimensión comparada: contribuciones a un campo en construcción

The study of exiles in Latin America has developed significantly in the last twenty years. Whereas most of this work concerns exiles from the Southern Cone (Argentina, Chile and Uruguay), texts, research and academic spaces relating to Brazil, Paraguay, Peru, Colombia and, to a lesser extent Central America, have begun to make an appearance. We believe that the point has now been reached where national studies should be transcended, to begin a reflection on other aspects, including theoretical and methodological approaches, seeking to provide elements to assist in the analysis of these forced migrations. The objective is to reflect on the relevance of comparative studies to the issue of exile in or from Latin America in the twentieth century, consider the progress already made and the circumstances around forced migrations especially those daily movements of displaced people that challenge us.

On homogeneous locally conical spaces

The main result of this article is: THEOREM. Every homogeneous locally conical connected separable metric space that is not a $1$-manifold is strongly $n$-homogeneous for each $n \geq 2$ and countable dense homogeneous. Furthermore, countable dense homogeneity can be proven without assuming the space is connected. This theorem has the following two consequences. COROLLARY 1. If $X$ is a homogeneous compact suspension, then $X$ is an absolute suspension (i.e., for any two distinct points $p$ and $q$ of $X$, there is a homeomorphism from $X$ to a suspension that maps $p$ and $q$ to the suspension points). COROLLARY 2. If there exists a locally conical counterexample $X$ to the Bing-Borsuk Conjecture (i.e., $X$ is a locally conical homogeneous Euclidean neighborhood retract that is not a manifold), then $X$ is strongly $n$-homogeneous for all $n \geq 2$ and countable dense homogeneous.

Fredholm theory for elliptic operators on quasi‐asymptotically conical spaces

We consider the mapping properties of generalized Laplace-type operators L = ∇ ∗ ∇ + R on the class of quasi-asymptotically conical (QAC) spaces, which provide a Riemannian generalization of the QALE manifolds considered by Joyce. Our main result gives conditions under which such operators are Fredholm when acting between certain weighted Sobolev or weighted Hölder spaces. These are generalizations of well-known theorems in the asymptotically conical (or asymptotically Euclidean) setting, and also sharpen and extend corresponding theorems by Joyce. The methods here are based on heat kernel estimates originating from old ideas of Moser and Nash, as developed further by Grigor'yan and Saloff-Coste. As demonstrated by Joyce's work, the QAC spaces here contain many examples of gravitational instantons, and this work is motivated by various applications to manifolds with special holonomy.

Visual resolution and cone spacing in the nasal and inferior retina.

To determine the retinal eccentricity at which cones are no longer an observable substitute for ganglion cells on nasal and inferior parafoveal visual acuity. Visual acuities were measured on 12 healthy volunteers, under dynamic adaptive optic aberrations correction (crx1™) in white light, from 0° to 6°, every two degrees, along the nasal and inferior retinal meridians. Cone spacing was measured on images of the retina acquired using an adaptive optic flood illumination retina camera (rtx1™) at the same eccentricity, except at 0°. Cone spacing increased by around 0.13min of arc per degree of eccentricity and a difference of 7% between both meridians was observed (higher cone spacing in the inferior retinal meridian). Visual resolution was higher in the nasal retinal meridian (difference of around 28% or 0.15 logMAR at 6°). Cone spacing can predict minimum angle of resolution (MAR) at 2° in both semi retinal meridians. In the inferior retinal meridian, MAR measurements are fairly well predicted by Watson's 50% mathematical model based on the midget retinal ganglion cell density. Along the nasal retinal meridian, the measured MAR lies between Watson's 50% and 100% models. At 2° of eccentricity, cone density accurately predicts visual resolution in both the nasal and inferior retina, supporting the idea that only 50% of the foveal midget retinal ganglion cells determine VA. The 50% model can also predict VA in the inferior retinal meridian at 4° and 6° of eccentricity. However, the 50% model underestimated visual acuity in the nasal retinal meridian at 4° and 6° of eccentricity consistent with the partially overlapping ON and OFF midget retinal ganglion cell receptive fields.

Labeling the lines: A test of a six-mechanism model of chromatic detection.

Six linear chromatic mechanisms are sufficient to account for the pattern of threshold elevations produced by chromatic noise masking in the (L,M) plane of cone space (Shepard, Swanson, McCarthy, & Eskew, 2016). Here, we report results of asymmetric color matching of the threshold-level tests from that detection study and use those matches to test the detection model. We assume the mechanisms are univariant labeled lines (Rushton, 1972; Watson & Robson, 1981), implying that the chromaticities of physically different stimuli that are detected by a single mechanism should all be the same-they are postreceptoral metamers-but the chromaticities of two stimuli detected by different mechanisms should be different. The results show that color matches fall into six clusters in CIE (u',v') space (across all the noise conditions) and that these clusters correspond closely to the six mechanisms in the model. Most importantly, where the detection model determines that a given test angle is detected by different mechanisms under different noise conditions, the hue of that test angle changes in a consistent way. These color matches allow us to apply a color label to each of the mechanisms, confirm the six-mechanism model, and quantify the hue signaled by each mechanism.

High-resolution Imaging in Male Germ Cell–Associated Kinase (MAK)-related Retinal Degeneration

To describe the characteristics of MAK-related retinal degeneration using optical coherence tomography angiography (OCTA) and adaptive optics scanning laser ophthalmoscopy (AOSLO). Cross-sectional study. Six patients with rod-cone degeneration and disease-causing mutations in MAK were evaluated with visual acuity, spectral-domain OCT, confocal AOSLO, and OCTA. Foveal avascular zone (FAZ) area, vessel densities, and perfusion densities of the superficial capillary plexus (SCP) and deep capillary plexus (DCP) in the central macula in all 6 patients were compared with 5 normal subjects. Cone spacing was measured in 4 patients from AOSLO images and compared with 37 normal subjects. Patients ranged from 25 to 81 years of age (mean, 52 years). Visual acuity varied from 20/13 to 20/40+2, except in 1 patient with cystoid macular edema whose vision was 20/60- and 20/70+1. The SCP (P= .012) and DCP (P= .013) vessel density and perfusion density (P=.015 and .013, respectively) were significantly lower in patients compared to normal subjects in the parafoveal region 1.0-3.0mm from the fovea, but were similar to normal subjects within 1.0mm of the fovea. The FAZ area was not significantly different from normal (all P ≥ .24). Cone spacing was normal at almost all locations in 2 patients with early disease and increased in 2 patients with advanced disease. Although retinal vascular densities are reduced and cone spacing is increased in advanced disease, central foveal structure is maintained until late stages of disease, which may contribute to preservation of foveal vision in eyes with MAK-related retinal degeneration.

Gauge-reversing maps on cones, and Hilbert and Thompson isometries

We show that a cone admits a gauge-reversing map if and only if it is a symmetric cone. We use this to prove that every isometry of a Hilbert geometry is a collineation unless the Hilbert geometry is the projective space of a non-Lorentzian symmetric cone, in which case the collineation group is of index two in the isometry group. We also determine the isometry group of the Thompson geometry on a cone.

Horizon fluff, semi-classical black hole microstates \u2014 Log-corrections to BTZ entropy and black hole/particle correspondence

According to the horizon fluff proposal microstates of a generic black hole belong to a certain subset of near horizon soft hairs that cannot be extended beyond the near horizon region. In [1, 2] it was shown how the horizon fluff proposal works for AdS3 black holes. In this work we clarify further this picture by showing that BTZ black hole microstates are in general among the coherent states in the Hilbert space associated with conic spaces or their Virasoro descendants, provided we impose a (Bohr-type) quantization condition on the angular deficit. Thus BTZ black holes may be viewed as condensates (or solitonic states) of AdS3 particles. We provide canonical and microcanonical descriptions of the statistical mechanical system associated with BTZ black holes and their microstates, and relate them. As a further non-trivial check we show the horizon fluff proposal correctly reproduces the expected logarithmic corrections to the BTZ entropy.

Developed optimization technique used for the distribution of U-shaped permittivity for cone type spacer in GIS

The solid/gas interface formed by solid spacer and insulating gas represents the weakest point in gas insulated systems (GIS) which is due to field intensification on spacer surface especially near triple junctions (Solid insulator – Gas – Electrodes) at HV and ground electrodes. Functionally Graded Material (FGM) is applied to the spacer design instead of uniform distribution to improve the electric field distribution across the spacer surface without changing its simple profile. Cone spacer model with uniform and FGM permittivity distribution has been introduced to study the effect of FGM in improving the electric field characteristics along spacer surface and near triple junctions. The verification of the proposed model has been investigated by comparing the obtained simulation results of the field to these given by others. Developed computerized optimization technique for automatic U-shape permittivity distribution is presented. U-shape permittivity distribution is used to mitigate the electric field strength not only near HV triple junction (Solid insulator – Gas – HV electrode) but also near ground triple junction (Solid insulator – Gas – Ground electrode). The simulation of the electric field is presented by the concept of Finite Element Method (FEM) using Comsol Multiphysics software. The optimization algorithm is programmed using Comsol LiveLink™ for MATLAB.

Reliability and Agreement Between Metrics of Cone Spacing in Adaptive Optics Images of the Human Retinal Photoreceptor Mosaic.

To assess reliability and agreement among three metrics used to evaluate the distribution of cell distances in adaptive optics (AO) images of the cone mosaic. Using an AO flood illumination retinal camera, we acquired images of the cone mosaic in 20 healthy subjects and 12 patients with retinal diseases. The three spacing metrics studied were the center-to-center spacing (Scc), the local cone spacing (LCS), and the density recovery profile distance (DRPD). Each metric was calculated in sampling areas of different sizes (64 × 64 μm and 204 × 204 μm) across the parafovea. Both Scc and LCS were able to discriminate between healthy subjects and patients with retinal diseases; DRPD did not reliably detect any abnormality in the distribution of cell distances in patients with retinal diseases. The agreement between Scc and LCS was high in healthy subjects (intraclass correlation coefficient [ICC] ≥ 0.79) and moderate in patients with retinal diseases (ICC ≤ 0.51). The DRPD had poor agreement with Scc (ICC ≤ 0.47) and LCS (ICC ≤ 0.37). The correlation between the spacing metrics of the two sampling areas was greater in healthy subjects than in patients with retinal diseases. The Scc and LCS provided interchangeable estimates of cone distance in AO retinal images of healthy subjects but could not be used interchangeably when investigating retinal diseases with significant cell reflectivity loss (≥30%). The DRPD was unreliable for describing cell distance in a human retinal cone mosaic and did not correlate with Scc and LCS. Caution is needed when comparing spacing metrics evaluated in sampling areas of different sizes.

Human photoreceptor cone density measured with adaptive optics technology (rtx1 device) in healthy eyes: Standardization of measurements.

The anatomic structures of the anterior segment of the eye enable correct reception of stimuli by the retina, which contains receptors that receive light impulses and transmit them to the visual cortex. The aim of this study was to assess the effect of the size of the sampling window in an adaptive optics (AO) flood-illumination retinal camera (rtx1) on cone density measurements in the eyes of healthy individuals and to investigate the differences in cone density and spacing in different quadrants of the retina. Thirty-three subjects with no ophthalmic or systemic disease underwent a detailed ophthalmologic examination. Photographs of retinal fragments 3 degrees from the fovea were taken using the rtx1 AO retinal camera. We used sampling windows with 3 sizes (50 × 50, 100 × 100, and 250 × 250 μm). Cone density, spacing, and shape were determined using AOdetect software. The median (interquartile range) cone density was 19,269 (4964) cones/mm2. There were statistically significant differences between measurements taken with the 50/50 and 250/250-m windows. There were no significant differences in the cone spacing results between any of the windows examined, but the measurements differed according to location between the superior and temporal quadrants. The most common cone shape was hexagonal (47.6%) for all window sizes and locations. These findings may help in the development of a normative database for variation in cone density in healthy subjects and to allow the best window to be chosen for obtain the most correct values for eccentricity measurements of 3 degrees. In our study, the optimal sampling window was 100 × 100 μm.

Pseudomagnetic field in curved graphene

The general covariance of the Dirac equation is exploited in order to explore the curvature effects appearing in the electronic properties of graphene. Two physical situations are then considered: the weak curvature regime, with $\left|R\right|<1/L^2$, and the strong curvature regime, with $1/L^2\ll \left|R\right|<1/d^2$, where $R$ is the scalar curvature, $L$ is a typical size of a sample of graphene and $d$ is a typical size of a local domain where the curvature is pronounced. In the first scenario, we found that the curvature transforms the conical nature of the dispersion relation due to a shift in the momentum space of the Dirac cone. In the second scenario, the curvature in the local domain affects the charge carriers in such a manner that bound states emerge; these states are declared to be pseudo-Landau states because of the analogy with the well known Landau problem; here the curvature emulates the role of the magnetic field. Seeking more tangible curvature effects we calculate e.g. the electronic internal energy and heat capacity of graphene in the small curvature regime and give an expresssion for the ground state energy in the strong curvature regime.