Inverse Radius Research Articles

Embeddings of integrable models in supergravity and their perturbative stability

We discuss the perturbative stability of an AdS 3 non-supersymmetric solution of the type-IIB supergravity, whose internal geometry is given by the direct product of a round three-sphere and two λ-deformed factors based on the coset CFTs SU(2)/U(1) and SL(2, ℝ)/SO(1,1). This solution admits a two-dimensional parametric space spanned by the inverse radius of the AdS 3 and the deformation parameter λ. Reality of the background imposes restrictions on the values of these parameters. Further limitations on the values of the inverse radius and the parameter λ arise after requiring the stability of the solution. Our approach relies on the study of scalar perturbations around the AdS 3 vacuum of a three-dimensional effective theory. This reveals the existence of a region in the parametric space where the Breitenlohner-Freedman bound is not violated.

Vortical Effects for Free Fermions on Anti-De Sitter Space-Time

Here, we study a quantum fermion field in rigid rotation at finite temperature on anti-de Sitter space. We assume that the rotation rate Ω is smaller than the inverse radius of curvature ℓ−1, so that there is no speed of light surface and the static (maximally-symmetric) and rotating vacua coincide. This assumption enables us to follow a geometric approach employing a closed-form expression for the vacuum two-point function, which can then be used to compute thermal expectation values (t.e.v.s). In the high temperature regime, we find a perfect analogy with known results on Minkowski space-time, uncovering curvature effects in the form of extra terms involving the Ricci scalar R. The axial vortical effect is validated and the axial flux through two-dimensional slices is found to escape to infinity for massless fermions, while for massive fermions, it is completely converted into the pseudoscalar density −iψ¯γ5ψ. Finally, we discuss volumetric properties such as the total scalar condensate and the total energy within the space-time and show that they diverge as [1−ℓ2Ω2]−1 in the limit Ω→ℓ−1.

Changes in Corneal Biomechanical Properties After Small-Incision Lenticule Extraction and Photorefractive Keratectomy, Using a Noncontact Tonometer.

The aim of this study was to evaluate and compare early corneal biomechanical changes after small-incision lenticule extraction (SMILE) and photorefractive keratectomy (PRK). The study comprised 74 patients eligible for refractive surgery, equally allocated to PRK (37 patients) and SMILE (37 patients). Corneal biomechanical properties were recorded and compared between the 2 groups at preoperatively and 3 months after surgery using a dynamic ultra-high-speed Scheimpflug camera equipped with a noncontact tonometer. Both procedures significantly affected corneal biomechanical properties at 3 months after surgery. Patients in the PRK group showed significantly better results for deformation amplitude ratio (DA ratio) ( P = 0.03), maximum inverse radius (InvRadMax) ( P = 0.02), and A2 time ( P = 0.03). The mean changes in DA ratio, HC radius, InvRadMax, and Ambrosio relational thickness were significantly higher in the SMILE group in comparison with those of the PRK group (all, P < 0.05). In both groups, change in CCT was significantly correlated with changes in DA ratio and InvRadMax ( P < 0.05). Both SMILE and PRK refractive surgeries significantly altered corneal biomechanical properties but the changes were more prominent after SMILE.

Detection of postlaser vision correction ectasia with a new combined biomechanical index.

To validate and evaluate the use of a new biomechanical index known as the Corvis biomechanical index-laser vision correction (CBI-LVC) as a method for separating stable post-LVC eyes from post-LVC eyes with ectasia. 10 clinics from 9 countries. Retrospective, multicenter, clinical study. The study was designed with 2 purposes: to develop the CBI-LVC, which combines dynamic corneal response (DCR) parameters provided by a high-speed dynamic Scheimpflug camera (CorVis ST; OCULUS Optikgeräte GmbH) and then to evaluate its ability to detect post-LVC ectasia. The CBI-LVC includes integrated inverse radius, applanation 1 (A1) velocity, A1 deflection amplitude, highest concavity and arclength, deformation amplitude ratio of 2 mm, and A1 arclength in millimeters. Logistic regression with Wald forward stepwise approach was used to identify the optimal combination of DCRs to create the CBI-LVC and then separate stable from LVC-induced ectasia. Eighty percentage of the database was used for training the software and 20% for validation. 736 eyes of 736 patients were included (685 stable LVC and 51 post-LVC ectasia). The receiver operating characteristic curve analysis showed an area under the curve of 0.991 when applying CBI-LVC in the validation dataset and 0.998 in the training dataset. A cutoff of 0.2 was able to separate stable LVC from ectasia with a sensitivity of 93.3% and a specificity of 97.8%. The CBI-LVC was highly sensitive and specific in distinguishing stable from ectatic post-LVC eyes. Using CBI-LVC in routine practice, along with topography and tomography, can aid the early diagnosis of post-LVC ectasia and allow intervention prior to visually compromising progression.

A Novel Indentation Assessment to Measure Corneal Biomechanical Properties in Glaucoma and Ocular Hypertension.

PurposeTo evaluate the ability of the new in vivo corneal indentation device (CID) to measure corneal biomechanical properties.Methods and ResultsIn total, 186 eyes from 46 healthy subjects, 107 patients with primary open-angle glaucoma, and 33 patients with ocular hypertension were enrolled in a cross-sectional study. Measurements were performed using corneal visualization Scheimpflug technology (Corvis ST) and the CID. The deformation amplitude (DA), inward applanation time, inward applanation velocity (A1V), outward applanation time (A2T), outward applanation velocity (A2V), highest concavity time, DA ratio, max inverse radius (MIR), integrated radius, and stiffness parameter A1 were included as Corvis ST parameters, and stiffness and modulus were included as CID parameters. Associations between the Corvis ST and CID parameters and correlations between central corneal thickness and corneal biomechanical parameters were analyzed. The stiffness was significantly correlated with all the Corvis ST parameters (P < 0.05). The modulus was significantly correlated with the DA, A1V, A2T, A2V, highest concavity time, and MIR (P < 0.05). The DA, inward applanation time, A1V, A2T, A2V, DA ratio, MIR, integrated radius, and stiffness parameter A1 values and both CID-derived values were significantly correlated with central corneal thickness (P < 0.05).ConclusionsParameters derived from the CID and Corvis ST demonstrated agreement in the measurement of corneal biomechanical properties. The stiffness and modulus can characterize in vivo corneal biomechanical properties.Translational RelevanceAgreeing with the Corvis ST regarding the assessment of corneal biomechanical properties, the CID can be a novel clinical tool for biomechanical evaluation of the cornea.

Comparison of ultrasonic attenuation models for small droplets measurement based on numerical simulation and experiment

Ultrasonic method has developed rapidly in particle measurement. Suitable ultrasonic attenuation theoretical models are very important for measuring different kinds of particles. In this paper, the ultrasonic measurement technique for small droplets in air is studied based on simulation and experiment, and the applicability of some theoretical models is discussed. In simulation method, both pressure acoustic module and thermoviscous acoustic module are compared, and a method of randomly placing small droplets is proposed. Based on the thermoviscous acoustic module, four ultrasonic attenuation theoretical models including ECAH model, McClements model, Hemar model and Qian model are compared. The mechanism of ultrasonic attenuation under different ultrasonic frequency, droplet radius and concentration is analyzed. And the results show that ECAH model and McClements model are closer to the simulation results, but ECAH model is the most consistent with the simulation data. Furthermore, the flowing experiment is carried out to measure the ultrasonic attenuation coefficient of small droplets in air. The experimental results are inverted using above four theoretical models and hybrid particle swarm optimization algorithm to obtain the droplet radius and concentration. Compared with the results of optical photographing method, the error of ECAH model and McClements model is the smallest within ± 10%. Based on the simulation results and experimental results, ECAH model is the most suitable theoretical model for ultrasonic attenuation method to inverse droplet radius and concentration for small droplets in air measurement at low concentrations, and McClements model has a very close performance to ECAH model.

Corneal biomechanical parameters in keratoconus eyes with abnormal elevation on the back corneal\xa0surface only versus both back and front surfaces

Corneal biomechanical parameters were compared in 100 keratoconus eyes with abnormal elevation on the back corneal surface only (group 1), versus both the back and front surfaces (group 2). Scheimpflug tomography with Pentacam HR, corneal biomechanical assessments using Corvis ST and Ocular Response Analyzer (ORA) and corneal epithelium thickness maps using anterior segment optical coherence tomography were assessed. There were no significant differences in the IOP measured using Corvis ST and ORA, age or sex between the two groups. Statistically significant differences were found in all corneal shape parameters and all new parameters of Corvis ST: corneal stiffness parameter at first applanation (SP-A1), integrated inverse radius (IR) and deformation amplitude ratio (DAR)) between groups (p < 0.001). The classic parameters of ORA including corneal hysteresis (CH) and corneal resistance factor (CRF) were about 1.00 mmHg higher in group 1 (p < 0.001). In conclusion, keratoconus eyes with abnormal elevation limited to the back corneal surface have lower grade, stiffer corneal biomechanical parameters and less asymmetric shape. This is consistent with progressive biomechanical weakening from the first detectable back surface elevation to manifestation on the front surface as the severity overwhelms the ability of the epithelium to compensate.

Global properties of the conformal manifold for S-fold backgrounds

We study a one-parameter family of mathcal{N} = 2 anti-de Sitter vacua with U(1)2 symmetry of gauged four-dimensional maximal supergravity, with dyonic gauge group [SO(6) × SO(1, 1)] ⋉ ℝ12. These backgrounds are known to correspond to Type IIB S-fold solutions with internal manifold of topology S1 × S5. The family of AdS4 vacua is parametrized by a modulus χ. Although χ appears non-compact in the four-dimensional supergravity, we show that this is just an artefact of the four-dimensional description. We give the 10-dimensional geometric interpretation of the modulus and show that it actually has periodicity of frac{2pi }{T} , which is the inverse radius of S1. We deduce this by providing the explicit D = 10 uplift of the family of vacua as well as computing the entire modulus-dependent Kaluza-Klein spectrum as a function of χ. At the special values χ = 0 and χ = frac{pi }{T} , the symmetry enhances according to U(1)2 → U(2), giving rise however to inequivalent Kaluza-Klein spectra. At χ = frac{pi }{T} , this realizes a bosonic version of the “space invaders” scenario with additional massless vector fields arising from formerly massive fields at higher Kaluza-Klein levels.

Comparison of corneal biomechanics among primary open-angle glaucoma with normal tension or hypertension and controls.

Background:Normal tension glaucoma (NTG) is a less pressure-dependent type of glaucoma with characteristic optic neuropathy. Recently, the biomechanical mechanism has been thought to account for glaucomatous optic neuropathy to some degree. We intended to compare dynamic corneal response parameters (DCRs) among patients with primary open-angle glaucoma with normal tension or hypertension and controls. The correlations between DCRs and known risk factors for glaucoma were also analyzed.Methods:In this cross-sectional study, 49 NTG subjects, 45 hypertension glaucoma (HTG) subjects, and 50 control subjects were enrolled. We compared the differences in DCRs using corneal visualization Scheimpflug technology among the NTG, HTG, and control groups. We also analyzed the correlations between DCRs and known risk factors for glaucoma (eg, central corneal thickness [CCT], intraocular pressure [IOP], etc).Results:The maximum inverse concave radius (NTG: 0.18 [0.17, 0.20] mm−1; control: 0.17 [0.16, 0.18] mm−1; P = 0.033), deformation amplitude ratio of 2 mm (DAR 2 mm, NTG: 4.87 [4.33, 5.39]; control: 4.37 [4.07, 4.88]; P < 0.001), and DAR 1 mm (NTG: 1.62 [1.58, 1.65]; control: 1.58 [1.54, 1.61]; P < 0.001) were significantly higher in NTG than in the controls. The integrated radius (IR, NTG: 8.40 ± 1.07 mm−1; HTG: 7.64 ± 1.31 mm−1; P = 0.026) and DAR 2 mm (NTG: 4.87 [4.33, 5.39]; HTG: 4.44 [4.12, 5.02]; P < 0.007) were significantly higher, whereas the stiffness parameter at the first applanation (SP-A1, NTG: 91.23 [77.45, 107.45]; HTG: 102.36 [85.77, 125.12]; P = 0.007) was lower in NTG than in HTG. There were no significant differences in the DCRs between HTG and control groups (P > 0.05). In the univariate and multivariate analyses, some of the DCRs, such as IR, were negatively correlated with CCT and IOP, whereas SP-A1 was positively correlated with CCT and IOP.Conclusions:The cornea was more deformable in NTG than in HTG or controls. There were no significant differences in corneal deformability between HTG and controls. The cornea was more deformable with the thinner cornea and lower IOP.

Postoperative corneal biomechanics and influencing factors during femtosecond-assisted laser in situ keratomileusis (FS-LASIK) and laser-assisted subepithelial keratomileusis (LASEK) for high myopia.

The purpose of this study is to compare the postoperative corneal biomechanics and assess the influence factors after femtosecond-assisted laser in situ keratomileusis (FS-LASIK) and laser-assisted subepithelial keratomileusis (LASEK) for high myopia. In this retrospective study, patients who completed 1-year follow-up were included. The corneal biomechanical parameters, including deformation amplitude ratio 2.0 mm (DA ratio 2.0 mm), integrated inverse radius (IntInv Rad), stiffness parameter at first applanation (SP-A1), and Ambrosio relational thickness through the horizontal meridian (ARTh), were measured with Corvis STII. We also investigated the relationship between these biomechanics and preoperative or intraoperative variables. Thirty eyes had FS-LASIK and 30 eyes had LASEK. The changes in DA ratio 2.0 mm, IntInv Rad, and SP-A1 after surgery were significantly smaller in the LASEK group than in the FS-LASIK group, while the change in the ARTh was not significantly different between groups. No significant differences were detected in the mean values of postoperative DA ratio 2.0 mm, IntInv Rad, and SP-A1 between LASEK and FS-LASIK, while significant difference was detected in the mean value of postoperative ARTh. There was a significant correlation between the resident stromal bed thickness and the postoperative DA ratio 2.0 mm, IntInv Rad, or SP-A1. The postoperative ARTh has shown significant correlation with postoperative central corneal thickness and the amount of myopic correction. The effect of LASEK on corneal biomechanics was smaller than FS-LASIK when the same central corneal thickness was consumed. LASEK may be performed with a lower risk of postoperative corneal ectasia than FS-LASIK.

Continuous spin representation from contraction of the conformal algebra

In this paper, we discuss the Inönü–Winger contraction of the conformal algebra. We start with the light-cone form of the Poincaré algebra and extend it to write down the conformal algebra in d dimensions. To contract the conformal algebra, we choose five dimensions for simplicity and compactify the third transverse direction to a circle of radius R following the Kaluza–Klein dimensional reduction method. We identify the inverse radius, 1/R, as the contraction parameter. After the contraction, the resulting representation is found to be the continuous spin representation in four dimensions. Even though the scaling symmetry survives the contraction, the special conformal translation vector changes and behaves like the four-momentum vector. We also discuss the generalization to d dimensions.

Five-dimensional gauge theories on spheres with negative couplings

We consider supersymmetric gauge theories on S5 with a negative Yang-Mills coupling in their large N limits. Using localization we compute the partition functions and show that the pure SU(N) gauge theory descends to an SU(N/2)+N/2× SU(N/2)−N/2× SU(2) Chern-Simons gauge theory as the inverse ’t Hooft coupling is taken to negative infinity for N even. The Yang-Mills coupling of the SU(N/2)±N/2 is positive and infinite, while that on the SU(2) goes to zero. We also show that the odd N case has somewhat different behavior. We then study the SU(N/2)N/2 pure Chern-Simons theory. While the eigenvalue density is only found numerically, we show that its width equals 1 in units of the inverse sphere radius, which allows us to find the leading correction to the free energy when turning on the Yang-Mills term. We then consider USp(2N) theories with an antisymmetric hypermultiplet and Nf< 8 fundamental hypermultiplets and carry out a similar analysis. Along the way we show that the one-instanton contribution to the partition function remains exponentially suppressed at negative coupling for the SU(N) theories in the large N limit.

Relativity Isoframes—A Useful and Potentially Unifying Conceptual Framework

This brief note introduces the conceptual framework of special and general relativity isoclocks and isoframes. Isoclocks and isoframes, as defined herein, can be used to create geometrical maps of space and time (“space-time”) with and without matter embedded. They are useful for having a mental picture of space-time relationships without having to picture 4-dimensional manifolds, which very few students and scientists are able to do. With the aid of the optical lensing definition of curvature as inverse radius, a new gravitational force equation is derived, which also incorporates Einstein’s mass/energy relation in the mx term. Thus, one may see how it is that gravitational force correlates with its time-embedded curvature-squared (Cx2) space in a more accurate formulation than could be envisioned by Newton. This becomes more apparent in high gamma fields, such as found near a black hole horizon. It is hoped that probability theories, such as quantum field theories in curved space-time, might be adaptable to the general relativity isoframe concept introduced herein.

Relationship between corneal stiffness parameters and lamina cribrosa curvature in normal tension glaucoma

To evaluate the relationship between corneal biomechanical parameters and lamina cribrosa (LC) curvature in normal tension glaucoma (NTG). 95 eyes of 56 NTG patients were enrolled in this prospective, observational study. Corneal biomechanical parameters, including stiffness parameters at applanation 1 (SP-A1), deformation amplitude ratio (DA ratio), inverse concave radius and biomechanically corrected intraocular pressure estimate (bIOP), were captured using the Corneal Visualization Scheimpflug Technology instrument (Corvis-ST). LC curvature was evaluated by mean adjusted LC curvature index (maLCCI) averaged by the measurements on 12 radial B-scan images obtained using swept-source optical coherence tomography (SS-OCT). Linear mixed models were constructed to assess the relationship between corneal biomechanical parameters and LC curvature. The mean age of participants was 51.04 ± 13.74 years (range, 24-82 years). The SP-A1 and maLCCI were 93.50 ± 13.82 mm Hg/mm and 7.57 ± 1.58, respectively. In univariate and multivariate analysis, SP-A1 (p < 0.001 and p = 0.001) and age (p = 0.010 and p = 0.024) were both significantly associated with maLCCI. The LC curvature increased with softer cornea demonstrated by lower SP-A1 and younger eyes. There was no statistical significance interaction between SP-A1 and age (p = 0.194). The greater posterior LC curvature was associated with lower corneal stiffness parameters and younger eyes in NTG patients. Chinese Clinical Trial Registry, ChiCTR1900021465.

Descemet membrane endothelial keratoplasty and corneal biomechanics

Abstract Objective To study the behaviour of the biomechanical properties of the cornea in DMEK (Descemet membrane endothelial keratoplasty). Methods Prospective longitudinal observational study. 21 pre and post-DMEK eyes. 3-month follow-up with the dynamic Scheimpflug Analyzer (CorvisST). The following parameters were measured: PIOnc: non-contact intraocular pressure (IOP), PIOb: corrected by biomechanics, maximum deflection amplitude (DefA), CCT: central corneal pachymetry, flattening speed 1 and 2, peak distance, HC deformation amplitude: deformation amplitude in maximum concavity, integrated inverse concave radius, DAR 1 and 2: deformation amplitude at 1 mm and 2 mm from the corneal apex, respectively. ARTh: Ambrosial pachymetric ratio, SP1: stiffness parameter, IWC: Biomechanical index corvis and the maximum inverse radius. Pre-operative and post-operative measurements were performed with a 3-month follow-up and compared with a paired sample t-test. Results There was a significant decrease in the PIOnc of 1.54 ± 3 mmHg (p Conclusions Variables indicate a decrease in corneal strength post DMEK, with an increase in IOB, at least the first 3 months after surgery. This finding is especially relevant in the follow-up of patients with coexisting glaucoma.

Queratoplastia endotelial de la membrana de Descemet y biomecánica corneal

ObjectiveTo study the behaviour of the biomechanical properties of the cornea in DMEK (Descemet membrane endothelial keratoplasty). MethodProspective longitudinal observational study. 21 pre and post-DMEK eyes. 3-month follow-up with the dynamic Scheimpflug Analyzer (Corvis ST, Oculus; Wetzlar, Germany). The following parameters were measured: IOPnc: non-corrected intraocular pressure (IOP), IOPb: IOP corrected by biomechanics, maximum deflection amplitude (DefA), CCT: central corneal pachymetry, flattening speed 1 and 2, peak distance, HC deformation amplitude: deformation amplitude in maximum concavity, integrated inverse concave radius, DAR 1 and 2: deformation amplitude at 1mm and 2mm from the corneal apex, respectively. ARTh: Ambrosial pachymetric ratio, SP1: stiffness parameter, CBI: Corvis Biomechanical index and the maximum inverse radius. Pre-operative and post-operative measurements were performed with a 3-month follow-up and compared with a paired sample t-test. ResultsThere was a significant decrease in the IOPnc of 1.54±3mmHg (p<0.05), a significant increase in the post-surgical IOPb of 3.79±3.18mmHg (p<0.001), a significant pachymetric decrease of 164.4±91.35μm (p<0.001) after the intervention. All dynamic parameters of the Scheimpflug analyzer changed significantly after surgery (p<0.05), except the ARTh and IWC variables. ConclusionsVariables indicate a decrease in corneal strength post-DMEK, with an increase in IOPb, at least the first 3 months after surgery. This finding is especially relevant in the follow-up of patients with coexisting glaucoma.

Coulomb interaction in quasibound states of graphene quantum dots

Coulomb interaction is of central importance in localized energy levels (bound states) or electronic flat bands and could result in many exotic quantum phases, such as magnetic, superconducting, and topological phases in graphene systems1-14. In graphene monolayer, the relativistic massless Dirac fermion nature of the charge carriers enables us to realize unprecedented quasibound states, which are trapped temporarily via whispering-gallery modes (WGMs) with the lifetime (trapping time) of ~ 10 fs, in circular graphene quantum dots (GQDs)15-20. Here we show that Coulomb interaction still plays a dominating role in determining the electronic properties of the temporarily-confined quasibound states. Our scanning tunneling microscopy (STM) and spectroscopy (STS) measurements demonstrate that the discrete quasibound state in a GQD will split into two peaks when it is partially filled. The energy separation of the two split peaks increases linear with inverse effective radius of the GQDs, indicating that the splitting arises from the Coulomb interaction. Moreover, we show that the real space distribution of the two split states separates in different regions of the GQD to reduce the Coulomb interaction, leading to the breaking of the WGM of the quasibound states.

Measurement of In Vivo Biomechanical Changes Attributable to Epithelial Removal in Keratoconus Using a Noncontact Tonometer.

To compare the biomechanical properties of the cornea after epithelial removal in eyes with keratoconus undergoing corneal cross-linking. Prospective interventional case series at a university hospital tertiary referral center. Corneal biomechanical properties were measured in patients with keratoconus undergoing corneal cross-linking, immediately before and after epithelial debridement by using a dynamic ultrahigh-speed Scheimpflug camera equipped with a noncontact tonometer. The study comprised 45 eyes of 45 patients with a mean age of 19.6 ± 4.9 years (range 14-34). The cornea was found to be 23.7 ± 15.7 μm thinner after epithelial removal (P < 0.01). Corneal stiffness was reduced after epithelial removal as demonstrated by a significant decrease of parameters such as stiffness parameter A1 (12.31, P < 0.01), stiffness parameter-highest concavity (2.25, P < 0.01), A1 length (0.13 mm, P = 0.04), highest concavity radius of curvature (0.26 mm, P = 0.01), highest concavity time (0.22 ms, P = 0.04) and an increase in A1 velocity (-0.01 m/s, P = 0.01), A1 deformation amplitude (-0.03 mm, P ≤ 0.01), A1 deflection length (-0.32 mm, P < 0.01), A2 deformation amplitude (-0.03 mm, P = 0.01), and A2 deflection length (-1.00 mm, P < 0.01). There were no significant differences in biomechanical intraocular pressure (0.15 mm Hg, P = 0.78), deformation amplitude (0.03, P = 0.54), maximum inverse radius (-0.01 mm, P = 0.57), and whole eye movement length (-0.02 mm, P = 0.12). Dynamic ultrahigh-speed Scheimpflug camera equipped with a noncontact tonometer offers an alternative method for in vivo measurements of the epithelial layer's contribution to corneal biomechanical properties. Our results suggest that corneal epithelium may play a more significant role in corneal biomechanical properties in patients with keratoconus than previously described.

Evaluation of new Corvis ST parameters in normal, Post-LASIK, Post-LASIK keratectasia and keratoconus eyes

The aim of this study was to evaluate the distribution of new Corneal Visualisation Scheimpflug Technology (Corvis ST) parameters in normal, Post-laser in situ keratomileusis (LASIK), Post-LASIK keratectasia (KE) and keratoconus (KC) eyes, and explore the diagnostic ability of these parameters in distinguishing KE from LASIK eyes. Twenty-three normal eyes, 23 LASIK eyes, 23 KE eyes and 23 KC eyes were recruited in this study. The following new Corvis ST parameters were measured: Max Inverse Radius, deformation amplitude (DA) Ratio Max [2 mm], Pachy Slope, DA Ratio Max [1 mm], Ambrosio’s relational thickness horizontal (ARTh), Integrated Radius, stiffness parameter at first applanation (SP-A1) and Corvis biomechanical index (CBI). The general linear model, linear regression model, relation analysis and receiver operating characteristic (ROC) curve were performed. The Max Inverse Radius, DA Ratio Max [2 mm], Pachy Slope, DA Ratio Max [1 mm], Integrated Radius and CBI in LASIK eyes, KE eyes and KC eyes were higher than in normal eyes, while the ARTh and SP-A1 parameters were lower than in normal eyes. The KE eyes had higher Max Inverse Radius, DA Ratio Max [2 mm], Pachy Slope, DA Ratio Max [1 mm], Integrated Radius, and lower SP-A1 value than LASIK eyes (all P < 0.05). The central corneal thickness was related to the Pachy Slope (r = −0.485), ARTh (r = −0.766), SP-A1 (r = 0.618) in KE eyes (all P < 0.05). The area under the ROC curve of Integrated Radius, Max Inverse Radius, DA Ratio Max [2 mm] and SP-A1 were above 0.800 in identifying KE from LASIK eyes. Thus, the new Corvis ST parameters were different between LASIK and KE eyes, suggesting that they might be helpful in distinguishing KE eyes from LASIK eyes. However, a further multi-center and large sample study is necessary to confirm these findings.

θ -dependence and center symmetry in Yang-Mills theories

We investigate the relation between the realization of center symmetry and the dependence on the topological parameter $\theta$ in $SU(N)$ Yang-Mills theories, exploiting trace deformations as a tool to regulate center symmetry breaking in a theory with a small compactified direction. We consider, in particular, $SU(4)$ gauge theory, which admits two possible independent deformations, and study, as a first step, its phase diagram in the deformation plane for two values of the inverse compactified radius going up to $L^{-1} \sim 500$ MeV, comparing the predictions of the effective 1-loop potential of the Polyakov loop with lattice results. The $\theta$-dependence of the various phases is then addressed, up to the fourth order in $\theta$, by numerical simulations: results are found to coincide, within statistical errors, with those of the standard confined phase iff center symmetry is completely restored and independently of the particular way this happens, i.e. either by local suppression of the Polyakov loop traces or by long range disorder.