Toric Model Research Articles

Systematic bibliometric analysis of research hotspots and trends on the application of premium IOLs in the past 2 decades.

To analysis of research hotspots and trends on the application of premium intraocular lens (PIOLs) in the past 2 decades. The literature search was performed on the Web of Science and included PIOLs studies published between January 2000 and December 2022. The retrieved literature was collated and analyzed by R-tool's Bibliometrix package, CitNetExplorer, CiteSpace and other software. A total of 1801 articles about PIOLs were obtained, most of which were published in Spain and the United States. The organization that published the most articles was the University of Valencia in Spain. Alió JL, and Montés-Micó R, from Spain were the most influential authors in this field. The Journal of Cataract and Refractive Surgery and Journal of Refractive Surgery were the core journals for this field; the top 10 cited articles mainly focus on postoperative satisfaction with multifocal intraocular lens (IOLs) and postoperative results of toric IOLs. Through the keyword analysis, we found that trifocal IOLs, astigmatism and extended depth of focus (EDoF) IOLs are the most discussed topics at present, and the importance of astigmatism and the clinical application of the new generation of PIOLs are the emerging research trends. Bibliometric analysis can effectively help to identify multilevel concerns in PIOLs research and the prevailing research trends in the realm of PIOLs encompass the adoption of EDoF IOLs, trifocal IOLs, and their respective Toric models.

Implantation of Hydrophobic Acrylic Toric Intraocular Lens with High-Water Contents Using Swept-Source Optical Coherence Tomography Biometer Integrated with a Surgical Guiding System.

To evaluate postoperative outcomes after implantation of toric intraocular lenses (IOLs) made of high-water-content hydrophobic acrylic material in Japanese patients using a swept-source optical coherence tomography (SS-OCT) biometer integrated with a surgical guiding system. In this prospective observational study, toric IOL models CNW0T3 to CNW0T9 (Alcon) were implanted in 33 eyes of 33 patients and followed-up for one month. Powers and toric models were determined using an SS-OCT biometer ARGOS® Ver 1.5 (Alcon), and the IOLs were aligned using surgical guidance. Differences between planned and actual axis positions at the end of the surgery (misalignment) and rotations from the end of surgery to one month postoperatively were measured. Additionally, postoperative uncorrected visual acuity, refraction, and residual astigmatism were evaluated. Mean and median misalignments were 2.3° (standard deviation [SD]: 1.6, 95% confidence interval [CI]: 1.7-2.9) and 2°, and those of postoperative rotation were 2.4° (SD: 2.6, 95% CI: 1.5-3.4) and 2°, respectively. Mean postoperative refraction was 0.06 D (SD: 0.62). Prediction errors within ±0.5 and ±1.0 D were 69.7% and 93.9%, respectively. Mean residual astigmatisms were 0.19 D (SD: 0.41), and mean uncorrected visual acuity was 0.00 logMAR (SD: 0.11), and 64% of the eyes scored 20/20 or better. Implantation of high-water-content hydrophobic acrylic toric IOLs using SS-OCT biometry integrated with a surgical guiding system effectively corrected corneal astigmatism with accurate IOL alignment in Japanese patients.

Quantum circuits for toric code and X-cube fracton model

We propose a systematic and efficient quantum circuit composed solely of Clifford gates for simulating the ground state of the surface code model. This approach yields the ground state of the toric code in ⌈2L+2+log2(d)+L2d⌉ time steps, where L refers to the system size and d represents the maximum distance to constrain the application of the CNOT gates. Our algorithm reformulates the problem into a purely geometric one, facilitating its extension to attain the ground state of certain 3D topological phases, such as the 3D toric model in 3L+8 steps and the X-cube fracton model in 12L+11 steps. Furthermore, we introduce a gluing method involving measurements, enabling our technique to attain the ground state of the 2D toric code on an arbitrary planar lattice and paving the way to more intricate 3D topological phases.

Q-Painlevé equations on cluster Poisson varieties via toric geometry

We provide a relation between the geometric framework for q-Painlevé equations and cluster Poisson varieties by using toric models of rational surfaces associated with q-Painlevé equations. We introduce the notion of seeds of q-Painlevé type by the negative semi-definiteness of symmetric bilinear forms associated with seeds, and classify the mutation equivalence classes of these seeds. This classification coincides with the classification of q-Painlevé equations given by Sakai. We realize q-Painlevé systems as automorphisms on cluster Poisson varieties associated with seeds of q-Painlevé type.

Quartic surfaces up to volume preserving equivalence

We study log Calabi–Yau pairs of the form (P3,Δ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(\\mathbb {P}^3,\\Delta )$$\\end{document}, where Δ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Delta $$\\end{document} is a quartic surface, and classify all such pairs of coregularity less than or equal to one, up to volume preserving equivalence. In particular, if (P3,Δ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(\\mathbb {P}^3,\\Delta )$$\\end{document} is a maximal log Calabi–Yau pair then we show that it has a toric model.

Результаты имплантации интраокулярных линз с расширенной глубиной фокуса

Purpose. Analysis of clinical and functional results and the subjective assessment by patients of the quality of visual functions after IOL implant with an extended depth of focus (EDOF) of different designs. Material and methods. The study included 29 patients (45 eyes). DFT015 Vivity IOL (Alcon) were implanted in 11 patients, LS-313 MF-15 Lentis Comfort IOL (Teleon) were implanted in 18 patients. Bilateral Vivity implantation in 5 patients, Lentis Comfort – in 11 patients. Monolateral Vivity implantation – 6, Lentis Comfort – 7. Toric models of IOL were implanted in patients with clinically significant astigmatism. Patients were examined before surgery, on the first day after surgery, one month later and three months after surgery. During the examination 3 months after the operation, the visometry of the operated eye was performed for near, at an intermediate distance and in the distance. In patients with bilateral IOL implantation, visometry was performed both monocularly and binocularly. The subjective quality of vision was carried out according to the Visual Function – 14 questionnaire. Results. Phacoemulsification with the implantation of EDOF IOL leads to a significant increase vision acuity in the distance, at an average distance and near, which is especially evident after bilateral implantation and allows patients to perform most of the usual actions without glasses. An increase in visual acuity both at a distance and at an intermediate distance and near was noted by all patients, regardless of the implanted IOL model. The level of satisfaction of patients with their vision after surgery is higher in male patients and with bilateral intervention. The smallest error in calculating the EDOF IOL is marked by the Kane formula. Conclusion. This paper presents a comparison of the clinical and functional results of phacoemulsification with implantation of IOL with EDOF of different designs. The presented data indicate that patients can perform most everyday tasks after these operations without additional correction with glasses. Keywords: cataract, phacoemulsification, IOL with extended depth of focus, EDOF.

The predictive accuracy of Barrett toric calculator using measured posterior corneal astigmatism derived from swept source-OCT and Scheimpflug camera.

To compare the performance of Barrett toric calculator incorporated with measured posterior corneal astigmatism (PCA) derived from IOL Master 700 and Pentacam HR versus predicted PCA. The predicted residual astigmatism using Barrett toric IOL calculator with predicted PCA, measured PCA from IOL Master 700 and measured PCA from Pentacam were calculated with the preoperative keratometry and intended IOL axis with modification. The vector analysis was performed to calculate the mean absolute prediction error (MAE), the centroid of the prediction error and the percentage of eyes with a prediction error within ±0.50 D, ±0.75 D, and ±1.00 D. In 57 eyes of 57 patients with mean age of 70.42 ± 10.75 years, the MAE among the three calculation methods were 0.59 ± 0.38 D (Predicted PCA), 0.60 ± 0.38 D (Measured PCA from IOL Master 700) and 0.60 ± 0.36 D (Measured PCA from Pentacam) with no significant difference, either in the whole sample, the WTR eyes and the ATR eyes (F = 0.078, 0.306 and 0.083, p = 0.925, 0.739 and 0.920, respectively). Measured PCA obtained from IOL Master 700 resulted in one level reduction (from Tn to Tn-1) in 49.12% eyes in cylindrical model selection, while measured PCA obtained from Pentacam resulted in one level reduction of toric model selection in 18.18% eyes. The present study suggested that the incorporation of measured PCA values derived from IOL Master 700 and Pentacam produce comparable clinical outcome with the predicted PCA mode in Barrett toric calculator.

Semiclassics of three-dimensional SCFTs from holography

We use holography to compute the large-N effective field theory along the moduli space of vacua of an infinite class of three-dimensional mathcal{N} = 2 SCFTs admitting a dual M-theory description. We focus in particular on toric models and show how the spectrum of large R-charge SCFT chiral scalar operators corresponds to a set of explicit semiclassical solutions of our effective field theory, which describe bound states of backreacting giant gravitons and baryonic-like M5-branes. Our semiclassical description allows for a direct computation of the scaling dimensions of these operators and provides a starting point for a semiclassical investigation of the SCFT data in the large R-charge sector. We consider the models corresponding to the Y12(ℙ2) and Q111 Sasaki-Einstein spaces as explicit examples.

Weyl Groups and Cluster Structures of Families of Log Calabi–Yau Surfaces

Abstract Given a generic Looijenga pair $(Y,D)$ together with a toric model $\rho :(Y,D)\rightarrow (\overline {Y},\overline {D})$, one can construct a seed $\textbf {s}$ such that the corresponding $\mathcal {X}$-cluster variety $\mathcal {X}_{\textbf {s}}$ can be viewed as the universal family of the log Calabi–Yau surface $U=Y\setminus D$. In cases where $(Y,D)$ is positive and $\mathcal {X}_{\textbf {s}}$ is not acyclic, we describe the action of the Weyl group of $(Y,D)$ on the scattering diagram $\mathfrak {D}_{\textbf {s}}$. Moreover, we show that there is a Weyl group element $\textbf {w}$ of order $2$ that either agrees with or approximates the Donaldson–Thomas transformation $\textrm {DT}_{\mathcal {X}_{\textbf {s}}}$ of $\mathcal {X}_{\textbf {s}}$. As a corollary, $\textrm {DT}_{\mathcal {X}_{\textbf {s}}}$ is cluster. In positive non-acyclic cases, we also apply the folding technique as developed in [20] and construct a maximally folded new seed $\overline {\textbf {s}}$ from $\textbf {s}$. The $\mathcal {X}$-cluster variety $\mathcal {X}_{\overline {\textbf {s}}}$ is a locally closed subvariety of $\mathcal {X}_{\textbf {s}}$ and corresponds to the maximally degenerate subfamily in the universal family. We show that the action of the special Weyl group element $\textbf {w}$ on $\mathfrak {D}_{\textbf {s}}$ descends to $\mathfrak {D}_{\overline {\textbf {s}}}$ and permutes distinct subfans in $\mathfrak {D}_{\overline {\textbf {s}}}$, generalizing the well-known case of the Markov quiver.

Pseudoholomorphic curves relative to a normal crossings symplectic divisor: compactification

Inspired by the log Gromov-Witten (or GW) theory of Gross-Siebert/Abramovich-Chen, we introduce a geometric notion of log J-holomorphic curve relative to a simple normal crossings symplectic divisor defined in [FMZ1]. Every such moduli space is characterized by a second homology class, genus, and contact data. For certain almost complex structures, we show that the moduli space of stable log J-holomorphic curves of any fixed type is compact and metrizable with respect to an enhancement of the Gromov topology. In the case of smooth symplectic divisors, our compactification is often smaller than the relative compactification and there is a projection map from the latter onto the former. The latter is constructed via expanded degenerations of the target. Our construction does not need any modification of (or any extra structure on) the target. Unlike the classical moduli spaces of stable maps, these log moduli spaces are often virtually singular. We describe an explicit toric model for the normal cone (i.e. the space of gluing parameters) to each stratum in terms of the defining combinatorial data of that stratum. In [FT2], we introduce a natural set up for studying the deformation theory of log (and relative) curves and obtain a logarithmic analog of the space of Ruan-Tian perturbations for these moduli spaces. In a forthcoming paper, we will prove a gluing theorem for smoothing log curves in the normal direction to each stratum. With some modifications to the theory of Kuranishi spaces, the latter will allow us to construct a virtual fundamental class for every such log moduli space and define relative GW invariants without any restriction.

Mirror Symmetry for Truncated Cluster Varieties

In the algebraic setting, cluster varieties were reformulated by Gross-Hacking-Keel as log Calabi-Yau varieties admitting a toric model. Building on work of Shende-Treumann-Williams-Zaslow in dimension 2, we describe the mirror to the GHK construction in arbitrary dimension: given a truncated cluster variety, we construct a symplectic manifold and prove homological mirror symmetry for the resulting pair. We also describe how our construction can be obtained from toric geometry, and we relate our construction to various aspects of cluster theory which are known to symplectic geometers.

Анализ влияния наклона и децентрации ИОЛ на индуцированный астигматизм при исследовании методом трассировки лучей на модели глаза

Purpose. Determination of the influence of the intraocular lens (IOL) inclination and decentration on the magnitude of induced astigmatism in a theoretical study using software on an eye model. Material and methods. An eye model with the specified parameters was performed to carry out the calculation. Modulation of the change in the wavefront was carried out using the Zemax program (LLC, USA). In the model eye, the probability of induction of astigmatism was analyzed depending on the change in the position of the aspherical IOL Acrysof IQ 16.0, 22.0 and 24.0 diopters and the toric model Acrysof IQ Toric SN6AT3, SN6AT4 and SN6AT5. The angle of inclination of the IOL relative to the horizontal plane was examined from 0° to 10° with a step of 1°, decentration from 0.1 to 1.5 mm with a step of 0.1 mm. At each IOL position, aberration data of the 2nd order Z (2, 2) were recorded. The obtained results were used to calculate the critical tilt angle and decentration. Results. The magnitude of induced astigmatism increased with the rise of the degree of inclination and decentration, corresponding to an increase in the optical power of the IOL. Accordingly, critically significant were the values of 3.0° inclination for the aspherical IOL with an optical power of 22.0 and 22.0 diopters and 3.5° for 16.0 diopters, decentration – 0.7 mm and 1.0 mm. The inclination of the TIOL relative to the horizontal plane revealed the induction of the magnitude of inverse astigmatism, according to an increase in the inclination angle of 0.3 diopters at a slope of 3–4°. Conclusions. The tilt and decentration of the aspherical and TIOL patterns induce astigmatism depending on the increase in IOL power. The inclination of the TIOL in relation to the horizontal plane set at 90 ° promotes the induction of astigmatism. Key words: astigmatism, toric intraocular lenses, tilt and decentration of the intraocular lens, ray tracing

Fermionic Topological Order on Generic Triangulations

Consider a finite triangulation of a surface M of genus g and assume that spin-less fermions populate the edges of the triangulation. The quantum dynamics of such particles takes place inside the algebra of canonical anti-commutation relations (CAR). Following Kitaev’s work on toric models, we identify a sub-algebra of CAR generated by elements associated to the triangles and vertices of the triangulation. We show that any Hamiltonian drawn from this sub-algebra displays topological spectral degeneracy. More precisely, if $${{\mathcal {P}}}$$ is any of its spectral projections, the Booleanization of the fundamental group $$\pi _1(M)$$ can be embedded inside the group of invertible elements of the corner algebra $${{\mathcal {P}}}\, \mathrm{CAR} \, {{\mathcal {P}}}$$ . As a consequence, $${{\mathcal {P}}}$$ decomposes in $$4^g$$ lower projections. Furthermore, a projective representation of $${{\mathbb {Z}}}_2^{4g}$$ is also explicitly constructed inside this corner algebra. Key to all these is a presentation of CAR as a crossed product with the Boolean group $$(2^X,\Delta )$$ , where X is the set of fermion sites and $$\Delta $$ is the symmetric difference of its sub-sets.

A computer code for topological quantum spin systems over triangulated surfaces

We derive explicit closed-form matrix representations of Hamiltonians drawn from tensored algebras, such as quantum spin Hamiltonians. These formulas enable us to soft-code generic Hamiltonian systems and to systematize the input data for uniformly structured as well as for un-structured Hamiltonians. The result is an optimal computer code that can be used as a black box that takes in certain input files and returns spectral information about the Hamiltonian. The code is tested on Kitaev’s toric model deployed on triangulated surfaces of genus 0 and 1. The efficiency of our code enables these simulations to be performed on an ordinary laptop. The input file corresponding to the minimal triangulation of genus 2 is also supplied.

Subjective Perception Of Trifocal IOL Performance, Including Toric Models.

PurposeTo study the patients’ perception of trifocal IOL (Panoptix™) performance.Patients and methods60 eyes of 35 were implanted with trifocal IOL. Refractive (sphere – S, cylinder – Cyl and spherical equivalent – SE, all in D) and visual (distance uncorrected – VAsc, distance corrected – VAcc, intermediate – IntVA, near uncorrected – NVAsc and distance corrected near – NVAcc, all in LogMAR) results were recorded. Patients were asked about satisfaction (per eye), spectacle independence, near and intermediate activities, distance activities in quantity and quality, finally about personal facial care (per patient). Comparison was made between non-toric (48) and toric models, genders (18 males) and between bilateral (25 patients) and unilateral implantations. Results were correlated to age and IOL power.ResultsWith a SE of mean −0.3 ± 0.5 D, cases achieved mean VAsc 0.09 ± 0.1 (~20/25), VAcc 0.05 ± 0.1 (~20/22), IntVA 0.05 ± 0.9 (~20/22), NVAsc 0.05 ± 0.09 (~~20/22) and NVAcc 0.04 ± 0.8 (~~20/22). Mean level of satisfaction was 85.7 ± 16.5, spectacle independence 96.0 ± 10.6, near activities 95.4 ± 9.8, intermediate activities 97.7 ± 6.4, quantity of distance activities 90.2 ± 10.1, quality of distance activities 88.0 ± 12.1 and facial care 92.6 ± 11.9. All comparisons (non-toric and toric, male and female and bilateral and unilateral implantation) were statistically insignificant (P>0.05). Correlation with age and IOL power was also statistically insignificant (P>0.05).ConclusionAs perceived by patients, trifocal IOL resulted in very high level of satisfaction. This satisfaction is reflected on diverse visual activities. This level is achieved regardless of gender, IOL model or even unilateral implantation. It is also achieved regardless the age of patients or preoperative eye status.

Squashed toric manifolds and higher depth mock modular forms

Squashed toric sigma models are a class of sigma models whose target space is a toric manifold in which the torus fibration is squashed away from the fixed points so as to produce a neck-like region. The elliptic genera of squashed toric-Calabi-Yau manifolds are known to obey the modular transformation property of holomorphic Jacobi forms, but have an explicit non-holomorphic dependence on the modular parameter. The elliptic genus of the simplest one-dimensional example is known to be a mixed mock Jacobi form, but the precise automorphic nature for the general case remained to be understood. We show that these elliptic genera fall precisely into a class of functions called higher-depth mock modular forms that have been formulated recently in terms of indefinite theta series. We also compute a generalization of the elliptic genera of these models corresponding to an additional set of charges corresponding to the toric symmetries. Finally we speculate on some relations of the elliptic genera of squashed toric models with the Vafa-Witten partition functions of mathcal{N} = 4 SYM theory on ℂℙ2.

Squashed Toric Sigma Models and Mock Modular Forms

We study a class of two-dimensional {mathcal{N}=(2,2)} sigma models called squashed toric sigma models, using their Gauged Linear Sigma Models (GLSM) description. These models are obtained by gauging the global {U(1)} symmetries of toric GLSMs and introducing a set of corresponding compensator superfields. The geometry of the resulting vacuum manifold is a deformation of the corresponding toric manifold in which the torus fibration maintains a constant size in the interior of the manifold, thus producing a neck-like region. We compute the elliptic genus of these models, using localization, in the case when the unsquashed vacuum manifolds obey the Calabi–Yau condition. The elliptic genera have a non-holomorphic dependence on the modular parameter {tau} coming from the continuum produced by the neck. In the simplest case corresponding to squashed {mathbb{C} / mathbb{Z}_{2}} the elliptic genus is a mixed mock Jacobi form which coincides with the elliptic genus of the {mathcal{N}=(2,2)}{SL(2,mathbb{R}) / U(1)} cigar coset.

On the Rost nilpotence theorem for threefolds

We show that Rost nilpotence holds for a geometrically integral threefold X over a field k of characteristic 0 if and only if αk(X)*∘N( CH 0(Xk(X)))=0 for some integer N>0 for all correspondences α of degree 0 which vanish over some field extension of k. As a corollary we get the Rost nilpotence property for three-dimensional smooth projective geometrically integral schemes over a field of characteristic zero, which are birationally isomorphic to a toric model.

Discrete symmetries in Heterotic/F-theory duality and mirror symmetry

We study aspects of Heterotic/F-theory duality for compactifications with Abelian discrete gauge symmetries. We consider F-theory compactifications on genus-one fibered Calabi-Yau manifolds with n-sections, associated with the Tate-Shafarevich group {mathbb{Z}}_n . Such models are obtained by studying first a specific toric set-up whose associated Heterotic vector bundle has structure group {mathbb{Z}}_n . By employing a conjectured Heterotic/F-theory mirror symmetry we construct dual geometries of these original toric models, where in the stable degeneration limit we obtain a discrete gauge symmetry of order two and three, for compactifications to six dimensions. We provide explicit constructions of mirror-pairs for symmetric examples with {mathbb{Z}}_2 and {mathbb{Z}}_3 , in six dimensions. The Heterotic models with symmetric discrete symmetries are related in field theory to a Higgsing of Heterotic models with two symmetric abelian U(1) gauge factors, where due to the Stückelberg mechanism only a diagonal U(1) factor remains massless, and thus after Higgsing only a diagonal discrete symmetry of order n is present in the Heterotic models and detected via Heterotic/F-theory duality. These constructions also provide further evidence for the conjectured mirror symmetry in Heterotic/F-theory at the level of fibrations with torsional sections and those with multi-sections.

Toric constructions of monotone Lagrangian submanifolds in $\mathbb{CP}^2$ and $\mathbb{CP}^1 \times \mathbb{CP}^1$

We extract from a toric model of the Chekanov-Schlenk exotic torus in $\mathbb{CP}^2$ methods of construction of Lagrangian submanifolds in toric symplectic manifolds. These constructions allow for some control of the monotonicity. We recover this way some known monotone Lagrangians in the toric symplectic manifolds $\mathbb{CP}^2$ and $\mathbb{CP}^1 \times \mathbb{CP}^1$ as well as new examples.