3D Mirror Research Articles

A digital workflow for pair matching of maxillary anterior teeth using a 3D segmentation technique for esthetic implant restorations

We investigated a state-of-the-art algorithm for 3D reconstruction with a pair-matching technique, which enabled the fabrication of individualized implant restorations in the esthetic zone. This method compared 3D mirror images of crowns and emergence profiles between symmetric tooth pairs in the anterior maxilla using digital slicewise DICOM segmentation and the superimposition of STL data. With the outline extraction of each segment provided by 100 patients, the Hausdorff distance (HD) between two point sets was calculated to identify the similarity of the sets. By using HD thresholds as a pair matching criterion, the true positive rates of crowns were 100, 98, and 98%, while the false negative rates were 0, 2, and 2% for central incisors, lateral incisors, and canines, respectively, indicating high pair matching accuracy (> 99%) and sensitivity (> 98%). The true positive rates of emergence profiles were 99, 100, and 98%, while the false negative rates were 1, 0, and 2% for central incisors, lateral incisors, and canines, respectively, indicating high pair matching accuracy (> 99%) and sensitivity (> 98%). Therefore, digitally flipped contours of crown and emergence profiles can be successfully transferred for implant reconstruction in the maxillary anterior region to optimize esthetics and function.

Three-dimensional stitching of stereo-deflectometry based on marker points.

As a non-contact and three-dimensional (3D) mirror surface measurement method, stereo-deflectometry has been developing rapidly in recent years. For solving the problem of the measurement of large surface inclination with traditional stereo-deflectometry, 3D stitching of stereo-deflectometry based on marker points is proposed. In this method, the 3D points in the subregions under different perspectives were measured. Meanwhile, the 3D coordinates of the marker points on the sample table, which were calculated by binocular stereo vision, were used for coarse stitching, and the ICP algorithm was used for fine stitching. In order to verify the 3D stitching algorithm, we built a measurement system for the freeform surface of an ultra-short lens with a diameter of about 100 mm and a steepness of 52.6°. The spherical fitting error of the reflective bowl after stitching is within 60 mm. The experimental results verify the feasibility of the method, leading to potential mass application of stereo-deflectometry in 3D measurement of complex optical surfaces with a large aperture and high steepness.

Higgs branches of U/SU quivers via brane locking

We solve a long standing problem on the computation of the Higgs branch mathcal{H} of linear quivers with 8 supercharges and with both unitary and special unitary gauge nodes. The solution uses the concept of magnetic quivers, where components of mathcal{H} are described as 3d mathcal{N} = 4 Coulomb branches. When the starting quiver is good, there is a single component in mathcal{H} and the magnetic quiver is a 3d mirror. The magnetic quivers are obtained from studying the brane web for an auxiliary 5d theory (with only special unitary gauge groups), constrained by a new notion called brane locking, where some branes are required to move together. We view this as a computational tool rather than an operation in 5d. A detailed algorithm is provided.

Pursuing Quantum Difference Equations II: 3D mirror symmetry

Abstract Let $\textsf {X}$ and $\textsf {X}^{!}$ be a pair of symplectic varieties dual with respect to 3D mirror symmetry. The $K$-theoretic limit of the elliptic duality interface is an equivariant $K$-theory class $\mathfrak {m} \in K(\textsf {X}\times \textsf {X}^{!})$. We show that this class provides correspondences $$ \begin{align*} & \Phi_{\mathfrak{m}}: K(\textsf{X}) \leftrightarrows K(\textsf{X}^{!}) \end{align*}$$mapping the $K$-theoretic stable envelopes to the $K$-theoretic stable envelopes. This construction allows us to relate various representation theoretic objects of $K(\textsf {X})$, such as action of quantum groups, quantum dynamical Weyl groups, $R$-matrices, etc., to those for $K(\textsf {X}^{!})$. In particular, we relate the wall $R$-matrices of $\textsf {X}$ to the $R$-matrices of the dual variety $\textsf {X}^{!}$. As an example, we apply our results to $\textsf {X}=\textrm {Hilb}^{n}({{\mathbb {C}}}^2)$—the Hilbert scheme of $n$ points in the complex plane. In this case, we arrive at the conjectures of Gorsky and Negut from [10].

Euler characteristic of stable envelopes

In this paper we prove a formula relating the equivariant Euler characteristic of K-theoretic stable envelopes to an object known as the index vertex for the cotangent bundle of the full flag variety. Our formula demonstrates that the index vertex is the power series expansion of a rational function. This result is a consequence of the 3d mirror self-symmetry of the variety considered here. In general, one expects an analogous result to hold for any two varieties related by 3d mirror symmetry.

Evaluation of measurement uncertainty of the orthogonal deviation angle of the target mirror based on AMCM

Abstract The combination of the three-dimensional (3D) target mirror and laser interferometers can achieve 3D precision measurement, and the orthogonality between the target mirror has a significant impact on the accuracy of the measurement system. In order to ensure the accuracy of the measurement system, it is necessary to measure the orthogonal deviation angle of the 3D target mirror and evaluate the uncertainty to verify whether the machining accuracy of the target mirror meets the requirements. In this paper, to test the orthogonality of the X-Y reflection planes of the 3D target mirror, which is glued by three plane mirrors, the evaluation methods of measurement uncertainty of the orthogonal deviation angle θxy are studied. The measurement model of uncertainty evaluation is built based on the quantitative characteristics analysis method, and the evaluation results of measurement uncertainty are obtained based on the adaptive Monte Carlo method (AMCM). Moreover, the evaluation results are compared with those evaluation results obtained respectively based on the traditional assessment method of measurement uncertainty (called as GUM method) and Monte Carlo method (MCM). Through the comparison of the evaluation results, it can be concluded that the best estimate of the orthogonal deviation angle θxy is about -3.09”, the corresponding standard uncertainty is about 0.69”, and the machining accuracy of the X-Y reflection planes of the target mirror meets the requirements. Moreover, the AMCM evaluation results is reliable, and AMCM is more convenient and efficient than GUM and MCM methods. The research work provides valuable reference for solving practical measurement evaluation problems.

Coulomb and Higgs branches from canonical singularities. Part I. Hypersurfaces with smooth Calabi-Yau resolutions

Compactification of M-theory and of IIB string theory on threefold canonical singularities gives rise to superconformal field theories (SCFTs) in 5d and 4d, respectively. The resolutions and deformations of the singularities encode salient features of the SCFTs and of their moduli spaces. In this paper, we build on Part 0 of this series [1] and further explore the physics of SCFTs arising from isolated hypersurface singularities. We study in detail these canonical isolated hypersurface singularities that admit a smooth Calabi-Yau (crepant) resolution. Their 5d and 4d physics is discussed and their 3d reduction and mirrors (the magnetic quivers) are determined in many cases. As an explorative tool, we provide a Mathematica code which computes key quantities for any canonical isolated hypersurface singularity, including the 5d rank, the 4d Coulomb branch spectrum and central charges, higher-form symmetries in 4d and 5d, and crepant resolutions.

Optimizing femur symmetry judgment using three-dimensional data correction scheme in fractures of the proximal femur

BackgroundThe application of the 3D printing mirror image model is based on the symmetry of the limbs. Different from image fusion to judge the similarity, based on the commonality of the limb morphology of the same organism and the isotropic of the long bone cross-section, the symmetry of the femur has been determined by calculating the dimension difference of the corresponding cross-section of the non-fractured area. However, the previous version used equidistant cross-sections for measurement and two-dimensional data correction, and there were problems with insufficient reliability and data failure. The purpose of this study is to achieve a more accurate and universal symmetry verification scheme for bilateral tubular bones through an improved method. MethodsForty-five imaging data of proximal femoral fracture and osteopathy were selected from October 2015 to September 2017. 10%, 30%, and 50% of the full-length of the bilateral femur is sliced to judge the similarity between paired femurs. Long and short axes of the bilateral femoral cross-sections on the two-dimensional slices were measured and compared. A stylized trigonometric were used to correct the measured axes lengths such that they more closely match with measurements taken from slices perpendicular to femoral shaft axis. Results540 valid data items from the long axis and short axis of the bilateral side of the distal femur were obtained, and 192 of these were corrected. There were no significant differences between the left and right of the long and short axis of each cross-section in paired cases (P>0.05). ConclusionsThis study have demonstrated symmetricity of the left and right femurs. The availability of CT data at any position of the patient's lower limbs is realized through replacing the previous “two-dimensional data correction” with “three-dimensional data correction”.

Conformal manifolds and 3d mirrors of (Dn, Dm) theories

The Argyres-Douglas (AD) theories of type (Dn, Dm), realized by type IIB geometrical engineering on a single hypersurface singularity, are studied. We analyze their conformal manifolds and propose the 3d mirror theories of all theories in this class upon reduction on a circle. A subclass of the AD theories in question that admits marginal couplings is found to be SO or USp gaugings of certain Dp(SO(2N)) and Dp(USp(2N)) theories. For such theories, we develop a method to derive this weakly-coupled description from the Newton polygon associated to the singularity. We further find that the presence of crepant resolutions of the geometry is reflected in the presence of a (non-abelian) symplectic-type gauge node in the quiver description of the 3d mirror theory. The other important results include the 3d mirrors of all Dp(SO(2N)) theories, as well as certain properties of the Dp(USp(2N)) theories that admit Lagrangian descriptions.

3d mirror symmetry and quantum K-theory of hypertoric varieties

Following the idea of Aganagic–Okounkov [2], we study vertex functions for hypertoric varieties, defined by K-theoretic counting of quasimaps from P1. We prove the 3d mirror symmetry statement that the two sets of q-difference equations of a 3d hypertoric mirror pairs are equivalent to each other, with Kähler and equivariant parameters exchanged, and the opposite choice of polarization. Vertex functions of a 3d mirror pair, as solutions to the q-difference equations, satisfying particular asymptotic conditions, are related by the elliptic stable envelopes. Various notions of quantum K-theory for hypertoric varieties are also discussed.

Collisionless plasma transport mechanisms in stochastic open magnetic field lines in tokamaks

The collisionless plasma transport in stochastic magnetic fields connecting to wall boundary has been studied to understand the underlying mechanisms of thermal quench physics in tokamak disruption. In this study, we present a comprehensive understanding of the plasma dynamics in three-dimensional stochastic open magnetic field lines, taking into account the consistent coupling of electron and ion dynamics through the ambipolar electric field. The open stochastic field lines act as a 3D magnetic mirror consisting of the magnetic well and hill regions. It was found that the magnetic hill regions play a critical role in enhancing electron thermal transport. When the plasma collapses to the wall, the 3D ambipolar potential arises in the stochastic layer to maintain the quasi-neutrality of the plasma. The E × B vortices induced by the 3D ambipolar potential mix the plasma across stochastic field lines and enhance the radial transport. Particularly, the E × B mixing between the magnetic well and hill regions provides a collisionless detrapping mechanism that plays a major role in the loss of high-energy trapped electrons. As a result, the electron temperature steadily decreases at a rate of about −0.5 keV ms−1, comparable to the rate observed in thermal quench experiments.

Conformal manifolds and 3d mirrors of Argyres-Douglas theories

Argyres-Douglas theories constitute an important class of superconformal field theories in 4d. The main focus of this paper is on two infinite families of such theories, known as {D}_p^b (SO(2N)) and (Am, Dn). We analyze in depth their conformal manifolds. In doing so we encounter several theories of class \U0001d4ae of twisted Aodd, twisted Aeven and twisted D types associated with a sphere with one twisted irregular puncture and one twisted regular puncture. These models include Dp(G) theories, with G non-simply-laced algebras. A number of new properties of such theories are discussed in detail, along with new SCFTs that arise from partially closing the twisted regular puncture. Moreover, we systematically present the 3d mirror theories, also known as the magnetic quivers, for the {D}_p^b (SO(2N)) theories, with p ≥ b, and the (Am, Dn) theories, with arbitrary m and n. We also discuss the 3d reduction and mirror theories of certain {D}_p^b (SO(2N)) theories, with p < b, where the former arises from gauging topological symmetries of some {T}_p^{sigma } [SO(2M)] theories that are not manifest in the Lagrangian description of the latter.

Three dimensional mirror symmetry beyond ADE quivers and Argyres-Douglas theories

Mirror symmetry, a three dimensional mathcal{N} = 4 IR duality, has been studied in detail for quiver gauge theories of the ADE-type (as well as their affine versions) with unitary gauge groups. The A-type quivers (also known as linear quivers) and the associated mirror dualities have a particularly simple realization in terms of a Type IIB system of D3-D5-NS5-branes. In this paper, we present a systematic field theory prescription for constructing 3d mirror pairs beyond the ADE quiver gauge theories, starting from a dual pair of A-type quivers with unitary gauge groups. The construction involves a certain generalization of the S and the T operations, which arise in the context of the SL(2, ℤ) action on a 3d CFT with a U(1) 0-form global symmetry. We implement this construction in terms of two supersymmetric observables — the round sphere partition function and the superconformal index on S2 × S1. We discuss explicit examples of various (non-ADE) infinite families of mirror pairs that can be obtained in this fashion. In addition, we use the above construction to conjecture explicit 3d mathcal{N} = 4 Lagrangians for 3d SCFTs, which arise in the deep IR limit of certain Argyres-Douglas theories compactified on a circle.

Schur correlation functions from q -deformed Yang-Mills theory

We construct the wave functions in the $q$-deformed 2D Yang-Mills theory that compute torus correlation functions of affine currents in the vertex operator algebra associated to a class of 4D $\mathcal{N}=2$ superconformal field theory. These wave functions are then shown to reduce to the topological correlators of a set of Coulomb branch operators in the $T[SU(N)]$ theory, from which those correlators in the 3D mirror dual of the 4D ${T}_{N}$ theories can be computed.

Intersecting surface defects and 3d superconformal indices

We compute the 3d mathcal{N} = 2 superconformal indices for 3d/1d coupled systems, which arise as the worldvolume theories of intersecting surface defects engineered by Higgsing 5d mathcal{N} = 1 gauge theories. We generalize some known 3d dualities, including non-Abelian 3d mirror symmetry and 3d/3d correspondence, to some of the simple 3d/1d coupled systems. Finally we propose a q-Virasoro construction for the superconformal indices.

Homemade 3D mirror imaging models utility for surgical treatment of complex fractures of scapula

<h2>Summary</h2> The treatment of complex articular scapular fractures requires obtaining an anatomic reduction. The experience of the surgeon and the surgical skills needed are still the most important aspect in this surgical field. 3D printed models at a 1:1 scale provides tactile and visual experience. We used a specular healthy scapula (reverse engineering) as a reliable template for preoperative planning. We pre-contour plates directly over a printed mold, for direct application, without further corrections during the surgical procedure. This reduces improvisation during surgery, the risks of complications and the total costs while improving the accuracy of the anatomical restoration of the native glenopolar angle derived from the indirect reduction of the fracture. Until recently, the use of RP (rapid prototyping) models for managing complex fractures required contracting the services provided by external companies, with the constraints posed on cost and time. We made the whole process ourselves in a DIY mode: from the post-processed radiological images to the 3D model printing, pre contoured plates and surgical simulation.

Elliptic classes on Langlands dual flag varieties

Characteristic classes of Schubert varieties can be used to study the geometry and the combinatorics of homogeneous spaces. We prove a relation between elliptic classes of Schubert varieties on a generalized full flag variety and those on its Langlands dual. This new symmetry is motivated by 3D mirror symmetry, and it is only revealed if Schubert calculus is elevated from cohomology or K theory to the elliptic level.

Three-Dimensional Mirror Symmetry and Elliptic Stable Envelopes

Abstract We consider a pair of quiver varieties $(X;X^{\prime})$ related by 3D mirror symmetry, where $X =T^*{Gr}(k,n)$ is the cotangent bundle of the Grassmannian of $k$-planes of $n$-dimensional space. We give formulas for the elliptic stable envelopes on both sides. We show an existence of an equivariant elliptic cohomology class on $X \times X^{\prime} $ (the mother function) whose restrictions to $X$ and $X^{\prime} $ are the elliptic stable envelopes of those varieties. This implies that the restriction matrices of the elliptic stable envelopes for $X$ and $X^{\prime}$ are equal after transposition and identification of the equivariant parameters on one side with the Kähler parameters on the dual side.

Quasimaps and stable pairs

AbstractWe prove an equivalence between the Bryan-Steinberg theory of$\pi $-stable pairs on$Y = \mathcal {A}_{m-1} \times \mathbb {C}$and the theory of quasimaps to$X = \text{Hilb}(\mathcal {A}_{m-1})$, in the form of an equality of K-theoretic equivariant vertices. In particular, the combinatorics of both vertices are described explicitly via box counting. Then we apply the equivalence to study the implications for sheaf-counting theories onYarising from 3D mirror symmetry for quasimaps toX, including the Donaldson-Thomas crepant resolution conjecture.

Direct laser writing of volumetric gradient index lenses and waveguides

Direct laser writing (DLW) has been shown to render 3D polymeric optical components, including lenses, beam expanders, and mirrors, with submicrometer precision. However, these printed structures are limited to the refractive index and dispersive properties of the photopolymer. Here, we present the subsurface controllable refractive index via beam exposure (SCRIBE) method, a lithographic approach that enables the tuning of the refractive index over a range of greater than 0.3 by performing DLW inside photoresist-filled nanoporous silicon and silica scaffolds. Adjusting the laser exposure during printing enables 3D submicron control of the polymer infilling and thus the refractive index and chromatic dispersion. Combining SCRIBE’s unprecedented index range and 3D writing accuracy has realized the world’s smallest (15 µm diameter) spherical Luneburg lens operating at visible wavelengths. SCRIBE’s ability to tune the chromatic dispersion alongside the refractive index was leveraged to render achromatic doublets in a single printing step, eliminating the need for multiple photoresins and writing sequences. SCRIBE also has the potential to form multicomponent optics by cascading optical elements within a scaffold. As a demonstration, stacked focusing structures that generate photonic nanojets were fabricated inside porous silicon. Finally, an all-pass ring resonator was coupled to a subsurface 3D waveguide. The measured quality factor of 4600 at 1550 nm suggests the possibility of compact photonic systems with optical interconnects that traverse multiple planes. SCRIBE is uniquely suited for constructing such photonic integrated circuits due to its ability to integrate multiple optical components, including lenses and waveguides, without additional printed supports.