Flat Curvature Research Articles

Capacitive Touch Sensing on General 3D Surfaces

Mutual-capacitive sensing is the most common technology for detecting multi-touch, especially on flat and simple curvature surfaces. Its extension to a more complex shape is still challenging, as a uniform distribution of sensing electrodes is required for consistent touch sensitivity across the surface. To overcome this problem, we propose a method to adapt the sensor layout of common capacitive multi-touch sensors to more complex 3D surfaces, ensuring high-resolution, robust multi-touch detection. The method automatically computes a grid of transmitter and receiver electrodes with as regular distribution as possible over a general 3D shape. It starts with the computation of a proxy geometry by quad meshing used to place the electrodes through the dual-edge graph. It then arranges electrodes on the surface to minimize the number of touch controllers required for capacitive sensing and the number of input/output pins to connect the electrodes with the controllers. We reach these objectives using a new simplification and clustering algorithm for a regular quad-patch layout. The reduced patch layout is used to optimize the routing of all the structures (surface grooves and internal pipes) needed to host all electrodes on the surface and inside the object's volume, considering the geometric constraints of the 3D shape. Finally, we print the 3D object prototype ready to be equipped with the electrodes. We analyze the performance of the proposed quad layout simplification and clustering algorithm using different quad meshing and characterize the signal quality and accuracy of the capacitive touch sensor for different non-planar geometries. The tested prototypes show precise and robust multi-touch detection with good Signal-to-Noise Ratio and spatial accuracy of about 1mm.

Refraction and topographic risk factors for early myopic regression after small-incision lenticule extraction surgery.

We sought to evaluate the topographic risk factors for early myopic regression after small-incision lenticule extraction (SMILE). A retrospective case‒control study was conducted, and individuals who underwent SMILE surgery were enrolled. Among them, 406 and 14 eyes were categorized into the nonregression and regression groups, respectively. The preoperative and postoperative parameters in the two groups were collected, including spherical refraction (SE), axial length (AXL) and topographic data. A generalized linear model was adopted to analyze the difference in each parameter between the two groups. After 6months, UCVA decreased in the regression group, and SE increased in the regression group (both P < 0.05). The increase in the CCT at the thinnest point (P = 0.044), flat corneal curvature (P = 0.012) and TCRP (P = 0.001) were significantly greater in the regression group. Regarding the risk factors for myopic regression, preoperative SE, preoperative sphere power, preoperative AXL, preoperative flat corneal curvature, preoperative SA, early postoperative SE, early postoperative sphere power, early postoperative AXL and early postoperative CCT difference were significantly greater in the regression group (all P < 0.05). The SE, sphere power, AXL, preoperative flat corneal curvature, preoperative SA, and postoperative CCT difference correlate with early myopic regression after SMILE.

Factors influencing dominant eye selection in refractive surgery patients: A correlation analysis

ObjectiveThis study aims to reveal the factors influencing the selection of the dominant eye in refractive surgery patients, and enhance the accuracy of clinical evaluation and surgical treatment. MethodsA retrospective study method was employed. The ocular biometric parameters were analyzed in 4,114 patients who underwent refractive surgery at the affiliated hospital of Southwest Medical University from 2019 to 2023. ResultsThe study found that 79.07% of the patients had the right eye as the dominant eye, while 20.93% had the left eye. Although there was no significant difference between the dominant and non-dominant eyes in terms of uncorrected visual acuity and Kappa angle, the dominant eye performed better in aspects such as spherical lens, eye axis, and corneal flat curvature. Furthermore, univariate and multivariate logistic regression results showed that best-corrected visual acuity, pupil diameter, horizontal displacement x-value of the Kappa angle, and astigmatism vector J45 were significant influencing factors for the selection of the dominant eye. ConclusionThere are numerous factors affecting the dominant eye, and the most important core factor is J45. This study comprehensively evaluated the possible factors affecting the dominant eye in patients undergoing refractive surgery, which provides a foundation for the designation of refractive surgical modalities and assurance of surgical outcomes, and opens up new perspectives on understanding the mechanisms of the formation and development of the dominant eye.

Deep learning prediction of steep and flat corneal curvature using fundus photography in post-COVID telemedicine era.

Recently, fundus photography (FP) is being increasingly used. Corneal curvature is an essential factor in refractive errors and is associated with several pathological corneal conditions. As FP-based examination systems have already been widely distributed, it would be helpful for telemedicine to extract information such as corneal curvature using FP. This study aims to develop a deep learning model based on FP for corneal curvature prediction by categorizing corneas into steep, regular, and flat groups. The EfficientNetB0 architecture with transfer learning was used to learn FP patterns to predict flat, regular, and steep corneas. In validation, the model achieved a multiclass accuracy of 0.727, a Matthews correlation coefficient of 0.519, and an unweighted Cohen's κ of 0.590. The areas under the receiver operating characteristic curves for binary prediction of flat and steep corneas were 0.863 and 0.848, respectively. The optic nerve and its peripheral areas were the main focus of the model. The developed algorithm shows that FP can potentially be used as an imaging modality to estimate corneal curvature in the post-COVID-19 era, whereby patients may benefit from the detection of abnormal corneal curvatures using FP in the telemedicine setting.

Gauge and Poincaré properties of the UV cutoff and UV completion in quantum field theory

The ultraviolet (UV) cutoff on a quantum field theory (QFT) can explicitly break or conserve the Poincare (translation) symmetry. And the very same cutoff can explicitly break or conserve the gauge symmetry. In the present work, we perform a systematic study of the UV cutoff in regard to its gauge and Poincare properties, and construct UV completions restoring the broken gauge symmetry. In the case of Poincare-conserving UV cutoff, we find that the gauge symmetry gets restored via the Higgs mechanism. In the case of Poincare-breaking UV cutoff, however, we find that the flat spacetime affine curvature takes the place of the Higgs field and, when taken to curved spacetime, gauge symmetry gets restored at the extremum of the metric-affine action. We also find that gravity emerges at the extremum if the QFT under concern consists of new particles beyond the known ones. The resulting emergent gravity plus renormalized QFT setup has the potential to reveal itself in various astrophysical, cosmological and collider phenomena.

Variability in depth of curve of Spee and its associated skeletal and dental implications in population of Pakistan

Background and Aim: The curve of Spee (COS) is a physiological entity in human dentition. A functional masticatory system necessitates an appropriate occlusal curvature. The primary objective of this investigation was to assess the skeletal and dental parameters in individuals with variation in the depth of curve of Spee. Materials and Methods: A total of 276 patients with pre-treatment lateral cephalograms and dental cast models were investigated in the Orthodontics and Dentofacial Orthopedics Unit of a Tertiary Care Hospital of Mardan, Pakistan from January 2021 to December 2022. Patients with no prior history of orthopedic treatment for functional jaw, prosthodontic treatment, no prior history of cleft lip and palate and cranio-facial disorders were enrolled. Ethical approval was obtained and all the patients were categorized into three groups based on the depth of curve of Spee (COS): Group-I (flat curvature &lt; 2 mm), Group-II (normal curvature 2-3 mm), and Group-III (deep curvature &gt; 3 mm). Lateral cephalometric analysiswas done to measure the four angular and four linear parameters. Molar relation, overbite, COS depth, and overjet were measured based on the occlusal classification. SPSS version 27 was used for data analysis.

Characterizations of -flat curvature tensor on spacetimes and -gravity

The prime goal of this article is to characterize spacetimes endowed with -flat curvature tensor. It is demonstrated that a 4-dimensional -flat perfect fluid spacetime is either a de-Sitter spacetime or locally isometric to Minkowski spacetime under certain energy condition. Moreover, it is established that a Ricci simple -flat spacetime becomes a Robertson-Walker spacetime. In addition, we shown that a Ricci simple spacetime with harmonic -curvature tensor is a generalized Robertson-Walker spacetime. Also, we explain several conclusions based on -flat generalized Robertson-Walker spacetimes. Finally, we investigate -flat spacetimes that satisfy the -gravity and -gravity.

Predictors of long-term visual field outcome after an episode of acute primary angle closure.

To investigate the long-term visual field (VF) outcome and baseline factors associated with functional sequelae in patients who experienced an episode of acute primary angle closure (APAC) and underwent subsequent lens extraction. Fifty patients (50 eyes) who experienced an APAC episode and underwent subsequent lens extraction at Chonnam National University Hospital were enrolled in this retrospective study. Patients underwent VF examinations after 1 year of an acute episode. They were classified into two groups based on whether they had significant VF defects or not. Demographic data were recorded, and baseline anterior-segment OCT (AS-OCT) images were analysed. Multivariate logistic regression analysis was performed to assess baseline risk factors for presence of VF defects. Twenty-five (50%) eyes were found to have varied degree of VF defects after 1 year of an acute episode. Longer duration between the symptom onset and IOP lowering (p=0.005), a higher presenting IOP (p=0.014), and flat iris curvature (p=0.037) at baseline AS-OCT measurement were significant predictors of VF loss. The area under the receiver operating characteristic curve (AUC) revealed that combination of these three potential baseline factors could predict the long-term VF outcome (AUC=0.921). Patients exhibiting a long duration between symptom onset and IOP lowering, a high presenting IOP, and flat iris curvature were at a higher risk of visual impairment after an episode of APAC. The eyes with such features may require more careful follow-up after an episode of APAC.

Comparison of anterior segment parameters in myopia with and without primary open-angle glaucoma.

To compare anterior segment parameters between myopes with and without primary open-angle glaucoma using Pentacam scheimpflug tomography. This was a single-center retrospective cross-sectional study. Records of patients examined with a Pentacam scheimpflug tomographer (Wavelight-Allegro Oculyzer, GmbH, Erlangen, Germany) were reviewed. Variables studied were recorded from the topographic map and included anterior chamber angle, anterior chamber volume, anterior chamber depth, keratometric readings, and corneal thickness. A general linear model for age-and spherical equivalent refraction-adjusted intergroup comparisons of the anterior segment parameters was conducted. The study included myopes previously diagnosed with primary open-angle glaucoma (POAG) [Mild defect, n = 81; Moderate-severe defect, n = 50] and non-glaucomatous myopes (n = 247). The results revealed a smaller anterior chamber angle, shallower anterior chamber depth, and flatter cornea curvature in the mildly glaucomatous group compared to the non-glaucomatous group (p < 0.05). Smaller anterior chamber angle, shallower anterior chamber depth, and thinner cornea thickness were also observed in the moderate-severely glaucomatous group compared to the non-glaucomatous group (p < 0.05). Glaucomatous damage in myopic patients with POAG was associated with comparatively small anterior chamber angle, shallow anterior chamber depth, flat cornea curvature, and thin cornea.

Some cosmological features of 4D Gauss–Bonnet gravity with varying cosmological constant

We explore some cosmological features of the newly suggested 4D Gauss–Bonnet gravity through two different models assuming a varying cosmological constant [Formula: see text]. Observational constraints, such as the cosmic transit and the flat curvature, have been considered in constructing the models. The cosmology in this work has been probed using a given scale factor derived from the desired cosmic behavior which is the inverse of the usual viewpoint. Several models for [Formula: see text] have been proposed in the literature; we use two different ansatze of varying [Formula: see text] and compare the obtained result. We have found that the second ansatz for the varying [Formula: see text], expressed in terms of the Hubble parameter H, gives better results than the first one. The sound speed causality condition along with all nonlinear energy conditions are satisfied for the case of [Formula: see text]. The cosmographic parameters have been investigated.

Construction of canal surfaces based on a specified flat curvature line

The research relevance is predefined by the widespread use of elements and structures that have the shape of canal surfaces in engineering practice and the possibilities of reproducing the surface through kinematics. The research aims to develop new means of modeling canal surfaces referred to as a grid of curvature lines by introducing elements with special properties into the structural model that simplify the solution of differential equations and reduce the amount of computation. To achieve the research methods, the synthetic geometric method, methods of linear algebra, the theory of differential equations and differential geometry, as well as methods of computer geometric modeling and visualization of three-dimensional objects were used. Studies on modeling and studying the properties of channel surfaces are analyzed. The research on the problem of the surfaces and lines of curvature is considered in more detail and the conditions under which it is possible to simplify the solution of the differential equation are identified. It was proved that the condition of contact between the canal surface and the plane along a given plane curve is sufficient for this curve to be one of the curvature lines of the family of orthogonal to the generating circles. This allowed to reduce the solution of the differential equation to two quadratures. The expressions of the corresponding integrals and an algorithm for modeling the canal surface with the possibility of referring to a grid of curvature lines were obtained. The expressions that define the desired surface include the parametric equations of a given plane line; a function that determines the radii of the spheres of the family depending on the parameter of this line. A specific example of modeling a surface based on a defined formula was also considered, and images of this surface with visualization of the coordinate grid were presented. The research’s practical values are defined by the possibility of using the developed modeling tools in the design and computer-aided design of the geometry of real products containing surfaces of a smooth transition of variable radius

Investigating the Role of Surface Roughness and Defects on EC Breakdown, as a Precursor to SEI Formation in Hard Carbon Sodium-Ion Battery Anodes.

Hard carbon (HC) anodes together with ethylene carbonate (EC)-based electrolytes have shown significant promise for high-performing sodium-ion batteries. However, questions remain in relation to the initial contact between the carbon surface and the EC molecules. The surface of the HC anode is complex and can contain both flat pristine carbon surfaces, curvature, nanoscale roughness, and heteroatom defects. Combining density functional theory and experiments, the effect of different carbon surface motifs and defects on EC adsorption are probed, concluding that EC itself does not block any sodium storage sites. Nevertheless, the EC breakdown products do show strong adsorption on the same carbon surface motifs, indicating that the carbon surface defect sites can become occupied by the EC breakdown products, leading to competition between the sodium and EC fragments. Furthermore, it is shown that the EC fragments can react with a carbon vacancy or oxygen defect to give rise to CO2 formation and further oxygen functionalization of the carbon surface. Experimental characterization of two HC materials with different microstructure and defect concentrations further confirms that a significant concentration of oxygen-containing defects and disorder leads to a thicker solid electrolyte interphase, highlighting the significant effect of atomic-scale carbon structure on EC interaction.

Refractive Characteristics and Related Factors of Amblyopia after Lamellar Keratoscleroplasty in Children with Limbal Dermoids.

We examined the refractive characteristics and related factors of amblyopia in pediatric patients with limbal dermoids undergoing lamellar keratoscleroplasty. Forty-one children (mean age: 56.15 ± 22.47 months) were enrolled. Cycloplegic refraction, corneal topography, and anterior segment photography were performed. The corneal topographic and distribution characteristics of the refractive state were summarized, and the relationship between limbal dermoid invasion size and the refractive state was analyzed. The relationship between invasion size and amblyopia severity and the effect of clinical intervention at different times on amblyopia treatment were also analyzed. The spherical power distribution was −1.0–+10.75 D (average: +4.79 ± 3.09 D). The cylinder power was −1.25–−8.75 D (average: −4.19 ± 1.93 D). The axial range of astigmatism was 10–180° (average: 103.54 ± 58.16°). Equivalent spherical refraction was −3.88–+7.76 D (average: +2.70 ± 3.08 D). Twenty-five, fifteen, and one case had limboid dermoid invasion of the central circular zone (CCZ), paracentral annular zone (PCZ), and corneal limbus within 1 mm, respectively. Corneal topography of 39 patients showed flat, steep, and mean curvatures of 38.48 ± 2.12 D, 43.29 ± 1.97 D, and 40.70 ± 1.48 D, respectively. The mean astigmatism was 4.80 ± 2.93 D in the 3-mm optical region. Astigmatism was higher in CCZ than in PCZ invasion (p < 0.05). Postoperative visual acuity was positively correlated with patients’ age and amblyopia treatment duration (r = 0.392, p = 0.048; r = 0.488, p = 0.011), and was negatively correlated with astigmatism (r = −0.646, p < 0.001). High hyperopia and astigmatism are the dominant refractive errors in patients with limbal dermoids undergoing lamellar keratoscleroplasty.

Effects of blade curvature on flow and heat transfer characteristics of internal cooling at trailing edge

In modern turbine blade designs, a large number of internal cooling technologies have been developed and blade curvature is one of the most important factors. This paper numerically simulates the heat transfer process of the internal cooling channel with flat plate and wall curvature at the trailing edge and analyses Nu distribution and deviation between these two structures. The results show that due to the disruptive and reorganising effects of blade curvature on the vortex structure, blade curvature strengthens the heat transfer. There are significant heat transfer differences at the individual surface of each path.

Leaflet Asymmetry Modeling in the Lipid Composition of Escherichia coli Cytoplasmic Membranes.

Lipid composition asymmetry between leaflets is important to cell function and plays a key role in the "positive inside" rule in transmembrane proteins. In this work, Escherichia coli inner plasma membrane models reflecting this asymmetry have been investigated at the early-log and stationary stages during the bacterial lifecycle using all-atom molecular dynamics simulations. The CHARMM36 lipid force field is used, and selected membrane properties are tested for variations between two leaflets and whole membranes. Our models include bacterial lipids with a cyclopropane moiety on the sn-2 acyl chain in the stationary membrane model. The PE/PG ratio for two leaflets reflects the "positive inside" rule of membrane proteins, set to 6.8 and 2.8 for the inner and outer leaflets of the two models, respectively. We are the first to model leaflet asymmetry in the lipid composition of E. coli cytoplasmic membranes and observe the effect on membrane properties in leaflets and whole membranes. Specifically, our results show that for the stationary phase bilayer, the surface area per lipid (SA/lipid) is larger, the thickness (2DC and DB) is smaller, the tilt angle is larger, the tilt modulus is smaller, and the deuterium order parameters (SCD) of sn-1 and sn-2 tails are lower, compared to the early-log stage. Moreover, the stationary stage bilayer has a positive spontaneous curvature, while the early-log stage has a near flat spontaneous curvature. For leaflet asymmetry, the inner leaflet has a larger SA/lipid, a smaller thickness, a smaller elastic tilt modulus (a larger tilt angle), and lower SCD, compared to the outer leaflet in both stages. Moreover, an asymmetric membrane involves a lipid tilt and a lateral extension, varying from a reference state of a pre-equilibrium membrane. This work encourages a more profound exploration of leaflet asymmetry in various other membrane models and how this might affect the structure and function of membrane-associated peptides and proteins.

$d$-Minimal Surfaces in Three-Dimensional Singular Semi-Euclidean Space $\mathbb{R}^{0,2,1}$

In this paper, we investigate surfaces in singular semi-Euclidean space $\mathbb{R}^{0,2,1}$ endowed with a degenerate metric. We define $d$-minimal surfaces, and give a representation formula of Weierstrass type. Moreover, we prove that $d$-minimal surfaces in $\mathbb{R}^{0,2,1}$ and spacelike flat zero mean curvature (ZMC) surfaces in four-dimensional Minkowski space $\mathbb{R}^{4}_{1}$ are in one-to-one correspondence.

Weighted projective Ricci curvature in Finsler geometry

AbstractIn this paper, we introduce the weighted projective Ricci curvature as an extension of projective Ricci curvature introduced by Z. Shen. We characterize the class of Randers metrics of weighted projective Ricci flat curvature. We find the necessary and sufficient condition under which a Kropina metric has weighted projective Ricci flat curvature. Finally, we show that every projectively flat metric with isotropic weighted projective Ricci and isotropic S-curvature is a Kropina metric or Randers metric.

Distribution of ocular biometry in young Chinese eyes: The Anyang University Students Eye Study

To investigate the distribution of ocular biometric parameters and its association to refraction in university students in central China. Ocular biometric parameters including axial length (AL), central corneal thickness (CCT), keratometry power (K), anterior chamber depth (AQD) and lens thickness (LT) were measured by an optical biometry in a cohort of university students. Corneal radius of curvature (CR), lens position (LP), lens power (PBennett ), vitreous chamber depth (VCD) and AL to corneal radius ratio (AL/CR) were calculated. Cycloplegic refraction was measured using an autorefractor. A total of 7650 undergraduate students participated in this study, with a mean age of 20.0±1.4years. The following ocular biometric parameters were measured: AL (24.78±1.21mm), CCT (539.83±33.03μm), AQD (3.23±0.25mm), LT (3.47±0.18mm), CR (7.79±0.27mm), LP (4.97±0.23mm), VCD (17.55±1.15mm), PBennett (25.00±1.07 dioptres) and AL/CR (3.18±0.15). Male subjects were found to have longer AL, thicker CCT, flatter CR, thinner lens, deeper AQD and VCD than female ones. Myopic subjects were found to have longer AL, thinner CCT, steeper CR, thinner and posterior lens, deeper AQD and VCD, lower PBennett and larger AL/CR than emmetropes and hyperopes. Spherical equivalent (SE) showed a negative correlation with AL/CR (r=-0.914), AL (r=-0.755) and VCD (r=-0.751). This study provided a range of reference values for the main ocular biometric parameters in young adults and reported their distributions based on gender and refractive status. Our study indicates that SE has a strong correlation with AL/CR ratio, AL and VCD.

Practical Considerations with Radar Data Height and Great Circle Distance Determination

AbstractOwing to their ease of use, “simplified” propagation models, like the Equivalent Earth model, are commonly employed to determine radar data locations. With the assumption that electromagnetic rays follow paths of constant curvature, which is a fundamental assumption in the Equivalent Earth model, propagation equations that do not depend upon the spatial transformation that is utilized in the Equivalent Earth model are derived. This set of equations provides the true constant curvature solution and is less complicated, conceptually, as it does not depend upon a spatial transformation. Moreover, with the assumption of constant curvature, the relations derived herein arise naturally from ray tracing relations.Tests show that this new set of equations is more accurate than the Equivalent Earth equations for a “typical” propagation environment in which the index of refraction n decreases linearly at the rate dn/dh = -1/4a, where h is height above ground and a is the Earth’s radius. Moreover, this new set of equations performs better than the Equivalent Earth equations for an exponential reference atmosphere, which provides a very accurate representation of the average atmospheric n structure in the United States. However, with this n profile the equations derived herein, the Equivalent Earth equations, and the relation associated with a flat Earth constant curvature model produce relatively large height errors at low elevations and large ranges.Taylor series approximations of the new equations are examined. While a second-order Taylor series approximation for height performs well under “typical” propagation conditions, a convenient Taylor series approximation for great circle distance was not obtained.

Experimental production of samples and prototype parts from titanium-polymer composite material

Work on the current topic of hybrid titanium-polymer composite materials (Ti-PCM) is continuing. After checking the technological feasibility of the two-stage process of manufacturing flat and single curvature of parts, work is carried out to optimize the composition, including through the introduction of elastic intermediate layers, the selection of the optimal parameters of the process.