Geometric Point Research Articles

Mitral annulus strain by 3D echo reveals regional annular dysfunction in Barlow's disease

Abstract Background Barlow's disease (BD) provides both diagnostic and therapeutic challenges. Annular dilation is typically seen in BD, however, data on regional deformation is lacking. Purpose We hypothesized that mitral annulus dilates non-homogenously during ventricular systole in BD. A method to calculate annular regional strain was developed and applied in a subset of BD patients and healthy controls. Methods Ten patients with BD and late systolic mitral regurgitation and nine healthy controls were studied. For each subject, the mitral annulus was segmented throughout the cardiac cycle using 3D echocardiography. Twelve evenly distributed geometrical points were annotated along the annular perimeter, enabling the creation of periodic degree-3 spline curves parameterized by arc length at each discrete time-frame. The motion of the mitral annulus was then acquired by assuming that heterogeneity in annular strain is small and finding the point-wise map that minimized the total displacement between the consecutive curves. Then, the end-diastolic annular curve was divided into 200 evenly distributed points around the annular perimeter, and the point-wise mapping was implemented to create a continuous movement of the discretized annulus throughout the cycle. Annular strain was then calculated for each individual line segment. The method presented herein is validated by comparing the strain between sonomicrometric crystals in pigs and the method described above. The timescale was normalized from ED (end-diastole) to mitral valve opening for each individual. The regional strains of the annulus were calculated with the ED configuration as reference. Results Hemodynamic data are presented in Table 1. In BD annulus area increased from 16.6±3.2 to 21.7±4.2 cm2 at end-diastole and peak systole, respectively (p<0.001). In controls, annulus area at end-diastole and end-systole was 9.6±2.2 cm2 and 9.2±1.8 cm2, respectively (NS). Figure 1 demonstrates non-homogenous regional strain at peak systole, with the most severe deformation in the posteromedial region. In healthy controls, peak systolic strain was similar in all segments. Conclusions In the present study, we have applied a novel non-invasive method to demonstrate non-homogenous deformation of the mitral annulus in Barlow patients. On average, the most severe deformation was seen in the posteromedial region. This finding may reveal further insight into the mechanisms of late systolic mitral regurgitation in BD as well as the design of annuloplasty in the future. Funding Acknowledgement Type of funding sources: Foundation. Main funding source(s): Trond Mohn Foundation

DECISION SUPPORT SYSTEM FOR HOME SURGERY ASSISTANCE RECIPIENT USING TECHNIQUE FOR ORDER PERFORMANCE BY SIMILARY TO IDEAL SOLUTIONS (TOPSIS) METHOD (CASE STUDY : KOTAPULU VILLAGE, DOLO DISTRICT)

This study aims to create a decision support system for home renovation aid recipients that can speed up and simplify the decision-making process in providing home surgery assistance so that home surgery assistance is more objective in accordance with community priorities or on target using the TOPSIS method. The TOPSIS method uses the principle that the chosen alternative must have the closest distance from the positive ideal solution and the longest (farthest) distance from the negative ideal solution from a geometric point of view by using the Euclidean distance (distance between two points) to determine the relative proximity of an alternative to the optimal solution. . The criteria used in the system are land ownership, roof conditions, wall conditions and floor conditions. The data used by the author is 210 original data from the Kotapulu village office. so that the system created by the author can make it easier for the Kotapulu village office to determine the recipient of the house renovation assistance only by inputting population data based on the survey results.

A geometrical point of view for branching problems for holomorphic discrete series of conformal Lie groups

This paper is devoted to branching problems for holomorphic discrete series representations of a conformal group [Formula: see text] of a tube domain [Formula: see text] over a symmetric cone [Formula: see text] restricted to the conformal group [Formula: see text] of a tube domain [Formula: see text] holomorphically embedded in [Formula: see text]. The goal of this work is the explicit construction of the symmetry breaking and holographic operators in this geometrical setting. We answer this program with the introduction of another functional model for holomorphic discrete series representations. This model leads to a geometrical interpretation and a close relation to the theory of orthogonal polynomials for such branching problems. This program is illustrated by three cases. First, we consider the [Formula: see text]-fold tensor product of holomorphic discrete series of the universal covering of [Formula: see text]. Then, it is tested on the restrictions of a member of the scalar-valued holomorphic discrete series of the conformal group [Formula: see text] to the subgroup [Formula: see text], and finally to the subgroup [Formula: see text].

Étale Covers and Fundamental Groups of Schematic Finite Spaces

We introduce the category of finite étale covers of an arbitrary schematic space X and show that, equipped with an appropriate natural fiber functor, it is a Galois Category. This allows us to define the étale fundamental group of schematic spaces. If X is a finite model of a scheme S, we show that the resulting Galois theory on X coincides with the classical theory of finite étale covers on S, and therefore, we recover the classical étale fundamental group introduced by Grothendieck. To prove these results, it is crucial to find a suitable geometric notion of connectedness for schematic spaces and also to study their geometric points. We achieve these goals by means of the strong cohomological constraints enjoyed by schematic spaces.

How Rough Is the Path? Terrain Traversability Estimation for Local and Global Path Planning

Perception and interpretation of the terrain is essential for robot navigation, particularly in off-road areas, where terrain characteristics can be highly variable. When planning a path, features such as the terrain gradient and roughness should be considered, and they can jointly represent the traversability cost of the terrain. Despite this range of contributing factors, most cost maps are currently binary in nature, solely indicating traversible versus non-traversible areas. This work presents a joint local and global planning methodology for building continuous cost maps using LIDAR, based on a novel traversability representation of the environment. We investigate two approaches. The first, a statistical approach, computes terrain cost directly from the point cloud. The second, a learning-based approach, predicts an IMU response solely from geometric point cloud data using a 2D-Convolutional-LSTM neural network. This allows us to estimate the cost of a patch without directly driving over it, based on a data set that maps IMU signals to point cloud patches. Based on the terrain analysis, two continuous cost maps are generated to jointly select the optimal path considering distance and traversability cost for local navigation. We present a real-time terrain analysis strategy applicable for local planning, and furthermore demonstrate the straightforward application of the same approach in batch mode for global planning. Off-road autonomous driving experiments in a large and hybrid site illustrate the applicability of the method. We have made the code available online for users to test the method.

Bifurcation and traveling wave solutions of stochastic Manakov model with multiplicative white noise in birefringent fibers

Manakov model is an extended form of Schrödinger equation. It is a coupled partial differential equation governing the dual-mode transmission of optical fiber communication and the deep-sea transportation with double-layer constraints. In this paper, the bifurcation and traveling wave solutions of the stochastic Manakov model(SMM) describing the multiplicative white noise of optical signal propagation in birefringent fibers are studied. The research work is carried out in the following three steps. Firstly, by the help of traveling wave transformation and first integral, the SMM with multiplicative white noise is simplified to a 2D planar dynamic system. Secondly, the phase diagrams of the planar dynamic system are drawn to determine the possible traveling wave solutions. Finally, based on the classification of parameter group, combined with the elliptic integral technique, the solitary wave solutions and traveling wave solutions of SMM are constructed. The obtained bifurcation results reveal the dynamic behavior of SMM from a geometric point of view. According to the phase portraits, we get abundant solitary wave solutions and traveling wave solutions, including elliptic function periodic solution, trigonometric function solution and singular periodic solution. This is the first study on the bifurcation of SMM with multiplicative white noise, and the obtained results provide the propagation of optical solitons in nonlinear optics.

Approximation of conic sections by weighted Lupaş post-quantum Bézier curves

Abstract This paper deals with weighted Lupaş post-quantum Bernstein blending functions and Bézier curves constructed with the help of bases via ( p , q ) \left(p,q) -integers. These blending functions form normalized totally positive bases. Due to the rational nature of weighted Lupaş post-quantum Bézier curves and positive weights, they help in investigating from geometric point of view. Their degree elevation properties and de Casteljau algorithm have been studied. It has been shown that quadratic weighted Lupaş post-quantum Bézier curves can represent conic sections in two-dimensional plane. Graphical analysis has been presented to discuss geometric interpretation of weight and conic section representation by weighted Lupaş post-quantum Bézier curves. This new generalized weighted Lupaş post-quantum Bézier curve provides better approximation and flexibility to a particular control point as well as control polygon due to extra parameter p p and q q in comparison to classical rational Bézier curves, Lupaş q q -Bézier curves and weighted Lupaş q q -Bézier curves.

Achromatic stigmatism: achromatic Cartesian ovoid.

Monochromatic and chromatic aberrations are imaging defects mainly studied from a geometrical optics point of view. These defects are treated through optimization and minimization methods to achieve acceptable performance in optical imaging systems, where the correct choice of glass materials is one of the main challenges. The selection of glass materials is a complex issue that requires a large amount of computing power within sophisticated computational algorithms and enough professional experience in the area. However, in this work, we propose a new methodology to treat the chromatic and geometrical aberrations simultaneously by taking advantage of the relationship between form parameters of Cartesian surfaces and wavelength in the material. From this relationship, we obtain an achromatism principle that establishes the conditions for refracting systems to present a strictly achromatic stigmatism.

The evolution of single-site Pd1/AC catalyst during the process of acetylene dialkoxycarbonylation

The stability of heterogeneous single-metal-site catalysts (HSMSCs) is always a challenging issue. Deactivation of HSMSCs often occurred and draw much intention. The investigation of the single-metal-site evolution during the deactivation process is great significance to maintain the stability of HSMSCs. Herein, a fundamental understanding of the deactivation process of an initially efficient single-Pd-site catalyst (Pd1/AC) for acetylene dialkoxycarbonylation was revealed from geometrical and electronic point of view via a series of characterizations. Synergistic effect of O2 and iodine ligands contributed to the stability of Pd1/AC catalyst to some extent. The valence of single Pd ions gradually changed from [Pdδ+] to [Pd0], leading to the formation of Pd nanoparticles (Pd black). In addition, the blockage of support microspores also worsened the deactivation of Pd1/AC.

Influence of distance from lens to sample surface on spectral sensitivity of femtosecond laser-induced breakdown spectroscopy with NaCl water film

Increasing the emission intensity of laser-induced breakdown spectroscopy (LIBS) is an effective way to improve the sensitivity of LIBS technology to elements analysis in liquid samples. In this work, the influence of the distance from lens to sample surface (DFLS) on the spectral emission of femtosecond laser-induced plasma of NaCl water film was studied by measuring Na atomic line. The results showed that the emission intensity of the spectral line presented the phenomenon of double peaks with an increase in the DFLS. The position for the highest spectral intensity was not geometric focal point of focusing lens, but was located in front of the geometric focal point. In addition, we carried out quantitative analysis on Na element with different concentrations, showing a calibration curve of Na element, and calculating limit of detection (LOD) and relative standard deviation (RSD) for different DFLSs. Subsequently, the changes in the LOD and RSD with the DFLS are discussed. With the increase of the DFLS, the LOD and RSD were greatly reduced. At the DFLS of 99.0 mm, the line intensity was highest, and the LOD and RSD were better. Therefore, it can be confirmed that femtosecond LIBS of water film can be optimized by changing the DFLS, the experiment shows great potential in real-time water quality monitoring.

Complex coupled dispersionless equations in Minkowski 3-space

ABSTRACT In this study, we investigate the geometric and algebraic aspects of defocusing Complex Coupled Dispersionless (CCD) equations in Minkowski space. We give the conditions for obtaining CCD equations from moving spacelike or timelike space curves using the Frenet and Darboux frames. Besides, we present the Lax pairs that indicate that the corresponding CCD equations are integrable. Finally, we evaluate the conserved quantities for CCD equations from the geometric point of view.

Geometric Mapping Evaluation for Real-Time Local Sensor Simulation.

Medical augmented reality and simulated test environments struggle in accurately simulating local sensor measurements across large spatial domains while maintaining the proper resolution of information required and real time capability. Here, a simple method for real-time simulation of intraoperative sensors is presented to aid with medical sensor development and professional training. During a surgical intervention, the interaction between medical sensor systems and tissue leads to mechanical deformation of the tissue. Through the inclusion of detailed finite element simulations in a real-time augmented reality system the method presented will allow for more accurate simulation of intraoperative sensor measurements that are independent of the mechanical state of the tissue. This concept uses a coarse, macro-level deformation mesh to maintain both computational speed and the illusion of reality and a simple geometric point mapping method to include detailed fine mesh information. The resulting system allows for flexible simulation of different types of localized sensor measurement techniques. Preliminary simulation results are provided using a real-time capable simulation environment and prove the feasibility of the method.

The interactive fuzzy linguistic term set and its application in multi-attribute decision making

In multi-attribute decision making problems, some decision information interact with each other. The paper proposes an interactive fuzzy linguistic term set to describe the interactive information in multi-attribute decision making problems. The properties of the interactive fuzzy linguistic term set and its advantages of improving the consistency of decision information are discussed, which are also interpreted from the geometric point of view. Meanwhile, some numerical examples are given to illustrate its application in dealing with the interactive information in multi-attribute decision making problems, which can improve the effectiveness of the decision results and promote the development of artificial intelligence.

Algebraic traits of structurally balanced nodes and structurally unbalanced nodes via a geometric-based method

A node is a structurally balanced (respectively, unbalanced) node if and only if the absolute value of its corresponding entry in the right eigenvector associated with the zero eigenvalue of the Laplacian matrix is equal to (respectively, is less than) one. The corresponding entry in the right eigenvector is called the algebraic trait for the structurally balanced property of a node. This paper aims to explore the algebraic trait for the structurally balanced property of a node under a signed digraph with a spanning tree by using a geometric-based method. Such a geometric point of view reveals the relationships of the links in a network for structurally balanced and structurally unbalanced nodes. The structurally balanced property of a node is determined by its parent nodes, and the connections between itself and its parent nodes. First of all, a hierarchical structure of its parent nodes is proposed, based on which the Laplacian matrix of the underlying topology can be written as a lower triangular matrix. Then, according to the lower triangular Laplacian matrix, the mathematical expression of the right eigenvector associated with the zero eigenvalue is derived. Based on this, as well as the definition of the structurally balanced node, the algebraic trait for the structurally balanced property of a node is obtained. Finally, a numerical example is provided to verify theoretical results.

Integration of Morphometrics and Machine Learning Enables Accurate Distinction between Wild and Farmed Common Carp.

Morphology and feature selection are key approaches to address several issues in fisheries science and stock management, such as the hypothesis of admixture of Caspian common carp (Cyprinus carpio) and farmed carp stocks in Iran. The present study was performed to investigate the population classification of common carp in the southern Caspian basin using data mining algorithms to find the most important characteristic(s) differing between Iranian and farmed common carp. A total of 74 individuals were collected from three locations within the southern Caspian basin and from one farm between November 2015 and April 2016. A dataset of 26 traditional morphometric (TMM) attributes and a dataset of 14 geometric landmark points were constructed and then subjected to various machine learning methods. In general, the machine learning methods had a higher prediction rate with TMM datasets. The highest decision tree accuracy of 77% was obtained by rule and decision tree parallel algorithms, and “head height on eye area” was selected as the best marker to distinguish between wild and farmed common carp. Various machine learning algorithms were evaluated, and we found that the linear discriminant was the best method, with 81.1% accuracy. The results obtained from this novel approach indicate that Darwin’s domestication syndrome is observed in common carp. Moreover, they pave the way for automated detection of farmed fish, which will be most beneficial to detect escapees and improve restocking programs.

Kinematic and Geometric Characterization of the Vögelsberg Rockslide (Tyrol, Austria) by Means of MT-InSAR Data

This paper focuses on the study of the Vögelsberg landslide located in the municipality of Wattens (Tyrol, Austria), which reactivated in 2016, causing damages to nearby buildings and infrastructures. Since the date of reactivation, a modern monitoring system has been implemented with the installation of in-situ geodetic automated tracking total stations (ATTS), an inclinometer and two piezometers. Here, we describe two distinctive methods, the Breaks for Additive Seasonal and Trend (BFAST) and the Vector Inclination Method (VIM) used to characterize the landslide from the kinematic and geometrical point of view. The main input data, used for both methods, derive from processing a stack of several Sentinel-1 differential interferograms with the Multiple Small Baseline Subset (MSBAS) 2D and 3D algorithms. BFAST allowed highlighting the seasonality of the phenomenon from the analysis of the time series as well as the trend and the breakpoints that identify the landslide reactivation phases. These latter were then correlated with the main triggering factors such as rain and snow melting. The application of the VIM through the exploitation of the MSBAS displacement vectors allowed the reconstruction of the depth of the landslide slip surface along both the longitudinal and transversal direction and, in turn, the evaluation of the volumes of material mobilized by the landslide. The results obtained further prove that procedures for the in-depth analysis of Multi-Temporal Interferometric Synthetic Aperture Radar (MT-InSAR) data can contribute to slow-moving landslide characterization, which represents a fundamental step for landslide hazard assessment within quantitative risk analyses.

Kantowski–Sachs model in non-minimally coupled scalar theory

In this study, our main purpose is to study a model which is homogenous and anisotropic describing early stage of Universe in non-minimally coupled scalar theory. It is quite interesting to study a model describing early stage in modified theory which is related to scalar field. In this context, we introduced Kantowski–Sachs metric for perfect fluid in non-minimally coupled scalar theory. Exact solution of field equations is attained for [Formula: see text] model. Matter distributions for radiation, cosmic string and cosmological constant are investigated for constructed model. For different selections of arbitrary constants, Kantowski–Sachs model shows three different behaviors related with Hubble parameter and deceleration parameter. Also, some observational parameters, such as luminosity distance, angular diameter distance and distance modulus, are obtained for Kantowski–Sachs Universe. Lastly, we get Statefinder parameters for the model. All properties of constructed model are discussed from a physical and geometric point of view.

Accuracy of patellar tendon at the attachment as anatomic landmark for rotational alignment of tibial component

To investigate the accuracy of the modified Akagi line which referenced the patellar tendon at the attachment and the geometrical center point of the tibial osteotomy surface for tibial rotational alignment. Between July 2021 and December 2021, 72 patients who underwent three-dimension (3D) CT for varus osteoarthritis knees were enrolled. Among 72 patients, 18 were male and 54 were female with a mean age of 64.9 years (range, 47-84 years). The preoperative hip-knee-ankle angle ranged from 0° to 26°, with a mean of 9.3°. CT images were imported into Mimics 21.0 medical image control system to establish 3D models of the knees. The prominent point of lateral epicondyle and the medial epicondylar sulcus were identified in femoral 3D models to construct the surgical transepicondylar axis and the vertical line of its projection [anteroposterior (AP) axis]. In tibial 3D models, the patellar tendon at the attachment was used as anatomical landmarks to construct rotational alignment for tibial component, including the line connecting the medial border of the patellar tendon at the attachment (C) and the middle (O) of the posterior cruciate ligament insertion (Akagi line), the line connecting the point C and the geometric center (GC) of the tibial osteotomy plane [medial border axis of the patellar tendon (MBPT)], the line connecting the medial sixth point of the patellar tendon at the attachment and the point GC [medial sixth axis of the patellar tendon (MSPT)], the line connecting the medial third point of the patellar tendon at the attachment and point O [medial third axis of the patellar tendon 1 (MTPT1)], and the line connecting the medial third point of the patellar tendon at the attachment and point GC [medial third axis of the patellar tendon 2 (MTPT2)]. The angles between the five reference axes and the AP axis were measured, and the distribution of the rotational mismatch angles with the AP axis was counted (≤3°, 3°-5°, 5°-10°, and >10°). Relative to the AP axis, the Akagi line and MBPT were internally rotated (1.6±5.9)° and (2.4±6.9)°, respectively, while MSPT, MTPT1, and MTPT2 were externally rotated (5.4±6.6)°, (7.0±5.8)°, and (11.9±6.6)°, respectively. There were significant differences in the rotational mismatch angle and its distribution between reference axes and the AP axis ( F=68.937, P<0.001; χ 2=248.144, P<0.001). The difference between Akagi line and MBPT showed no significant difference ( P=0.067), and the differences between Akagi line and MSPT, MTPT1, MTPT2 were significant ( P<0.012 5). When the position of the posterior cruciate ligament insertion can not be accurately identified on total knee arthroplasty, MBPT can be used as the modified Akagi line in reference to the geometrical center point of the tibial osteotomy surface to construct a reliable rotational alignment of the tibial component.

Discretization and de-geometrization (II): Quantizing Minkowski's spacetime continuum

A path toward quantizing gravity is suggested by describing the emergence of the spacetime continuum and its curvature using a mechanistic substratum model of discrete entities. By fusing pregeometry and the new mathematics of endo-geometry, a concept of a dynamically changing hyperspherical “quantized bubble” replaces the conventional geometric point. A quantum foam is an assemblage of these interacting bubbles. The structure of the cosmos, particles, and black holes are treated as naturally emerging four-dimensional hyperspheres. An insight into dark energy is considered.

825-P: Composite Glucose and C-Peptide Endpoints Show Early Efficacy in Recent-Onset Type 1 Diabetes (T1D) Clinical Trials

C-peptide area under the curve (AUC) at ≥1 year, a standard endpoint of recent-onset T1D clinical trials, is derived from a 120-minute mixed meal tolerance test (MMTT) . We analyzed whether composite glucose and C-peptide endpoints, useful in post hoc analyses of prevention trials, could detect treatment effects as early as 3 months between the combined treated and placebo groups from 3 TrialNet recent-onset T1D trials that met their primary endpoint. Comparisons were made between treated and placebo groups after adjustments for age, sex, and BMI Z-score using AUC C-peptide (standard measure) , AUC C-peptide/AUC glucose (AUC ratio) , and a new measure, the centroid ratio. Centroids, geometric central points of shapes, were derived from MMTT shapes formed from mean glucose and C-peptide values at 30, 60, 90, and 120 minutes. The centroid ratio is the C-peptide coordinate/glucose coordinate of the centroid. A treatment effect at 3 months was evident for centroid and AUC ratios (p&amp;lt;0.0 and p=0.002, respectively) and not AUC C-peptide (p=0.056) . Similar results were seen when individual trials were compared. The difference between combined groups at 3, 6, and 12 months is demonstrated by vectors that start at baseline (Figure) . In conclusion, composite glucose and C-peptide endpoints appear to identify early treatment efficacy and should be considered in future new-onset pilot studies and trials. Disclosure L.M.Jacobsen: None. A.Pugliese: Advisory Panel; Provention Bio, Inc., Consultant; Quell Tx. P.Gottlieb: Advisory Panel; Janssen Research &amp; Development, LLC, ViaCyte, Inc., Other Relationship; IM Therapeutics, Research Support; Caladrius Biosciences, Inc., Immune Tolerance Network, National Institute of Diabetes and Digestive and Kidney Diseases, Novo Nordisk, Precigen, Inc., Tolerion, Inc. J.Sosenko: None. D.D.Cuthbertson: None. M.J.Haller: Advisory Panel; SAB Biotherapeutics , Consultant; MannKind Corporation, Sanofi. H.M.Ismail: n/a. E.K.Sims: Other Relationship; Medscape, Patent. S.E.Gitelman: Advisory Panel; Abata Therapeutics, Avotres Inc., Biolojic Design, Ltd., Provention Bio, Inc., Rubius, SAB Biotherapeutics, Inc., Tolerion, Inc. D.K.Wherrett: n/a. A.Moran: Advisory Panel; Dompé, Other Relationship; Novo Nordisk, Research Support; Abbott Diabetes, Provention Bio, Inc. M.A.Atkinson: None.