Geometric Approximation Research Articles

An efficient geometric octal zones distance estimation and attribute-based encryption for secure transfer of sensitive data

An efficient geometric octal zones distance estimation and attribute-based encryption for secure transfer of sensitive data

A framework for heart-lung interaction and its application to prone position in the acute respiratory distress syndrome.

While both cardiac output (Qcirculatory) and right atrial pressure (PRA) are important measures in the intensive care unit (ICU), they are outputs of the system and not determinants. That is to say, in a model of the circulation wherein venous return and cardiac function find equilibrium at an 'operating point' (OP, defined by the PRA on the x-axis and Qcirculatory on the y-axis) both the PRA and Qcirculatory are, necessarily, dependent variables. A simplified geometrical approximation of Guyton's model is put forth to illustrate that the independent variables of the system are: 1) the mean systemic filling pressure (PMSF), 2) the pressure within the pericardium (PPC), 3) cardiac function and 4) the resistance to venous return. Classifying independent and dependent variables is clinically-important for therapeutic control of the circulation. Recent investigations in patients with acute respiratory distress syndrome (ARDS) have illuminated how PMSF, cardiac function and the resistance to venous return change when placing a patient in prone. Moreover, the location of the OP at baseline and the intimate physiological link between the heart and the lungs also mediate how the PRA and Qcirculatory respond to prone position. Whereas turning a patient from supine to prone is the focus of this discussion, the principles described within the framework apply equally-well to other more common ICU interventions including, but not limited to, ventilator management, initiating vasoactive medications and providing intravenous fluids.

Improving geometric iterative approximation methods using local approximations

In this study, we propose improvements to Geometric Iterative Methods (GIM) for curve and surface approximation. Our key contributions include introducing an error vector function and deriving new error vectors, which enhance the approximation quality compared to the Least Squared Progressive and Iterative Approximation (LSPIA) methods. Additionally, we integrate parameter correction and control points update based on local approximations, achieving comparable accuracy to Geometric Approximation (GA) methods while being more computationally efficient. Extensive experiments demonstrate the superior accuracy and computational efficiency of our method.

CALIBRATION OF A ONE-DIMENSIONAL MECHANICAL EARTH MODELS USING GEOMETRIC APPROXIMATION OF BOREHOLE BREAKOUTS

Link for citation: Konoshonkin D.V., Rukavishnikov V.V., Shadrin A.S., Antonov A.E., Kupriyanova K.A. Calibration of a one-dimensional mechanical earth models using geometric approximation of borehole breakouts. Bulletin of the Tomsk Polytechnic University. Geo Аssets Engineering, 2023, vol. 334, no. 7, рр. 102-110. In Rus. The relevance. Mechanical earth modeling is widely used in various fields of science and technology. In the oil and gas industry, one-dimensional mechanical earth models are used to analyze wellbore stability, to design hydraulic fracturing, to assess the probability of sand production with oil and gas flow, and as input data for three-dimensional mechanical earth models. One-dimensional mechanical earth models are very demanding on the volume and quality of the initial data, for example, when calibrating the model to define the uniaxial compression strength and horizontal stresses, borehole imager data are required, which are usually not recorded in all wells and in whole interval. At the same time, almost every well has caliper data. Therefore, solving the problem of calibration of a one-dimensional mechanical earth model using more accessible caliper data is an urgent problem, the solution of which will allow building calibrated geomechanical models for a larger number of wells. The main aim: to develop an approach for calibration of one-dimensional mechanical earth models based on well caliper data. Methods: geometric approximation, analysis of laboratory studies, as well as analytical methods for calculating the stress-strain state near the well wall. Results. The paper introduces the equations and the algorithm to define the stresses and uniaxial compression strength of rocks using geometric approximation of borehole breakouts according to caliper data in wells.

Mobile terrestrial laser scanner vs. UAV photogrammetry to estimate woody crop canopy parameters – Part 2: Comparison for different crops and training systems

The measurement of geometric canopy parameters in woody crops is an important task in Precision Agriculture because of their correlation with crop condition and productivity. In recent years, several technological approaches have been developed as an alternative to manual measurements, which are time- and labour-consuming. Two of the most commonly used 3D canopy characterization technologies are mobile terrestrial laser scanning (MTLS) based on light detection and ranging (LiDAR) sensors, and digital aerial photogrammetry (DAP) using imagery from uncrewed aerial vehicles (UAVs). Although both are state-of-the-art and have been fully tested and validated, a complete comparison between their geometric canopy parameter estimations in different woody crops and training systems has not been carried out. For this reason, a set of geometric parameters (canopy height, projected area, and volume) of a vineyard, an intensive peach orchard, and an intensive pear orchard were measured using UAV-DAP and MTLS-LiDAR. A comparison between both kinds of measurements was performed, accounting for the length of the sections in which the crop hedgerows were divided to extract the geometric parameters. Measurements from the UAV and the MTLS were highly correlated (R2 from 0.82 to 0.94) when considering the data from the three crops together, and the correlations were higher when analysing longer row sections. The canopy geometric parameters estimated using the MTLS-LiDAR always had higher values than those from the UAV-DAP. The results presented in this work provide useful data for a more informed selection of technological approaches for 3D crop characterization in Precision Fruticulture and high-throughput phenotyping.

MmWave 6D Radio Localization With a Snapshot Observation From a Single BS

Accurate and ubiquitous localization is crucial for a variety of applications such as logistics, navigation, intelligent transport, monitoring, control, and also for the benefit of communications. Exploiting millimeter-wave (mmWave) signals in 5G and Beyond 5G systems can provide accurate localization with limited infrastructure. We consider the single base station (BS) localization problem and extend it to 3D position and 3D orientation estimation of an unsynchronized multi-antenna user equipment (UE), using downlink multiple-input multiple-output orthogonal frequency-division multiplexing (MIMO-OFDM) signals. Through a Fisher information analysis, we show that the problem is often identifiable, provided that there is at least one multipath component in addition to the line-of-sight (LoS), even if the position of corresponding incidence point (IP) is a priori unknown. Subsequently, we pose a maximum likelihood (ML) estimation problem, to jointly estimate the 3D position and 3D orientation of the UE as well as several nuisance parameters (the UE clock offset and the positions of IPs corresponding to the multipath). The ML problem is a high-dimensional nonconvex optimization problem over a product of Euclidean and non-Euclidean manifolds. To avoid complex exhaustive search procedures, we propose a geometric initial estimate of all parameters, which reduces the problem to a 1-dimensional search over a finite interval. Numerical results show the efficiency of the proposed ad-hoc estimation, whose gap to the Cramér-Rao bound (CRB) is tightened using the ML estimation.

A confocal laser-induced fluorescence diagnostic with an annular laser beam

In this work, we report an annular beam confocal laser-induced fluorescence (LIF) configuration, which allows for high spatial resolution measurements of plasma properties in plasma setups and sources with limited optical access. The proposed LIF configuration utilizes the annular laser beam generated by a pair of diffractive axicons. The LIF signal is collected along the main optical axis within the ring region. It is shown experimentally that at a focal distance of 300 mm, a spatial resolution of ∼5.3 mm can be achieved. Using geometric optics estimations, we showed that ∼1 mm resolution at the same focal distance could potentially be achieved by modifying laser beam parameters. This approaches the localization accuracy of conventional LIF collection methods (with crossing laser beam injection and fluorescence collection optical paths). Measurements of the ion velocity distribution function in an argon plasma using both the confocal LIF with an annular laser beam and conventional LIF demonstrate a satisfactory agreement. The proposed LIF setup has potential applications for diagnostics in various plasma processing equipment and plasma sources, such as hollow cathodes, microplasmas, electric propulsion, etc.

Heat transfer evaluation of liquid lead-bismuth eutectic cross flow tube bundle: Experimental part

Helical coil once-through tube steam generator (HCOTSG) is an excellent form of heat exchanger. HCOTSG is adopted in various industries, such as Lead-bismuth Fast Reactor (LFR). The flow and heat transfer in the shell side of HCOTSG are important for its design and optimization. It is of great significance to carry out relevant experiments to obtain empirical correlations. In this paper, experimental study on the lead-bismuth eutectic (LBE) cross flow around the tube bundle is carried out to investigate the thermal-hydraulic characteristics based on geometric approximation of local region. Three test sections with different inclination angles of 0°, 4°, 8° are adopted in the experiments with Peclect number (Pe) up to 350. The experimental sections are uniformly heated with heat flux ranging from 20 to 100 kW/m2. The heat transfer characteristic of LBE cross flow around inclined tube bundle is obtained, considering the effects of inclination angle of the test section. The heat transfer correlation of LBE cross flow around inclined tube bundle is proposed for the first time. By comparing the data of the experiments, the results are all within the error range of 10%. The correlation is appropriate for the program development of LBE HCOTSG. This study can provide essential experimental data for the design and code development of LBE HCOTSG.

Incorporating species-specific morphology improves model predictions of thermal and hydric stress in the sand fiddler crab, Leptuca pugilator

Understanding where and why organisms are experiencing thermal and hydric stress is critical for predicting species' responses to climate change. Biophysical models that explicitly link organismal functional traits like morphology, physiology, and behavior to environmental conditions can provide valuable insight into determinants of thermal and hydric stress. Here we use a combination of direct measurements, 3D modeling, and computational fluid dynamics to develop a detailed biophysical model of the sand fiddler crab, Leptuca pugilator. We compare the detailed model's performance to a model using a simpler ellipsoidal approximation of a crab. The detailed model predicted crab body temperatures within 1 °C of observed in both laboratory and field settings; the ellipsoidal approximation model predicted body temperatures within 2 °C of observed body temperatures. Model predictions are meaningfully improved through efforts to incorporate species-specific morphological properties rather than relying on simple geometric approximations. Experimental evaporative water loss (EWL) measurements indicate that L. pugilator can modify its permeability to EWL as a function of vapor density gradients, providing novel insight into physiological thermoregulation in the species. Body temperature and EWL predictions made over the course of a year at a single site demonstrate how such biophysical models can be used to explore mechanistic drivers and spatiotemporal patterns of thermal and hydric stress, providing insight into current and future distributions in the face of climate change.

Comments on “horizontal gravity disturbance vector in atmospheric dynamics” by Peter C. Chu

In a recent paper [Chu (2023; Chu23)], the author formulated the equations governing atmospheric motion in a spheroidal coordinate system. Since the mass distribution of the Earth is not exactly spheroidal, the true gravity is not vertical in that coordinate system. Chu23 compared the magnitude of the static horizontal component of gravity in that system to those of the dynamically active forces and concluded that the horizontal components of gravity should not be neglected. In recent papers by the authors [Chang and Wolfe (2022; CW22) and Stewart and McWilliams (2022; CW22)], we explained that the actual interpretation of the approximation made in atmospheric and oceanic modeling is not neglecting the horizontal component of the true gravity, but is a geometrical approximation, approximating nearly spheroidal geopotential surfaces with bumps on which the true gravity is vertical by exactly spheroidal surfaces. We showed that under such an interpretation, the errors due to the geometrical approximation are small. Chu23 claimed that CW22 and SM22 erroneously neglected the gravity perturbations in their analyses. Here, we explain further the differences between these approaches, in the process showing that the criticisms of Chu23 on CW22 and SM22 are invalid, further supporting our conclusion that the horizontal component of the true gravity is not relevant in ocean and atmospheric dynamics. Physically, the reason why horizontal gravity is irrelevant in the coordinate system used by Chu23 is that it is balanced by a static horizontal pressure gradient force.

Sparsity preserving projection aided baselined hyperdisk modeling for interpretable machine health monitoring

Geometric representation optimization models have been widely introduced for machine health monitoring. Nevertheless, their extracted features for machine fault diagnosis lack physical interpretability and health indicators (HIs) have inapparently initial degradation points. In this study, a sparsity preserving projection aided baselined hyperdisk model for interpretable initial fault detection, diagnosis, and degradation assessment is proposed. Herein, a hyperdisk that constructs a proper geometric approximation of a dataset is defined as the cross zone between a hypersphere and an affine hull. Firstly, based on sparsity preserving projection, a physics-informed methodology is proposed to extract interpretable projection features for immediate fault diagnosis. Simultaneously, based on extracted low-dimensional features, a hyperdisk based degradation modeling methodology is proposed to construct a HI for initial fault detection. Herein, once a baselined hyperdisk model is constructed, a HI can be efficiently computed by simultaneously considering the projection and relative distances of the baselined hyperdisk model. Case studies show that the proposed methodology has superior performances than support vector data description (SVDD), hyperplane based degradation modeling, and other statistical based HIs.

Two-Way Crossover Phase 1 Bioequivalence and Safety Studies in Healthy Adults for a Ready-to-Use, Room-Temperature, Liquid-Stable Glucagon Administered by Autoinjector, Prefilled Syringe, or Vial and Syringe.

To demonstrate bioequivalence and safety for a ready-to-use room-temperature liquid-stable glucagon administered subcutaneously (SC) through a glucagon autoinjector (GAI) or a glucagon vial and syringe kit (GVS), versus a glucagon prefilled syringe (G-PFS). Healthy adults (N = 32) were randomly assigned to receive 1-mg glucagon as GAI or G-PFS, and then as the alternative three to seven days later. Other healthy adults (N = 40) were randomly assigned to receive 1-mg glucagon as GVS or G-PFS, and then as the alternative two days later. Samples for plasma glucagon were obtained through 240 minutes after glucagon injection. Bioequivalence was declared when the geometric mean estimate ratio of the area under-the-concentration-versus-time curve from 0 to 240 minutes (AUC0-240) and maximum concentration (Cmax) for plasma glucagon between treatment groups was contained within the bounds of 80% and 125%. Adverse events (AEs) were recorded. The 90% confidence intervals (CIs) for AUC0-240 and Cmax geometric mean ratios for G-PFS to GAI and GVS to G-PFS were contained within the bounds 80% to 125% (G-PFS:GAI AUC0-240 95.05%, 119.67% and Cmax 88.01%, 120.24%; GVS:G-PFS AUC0-240 87.39%, 100.66% and Cmax 89.08%, 106.08%). At least one AE occurred in 15.6% (5/32) participants with GAI, 25% (18/72) with G-PFS, and 32.5% (13/40) with GVS. Sixty-nine of 73 (94.5%) AEs were mild, and none were serious. Nausea was the most common (33/73 [45%]). Bioequivalence and safety were established after 1 mg of this ready-to-use room-temperature liquid-stable glucagon, administered SC to healthy adults, by autoinjector, prefilled syringe, or vial and syringe kit.

The Tapering Length of Needles in Martensite/Martensite Macrotwins

We study needle formation at martensite/martensite macro interfaces in shape-memory alloys. We characterize the scaling of the energy in terms of the needle tapering length and the transformation strain, both in geometrically linear and in finite elasticity. We find that linearized elasticity is unable to predict the value of the tapering length, as the energy tends to zero with needle length tending to infinity. Finite elasticity shows that the optimal tapering length is inversely proportional to the order parameter, in agreement with previous numerical simulations. The upper bound in the scaling law is obtained by explicit constructions. The lower bound is obtained using rigidity arguments, and as an important intermediate step we show that the Friesecke–James–Müller geometric rigidity estimate holds with a uniform constant for uniformly Lipschitz domains.

3D simulations of AGB stellar winds

Context. Stars with an initial mass below ~8 M⊙ evolve through the asymptotic giant branch (AGB) phase, during which they develop a strong stellar wind, due to radiation pressure on newly formed dust grains. Recent observations have revealed significant morphological complexities in AGB outflows, which are most probably caused by the interaction with a companion. Aims. We aim for a more accurate description of AGB wind morphologies by accounting for both the radiation force in dust-driven winds and the impact of a companion on the AGB wind morphology. Methods. We present the implementation of a ray tracer for radiative transfer in the smoothed particle hydrodynamics (SPH) code PHANTOM. Our method allows for the creation of a 3D map of the optical depth around the AGB star. The effects of four different descriptions of radiative transfer, with different degrees of complexity, are compared: the free-wind approximation, the geometrical approximation, the Lucy approximation, and the attenuation approximation. Finally, we compare the Lucy and attenuation approximation to predictions with the 3D radiative transfer code MAGRITTE. Results. The effects of the different radiative transfer treatments are analysed considering both a low and high mass-loss rate regime, and this both in the case of a single AGB star, as well as for an AGB binary system. For both low and high mass-loss rates, the velocity profile of the outflow is modified when going from the free-wind to the geometrical approximation, also resulting in a different wind morphology for AGB binary systems. In the case of a low mass-loss rate, the effect of the Lucy and attenuation approximation is negligible due to the low densities but morphological differences appear in the high mass-loss rate regime. By comparing the radiative equilibrium temperature and radiation force to the predictions from MAGRITTE, we show that for most of the models, the Lucy approximation works best. Although, close to the companion, artificial heating occurs and it fails to simulate the shadow cast by the companion. The attenuation approximation leads to stronger absorption of the radiation field, yielding a lower equilibrium temperature and weaker radiation force, but it produces the shadow cast by the companion. From the predictions of the 3D radiative transfer code MAGRITTE, we also conclude that a radially directed radiation force is a reasonable assumption. Conclusions. The radiation force plays a critical role in dust-driven AGB winds, impacting the velocity profile and morphological structures. For low mass-loss rates, the geometrical approximation suffices, however for high mass-loss rates, a more rigorous method is required. Among the studied approaches, the Lucy approximation provides the most accurate results, although it does not account for all effects.

Optimal Hovering Height and Power Allocation for UAV-Aided NOMA Covert Communication System

In this letter, we consider an unmanned aerial vehicle (UAV) aided covert communication system in which the UAV provides downlink transmission to the public user and covert user with non-orthogonal multiple access (NOMA). In the considered system, the covert performance can be effectively enhanced by the mobility of the UAV and the transmission from UAV to the public user. Aiming at improving the covert signal-to-noise ratio (SNR), we jointly optimize the hovering height and power allocation of UAV and formulate a signomial programming (SP) problem. To tackle the nonconvex optimization, we develop a successive geometric programming approximation (SGPA) algorithm. The optimal hovering height and power allocation are provided with numerical results and the outperformance of our design is verified.

Asymptotic Properties of Solutions to Discrete Sturm-Liouville Monotone Type Equations

Abstract We investigate the discrete equations of the form Δ ( r n Δ x n ) = a n f ( x σ ( n ) ) + b n . \Delta \left( {{r_n}\Delta {x_n}} \right) = {a_n}f\left( {{x_{\sigma \left( n \right)}}} \right) + {b_n}. Using the Knaster-Tarski fixed point theorem, we study solutions with prescribed asymptotic behaviour. Our technique allows us to control the degree of approximation. In particular, we present the results concerning harmonic and geometric approximations of solutions.

Semi-Automated BIM Reconstruction of Full-Scale Space Frames with Spherical and Cylindrical Components Based on Terrestrial Laser Scanning

As-built building information modeling (BIM) model has gained more attention due to its increasing applications in construction, operation, and maintenance. Although methods for generating the as-built BIM model from laser scanning data have been proposed, few studies were focused on full-scale structures. To address this issue, this study proposes a semi-automated and effective approach to generate the as-built BIM model for a full-scale space frame structure with terrestrial laser scanning data, including the large-scale point cloud data (PCD) registration, large-scale PCD segmentation, and geometric parameters estimation. In particular, an effective coarse-to-fine data registration method was developed based on sphere targets and the oriented bounding box. Then, a novel method for extracting the sphere targets from full-scale structures was proposed based on the voxelization algorithm and random sample consensus (RANSAC) algorithm. Next, an efficient method for extracting cylindrical components was presented based on the detected sphere targets. The proposed approach is shown to be effective and reliable through the application of actual space frame structures.

Physiologically Based Pharmacokinetic Model Development and Verification for Bioequivalence Testing of Bempedoic Acid Oral Suspension and Reference Tablet Formulation.

The bioequivalence of bempedoic acid oral suspension and commercial immediate release (IR) tablet formulations were assessed using a physiologically based pharmacokinetic (PBPK) model. The mechanistic model, developed from clinical mass balance results and in vitro intrinsic solubility, permeability, and dissolution data, was verified against observed clinical pharmacokinetics (PK) results. Model inputs included a fraction of a dose in solution (0.01%), viscosity (118.8 cps), and median particle diameter (50 µm) for the suspension and particle diameter (36.4 µm) for IR tablets. Dissolution was determined in the relevant media (pH 1.2-6.8) in vitro. Model simulations of bioequivalence predicted oral suspension (test) to IR tablet (reference) geometric mean ratio estimates of 96.9% (90% confidence interval [CI]: 92.6-101) for maximum concentration and 98.2% (90% CI: 87.3-111) for the area under the concentration-time curve. Sensitivity analyses showed gastric transit time had a minor impact on model predictions. Oral suspension biopharmaceutical safe space was defined by extremes of particle size and the percent of bempedoic acid in solution. PBPK model simulations predicted that the rate and extent of bempedoic acid absorption are unlikely to exhibit clinically meaningful differences when dosed as an oral suspension compared with an IR tablet without requiring a clinical bioequivalence study in adults.

Connectedness in asymmetric spaces

Inverse theorems for geometric approximation theory related to the structure of approximating sets are obtained. Various types of connectedness of sets in asymmetric spaces (generally nonmetrizable) are studied. In particular, conditions are established for an asymmetric space and a subset of this space that guarantee that the intersection of an open ball with this set is path-connected.

Geometry of CMC surfaces of finite index

Abstract Given r 0 > 0 {r}_{0}\gt 0 , I ∈ N ∪ { 0 } I\in {\mathbb{N}}\cup \left\{0\right\} , and K 0 , H 0 ≥ 0 {K}_{0},{H}_{0}\ge 0 , let X X be a complete Riemannian 3-manifold with injectivity radius Inj ( X ) ≥ r 0 \hspace{0.1em}\text{Inj}\hspace{0.1em}\left(X)\ge {r}_{0} and with the supremum of absolute sectional curvature at most K 0 {K}_{0} , and let M ↬ X M\hspace{0.33em}\looparrowright \hspace{0.33em}X be a complete immersed surface of constant mean curvature H ∈ [ 0 , H 0 ] H\in \left[0,{H}_{0}] and with index at most I I . We will obtain geometric estimates for such an M ↬ X M\hspace{0.33em}\looparrowright \hspace{0.33em}X as a consequence of the hierarchy structure theorem. The hierarchy structure theorem (Theorem 2.2) will be applied to understand global properties of M ↬ X M\hspace{0.33em}\looparrowright \hspace{0.33em}X , especially results related to the area and diameter of M M . By item E of Theorem 2.2, the area of such a noncompact M ↬ X M\hspace{0.33em}\looparrowright \hspace{0.33em}X is infinite. We will improve this area result by proving the following when M M is connected; here, g ( M ) g\left(M) denotes the genus of the orientable cover of M M : (1) There exists C 1 = C 1 ( I , r 0 , K 0 , H 0 ) > 0 {C}_{1}={C}_{1}\left(I,{r}_{0},{K}_{0},{H}_{0})\gt 0 , such that Area ( M ) ≥ C 1 ( g ( M ) + 1 ) {\rm{Area}}\left(M)\ge {C}_{1}\left(g\left(M)+1) . (2) There exist C > 0 C\gt 0 , G ( I ) ∈ N G\left(I)\in {\mathbb{N}} independent of r 0 , K 0 , H 0 {r}_{0},{K}_{0},{H}_{0} , and also C C independent of I I such that if g ( M ) ≥ G ( I ) g\left(M)\ge G\left(I) , then Area ( M ) ≥ C ( max 1 , 1 r 0 , K 0 , H 0 ) 2 ( g ( M ) + 1 ) {\rm{Area}}\left(M)\ge \frac{C}{{\left(\max \left\{1,\frac{1}{{r}_{0}},\sqrt{{K}_{0}},{H}_{0}\right\}\right)}^{2}}\left(g\left(M)+1) . (3) If the scalar curvature ρ \rho of X X satisfies 3 H 2 + 1 2 ρ ≥ c 3{H}^{2}+\frac{1}{2}\rho \ge c in X X for some c > 0 c\gt 0 , then there exist A , D > 0 A,D\gt 0 depending on c , I , r 0 , K 0 , H 0 c,I,{r}_{0},{K}_{0},{H}_{0} such that Area ( M ) ≤ A {\rm{Area}}\left(M)\le A and Diameter ( M ) ≤ D {\rm{Diameter}}\left(M)\le D . Hence, M M is compact and, by item 1, g ( M ) ≤ A / C 1 − 1 g\left(M)\le A\hspace{0.1em}\text{/}\hspace{0.1em}{C}_{1}-1 .