Geometric Fitting Research Articles

Physical, structural, thermal, and mechanical features combined with neutron and gamma radiation attenuation qualities of Sm2O3 doped transparent borate-rich glasses

Current work presents the synthesis of B2O3–Gd2O3–Li2O–Na2O–LiF‒Sm2O3 glass system via melt-quench approach and scrutiny of its mechanical, thermal, structural, physical, and nuclear radiation attenuation aspects. Raman scattering and Fourier transform infrared spectra revealed B–O stretching modes of BO4 groups linked to BO3 units with nonbridging oxygen atoms and BO3 and BO4 units' existence in the glass structure. By differential scanning calorimetry, glass transition and crystallization temperatures are identified. Relevant analysis showed all glasses' good thermal stability where glass transition temperature varied at 372–407 °C range. ΣR (fast neutron removal cross-section) and for energy 0.025 eV neutrons σT (total cross-section) are computed. In all glasses, 49.25 B2O3–10Gd2O3–10Li2O–10Na2O–20LiF-0.75Sm2O3 (mol%) sample holds higher ΣR (= 0.10207 cm−1). 48B2O3–10Gd2O3–10Li2O–10Na2O–20LiF–2Sm2O3 (mol%) glass possesses greater σT (= 736.675 cm−1) for thermal neutrons, hinting at added Sm2O3's favorable influence as Sm owns a better ability for neutron absorption than B. By Phy-X/PSD, μ/ρ (mass attenuation coefficient) is obtained at photon energy extent 15 keV‒15 MeV. Sm2O3 inclusion from 0 to 2 mol% minorly enhanced the μ/ρ values. Buildup factors estimated via geometric progression fitting method at 1–40 mean free path and energy 0.015–15 MeV span are maximal at medium energy region owing to Compton scattering process. 48B2O3–10Gd2O3–10Li2O–10Na2O–20LiF–2Sm2O3 (mol%) sample shows superior γ-ray blocking capacity in all glasses, suggesting Sm2O3's positive effect. Elastic moduli and Poisson's ratio are computed theoretically by bond compression and Makishima–Mackenzie models. It is identified that all glasses could tolerate longitudinal stress over shear stress.

Size, shape and orientation matter: fast and semi-automatic measurement of grain geometries from 3D point clouds

Abstract. The grain-scale morphology and size distribution of sediments are important factors controlling the erosion efficiency, sediment transport and the aquatic ecosystem quality. In turn, characterizing the spatial evolution of grain size and shape can help understand the dynamics of erosion and sediment transport in coastal, hillslope and fluvial environments. However, the size distribution of sediments is generally assessed using insufficiently representative field measurements, and determining the grain-scale shape of sediments remains a real challenge in geomorphology. Here we determine the size distribution and grain-scale shape of sediments located in coastal and river environments with a new methodology based on the segmentation and geometric fitting of 3D point clouds. Point cloud segmentation of individual grains is performed using a watershed algorithm applied here to 3D point clouds. Once the grains are segmented into several sub-clouds, each grain-scale morphology is determined by fitting a 3D geometrical model applied to each sub-cloud. If different geometrical models can be tested, this study focuses mostly on ellipsoids to describe the geometry of grains. G3Point is a semi-automatic approach that requires a trial-and-error approach to determine the best combination of parameter values. Validation of the results is performed either by comparing the obtained size distribution to independent measurements (e.g., hand measurements) or by visually inspecting the quality of the segmented grains. The main benefits of this semi-automatic and non-destructive method are that it provides access to (1) an un-biased estimate of surface grain-size distribution on a large range of scales, from centimeters to meters; (2) a very large number of data, mostly limited by the number of grains in the point cloud data set; (3) the 3D morphology of grains, in turn allowing the development of new metrics that characterize the size and shape of grains; and (4) the in situ orientation and organization of grains. The main limit of this method is that it is only able to detect grains with a characteristic size significantly greater than the resolution of the point cloud.

Synthesis and Characterization of Nanozeolite from Sugarcane Bagasse Ash and Its Nutrient Loading Potential

Sugarcane bagasse, a known agricultural waste product in the Philippines with 88% silica (SiO2) content based on elemental analysis, is a viable starting material for zeolite synthesis. In this study, silica derived from sugarcane bagasse ash (SBA) collected from La Carlota, Negros Occidental, Philippines, was extracted via an alkaline extraction method using 2M NaOH and precipitation with 5 N H2SO4 under constant stirring at elevated temperature. Sodium aluminate was added as aluminum source then subjected to ageing at 80°C for 72 h to form the clinoptilolite-type zeolite crystals. Characterization using Scanning Electron Microscopy – Energy Dispersive X-ray Spectroscopy and X-Ray Diffractometry confirmed the successful synthesis of the SBA silica and clinoptilolite, with an Si/Al ratio of 1.59 and average pore diameter of 85.77 nm. Surface modification was done by adding CTAB, a cationic surfactant. Nutrient loading was performed using synthesized nanozeolite (SNZ) for N and K loading and surface modified synthesized nanozeolite (SMSNZ) for PK loading which was compared with nutrient loading performance of commercial natural zeolite. The nanozeolite was added to 1 M urea for N loading, 1 M potassium chloride (KCl) for K loading, and 1 M potassium dihydrogen phosphate (KH2PO4) for PK loading at 1:10 (solid: liquid) solution ratio for 8 h under constant stirring followed by filtration and air drying. Chemical characterization of the synthesized nanozeolite revealed that it has a total CEC of 199.30 meq 100 g-1, ICEC of 182.51 meq 100 g-1, and ECEC of 16.79 meq 100 g-1. Nutrient loading resulted in a 9.62% N and 17.01% K2O content using SNZ and a 13.35% P2O5 and 16.26% K2O content using SMSNZ, which were relatively higher compared to using a commercial natural zeolite. These can be attributed to the high internal CEC due to the high quantity of nanopores in the zeolite, which can capture and store the K+ and NH4+ ions via geometric fit, then release them to the soil on-demand via ion-exchange or occlusion. The surface modification with a surfactant drastically alters the surface chemistry of zeolite allowing simultaneous adsorption of anions (PO4-) externally and cations (K+) internally. The chemical characterization confirmed successful loading of N, K, and PK to synthesize nanozeolite from SBA-derived silica, and its potential as a controlled release fertilizer can be tested in further studies.

Successes and Failures of Static Aptamer-Target 3D Docking Models.

While Molecular Dynamics simulation programs are probably superior for predicting the binding and affinity of aptamers and their cognate ligands, such molecular dynamics programs require more computing power and analysis time than static docking programs that are more widely accessible to the scientific community on the internet. Static docking programs can be used to investigate the geometric fit of rigid DNA or RNA aptamer 3D structures and their ligands to aid in predicting the relative affinities and cross-reactivity of various potential ligands. Herein, the author describes when such static 3D docking analysis has worked well to produce useful predictions or confirmation of high-affinity aptamer interactions or successful aptamer beacon behavior and when it has not worked well. The analysis of why failures may occur with static 3D computer models is also discussed.

Effect of the Anticaking Agent FeCN on the Creeping Properties of Alkali Halide Crystals

Fe(CN)64– (abbreviated as FeCN) is a well-known anticaking agent for NaCl that has a nearly perfect geometrical fit to the (001) surface. In this work, the investigation of the action of FeCN on nucleation and creeping is extended to a wide range of alkali halides of both the NaCl and CsCl structures. It was found that FeCN is a powerful nucleation inhibitor and enhances the creeping of alkali halides when FeCN geometrically fits well in the octahedral surface site of hosts with the NaCl crystal structure. The tested alkali halides that do not fall in this group or that have the CsCl structure show some reduction in creeping upon the addition of FeCN, while NaF and LiCl did not show a difference. For this category of crystals, there is a poor fit of the FeCN ion in the crystal surface. This study shows that a strong adsorption strength of FeCN enhances creeping, whereas a weak interaction reduces the creeping of alkali halide crystals.

A new long-term measure of sustainable growth under uncertainty.

The trade-off between short-term success and long-term sustainability is a common subject of great importance both in the biological evolution of organisms and in the economic activities of human beings. In evolutionary biology, bet-hedging theories have described it as the trade-off between the (within-generation) arithmetic mean fitness and the (between-generation) geometric mean fitness of a genotype. Accordingly, bet-hedging strategies observed in various organisms are regarded as optimizing the geometric mean fitness. To increase the geometric mean fitness signifies to suppress the between-generation variance in the mean fitness. Thus, this view is consistent with mean-variance portfolio analysis in which the standard deviation of a portfolio is regarded as a measure of risk. In the present study, we provide yet another measure of long-term sustainability, which is based on minimization of the probability of extinction/bankruptcy that randomly varying population/asset size after a long time becomes less than a certain small value. We present results for representative examples to show that the present criterion gives a qualitatively similar but quantitatively different prediction from the traditional ones. In particular, we emphasize that maximizing survival probability (i.e. minimizing extinction probability) is equivalent neither to maximizing geometric mean fitness nor to minimizing variance in mean fitness, while these three are consistently related to each other.

Influence of BaO/ZnCl2 content on gamma transmission properties of the optical TeO2-based glass system

Tellurite glasses possess attributes that make them attractive for potential radiation shielding uses. are Gamma radiation shielding quantities for three 70TeO2–(30-x)BaO–xZnCl2 glass samples (x = 5 (TBZC-A, 15 (TBZC-B), and 25 (TBZC-C) mol.%) were estimated and presented in this report. The mass attenuation coefficient MAC and buildup factors were estimated theoretically using XCOM and geometric progression fitting methods respectively for photon energies 15 keV ≤ E ≤ 15 MeV. The MAC vary within the limits 0.03374 − 45.20520 cm2/g for TBZC-A, 0.03321–44.30207 cm2/g for TBZC-B and 0.03267–43.37889 cm2/g for TBZC-C. Also, the mass energy absorption coefficients of the glasses ranged from 0.02021 to 42.32862, 0.02021–40.83892 0.02020–39.31615 cm2/g for TBZC-A, TBZC-B, and TBZC-C respectively. The effective atomic number of the glasses fluctuates within 25.01–52.03, 24.06–50.70 and 23.17–49.09 for TBZC-A, TBZC-B and TBZC-C, respectively. Analysis of sundry shielding and dosimetric parameters indicated higher photon intensity and energy absorption in BaO rich glasses compared to ZnCl2 rich glasses. The present glasses are relatively better than some existing glass shields thus making them potentially useful in gamma radiation absorption roles in gamma radiation based systems/facilities.

Structure and reactivity of sodium aluminate complexes in alkaline solutions

The underlying mechanism by which tetrahedrally-coordinated aluminate solution species react to precipitate octahedrally-coordinated Al3+ in gibbsite is unknown. Sodium aluminate solutions provide the opportunity to investigate the role of ion speciation and local structure in the reaction, as the solution metastability can be controlled by varying ratio of excess NaOD to Al3+. Here, capitalizing on this tunable precipitation behavior, aluminate speciation was investigated through a combination of Raman, infrared, and NMR spectroscopies, together with geometrical fitting of neutron and X-ray radial distribution functions. These techniques reveal a mixture of monomeric Al(OD)4− and dimeric Al2O(OD)62− in all compositions, but solutions avoiding precipitation for extended timescales (i.e. months to years) show an increased dimeric Al2O(OD)62− population formed at the expense of the Al(OD)4− monomer. Conversion between these species, as well the potential for further oligomerization and formation of larger pre-nucleation species is driven by the hydrogen/deuterium bonding (H/D-bonding) and proton/deuteron transfer reactions. Changes within the local environment around the aluminate anions, including solvation and the presence of solvent-shared ion pairs or contact ion pairs, will consequently govern the reactivity of these aluminate species to either promote or inhibit precipitation.

PriFit: Learning to Fit Primitives Improves Few Shot Point Cloud Segmentation

AbstractWe present PriFit, a semi‐supervised approach for label‐efficient learning of 3D point cloud segmentation networks. PriFit combines geometric primitive fitting with point‐based representation learning. Its key idea is to learn point representations whose clustering reveals shape regions that can be approximated well by basic geometric primitives, such as cuboids and ellipsoids. The learned point representations can then be re‐used in existing network architectures for 3D point cloud segmentation, and improves their performance in the few‐shot setting. According to our experiments on the widely used ShapeNet and PartNet benchmarks, PriFit outperforms several state‐of‐the‐art methods in this setting, suggesting that decomposability into primitives is a useful prior for learning representations predictive of semantic parts. We present a number of ablative experiments varying the choice of geometric primitives and downstream tasks to demonstrate the effectiveness of the method.

Additive Manufacturing of Subject‐Conformal Receive Coils for Magnetic Resonance Imaging

AbstractHigh signal‐to‐noise ratio (SNR) is crucial to obtaining high‐quality magnetic resonance (MR) images. However, a poor fit of fixed‐size radiofrequency (RF) coils to the subject often limits the SNR both in research and clinical magnetic resonance imaging (MRI) practice. Therefore, there is an urgent need to fabricate RF coils that exhibit a close geometrical fit (or are subject conformal) to the to‐be‐imaged region. A range of 3D printing methods are proposed for producing such conformal coils and overcoming constraints in geometrical complexity, production time, and cost. Laser powder bed fusion and stereolithography‐based methods are explored. The fully digital workflow allows for the seamless integration of electromagnetic simulations of geometrically complex coils, resulting in rapid design iterations. SNR gains up to 68% are observed for single 3D‐printed subject‐conformal coils compared to a state‐of‐the‐art commercially available (nonconformal) coil array. In addition to tests on phantoms, a conformal 3D‐printed coil is used to image the metacarpophalangeal joint of the thumb from a volunteer on an MRI scanner to demonstrate the improved image quality.

QADCGPIC–M: A point kernel shielding code with features for handling bulk shields up to 100 mean free path and stratified shielding configurations

Salient modifications and validations performed on a Point Kernel method based code QADCGPIC, which are important for optimizing shield design is presented in the paper. The geometric progression method based build–up factors (BUFs) for penetration depths of medium up to 100 mean free path is incorporated into the modified QADCGPIC–M code. Further improvement to the code is made by incorporating the modified Kalos’ formula of double layer gamma ray exposure build–up factor (DBUF) for the shielding materials used in the design of nuclear and radiological facilities. The modified code is validated by estimating the BUFs, DBUFs, and gamma dose rates at the exit of the shield with Monte Carlo simulation for various shielding configurations of lead, tungsten, iron, and concrete and published values. The validation exercise indicates a good agreement between the computed values by different methods. The incorporation of geometric progression fitting formula and modified Kalos’ formula into the QADCGPIC–M code increases the ability of the code to handle bulk shielding and optimization of thicknesses of double layered shielding configurations.

Free2CAD

CAD modeling, despite being the industry-standard, remains restricted to usage by skilled practitioners due to two key barriers. First, the user must be able to mentally parse a final shape into a valid sequence of supported CAD commands; and second, the user must be sufficiently conversant with CAD software packages to be able to execute the corresponding CAD commands. As a step towards addressing both these challenges, we present Free2CAD wherein the user can simply sketch the final shape and our system parses the input strokes into a sequence of commands expressed in a simplified CAD language. When executed, these commands reproduce the sketched object. Technically, we cast sketch-based CAD modeling as a sequence-to-sequence translation problem, for which we leverage the powerful Transformers neural network architecture. Given the sequence of pen strokes as input, we introduce the new task of grouping strokes that correspond to individual CAD operations. We combine stroke grouping with geometric fitting of the operation parameters, such that intermediate groups are geometrically corrected before being reused, as context, for subsequent steps in the sequence inference. Although trained on synthetically-generated data, we demonstrate that Free2CAD generalizes to sketches created from real-world CAD models as well as to sketches drawn by novice users. Code and data are at https://github.com/Enigma-li/Free2CAD.

An improved real-time model for divergent and dense lane detection of unmanned vehicles

Lane detection is the key technology of an advanced driver assistance system. This study proposed an efficient and novel lane detection method, Lane Kernel Parameter Module ResNet-18 (LKPM-ResNet-18), to improve the detection efficiency of lane with complex topologies (such as divergent lines and dense lines). This method can precisely predict the global structure in a bottom-up manner and directly output the curve parameters of the lane alignment model. In addition, LKPM was used to obtain accurately the local structure information and the slender shape of the lane with complex topology, and then the shape convolution kernel parameters of each instance are dynamically predicted to optimize the results of the subsequent output curves. Finally, the prior information of the global lane is fully integrated through the lane structure constraint loss, and the optimization results are fused into the global geometric curve fitting output, so that the fitted lanes are smoother and more continuous. The method proposed has real-time detection efficiency and requires little postprocessing because of the end-to-end direct approach. The validated results show that the efficiency of this method is obviously better than that of State-Of-The-Art (SOTA) methods, such as PointLaneNet and ENet-SAD. The F1 scores increase by 0.43% and 4.92%, respectively compared with the latest CurveLanes-NAS-L and SCNN on the CULane test dataset. The accuracy of 88.98% can be obtained on the CurveLanes test dataset. Meanwhile, the result from real driving environment detection exceeds the top performances of the other by 2.22% with the accuracy of 86.47%.

Comparative assessment of fast and thermal neutrons and gamma radiation protection qualities combined with mechanical factors of different borate-based glass systems

Adequate shielding from ionizing radiations is essential in nuclear facilities because of such radiations’ adverse effects on humans in the event of unwanted or accidental exposure. In the current work, for four distinct compositions of B2O3-Li2O, Li2O-Na2O-K2O-B2O3, Gd2O3-SiO2-B2O3, and Bi2O3-Li2O-ZnO-B2O3 glass systems, neutron and γ-ray attenuation competencies combined with elastic features have been examined for feasible nuclear radiation protection purposes. ΣR (fast neutron removal cross-section) and for thermal energy neutrons σT (total cross-section) and SP (shielding percentage) were estimated. Comparably, in all samples, 50B2O3-10K2O-40Li2O (mol%) glass possesses larger ΣR (=0.11755 cm−1), whereas 25B2O3-37.5Si2O-37.5Gd2O3 (mol%) glass shows large σT (=646.171 cm−1) and SP for thermal neutrons at minimal thickness, indicating the included Gd2O3’s positive effect as element Gd has a high neutron absorption capacity. Employing the Phy-X/PSD program and MCNPX code, μ/ρ (mass attenuation coefficient) of all selected glasses is calculated for a γ-ray energy span of 0.015 – 15 MeV. Gd2O3 or Bi2O3 addition improved μ/ρ, and such increment is significant at low energies owing to PEA (photoelectric absorption) dominance and Gd or Bi K-edges. Also, for 15B2O3-10ZnO-5Li2O-70Bi2O3 (mol%) glass, μ/ρ has been derived by the WinXCOM program and FLUKA, Geant4, and PHITS codes, and a good accord between such simulated and theoretical μ/ρ outcomes is noticed following the calculated relative differences. Next, linear attenuation coefficient, effective atomic number and electron density, MFP (mean free path), TVL (tenth-value layer), HVL (half-value layer), and RPE (radiation protection efficiency) have also been evaluated. Comparatively, at 1.25, 0.662, and 0.2 MeV energies, 15B2O3-10ZnO-5Li2O-70Bi2O3 (mol%) sample possesses lower MFP and HVL than five SCHOTT AG commercial glass shields. Approximated RPE results affirmed all Gd2O3-SiO2-B2O3 and Bi2O3-Li2O-ZnO-B2O3 samples’ potent absorption (almost 100%) ability for lower energy γ-rays. Moreover, equivalent atomic number, and by geometric progression fitting process, within energy 15 keV–15 MeV extent for ten different penetration depths at 1–40 mfp span buildup factors have been assessed. 15B2O3-10ZnO-5Li2O-70Bi2O3 (mol%) glass exhibits better gamma-ray shielding effectiveness in all chosen samples, specifying Bi2O3’s favorable impact. Changes in photon shielding factors were interpreted following pair production, Compton scattering, and PEA processes. Later, elastic (Young’s (Y), bulk (K), shear (S), and longitudinal (L)) moduli and Poisson’s ratio values have been calculated for all inspected glasses. BC (bond compression) and M-M (Makishima–Mackenzie) models were utilized for such elastic traits reckoning. All K, Y, S, and L values’ trends for binary B2O3-Li2O glasses were identical in both BC and M-M models, and Kbc was found to be raised from 73.63 to 89.89 GPa, while KM–M increased from 75.35 to 180.53 GPa accordingly when Li2O content improved from 9.6 to 39.9 mol% in the chemical composition.

Buildup Factor Computation and Percentage Depth Dose Simulation of Tissue Mimicking Materials for an External Photon Beam (0.15–15 MeV)

Nowadays, the use of tissue mimicking material (TMM) is widespread in both diagnostic and therapeutic medicine, as well as for quality assurance and control. For example, patient exposure evaluation during therapeutic tests has been commonly measured using TMMs. However, only a few materials have been developed for research use at the megavoltage photon energy encountered in medical radiology. In this paper, we extended our previous work to cover the photon energy range of 0.15–15 MeV for five human tissues (adipose, cortical bone, fat, lung and muscle). As a selection criterion for TMM, other than the attenuation coefficient, we introduced the computation of the buildup factor (BUF) for a given couple of energy and depth based on the geometric progression fitting method. Hence, we developed a C++ program able to compute BUF for depths up to 40 mean free path. Moreover, we simulated the percentage depth dose (PDD) of a 6 MV photon beam through each tissue and their equivalent materials using the Geant4 Monte Carlo toolkit (version 10.5). After the comparison of a set of parameters (mass attenuation and mass energy absorption coefficients, BUF, equivalent and effective atomic numbers, electron density, superficial and maximal dose and dose at 10 and 20 cm depths), we found that SB3 (a mixture of epoxy and calcium carbonate) and MS15 (a mixture of epoxy, phenol, polyethylene and aluminum oxide) accurately imitate cortical bone and muscle tissues, respectively. AP6 (a mixture of epoxy, phenol, polyethylene and teflon), glycerol trioleate and LN1 (a mixture of polyurethane and aluminum oxide) are also suitable TMMs for adipose, fat and lung tissues, respectively. Therefore, this work can be useful to physician researchers in dosimetry and radiological diagnosis.

The important choice of reference environment in microevolutionary climate response predictions.

It is well documented that individuals of wild populations can adjust to climate change by means of phenotypic plasticity, but few reports on adaptation by means of genetically based microevolution caused by selection. Disentanglement of these separate effects requires that the reference environment (the environmental zero point) is defined, and this should not be done arbitrarily. The problem is that an error in the reference environment may lead to large errors in predicted microevolution. Together with parameter values and initial mean trait values, the reference environment can be estimated from environmental, phenotypic and fitness data. A prediction error method for this purpose is described, with the feasibility shown by simulations. As shown in a toy example, an estimated reference environment may have large errors, especially for small populations. This may still be a better choice than use of an initial environmental value in a recorded time series, or the mean value, which is often used. Another alternative may be to use the mean value of a past and stationary stochastic environment, which the population is judged to have been fully adapted to, in the sense that the expected geometric mean fitness was at a global maximum. Exceptions are cases with constant phenotypic plasticity, where the microevolutionary changes per generation follow directly from phenotypic and environmental data, independent of the chosen reference environment.

Multi-Motion Segmentation: Combining Geometric Model-Fitting and Optical Flow for RGB Sensors

This paper presents a novel multi-motion segmentation framework by combining the geometric model fitting and optical flow. More precisely, we use the spatial information extracted by the multi-model fitting and the motion information provided by the optical flow to improve the practicality of the motion segmentation algorithm. The real scenes contain challenges such as multiple motions, camera translation, large field of views, and occlusions. To improve the segmentation accuracy of the real scenes, we first propose a cluster selection method to generate several clusters that can cover all motion models in the data, then a cluster merging strategy is proposed to estimate the basic motion models and the number of motions accurately for the scene. Finally, motion assignment of the remaining points is carried out to complete the motion segmentation. Detailed experiments on two challenging real-world benchmark datasets (62-clip and KT3DMoSeg) show that the proposed framework is superior to the state-of-the-art multi-motion segmentation methods.

Evolutionary bet‐hedging reconsidered: What is the mean–variance trade‐off of fitness?

AbstractIn traditional theories, bet‐hedging in evolutionary biology is defined as a trade‐off between the within‐generation arithmetic mean fitness (AMF) of a genotype and between‐generation variance (BGV) in AMF across generations. The rationale of this definition is that a bet‐hedger genotype suppresses the BGV to increase between‐generation geometric mean fitness (GMF; an index of long‐term sustainability), which in turn entails costs in terms of AMF. However, too strict interpretation of this definition causes confusion among empirical researchers. For example, in empirical studies comparing a putative bet‐hedger (e.g., producing a generalist phenotype or mixture of various phenotypes) and non‐bet‐hedger control (e.g., producing only a specialist phenotype), reviewers sometimes request that a necessary condition of bet‐hedging is that the bet‐hedger candidate shows a smaller arithmetic mean of AMFs obtained from multiple generations and larger GMF than the control. However, the cost of bet‐hedging is incurred at the potential genotypic level and thus the decrease of AMF mean is not necessarily observed at the phenotypic level (especially if bet‐hedger individuals have good conditions). Moreover, contrary to previous arguments, the “fine‐grained” environments would promote bet‐hedging because even monomorphic specialist genotypes increase GMF if their population size is sufficiently large. Computer simulations support these views. I try to shift the definition of bet‐hedging from the trade‐off‐based one to the GMF‐based one: bet‐hedging is any strategy to increase the between‐generational GMF to avoid extinction of its controlling genotype against unpredictable environmental fluctuation. Under this new light, bet‐hedging will be a universal law of biology.

Weighted geometric circle fitting for the Brogar Ring: Parameter-free approach and bias analysis

Geometric circle fitting is a fundamental task in scientific and engineering research. In this contribution, a parameter-free approach for weighted geometric circle fitting is proposed based on the iteratively linearized model with condition equations. Furthermore, the corresponding bias analysis is investigated by the classical theory of nonlinear least-squares. The simulated results show that: 1) Our new approach obtains the optimal solution in various weighted cases and its convergence behavior is more stable than the classical parametric method; 2) The biases caused by nonlinearity can be effectively removed in different situations. Finally, the measured coordinates of an archaeological site in Britain, the Brogar Ring, are adjusted and the results are analyzed.

Aperture measurement based on a conic invariant.

With the advantages of low cost, universal applicability, and in situ detection, the conic invariant of the tested aperture diameter was obtained by ellipse geometric fitting on the aperture surface. The world coordinate system was established, and the transformation relationship between the world coordinate system and the camera coordinate system was obtained by the calibration. The improved Candy algorithm and coordinate transformation relationship could be used to project the sub-pixel coordinates of the aperture edge onto the aperture surface. Then, the ellipse geometric fitting was performed on the aperture edge curve surface to obtain the conic invariant. Finally, the conic invariant was used to measure the aperture diameter on the test bench.