Third-degree Polynomial Research Articles

Evaluation of low-cost electronic sensors for monitoring soil moisture in an experimental area in the Brazilian semiarid

PurposeThis paper aims to determine and evaluate the calibration curve for low-cost electronic sensors in soils from a reclaimed and degraded area in the Brazilian semiarid region.Design/methodology/approachThe probes were made, programmed and inserted in soil previously conditioned in polyethylene cylinders. The sets “cylinder + probe + soil” were subjected to saturation for a period of 24 h and, subsequently, gravitational drainage at room temperature and daily weighings were performed. When the set reached constant weight, the samples were taken to dry in an oven at 105°C to determine the dry mass and later, determine the gravimetric moisture and convert it into volumetric. The volumetric moistures obtained were related to measured frequency variations and the adjustments were analyzed by regression, which was subjected to analysis of variance (p = 0.05), and related by a third-degree polynomial equation whose quality of the fit was verified with coefficient of determination (R2).FindingsThe obtained moistures were related to the estimated moistures and evaluated by the root-mean-square error and straight 1:1. The results demonstrate that the sensors are not accurate for moistures in saturation, but representative and statistically acceptable results for moistures up to field capacity.Originality/valueThis paper has not been published before in its current, or similar form.

Minority-carrier dynamics in β-gallium oxide probed by depth-resolved cathodoluminescence

The behavior of hole polarons in β-gallium oxide (Ga2O3) has attracted significant attention. Depth-resolved cathodoluminescence (CL) was used to investigate the minority carrier dynamics in β-Ga2O3. First, a model describing CL intensity was proposed by considering the depth-dose function and surface recombination. A universal depth-dose function for β-Ga2O3, which has the form of a third-degree polynomial, was presented based on Monte Carlo simulation by introducing a normalized depth, which is the depth normalized by the electron beam range. Second, two experimental approaches, plan-view and cross-sectional CL measurements, were applied to unintentionally doped β-Ga2O3 (−201) wafers, and the experimental results were compared with those of the proposed model. The hole diffusion length was estimated to be within the range of 200–400 nm through the plan-view measurement, whereas a hole diffusion length of 250 nm was obtained through the cross-sectional measurement. The values were consistent with each other, and the model reproduced the experimental results well. This indicates that the nonequilibrium minority hole in the unintentionally doped β-Ga2O3 is mobile and forms a ‘weak’ polaron. The reduced recombination velocity of the (−201) face was estimated to be approximately ten for the plan-view measurement, whereas that of ten or more was assumed for the cross-sectional measurement. No inconsistency was observed, but the low-energy plan-view measurement is considered more suitable for investigating the surface recombination velocity.

The Taxonomy of Mineral Occurrence Rarity and Endemicity

ABSTRACT Nearly a half of known IMA-approved minerals (as of November 2021) are reported from four localities or fewer and so may be considered rare mineral species. These minerals form a continuum with more common species (e.g., rock-forming minerals), all of which constitute important constituents of Earth and contributors to its dynamics. To better understand the taxonomy of mineral rarity, evaluations have been made on the basis of k-means clustering and kernel density estimation of one-dimensional data on mineral occurrence metrics. Results from second- and third-degree polynomial regression analyses indicate the presence of a divergence between the observed number of endemic minerals discovered since 2000 and those that are likely to represent “true” endemic species. The symmetry index, calculated using the approach of Urusov for each rarity cluster, reveals a gradual decrease from ubiquitous to endemic from 0.64 to 0.47. A network analysis of element co-occurrences within each rarity cluster suggests the existence of at least three different communities having similar geochemical affinities; the latter may reflect the relative abundance of minerals their elements tend to form. The analysis of element co-occurrence matrices within each group indicates that crustal abundance is not the only factor controlling the total number of minerals each element tends to form. Other significant factors include: (1) the geochemical affinity to the principal element in the group (i.e., sulfur for chalcophile and oxygen for lithophile elements) and (2) dispersion of the principal element through geochemical processes. There is a positive correlation between the lithophile element group's abundance in the Earth's crust and the number of common minerals they tend to form, but a negative correlation with the number of rare species.

Development of low complexity open circuit voltage model for state of charge estimation with novel curve modification technique

The accurate estimation of State of Charge (SOC) is crucial for safe operation and long-life cycle of lithium-ion battery (LiB) system. Out of the several methods used for SOC estimation, data-based approaches have favorable results. These methods require higher computations and extensive training. This restricts the implementation of such methods using low computational power, cost-effective general-purpose microcontroller. In this paper, a simple, low complexity, open-circuit voltage (OCV) model with seven coefficients, third-degree polynomial function has been proposed for the SOC estimation. The performance of the proposed model is compared with the existing OCV models. To enhance the accuracy further, the model is suitably modified using a two-degree polynomial function dependent on the remaining useful life (RUL). The proposed model is validated on the experimental as well as standard datasets and results in terms of RMS error and R2 score are presented. The investigational results show that the SOC estimation based on proposed OCV–SOC model can efficiently limit the error below 0.01885 for entire SOC range and 0.01448 for partial (10−90%) SOC range.

Low-complexity mapping of soil temperature for thermal treatment follow-up

Thermal desorption is a method of soil treatment that heats soil in order to vaporize and extract contaminants. It relies on temperature measurements to assess the progress of the remediation, but these measurements are generally not numerous because of cost constraints. This paper proposes a low-complexity method to interpolate sparse temperature data over the whole site to generate visual representations that ease the treatment follow-up. The temperatures of the points that are not monitored are approximated by a weighted average of the 3 closest measurements, then a third-degree polynomial is fitted to the data via a finite element method. The resulting approximations yield an overall Root Mean Square Error (RMSE) of the temperature estimation of 35 K, which allows for realistic representations of the temperature at each point of the map with reduced sensor deployment.

Predicting risk of falls in elderly using a single Inertial Measurement Unit on the lower-back by estimating spatio-temporal gait parameters.

One of the consequences of aging is the increased risk of falls, especially when someone walks in unknown or uncontrolled environments. Usually, gait is evaluated through observation and clinical assessment scales to identify the state and deterioration of the patient's postural control. Lately, technological systems for bio-mechanical analysis have been used to determine abnormal gait states being expensive, difficult to use, and impossible to apply in real conditions. In this article, we explore the ability of a system based on a single inertial measurement unit located in the lower back to estimate spatio-temporal gait parameters by analyzing the signals available in the Physionet repository "Long Term Movement Monitoring Database" which, together with automatic classification algorithms, allow predicting the risk of falls in the elderly population. Different classification algorithms were trained and evaluated, being the Support Vector Machine classifier with a third-degree polynomial kernel, cost function C = 2 with the best performance, with an Accuracy = 59%, Recall = 91%, and F1- score = 71%, providing promising results regarding a proposal for the quantitative, online and realistic evaluation of gait during activities of daily living, which is where falls actually occur in the target population. Clinical Relevance - This work proposes an early risk of falls detection tool, essential to start preventive treatment strategies to maintain the independence of the elderly through a non-invasive, simple, and low-cost alternative.

Microstructural view of anatase to rutile phase transformation examined by in-situ high-temperature X-ray powder diffraction

The phase transformation of commercial TiO2 was investigated carefully by in-situ high-temperature X-ray powder diffraction. The diffractograms between 25 ​°C and 800 ​°C were employed to determine the composition, unit cell parameters, and microstructure. The phase transition initiated slowly at 400 ​°C due to the seeding effect of pre-existing rutile and accelerated above 600 ​°C. The unit cell volume of anatase exhibits a third-degree polynomial distribution similar to c-direction, where the volume increased before and decreased during the phase transition. In contrast, a and b unit cell parameters increased with temperature, following a second-degree polynomial distribution. The unit cell parameters and volume of rutile increased continually with temperature following a third-degree polynomial distribution. A slight difference in expansion rates before and during phase transformation reflects the formation and amalgamation of newly materialized rutile with pre-existing one. Both lattice strain and crystallite size of anatase increased before and decreased during the phase transition. The vigorous lattice vibration of the dominant anatase lattice is likely responsible for minor changes in the crystallite shape of pre-existing rutile, resulting in a nominal size decrease before phase transition. The materialization of newly formed rutile occurred under decreased lattice strain and increased crystallite size.

Silicon Photomultipliers Coupled to Scintillators With the Emission Maximum at 550 nm

A majority of the silicon photomultipliers (SiPMs) are sensitive to blue and near-ultraviolet (NUV) photons that are not optimized for scintillators with the emission maximum at wavelengths longer than 500 nm. The red–green–blue (RGB) SiPM is developed for the maximum photon detection efficiency (PDE) at 550 nm, which is a good match for some high-light-yield scintillators, such as CsI:Tl (CsI) and Gd <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1.5</sub> Y <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1.5</sub> Ga <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> Al <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> O <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">12</sub> :Ce (GYGAG). Comparisons are made for the performance of these scintillators coupled to the RGB SiPM and a blue-sensitive SiPM. Because it takes tens of nanoseconds for the microcells to recharge after registering a photon hit, the linearity of these scintillation detectors was studied for high-energy gammas where numerous scintillation photons are generated. In addition, the energy resolution of the 662-keV gamma emitted by <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">137</sup> Cs was measured for temperatures between −20 °C and 50 °C. The nonlinearity was observed above 1 MeV for all measurements, and however, it can be corrected by energy calibration using a third-degree polynomial. For CsI, the energy resolution is better with the blue-sensitive SiPM because of the lower dark count rate (DCR). In contrast, GYGAG coupled to the RGB SiPM has a better energy resolution for temperatures below 30 °C because of the well-matched emission spectrum and PDE distribution. Nevertheless, the advantage disappears for temperatures above 30 °C due to the higher DCR. It would be useful to further develop the RGB SiPM with a lower DCR and higher operating temperatures.

Maturation Fetus Ascending Aorta Elastic Properties: Circumferential Strain and Longitudinal Strain by Velocity Vector Imaging.

ObjectiveThis study aimed to assess the circumferential and longitudinal strain of the fetal ascending aortic (AA) wall and establish a gestational age-associated longitudinal reference for aortic wall strain during the second half of pregnancy.MethodsSingleton fetuses with gestational age (GA) at 20 + 0 to 24 + 6 weeks were prospectively collected from a low-risk population. Global circumferential strain (GCS) and mean longitudinal strain (MLS) of the ascending aorta were measured serially at 4-week intervals using the velocity vector imaging (VVI) technique. Fractional polynomials were conducted to obtain the best-fitting curves between GA and AA strains. GA-specific reference percentiles of GCS and MLS were established by multilevel modeling.ResultsA total of 223 fetuses with a total of 1,127 serial observations were enrolled. GCS presented a second-degree fractional polynomial smoothing regression along GA (R2 = 0.635, P < 0.05). Fetal aortic GCS remained unchanged at ~27.29% (20.36–35.6%) before 31 weeks and increased significantly from 31.36% (26.38–37.12%) at 31 weeks to 43.29% (30.5–56.78%) at term. MLS presented a third-degree fractional polynomial smoothing regression along GA (R2 = 0.465, P < 0.05). MLS remained steady at ~10.03% (3.28–17.62%) between 20 and 31 weeks and then increased significantly from 12.68% (7.42–20.1%) at 32 weeks to 17.5% (9.67–25.34%) at term. The GCS was significantly higher than the MLS in the ascending aorta wall (p < 0.001).ConclusionThe fetal ascending aorta wall demonstrates obviously greater circumferential strain than longitudinal strain. Both strains remained steady before the late trimester and then gradually increased until delivery, suggesting progressive maturation of aortic elasticity mechanics.

An Experimental Study and Mathematical Modeling of Vibration Transfer in Pistachio Trees Using an Inertia-Type Trunk Shaker and Field-Adapted Wireless Sensors

Trunk shakers are the most widely used mechanical harvesting machines for harvesting nut trees, including pistachio in California. Improvement of these machines requires a better understanding of the shaking dynamics of the existing trunk shakers during harvest. In this study, the effects of four different shaking patterns on three sizes of pistachio trees of different ages, shapes, and sizes were investigated under field conditions. The vibration acceleration of the real pistachio tree was measured using a wireless network of 3-axis accelerometers installed on the shaker head and different parts of the trees during the shaking harvest. Changes in acceleration and the effect of tree morphology on the magnitude of acceleration in each pattern are presented and discussed. A new location index λ, which is based on the distance of the sensor from the shaking point and diameter of the branch at each sensor location, is introduced. This study focused on mathematical modeling of the variation and distribution of the acceleration throughout the tree canopy. The sensor location index, relative force ratio (RFR), and relative kinetic energy ratio (RKER) were defined to better understand the energy damping in each part of the tree. The results showed that the relationship between the acceleration peaks and the sensor location index could be expressed by a third-degree polynomial function with an acceptable coefficient of determination. Under different shaking patterns, similar changes in the RFR of the tree at different locations and for different trees were observed. This finding indicates that the vibration force is significantly damped as the distance from the shaker clamps increases. However, the RKER values at the same shaking pattern result in different effects at different points on the branches according to tree morphology.

Relationship between the sodium oxide activity of ceramic (Na-β + β″)-alumina and the sodium activity in the ambience of the material

Abstract By means of a solid state electrochemical method, the activity of sodium oxide dissolved in various samples of ceramic Na-(β + β″)-alumina was measured as a function of the composition of the ceramics, with the independent variable being adjusted by the sodium activity in the ambience. Taking into account all the relevant findings, the lg a Na 2 O $\lg {\rm{ }}a_{{\rm{Na}}_2 {\rm{O}}} $ vs. lg ⁡ a Na $\lg {\rm{ }}a_{{\rm{Na}}} $ relationship can quantitatively be described by a polynomial of third degree with respect to lg ⁡ a Na . $\lg {\rm{ }}a_{{\rm{Na}}} .$ The gradual change of the sodium oxide activity indicates that the thermodynamic behaviour of the material is mainly determined by the occurrence of nonstoichiometric phases with easy transitions from one stoichiometry to the other one.

Predicting height growth in bean plants using non-linear and polynomial models

Brazil has stood out worldwide as one of the main producers and consumers of beans, which makes their cultivation important for the economic and social development of the country. As the bean plant has a short growth cycle, its modeling is essential for optimizing management plans for this crop. This modeling can be performed by linear and non-linear models, but the latter have stood out for providing more information to the researcher, mainly due to the practical interpretation of their parameters. In this sense, in the R statistical software, the third-degree linear polynomial model and the Logistic and Gompertz non-linear models were adjusted to height data, in centimeters, in relation to time, in days after emergence, totaling 11 observations. As criteria to assess the quality of the fit, the adjusted coefficient of determination, the corrected Akaike information criterion and the residual standard deviation were used. The logistic model best fitted the data.

Analysis of the influence of solar cycles on meteorological variables in the central inter-Andean valley of Peru in the period 1986–2019

Solar activity transmitted in energy reaches the Earth, affecting atmospheric temperature and other global weather variables. This research aims to analyze the relationship between solar cycles and meteorological variables in the Central Inter-Andean Valley during the period 1986–2019. Sunspot data were obtained from the Royal Observatory of Belgium for solar cycles 22, 23 and 24, and the meteorological variables of the National Service of Meteorology and Hydrology of Peru from five stations that are distributed in the Valley. For the correlation of the variables, the nonparametric Spearman statistical test with a third-degree polynomial regression was applied. The results show that there is a decrease in the number of sunspots in cycle 24, and that the temperature varies by 3.85 °C in the study period. Of the five stations analyzed, four of them show that there is no relation between the variables and only in the station Viques there is an inverse relation for α<0.05 referring to the variables of maximum temperature and sunspots, obtaining a coefficient of determination of R2=0.619. Therefore, solar activity does not influence the climate variability of the study valley, and this is due to climate change due to the effects of anthropogenic activities.

A moving boundary model for oxygen diffusion in a sick cell

In this paper we use an approximate analytical method for numerical solution of one dimensional moving boundary problem. We consider the oxygen diffusion problem where the oxygen is allowed to diffuse into a sick cell which absorbs and immobilizes oxygen at a constant rate. Our main problem consists in tracking the moving boundary that represents the oxygen penetration depth inside the sick cell. We can find an accurate solution which is obtained by a polynomial of third and fourth degree and we show some mistakes in the paper published by Seval Çatal in (App.Math.Comput 145:361–369, 2003).

Marine aerosol properties over the Southern Ocean in relation to the wintertime meteorological conditions

Abstract. Given the vast expanse of oceans on our planet, marine aerosols (and sea salt in particular) play an important role in the climate system via multitude of direct and indirect effects. The efficacy of their net impact, however, depends strongly on the local meteorological conditions that influence their physical, optical and chemical properties. Understanding the coupling between aerosol properties and meteorological conditions is therefore important. It has been historically difficult to statistically quantify this coupling over larger oceanic areas due to the lack of suitable observations, leading to large uncertainties in the representation of aerosol processes in climate models. Perhaps no other region shows higher uncertainties in the representation of marine aerosols and their effects than the Southern Ocean. During winter the Southern Ocean boundary layer is dominated by sea salt emissions. Here, using 10 years of austral winter period (June, July and August, 2007–2016) space-based aerosol profiling by CALIOP-CALIPSO in combination with meteorological reanalysis data, we investigated the sensitivity of marine aerosol properties over the Southern Ocean (40–65∘ S) to various meteorological parameters, such as vertical relative humidity (RH), surface wind speed and sea surface temperature (SST) in terms of joint histograms. The sensitivity study is done for the climatological conditions and for the enhanced cyclonic and anticyclonic conditions in order to understand the impact of large-scale atmospheric circulation on the aerosol properties. We find a clear demarcation in the 532 nm aerosol backscatter and extinction at RH around 60 %, irrespective of the state of the atmosphere. The backscatter and extinction increase at higher relative humidity as a function of surface wind speed. This is mainly because of the water uptake by the wind-driven sea salt aerosols at high RH near the ocean surface resulting in an increase in size, which is confirmed by the decreased depolarization for the wet aerosols. An increase in aerosol backscatter and extinction is observed during the anticyclonic conditions compared to cyclonic conditions for the higher wind speeds and relative humidity, mainly due to aerosols being confined to the boundary layer, and their proximity to the ocean surface facilitates the growth of the particles. We further find a very weak dependency of aerosol backscatter on SSTs at lower wind speeds. However, when the winds are stronger than about 12 m s−1, the backscattering coefficient generally increases with SST. When aerosol properties are investigated in terms of aerosol verticality and in relation to meteorological parameters, it is seen that the aerosol backscatter values in the free troposphere (pressure &lt;850 hPa) are much lower than in the boundary layer, irrespective of the RH and the three weather states. This indicates that the local emissions from the ocean surface make the dominant contribution to aerosol loads over the Southern Ocean. A clear separation of particulate depolarization is observed in the free and lower troposphere, more prominent in the climatological mean and the cyclonic states. For RH &gt; 60 %, low depolarization values are noticeable in the lower troposphere, which is an indication of the dominance of water-coated and mostly spherical sea salt particles. For RH &lt; 60 %, there are instances when the aerosol depolarization increases in the boundary layer; this is more prominent in the mean and anticyclonic cases, which can be associated with the presence of drier aerosol particles. Based on the joint histograms investigated here, we provide third-degree polynomials to obtain aerosol extinction and backscatter as a function of wind speed and relative humidity. Additionally, backscattering coefficient is also expressed jointly in terms of wind speed and sea surface temperature. Furthermore, depolarization is expressed as a function of relative humidity. These fitting functions would be useful to test and improve the parameterizations of sea salt aerosols in the climate models. We also note some limitations of our study. For example, interpreting the verticality of aerosol properties (especially depolarization) in relation to the meteorological conditions in the free and upper troposphere (pressure &lt;850 hPa) was challenging. Furthermore, we do not see any direct evidence of sudden crystallization (efflorescence), deliquescence or hysteresis effects of the aerosols. Observing such effects will likely require a targeted investigation of individual cases considering tracer transport, rather than the statistical sensitivity study that entails temporally and geographically averaged large data sets.

Morphological Characterization and Phenological Modeling of &amp;lt;i&amp;gt;Jatropha platyphylla&amp;lt;/i&amp;gt; (Euphorbiaceae) Muell. Arg. Genotypes

Morphological characterization and phenological modeling were carried out on genotypes of Jatropha platyphylla collected from the states of Sinaloa and Durango, Mexico. The morphological characterization evidenced the existence of monoecious plants, finding individuals with male and female flowers in the same inflorescence. Fruit with four seeds was also found. The phenological study was divided into two phases and calculated in thermal requirement (°D): Vegetative [seedtime (0), germination (24), emergence (98), cotyledons (87), second (302) and fourth (524) true leaves, end of vegetative growth (302)] and reproductive [flowering (303), fructification (342), maturation (126), defoliation and senescence (450)]. The thermal constant (2558) was similar in all eight genotypes. The phenological stages and the accumulated degree days were adjusted with a third-degree polynomial (Stage = -0.0041x3 + 0.7446x2 - 8.6808x + 6.2448) (R2 = 0.99%) stage. The development of phenological models facilitates the prediction of the flowering date for the selection of varieties with high oil and protein content.

Построение и исследование метода CPP (Cubic Polynomial Projection) решения уравнения переноса

The present paper is devoted to the construction of the (Cubic Polynomial Projection) method for solving the linear transport of neutral particles or unpolarized radiation on tetrahedra. The paper presents and proves estimates for the accuracy of the resulting numerical solution. The absorption coefficient is approximated by a constant value in the cell, the source is a second-degree polynomial in the cell, and the boundary condition is a third-degree polynomial on the faces. Under additional conditions, the method can reach the third order of convergence. The method is based on the characteristic properties of the transport equation, and in some sense, it is a generalization of the CIP (cubic-Interpolation pseudo-particle) method based on Hermitian interpolation in tetrahedra. The success of the method is ensured by the use of projection operators for constructing the scheme instead of the interpolation ones.

Dynamical analysis of an iterative method with memory on a family of third-degree polynomials

&lt;abstract&gt;&lt;p&gt;Qualitative analysis of iterative methods with memory has been carried out a few years ago. Most of the papers published in this context analyze the behaviour of schemes on quadratic polynomials. In this paper, we accomplish a complete dynamical study of an iterative method with memory, the Kurchatov scheme, applied on a family of cubic polynomials. To reach this goal we transform the iterative scheme with memory into a discrete dynamical system defined on $ \mathbf{R}^2 $. We obtain a complete description of the dynamical planes for every value of parameter of the family considered. We also analyze the bifurcations that occur related with the number of fixed points. Finally, the dynamical results are summarized in a parameter line. As a conclusion, we obtain that this scheme is completely stable for cubic polynomials since the only attractors that appear for any value of the parameter, are the roots of the polynomial.&lt;/p&gt;&lt;/abstract&gt;

The Impact of Seasonality of Agricultural Production on Product Prices in Romania

"This paper aims to determine the possible impact of the seasonality of agricultural production on the prices of these products. Three main products were analysed, the majority of which are wheat, maize and sunflower production. With the help of national databases, product prices were analysed quantitatively and qualitatively, as well as statistically, over the last 5 years by calendar month. A series of researches have been carried out on the data, such as: analysing the dynamics of both annual and monthly prices, as well as determining the correlations between the price level for these products and the calendar month to which these prices refer. Following this analysis, the third-degree polynomial regression equations were determined, showing that product prices follow a sinuous trend, with high prices in the first part of the year, when supply is running out, then, during the harvesting period, there is a drop in price, given the sudden increase in supply on the market, and in the last months of the calendar year, the highest prices are recorded, given the additional cost of storing production following the harvesting campaign. "

A Model of Sky Temperature Estimation at 1.42 GHz using University of Baghdad’s Radio Telescope

The objective of this study is to select a suitable observing region at Baghdad location (44o 22' 48", 33o 16' 30") with low interference that may affect frequency of 1.42 GHz. Baghdad University Radio Telescope (BURT) is used in this study to determine a convenient region for observation in Baghdad sky. Different azimuths and elevations were chosen at different observations time. The results of this study showed that the best observations regions were located at azimuth (120o-160o) and (210o-260o). These regions included less sky temperature and estimated to be (42.8 to 163) K. The sky temperature model could be represented as a polynomial of third degree that could fit the behavior of the observation points.