Zero Values Research Articles

Development of an extended Schnute model for more physically realistic representations of soil water retention and moisture capacity curves

Commonly used soil water retention, θ( h), and moisture capacity, C( h), functions implicitly assume that ( i) the θ( h) data curve is sigmoid-shaped with an inflection and ( ii) the C( h) data curve has a value of zero at soil saturation. Desorption measurements on intact soils indicate, however, that the θ( h) data curve is frequently convex-monotonic in shape with no inflection, and C( h) at saturation is often a finite negative value rather than zero. As these model-data mismatches may cause substantial error in simulation or prediction of near-saturated soil hydraulic properties and water flow, a new “Extended Schnute” θ( h)– C( h) function was proposed that can provide θ( h) curve shapes and saturated C( h) values which are consistent with θ( h) and C( h) measurements. The new function and/or its nested Schnute sub-model provided high-quality and physically realistic fits to desorption data collected from intact cores of coarse sand, loamy sand, loam, clay loam, sandy clay loam, clay, and organic clay soils; and it out-performed or equalled the three-parameter van Genuchten θ( h)– C( h) function for every data-set. The new function also provided accurate and physically realistic representations of θ( h) and C( h) data from structured soils containing macropores and strongly graded pore size distributions. It was concluded that the Extended Schnute model is capable of providing accurate and physically realistic representations for a wide range of θ( h) and C( h) data, and it was further recommended that this model be considered over other models when measurements indicate that θ( h) is convex-monotonic in shape and/or C( h) is not zero at soil saturation.

Surfactant dysfunction due to e-cigarette aerosol exposure with and without additional insults

Introduction: The use of e-cigarettes (ECs) remains a popular habit for young populations, in part due to the variety of appealing flavours available. However, EC use has been associated with acute lung injury via unknown mechanisms. During a deep inhalation, one of the first compounds the EC aerosol comes into contact within the lungs is pulmonary surfactant. This complex mixture of lipids and surfactant associated proteins lines the alveolar surface and reduces surface tension to near zero values upon exhalation. Surfactant dysfunction, associated with serum protein leak and oxidative stress, contributes to lung injury. We hypothesized that exposure to EC aerosol impairs pulmonary surfactant function, and thereby increases its susceptibility to protein inhibition or oxidative stress. Methods: Bovine lipid extract surfactant (BLES) was used as a model exogenous surfactant. 2ml of BLES (2mg/ml) was placed in a syringe (30ml) attached to an EC, drawing in and expelling the aerosol 30 times. Vehicle e-liquid (VG:PG 50:50) as well as e-liquid containing flavouring additives and nicotine were utilized. Two models of injury were used, the first being addition of serum containing plasma proteins and the second oxidization by hypochlorous acid following aerosol exposure. Surface tension reduction of all samples after exposure was performed using a constrained drop surfactometer (CDS), where samples underwent 20 dynamic compression and expansion cycles. Results: Minimum surfaces tensions were significantly higher after exposure to EC aerosol across 20 compression/expansion cycles. Menthol and red wedding flavoured aerosol exposure resulted in significantly increased minimum surface tensions compared to unflavoured vehicle e-liquid, although nicotine had no additional effects beyond that of the vehicle e-liquid. The addition of plasma containing serum proteins significantly increased minimum surface tensions in aerosol exposed samples compared to those unexposed to serum and air controls. Oxidized surfactant had higher minimum surface tensions compared to control, however EC aerosol exposure had no additional effect on the inhibition of the surfactant’s function. Conclusion: EC aerosols alter surfactant function through increases in minimum surface tension. Variability in the severity of inhibition exists between flavouring additives, however the base common across all e-liquids is able to effectively inhibit surfactant. This inhibition is amplified in the presence of serum proteins. From these results we conclude that vaping impairs the pulmonary surfactant system and increases susceptibility to damage by secondary insults. Lawson Health Research Institute, NSERC This is the full abstract presented at the American Physiology Summit 2023 meeting and is only available in HTML format. There are no additional versions or additional content available for this abstract. Physiology was not involved in the peer review process.

ORIGIN AND CORRELATION OF VARIABLES IN SOME BOREHOLES OF BUI DIVISION IN THE NORTH WEST REGION OF CAMEROON

Multivariate data with inherent complexity can be simplified and interpretation eased with application of the Principal Component Analysis (PCA), while retaining trends and patterns. Huge data is reduced to fewer dimensions, maintaining the intrinsic relation between the variables. Sample bottles were cleaned and rinsed with the water sample from the boreholes, and finally filled to the brim to avoid any atmospheric oxidation. The samples were taken immediately to the Laboratory for physico-chemical analysis. The Boreholes were BH1 (Oku subdivision), BH2 (Mbven subdivision), BH3 (Nkum subdivision), BH4 (Jakiri subdivision) and BH5 for Kumbo subdivision. The PCA had application of the Software Package for Social Sciences SPSS), that converted the complex variables obtained from the analysis, at different periods and sites into a correlation matrix. Pearson’s correlation matrix applied in this work, reduced the data in correlation circles that were a range of geometrical projections from higher to lower dimensions. There was no strong correlation between the different variables indicating that they function independently. Most of the correlation values lie between +/- 0.29 and 0.1 which indicated a low degree of correlation. Nonetheless, absence of correlation never existed between the correlated pairs as no value of zero was obtained. Sixty-six variables were correlated, with 31 having a positive correlation, whereas 35 were negative. Consequently, 46.96 % variables had positive correlation and 50.04% with a negative correlation. The positive correlation values indicated a common source with the variables evolving similarly. A negative correlation of -0.185897 was expressed between Ca2+ and HCO3- within the boreholes. A negative correlation of pH with EC (-0.032559) and other anions (NO3- ; -0.137635, Cl-; -0.091810, SO42- ; -0.111072) indicated a decrease in pH (acidification) which can be linked to an increase in the mineralization process that increase anions into the milieu. The pairs of exchangeable bases; Na+- Ca2+; (0.138758) Na+- K+, (0.412315) had positive correlations which indicated that; increasing or decreasing of the concentration of cations was probably a combination of anthropogenic inputs and other processes governed by chemical reactions. An exception was with Na+- Mg2+ pair that gave an anomaly with a negative correlation (-0.090762). The anomaly was ignored because the low correlation coefficient was insignificant. The findings from this work enabled the origins of ions in the boreholes to be identified and related.

A STUDY OF SMALL AREA ESTIMATION TO MEASURE MULTIDIMENSIONAL POVERTY WITH MIXED MODEL POISSON, ZIP, AND ZINB

The research began with calculating the value of multidimensional poverty at the district level in West Java Province from SUSENAS 2021. The calculation of multidimensional poverty was based on individuals in each district or city household. The dimensional weights are weighed the same, and the indicators in the dimensions are also weighed the same. Furthermore, the simulation study used the Poisson, ZIP, and ZINB mixed models to examine the model's performance on data with cases of excess zero values and overdispersion. The simulation was by generating data without overdispersion and with overdispersion. Overdispersion data was generated with parameters of ω (0.1, 0.3, 0.5, and 0.7), and the model was evaluated from the AIC value. The best method in the simulation study was used to estimate multidimensional poverty in sub-districts in West Java Province using PODES 2021. Simulation studies on data without overdispersion showed no difference in the model's goodness. Overdispersion data shows Mixed Model ZIP and ZINB are better than Mixed Model Poisson. The percentage of the multidimensional poverty population at the sub-district level in West Java Province is quite diverse, from 0.04% to 75.54%.

Emotional complexity under high stress: Do protective associations for risk behaviors persist even during a pandemic?

Risk behaviors like substance use and binge eating are often used to cope with negative emotions. Engagement in these behaviors has been exacerbated by the COVID-19 pandemic. Past research suggests that complex emotion conceptualizations captured as emotion differentiation (ability to discriminate between emotional states) and polarity (ability to integrate positive and negative features of emotional experience) may be protective. We examined associations of mean affect intensity, emotion differentiation, and emotion polarity with frequency of daily substance use and binge eating across 10 days in a demographically diverse sample of U.S. adults (N = 353) recruited between March 24 and April 9, 2020, when stay-at-home orders were initiated. Owing to the nested data structure and excessive zero values, analyses were conducted using multilevel zero-inflated negative binomial regression. Consistent with past research, negative affect was positively associated with frequency of substance use and binge eating. Importantly, results indicated that negative emotion differentiation was protective, predicting greater likelihood of not using substances and binge eating at all across the sampling period. These effects remained even after controlling for mean affect intensity, emotion polarity, and positive emotion differentiation. Neither positive emotion differentiation nor emotion polarity were significantly associated with either behavior. Our results suggest that greater complexity in conceptualization of negative emotions facilitates some protection against risk behaviors such as substance use and binge eating, even during periods of high environmental stress. These findings have important implications for optimizing interventions to reduce engagement in risk behaviors. (PsycInfo Database Record (c) 2022 APA, all rights reserved).

Genome-wide association study of a semicontinuous trait: illustration of the impact of the modeling strategy through the study of Neutrophil Extracellular Traps levels.

Over the last years, there has been a considerable expansion of genome-wide association studies (GWAS) for discovering biological pathways underlying pathological conditions or disease biomarkers. These GWAS are often limited to binary or quantitative traits analyzed through linear or logistic models, respectively. In some situations, the distribution of the outcome may require more complex modeling, such as when the outcome exhibits a semicontinuous distribution characterized by an excess of zero values followed by a non-negative and right-skewed distribution. We here investigate three different modeling for semicontinuous data: Tobit, Negative Binomial and Compound Poisson-Gamma. Using both simulated data and a real GWAS on Neutrophil Extracellular Traps (NETs), an emerging biomarker in immuno-thrombosis, we demonstrate that Compound Poisson-Gamma was the most robust model with respect to low allele frequencies and outliers. This model further identified the MIR155HG locus as significantly (P=1.4×10-8) associated with NETs plasma levels in a sample of 657 participants, a locus recently highlighted to be involved in NETs formation in mice. This work highlights the importance of the modeling strategy for GWAS of a semicontinuous outcome and suggests Compound Poisson-Gamma as an elegant but neglected alternative to Negative Binomial for modeling semicontinuous outcome in the context of genomic investigations.

Self-Consistent Study of the Superconducting Gap in the Strontium-doped Lanthanum Cuprate

This work is aimed at numerically investigating the behavior of the Fermi energy in Strontium-doped Lanthanum Cuprate, using a numerical zero temperature elastic scattering cross-section procedure in the unitary collision regime. The main task is to vary the zero temperature superconducting energy gap from its zero value in the normal state, to the highest value of 60 meV. We find that there are two different reduced phase space regimes for the first harmonic line node's order parameter. The first one, represented by a Fermi energy with a value of - 0.4 meV, where the rest of the material parameters, and the degrees of freedom of the normal to the superconducting phase transition are not sensitive to the self-consistent variation of the zero temperature superconducting energy gap. A different case is found when in the self-consistent numerical procedure, the Fermi energy takes a value of - 0.04 meV, indicating that the fermion-dressed quasiparticles have material parameters strongly sensitive to the numerical changes in the zero temperature gap, resulting in a reduced phase space, where the input and output zero superconducting energy values, and the degrees of freedom are separated by the self-consistent numerical analysis. The first scenario considers that when the Fermi energy and the nearest hopping terms have the same order of magnitude, the physics can be described by a picture given by nonequilibrium statistical mechanics. A second scenario indicates, that when the Fermi energy parameter and the hopping term have different order of magnitude; the physical picture tends to be related to the nonrelativistic quantum mechanical degrees of freedom coming from quasi-stationary quantum energy levels, with a damping term seen in the probability density distribution function, that is described in the configuration space. Henceforth, it is concluded that the use of the zero temperature elastic scattering cross-section links the phase and configuration spaces through the inverse scattering lifetime, and helps to clarify the role of the degrees of freedom in Strontium-doped Lanthanum Cuprate. Finally, we think that the self-consistent numerical procedure with the reduced phase space, induces nonlocality in the inverse scattering lifetime.

Reducing bias and mitigating the influence of excess of zeros in regression covariates with multi-outcome adaptive LAD-lasso

Zero-inflated explanatory variables, as opposed to outcome variables, are common, for example, in environmental sciences. In this article, we address the problem of having excess of zero values in some continuous explanatory variables, which are subject to multi-outcome lasso-regularized variable selection. In short, the problem results from the failure of the lasso-type of shrinkage methods to recognize any difference between zero value occurring either in the regression coefficient or in the corresponding value of the explanatory variable. This kind of confounding will obviously increase the number of false positives – all non-zero regression coefficients do not necessarily represent true outcome effects. We present here the adaptive LAD-lasso for multiple outcomes, which extends the earlier work of multi-outcome LAD-lasso with adaptive penalization. In addition to well-known property of having less biased regression coefficients, we show that the adaptivity also improves method’s ability to recover from influences of excess of zero values measured in continuous covariates.

Development of Balance of Payments Concept and Theoretical Approach to Its Equilibrium (with the Emphasis on the Current Account)

The paper tries to find an answer to how to perceive the term balance of payments (dis)equilibrium. The text follows the individual editions of the IMF Balance of Payments Manual and concurrent opinions on balance of payments (dis)equilibrium from the point of view of both the IMF and economists outside the IMF. Despite the difficulty and complexity of balance of payments analysis, there was a considerable demand among the economic and lay communities for a "single figure" covering balance of payments (dis)equilibrium. Eventually, the current account balance was selected as the "single figure." The simplest way to perceive the current account balance equilibrium is as a tendency to return to its zero value. However, some more complex approaches allow considering a longterm non-zero balance of the current account as a state of equilibrium.

Experimental study of vibration effect on self-magnetic flux leakage measurement of corroded steel strands

The self-magnetic flux leakage (SMFL) method has excellent potential in corrosion measurement research of bridge stay cables and suspenders. However, the vibration effect in the cable’s SMFL measurement is unclear and short of the systematic experimental analysis. Based on the magnetic field superposition principle, this study interpreted the vibration effect on steel cable structure magnetic field. The effect was innovatively summarized by the magnetic field increment resulting from the measuring displacement (ΔBDis) and the defect deformation (ΔBDef). Then, the SMFL measurement experiment of the corroded steel strands during the vibration was carried out. The magnetic field distribution law and the influence of the corrosion loss ratio were also analyzed. The results show that ΔBDis presents a “zero value” distribution law via the statistical histogram. The increment of the magnetic field under vibration mainly depends on ΔBDef, which positively correlates with the structure’s corrosion degree and deformation curvature. An excellent linear correlation between the comprehensive characteristic parameter γsum and the corrosion ratio is obtained. So, the quantitative characterization analysis method under vibration was proposed, and γsum can weaken the vibration effect on the magnetic characteristics of cable structure.

Chatbot for Diagnosis of Pregnancy Disorders using Artificial Intelligence Markup Language (AIML)

Artificial Intelligence has evolved in sophistication and widespread use. This study aims to create a chatbot application in the health sector regarding the early diagnosis of pregnancy disorders. Based on basic health research, only 44 percent of pregnant women know the danger signs of pregnancy. The chatbot application developed is expected to facilitate and increase knowledge for pregnant women about the danger signs of pregnancy, especially early diagnosis of pregnancy disorders. The chatbot application was developed with artificial intelligence technology based on Artificial Intelligence Markup Language with the question-answer concept using the Pandorabots framework. The test is carried out in two stages: functional and pattern matching. The functional testing uses the black-box testing method, and the pattern-matching test on the chatbot uses the sentence similarity and bigram methods based on user input and keywords similarity in the bot's knowledge base. The functional testing results show that the chatbot application runs well, with the eligibility criteria reaching 81.4% and the results of the keyword similarity test (pattern matching) are zero to one, in the sense that the value of one has the same similarity between user input and pattern. Meanwhile, the zero value has no similarities, so the bot will respond to it as free input. So it can be concluded that the bot can respond to user questions when the pattern and input have the same level of similarity.

SEM Measurements of the Dimensions of Relief Structures in the Technological Process of Manufacturing Microcircuits

The problems of measuring the dimensions of relief elements on a scanning electron microscope (SEM) in the technological process of manufacturing microcircuits are considered. The first problem is related to the fact that the increase in the SEM during operation can vary over a wide range depending on the measured dimensions. The second problem is that the probe diameter determined in the SEM calibration process differs from the diameter used in operational measurements. The third problem is related to the fact that it is not known which relief parameter is measured in the SEM probe defocusing method. It is shown that to solve the first problem, it is necessary to calibrate the mark on the image using structures with a trapezoidal profile and large angles of inclination of the side walls. The solution of the second problem is based on the method of defocusing the SEM probe: determining the dependence of the sizes between certain points on the SEM signals on the probe diameter and extrapolating this dependence to the zero value of the diameter. The third problem is solved with the help of a virtual scanning electron microscope.

Learning-based padding: From connectivity on data borders to data padding

Padding is employed vastly in convolutional neural networks (CNNs) to maintain the output size. In current padding schemes, the input feature maps are padded using quite simple strategies, e.g., constant zero values in zero padding, which is the most common padding choice. In this work, we propose to use learning-based paradigms to calculate the padding data from the connectivity of the input images on the data borders. Two different modules, i.e., learning-based padding by convolution (LPC) and learning-based padding by attention (LPA), are designed to obtain the padding data from the interdependencies of the image border data along the channel and spatial dimensions, respectively. The designed LPC or LPA is formulated as a generic, plug-and-play unit, which can be a direct replacement for the conventional padding technique. Extensive experiments on image classification and semantic segmentation tasks show that the proposed padding schemes can consistently obtain higher accuracy than standard padding schemes, in various deep network backbones. The codes and trained modules are available at https://github.com/ICSResearch/LP.

Bayesian inference of heavy metals exposure in crayfish for assessing human non-carcinogenic health risk.

Contaminant concentrations often presented left censorship that below the limit of detection (LOD), which may contains true zero values because of no residue. In this study, we analyzed the concentrations of lead (Pb), cadmium (Cd), mercury (Hg), arsenic (As), and chromium (Cr) in 391 crayfish samples collected from 24 provinces of China, modelled the concentrations with two different models in a Bayesian framework, and evaluated health risk by estimating the target hazard quotient (THQ). The highest concentration was associated with Cr in Northwest China (0.1753 ± 0.1520 mg/kg w. w.), and the minimum concentration was Cd in Southwest China (0.0052 ± 0.0144 mg/kg w. w.), all heavy metal concentrations were below their safety limits. The posterior means of not detect rates P0 of Pb, Cd, Hg, As, and Cr obtained with two models were both nearly equal to the observed not detect rates (51.15%, 36.83%, 27.37%, 64.71%, and 43.73%, respectively). The posterior probabilistic density lines for Pb, Hg, and Cd concentrations obtained with two models were similar, and fitted the empirical distributions well. The posterior density lines of THQs showed that the non-carcinogenic risk of As and Hg were significant high. Moreover, Bayesian approach presented a better understanding of the percentage of population exposed to potential risk.

H2 superglass on an amorphous carbon substrate

The phase diagram of a para-H2 monolayer absorbed on a experimentally syntetized amorphous carbon sheet was calculated using a diffusion Monte Carlo technique. We found that the ground state of that system changed drastically from a perfectly flat substrate to a situation in which the carbon atoms were allowed a certain degree of disorder in the $z$ direction. In the first case, at zero pressure we have a glass of density 0.056 $\pm$ 0.003 \AA$^{-2}$ in equilibrium with an incommensurate solid of 0.068 $\pm$ 0.002 \AA$^{-2}$. At the equilibrium density, the glass was found to have a tiny, but non-negligible superfluid faction of less than 1 \% (0.44 $\pm$ 0.05 \%). In the $z$-disordered substrate, we observe a significant enhancement of the superfluid fraction in the glass phase as well as a smaller but not zero value in the incommensurate crystal.

Investigating the effect of stream reflux on optimum design of heat exchanger using Particle Swarm Algorithm

BackgroundA heat exchanger is a device that is used to transfer thermal energy between two or more fluids, between a solid surface and a fluid at different temperatures in thermal contact. In this paper, plate fin heat exchanger (PFHE) is optimally designed for a waste heat recovery purpose. MethodsFor optimal design of PFHE, total annual cost as well as effectiveness are considered as two objective functions and a multi-objective particle swarm optimization (MOPSO) algorithm is used. In addition, six design parameters related to the heat exchanger and fin variables are selected. Stream reflux is considered as a new idea to improve the thermoeconomic result of heat exchanger. As a result, an additional design parameter named “reflux ratio” is also considered in the case of heat exchanger with stream reflux. The optimum results in the case of stream reflux were compared with those without stream reflux (conventional heat exchanger). Significant findingsThe optimization results revealed that 4.42% improvement in the maximum effectiveness is obtained by refluxing the stream as compared with conventional case. In addition, the thermoeconomic improvement was obtained by stream reflux for the effectiveness higher than 0.8859. For example, 4.11% improvement in the effectiveness is observed in the case of stream reflux as compared with the conventional case for the fixed TAC=553.6 $/year. As it is predicted, the zero value for reflux ratio is selected for the effectiveness lower than 0.8859. On the other hand, the reflux ratio is selected in the range of 0–0.9311 for the effectiveness higher than 0.8859. In addition, the results reveal that the higher reflux ratio is required for the higher effectiveness.

Non-conventional failures caused by the edge effect in cross-ply laminates made of ultra-thin plies

In a fatigue testing programme of carbon/epoxy cross-ply laminates made of ultra-thin plies, non-conventional failures are observed. These non-conventional failures consist in longitudinal cracks in the 90° layer parallel to the loading direction instead of the conventional transverse cracks in the 90° layer perpendicular to the load direction. A potential reason for this failure is the presence of a normal stress in the thickness direction. Classical Lamination Theory predicts zero values for this stress component under longitudinal loading, but the presence of a free-edge alters the stress state. The so-called “edge-effect” has been widely studied in the past, but the presence of ultra-thin plies introduces new lower limits of the thickness of the 90° layer. Additionally, the presence of a stress singularity, in the bimaterial corner generated by the 0° and 90° plies, is also investigated to check its influence on the stress state due to the low thickness values of the 90° layer. A slight geometrical modification is conceived to remove the stress singularity, isolating its effect from the pure edge effect. Numerical simulations of the stress alteration in the free edge of the samples, due to mechanical and thermal loading, are carried out, and stress distributions are numerically computed, depending on the 90° layer thickness. Detailed failure inspection by 3D tomography is also done to assess the through-the-width propagation of the non-conventional failures from the free edge. Numerical predictions and experimental 3D X-ray inspections seem to corroborate that the edge effect is responsible for these non-conventional failures.

Peculiarities of Interannual Variability of Sea Ice Area in the Northern Hemisphere

The research has been made on the basis of an array of ice data for the maximums and minimums seasonal distribution of sea ice in the Northern Hemisphere. The probability range for the appearance of positive differences after the negative ones in March is greater than in September, and conversely. During the periods of minimum (March) and maximum (September) interannual changes, after positive differences with an increase in the number of differences in the group, the values of subsequent changes increase. There is an increase in the probability of a one sign occurrence interannual difference with an increase in the group of another sign previous differences. For the probability of zero differences (absence of variability), there is an increase in both the probability of zero values and the number of previous zero differences. The results indicate the presence of a stabilization mechanism in the stochastic interannual variability of the sea ice area, which is confirmed by an increase in the probability of the appearance of a one sign and the number of previous differences of another sign in the group. An increase in the probability of zero values with an increase in the number of previous zero differences confirms the presence of geographical areas in which there are no interannual changes in the area of sea ice.

Growth and temperature tuned band gap characteristics of NaBi(MoO4)2 single crystal

Structural and optical properties of double sodium–bismuth molybdate NaBi(MoO4)2 semiconductor compound was investigated by x-ray diffraction, Raman and transmission experiments. From the x-ray diffraction experiments, the crystal that has tetragonal structure was obtained. Vibrational modes of the crystal were found from the Raman experiments. Transmission experiments were performed in the temperature range of 10–300 K. Derivative spectroscopy analysis and absorption spectrum analysis were performed to get information about the change in band gap energy of the crystal with temperature. It was observed that the band gap energies of the crystal at different temperatures obtained from these techniques are well consisted with each other. By the help of absorption spectrum which was obtained from transmission measurements performed at varying temperatures, absolute zero value of the band gap and average phonon energy as 3.03 ± 0.02 eV and = 24 ± 0.2 meV, respectively. Moreover, based on absorption spectrum analysis the Urbach energy of the crystal was obtained as 0.10 eV.

Robot stiffness theory reconsideration based on Schur complement eigenvalues: Extension to GSP dynamic stiffness evaluation

The known robot stiffness evaluation algorithm based on the Schur complements’ eigenvalues (SCE) is refined and its application is extended to the dynamic stiffness problem. For the refinement, the Schur complements synthesis is reduced to standard transformations of the stiffness matrix into the triangular block matrices. In these terms, the Schur complements of the robot dynamic stiffness matrix are formulated for steady-state forced sinusoidal vibrations of a damping-free system. The interrelationships between the forced-frequency-dependent SCE and natural frequencies are established: the frequencies resulting in the SCE zero values are proven to be identical to the natural frequencies, and vice versa. The SCE of the dynamic stiffness matrix defines the range and extremes of the dynamic stiffness values that allow the building of the translational and rotational stiffness ellipsoids and formulation of the stiffness-related robot performance indices. In four application examples, the SCE-based dynamic stiffness values of the Gough-Stewart platform (GSP) on weightless supports are defined. The definitions allow the formulation of the dynamic stiffness-related performance indices which are used for quantitative evaluation and comparison of the GSP designs.