Mutual Consistency Research Articles

Testing the mutual consistency of different supernovae surveys

AbstractIt is now common practice to constrain cosmological parameters using supernovae (SNe) catalogues constructed from several different surveys. Before performing such a joint analysis, however, one should check that parameter constraints derived from the individual SNe surveys that make up the catalogue are mutually consistent. We describe a statistically-robust mutual consistency test, which we calibrate using simulations, and apply it to each pairwise combination of the surveys making up, respectively, the UNION2 catalogue and the very recent JLA compilation by Betoule et al. We find no inconsistencies in the latter case, but conclusive evidence for inconsistency between some survey pairs in the UNION2 catalogue.

Research on Service Update Dynamically Based on OSGi Frame

It is a key problem for a 7*24 running system to update and maintain online. According to the feature of OSGi (Open Service Gateway Initiative) framework, current service dynamic update policies for OSGi framework are analyzed. In order to solve the problem of service mutual consistency and service state consistency during service update, the service dynamic update policy based on publish & subscribe model is presented. This policy is based on quiescent state theory to ensure mutual consistency when services are updated online. The process of the dynamic service update policy is described by Petri net. We realize the policy using Event Admin Service in the experiment with well-defined program model. The result shows that the policy is validate and feasibility.

Gravity field expansion in ellipsoidal harmonic and polyhedral internal representations applied to Vesta

A 20th degree ellipsoidal harmonic gravity field of Vesta is determined by processing radiometric Doppler and range data from the Dawn mission. The gravity field shows sensitivity up to degree 18 and the coefficients are globally determined on average to degree 15. Gravity anomalies are mapped to the Brillouin ellipsoid (304×289×247-km), which is a substantially closer fit to the surface than the reference ellipsoid (290×290×265-km) used to map the conventional spherical harmonic series, especially near the poles. Two models of internal structure are subsequently explored, in which density variations are permitted in the uppermost layer (i.e., crust) in order to explain Vesta’s local gravitational signature. These models include the case of a two-layer model with an average crustal thickness of 55.5km and a three-layer model with an average crustal thickness of 22.4km. For both two-layer and three-layer scenarios, the Bouguer gravity anomaly is minimized for a crustal density of 2970kg/m3. The remaining Bouguer anomalies can be explained by lateral crustal density variation of 2310–3440kg/m3 and 2660–3240kg/m3 for the 22.4km and 55.5km crustal thickness models, respectively. The general trend of the estimated lateral crustal densities for the two cases is very similar, with a wider range for the 22.4km case due to a thinner crust. This indicates that a thick crust (e.g., 55.5km) would be more favorable for minimizing the range of lateral crustal density variations. Consideration of independent geochemical and petrological constraints suggests that a three-layer model is a more appropriate representation of Vesta’s internal structure, despite the fact that two-layer models provide a satisfactory fit to gravity data alone. In detail, it is found that densities derived from gravity data assuming three-layer models and those derived from the howardite–eucrite–diogenite meteorites and estimates of plausible bulk-Vesta composition show an excellent level of mutual consistency.

Time transfer functions as a way to validate light propagation solutions for space astrometry

Given the extreme accuracy of modern space astrometry, a precise relativistic modeling of observations is required. Concerning light propagation, the standard procedure is the solution of the null-geodesic equations. However, another approach based on the time transfer functions (TTF) has demonstrated its capability to give access to key quantities such as the time of flight of a light signal between two point-events and the tangent vector to its null-geodesic in a weak gravitational field using an integral-based method. The availability of several models, formulated in different and independent ways, must not be considered like an oversized relativistic toolbox. Quite the contrary, they are needed as validation to put future experimental results on solid ground. The objective of this work is then twofold. First, we build the time of flight and tangent vectors in a closed form within the TTF formalism giving the case of a time-dependent metric. Second, we show how to use this new approach to obtain a comparison of the TTF with two existing modelings, namely the Gaia RElativistic Model (GREM) and the Relativistic Astrometric MODel (RAMOD). In this way, we highlight the mutual consistency of the three models, opening the basis for further links between all the approaches, which is mandatory for the interpretation of future space missions data. This will be illustrated through two recognized cases: a static gravitational field and a system of gravitational mass monopoles in uniform motion.

A computational theory of visual receptive fields.

A receptive field constitutes a region in the visual field where a visual cell or a visual operator responds to visual stimuli. This paper presents a theory for what types of receptive field profiles can be regarded as natural for an idealized vision system, given a set of structural requirements on the first stages of visual processing that reflect symmetry properties of the surrounding world. These symmetry properties include (i) covariance properties under scale changes, affine image deformations, and Galilean transformations of space–time as occur for real-world image data as well as specific requirements of (ii) temporal causality implying that the future cannot be accessed and (iii) a time-recursive updating mechanism of a limited temporal buffer of the past as is necessary for a genuine real-time system. Fundamental structural requirements are also imposed to ensure (iv) mutual consistency and a proper handling of internal representations at different spatial and temporal scales. It is shown how a set of families of idealized receptive field profiles can be derived by necessity regarding spatial, spatio-chromatic, and spatio-temporal receptive fields in terms of Gaussian kernels, Gaussian derivatives, or closely related operators. Such image filters have been successfully used as a basis for expressing a large number of visual operations in computer vision, regarding feature detection, feature classification, motion estimation, object recognition, spatio-temporal recognition, and shape estimation. Hence, the associated so-called scale-space theory constitutes a both theoretically well-founded and general framework for expressing visual operations. There are very close similarities between receptive field profiles predicted from this scale-space theory and receptive field profiles found by cell recordings in biological vision. Among the family of receptive field profiles derived by necessity from the assumptions, idealized models with very good qualitative agreement are obtained for (i) spatial on-center/off-surround and off-center/on-surround receptive fields in the fovea and the LGN, (ii) simple cells with spatial directional preference in V1, (iii) spatio-chromatic double-opponent neurons in V1, (iv) space–time separable spatio-temporal receptive fields in the LGN and V1, and (v) non-separable space–time tilted receptive fields in V1, all within the same unified theory. In addition, the paper presents a more general framework for relating and interpreting these receptive fields conceptually and possibly predicting new receptive field profiles as well as for pre-wiring covariance under scaling, affine, and Galilean transformations into the representations of visual stimuli. This paper describes the basic structure of the necessity results concerning receptive field profiles regarding the mathematical foundation of the theory and outlines how the proposed theory could be used in further studies and modelling of biological vision. It is also shown how receptive field responses can be interpreted physically, as the superposition of relative variations of surface structure and illumination variations, given a logarithmic brightness scale, and how receptive field measurements will be invariant under multiplicative illumination variations and exposure control mechanisms.

Potential environmental implications of emerging organic contaminants in Taihu Lake, China: Comparison of two ecotoxicological assessment approaches

In this study, the hazard quotient (HQ) and a novel enhanced integrated biomarker response (EIBR) were applied to indirectly/directly estimate the ecotoxicological risk of emerging organic contaminants in Taihu Lake. Nine out of sixteen target compounds were detected in most sampling points at comparable concentrations (1.58–206.95ng/L). Simultaneously, changes in multi-biomarkers were measured in caged fish for 28days. The 0HQ results preliminarily indicated that most water areas were at significant risk for adverse effects to aquatic organisms (HQ>10). The prioritisation was then ranked and 17α-ethinylestradiol, diethylstilbestrol and 17β-estradiol were regarded as the greatest hazards. The EIBR, covering multi-biomarkers and their weighting, was applied to field study, and Zhushan Bay was suggested as the most stressful place, followed by Meiliang Bay. The HQ showed significant positive linear correlation with the EIBR (r=0.848, P<0.001), suggesting mutual consistency between the two approaches based on laboratory and field study in ecotoxicological risk assessment.

The BETHY/JSBACH Carbon Cycle Data Assimilation System: experiences and challenges

We present the concept of the Carbon Cycle Data Assimilation System and describe its evolution over the last two decades from an assimilation system around a simple diagnostic model of the terrestrial biosphere to a system for the calibration and initialization of the land component of a comprehensive Earth system model. We critically review the capability of this modeling framework to integrate multiple data streams, to assess their mutual consistency and with the model, to reduce uncertainties in the simulation of the terrestrial carbon cycle, to provide, in a traceable manner, reanalysis products with documented uncertainty, and to assist the design of the observational network. We highlight some of the challenges we met and experience we gained, give recommendations for operating the system, and suggest directions for future development.

Advances in pan‐European flood hazard mapping

AbstractFlood hazard maps at trans‐national scale have potential for a large number of applications ranging from climate change studies, reinsurance products, aid to emergency operations for major flood crisis, among others. However, at continental scales, only few products are available, due to the difficulty of retrieving large consistent data sets. Moreover, these are produced at relatively coarse grid resolution, which limits their applications to qualitative assessments. At finer resolution, maps are often limited to country boundaries, due to limited data sharing at trans‐national level. The creation of a European flood hazard map would currently imply a collection of scattered regional maps, often lacking mutual consistency due to the variety of adopted approaches and quality of the underlying input data.In this work, we derive a pan‐European flood hazard map at 100 m resolution. The proposed approach is based on expanding a literature cascade model through a physically based approach. A combination of distributed hydrological and hydraulic models was set up for the European domain. Then, an observed meteorological data set is used to derive a long‐term streamflow simulation and subsequently coherent design flood hydrographs for a return period of 100 years along the pan‐European river network. Flood hydrographs are used to simulate areas at risk of flooding and output maps are merged into a pan‐European flood hazard map. The quality of this map is evaluated for selected areas in Germany and United Kingdom against national/regional hazard maps. Despite inherent limitations and model resolution issues, simulated maps are in good agreement with reference maps (hit rate between 59% and 78%, critical success index between 43% and 65%), suggesting strong potential for a number of applications at the European scale. Copyright © 2013 John Wiley &amp; Sons, Ltd.

Radioactive Quality Evaluation and Cross Validation of Data from the HJ-1A/B Satellites’ CCD Sensors

Data from multiple sensors are frequently used in Earth science to gain a more complete understanding of spatial information changes. Higher quality and mutual consistency are prerequisites when multiple sensors are jointly used. The HJ-1A/B satellites successfully launched on 6 September 2008. There are four charge-coupled device (CCD) sensors with uniform spatial resolutions and spectral range onboard the HJ-A/B satellites. Whether these data are keeping consistency is a major issue before they are used. This research aims to evaluate the data consistency and radioactive quality from the four CCDs. First, images of urban, desert, lake and ocean are chosen as the objects of evaluation. Second, objective evaluation variables, such as mean, variance and angular second moment, are used to identify image performance. Finally, a cross validation method are used to ensure the correlation of the data from the four HJ-1A/B CCDs and that which is gathered from the moderate resolution imaging spectro-radiometer (MODIS). The results show that the image quality of HJ-1A/B CCDs is stable, and the digital number distribution of CCD data is relatively low. In cross validation with MODIS, the root mean square errors of bands 1, 2 and 3 range from 0.055 to 0.065, and for band 4 it is 0.101. The data from HJ-1A/B CCD have better consistency.

A Light-Weight Distributed System for the Processing of Replicated Counter-Like Objects

In order to increase availability in a distributed system some or all of the data items are replicated and stored at separate sites. This is an issue of key concern especially since there is such a proliferation of wireless technologies and mobile users. However, the concurrent processing of transactions at separate sites can generate inconsistencies in the stored information. We have built a distributed service that manages updates to widely deployed counter-like replicas. There are many heavy-weight distributed systems targeting large information critical applications. Our system is intentionally, relatively lightweight and useful for the somewhat reduced information critical applications. The service is built on our distributed concurrency control scheme which combines optimism and pessimism in the processing of transactions. The service allows a transaction to be processed immediately (optimistically) at any individual replica as long as the transaction satisfies a cost bound. All transactions are also processed in a concurrent pessimistic manner to ensure mutual consistency.

ВЗАИМНАЯ СОГЛАСОВАННОСТЬ ЗАКОНОМЕРНОСТЕЙ ТЕЧЕНИЯ И ГИДРАВЛИЧЕСКОГО СОПРОТИВЛЕНИЯ

Mutual consistency of regularities demonstrated by the flow and hydraulic resistance is analyzed in this article. It is proven that the values of friction factors of pipes, identified through the employment of traditional methods, differ from those of channels by 4 times. It is also proven that the average velocity deficit inside pipes and channels, identified by integrating velocity profiles that depend on the Karman parameter, differ by only 1.5 times. The relation between the Karman parameter and the average velocity deficit provides this parameter with a clear physical sense.The original method of reconciliation of the experimental regularity of smooth pipes against the resistance ratio formula, obtained by integrating the logarithmic velocity profile, adjusts the value of the Karman parameter and the second constant of the velocity profile, as both are slightly different from the experimental values identified by I. Nikuradze.The average velocity deficit identified for the flow in rough pipes by integrating the velocity profile coincides with the same in smooth pipes, and they both have the same dependence on the Karman parameter. The adjusted Karman parameter value is almost the same for rough and smooth pipes. The adjusted value of the second turbulence constant for rough pipes is a little higher than the experimental value identified by I. Nikuradze.Adjusted first and second constant values of turbulence for rough and smooth pipes assure more consistency between the regularities of resistance and distribution of velocities inside smooth and rough pipes.

Comparing the Language Skills and Grammatical Competences of German Language Teacher Trainees

Grammar, as a system of rules in a language, holds an important place in the process of foreign language teacher education. The knowledge of the linguistic structure of the German language combined with the skills of writing, reading, listening and speaking constitute a meaningful whole with a mutual consistency. They can also be referred to as declarative and procedural knowledge. They serve to develop a consciousness of language and/or language learning. Based on such understanding, the present study aims at examining the relationship between the development level of writing, reading, listening and speaking skills and of grammatical competence of the teacher trainees. Comparing the findings of the project ‘The Problem of Language Competence in German Language Teacher Education within the Context of Istanbul University’ carried out by the academic staff of the Department of German Language Teaching and the exam results of German Grammar II course, this study explores whether there is a significant correlation between the trainees’ success levels of language skills and grammar.

A non-possibility theorem for joint stability in interindustry models

Joint-stability in interindustry modeling relates to the mutual simultaneous consistency of the demand-driven and supply-driven models of Leontief and Ghosh, respectively. Previous work has claimed joint-stability to be an acceptable assumption from the empirical viewpoint, provided only small changes in exogenous variables are considered. We show in this note, however, that the issue has deeper theoretical roots, offering a mathematical demonstration that shows the impossibility of mutual consistency between demand-driven and supply-driven models. Mutual consistency would entail that coefficient matrices under both model versions would remain constant when the economic equilibrium changes following an external shock.

Sputum Biomarkers and the Prediction of Clinical Outcomes in Patients with Cystic Fibrosis

Lung function, acute pulmonary exacerbations (APE), and weight are the best clinical predictors of survival in cystic fibrosis (CF); however, underlying mechanisms are incompletely understood. Biomarkers of current disease state predictive of future outcomes might identify mechanisms and provide treatment targets, trial endpoints and objective clinical monitoring tools. Such CF-specific biomarkers have previously been elusive. Using observational and validation cohorts comprising 97 non-transplanted consecutively-recruited adult CF patients at the Intermountain Adult CF Center, University of Utah, we identified biomarkers informative of current disease and predictive of future clinical outcomes. Patients represented the majority of sputum producers. They were recruited March 2004-April 2007 and followed through May 2011. Sputum biomarker concentrations were measured and clinical outcomes meticulously recorded for a median 5.9 (interquartile range 5.0 to 6.6) years to study associations between biomarkers and future APE and time-to-lung transplantation or death. After multivariate modeling, only high mobility group box-1 protein (HMGB-1, mean = 5.84 [log ng/ml], standard deviation [SD] = 1.75) predicted time-to-first APE (hazard ratio [HR] per log-unit HMGB-1 = 1.56, p-value = 0.005), number of future APE within 5 years (0.338 APE per log-unit HMGB-1, p<0.001 by quasi-Poisson regression) and time-to-lung transplantation or death (HR = 1.59, p = 0.02). At APE onset, sputum granulocyte macrophage colony stimulating factor (GM-CSF, mean 4.8 [log pg/ml], SD = 1.26) was significantly associated with APE-associated declines in lung function (−10.8 FEV1% points per log-unit GM-CSF, p<0.001 by linear regression). Evaluation of validation cohorts produced similar results that passed tests of mutual consistency. In CF sputum, high HMGB-1 predicts incidence and recurrence of APE and survival, plausibly because it mediates long-term airway inflammation. High APE-associated GM-CSF identifies patients with large acute declines in FEV1%, possibly providing a laboratory-based objective decision-support tool for determination of an APE diagnosis. These biomarkers are potential CF reporting tools and treatment targets for slowing long-term progression and reducing short-term severity.

Nature as an engineer: one simple concept of a bio-inspired functional artificial muscle

The biological muscle is a powerful, flexible and versatile actuator. Its intrinsic characteristics determine the way how movements are generated and controlled. Robotic and prosthetic applications expect to profit from relying on bio-inspired actuators which exhibit natural (muscle-like) characteristics. As of today, when constructing a technical actuator, it is not possible to copy the exact molecular structure of a biological muscle. Alternatively, the question may be put how its characteristics can be realized with known mechanical components. Recently, a mechanical construct for an artificial muscle was proposed, which exhibits hyperbolic force–velocity characteristics. In this paper, we promote the constructing concept which is made by substantiating the mechanical design of biological muscle by a simple model, proving the feasibility of its real-world implementation, and checking their output both for mutual consistency and agreement with biological measurements. In particular, the relations of force, enthalpy rate and mechanical efficiency versus contraction velocity of both the construct’s technical implementation and its numerical model were determined in quick-release experiments. All model predictions for these relations and the hardware results are now in good agreement with the biological literature. We conclude that the construct represents a mechanical concept of natural actuation, which is suitable for laying down some useful suggestions when designing bio-inspired actuators.

Dynamics of bloggers’ communities: Bipartite networks from empirical data and agent-based modeling

We present an analysis of the empirical data and the agent-based modeling of the emotional behavior of users on the Web portals where the user interaction is mediated by posted comments, like Blogs and Diggs. We consider the dataset of discussion-driven popular Diggs, in which all comments are screened by machine-learning emotion detection in the text, to determine positive and negative valence (attractiveness and aversiveness) of each comment. By mapping the data onto a suitable bipartite network, we perform an analysis of the network topology and the related time-series of the emotional comments. The agent-based model is then introduced to simulate the dynamics and to capture the emergence of the emotional behaviors and communities. The agents are linked to posts on a bipartite network, whose structure evolves through their actions on the posts. The emotional states (arousal and valence) of each agent fluctuate in time, subject to the current contents of the posts to which the agent is exposed. By an agent’s action on a post its current emotions are transferred to the post. The model rules and the key parameters are inferred from the considered empirical data to ensure their realistic values and mutual consistency. The model assumes that the emotional arousal over posts drives the agent’s action. The simulations are preformed for the case of constant flux of agents and the results are analyzed in full analogy with the empirical data. The main conclusions are that the emotion-driven dynamics leads to long-range temporal correlations and emergent networks with community structure, that are comparable with the ones in the empirical system of popular posts. In view of pure emotion-driven agents actions, this type of comparisons provide a quantitative measure for the role of emotions in the dynamics on real blogs. Furthermore, the model reveals the underlying mechanisms which relate the post popularity with the emotion dynamics and the prevalence of negative emotions (critique). We also demonstrate how the community structure is tuned by varying a relevant parameter in the model. All data used in these works are fully anonymized.

Isotopic constraints on the age of the Earth’s core: Mutual consistency of the Hf-W and U-Pb systems

The estimation of the time of Earth’s core formation on the basis of isotopic systems with short-lived and long-lived parent nuclides gives significantly different results. Isotopic data for the 182Hf-182W system with a 182Hf half-life of approximately 9 Myr can be interpreted in such a way that the core was formed 34 Myr after the origin of the solar system assuming complete core-mantle equilibrium. Similar estimates on the basis of the U-Pb isotopic system suggest a significantly longer mean time of core formation of approximately 120 Myr. If the Earth’s core were formed instantaneously, both isotopic systems would have shown identical values corresponding to the true age. The discrepancy between the U-Pb and Hf-W systems can be resolved assuming prolonged differentiation of prototerrestrial material into silicate and metallic phases, which occurred not simultaneously and uniformly in different parts of the mantle. This resulted in the isotopic heterogeneity of the mantle, and its subsequent isotopic homogenization occurred slowly. Under such conditions, the mean isotopic compositions of W and Pb in the mantle do not correspond to the mean time of the separation of silicate and metallic phases. This is related to the fact that the exponential function of radioactive decay is strongly nonlinear at high values of the argument, and its mean value does not correspond to the mean value of the function. There are compelling reasons to believe that the early mantle was heterogeneous with respect to W isotopic composition and was subsequently homogenized by convective mixing. This follows from the fact that the lifetime of isotopic heterogeneities in the mantle is close to 1.8 Gyr for various long-lived isotopic systems. There is also no equilibrium between the mantle and the core with respect to the contents of siderophile elements. Because of this, the mean isotopic ratios of W and Pb cannot be used for the direct computation of the time of metal-silicate differentiation in the Earth. Such estimation requires more sophisticated models accounting for the duration of the differentiation process using several isotope pairs. Given the prolonged core formation, which has probably continued up to now, the question about its age becomes ambiguous, and only the most probable growth rate of the core can be estimated. The combined use of the U-Pb and Hf-W systems constrains the time of formation of 90% of the core mass between 0.12 and 2.7 billion years. These model estimates could have been realistic under the condition of complete disequilibrium between the silicate and metallic phases, which is as improbable as the suggestion of complete equilibrium between them on the whole Earth scale.

Performance measurement and management systems: state of the art, guidelines for design and challenges

PurposeRecently, performance measurement and management (PMM) has received increasing attention from both the academic and industrial environments. Companies that try to use PMM systems report experiencing implementation problems including goal incongruence. Based on a discussion of the state of the art of PMM, this paper aims to provide research guidelines for building a PMM system through a reference framework, and to identify major design challenges.Design/methodology/approachAt a macro level, the evolution of research is analyzed using citation and co‐citation analysis techniques. Further, the evolution of PMM systems in the last 20 years is traced. The feasibility and applicability of these frameworks/models are analyzed by considering five milestones that a performance measurement system should have. Based on this, an integrated framework is proposed as a basis for designing a cohesive PMM system.FindingsThe research on the subject is quite diverse. In fact, the research appears to be quite mature in terms of publications and citations, while PMM systems developed do not meet the PMM challenge faced in the current environment. The framework proposed for PMM system design integrates five systems: a performance system, a cost system, a capability evaluation system, a benchmarking system and a planning system. Integration among the five systems is to be viewed as the driver to address the PMM challenge.Research limitations/implicationsThe proposed framework is a starting point for PMM system design and it provides important guidelines for successful implementations of PMM initiatives for various types of companies in the current global business environment. However, further empirical studies are needed before the concepts described here can be assessed to ascertain its applicability.Practical implicationsThe paper provides a literature review of PMM research, discusses the mutual consistency of models and frameworks therein, and explores how the framework proposed might be implemented and improved, as well as the major challenges facing researchers. Practical implication and benefits of the proposed framework adoption are highlighted through an example.Originality/valueResearch in PMM has become increasingly important given the significant impact it can have on competitive strategy and operations of firms in the present global business environment. This paper demonstrates the need of an holistic approach to PMM, which requires an intensive and deep comprehension of the key activities in the company and their related drivers.

Reliable estimation of orbit errors in spaceborne SAR interferometry

An approach to improve orbital state vectors by orbit error estimates derived from residual phase patterns in synthetic aperture radar interferograms is presented. For individual interferograms, an error representation by two parameters is motivated: the baseline error in cross-range and the rate of change of the baseline error in range. For their estimation, two alternatives are proposed: a least squares approach that requires prior unwrapping and a less reliable gridsearch method handling the wrapped phase. In both cases, reliability is enhanced by mutual control of error estimates in an overdetermined network of linearly dependent interferometric combinations of images. Thus, systematic biases, e.g., due to unwrapping errors, can be detected and iteratively eliminated. Regularising the solution by a minimum-norm condition results in quasi-absolute orbit errors that refer to particular images. For the 31 images of a sample ENVISAT dataset, orbit corrections with a mutual consistency on the millimetre level have been inferred from 163 interferograms. The method itself qualifies by reliability and rigorous geometric modelling of the orbital error signal but does not consider interfering large scale deformation effects. However, a separation may be feasible in a combined processing with persistent scatterer approaches or by temporal filtering of the estimates.

The Gibbs–Helmholtz Equation and the Thermodynamic Consistency of Chemical Absorption Data

The Gibbs–Helmholtz (G-H) equation connects vapor–liquid equilibrium (VLE) and calorimetric data. If experimental measurements for the heat of solution are not available, they may be estimated through the G-H equation. Further, if both VLE and heat-of-solution data are available, their mutual thermodynamic consistency can be evaluated through the G-H equation, to develop the most accurate and reliable model. This kind of analysis is particularly useful for chemical-absorption systems, such as the capture of CO2 using aqueous solutions of amines, where regeneration energies are significant. In this work, the G-H equation is derived to unambiguously relate the commonly used form to the rigorous and general form, including for systems where phase equilibrium is accompanied by chemical reactions in any phase. The effect of approximations and the range of applicability of the common G-H equation are first applied to data generated for a simple VLE system by an equation of state, with different reliability foun...