Simple Arithmetic Average Research Articles

Median Aggregation of Distribution Functions

When multiple redundant probabilistic judgments are obtained from subject matter experts, it is common practice to aggregate their differing views into a single probability or distribution. Although many methods have been proposed for mathematical aggregation, no single procedure has gained universal acceptance. The most widely used procedure is simple arithmetic averaging, which has both desirable and undesirable properties. Here we propose an alternative for aggregating distribution functions that is based on the median cumulative probabilities at fixed values of the variable. It is shown that aggregating cumulative probabilities by medians is equivalent, under certain conditions, to aggregating quantiles. Moreover, the median aggregate has better calibration than mean aggregation of probabilities when the experts are independent and well calibrated and produces sharper aggregate distributions for well-calibrated and independent experts when they report a common location-scale distribution. We also compare median aggregation to mean aggregation of quantiles.

Determining regionally applicable economic values for coastal habitats and their use in evaluating the cost effectiveness of regional conservation actions: the example of mangroves, in the South China Sea

This paper outlines the process of: assembling an empirical data set relating to the values of resource ‘goods and services11The term ‘goods and services’ is used in this paper to encompass all the elements normally evaluated as part of the process of determining total economic value.’ derived from coastal habitats bordering the South China Sea; standardising these data as production values per hectare per annum; converting local currencies to US dollars; and converting these values to a standard year (2007) by means of the consumer price index. In order to address the problem of the wide variation in prices within one country, the data were weighted to determine a ‘Weighted Mean National Value’ that reflected both the prices for the same resource at each location and the ‘stock’ of that resource at the same locations. This results in a national value that reflects the totality of the national stock rather than being a simple arithmetic average of all values. The determination of weighted mean regional values was undertaken in a similar manner to the computation of weighted mean national values but using data and information concerning the total stock (or area) in each country and the weighted mean national values. These weighted regional mean values were subsequently used in a cost benefit analysis of actions to conserve regional coastal habitats.What has resulted from this work is a standardised method for calculating national and regional weighted mean values of resource ‘goods and services’ that can be applied more widely in handling and manipulating economic valuation data from multiple locations across any time span. The method can be applied in any region where multiple currencies, varying exchange rates and widespread inter-location variations in farm gate prices are found. The specific targets of the revised Strategic Action Plan for the South China Sea have been valued or, more specifically, the incremental benefit derived from achieving the SAP target has been valued. The values saved by achieving the targets are then compared with the costs of implementing the actions defined in the regional SAP through a cost benefit analysis.

Comparison of missing value imputation methods in time series: the case of Turkish meteorological data

This study aims to compare several imputation methods to complete the missing values of spatio–temporal meteorological time series. To this end, six imputation methods are assessed with respect to various criteria including accuracy, robustness, precision, and efficiency for artificially created missing data in monthly total precipitation and mean temperature series obtained from the Turkish State Meteorological Service. Of these methods, simple arithmetic average, normal ratio (NR), and NR weighted with correlations comprise the simple ones, whereas multilayer perceptron type neural network and multiple imputation strategy adopted by Monte Carlo Markov Chain based on expectation–maximization (EM-MCMC) are computationally intensive ones. In addition, we propose a modification on the EM-MCMC method. Besides using a conventional accuracy measure based on squared errors, we also suggest the correlation dimension (CD) technique of nonlinear dynamic time series analysis which takes spatio–temporal dependencies into account for evaluating imputation performances. Depending on the detailed graphical and quantitative analysis, it can be said that although computational methods, particularly EM-MCMC method, are computationally inefficient, they seem favorable for imputation of meteorological time series with respect to different missingness periods considering both measures and both series studied. To conclude, using the EM-MCMC algorithm for imputing missing values before conducting any statistical analyses of meteorological data will definitely decrease the amount of uncertainty and give more robust results. Moreover, the CD measure can be suggested for the performance evaluation of missing data imputation particularly with computational methods since it gives more precise results in meteorological time series.

Comparative evaluation of set-level techniques in predictive classification of gene expression samples

BackgroundAnalysis of gene expression data in terms of a priori-defined gene sets has recently received significant attention as this approach typically yields more compact and interpretable results than those produced by traditional methods that rely on individual genes. The set-level strategy can also be adopted with similar benefits in predictive classification tasks accomplished with machine learning algorithms. Initial studies into the predictive performance of set-level classifiers have yielded rather controversial results. The goal of this study is to provide a more conclusive evaluation by testing various components of the set-level framework within a large collection of machine learning experiments.ResultsGenuine curated gene sets constitute better features for classification than sets assembled without biological relevance. For identifying the best gene sets for classification, the Global test outperforms the gene-set methods GSEA and SAM-GS as well as two generic feature selection methods. To aggregate expressions of genes into a feature value, the singular value decomposition (SVD) method as well as the SetSig technique improve on simple arithmetic averaging. Set-level classifiers learned with 10 features constituted by the Global test slightly outperform baseline gene-level classifiers learned with all original data features although they are slightly less accurate than gene-level classifiers learned with a prior feature-selection step.ConclusionSet-level classifiers do not boost predictive accuracy, however, they do achieve competitive accuracy if learned with the right combination of ingredients.AvailabilityOpen-source, publicly available software was used for classifier learning and testing. The gene expression datasets and the gene set database used are also publicly available. The full tabulation of experimental results is available at http://ida.felk.cvut.cz/CESLT.

Utilização de redes neurais artificiais para a determinação do número de refeições diárias de um restaurante universitário

OBJETIVO: Construir uma rede neural artificial para auxiliar os gestores de restaurantes universitários na previsão de refeições diárias. MÉTODOS: O estudo foi desenvolvido a partir do levantamento de oito variáveis que influenciam o número de refeições diárias servidas no restaurante universitário. Utiliza-se o algoritmo de treinamento Backpropagation. Os resultados por meio da rede são comparados com os da série estudada e com resultados da estimação por média aritmética simples. RESULTADOS: A rede proposta acompanha as inúmeras alterações que ocorrem no número de refeições diárias do restaurante universitário. Em 73% dos dias analisados, o método das redes neurais artificiais apresenta uma taxa de acerto maior do que o método da média aritmética simples. CONCLUSÃO: A rede neural artificial mostrou-se mais adequada para a previsão do número de refeições do que a metodologia de média simples ou quando a decisão do número de refeições é feita de forma subjetiva, sem critérios científicos.

An ensemble estimation of the variability of upper-ocean heat content over the tropical Atlantic Ocean with multi-ocean reanalysis products

Current ocean reanalysis systems contain considerable uncertainty in estimating the subsurface oceanic state, especially in the tropical Atlantic Ocean. Given this level of uncertainty, it is important to develop useful strategies to identify realistic low-frequency signals optimally from these analyses. In this paper, we present an “ensemble” method to estimate the variability of upper-ocean heat content (HC) in the tropical Atlantic based on multiple-ocean reanalysis products. Six state-of-the-art global ocean reanalaysis products, all of which are widely used in the climate research community, are examined in terms of their HC variability from 1979 to 2007. The conventional empirical orthogonal function (EOF) analysis of the HC anomalies from each individual analysis indicates that their leading modes show significant qualitative differences among analyses, especially for the first modes, although some common characteristics are discernable. Then, the simple arithmetic average (or ensemble mean) is applied to produce an ensemble dataset, i.e., the EM analysis. The leading EOF modes of the EM analysis show quantitatively consistent spatial–temporal patterns with those derived from an alternative EOF technique that maximizes signal-to-noise ratio of the six analyses, which suggests that the ensemble mean generates HC fields with the noise reduced to an acceptable level. The quality of the EM analysis is further validated against AVISO altimetry sea level anomaly (SLA) data and PIRATA mooring station data. A regression analysis with the AVISO SLA data proved that the leading modes in the EM analysis are realistic. It also demonstrated that some reanalysis products might contain higher level of intrinsic noise than others. A quantitative correlation analysis indicates that the HC fields are more realistic in the EM analysis than in individual products, especially over the equatorial regions, with signals contributed from all ensemble members. A direct comparison with the HC anomalies derived from in situ temperature measurements showed that the EM analysis generally gets realistic HC variability at the five chosen PIRATA mooring stations. Overall, these results demonstrate that the EM analysis is a promising alternative for studying physical processes and possibly for initializing climate predictions.

Sustentabilidade em Silvânia (GO): o caso dos assentamentos rurais São Sebastião da Garganta e João de Deus

A proposta básica do trabalho foi analisar e verificar a sustentabilidade nos assentamentos São Sebastião da Garganta (ASSG) e João de Deus (AJD) no município de Silvânia (GO). Aplicou-se questionário com variáveis socioeconômicas, ambientais e de capital social, que possibilitaram os cálculos dos respectivos índices: Índice de Desenvolvimento Socioeconômico (Idese) de 0,6779 e 0,2868; Índice Ambiental (IA) de 0,6470 e 0,2742; e Índice de Capital Social (IKS) de 0,8939 e 0,2778, que permitiram a composição pela média aritmética simples do Índice de Sustentabilidade (IS), que atingiu o valor de 0,7396 e 0,2796, respectivamente, para ASSG e AJD, caracterizando nível médio de sustentabilidade no primeiro e nível baixo de sustentabilidade no segundo. Os valores dos índices em separado indicaram que ocorreu nível médio de desenvolvimento socioeconômico, alto de capital social e médio no aspecto ambiental para o ASSG e níveis baixos de desenvolvimento socioeconômico, de capital social e no aspecto ambiental para o AJD.

A randomized model ensemble approach for reconstructing signals from faulty sensors

On-line sensor monitoring aims at detecting anomalies in sensors and reconstructing their correct signals during operation. The techniques used for signal reconstruction are commonly based on auto-associative regression models. In full scale implementations however, the number of sensors to be monitored is often too large to be handled effectively by a single reconstruction model. In this paper we propose to tackle the problem by resorting to a pool (ensemble) of reconstruction models, each one handling an individual group of signals. This approach involves two main technical steps: firstly, a procedure for constructing signal groups, and secondly a procedure for combining the outputs of the reconstruction models associated to the groups. For the signal grouping step, a wrapper optimization search is proposed to identify the optimal number of groups in the ensemble and the size of the groups. For the model output aggregation step, a simple arithmetic average is adopted. Ensemble accuracy and robustness is achieved by promoting diversity between the signal groups through the use of the Random Feature Selection Ensemble (RFSE) technique in combination with the Bootstrapping AGGregatING (BAGGING) technique for training data selection. The individual reconstruction models are based on Principal Components Analysis (PCA). The proposed approach has been applied to a real case study concerning 215 signals monitored at a Finnish nuclear pressurized water reactor. The results obtained have been compared with those achieved by an equivalent ensemble of models based on a grouping directly optimized by a Multi-Objective Genetic Algorithm (MOGA).

Financial Ratio Analysis of the Textile and Apparel Industries

This paper is to focus the financial ratio analysis of the Korean textile and apparel com- panies due to fast changing domestic industry. Financial ratios are playing a pivotal role in management analysis to assess the present conditions to predict the future. Subjects are belonging to textile and apparel manufacturers based on Firm Classification Standard while registered as securities listed-firms or Kosdaq-listed firms under the Electronic Notification System of Korean Banking Supervisory Authority. 41 companies' data have been analyzed including 17 apparel companies and 24 textile companies. 14 representative financial ratios are analyzed. In this paper, financial ratios can be clas- sified into four categories as follows: stability ratios, profitability ratios, growth ratios and activity ratios. The independent t-test was performed using SPSS 18 for a 10 year simple arithmetic average. The following conclusion has reached regarding aspects of management conditions and performances. When compared the ratios indicating stability, textile and apparel companies did not show much difference in debt ratio and the ratio of earning to interests. However, when compared the profitability ratios measuring the ability to produce incomes, apparel companies showed higher ratios than textile companies. Thus it is important to recognize financial characteristics of each industry.

Limited Liability Leverage (L3): A New Measure of Leverage

Average leverage is often used as a measure of risk. However, average leverage in a limited liability context should not be computed as a simple arithmetic average of the underlying constituents. In fact, using a simple arithmetic average can give misleading results. For example, the simple arithmetic average leverage may give results which run counter to the actual risk exposure for certain portfolios. This article introduces a new measure, Limited Liability Leverage (<i>L</i>³), which corrects the simple average for the limited liability framework. This new measure is discussed in the context of a portfolio of hedge funds and compared to a multi-strategy hedge fund structure, where trading units do not have limited liability. This perspective can also be extended to reflect the lower risk of a financial system with many small institutions relative to a system with large, “too-big-to-fail” institutions. <b>TOPICS:</b>Real assets/alternative investments/private equity, legal/regulatory/public policy, risk management, portfolio construction

Study of Data-Merging and Interpolation Methods for Use in an Interactive Online Analysis System: MODIS Terra and Aqua Daily Aerosol Case

Data merging with interpolation is a method of combining near-coincident satellite observations to provide complete global or regional maps for comparison with models and ground station observations. We investigate various methods and limitations of data merging (or data fusion), with and without interpolation, as a first step toward merging data sets archived in the National Aeronautics and Space Administration Goddard Earth Sciences Data and Information Services Center and made public through the Goddard Interactive Online Visualization and ANalysis Infrastructure (Giovanni) data portals. As a prototype for the data-merging algorithm, this paper uses daily global observations of aerosol optical thickness (AOT), as measured by the MODerate resolution Imaging Spectroradiometer onboard the Terra and Aqua satellites. The goal is to develop a very fast and accurate online method of data merging for implementation into Giovanni. We demonstrate three different methods for pure merging (without interpolation): simple arithmetic averaging (SAA), maximum likelihood estimate (MLE), and weighting by pixel counts. All three methods are roughly comparable, with the MLE (SAA) being slightly preferable when validating with respect to the AOT standard deviations (AOT means). To evaluate the merged product, we introduce two confidence functions, which characterize the percentage of the merged AOT pixels as a function of the relative deviation of the merged AOT from the initial Terra and Aqua AOTs. Eight combinations of merging-interpolation are applied to scenes with regular and irregular data gap patterns. Our results show that the merging-interpolation procedure can produce complete spatial fields with acceptable errors.

Limited Liability Leverage (L^3): A New Measure of Leverage

Average leverage is often used as a measure of risk. However, average leverage in a limited liability context should not be computed as a simple arithmetic average of the underlying constituents. In fact, using a simple arithmetic average can give misleading results. For example, the simple arithmetic average leverage may give results which run counter to the actual risk exposure for certain portfolios. This paper introduces a new measure, Limited Liability Leverage (L3), which corrects the simple average for the limited liability framework. This new measure is discussed in the context of a portfolio of hedge funds and compared to a multi-strategy hedge fund structure, where trading units do not have limited liability. This perspective can also be extended to reflect the lower risk of a financial system with many small institutions relative to a system with large, “too-big-to-fail” institutions.

Sound insulation between dwellings – Descriptors applied in building regulations in Europe

Regulatory sound insulation requirements for dwellings have existed since the 1950s in some countries and descriptors for evaluation of sound insulation have existed for nearly as long. However, the descriptors have changed considerably over time, from simple arithmetic averaging of frequency bands in the beginning, to a variety of more complex descriptors developed in different countries and later included in EN ISO 717:1996. As a result, this EN ISO standard provides a large variety of descriptors rather than presenting a more limited number of harmonized descriptors. In 2008 a comparative study was carried out of legal sound insulation requirements in 24 countries in Europe. The comparison of requirements for sound insulation between dwellings revealed significant differences in descriptors as well as levels. This paper focuses on descriptors and summarizes the history of descriptors, the problems of the present situation and the benefits of consensus concerning descriptors for airborne and impact sound insulation between dwellings. The descriptors suitable for evaluation should be well-defined under practical situations in buildings and be measurable. Measurement results should be reproducible and of course correlate well with subjective evaluation. More noise sources – including neighbours’ activities – and an increased demand for high quality and comfort, together with a trend towards light-weight constructions, are contradictory and challenging. This calls for exchange of data and experience, implying a need for harmonized descriptors. A suggestion to harmonize airborne and impact sound insulation descriptors in building regulations is given. This paper is one of two related papers about sound insulation of dwellings, dealing with requirements and descriptors in building regulations in Europe. This paper will focus on descriptors for requirements, the other paper [1] focuses on the strictness of requirements.

An error analysis for the hybrid gridding of Texas daily precipitation data

AbstractThis paper reports the error analysis results for the gridded daily precipitation data over the state of Texas of the United States from January 1, 1901 to December 31, 2000. The Global Daily Climatology Network dataset is used for both the data gridding and error analysis. The station data have been interpolated onto a 0.2° × 0.2° grid which starts at the base point (25°50′N, 106°38′W). The data gridding approach is a hybrid method, which is a blend of two simple methods: inverse distance weighting and nearest station assignment. Our gridding results are compared with those obtained by other gridding methods. The cross‐validation method is used for the error analysis. Our error analysis of the interpolated products includes not only the conventional errors, such as the mean bias error, but also the probabilistic distribution of the relative errors of precipitation frequency and the spatial distribution of a major Texas historical storm. The following results have been found: (1) a simple arithmetic average of station data usually overestimates Texas' average precipitation by 2.4 mm per day, (2) the relative error of the precipitation frequency follows a lognormal distribution, and (3) the hybrid gridding data do not have obvious bias and can reasonably display storm‐covered areas in Texas. The gridded data and error results are useful for the validation of climate models, calibration of satellite borne remote sensing devices, and numerous agricultural and hydrological applications. The statistical methods of our analysis and some of our results are applicable to other regions of the world. Copyright © 2009 Royal Meteorological Society

Revisiting the Market Risk Premium

Though the profound importance of the market risk p remium to finance is unquestioned, its actual measurement has been problematic for both academics and analysts alike. What exactly is the magnitude of the ex post market risk premium? What is its relationship with the expected or ex ante premium? Though finance theory estimates an hi storical equity premium of 1-2%, simple arithmetic averaging of historical data gives a gre ater mean of 5-6%, an anomaly known as the equity premium puzzle. More recent findings provide a still greater equity premium point estimate. This paper shows that statistical misspecification of historical equity premium data may be an important contributing factor for such contradictio ns.

Sources and Management Styles of Funds, and Size and Structure of Firms Portfolios: Survey from VC and PE in Mainland China

Through total coverage survey and comparative analysis on VC funds in mainland China, some evidence findings are as follows in this paper. Firstly, these facts about the average size (number) and entrepreneurs (enterprise management teams) ownership percentage of firms' portfolios of funds invested in mainland China, are consistent with theorem in the VC literature. Instead in the Western Countries, holding equity percentage by entrepreneurs is empirical very different from VC theorem. The portfolio firms' number or entrepreneurs' profit share of government-sponsored VC funds is higher than other funds in China, which is wholly consistent with theory proposition in the VC literature and the evidence in Canada. Secondly, entrepreneurs' ownership percentage is less obviously with no more than 40% equity compared with Western Countries. Meanwhile, through comparative analysis, the management teams' average age is smaller in China, but the higher level of education. Thirdly, all fund managers concern the invested industry competition. Despite China's investment managers, which also even work longer hours to invested firms, copy the methods from Western Countries in the investment technical level, however, a notable fact is: domestic investment managers in China, whether educated period or work experience, much shorter than the counterparts in the Western Countries especially USA. Finally, holding periods of firms by the funds invested in mainland China, are even shorter than in Western Countries. The ratios of seeds to whole projects by all funds are simple arithmetic average of less than 5%. All these signal: VC in the traditional classic sense being the majority of similar PE business in mainland China.

Comparing Performance and Parameterization of a One‐Dimensional Unsaturated Zone Model across Scales

The utility of an unsaturated zone soil moisture model is not only its ability to describe the soil moisture dynamics at a given point but also the possibility to generalize the results to larger areas. In this study we investigated the predictive performance of a one‐dimensional unsaturated zone soil moisture model when applied at point, field, response unit, and catchment scales, using detailed field observations from a 0.42‐km2 catchment in the Netherlands. Our main question was how model parameterization and model performance could be compared across these scales. We considered two different calibration–validation schemes and three performance statistics. In all cases we applied the same Levenberg–Marquardt optimization scheme. Differences between calibration–validation schemes (interpolation vs. extrapolation) were surprisingly small. Using one particular model parameterization across the various aggregation levels, the optimal Mualem–van Genuchten parameters for a coarser aggregation level can be derived from an underlying level by simple arithmetic averaging. The different performance indices (RMSE, index of agreement, and Nash–Sutcliffe coefficient) were highly variable between observation locations and for different aggregation levels. Overall, the indices were more favorable at higher aggregation levels, and in correspondence with errors reported in comparable studies. The unsaturated‐zone model did not, however, provide satisfactory predictions of independent flux observations, in this case daily catchment discharge. Moreover we did not succeed in deriving a meta‐model to scale model performance indices with aggregation level. Our case study therefore supports the view that multiscale calibration studies that use both state and flux observations are required to compare results from unsaturated zone models at different aggregation levels.

SASSI: A RESPONSE TO LAZOWSKI &amp; MILLER (2007)

In response to our review of research on the reliability and validity of the Substance Abuse Subtle Screening Inventory (SASSI) [1], Lazowski & Miller [2], of the SASSI Institute, make several claims. The first is that we used ‘incorrect methods to calculate accuracy’. This is not so. We specified our calculation methods clearly, which are the traditional psychometric procedures for computing sensitivity (the percentage of true positives identified as positive) and specificity (the percentage of true negatives identified as negative). The alleged ‘inaccuracy’ pertains to one parenthetical point from page 46 of our review: how to weight evidence from different studies. The sensitivity values reported in eight independent studies were 0.33, 0.52, 0.59, 0.60, 0.65, 0.72, 0.85 and 0.87. We reported an average of 69.8% when weighting studies by N, essentially pooling all tested cases. The simple arithmetic average, which gives equal weight to smaller and larger studies, is less favorable still: 64.1%, and the median is 62.5%. The SASSI authors favor weighting studies by prevalence rate and arrived at a calculated average sensitivity of 84%, a figure that we were unable to reproduce. It is true that of the 36 studies we reviewed, only 10 included a criterion measure against which SASSI accuracy could be judged, and that only three of these used the SASSI-3. This is because, to the best of our knowledge, that is the entire peer-reviewed literature on the validity of the SASSI. The fact remains that no peer-reviewed study has replicated the sensitivity rate of 0.94 claimed in the test manual and the average, however computed, is well below that figure. The SASSI authors also allege ‘unsubstantiated claims of bias’ by stating that a screener may validly report a higher positive rate for an ethnic group if the true prevalence rate is also higher for that group. True prevalence rates for ethnic subgroups were not reported in the studies we cited, but US population studies generally show aggregate prevalence rates for substance use disorders in Hispanic and African American groups to be similar to or lower than those for the US majority population [3]. Furthermore, other screening instruments such as the Alcohol Use Disorders Identification Test (AUDIT) do not overclassify ethnic minorities. We believe that there remains reason for concern from the four studies pointing to racial/ethnic differences in SASSI classifications [4,5] and scale scores [6,7]. Lazowski & Miller did identify one typographical error in our review. The sensitivity of the SASSI direct scales as reported in a footnote in their test manual was indeed 74%, and not 79%. We apologize for this error, noting that the method used to compute sensitivity in their table is the same one used in our review. The central claim of the SASSI authors' letter, and indeed of each version of the SASSI test manual [8,9], is that ‘the subtle scales improve detection’. In defense of this claim, they cite statistics from their own test manual. Although the indirect scales do increase the proportion classified as positive by the SASSI, we stand by our conclusion that independent studies do not support this claim for any version of the SASSI. Six studies in our review found that the direct scales performed on a par with or better than the SASSI when its indirect scales were included [7,10–14]. This is consistent with the larger research literature across five decades, indicating that allegedly indirect scales are no more accurate than direct self-report scales [15]. Their final claimed advantage, that the SASSI goes ‘beyond mere screening’, is precisely a reason for concern. Although sold as a screening instrument, the SASSI is sometimes used (inappropriately in our view) to establish a diagnosis and make treatment decisions. Indeed, the SASSI manuals provide guidelines for using the instrument to determine severity of substance dependence, need for supervised detoxification, risk for criminality and suggested treatment approach and directions. We found no independent research evidence that the SASSI provides additional valid information unavailable from direct scales or client self-report. Properly used, a valid screening instrument signals the need for more careful evaluation and clinical confirmation of diagnosis, and does not itself serve or replace these functions.

Independent Venture Capital, Size and Structure of Firms' Portfolio: Comparative Study from Some Cases in Mainland China

Through all coverage survey and comparative analysis on VC funds in mainland China, some evidence findings are as follows in this paper. Firstly, these facts about the average size (number) and entrepreneurs (enterprise management teams) ownership percentage of firms' portfolios of VC funds invested in mainland China, are consistent with theorem in the VC literature. The portfolio firms' number or entrepreneurs' profit share of government-sponsored VC funds is higher than other funds in China, which is wholly consistent with theory proposition in the VC literature and the evidence in Canada. Secondly, entrepreneurs' ownership percentage is less obviously with no more than 40% equity compared with Western Countries. This might be related with the majority of VC engaged in similar PE business or the later stage of firms-invested in mainland China. Finally, holding periods of firms by the funds invested in mainland China, are even shorter than in Western Countries; Meanwhile, the ratios of seeds to total projects by all funds are simple arithmetic average of less than 5%. All these signal: VC in the traditional classic sense being the majority of similar PE business in mainland China.

Modelling of diffusion-limited retardation of contaminants in hydraulically and lithologically nonuniform media

A new reactive transport modelling approach and examples of its application are presented, dealing with the impact of sorption/desorption kinetics on the spreading of solutes, e.g. organic contaminants, in groundwater. Slow sorption/desorption is known from the literature to be strongly responsible for the retardation of organic contaminants. The modelling concept applied in this paper quantifies sorption/desorption kinetics by an intra-particle diffusion approach. According to this idea, solute uptake by or release from the aquifer material is modelled at small scale by a “slow” diffusion process where the diffusion coefficient is reduced as compared to the aqueous diffusion coefficient due to (i) the size and shape of intra-particle pores and (ii) retarded transport of solutes within intra-particle pores governed by a nonlinear sorption isotherm. This process-based concept has the advantage of requiring only measurable model parameters, thus avoiding fitting parameters like first-order rate coefficients. In addition, the approach presented here allows for modelling of slow sorption/desorption in lithologically nonuniform media. Therefore, it accounts for well-known experimental findings indicating that sorptive properties depend on (i) the grain size distribution of the aquifer material and (ii) the lithological composition (e.g. percentage of quartz, sandstone, limestone, etc.) of each grain size fraction. The small-scale physico-chemical model describing sorption/desorption is coupled to a large-scale model of groundwater flow and solute transport. Consequently, hydraulic heterogeneities may also be considered by the overall model. This coupling is regarded as an essential prerequisite for simulating field-scale scenarios which will be addressed by a forthcoming publication. This paper focuses on mathematical model formulation, implementation of the numerical code and lab-scale model applications highlighting the sorption and desorption behavior of an organic contaminant (Phenanthrene) with regard to three lithocomponents exhibiting different sorptive properties. In particular, it is shown that breakthrough curves (BTCs) for lithologically nonuniform media cannot be obtained via simple arithmetic averaging of breakthrough curves for lithologically uniform media. In addition, as no analytical solutions are available for model validation purposes, simulation results are compared to measurements from lab-scale column experiments. The model results indicate that the new code can be regarded as a valuable tool for predicting long-term contaminant uptake or release, which may last for several hundreds of years for some lithocomponents. In particular, breakthrough curves simulated by pure forward modelling reproduce experimental data much better than a calibrated standard first-order kinetics reactive transport model, thus indicating that the new approach is of high quality and may be advantageously used for supporting the design of remediation strategies at contaminated sites where some lithocomponents and/or grain size classes may provide a long-term pollutant source.