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Admissible measures of diversity allow specification of the number of types (species, alleles, etc.) that are “effectively” involved in producing the diversity (the “diversity effective number”, also referred to as “true diversity”) of a community or population. In metacommunities, effective numbers additionally serve in partitioning the total diversity (symbolized by γ) into one component summarizing the diversity within communities (symbolized by α) and an independent component summarizing the differences between communities (symbolized by β). There is growing consensus that the β-component should be treated in terms of an effective number of “distinct” communities in the metacommunity. Yet, the notion of distinctness is shown in the present paper to remain conceptually ambiguous at least with respect to the diversity within the “distinct” communities. To overcome this ambiguity and to provide the means for designing further desirable effective numbers, a new approach is taken that involves a generalized concept of effective number. The approach relies on first specifying the distributional characteristics of partitioning diversity among communities (among which are differentiation, where the same types tend to occur in the same communities, and apportionment, where different types tend to occur in different communities), then developing the indices which measure these characteristics, and finally inferring the effective numbers from these indices. Major results: (1) The β-component reflects apportionment characteristics of metacommunity structure and is quantified by the “apportionment effective number” of communities (number of effectively monomorphic communities). Since differentiation between communities arises only as a side effect of apportionment, the common interpretation of the β-component in terms of differentiation is unwarranted. (2) Multiplicative as well as additive methods of partitioning the total type diversity (γ) involve apportionment effective numbers of communities that are based on different apportionment indices. (3) “Differentiation effective numbers” of communities exist but do not conform with the classical concept of partitioning total type diversity into components within and between communities. (4) Differentiation characteristics are measured as effective numbers of distinct types (rather than communities) from the dual perspective, in which the roles of type and community membership are exchanged. This is relevant e.g. in studies of endemism and competitive exclusion. (5) For Shannon-Wiener diversity, all of the differentiation and apportionment effective numbers are equal, with the exception of those representing additive partitioning. (6) Under either perspective, that is dual or non-dual, measures of compositional differentiation (as originally suggested for the assessment of β-diversity) do not figure in the partitioning of total diversity into components, since they do not build on the intrinsic concept of diversity.

Haze weather frequently occurs in many cities in China. Polycyclic aromatic hydrocarbons(PAHs) in fine particulate matter(PM2.5) can adversely affect the environment and human health. In this paper, PM2.5 samples were collected at nine sites in a city in northeastern China from September 2013 to October 2014. Sixteen USEPA(US Evironment Protection Agency) priority PAHs in PM2.5 were analyzed to determine their spatial and temporal distribution characteristics. The source apportionment of PAHs was conducted with the Positive Matrix Factorization(PMF) model. The results indicate that the concentrations of total PAHs(T-PAHs) in PM2.5 are within the range of 0.26 to 72.48 ng/m3. The seasonal variation of T-PAHs is winter>spring>autumn>summer, and the space distribution of PAHs is JZP>DP>BFH>LP> EESA>IPT>CP>HZMC>JYP. In all types of PAHs, three-ring and five-ring PAHs are significantly prominent(62%) in the heating period due to petrogenic sources and traffic emissions. Middle- and high-ring PAHs in the non-heating period are caused by coal combustion and vehicle exhaust, which accounts for 77% of the total emissions. The source apportionment results obtained by the diagnostic ratio of PAHs reflect that coal burning, traffic and other sources have a distinct influence on PAH emissions in this city. Six factors are defined by PMF v5.0, namely, coke oven emissions(7.7%), biomass burning(44.3%), petrogenic sources(10.7%), coal combustion(10.4%), gasoline engine emissions(16.7%), and diesel engine emissions(10.3%). The results indicate that the PAHs in PM2.5 in the city are primarily caused by combustion processes and vehicle exhaust.

Systems of proportional division of seats between parties, based on the results of the election, and between constituencies on the basis of demographic data, are usually judged on the basis of the compatibility of the final divisions with the criterion of proportionality. In certain situations, moving away from a straightforward proportionality towards degressive or progressive proportionality is intentional and should not be considered as a form of error. This issue has already been analyzed with regard to the degressively proportional distribution of seats, primarily in the context of the distribution of seats between the national delegations in the European Parliament. In this paper, however, I focus on the question of the progressive proportionality of division of seats between parties and propose a tool for measuring the strength of progressivity of division. I use the new measure to describe electoral systems in European countries, as well as to assess the impact of the size of the constituency and the apportionment method used (d'Hondt or Sainte-Lague) on the progressivity of the distribution of seats.

The Songhua River represents one of the seven major river systems in China. It flows through Harbin city with 66 km long, locating in the northern China with a longer winter time. This paper aimed to study concentration distributions, stability, risk assessment, and source apportionment of heavy metals including chromium (Cr), cadmium (Cd), lead (Pb), mercury (Hg), arsenic (As), copper (Cu), zinc (Zn), and nickel (Ni) in 11 selected sections of the Songhua River Harbin region. Results showed that Cr, Cd, Pb, Hg, and As exceeded their respective geochemical background values in sediments of most monitoring sections. Compared with other important rivers and lakes in China, Cr, Hg, Cd, and As pollutions in surface sediments were above medium level. Further analysis of chemical speciation indicated that Cr and As in surface sediments were relatively stable while Pb and Cd were easily bioavailable. Correlation analysis revealed sources of these metals except As might be identical. Pollution levels and ecological risks of heavy metals in surface sediments presented higher in the mainstream region (45° 47.0' N ~ 45° 53.3' N, 126° 37.0' E ~ 126° 42.1' E). Source apportionment found Hejiagou and Ashi River were the main contributors to metal pollution of this region. Thus, anthropogenic activities along the Hejiagou and Ashi River should be restricted in order to protect the Songhua River Harbin region from metal contamination.

The combination of government reserve and enterprise reserve is one of the main models of emergency material storage in Beijing City. In recent years, China was advocating the government and enterprises to establish multi level and multi mode of the storage mode to save cost and improve efficiency. This paper uses mathematical model to establish a cooperative game premise condition, then analyses the emergency material storage cooperative game between the government and the enterprise and establishes binding cost apportionment and punishment measures to get a stable cooperation, so that both sides obtain the biggest benefit. Finally, based on the game of government and enterprise cooperation establish cost lowest Beijing emergency materials storage and transportation mode.

Common consolidated corporate tax base (CCCTB) and tax allocation via formula apportionment (FA) are hotly debated in the European Union (EU). The objective of this paper is to analyze the tax-induced distortions of managerial incentives and remuneration packages caused by FA. We set up a LEN-type principal-agent model with agents in two different jurisdictions. There are no transactions between the two jurisdictions, thus all findings are driven by FA. If payroll enters the FA formula, the principal demands increased effort and pays an increased compensation to managers in low-tax jurisdictions compared to the benchmark case. Managers in high-tax jurisdictions face the opposite effect. Furthermore, the composition of the remuneration changes, which distorts incentives in addition to the excessive pay. Lastly, net profit increases because FA offers new potential for profit shifting. VHB-JOURQUAL-Ranking: B

This paper considers the role and position of the government control of location and specialization of the main types of agricultural production in the region. Technical approaches to agricultural subsidizing are assessed. Principles of budgeting apportionment are formed. The technique of the government control of the location of agricultural production across the region is expounded.

Despite growing scientific interest in obesity and the uncritical nature of a considerable proportion of the scientific community, a variety of other researchers have queried the idea of an epidemic of obesity. Some of this questioning has highlighted the uncertain moral and ideological nature of the biomedical arguments about the risks of obesity. It should be researchers’ responsibility to question whether the hegemonic discourse against obesity has led to a process of stigmatization and apportionment of blame, such that obese individuals are judged as having socially expensive, lazy and dangerous bodies that they do not take care of, and as being bad bio-citizens. It may therefore be of interest, in addition to discussing the onus of obesity, to identify and debate who the “economic problem of obesity” is of concern or interest to, and also who profits (politically and economically) from maintaining this state or combating it. The aim of the present text was not to establish methodological judgment over papers that have addressed the costs associated with obesity. Our objectives were: 1) to establish a critique of the non-explicit discourse that stems from these investigations; and 2) to reveal the set of factors that contribute towards such expenditure.

This paper presents aerosol studies carried out in the capital city of Botswana. The use of backward air mass trajectories has shown that elevated concentrations of fine particles correspond to situations when the air mass originated in the Pretoria and Johannesburg region in South Africa. This illustrated transboundary pollution and also served as an example of long distance transport. The results also show a significant contribution of a local generated pollution. The data has been subjected to principal component analysis (PCA) in order to make source apportionment.

Source apportionments have become increasingly performed to determine the origins of ambient particulate pollution. The results can be helpful in designing mitigation strategies to improve air quality. Source specific particulate matter (PM) concentrations are also being used in health effects studies to be able to focus attention on those sources most likely to be responsible for the observed adverse health effects. In 2015, the World Health Organization (WHO) released its initial compilation of source apportionment studies published through August 2014. This initial database was described by Karagulian et al. (Atmospheric Environment120 (2015) 475–483). In the present report, a new compilation has been prepared of those apportionments published since 2014 through December 2019. In addition, the database has been expanded to include apportionments of heavy metals, water-soluble components, and carbonaceous components in ambient PM. As a result of this work, we have developed and presented some perspectives on source apportionment going forward. We also have made a series of recommendations for source apportionment studies and reporting them. It is essential for papers to provide a minimum set of information so that the study can be adequately assessed, and the results utilized by others in making policy decisions or as part of other scientific studies., Graphical abstract Unlabelled Image, Highlights • Comprehensive review of the PM2.5/PM10 source apportionment literature since 2014 • Includes apportionments for heavy metals, water-soluble species, and carbonaceous PM • Major increase in source apportionment studies in China • Most commonly used source apportionment method is positive matrix factoriztion

Enriched and bio-refractory soil heavy metals (SHMs) originate from the underground mineral, which supplies energy and materials for the development of economy and industry. Investigating soil metal contents and their adverse health impacts is the principal concern associated metal contaminated industrial areas, including both current assessments and future projections. In this research, we create a novel spatiotemporal model of SHMs prediction and risk characterization for future by citing a rigorous theory of industrial economics, and time series of activity intensity changes of various pollution sources are forecasted. The dynamic change of source contributions is quantitatively resolved and the mean SHMs concentrations are estimated by classical formulas for heavy metal accumulation. Human health risk in the future is described in a manner of time series. The results of the case study show that contribution rates of the five sources of the six metals change continuously over time. Pb, Cd and As assume the highest growth rates (400%, 500% and 165%), while Zn, Ni, Cr possesses relatively lower growth (< 130%), compared to their corresponding background values. Health risk of local sensitive population (children) is estimated at exceeding threshold in 2022 (non-carcinogenic) and 2012 (carcinogenic), and the upward trend will continue. Traffic emission, agriculture and household garbage are identified as major risky sources in the coming decades at the studied area, and improvement measures are recommended. Although a degree of uncertainties exists, the overall tendency is a conservative bias for chemical risk. Additionally, this paper is the first to explore a methodology of predicting future SHMs and associated human health risk, based on industrial economics and temporal source apportionment.

Deteriorating air quality with high levels of fine particulate matter (PM2.5) over National Capital Region (NCR) of India is one of the serious environmental and scientific issues. In this paper, PM2.5 samples were collected for 24 h twice or thrice a week during December 2016–December 2017 at three sites [Delhi (IG), Modinagar (MN) and Mahendragarh (HR)] over NCR to analyse the carbonaceous aerosols. Source apportionment of PM2.5 was attempted using Principal Component analysis (PCA) and Positive Matrix Factorization (PMF) based on the analysed carbonaceous fractions [Organic carbon, Elemental carbon, Secondary organic carbon (SOC)]. Organic compounds: alkanes, hopanes, steranes, polycyclic aromatic hydrocarbons (PAHs), phthalates, levoglucosan and n-alkanoic acids were analysed to distinguish the emission sources. Total Carbonaceous Aerosols (TCA) contributed significantly (∼26%) to PM2.5 which revealed their importance in source apportionment. Estimated SOC contributed 43.2%, 42.2% and 58.2% to OC and 5.4%, 5.3% and 7.8% to PM2.5 at IG, MN and HR sites respectively. PCA and PMF apportion five emission sources i.e., vehicular emissions (34.6%), biomass burning (26.8%), cooking emissions (15.7%), plastic and waste burning (13.5%) and secondary organic carbon (9.5%) for PM2.5. Source attributed health risk has also been calculated in terms of Lung cancer risk (LCR) associated with PAHs exposure and concluded that vehicular emissions (40.3%), biomass burning (38.1%), secondary organic carbon (12.8%) contributed higher to LCR (503.2 × 10−5; ∼503 cases in 1,00,000). Health risk assessment combined with source apportionment inferences signifies the immediate implementation of emissions reduction strategies with special target on transport sector and biomass burning over the NCR of India.

Traditionally, airport asphalt resurfacing works were delivered using a construct-only contract, requiring compliance with a design provided by the client, usually prepared by a design consultant. However, a number of generally compliant airport asphalt surfaces have failed to performed as required. Consequently, there is a desire to make asphalt contractors more responsible for the performance of airport asphalt surface that they have constructed. This paper describes the recent use of design and construct contracts for the delivery of airport asphalt resurfacing works in Australia. It is recommended that suitably sized and scoped airport asphalt resurfacing project consider a design and construct approach in the future. However, a robust preliminary design, nominated quantities for tendering and appropriate risk apportionment are all critical to project success.

Entrenched Western water rights regimes may appear to function relatively well in wet years, but extreme drought events can expose the kinds of harsh ecological and socio-economic outcomes that the hard edges of prior appropriation inherently generate. During the 2012–2016 California drought some irrigators received little or no water at all in consecutive years while others received comparatively large allocations. This paper focuses on the role that California’s water rights priority system and its administration via Central Valley Project contracts have played in generating disproportionate water allocations and impacts during the drought. The analysis is structured around two key questions: (a) in what ways does strict adherence to a priority system of water allocations produce inequitable socio-ecological outcomes during severe drought? (b) how might the system be changed to foster outcomes that are more equitable and fair, and with less costly and less serious conflicts in a non-stationary climate future marked by extreme events? Using an equity perspective, I draw from the doctrine of equitable apportionment to imagine a water rights regime that is better able to create a fairer distribution of drought impacts while meaningfully elevating the importance of future generations and increasing adaptive capacity.

This paper presents the findings of a research project evaluating community benefit models for offshore renewables. We identify and analyse UK and international case studies of different forms of community benefit, and provide evidence of how such benefits are delivered. In particular we consider the key relationship between the identification of communities, perception of impact, and the apportionment of benefits. In doing so, we develop a range of different definitions of ‘community’, ‘benefit’, and ‘impact’ when considering community benefits. We propose that the way in which community, benefit, and impact are understood is crucial in determining whether or how benefits should be apportioned and delivered; and that these definitions are closely connected to each other. We develop a new series of typologies as a way to understand this. Finally, we assess different mechanisms and schemes of community benefits to identify good practice and key points of learning for policy and planning.

A large and fruitful literature has focused on the impact of colonial legacies on long-term development. Yet the mechanisms through which these legacies get transmitted over time remain ambiguous. This paper analyzes the choice and effects of legislative representation as one such mechanism, driven by elites interested in maximizing jointly economic prospects and political influence over time. We focus on malapportionment in the legislatures of the original thirteen British North-American colonies. Their joint independence created a unique juncture in which postcolonial elites simultaneously chose the legislative and electoral institutions under which they would operate. We show that the initial choice of apportionment in the state legislatures is largely a function of economic geography, that such a choice generated persistent differences in representation patterns within states (political inequality), and that the latter shaped public goods provision in the long run.

In this paper we consider three methods used in proportional electoral systems: the Hare-Nimeyer method, the D’Hondt method and the Saint-Lague method. Under certain conditions the last two methods can expose extremely strange behavior producing results which strongly violate the Quota rule. The latter states that the number of seats of a party with v votes should be between the lower and upper integer bounds of the fraction Mv/V, where M is the total number of seats and V is the total number of votes. For the Bulgarian system (M = 240 seats and barrier 4%) the deviation of the D’Hondt method from Quota rule can be at least 5 seats. For M = 240 and very small barrier this deviation can reach 41 seats. For the Saint-Lague method the deviation is at least 17.

Secondary organic aerosol (SOA) is known to account for a major fraction of airborne particulate matter, with significant impacts on air quality and climate at the global scale. Despite the substantial amount of research studies achieved during these last decades, the source apportionment of the SOA fraction remains difficult due to the complexity of the physicochemical processes involved. The selection and use of appropriate approaches are a major challenge for the atmospheric science community. Several methodologies are nowadays available to perform quantitative and/or predictive assessments of the SOA amount and composition. This review summarizes the current knowledge on the most commonly used approaches to evaluate secondary organic carbon (SOC) contents: elemental carbon (EC) tracer method, chemical mass balance (CMB), SOA tracer method, radiocarbon (14C) measurement and positive matrix factorization (PMF). The principles, limitations, challenges and good practices of each of these methodologies are discussed in the present article. Based on a comprehensive—although not exhaustive—review of research papers published during the last decade (2006⁻2016), SOC estimates obtained using these methodologies are also summarized for different regions across the world. Conclusions of some studies which are directly comparing the performances of different methodologies are then specifically discussed. An overall picture of SOC contributions and concentrations obtained worldwide for urban sites under similar conditions (i.e., geographical and seasonal ones) is also proposed here. Finally, further needs to improve SOC apportionment methodologies are also identified and discussed.

The apportionment of waters of the Indus River System between the provinces of Pakistan is widely hailed as a historic agreement. This agreement (herein referred to as the Accord) was signed into effect in 1991, just over 25 years ago. The Accord lacks a clearly stated objective and hence it is difficult to review the Accord against its objective. This paper presents a detailed thematic review of the Accord and interprets the literature and data sets that have become available over the last 25 years. Although the Accord leaves room for interpretation, which is often biased to a particular perspective, an obvious starting point that has been highlighted in the literature is to improve water accounting in the Indus basin and to clarify and document the Operating Rules. Over the next 25 years, demographic change, socioeconomic change, and climate change in the Indus Basin will place this Accord under increased scrutiny.

This paper relates civil joint and several liability of members of a cartel, contribution claims, liability allocation, as well as the anatomy and effects of settlements with less than all parties. Because the substantive rules of Directive 2014/104/EU (the Directive) do not apply to damages that occurred prior to its implementation, the pre-Directive legal framework will continue to be relevant for years. This work therefore analyses both the old and the new sets of rules and how the changing regimes influence incentives. Under pre-Directive law, victims of competition law infringements can claim their entire damages from any of the cartelists. Under some pre-Directive national laws, cartelists sued by the claimant might not be able to take effective recourse against members of the cartel that the claimant did not sue. The effect of a partial settlement in terms of claim reduction and liability of the settling cartelist varies depending on the jurisdictions involved and the wording chosen. Under the Directive, cartelists are also jointly liable for the entire damage caused; however, there are exceptions for the immunity recipient and small and medium enterprises that modify this basic rule. Cartelists do have effective recourse against each other. The effect of a partial settlement is uniform throughout the EU: It always reduces the plaintiff’s claim by the settling cartelist’s share of the harm, and the remaining cartelists can no longer bring contribution claims against the settling cartelist. This facilitates the conclusion of incentive-compatible settlement agreements to cooperate in pursuing the remaining cartelists for damages. This work discusses a multitude of criteria for liability apportionment amongst cartelists, leading into an assessment of two proposals that have been advanced to make the liability apportionment amongst cartelists more predictable: (A) using the ratio of the cartelists’ relative sales and (B) calculating Shapley values of the cartelists’ contributions to the cartel’s effects. I find that relative sales are a suitable starting heuristic for most cases, but there are constellations in which this method leads to absurd results. Shapley values theoretically provide the perfect metric to measure relative responsibility for the harm but require input that is usually exceedingly difficult to obtain. The final part briefly contrasts these results to the situation under US federal law and finds that the combination of no contribution rights amongst cartelists, the trebling of damages and pro tanto claim reduction create stronger incentives to settle than in Europe.

This paper investigates the impact of separate accounting (SA) versus that of formula apportionment (FA) on investment decisions in high- and low-corporate income tax countries. As the investment decisions of multinational enterprises are commonly taken by managers and not by owners, the focus is on the impact of SA versus that of FA on the investment location decided by managers. This is done within the framework of the principal-agent setting, where a Monte Carlo simulation is carried out. Considering taxation under SA supports investing in a less risky investment, even if it is located in the country with the highest tax rate. In analysis of FA, allocation of the tax base based on formula and the cross-border loss offset encourages investing in a risky investment. This is in line with the aim of the European Commission regarding making investments more attractive and supporting cross-border investments within the EU. These results also show that the delegation of investment decisions to managers facilitates the investment in the high-tax country, under both systems, SA as well as FA. As a contribution to the literature reviewed, this study demonstrates that taking the differences in expected returns of investments across the countries, as well as the risk-averse behavior of investors, into account, reveals different impacts of taxation on the invested amount under SA and FA.

In a recent paper in this journal, Gilmer and Morgan attempted to prove that there is equivalence among certain forms of education subsidy programs-flat grants, foundation programs, and equalized apportionment formulas. This paper demonstrates that the proof presented by Gilmer and Morgan does not support the conclusion that these subsidy programs are equivalent.

This paper is concerned with the use of benefit-cost analysis to appraise investment in the construction of grade separations to eliminate or reduce highway traffic over existing rail/highway grade crossings. The paper deals with the measurement and valuation problems involved, and presents the results of a study of five grade separations authorised in Canada. A second issue considered is that of the determination of the appropriate apportionment of capital costs among the parties, rail and highway, involved. Alternative principles for determining who should bear the cost burden of grade separations are developed, and the implications of these cost apportionment procedures for the five Canadian case studies explored.

The Prairie Provinces Water Board was created by the Governments of Alberta, Saskatchewan, Manitoba and Canada to resolve possible conflicts in water use of interprovincial rivers. This paper reviews the master agreement on water apportionment which the Water Board administers, the make-up and function of the Water Board, provides a detailed examination of the various Water Board Committees, and the past and present projects undertaken by these Committees. The paper concludes with an overview of future Water Board, operations.

The paper considers the benefits to be gained from diversification of an insurance operation into a number of classes of business. This is formulated mathematically. It is assumed that the insurer's objective is to maximize increase in utility of wealth over the period up to his planning horizon (Section 2). Several forms of solution of this problem are considered (Section 3). In particular, it is found that there is no benefit in diversification if the parameters characterizing the stochastic properties of the claims of each class of business are known with certainty. In these circumstances, utility is maximized by underwriting all premium in that class of business projected to produce the greatest profitability. It is also seen that, unless the concept of the insurer's risk aversion is incorporated somehow, for example by means of a utility function, no benefits from diversification appear (Section 5.2). The benefits of diversification arise from uncertainty concerning the basic parameters of the claims process in the various classes of business. A parallel with the concepts of diversifiable and undiversifiable risk from Modern Portfolio Theory is pointed out (Section 4). A measure of the balance achieved within a portfolio is constructed. A somewhat simplified version of the problem is considered in Section 5, and an explicit algebraic solution obtained. Of the total budgeted premium to be underwritten in a particular year, the solution prescribes the percentages to be underwritten in the various classes of business. The solution depends upon the projected profitability and the parameters underlying the claims process in each of the classes. Some verbal interpretation of the algebraic solution is provided. That solution is applied to a realistic numerical example (Section 6). The apportionment of total budget premium by class of business arrived at in the numerical example is compared with the actual budget of a particular insurer. A number of qualifying remarks concerning the application of the results of the paper are made in Section 7.

The paper presents a novel ex post income concept, called Earned Economic Income (EEI), which would provide periodic accounting signals that are consistent with those derived from Net Terminal Value (NTV) analyses. EEI assigns interest adjusted NTV to the periods in which it is earned. The allocation is made via the apportionment of interest adjusted original cost. Inflation adjusted and monetary EEI figures are identical, so that the concept provides an integrating framework for interest adjusted inflation accounting and historical cost matching approaches. In developing the model the paper discusses the significance of conceptual models and of Economic Income (EI).

The concept of reliability apportionment is general and has even been applied to the allocation of man-machine reliability. Typically, however, the process of optimally apportioning individual component reliability to meet some desired system reliability level subject, perhaps, to constraints on cost, volume, weight, etc. has always been imprecise and vague at best. In real problems, the resource constraints are no more sacred than the objective system reliability; they are frequently flexible. In view of the inherent vagueness of the reliability objective as well as constraints in a typical ill-structured reliability apportionment problem, this paper formulates the nonlinear optimization problem in the fuzzy-set theoretic perspective. To illustrate the philosophy, a simple reliability apportionment example with a budgetary constraint for a 2-component series structure is analyzed. Then the concept is generalized into a more realistic problem with multiple components and constraints. This tutorial paper is an easy introduction for the newcomer to fuzzy-system theory.

In 1907 I had the honour of reading before the Institute a paper dealing with the Comparative Bonuses under Whole-Life and Endowment Assurances, and therein I pointed out that the method of apportioning the expenses between the two classes had a considerable effect upon the rates of bonus, and in the discussion more than one speaker referred to the relative premiums as vitally affecting the conclusions to be drawn from any investigation. The solution of the first problem will, mortality apart, also give us the key to the rates of premium which an office should charge for Whole-Life and Endowment Assurances respectively. As the premiums are the foundation of our business it is of the utmost importance that an analysis of the expenses should be made periodically in order to ascertain the adequacy of the remuneration the office receives for the risks it undertakes. The question of the office premiums has been frequently discussed, but I do not think any paper has been submitted to this Institute in which an agreement has been shown between the loadings adopted in obtaining the office premiums and the actual expenses of the office. The object of the paper is to elicit the views of the profession upon this subject.The commission paid by the majority of offices is, for the principal classes of Assurance, usually a percentage of the sum assured on payment of the first annual premium and a percentage of the office renewal premiums. The loading required to provide for the commissions is therefore easily ascertained and requires no discussion.

The subject of this paper has on two previous occasions been brought before the Institute; namely, by Mr. Jellicoe on 26 November 1855, and by Mr. Baden on 27 March 1871. The former of these gentlemen stated that, at the time his paper was written, a great diversity of opinion existed among actuaries, as to the proper method to be adopted in advising upon the proportions in which a settld fund should be divided by mutual consent between the life tenant and the reversioner; and so far as can be judged from the discussion that followd the reading of the latter paper, a similar diversity still existed then. One point, however, was clearly establisht by the discussion, namely, that Mr. Baden was quite mistaken in supposing that, because Mr. Jellicoe's conclusions had not been publicly calld in question, therefore they wer generally accepted by members of the profession.

…the solutions given…are so various as to excite no little surprise and distrust in the minds of those unacquainted with the subject, under whose notice such solutions are brought.…a great deal of judgment and discretion must always be required from the actuary, and…it is not possible to lay down any general rule which shall altogether obviate such requirement.The quotations above are taken from a paper by Jellicoe (J.I.A.6, 61) which was discussed by this Institute in 1855. It is a salutary thought that there are no subsequent statements recorded in J.I.A. on the subject which seem to express so succinctly the two principal points which should always be borne in mind when the apportionment of a trust fund is under consideration. It must be stated immediately, however, that since 1855 problems of apportionment have been discussed only in 1871 (J.I.A.16, 269), 1873 (J.I.A.18, 77) and 1925 (J.I.A.56, 243); indeed, reversions and life interests have scarcely been mentioned in Institute discussions since 1935, when O. I'A. Thurston presented his paper on Death Duties (J.I.A.66, 369).

SynopsisThe paper records the growth in the number of apportionments of trust funds due to the passing of the “Trusts (Scotland) Act 1961”. It considers the problems, as they arise in Scotland, of allowing for the impact of taxation, both in determining the interests to be valued and in fixing the valuation rate of interest, and it is suggested that the same net rate of interest need not necessarily be appropriate for all the beneficiaries.Numerical examples are given of the effects on funds of varying size and investment content of various valuation assumptions, and the problem of disposing of the potential savings in taxation is discussed. The paper ends with a general section covering some practical points in the preparation of schemes to vary trust purposes.

If any excuse be wanting for once more bringing this question forward for your consideration, it is not because the question itself is unimportant. The frequency of the cases involving it upon which the opinion of actuaries is sought, and the magnitude of the interests concerned, will be allowed by all to furnish ample grounds for the utmost possible care and pains in determining the principles by which the advice given should be regulated. Upwards of 15 years have elapsed since Mr. Jellicoe's well-known paper on this subject was read before the Institute. How far the practice of actuaries has been influenced by the conclusions laid down in that paper I do not know; but from the fact that (so far as I am aware, at least,) the subject has not been reopened since, it would seem that these conclusions have been accepted by the profession, and that in the opinion of those most competent to form a judgment there is nothing more to be said about them. If this be so, I am afraid that I shall incur the suspicion of rashness when I say that the excuse I have to urge for reopening the question is, that the conclusions laid down by Mr. Jellicoe do not commend themselves to my mind as perfectly satisfactory. I propose very briefly to state my reasons for differing from him; and should I fail, as I well may, in convincing others of the correctness of my views, I shall be consoled by the reflection, that however firmly established, and apparently beyond discussion, any truth may be, it is a profitable thing for most, perhaps for all of us, if a rash sceptic now and then compels us to review the grounds of our confidence, and to restate to ourselves, if not to others, the reasons for the faith that is in us.

This paper is mainly concerned with the division of a trust fund between the beneficiaries, when an actuary is asked for a solution which, in his opinion, is fair to all parties concerned. It may be that the beneficiaries are all sui juris and form a closed class, in which case they approach the actuary as umpire, and adopt a passive role, at least until they have considered the implications of his recommendations. Alternatively, the actuary's report may be required to assist the Court to approve a scheme involving beneficiaries, e.g. infants, whom it is the Court's object to protect. In that case the actuary's role—as discussed later in the paper—is rather different, but it may still be necessary for him to state what in his judgment would be an impartial solution.

Setting the proper objective functions to optimize the decision making situations is prevalent in most of the mathematical programming problems. In this paper, we formulate the mathematical models of product rate variation and discrete apportionment problems. Furthermore, a brief comparative study of the objective functions to both the problems is reported in terms of inequality measures, precisely indicating the equitably efficient frontier for production rate variation problem via discrete apportionment. The largest reminder algorithm and rank-index algorithm for the apportionment problem are discussed briefly.Journal of Institute of Science and Technology, 2014, 19(1): 69-74

Psychologists serving as Qualified Medical Examiners (QMEs) in settings where mental and emotional damage claims (i.e., psychological disability stemming from psychological injury) are involved typically must comment not only upon the impact of the injury on the individual’s functioning and quality of life, but also on the causality of the psychological disability. This is a highly specialized endeavor for which little guidance exists. The disparate conceptualizations of causality in the fields of psychology and law and the unavoidable complexities associated with determining causality, especially the apportionment of causality across industrial and non-industrial factors, are discussed. The questions at the core of the present paper are: 1) What are the ethical challenges facing psychologists working as QMEs who are tasked with determining causality of psychological disability in the ways currently required by the law, and 2) What considerations should guide ethically-minded psychologists in such settings? The authors argue that, although some level of subjectivity is unavoidable, psychologists working within the legal system can take the lead in bringing an evidence-based approach and greater scientific rigor to the high-stakes causal evaluations required as a basis for determining compensation for injured workers.

Segmental apportionment of lumbar (L2-S1) rotation is a critical input parameter for musculoskeletal models and a candidate metric for clinical assessment of spinal health, but such data are sparse. This paper aims to quantify the time-variant and load-dependent characteristics of intervertebral contributions to L2-S1 extension during a dynamic lifting task. Eleven healthy participants lifted multiple weights (4.5, 9.1, and 13.6 kg) from a trunk-flexed to an upright position while being imaged by a dynamic stereo X-ray system at 30 frames/s. Vertebral (L2-S1) motion was tracked using a previously validated volumetric model-based tracking method that employs 3D bone models reconstructed from subject-specific CT images to obtain high-accuracy (≤0.26°, 0.2 mm) 3D vertebral kinematics. Individual intervertebral motions as percentages of the total L2-S1 extension were computed at each % increment of the motion to show the segmental apportionment. Results showed L3-L4 (25.8±2.2%) and L4-L5 (31±3.1%) together contributed a larger share (∼60% combined) compared to L2-L3 (21.7±3.7%) and L5-S1 (22.6±4.7%); L4-L5 consistently provided the largest contribution of the measured segments. Relative changes over time in L3-L4 (6±12.5%) and L4-L5 (0.5±10.2%) contribution were minimal; in contrast, L2-L3 (18±20.1%) contribution increased while L5-S1 (-33±22.9%) contribution decreased in a somewhat complementary fashion as motion progressed. No significant effect of the magnitude of load lifted on individual segmental contribution patterns was detected. The current study updated the knowledge regarding apportionment of lumbar (L2-S1) motion among individual segments, serving both as input into musculoskeletal models and as potential biomechanical markers of low back disorders.

Summary Across the southern Canadian Prairies, annual precipitation is relatively low (200–400 mm) and periodic water deficits limit economic and environmental productivity. Rapid population growth, economic development and climate change have exposed this region to increasing vulnerability to hydrologic drought. There is high demand for surface water, streamflow from the Rocky Mountains in particular. This paper describes the application of dendrohydrology to water resource management in this region. Four projects were initiated by the sponsoring organizations: a private utility, an urban municipality and two federal government agencies. The fact that government and industry would initiate and fund tree-ring research indicates that practitioners recognize paleohydrology as a legitimate source of technical support for water resource planning and management. The major advantage of tree-rings as a proxy of annual and seasonal streamflow is that the reconstructions exceed the length of gauge records by at least several centuries. The extent of our network of 180 tree-ring chronologies, spanning AD 549–2013 and ∼20° of latitude, with a high density of sites in the headwaters of the major river basins, enables us to construct large ensembles of tree-ring reconstructions as a means of expressing uncertainty in the inference of streamflow from tree rings. We characterize paleo-droughts in terms of modern analogues, translating the tree-ring reconstructions from a paleo-time scale to the time frame in which engineers and planners operate. Water resource managers and policy analysts have used our paleo-drought scenarios in their various forms to inform and assist drought preparedness planning, a re-evaluation of surface water apportionment policy and an assessment of the reliability of urban water supply systems.

International audience; In this paper, we consider the composition of an optimal portfolio made of two dependent risky assets. The investor is first assumed to be a risk-averse expected utility maximizer, and we recover the existing conditions under which all these investors hold at least some percentage of their portfolio in one of the assets. Then, we assume that the decision maker is not only risk-averse, but also prudent and we obtain new minimum demand conditions as well as intuitively appealing interpretations for them. Finally, we consider the general case of investor’s preferences exhibiting risk apportionment of any order and we derive the corresponding minimum demand conditions. As a byproduct, we obtain conditions such that an investor holds either a positive quantity of one of the assets (positive demand condition) or a proportion greater than 50 % (i.e., the “50 % rule”).

This paper presents simple yet efficient formula for apportionment of cost generated by the variability of flow of requirements (objects, inventory, money) through the shared service center (distribution center, internal bank, some service center) as well as formula for apportionment of the cost generated by the flow, if it were steady. The presented formula assures that shared service center cost are charged fairly and provide incentive for the shared services center counterparts to optimize timing and size of their requirements towards shared services center and minimize the total cost of handling them. Additionally we challenge the marginalist transfer pricing theory.

Age-period-cohort analysis of incidence and/or mortality data has received much attention in the literature. To circumvent the non-identifiability problem inherent in the age-period-cohort model, additional constraints are necessary on the parameters estimates. We propose setting the constraint to reflect the different nature of the three temporal variables: age, period, and birth cohort. There are two assumptions in our method. Recognizing age effects to be deterministic (first assumption), we do not explicitly incorporate the age parameters into constraint. For the stochastic period and cohort effects, we set a constant-relative-variation constraint on their trends (second assumption). The constant-relative-variation constraint dictates that between two stochastic effects, one with a larger curvature gets a larger (absolute) slope, and one with zero curvature gets no slope. We conducted Monte-Carlo simulations to examine the statistical properties of the proposed method and analyzed the data of prostate cancer incidence for whites from 1973-2012 to illustrate the methodology. A driver for the period and/or cohort effect may be lacking in some populations. In that case, the CRV method automatically produces an unbiased age effect and no period and/or cohort effect, thereby addressing the situation properly. However, the method proposed in this paper is not a general purpose model and will produce biased results in many other real-life data scenarios. It is only useful in situations when the age effects are deterministic and dominant, and the period and cohort effects are stochastic and minor.

Inter-country equity in the taxation of IP is a contentious issue. With its BEPS initiative, the OECD aims at taxing in accordance with value creation even though there are admitted difficulties in determining the actual place of value creation. The European Commission promotes the introduction of unitary taxation. The proposal’s drawback is that it lacks incentive compatibility in information exchange. Furthermore, it stipulates a cost-dependent apportionment of the common consolidated corporate tax base that incentivizes locating R&D in low-tax countries. Against this background, this paper makes a case for an internationally regulated split of the profit earned with imported IP.

As an economist, I find the current state of the law regarding damages for patent infringement – most particularly that relating to apportionment – frustrating at best and woefully incomplete at worst. Namely, damages case law for utility patent infringement provides two very different, but insufficient, guidance frameworks for calculating damages: the entire market value rule (EMVR) versus the smallest salable patent practicing unit (SSPPU) principle. The modern pair of EMVR and SSPPU options is far narrower than the approaches afforded by the original 1884 Supreme Court ruling establishing apportionment for damages, Garretson. In this paper, I present the economic case for expanding the allowable damages frameworks beyond EMVR or SSPPU, to fill in the gap in reasonable damages approaches created by an EMVR and SSPPU dichotomy.

There are a variety of methods that state legislatures can use to pass legislation which relates to municipalities. This paper explores why, how and when states changed their constitutions from allowing special legislation for municipalities to requiring general laws which would apply to all municipalities. Historians have put forward several explanations for why special legislation was harder to maintain as the nineteenth century progressed. A new way of framing the story is presented here by considering how the passage of special legislation was maintained through a logroll; legislators formed a coalition to vote on each other’s local legislation. As the size of the legislature expanded and the composition of the legislature changed, it may have been harder for legislators to maintain a coalition in order to logroll each other’s proposed local legislation. The previous theories along with the new one presented here are empirically tested. Evidence suggests a link between the size of the state legislature and the probability of instituting general legislation for municipalities, indicating that one motivation for adopting general laws was the dissolution of a stable logroll.

This paper focuses on the toxicity evaluation and source apportionment of Polycyclic Aromatic Hydrocarbons (PAHs) in three monitoring stations in Istanbul, Turkey. A total of 326 airborne samples were collected and analyzed for 16 PAHs and Total Suspended Particles (TSP) for the period of September 2006-December 2007. The total average PAH concentrations were 100.7 +/- 613, 84.6 +/- 46.7 and 25.1 +/- 13.3 ng m(-3) and the TSP concentrations were 101.2 +/- 53.2, 152.3 +/- 99.1, 49.8 +/- 18.6 mu g m(-3) for URB1, URB2 and RUR stations, respectively. Benzo(a)Pyren (BaP) toxic equivalency factors to PAH concentration values were calculated indicating that the health risk of BaP and DiBenz(a,h)Anthracene (markers of traffic emissions) have the highest contribution compared to all of the other species measured at the sampling sites. In order to determine PAH sources, two different source apportionment techniques were applied to the measurements; diagnostic ratios (DR) and Positive Matrix Factorization (PMF). The results of the two applications were compatible indicating the vehicle emissions especially diesel engines - as the major source for urban stations. (C) 2013 Elsevier B.V. All rights reserved.

The landscape water body is studied in this paper. Through the monitoring of pollution sources of receiving conventional index and risk index, the distribution of pollution sources and river pollution factor is detailed analyzed, as nutrient salts, heavy metals, and environmental endocrine disruptors. And source of the pollution factor is studied by principal component analysis to get the main pollution factors in this channel.

Computing a biproportional apportionment that satisfies some given properties may require a high degree of mathematical expertise, that very few voters can share. It seems therefore that the voters have to accept the electoral outcome without any possibility of checking the validity of the stated properties. However, it is possible in some cases to attach to the computed apportionment a certificate which can guarantee the voters of the validity of the apportionment. This type of investigation has been first proposed in Serafini and Simeone (Soc Choice Welf 38:247–268, 2012. In this paper we pursue the same line of approach and show that a certificate can be produced and easily checked by a layman for apportionments that minimize either an $$L_1$$ - or an $$L_2$$ -norm deviation from given quotas.

In this paper, the contamination of heavy metals in atmospheric particles of PM2.5 and PM10 in a city in China was analyzed, meanwhile the sources of different heavy metals (Cd, Hg, As and Pb) in atmospheric particles (PM2.5 and PM10) were confirmed by source apportionment in a city in China area through principal component analytical method. The research results showed that the heavy metals in PM2.5 and PM10 contaminated the atmosphere environment dramatically. The heavy metal Cd, Hg and Pb came mainly from incomplete combustion of petrol, while the heavy metal of As was the product of electronic metallurgy, which provides the theoretical basis for controlling of atmospheric heavy metal contamination. This method can be also applied to source apportionment of other heavy metals in atmosphere environment.

Objectives: This paper presents software reliability apportionment using fuzzy logic. Methods/Statistical Analysis: The proposed methodology attempts to allocate target reliability to its modules. For calculation of reliability, the first step is to aggregate the opinion of all team members of ith module. Second step is to calculate proportionality factor of the software system. Defuzzify the Fuzzy Proportionality Factor by using defuzzification formula. After obtaining crisp values, we have to calculate weightage of each module. Based on weightage, reliability of each module is calculated. Findings: Operational Profile is one of the main parameters for making effective testing and improved reliability by testing most used functions in first phase and lesser used function in next phase. Comparing with the previous result, reliability has been improved. Application/Improvements: It helps to allocate reliability to all modules before the actual system is built. Also it considers Operational Profile as a parameter in proportionality factor, which helps to allocate reliability to most used modules, therefore making reliability apportionment beneficial for every module.

Receptor models are, rarely utilized in soil but are often used to identify pollutant sources and quantify their contribution. This paper focuses on the soil in oasis farmland. A geochemical baseline is used to assess the pollution of the soil, and then three models are tentatively utilized to apportion heavy metals and compare the sources, the contributions and the operation effects. Pollution assessment indicated that the farmland soil of Wuwei was lightly contaminated by heavy metals. Source apportionments suggested that atmospheric deposition contributed the most pollution (53.95%–65.35%). The three models supplemented each other, and the grouped principal component analysis/absolute principal component scores (GPCA/APCS) was outstanding. GPCA/APCS and UNMIX suggested that agricultural activities were the prime anthropogenic source (51.06%–61.56%), followed by the combustion of fossil fuels (coal and oil) (27.92%–28.66%) and building materials-related activities source (10.52%–20.29%). Fertilizers and pesticides (67.88%–74.81%) contributed more than traffic emissions (25.19%–32.12%) in agricultural activities. Similar results were acquired via positive matrix factorization (PMF), while industrial activity was the highest individual contributor (29.91%). Therefore, combining these three models was the most effective approach, and more attention should be paid to mitigating the pollution caused by the use of fertilizers and pesticides as well as the industrial activities in Wuwei. The results of this study could provide reference in reduction of heavy metal pollution in farmland soil.

We read with great interest the paper by Mortensen et al. [(1)][1] on negative risk markers and cardiovascular events in older adults (age >65 years) published in the Journal . “Derisking” and appropriate apportionment of therapies allow clinicians and patients to withhold or de-escalate