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To apportion a complex matrix means to apply a similarity so that all entries of the resulting matrix have the same magnitude. We initiate the study of apportionment, both by unitary matrix similarity and general matrix similarity. There are connections between apportionment and classical graph decomposition problems, including graceful labellings of graphs, Hadamard matrices, and equiangular lines, and potential applications to instantaneous uniform mixing in quantum walks. The connection between apportionment and graceful labellings allows the construction of apportionable matrices from trees. A generalization of the well-known Eigenvalue Interlacing Inequalities using graceful labellings is also presented. It is shown that every rank one matrix can be apportioned by a unitary similarity, but there are 2 × 2 matrices that cannot be apportioned. A necessary condition for a matrix to be apportioned by unitary matrix is established. This condition is used to construct a set of matrices with nonzero Lebesgue measure that are not apportionable by a unitary matrix. [ABSTRACT FROM AUTHOR]

Serendipity, curiosity, and lived experience shaped my career as a social demographer and my interests in social policy. I transitioned from the humanities to sociology and demography as a graduate student at the University of Texas at Austin, where I discovered my affinity for quantitative research. My interest in Latin American demography gave way to domestic concerns as new opportunities arose at each of the three institutions where I have had the privilege to work—the University of Wisconsin-Madison, the University of Chicago, and Princeton University. That all three institutions hosted vibrant demography and policy programs facilitated my research about the Hispanic population, family structure, urban poverty, college access, and myriad aspects of socioeconomic inequality and immigrant integration. Superb colleagues and talented graduate student collaborators deserve major credit for my career accomplishments. I attribute numerous opportunities to serve on philanthropic and corporate boards to the strength of weak ties. [ABSTRACT FROM AUTHOR]

In the classic apportionment problem, the goal is to decide how many seats of a parliament should be allocated to each party as a result of an election. The divisor methods solve this problem by defining a notion of proportionality guided by some rounding rule. Motivated by recent challenges in the context of electoral apportionment, we consider the question of how to allocate the seats of a parliament under parity constraints between candidate types (e.g., an equal number of men and women elected) while at the same time satisfying party proportionality. We study two different approaches to solve this question. We first provide a theoretical analysis of a recently devised mechanism based on a greedy approach. We then propose and analyze a mechanism that follows the idea of biproportionality introduced by Balinski and Demange. In contrast with the classic biproportional method by Balinski and Demange, this mechanism is ruled by two levels of proportionality: Proportionality is satisfied at the level of parties by means of a divisor method, and then biproportionality is used to decide the number of candidates allocated to each type and party. A typical benchmark used in the context of two-dimensional apportionment is the fair share (a.k.a matrix scaling), which corresponds to an ideal fractional biproportional solution. We provide lower bounds on the distance between these two types of solutions, and we explore their consequences in the context of two-dimensional apportionment. [ABSTRACT FROM AUTHOR]

Several different arguments support the use of Webster's method when seats in a parliament are to be apportioned proportionally according to populations. This note—instigated by a new property—summarizes the reasons. [ABSTRACT FROM AUTHOR]

An apportionment paradox occurs when the rules for apportionment in a political system or distribution system produce results which seem to violate common sense. For example, The Alabama paradox occurs when the total number of seats increases but decreases the allocated number of a state and the population paradox occurs when the population of a state increases but its allocated number of seats decreases. The Balinski-Young impossibility theorem showed that there is no deterministic apportionment method that can avoid the violation of the quota rule and doesn’t have both the Alabama and the population paradoxes. In this paper, we propose a randomized apportionment method as a stochastic solution to the Balinski-Young impossibility. [ABSTRACT FROM AUTHOR]

Copyright of Ruch Prawniczy, Ekonomiczny i Socjologiczny (0035-9629) is the property of Adam Mickiewicz University and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Numerous states have altered the sales factor weight in their corporate income tax (CIT) apportionment formulas. We are among the first to examine which political and economic factors are important in determining whether and when states manipulate sales factor weights. We apply survival model techniques to a panel of state-level data for the years 1985−2012. Our most striking result is that a higher CIT rate is associated with faster movement to a higher sales factor weight. Perhaps indicating that, for economic development, states use sales factor manipulation in lieu of reducing CIT rates broadly, or alternatively, that states raise sales factor weights to compensate for higher statutory CIT rates. Results also indicate that stronger growth in the CIT base and in non-corporate tax revenues hasten sales factor weight increases. Democratic control of the state government and gubernatorial election years are also important in the timing of sales factor manipulation. [ABSTRACT FROM AUTHOR]

We reported the seasonal variations of columnar aerosol optical depth (AOD) and equivalent black carbon (EBC) from December 2018 to November 2019 in semi-arid station, Anantapur. Furthermore, using the two-component source apportionment model, we estimated the contribution of biomass burning (EBCbb) and fossil fuel combustion (EBCff) to the total EBC. The high AOD values at shorter wavelengths indicate that particle loading occurs primarily in fine mode aerosols. The high AOD500 was observed in the month of May (0.77 ± 0.19), and the low was in July (0.32 ± 0.11). The seasonal highest mean AOD500 was noticed during the summer (0.67 ± 0.12) followed by winter (0.49 ± 0.01), post-monsoon (0.43 ± 0.15) and monsoon (0.43 ± 0.17). The results revealed that both local emissions and long-range transported aerosols are primarily responsible for a significant spectral and temporal variability in AOD. In winter, the Angstrom exponent (α) was relatively high, whereas it was low in monsoon season. The mass concentrations of EBC, EBCff and EBCbb showed a strong diurnal and seasonal variations with in the study period. The highest and lowest EBC was noticed in winter and monsoon that is 2.64 ± 0.32, and 0.625 ± 0.16 μg/m3, respectively. The percentage contribution of annual mean EBC was 52.13% during the day and 47.86% during the night, respectively. With an average of 91.48%, EBCff contributes the most to total EBC during the study period. Furthermore, during all seasons, the hourly mean concentrations of EBC showed good agreement (r = 80) between the observed (Aethalometer) and MERRA-2 (Modern-Era Retrospective Study for Research and Applications). According to the MERRA-2 winds and Moderate Resolution Imaging Spectroradiometer (MODIS), the prevalence of fine mode particles throughout winter and summer is connected with continental air masses originating from India's central and northern regions. [ABSTRACT FROM AUTHOR]

Chemical contamination from point source discharges in developed (resource‐rich) countries has been widely regulated and studied for decades; however, diffuse sources are largely unregulated and widespread. In the European Union (EU), large dischargers report releases of some chemicals, yet little is known of total emissions (point and diffuse) and their relative significance. We estimated copper loadings from all significant sources including industry, sewage treatment plants, surface runoff (from traffic, architecture, and atmospheric deposition), septic tanks, agriculture, mariculture, marine transport (antifoulant leaching), and natural processes. A combination of European datasets, literature, and industry data were used to generate export coefficients. These were then multiplied by activity rates to derive loads. A total of approximately 8 kt of copper per annum (ktpa) is estimated to enter freshwaters in the EU, and another 3.5 ktpa enters transitional and coastal waters. The main inputs to freshwater are natural processes (3.7 ktpa), agriculture (1.8 ktpa), and runoff (1.8 ktpa). Agricultural emissions are dominated by copper‐based plant protection products and farmyard manure. Urban runoff is influenced by copper use in architecture and by vehicle brake linings. Antifoulant leaching from boats (3.2 ktpa) dominates saline water loads of copper. It is noteworthy that most of the emissions originate in a limited number of copper uses where environmental exposure and pathways exist, compared with the bulk of copper use within electrical and electronic equipment and infrastructure that has no environmental pathway during its use. A sensitivity analysis indicated significant uncertainty in data from abandoned mines and urban runoff load estimates. This study provided for the first time a methodology and comprehensive metal load apportionment to European aquatic systems, identifying data gaps and uncertainties, which may be refined over time. Source apportionments using this methodology can inform more cost‐effective environmental risk assessment and management. Integr Environ Assess Manag 2023;19:1031–1047. © 2022 The Authors. Integrated Environmental Assessment and Management published by Wiley Periodicals LLC on behalf of Society of Environmental Toxicology & Chemistry (SETAC). Key Points: For the first time, a source apportionment of copper to the aquatic environment has been achieved for all significant point and diffuse sources of copper.A total of approximately 8 kt of copper per annum (ktpa) is estimated to enter freshwaters in the European Union, and another 3.5 ktpa enters transitional and coastal waters.The main inputs to freshwater are natural processes (3.7 ktpa), agriculture (1.8 ktpa), and runoff (1.8 ktpa), with agricultural emissions dominated by copper‐based plant protection products and farmyard manure and urban runoff by architecture and brake lining wear.Antifoulant leaching from boats (3.2 ktpa) dominates saline water loads of copper. [ABSTRACT FROM AUTHOR]

Ideally, a representative democracy awards a genuine vote to each adult. We study this issue in competitive democracies with an election model combining district apportionment and proportional representation. Four classic seat allocation rules, including d'Hondt, are reframed as Dutch auctions, allowing important properties to be easily derived. The pros and cons of these methods are stated in terms of economic inequality; Sainte Laguë's is shown to best carry the genuine vote ideal, both for elections and for apportionment. We next expound the interplay between these two components in generating an inequitable treatment of voters and develop the scale-free index of inequity best fitted to their concern. We apply it to 40 countries for the apportionment of electoral districts. Lastly, we compute the same inequity index for recent parliamentary elections in 80 countries, finding that the majority system mistreats electors, thus putting a 'price' on government stability. [ABSTRACT FROM AUTHOR]

(1) Background: Is variation among the communities of a metacommunity higher than within the communities? Community ecologists and population geneticists often characterize the structure of metacommunities by partitioning variation (diversity) into the two following components using measures such as F S T or G S T and α - and β -diversity. The within-communities component is usually some average of (type, species, genetic) diversities within the communities, and the among-communities component is the additive or multiplicative complement of the overall diversity. Such an among-communities component lacks independent conceptual specification, a matter of long-standing dispute. Only if the two components are independently and commensurably specified can the central question of comparability be answered meaningfully. (2) Methods: A novel approach to overcoming this conceptual weakness identifies two principles of the partitioning of variation among communities (concentration and division) then relates these principles to the common notions of variation (diversity) within and among communities, distinguishes primary indicators to quantify the partitioning principles, transforms the indicators into conceptually independent measures (indices) of variation within and among communities, and by this attains their commensurability and thus comparability. The application of the methods to quantifying the effects of evolutionary mechanisms is outlined. (3) Results: Common approaches are corrected and extended. (a) Analyses of metacommunity/metapopulation structures that rely on apportionment or related indices and take its complement to be differentiation yield incomparable measures of variation within and among communities. (b) The common practice of partitioning the total diversity into additive or multiplicative components produces the inconsistent ranking of the two components. (c) Community concentration and division can result from elementary processes of adaptive differentiation and migration (gene flow) among communities, where the (commensurable) amounts of community concentration and division reflect the relative participation of these processes in metacommunity structuring and translate directly into the measures of diversity within and among communities. (d) The modelling of the contributions of the two partitioning principles to the metacommunity structure is restricted by the marginal distributions of types and community affiliation. (e) The model demonstrates the degree to which adaptational processes at the metacommunity level are mixtures of adaptational events within and among communities. [ABSTRACT FROM AUTHOR]

In 1998 a long-lost proposal for an election law by Gottlob Frege (1848–1925) was rediscovered in the Thüringer Universitäts- und Landesbibliothek in Jena, Germany. The method that Frege proposed for the election of representatives of a constituency features a remarkable concern for the representation of minorities. Its core idea is that votes cast for unelected candidates are carried over to the next election, while elected candidates incur a cost of winning. We prove that this sensitivity to past elections guarantees a proportional representation of political opinions in the long run. We find that through a slight modification of Frege's original method even stronger proportionality guarantees can be achieved. This modified version of Frege's method also provides a novel solution to the apportionment problem, which is distinct from all of the best-known apportionment methods, while still possessing noteworthy proportionality properties. [ABSTRACT FROM AUTHOR]

Objective.—: To demonstrate a method which is being used to apportion between risk factors for occupationally related disease and compensate individuals with multiple risk factors. The application to individuals will be demonstrated for varicose veins., Background.—: The National Insurance Institute (NII) is tasked with compensating work related injuries and illness in Israel. Population attributable fraction (PAF) has been utilized in order to estimate the amount of disease that can potentially be eliminated in a population through the elimination of individual risk factors. PAF is based on relative risks and the prevalence of these risks., Methods.—: A review of the medical literature consisting of epidemiological studies of varicose veins and its multiple risk factors was conducted, with special attention to prolonged occupational standing. Summary, weighted, relative risks were calculated for eight different risk factors. The proposed formula then allowed for apportioning among those risk factors in the individual., Results.—: The findings of the current study indicate that prolonged standing may be associated with the presence of varicose veins, however in light of the multiple other risk factors associated, its overall contribution is generally minor., Conclusion.—: Apportionment among multiple risk factors for varicose veins can be accomplished mathematically in individuals. This application is being applied successfully for other diseases as well., (Copyright © 2024 Journal of Insurance Medicine.)

Introduction Geography explains the man-environment relationships and the geographical environments and spaces need the political organization of space is needed for optimal governance. It is impossible or it will be accompanied by many difficulties to manage space without political management and to define clear boundaries by dividing space into local, national and regional dimensions. Thus, political geography examines the effect of political decisions on the environment and geographical space and human relations. If sovereignty arises from the nation, political decisions have acceptability and legitimacy. In this geographical debate, elections as a branch of political geography examine the proportionality or disproportion of electoral areas' seats to the population, as well as the manipulation of electoral areas' boundaries (Gerrymandering) that leads to the continued victory of a person or political faction. The Islamic Consultative Assembly is considered as the main and most important decision-making element in the Islamic Republic of Iran, which periods have passed since the beginning of the Islamic Revolution, and according to the existing laws (Article 64 of the Constitution), each area can change according to decreasing or increasing the number of members of parliament in each ten-year period and the geographical boundaries, which necessarily leads to changes in the boundaries of the electoral area and manipulation of the boundaries, in the meantime, the examination of voting patterns and voting and ballots can manipulate and change boundaries in favor of one person or party, and lead to continued victory in electoral areas. On the other hand, if there is a mismatch between these manipulations with the proportion of the population and electoral seats call into question spatial justice and democracy, so political geographers, especially election geographers, examine these issues and analyze electoral areas Materials and methods In the present study, the dispersion and deviation from the criteria and division of electoral areas has been investigated using library resources, approvals of the Islamic Consultative Assembly, Statistics Center of Iran, field observation, interviews with representatives and using Spss v22 software, as well as electoral areas maps in different periods are examined using the GIS software geographic information system, and the maps of each electoral area are drawn before and after the changes, and based on one or more of six methods, Gerrymandering is discovered as follows. Obvious declared method 2. Conditions generality method 3- The evaluation method of the border change process 4- The inspection method 5- The preliminary comparison method 6- Clear superiority method and accordingly the division in the electoral areas of East Azerbaijan province is in the following categories. 1- Very high negative difference 2- High negative difference 3- Low negative difference 4- Very low negative difference 5- Normal 6- Very low positive difference 7- Low positive difference 8- High positive difference 9- Very high positive difference Results and Discussion The study of the variance of constituencies indicates that a very sparsely populated constituency with a large and representative Shahin Dej constituency and a densely populated and under-represented constituency of Urmia and Khoy and Charpareh do not have a suitable share ratio. The variance of the constituencies of West Azerbaijan province compared to the national average shows that the constituency of Urmia is underrepresented and this should beconsidered in future studies. Examining the proportionality of the share in the constituencies of West Azerbaijan province confirms that there is less spatial justice in terms of population and number of seats. The provincial average population of constituencies is 272,101; the sum of its variance is equal to 6.31 and its average variance is equal to 63. Percent. And for the total population of the province, 11.37 representatives are assigned. In examining the manipulations carried out at the borders of some constituencies, especially at the time of the separation of Shahin Dej, Takab and Miando Ab, the proportionality of population sharing has been disturbed. Therefore, in future revisions, this disproportion should be considered and spatial justice Replace with disproportionate sharing. On the other hand, the manipulations in the constituencies should be done with careful and expert attention, and the investigation of Jerry Mandering in this province shows that Jerry Mandering has not taken place. Conclusion Analysis of the population and number of seats in West Azerbaijan Province shows that the three constituencies of Urmia, Khoy and Charpareh and Miando Ab are under-represented constituencies and the two constituencies of Shahin Dej and Salmas are among the most representative constituencies, although According to the 2016 census, most of the constituencies are in the normal range, but in some constituencies, the disproportion of distribution is obvious. The suggestions that can be made about this province are as follows. With the increase in the population of Urmia constituency, this constituency has the potential to increase the representative to 4 seats, which can be considered in future decisions due to the increase in population from 2016 until now. Other constituencies, without considering this important component, will face more gaps in any change, intrusion, occupation, limitation, and increase of the share and spatial justice.

This paper examines state interest in the nine bases of congressional seat apportionment considered for the House of Representatives as part of the Fourteenth Amendment to the US Constitution. We ask, what if voters preferred apportionments that delivered larger vote shares to their state? We then show that among all states, one basis of apportionment was a weak Condorcet winner, while the others were in a vote cycle. In both chambers of Congress, however, pure majority voting created orderings of the nine bases and a different Condorcet winner. Ironically, Congress did not select either Condorcet winner. Instead, a population-based apportionment was reported out of committee and passed both chambers as a consequence of agenda control and lack of pairwise voting. Our analysis provides an example of how agenda setting with incomplete information unintentionally can produce undesirable outcomes for a legislature. [ABSTRACT FROM AUTHOR]

Activities performed at mineral processing operations are capable of producing significant quantities of dust. To ensure that regulatory compliance is maintained throughout operation, dust levels are monitored by routine analysis of air filter samples. Determining the quantity and type of particulate matter present in dust allows for the operation to identify the sources of dust and where warranted, implement a dust suppressant strategy. Conventional methods of analysis, such as chemical assay, are unable to rigorously differentiate between phases containing the same elements and may result in ambiguity related to the identification of dust sources. By incorporating Quantitative Evaluation of Materials by Scanning Electron Microscope (QEMSCAN) into their routine monitoring programs, the Sudbury INO smelter has greatly improved characterization of the Ni and Co dust emissions generated at the operation. To determine specific activities responsible for emissions, bulk particulate matter was sampled from several key locations at the smelter that regularly produce dust. QEMSCAN was able to distinguish between critical subspecies of Ni and Co and mineralogical, and chemical signatures in the dust that are representative of locational activity were established. An apportionment of elements contributed by each source was calculated based on this information. The results of the characterization study assisted personnel in developing strategies to mitigate dust emissions that originate from the Smelter operations, and have general implications to occupational hygiene and environmental risk assessment.

Introduction. The article analyzes tax apportionment for Kalmyk population in the 19th century through examining aimak-level (Kalm. ‘locality, settlement’) data. Goals. The study mainly aims at identification of categories of taxes adopted at the aimak level, determination of the tax apportionment mechanism, analysis of average amounts of taxes across different aimaks. Materials. The analyzed documents include reports of 1882 on taxes from southern aimaks of Baga Dorbet (Russ. Maloderbetovsky) Ulus housed by the National Archive of the Kalmykia (Coll. И-15). Results. Apportionment, i.e. a financial method which assumes distribution of the total amount of a certain type of income for a set of taxable objects, was officially adopted by Kalmyks in the second half of the 19th century. The materials show the form in which it was used by the Kalmyks on the eve of the obligatory relationships’ cancellation, i.e. in the 1880s. Kalmyk commoners paid both official and non-official taxes — in terms of the Regulations introduced by the Imperial Court for the Kalmyk People’s Directorate. The non-official ones included ‘dark’ and household fees, as well as a ‘public needs’ fee, which, in our view, went to ulus-level budgets. The period under study witnessed the application of the apportionment principle (guideline) to the entire amount of taxes. Aimak meetings decided which families would not pay taxes to further divide the entire amount into two parts: the first one was apportioned for a certain number of heads of cattle, while the other was paid by each truly dutiable family at a rate set by the meeting. There was a rather tangible difference between aimaks in the average values of taxes per family. This indicator depended mainly on the share of tax-exempt families and the specific value of ‘unofficial’ taxes in the aimak.

Copyright of Journal of Economic Administrative & Legal Sciences is the property of Arab Journal of Sciences & Research Publishing (AJSRP) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Deciding how to allocate the seats of a deliberative assembly is one of the most fundamental problems in the political organization of societies and has been widely studied over two centuries already. The idea of proportionality is at the core of most approaches to tackle this problem, and this notion is captured by the divisor methods, such as the Jefferson/D'Hondt method. In a seminal work, Balinski and Demange extended the single-dimensional idea of divisor methods to the setting in which the seat allocation is simultaneously determined by two dimensions and proposed the socalled biproportional apportionment method. The method, currently used in several electoral systems, is, however, limited to two dimensions and the question of extending it is considered to be an important problem both theoretically and in practice. In this work we initiate the study of multidimensional proportional apportionment. We first formalize a notion of multidimensional proportionality that naturally extends that of Balinski and Demange. By means of analyzing an appropriate integer linear program we are able to prove that, in contrast to the two-dimensional case, the existence of multidimensional proportional apportionments is not guaranteed and deciding their existence is a computationally hard problem (NP-complete). Interestingly, our main result asserts that it is possible to find approximate multidimensional proportional apportionments that deviate from the marginals by a small amount. The proof arises through the lens of discrepancy theory, mainly inspired by the celebrated Beck-Fiala theorem. We finally evaluate our approach by using the data from the recent 2021 Chilean Constitutional Convention election. [ABSTRACT FROM AUTHOR]

Urban areas are increasingly recognized as a globally important source of methane to the atmosphere; however, the location of methane sources and relative contributions of source sectors are not well known. Recent atmospheric measurements in Los Angeles, California, USA, show that more than a third of the city’s methane emissions are unaccounted for in inventories and suggest that fugitive fossil emissions are the unknown source. We made on-road measurements to quantify fine-scale structure of methane and a suite of complementary trace gases across the Los Angeles Basin in June 2013. Enhanced methane levels were observed across the basin but were unevenly distributed in space. We identified 213 methane hot spots from unknown emission sources. We made direct measurements of ethane to methane (C2H6/CH4) ratios of known methane emission sources in the region, including cattle, geologic seeps, landfills, and compressed natural gas fueling stations, and used these ratios to determine the contribution of biogenic and fossil methane sources to unknown hot spots and to local urban background air. We found that 75% of hot spots were of fossil origin, 20% were biogenic, and 5% of indeterminate source. In regionally integrated air, we observed a wider range of C2H6/CH4 values than observed previously. Fossil fuel sources accounted for 58–65% of methane emissions, with the range depending on the assumed C2H6/CH4 ratio of source end-members and model structure. These surveys demonstrated the prevalence of fugitive methane emissions across the Los Angeles urban landscape and suggested that uninventoried methane sources were widely distributed and primarily of fossil origin.

Given a real number α ∈ (0 , 1) , we define the Webster sequence of density α to be W α = (⌈ (n − 1 / 2) / α ⌉) n ∈ N , where ⌈ x ⌉ is the ceiling function. It is known that if α and β are irrational with α + β = 1 , then W α and W β partition N. On the other hand, an analogous result for three-part partitions does not hold: There does not exist a partition of N into sequences W α , W β , W γ with α , β , γ irrational. In this paper, we consider the question of how close one can come to a three-part partition of N into Webster sequences with prescribed densities α , β , γ. We show that if α , β , γ are irrational with α + β + γ = 1 , there exists a partition of N into sequences of densities α , β , γ , in which one of the sequences is a Webster sequence and the other two are "almost" Webster sequences that are obtained from Webster sequences by perturbing some elements by at most 1. We also provide two efficient algorithms to construct such partitions. The first algorithm outputs the n th element of each sequence in O (1) time and the second algorithm gives the assignment of the m th positive integer to a sequence in O (1) time. We show that the results are best-possible in several respects. Moreover, we describe applications of these results to apportionment and optimal scheduling problems. [ABSTRACT FROM AUTHOR]

Modern democratic political systems are hardly conceivable without political representation. This also applies to the European Union, a unique political system with a directly elected and fully-fledged assembly representing the EU citizens, with the European Parliament being the first international parliamentary assembly to strive for democratic political representation. The case study addresses the composition of the European Parliament, or more specifically, it focuses on methods of apportioning the European Parliamentary seats among the EU Member States according to the degressive proportionality principle as codified by the Lisbon Treaty. First, the paper discusses the principle of degressive proportionality, both from a theoretical and empirical perspective, in the latter case taking into account the composition of the European Parliament since the first popular elections in 1979. Subsequently, the study discusses the most relevant proposed European Parliamentary seat apportionment methods, i.e. the Cambridge Compromise, the Power Compromise and the 0,5-DPL method, and seeks to analyse their consequences on the representation of the EU Member States in the European Parliament. The paper concludes that the Cambridge compromise is the most appropriate of the methods discussed as it best meets the requirements of the Lisbon Treaty and related documents for the composition of the European Parliament. [ABSTRACT FROM AUTHOR]

(1) Background: Is variation among the communities of a metacommunity higher than within the communities? Community ecologists and population geneticists often characterize the structure of metacommunities by partitioning variation (diversity) into the two following components using measures such as FST or GST and α- and β-diversity. The within-communities component is usually some average of (type, species, genetic) diversities within the communities, and the among-communities component is the additive or multiplicative complement of the overall diversity. Such an among-communities component lacks independent conceptual specification, a matter of long-standing dispute. Only if the two components are independently and commensurably specified can the central question of comparability be answered meaningfully. (2) Methods: A novel approach to overcoming this conceptual weakness identifies two principles of the partitioning of variation among communities (concentration and division) then relates these principles to the common notions of variation (diversity) within and among communities, distinguishes primary indicators to quantify the partitioning principles, transforms the indicators into conceptually independent measures (indices) of variation within and among communities, and by this attains their commensurability and thus comparability. The application of the methods to quantifying the effects of evolutionary mechanisms is outlined. (3) Results: Common approaches are corrected and extended. (a) Analyses of metacommunity/metapopulation structures that rely on apportionment or related indices and take its complement to be differentiation yield incomparable measures of variation within and among communities. (b) The common practice of partitioning the total diversity into additive or multiplicative components produces the inconsistent ranking of the two components. (c) Community concentration and division can result from elementary processes of adaptive differentiation and migration (gene flow) among communities, where the (commensurable) amounts of community concentration and division reflect the relative participation of these processes in metacommunity structuring and translate directly into the measures of diversity within and among communities. (d) The modelling of the contributions of the two partitioning principles to the metacommunity structure is restricted by the marginal distributions of types and community affiliation. (e) The model demonstrates the degree to which adaptational processes at the metacommunity level are mixtures of adaptational events within and among communities.

The relative uptake by plants of the two ionic nitrogen (N) forms, ammonium (NH4+) and nitrate (NO3−), has been the subject of much interest during the past 50 years, resulting in a considerable scientific literature. The general idea is that plants have choice, resulting in preference for either one mineral N form or the other. Unfortunately, there is no specific definition of preference or agreement on how it should be measured. In this review, we critically examine the alternative techniques that have been used to measure the relative uptake of NH4+ and NO3− by plants, including those based on unlabelled sources, 15N‐enriched mineral N forms and variations in the 15N natural abundance of mineral N sources. The main difficulty with using unlabelled N is the antecedent N in plant tissue prior to the imposition of treatments. Although 15N‐enrichment overcomes this obstacle, it is nevertheless difficult to separate uptake as 15NH4+, uptake as 15NO3− and uptake as 15NO3− derived from the nitrification of 15NH4+. With 15N natural abundance, isotopic fractionation during plant uptake complicates the interpretation of data. There is increasing evidence that plants exhibit flexibility or plasticity with respect to the use of mineral N forms rather than preference. Highlights: The concept of plant preference for NH4+ or NO3− forms of mineral N is examinedExperiments using 15N‐enrichment and 15N natural abundance are reviewedThe direct uptake of 15NO3− is confounded with the uptake of 15NO3− derived from nitrified 15NH4+Plants exhibit plasticity rather than preference in the acquisition of ammonium and nitrate [ABSTRACT FROM AUTHOR]

Teaching gerrymandering in our high school geometry classrooms provides students with a unique opportunity to use mathematics to describe, analyze and make sense of the world around them. Our purpose is to provide our students the opportunity to apply learned definitions and formulas of area and perimeter to a sociopolitical context. We present a unit that we designed for teaching high school students about gerrymandering and describe how teachers may implement this unit in their classrooms. In this unit, students discovered the mechanics of gerrymandering. They made calculations and observations about area, perimeter, and the ratio of area to perimeter. They considered compactness as a potential tool to indicate gerrymandering. They used proportional reasoning to measure the fairness of the partisan split for a given map. We provide supporting examples of student work and discourse and make recommendations for future iterations of this unit.

Teaching gerrymandering in our high school geometry classrooms provides students with a unique opportunity to use mathematics to describe, analyze and make sense of the world around them. Our purpose is to provide our students the opportunity to apply learned definitions and formulas of area and perimeter to a sociopolitical context. We present a unit that we designed for teaching high school students about gerrymandering and describe how teachers may implement this unit in their classrooms. In this unit, students discovered the mechanics of gerrymandering. They made calculations and observations about area, perimeter, and the ratio of area to perimeter. They considered compactness as a potential tool to indicate gerrymandering. They used proportional reasoning to measure the fairness of the partisan split for a given map. We provide supporting examples of student work and discourse and make recommendations for future iterations of this unit. [ABSTRACT FROM AUTHOR]

Identification of sediment sources within catchments is crucial for river and catchment management. A multivariate mixing model in conjunction with two sets of statistically verified composite fingerprints was employed to identify the main sediment source areas at five locations along the main channel of the Shouchang River, southeastern China. The fingerprint composite fingerprints derived from the principle component analysis (PCA) and discriminant function analysis (DFA) combination can better apportion the five types of potential sediment sources. This combination demonstrated that over 33.0% sediment at each location came from river bed, with the largest contribution of 42.9%. The contributions from construction lands ranged from 16.0 to 26.8%. Sediment contributions from forest lands ranged from 7.8 to 22.1%. A large portion of sediment came from paddy fields, varying from 8.7 to 31.4% at the five locations. The sediment from dry land was the smallest, with the largest contribution of 18.4%, and the least contribution of 4%. Similar findings were also identified using the composite fingerprints derived from KW-H and DFA combination. Land use, topography, precipitation, and human activities were responsible for the sediment source apportionments and their variations at the five sediment sampling sites. This study implies that the available sediment from road and bridge built as well as plant production should well be supervised, laws should be made to inhibit in-stream sand mining activity, and the connectivity between paddy fields and channels should be reduced. [ABSTRACT FROM AUTHOR]

Apportionment laws have both mathematical and political components framed by law. In order to conduct an appropriate analysis, it is necessary to examine how apportionment laws are negotiated, passed and turned into legally binding documents. The reason for choosing the United States of America's current apportionment legislation as the object of this study, is due to the fact that in the process of discussion and passing of said legislation we can observe a great dichotomy between mathematics and politics. While the aim of mathematics is to find the most equitable form of seat apportionment, the political justification for choosing this or another solution will be simply based on furthering political interest. Additionally, in this particular case, the legislative processes are mirrored by academic discussions on the subject matter, that influence the decision-making process. This inquiry also focuses on how constitutional techniques can interfere in the proportional representation system, thus producing an inherent bias in the applied method of apportionment, whichever this may be. These findings can be extrapolated to any modern democracy. [ABSTRACT FROM AUTHOR]

We have studied the black carbon (BC) mass concentrations, contributions from Fossil Fuels (FF), and Biomass burning (BB) to total BC mass concentrations using a 7-wavelength Aethalometer (Model, AE-31; Make, Magee Scientific, USA) at a rural continental location in the northeastern India. We have taken the continuous measurements of BC from January 2011 to December 2017 (excluding the year 2016 due to nonavailability of data). The annual mean BC concentration at 880 nm is observed maximum 12.56±5.06 µgm-3 in the year 2011 with a minimum of 7.26±2.76 µgm-3 during the year 2015." is the final sentence. BC, BCff, and BCbb mass concentrations show significant variation during morning, afternoon, evening, and night hours. The significant monthly, seasonal, and annual variabilities in the BC concentration, equivalent BC from FF and BB, are due to seasonal change in the emission sources, boundary layer dynamics, and dispersion and dilution conditions. The determination of Angstrom exponent (α) for the BC emitted during burning of different biofuels by performing a burning experiment is an important part of the present study. We have conducted a survey in and around the study location to know the different biofuels used by the people for daily household activities, and those biofuels are used in the burning experiment. As a result of biomass burning experiment to determine Angstrom exponent, we have found the α values to be ranging from 1.20 to 2.37 for flaming and a range from 1.59 to 2.33 for smoldering conditions for different biofuels. Annual mean contributions of BCff and BCbb to the total BC are found to be dominated by FF emissions during the whole study period. The percentage contribution of BCff and BCbb is found to be 56% and 44% during winter season due to increase in wood and biomass burning activities for various purposes. We have found the higher percentage contribution from BCff (85%) during monsoon season due to reduction in usage of biofuels. [ABSTRACT FROM AUTHOR]

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Systems for managing multiple taxing jurisdictions in a larger group are working to keep up with the evolution of the modern multijurisdictional taxpayer. Recent decisions from the high courts of several states have brought attention to a meaningful tension in the goals of the Multistate Tax Compact, an agreement between states. Though the federal government has ruled that no congressional approval is necessary based on the Compact Clause of the U.S. Constitution, this agreement between states has taken its place as an important accord among the vast majority of jurisdictions. Having operated as the most effective solution to the problems identified by Congress in the 1960’s Willis Report, the Compact simultaneously disavows its binding authority and relies on the reliance of States on it to meet its goal of promoting uniformity in state tax administration. With billions of dollars of much needed tax revenue at issue, this article seeks to examine the intricacies of the legal principles applied to this contract among states while understanding its role in the modern economy, both within the United States and beyond.

It is well understood thateven small differences in population can have a disproportionate impact on representation in the U.S. House of Representatives after a decennial census because of the peculiarities of rounding rules that require integer allocations. While the COVID‐19 pandemic can be held responsible for accelerating the trend toward the increased use of mail‐in balloting, and it affected the ability of the census to collect in‐person information, here we call attention to an unanticipated effect of the pandemic on the electoral process that, as far as we are aware, has never previously been identified. By rerunning the apportionment numbers for all states under the assumption that deaths from COVID‐19 prior to the start of the Census had not occurred, we show that New York's congressional delegation would not have lost a seat. New York was the only state whose House seat allocation was affected by disproportionate COVID‐19 deaths. [ABSTRACT FROM AUTHOR]

Not all urban low-voltage grids will be able to integrate new loads such as charging infrastructure for electric mobility or electrical heat pumps into existing structures without further measures. Therefore, this article analyzes to what extent load management is more cost-effective than conventional grid expansion. Methodically, the different load types are first apportioned from country to grid-level on the basis of different parameters. Subsequently, both conventional grid planning as a reference variant and innovative grid planning with different variants of load management are carried out. As a result, it can be summarized that the future success of load management is strongly dependent on its costs and whether the necessary information and communication technology is already deployed in the grids. Regardless of the costs, there is also considerable potential for savings in conventional grid expansions.