Division Rules Research Articles

Book Reviews

Alexander Nesterov of Higher School of Economics reviews “How to Divide When There Isn't Enough: From Aristotle, the Talmud, and Maimonides to the Axiomatics of Resource Allocation,” by William Thomson. The Econlit abstract of this book begins: “Explores the resolution of claims problems using division rules, focusing on an axiomatic approach.”

A greyness reduction framework for prediction of grey heterogeneous data

Existing operational rules of interval grey numbers do not make full use of possible background information when determining the interval boundaries, and this may result in inconsistent results if applying different logical operations. This paper finds that multiplication and division rules of interval grey numbers do not meet the calculation rule of inverse operators. Direct solution and inverse solution of the same interval grey number object may differ not only in numerical ranges but also in greyness degrees. To improve the accuracy of grey number calculation, new operational rules for multiplication and division of interval grey numbers are proposed. Then the traditional prediction modelling method of grey heterogeneous data is refined and expanded by integrating a greyness reduction preprocessing, which is based on the proposed calculation rules. Application of the expanded heterogeneous interval grey number prediction model to a stock replenishment scheduling problem in emergency rescue scenarios is included to illustrate the new operational rules of grey numbers and their application in prediction algorithm, and the proposed approach is compared with other existing methods to demonstrate its effectiveness.

(Post-)deuteronomistyczny zakaz transwestytyzmu (Pwt 22,5)? Pytanie o jego właściwy sens i motywację

Deut 22:5 is the only prohibition of transvestitism in the Bible and itscultural environment. The context in which it appears suggests that it wasinserted secondarily, in the period after the Babylonian Exile. This viewnarrows down various speculations concerning the original Sitz im Leben ofthis precept, and it leads one to understand it primarily within the frameworkof the canonical shape of the whole Pentateuch. Accordingly, this regulationmainly refers to the rule of the bisexual division of human nature (Gen 1–2),the rule of preserving the order of creation (not mixing species; Lev 19:19;Deut 22:9-11), as well as the preservation of the procreative force, heremainly related to masculinity (Gen 5:1-3; cf. 1:28; 9:1.7).

Interacting Subsystems and Their Molecular Ensembles

The molecular density-partition problem is reexamined and the information-theoretic (IT) justification of the stockholder division rule is summarized. The ensemble representations of the promolecular and molecular mixed states of constituent atoms are identified and the electron probabilities in the isoelectronic stockholder atoms-in-molecules (AIM) are used to define the molecular-orbital ensembles for the bonded Hirshfeld atoms. In the pure quantum state of the whole molecular system its interacting (entangled) fragments are described by the subsystem density operators, with the subsystem physical properties being generated by the partial traces involving the fragment density matrices.

Price of Fairness in Budget Division and Probabilistic Social Choice

A group of agents needs to divide a divisible common resource (such as a monetary budget) among several uses or projects. We assume that agents have approval preferences over projects, and their utility is the fraction of the budget spent on approved projects. If we maximize utilitarian social welfare, the entire budget will be spent on a single popular project, even if a substantial fraction of the agents disapprove it. This violates the individual fair share axiom (IFS) which requires that for each agent, at least 1/n of the budget is spent on approved projects. We study the price of imposing such fairness axioms on utilitarian social welfare. We show that no division rule satisfying IFS can guarantee to achieve more than an O(1/√m) fraction of maximum utilitarian welfare, in the worst case. However, imposing stronger group fairness conditions (such as the core) does not come with an increased price, since both the conditional utilitarian rule and the Nash rule match this bound and guarantee an Ώ(1/√m) fraction. The same guarantee is attained by the rule under which the spending on a project is proportional to its approval score. We also study a family of rules interpolating between the utilitarian and the Nash rule, quantifying a trade-off between welfare and group fairness. An experimental analysis by sampling using several probabilistic models shows that the conditional utilitarian rule achieves very high welfare on average.

Simulations of sea urchin early development delineate the role of oriented cell division in the morula-to-blastula transition

The sea urchin morula to blastula transition has long been thought to require oriented cell divisions and blastomere adherence to the enveloping hyaline layer. In a computer simulation model, cell divisions constrained by a surface plane division rule are adequate to effect morphological transition. The hyaline membrane acts as an enhancer but is not essential. The model is consistent with the orientation of micromere divisions and the open blastulae of direct developing species. The surface plane division rule precedes overt epithelization of surface cells and acts to organize the developing epithelium. It is a universal feature of early metazoan development and simulations of non-echinoid cleavage patterns support its role throughout Metazoa. The surface plane division rule requires only local cues and cells need not reference global positional information or embryonic axes.

A novel energy-aware bio-inspired clustering scheme for IoT communication

Nowadays, the internet of thing (IoT) is a novel paradigm that is rapidly gaining ground in the scenario of modern wireless telecommunications. Wireless sensor network (WSN) is an important part of IoT, and it is mainly responsible for acquiring and reporting data. As lifetime and coverage area of WSN directly determine IoT performance, how to design a method to conserve nodes energy and reduce nodes death rates become important issues. Sensor network clustering is one efficient method to solve these problems. It divides nodes into clusters and selects one to be cluster head (CH). The data transmission and communication within one cluster are managed by its CH. Many traditional strategies have been designed out, but because of network dynamic feature, machine learning methods become more attractive and many literature are working on them. Particle swarm optimization (PSO) is one evolutionary algorithm. Inspired by this algorithm, we propose a novel energy-aware bio-inspired clustering scheme (PSO-WZ). We firstly initialize CHs combination randomly and assign non-CHs based on division rules. Then, using the fitness function to guide the selection process until the maximum time is reached. Since the division rule is directly related with the network topology and node energy consumption distribution, we design it from two angles: non-CHs and the whole network, to save the energy of each node as much as possible. Meanwhile, in order to balance energy load among nodes, which contributes to lowering nodes reduction and preserving network coverage range, we introduce the Gini coefficient into the objective function. From the results obtained, we conclude that the proposed algorithm is able to keep more nodes alive over time, prolong the network life cycle, and improve the overall performance of IoT further.

Salaries and the logic of national income distribution in a market economy – described using a simple model

The level of prosperity available is the value of what is produced in the economy. This is a general truth, while the level of well-being of community members is a consequence of the value added and the rules and mechanisms of national income distribution. The purpose of the paper is to show the macroeconomic principles of the division of the generated GDP value, based on the example of a simple model of the economy in a classic style: the economy is presented as the Great Bakery, which produces loaves of bread shared between employees and its owner, the Baker. The author uses this model to demonstrate the consequences of the division of the generated surplus, which is the Baker’s profit from three sources: development-oriented investments and the savings associated with them, the public sector and exportation. The author shows the structural consequences of reducing wages and shifting the tax burdens to the employees. He proves that the reduction of labor costs should be accompanied by an increase in the tax burdens imposed on companies – the Baker in his model. These rules of division have macroeconomic consequences and the author shows the effects for Poland’s position in a group of countries, presented as international comparisons (mainly OECD countries). The author shows that one of the key factors determining prosperity is the place of industry in the product development cycles produced by the global division of production. The amount of added value obtained at various stages of these production cycles is illustrated by the so-called smile curve. The author shows the international division of labor has led to the location of the industries of post-communist countries, including Poland, around the minimum of this curve. This causes the average level of wages and, consequently, welfare to be low. The analysis leads to the conclusion that a policy of structural changes is needed, one that will shape this division so that the country regains full production cycles and thus strengthens its economy. The author discusses the simplified thesis formulated by Jeffrey Sachs that sustainable development is the most important for prosperity. The author justifies the thesis that it is not so much development as the amount of added value generated by industry and the mechanisms of its distribution, and points out that, as Justin Yifu Lin observes, it is the structural changes which will lead to an increase in added value and modifications in the principles of its distribution, so as to increase social well-being.

Zbieg prawa do świadczeń opiekuńczych i świadczeń z ubezpieczenia społecznego — uwagi de lege ferenda

CONCURRENCE OF THE RIGHTS TO CARE BENEFITSAND SOCIAL SECURITY BENEFITS —DE LEGE FERENDA COMMENTSThe text deals with the issue of the concurrence of care benefits and social security benefits regulated in the Act on Family Benefits. Such a situation occurs when a person who already has the right to a social insurance benefit, e.g. a retirement pension, acquires the right to one of the care benefits, e.g. an attendance benefit. The regulations included in the Act on Family Benefits are discussed against the background of the general principles according to which a particular type of risk can be protected with only one benefit and social insurance benefits take precedence over care benefits. According to the author’s opinion, the solutions adopted by the legislator are unadjusted to the current situation and are increasingly provoking controversy in practice and, consequently, in the author’s opinion, require changes. The lack of action on the part of the legislator causes courts to play its role, which should not occur in a properly functioning legal system based on the rule of the tripartite division of power.

General Method of Building a Real-Time Optimization Policy for Dynamic Vehicle Routing Problem

Abstract Currently, most of the policies for the dynamic demand vehicle routing problem are based on the traditional method for static problems as there is no general method for constructing a real-time optimization policy for the case of dynamic demand. Here, a new approach based on a combination of the rules from the static sub-problem to building real-time optimization policy is proposed. Real-time optimization policy is dividing the dynamic problem into a series of static sub-problems along the time axis and then solving the static ones. The static sub-problems’ transformation and solution rules include: Division rule, batch rule, objective rule, action rule and algorithm rule, and so on. Different combinations of these rules may constitute a variety of real-time optimization policy. According to this general method, two new policies called flexible G/G/m and flexible D/G/m were developed. The competitive analysis and the simulation results of these two policies proved that both are improvements upon the best existing policy.

A Two-Step Proportional Rule for Division with Multiple References

Proportionality is a primary principle generally accepted when dividing a commodity between a set of agents characterized by their reference with respect to a certain characteristic. However, when multiple characteristics have to be taken into account, it is not clear how to define proportionality. We propose a two-step proportional rule for the class of division problems with multiple characteristics. The rule is based on the best expectations of the agents and incorporates the extensions of two crucial properties which are inherent to proportionality: the proportions obtained with respect to the different references cannot be improved simultaneously, and the result does not depend on the scale in which each of the characteristics is measured. We also prove that the two-step proportional rule can be understood as the result of a negotiation in which the Kalai–Smorodinsky solution is applied to a bargaining game between parties each one aiming to maximize the proportions that the set of agents attain with respect to the references of the corresponding characteristic.

New extended grillage methods for the practical and precise modeling of concrete box-girder bridges

The Hambly plane grillage method has been regarded as one of the classic numerical methods in the design field for modeling wide box-girder bridge structures. However, when it comes to the in-depth design applications, its strict division rules and insufficient mechanical explanations often make engineers inconvenient or puzzled at bridge modeling. This article investigates whether this method may be extended to become more adaptable for the design of current concrete box-girder bridge structures in consideration of both convenience and precision. To this end, the defects of Hambly plane grillage method are recognized, and new extended grillage methods, including the single-layer folding surface grillage and spatial grillage, are proposed respectively, to deal with different bridge design objects completely in a beam-oriented environment. The former allows freer cross-sectional division by breaking the basic rule of Hambly plane grillage method to include longitudinal separate-type beam components for a better exhibition of shear lag effects. The latter emphasizes a complete consideration of spatial behavior, including the easily missed in-plane effects of the top and bottom plates. The effectiveness of the methods are demonstrated by comparison case studies in some benchmark models and by a discussion of their applications.

The Constitution – Chosen Premises Justifying the Need to Introduce Amendments

Abstract Indication of conditions constituting necessity of modifications within the scope of the Constitution shall be considered while perceiving the leading role of the Constitution in Polish legal order. Constitutional regulations determine standards for the entire legal system of the Republic of Poland. It is also worth a while to consider the need for unambiguous determination of relations of constitutional norms, also with regard to the law of the European Union. Doubts appearing within the scope of systemic rules concern mainly regulations specifying the rule of division and balancing of powers. Actually, they consist in lacks with regard to organization of bodies of each of three powers. Another issue is improvement of solutions determining coexistence of government and local government administration within the broader scope of principles of uniformity of the state and decentralization of public power. The article presents an analysis related to the aforementioned issues.

A new method to simulate restricted variants of polarizationless P systems with active membranes

According to the P conjecture by Gh. Păun, polarizationless P systems with active membranes cannot solve {mathbf {NP}}-complete problems in polynomial time. The conjecture is proved only in special cases yet. In this paper we consider the case where only elementary membrane division and dissolution rules are used and the initial membrane structure consists of one elementary membrane besides the skin membrane. We give a new approach based on the concept of object division polynomials introduced in this paper to simulate certain computations of these P systems. Moreover, we show how to compute efficiently the result of these computations using these polynomials.

Optimization of unmanned ship's parametric subdivision based on improved multi-objective PSO

The optimization of ship's subdivision arrangement is an important part of ship general layout design. However, optimization to an unmanned ship's subdivision considering the complex multi-objective is less studied. In this paper, the multi-objective optimization of a V-type non-ballasted water unmanned ship compartment division is investigated based on parametric model. The principal rules of cabin division for unmanned ship are determined first. The shape and composition of the longitudinal inner shell layout and transverse inner shell structure are studied by three-dimensional parametric representation method. The cabin capacity, bending moment and water immersion factor are used as the objective functions to establish the mathematical model. The improved multi-objective particle swarm optimization (PSO) algorithm are used to optimize the unmanned ship's subdivision arrangement in which the generated front-end solutions are normalized and sorted by the distance from the origin to solved the multiple objectives. The grey relational degree calculation method is applied to verify the method. Finally, different subdivision scheme based on different objective is given. The findings provide useful guidelines for the design optimization of non-ballast water unmanned ships.

SEMANTIZATION IN THE GOVERNMENT STANDARDS OF UKRAINE (BASED ON FOOD INDUSTRY TERMS MATERIAL)

The purpose of the article is to analyse peculiarities of semantization of Ukrainian terminology in the government standards of Ukraine. Definitions of the terms of the Food Industry in the government standards of Ukraine were defined as an object of this paper. Our study is based on categorical approach, according to which in definitions that reveal semantic of term, we searched for patterns, determined by some term category. Research material are definitions of terms of the Food Industry that belong to the same notion category / theme group / subgroup. Usage of methods of logical-notional, lexical-semantic and component analysis gives the opportunity to define non-system notions, connected to inaccurate phrasing of terms definitions in regulatory technical documentation. As the result of performed analysis typical errors in the definitions of the terms of this scientific and manufacturing areas were defined. First of all it is logical mistakes, that appear mainly as a result of breaking the rule of notions division (correlative division, the unity principle of division, continuity of division). In question is still the necessity of further execution of works in field of removal of unwanted synonymity of naming of terms of Food Industry, that left its mark in terminological area of practice. The article concludes that in order to normalize the national-linguistic forms of expression of terminological units and unification of their logical-notional substance it is necessary to remove the above mentioned problems. Practical significance of the results of the research is that its results can be used in the training courses «Fundamentals of Terminology», «Lexicology», «Lexicography» as well as in compiling government and industry standards of Ukraine.

Cell-like P systems with polarizations and minimal rules

P systems with active membranes are a class of computation models in the area of membrane computing, which are inspired from the mechanism by which chemicals interact and cross cell membranes. In this work, we consider a normal form of P systems with active membranes, called cell-like P systems with polarizations and minimal rules, where rules are minimal in the sense that an object evolves to exactly one object with the application of an evolution rule or a communication rule, or an object evolves to two objects that are assigned to the two new generated membranes by applying a division rule. The present work investigates the computational power of P systems with polarizations and minimal rules. Specifically, results about Turing universality and non-universality are obtained with the combination of the number of membranes, the number of polarizations, and the types of rules. We also show that polarizationless P systems with minimal rules are equivalent to Turing machines working in a polynomial space, that is, the class of problems that can be solved in polynomial time by polarizationless P systems with minimal rules is equal to the class PSPACE.

A aplicação do princípio da solidariedade na judicialização da saúde a partir dos princípios do SUS, da fixação de entendimento pelo STF e da trajetória do Rio Grande do Sul

Objetivo: analisar o fenômeno da judicialização da saúde e a temática da solidariedade entre os entes federados a partir dos princípios da integralidade e da universalidade que orientam o Sistema Único de Saúde (SUS), bem como do recente posicionamento do Superior Tribunal Federal (STF) a partir da trajetória da judicialização no Estado do Rio Grande do Sul. Métodos: realizou-se levantamento bibliográfico e análise de dados coletados junto ao Sistema de Administração de Medicamentos da Secretaria de Saúde do Estado do Rio Grande do Sul. Resultados: a reiterada adoção da tese de solidariedade entre os entes pelos tribunais nas ações de saúde acaba por vulnerar o SUS, na medida em que não observa os princípios de organização e financiamento da política pública de saúde. Conclusão: a despeito do novo posicionamento do STF significar um avanço, no sentido de que a obrigação é solidária entre os entes, mas compete à autoridade judicial direcionar o cumprimento conforme as regras de repartição de competências, bem como o ressarcimento a quem suportou o ônus financeiro, muitas dúvidas de ordem processual ainda se impõe, sendo que a observância dos princípios de organização e financiamento do SUS são fundamentais para que se possa garantir a existência de um Sistema universal.

Fair Division in the Internet Age

Fair division, a key concern in the design of many social institutions, has for 70 years been the subject of interdisciplinary research at the interface of mathematics, economics, and game theory. Motivated by the proliferation of moneyless transactions on the internet, the computer science community has recently taken a deep interest in fairness principles and practical division rules. The resulting literature brings a fresh concern for computational simplicity (scalable rules) and realistic implementation. In this review of the most salient fair division results of the past 30 years, I concentrate on division rules with the best potential for practical implementation. The critical design parameter is the message space that the agents must use to report their individual preferences. A simple preference domain is key both to realistic implementation and to the existence of division rules with strong normative and incentive properties. I discuss successively the one-dimensional single-peaked domain, Leontief utilities, ordinal ranking, dichotomous preferences, and additive utilities. Some of the theoretical results in the latter domain are already implemented in the user-friendly SPLIDDIT platform ( http://spliddit.org ).

A bottom-up approach for delineating urban areas minimizing the connection cost of built clusters: Comparison with top-down-based densely inhabited districts

The main purpose of my research is to propose a consistent and bottom-up-based approach for delineating present and future urban areas on the foundation of investigating the relationship between delineating urban areas and the connection cost of built clusters. In my approach, optimal urban built clusters are defined as the delineation of urban areas by grouping buildings that satisfy the following rules based on the head/tail division rule: (1) the nearest neighbour distance from a building centroid is shorter than the criterion that can minimize the average total cost to provide public infrastructure (road networks); and (2) the size of grouped buildings (called an urban built cluster) is equal to or more than the mean of urban built cluster sizes. In the literature, the difference between optimal urban built clusters and densely inhabited districts (DIDs), a top-down-based approach, has not been analysed in detail. In replacing a top-down approach (DIDs) with a bottom-up one (e.g., the method proposed in this article), this difference needs to be evaluated. Therefore, the difference between DIDs and optimal urban built clusters was investigated. For the empirical study, I have selected Chiba prefecture, in the east of the Tokyo metropolitan region. Results show that (1) the overlapping relations of urban built clusters and DIDs can be distinguished based on their hierarchical levels; and (2) 55% of DIDs are optimal urban built clusters. However, the size of optimal urban built clusters that are not intersected by DIDs is the same as that of those intersected by DIDs. This poses to urban planners the important question of how to deal with two types of zones: zones overlapping not DIDs but optimal urban built clusters, and zones overlapping not optimal urban built clusters but DIDs.