Division Problems Research Articles

The Price of Connectivity in Fair Division

We study the allocation of indivisible goods that form an undirected graph and quantify the loss of fairness when we impose a constraint that each agent must receive a connected subgraph. Our focus is on well-studied fairness notions including envy-freeness and maximin share fairness. We introduce the price of connectivity to capture the largest gap between the graph-specific and the unconstrained maximin share, and derive bounds on this quantity which are tight for large classes of graphs in the case of two agents and for paths and stars in the general case. For instance, with two agents we show that for biconnected graphs it is possible to obtain at least $3/4$ of the maximin share with connected allocations, while for the remaining graphs the guarantee is at most $1/2$. In addition, we determine the optimal relaxation of envy-freeness that can be obtained with each graph for two agents, and characterize the set of trees and complete bipartite graphs that always admit an allocation satisfying envy-freeness up to one good (EF1) for three agents. Our work demonstrates several applications of graph-theoretic tools and concepts to fair division problems.

An Ensemble Clustering Approach (Consensus Clustering) for High-Dimensional Data

Due to the plurality of irrelevant attributes, sparse distribution, and complicated calculations in high-dimensional data, traditional clustering algorithms, such as K-means, do not perform well on high-dimensional data. To address the clustering problem of high-dimensional data, this paper studies an integrated clustering method for high-dimensional data. A method of subspace division based on minimum redundancy is proposed to solve the problem of subspace division of high-dimensional data; subspace division is improved by using the K-means algorithm. Additionally, this method uses mutual information between the characteristic variables of the data to replace the calculation in the K-means algorithm. The distance between the characteristic variables of the data is used to divide the data into subspaces according to the mutual information values between the characteristic variables of the data. To achieve high clustering accuracy and diversity based on clustering requirements, this paper uses a genetic algorithm as the consistency integration function. The fitness function is designed according to the clustering fusion target, and the selection operator is designed according to the maximum number of overlapping elements in the base clustering. The experimental results show that the clustering algorithm proposed in this paper outperforms other methods on most datasets and is an effective clustering integration algorithm. The proposed clustering algorithm is compared with other commonly used clustering fusion algorithms on datasets to prove the advantages of the proposed algorithm.

The Hasse principle for finite Galois modules allowing exceptional sets of positive density

We study a variant of the Hasse principle for finite Galois modules, allowing exceptional sets of positive density. For a Galois module whose underlying abelian group is isomorphic to [Formula: see text] ([Formula: see text]), we show that the product of the restriction maps for places in a set of places [Formula: see text] is injective if the Dirichlet density of [Formula: see text] is strictly larger than [Formula: see text]. We give applications to the local–global divisibility problem for elliptic curves and the Hasse principle for flexes on plane cubic curves.

Task package division method for the integrated scheduling framework of mixed model car-sequencing problem

Car mixed model production can realize that cars with different models can be produced in a same production line at the same time, which is an effective way to respond the diversified market demand timely. How to design the optimal and feasible car sequences for multi car workshops is a key point for each car manufacturing enterprise. This paper presents an integrated scheduling framework of mixed model car-sequencing problem that includes order sequencing, task package division, and integrated scheduling of mixed model workshops. In this paper, task package division problem as the middle link of the integrated scheduling framework is concerned and investigated, considering the stereo garbage inventory and subsequent scheduling factors of multi workshops. Then, a mathematic model is constructed optimizing three objectives: (1) maximize the proportion of extra inventory cars in buffer; (2) minimize the number of car type changeover and color changeover in the task package; (3) minimize the difference of car type and quantity in the task package. Furthermore, an evolutionary algorithm based on solution information is presented to solve the model. In the proposed algorithm, three strategies adopting domain knowledge and solution information generated on iteration process are utilized to improve the searching ability and efficiency of the algorithm. The validity of the algorithm is verified by a real case. The computational results reveal that the proposed model and algorithm obtain appropriate results and have the potential to be applied to other similar problems.

Effective Ship Domains Considering Ship Encounter Situations and Speeds

Abstract Ship domain is an important concept in assessing navigation situation and planning collision avoidance manoeuvres of a ship. For purpose of improving the precision and adaptability of the ship domains, effective ship domains are proposed for ships with different speeds in a variety of encounter situations in this work. Firstly, the COLREGs-based division of encounter types and corresponding collision avoidance actions are further optimized. Therefore, the problem of unclear division of responsibilities caused by the intersection of relative position and relative heading is resolved. On this basis, ship domains are determined by the encounter situations and the target ship’s speed. More specifically, the ship domain is approximated to a circle, and the dependence of the domain size on the encounter situation and the target ship’s speed has been analysed and described, that enable us to determine effective ships domains for ships varying in speeds and encounter situations. The simulation results show that ships can make effective collision-avoidance actions in different encounter scenarios based on the optimized COLREGs-based division of encounter types and effective ship domains.

Little Fermat Theorem Applying For Problems about Division

This article provides solutions to some divisibility problems using Fermat's little theorem. To have beautiful solutions for each of those problems, mathematicians have combined knowledge of: Theory of divisibility and division with remainder, greatest common divisor, least common multiple, prime numbers, congruences, exponentiation, etc. This helps students think positively and flexibly about their existing knowledge and skills, and present concise and creative solutions.

Impact of China’s environmental decentralization on carbon emissions from energy consumption: an empirical study based on the dynamic spatial econometric model

Facing the growing problem of carbon emission pollution, the scientific and reasonable division of environmental management power between governments is the premise and institutional foundation for realizing China’s carbon emission reduction target in 2030. In this article, we directly assess the degree of environmental decentralization according to the allocation of environmental managers among different levels of government. By incorporating fiscal decentralization indicators, the provincial panel data and dynamic spatial econometric model are used to empirically test the impact of environmental decentralization on carbon emissions from a spatial perspective. The results show that (1) China’s provincial carbon emissions have significant inertia dependence and spatial path dependence. The increase (decrease) of provincial carbon emissions will lead to the increase (decrease) of carbon emissions in neighboring regions. (2) At the national level, environmental decentralization, environmental administrative decentralization, and environmental monitoring decentralization significantly reduce China’s carbon emissions, while environmental supervision decentralization and fiscal decentralization significantly increase carbon emissions. Similarly, the interaction of environmental decentralization and its decomposition indicators and fiscal decentralization also significantly promotes carbon emissions, and the impact is related to the types of environmental management decentralization. (3) The carbon emission effects of environmental decentralization in different regions are heterogeneous. The inhibition effect of environmental decentralization, environmental administrative decentralization, and environmental monitoring decentralization on carbon emissions in the western region is significantly greater than that in the eastern and central regions, but the inhibitory effect of the interaction of environmental decentralization and its decomposition index and fiscal decentralization on carbon emissions in the eastern region was significantly stronger than that in the central and western regions. The above results provide theoretical support for China to construct a differentiated carbon emission environmental management system from two aspects of regional differences and environmental management power categories.

GravCPA: Controller Placement Algorithm Based on Traffic Gravitation in SDN

Software-defined network separates the control plane and the data plane, making the network more flexible. With the expansion of the network scale, one centralized controller cannot meet the latency needs of large-scale networks. Therefore, it is necessary to use multicontroller architecture, which has some problems with the controller placement. In this article, we take both the average latency and the worst latency between switch and controller into consideration and make a multi-objective optimization model. An improved label propagation algorithm based on traffic gravitation is proposed to solve the subdomain division problem, and a heuristic method is for subdomain controller placement. The simulation experiments show the effectiveness of the proposed algorithm and the time complexity guarantee for large-scale networks.

Envy-Free Solutions to the Problem of Room Assignment and Rent Division

Envy-Free Solutions to the Problem of Room Assignment and Rent Division

Math Fluency during Primary School

Math fluency is the ability to solve arithmetic facts quickly and accurately (i.e., addition and subtraction problems up to 20, and multiplication and division problems from the multiplication table). Curricula in primary school devote a significant period of time for learning and retrieval of arithmetic facts. Recently, a new computerized tool to assess math fluency—the BGU-MF (Ben-Gurion University Math Fluency) test—was developed and found to be a reliable and valid tool for adults. In the current study, we examine the performance of first to sixth-grade children in math fluency using the BGU-MF. The results present the performance of MF during childhood and emphasize that it continues to develop during primary school. Importantly, proficiency of MF differed by operations, and the automaticity of math facts was acquired in different grades. Moreover, we found that the BGU-MF is a reliable and valid tool not only for adults but also for children during primary school. Our study has educational implications for the teaching, practice, and retrieval of arithmetic facts.

Cutting a Cake for Infinitely Many Guests

Fair division with unequal shares is an intensively studied resource allocation problem. For $i\in [n] $, let $\mu_i $ be an atomless probability measure on the measurable space $(C,\mathcal{S})$ and let $t_i$ be positive numbers (entitlements) with $\sum_{i=1}^{n}t_i=1$. A fair division is a partition of $C$ into sets $S_i\in \mathcal{S} $ with $\mu_i(S_i)\geq t_i$ for every $i\in [n]$. 
 We introduce new algorithms to solve the fair division problem with irrational entitlements. They are based on the classical Last diminisher technique and we believe that they are simpler than the known methods. Then we show that a fair division always exists even for infinitely many players.

Diagnostic value and safety of thoracoscopic pleural biopsies in pleural exudative effusions of unknown origin, including follow-up

IntroductionPleural exudative effusions without diagnosis after initial work up are a frequent problem in any respiratory division. Several ways to obtain pleural biopsy exist. Thoracoscopy is one of the most...

On the division fields of an elliptic curve and an effective bound to the hypotheses of the local-global divisibility

We investigate some aspects of the [Formula: see text]-division field [Formula: see text], where [Formula: see text] is an elliptic curve defined over a field [Formula: see text] with [Formula: see text] and [Formula: see text] is a positive integer. When [Formula: see text], with [Formula: see text] a prime and [Formula: see text] a positive integer, we prove [Formula: see text], where [Formula: see text] is a generating system of [Formula: see text] and [Formula: see text] is a primitive [Formula: see text]th root of unity. If [Formula: see text] has a [Formula: see text]-rational point of order [Formula: see text], then [Formula: see text] for some [Formula: see text] and [Formula: see text]. For every number field [Formula: see text], we produce an upper bound to the logarithmic height of the discriminant of the extension [Formula: see text] for all [Formula: see text]. As a consequence, we consider a version of the local-global divisibility problem in elliptic curves over number fields, where the local conditions are known only for finitely many places.

Clustering with Nature-Inspired Algorithm Based on Territorial Behavior of Predatory Animals

Clustering constitutes a well-known problem of division of unlabelled dataset into disjoint groups of data elements. It can be tackled with standard statistical methods but also with metaheuristics, which offer more flexibility and decent performance. The paper studies the application of the clustering algorithm—inspired by the territorial behaviors of predatory animals—named the Predatory Animals Algorithm (or, in short: PAA). Besides the description of the PAA, the results of its experimental evaluation, with regards to the classic k-means algorithm, are provided. It is concluded that the application of newly-created nature-inspired technique brings very promising outcomes. The discussion of obtained results is followed by areas of possible improvements and plans for further research.

Analysis of Patterns for Inheritance Dispute Settlement in the Tradition of Sasak Community in Lombok

There are several ways conducted by Muslims in solving the problem of inheritance division in Lombok. This article aimed at looking at several patterns of inheritance dispute resolution in the Lombok people tradition (Sasak community. It is derived from qualitative field research by using both theoretical and empirical legal approaches. The data was obtained using observation, interview, and documentation techniques. Lombok people often postpone dividing the inheritance, which eventually causes problems. According to Lombok customary law, postponing inheritance is carried out due to several cultural factors, i.e.: the existence of the parent (either father or mother), the existence of the heirs, and the condition of the heirs. Apart from these factors, several consequences arise including loss of ownership rights, changes in inheritance portion, loss of inheritance rights, vulnerability to manipulation, and triggering family conflicts. The results indicate that: first, the inheritance land division is conducted in different ways such as grants, discussion, and faraid. Second, factors influencing the land dispute cases are greed and lack of information about the inheritance legal system. Third, revitalization is important because it is ruled out in Islamic teachings and is considered absolute for Islam society. This research concludes that the Islamic Inheritance legal system is the proper method to settle land disputes in the Sasak community.
 Keywords: Islamic inheritance, postponing inheritance, settlement of inheritance disputes.

Using Image Feature Extraction to Identification of Ancient Ceramics Based on Partial Differential Equation

This paper presents an in-depth study and analysis of the image feature extraction technique for ancient ceramic identification using an algorithm of partial differential equations. Image features of ancient ceramics are closely related to specific raw material selection and process technology, and complete acquisition of image features of ancient ceramics is a prerequisite for achieving image feature identification of ancient ceramics, since the quality of extracted area-grown ancient ceramic image feature extraction method is closely related to the background pixels and does not have generalizability. In this paper, we propose a deep learning-based extraction method, using Eased as a deep learning support platform, to extract and validate 5834 images of 272 types of ancient ceramics from kilns, celadon, and Yue kilns after manual labelling and training learning, and the results show that the average complete extraction rate is higher than 99%. The implementation of the deep learning method is summarized and compared with the traditional region growth extraction method, and the results show that the method is robust with the increase of the learning amount and has generalizability, which is a new method to effectively achieve the complete image feature extraction of ancient ceramics. The main content of the finite difference method is to use the ratio of the difference between the function values of two adjacent points and the distance between the two points to approximate the partial derivative of the function with respect to the variable. This idea was used to turn the problem of division into a problem of difference. Recognition of ancient ceramic image features was realized based on the extraction of the overall image features of ancient ceramics, the extraction and recognition of vessel type features, the quantitative recognition of multidimensional feature fusion ornamentation image features, and the implementation of deep learning based on inscription model recognition image feature classification recognition method; three-layer B/S architecture web application system and cross-platform system language called as the architectural support; and database services, deep learning packaging, and digital image processing. The specific implementation method is based on database service, deep learning encapsulation, digital image processing, and third-party invocation, and the service layer fusion and relearning mechanism is proposed to achieve the preliminary intelligent recognition system of ancient ceramic vessel type and ornament image features. The results of the validation test meet the expectation and verify the effectiveness of the ancient ceramic vessel type and ornament image feature recognition system.

The concept of the actual division in the English scientific text

In the present work the research of the problem of actual division of the scientific text and its role in English is carried out, the question of lexical subject and lexical predicate is considered. The paper discusses several means of expressing the actual division such as semantic highlighting of the subject, constructions with introducing “there” and “it”, using direct objects to the subject at the beginning of the sentence, semantic highlighting the adverbial modifiers in the sentence, inverting the final rheme to the beginning of the sentence, expressing the theme and the rheme in infinitive constructions, in the interrogative sentences and in the sentences lacking a finite verb. The work concludes that the most common means of expressing the actual division of the English sentence is a logical stress.

The main problems of land division by purpose into categories

The main problems of land division by purpose into categories

Dante's New Life of the Book: A Philology of World Literature by Martin Eisner

Reviewed by: Dante's New Life of the Book: A Philology of World Literature by Martin Eisner Andrea Quaini Martin Eisner, Dante's New Life of the Book: A Philology of World Literature ( Oxford: Oxford University Press, 2021), xviii + 259 pp. Martin Eisner's initial observation is that Dante's Vita nuova (1294) is an innovative and lively book whose possible readings are constantly evolving: reproduced in different formats, translated into various languages, and transposed into different media, in each of its transformations it says something new and different. In the present volume, Eisner translates this finding into an effective working method and proposes a way of reading that overturns the traditional one: instead of starting from a supposed "original," in order to see if and how other interventions have "betrayed" the Vita nuova, Eisner starts each chapter with a different incarnation of Dante's work, showing how each transformation enlightens Dante's text and themes in a new and particular way. Eisner's methodology follows the idea that the book is not "the single material object but also to the network of multiple objects that contributes to the work's survival through time" (6). The prologue is thus fundamentally important for understanding the theory behind Eisner's book, and indeed functions as a short essay of critical methodology. Referring in a continuous dialogue to the ideas of Plato, Singleton, Auerbach, Barthes, and Barolini, among others, this prologue is argued at a theoretical level that perhaps could benefit from more thorough consideration in a separate work; indeed, an elaboration of Eisner's methodology would be of great service to other scholars. In the prologue, Eisner proposes a "philology of world literature that investigates the significance of the work's material survival in the world" (3). Therefore, he does not start with what came before Dante's text, but instead begins with its afterlife: not only the readings and literary rewritings made by Boccaccio, Rossetti, and Mandelstam, but also its transformations in painting, music, postcards, and in Hollywood movies. Eisner's book is divided into three parts that each address the classic problems regarding the Vita nuova, while each chapter starts with one of the hundreds of incarnations that the text has had over the centuries. Beatrice is the metaphor image for each of the three parts: chapters addressing problems of interpretation fall under "Interpreting Beatrice"; those concerning comments under "Glossing Beatrice"; and those about time under "Remembering Beatrice." In the first part, "Interpreting Beatrice," Eisner shows the extent to which the Vita nuova innovates upon previous poetic traditions. Chapter 1 opens with an [End Page 249] image of a postcard by illustrator Ezio Anichini (1888–1948) for a Dante calendar; in the bottom part of it, there is a quote from Sermartelli's 1576 edition of the Vita nuova that censored Dante's original term gloriosa, replacing it with graziosa. In this chapter, Beatrice is presented as a Homeric character for whom Dante performs an operation that had only been carried out by the Greek poet: that of showing a human being and a god on almost the same level. Starting with the Hollywood film Hannibal (2001) and Augusto de Campos's Antropófago movement based on Oswaldo Andrade's "Cannibalist Manifesto" (1928), chapter 2 shows how Dante "not only mixes poetry with two kinds of prose; he also includes Cavalcanti's poetry" in a sort of real cannibalization of other people's poetry (51). Chapter 3 is dedicated to music: the transcription by Alfred Mercer for Dante Gabriel Rossetti's edition of the Vita nuova provides Eisner with the opportunity to investigate the musicality of the text and the relationship that the poem had with performance, especially in relation to the ballata. In the second part, "Glossing Beatrice," Eisner returns to the problem of Dante's divisions of the text and to the alternating fortune they have had over time. Chapter 4 deals with the problematic reference to Beatrice's mouth in Dante's division of Donne ch'avete in order to introduce an analysis of the value of the body and corporeality in Dante's poetry. Chapter 5 is dedicated to the visual arts. Beginning with an ultraviolet...

Problems of power division between the devices of agricultural machine-tractor units

Purpose. Determination of the rational use of various types of transmissions in the creation of multi-moving agricultural machine-tractor units. Methods. Analysis of technical characteristics of sources of mechanical energy, synthesis of power distribution system using motor-wheels. Results. Based on the analysis of literary sources, proposals were received for the choice of transmissions for multi-moving agricultural machine-tractor units. A kinematic synthesis of an electromechanical transmission for individual propellers for various purposes is proposed. Conclusions 1. The maximum transport speed of modern agricultural tractors is in the range of 40 ÷ 50 km/h, and the minimum technological speed at the maximum power of the traction vehicle (TV) can be within 4 ÷ 5 km/h when working with a soil loosener. 2. Modern agricultural TV should have a ratio of maximum speed to minimum speed up to 10. 3. The nominal range of rotation frequencies of traction electric motors available on the market is not able to overlap the ratio more than 2 ÷ 2.5. 4. The kinematic combination of the rotation frequencies of two electric motors allows you to cover the range of operating speeds of the MTA without mechanical switching of the transmission elements. 5. The proposed autonomous motor-transmission unit allows to compose MTA with the distribution of electrical power between additional engines of technological modules of MTA. Keywords: machine-tractor unit, transmission, traction concept, mover, electric wheel motor.