Core Notions Research Articles

A note on the finesse point

Introduced by Saari and Asay (2010), the “finesse point” extends the notion of core. Its definition is similar to the finagle point. Unlike the finagle point, there is a relatively simple geometrical construction of finesse point. In this note, we show that the aforementioned points do not agree. This questions the original definition of finesse point.

The Core of School Choice Problems

We propose a notion of core for school choice problems. We say that a coalition of students is able to enforce a subassignment among them if, given their priorities at schools, other students together cannot exclude any of them from her assignment. An assignment is in the core if no coalition of students can enforce any subassignment among them that Pareto improves their assignments. We show that the core is always nonempty and all assignments in it are Pareto efficient. When the student-proposing deferred acceptance mechanism is a Pareto efficient mechanism, it always produces the unique assignment in the core..

Analysis and Estimation of Interaction and Reusability Complexities of Components in Component-Based Software Engineering

Reuse is the elementary and essential attribute of the component-based software engineering. Reusability focuses on building huge and complex software through assembling pre-fabricated software constructs. In this paper, our emphasis is on to analyze and quantify the two core notions of component-based software, that is, reusability and interaction behavior of the components with the goal of minimum complexity generation. We analyse prominent works available in the literature in the area of reuse and interaction complexities. We Analyze and Estimate reusability complexities of components in Component-Based Software Engineering and we propose efficient and useful metrics to compute the reusability of components. Reusability metrics are defined for individual components as well as overall system level. Different types of components are defined on the basis of their reusability, that is, components that can be reused as it as, and tailored components. To define the metrics we have used lines-of-code as the basic parameter due to its simplicity and countability. We proposed a matrics which select the best component on the basis LOC based complexity.We compare IRMCcTotal-i matrics with SCCp metrics and SCCr metrics and analyses that negative relationship between SCCp and IRMCcTotal-i shows low portability and positive relationship between SCCr and IRMCcTotal-i shows high portability.

On the Core of Markets with Co-ownerships and Indivisibilities

Following Balbuzanov and Kotowski (2019a), we study the exchange of indivisible objects among agents with unit demand, where initially each object is either privately owned or is co-owned by multiple agents. We propose a new notion of core called the effective core for these problems to address the inadequacies of conventional notions of core. We say that a coalition effectively blocks an assignment if it weakly blocks it–as in the definition of the strong core–and the blocking is credible in the sense that no agent in the coalition free-rides on other agents in it. We show that the effective core is a nonempty subset of the weak core and a superset of the strong core, and all assignments in it are Pareto efficient. We also propose an algorithm to find assignments in it. Lastly, we make detailed comparison between the effective core and Balbuzanov and Kotowski’s exclusion core.

T‐Cores for (Δ+t)‐edge‐coloring

AbstractWe extend the edge‐coloring notion of core (subgraph induced by the vertices of maximum degree) to ‐core (subgraph induced by the vertices with ), and find a sufficient condition for ‐edge‐coloring. In particular, we show that for any , if the ‐core of has multiplicity at most , with its edges of multiplicity inducing a multiforest, then . This extends previous work of Ore, Fournier, and Berge and Fournier. A stronger version of our result (which replaces the multiforest condition with a vertex‐ordering condition) generalizes a theorem of Hoffman and Rodger about cores of ‐edge‐colorable simple graphs. In fact, our bounds hold not only for chromatic index, but for the fan number of a graph, a parameter introduced by Scheide and Stiebitz as an upper bound on chromatic index. We are able to give an exact characterization of the graphs such that whenever has as its ‐core.

Towards more reasonable prescription in private law?

The author presents original research method enabling to answer the question ‘what is the ratio (rationale, justification) of prescription?’ not from theoretical but practical standpoint, as well as the results of its application in historical-comparative study. This study demonstrates that even bearing in mind the potential differences across legal systems and historical periods, it may be argued that there is something permanent and common in prescription, that the notion of a universal core of the ratio is indeed viable. Thus the aim of this paper is to assess — taking into account findings concerning the ratio of prescription — Swiss (OR 2020) and Polish proposals of modification and recent developments in the civil-law regulation of the said institution.

Un modelo para el análisis estratégico conjunto de los activos intangibles de la marca y el conocimiento: el aporte de las ciencias cognitivas a la estrategia competitiva

En este artículo presentamos, desde una perspectiva constructivista, sistémica, cognitiva y lingüística, un modelo teórico sobre el concepto de segmento de mercado, sobre el proceso decisorio de un consumidor, sobre el posicionamiento de las marcas y sobre las ventajas competitivas. Asimismo, desde esta perspectiva constructivista, sistémica, cognitiva y lingüística y en el mismo modelo, consideramos el concepto de requerimientos competitivos clave de un sector, el diseño de la oferta y las capacidades distintivas. Por fin, presentamos el concepto de núcleo estratégico como la liga entre ventajas competitivas y capacidades distintivas como la base de la estrategia competitiva en el transcurso del tiempo y la innovación.

Plurality, normativity, and the body: Response to Sanja Bojanic and Adriana Zaharijevic

The first part of the text is a pr?cis of the monograph Phenomenology of Plurality: Hannah Arendt on Political Intersubjectivity, a phenomenological analysis of Arendt?s core notion of plurality that unites the fields of phenomenology, political theory, social ontology, and Arendt studies. In the second, larger part, the author responds to the comments given by Sanja Bojanic and Adriana Zaharijevic, in order to clarify some key concepts and positions presented in the book.

Husserl’s Sachhaltigkeit and the Question of the Essence of Individuals

Phenomenology can be roughly described as the theory of the pure essences of phenomena. Yet the meaning of essence and of concepts traditionally tied to it (such as the concepts of a priori and of essential necessity) are far from settled. This is especially true given the impact modern science has had on established philosophical views and the need for revisiting certain core notions of philosophy. In this paper I intend to review Husserl’s view on thingness-essence and his conception of the essence of individuals, based mainly in his writings from the time of Logical Investigations, Ideas, and later of Experience and Judgment. Taking account of the work of Lothar Eley in Die Krise des Apriori, among others, I will inquire into the ways in which phenomenology may undermine (one could even say fully “destroy”) the view of essences as non-factual, as well as undermine their ontological priority. Doing so may help to shape a conception of material or formal individual essences and generally of essences as concrete objects of experience in virtue of well-defined epistemic ones.

“Fractal Heuristics” for Mixed Methods Research: Applying Abbott’s “Fractal Distinctions” as a Conceptual Metaphor for Method Integration

With the interest in advancing integration in the field of mixed methods research (MMR), researchers need powerful metaphors for conceiving and implementing mixing strategies. This article contributes to the field of MMR by showing how Abbott’s “fractal distinctions” provide a valuable heuristic for the application of method combinations as well as the methodological reflection of MMR. Based on its core notion, the “self-similarity” of methods approaches, I propose three heuristic guidelines: (a) deliberately seek out qualitative aspects in quantitative methods (and vice versa); (b) assume a nonessentialist, theory-oriented approach toward method integration; and (c) aim to reconcile rigor and innovation in empirical research. I discuss similarities between fractal heuristics and other conceptualizations of difference-within, including dialectical and feminist approaches to MMR.

On the $$\gamma $$-core of asymmetric aggregative games

This paper analyzes the core of cooperative games generated by asymmetric aggregative normal-form games, i.e., games where the payoff of each player depends on his strategy and the sum of the strategies of all players. We assume that each coalition calculates its worth presuming that the outside players stand alone and select individually best strategies (Hart and Kurz Econometrica 51:1047–1064, 1983; Chander and Tulkens Int J Game Theory 26:379–401, 1997). We show that under some mild monotonicity assumptions on payoffs, the resulting cooperative game is balanced and has a non-empty core (which is the $$\gamma $$-core). Our paper thus offers an existence result for a core notion which is frequently encountered in the theory and applications of cooperative games with externalities.

Human Rights as Basic Rights: A Path to Universality?

The paper aims to support a view of human rights as essentially characterized by a basic content and in this sense focuses on the notion of basic rights. The key features associated with the notion of human rights – moral embedding and universality – should lead to regard human rights as essentially basic rights. The analysis will (i) argue for a notion of ‘basicness’ that is different from the notion occurring both within the so-called minimalist theories and the one worked out by Henry Shue; (ii) address the link between the idea of basic rights and the doctrine of the minimum core/content and (iii) criticize a deviation from the desirable path, which lies in shifting from the notion of minimum core of rights to the notion of core rights.

Linear-State Differential Games in Partition Function Form

We introduce a partition function for [Formula: see text]-player linear-state cooperative differential games. The value of a coalition within a given coalition structure is defined as its noncooperative equilibrium payoff of a game played between the coalitions. We also define two core notions, namely, the cautious and the singleton core. If the game is convex, then the cores are nonempty. In order to illustrate the approach, we consider a symmetric game of pollution accumulation.

Aristotle and Iranian Ethicists

From Aristotle to the end of the Middle Ages, friendship was considered to be a core notion in Western political philosophy. However, as Von Heyking and Avramenko argue, friendship has lost its prominent politico-philosophical status in the modern era, particularly in the Western liberal tradition. In the Muslim tradition, and specifically in the history of Iranian thought, friendship as a moral paradigm went through a different course of development. In this article, I will present a comparative view of friendship as reflected in the works of Aristotle and three major Iranian ethicists: Ab? ?Al? A?mad Miskawayh (d. 1030), Ab??l-Q?sim ?usayn al-R?ghib al-Isfah?n? (d. ca. 1108) and Na?ir al-D?n ??s? (d. 1274). I will examine friendship-related perspectives rooted in the Irano-Islamic philosophical traditions that represent a significant but overlooked dimension of Iranian cosmopolitanism valuable for modern peacemaking approaches beyond such concepts as: “justice before peace,” “liberal peace” and “cold peace.”

Do coalitions matter in designing institutions?

In this paper, we re-examine the classical questions of implementation theory under complete information in a setting where coalitions are fundamental behavioral units, and the outcomes of their interactions are predicted by applying the solution concept of the core. The planner's exercise includes designing a code of rights that specifies the collection of coalitions having the right to block one outcome by moving to another. A code of individual rights is a code of rights in which only unit coalitions may have blocking powers. We provide the necessary and sufficient conditions for implementation (under core equilibria) by codes of rights, as well as by codes of individual rights. We also show that these two modes of implementation are not equivalent. The results are robust and extend to alternative notions of core, such as an externally stable core. Therefore, coalitions are shown to bring value added to institutional design. The characterization results address the limitations that restrict the relevance of the existing implementation theory.

Consistent updating of databases with marked nulls

This paper revisits the problem of consistency maintenance when insertions or deletions are performed on a valid database containing marked nulls. This problem comes back to light in real-world linked data or RDF databases when blank nodes are associated with null values. This paper proposes solutions for the main problems one has to face when dealing with updates and constraints, namely update determinism, minimal change and leanness of an RDF graph instance. The update semantics is formally introduced and the notion of core is used to ensure a database as small as possible (i.e. the RDF graph leanness). Our algorithms allow the use of constraints such as tuple-generating dependencies, offering a way for solving many practical problems.

Matching with partners and projects

We propose a model where agents are matched in pairs in order to undertake a project. Agents have preferences over both the partner and the project they are assigned to. These preferences over partners and projects are separable and dichotomous. Each agent partitions the set of partners into friends and outsiders, and the set of projects into good and bad ones. Friendship is mutual and transitive. In addition, preferences over projects among friends are correlated (homophily). We define a suitable notion of the weak core and propose an algorithm, the minimum demand priority algorithm (MDPA) that generates an assignment in the weak core. In general, the strong core does not exist but the MDPA assignment satisfies a limited version of the strong core property when only friends can be members of the blocking coalition. The MDPA is also strategy-proof. Finally we show that our assumptions on preferences are indispensable. We show that the weak core may fail to exist if any of the assumptions of homophily, separability and dichotomous preferences are relaxed.

Blocking Coalitions and Fairness in Asset Markets and Asymmetric Information Economies

Abstract This paper analyses two properties of the core in a two-period exchange economy under uncertainty: the veto power of arbitrary sized coalitions; and coalitional fairness of core allocations. We study these properties in relation to classical (static) and sequential (dynamic) core notions and apply our results to asset markets and asymmetric information models. We develop a formal setting where consumption sets have no lower bound and impose a series of general restrictions on the first period trades of each agent. All our results are applications of the same lemma about improvements to an allocation that is either non-core or non-coalitionally fair. Roughly speaking, the lemma states that if all the members of a coalition achieve a better allocation in some way (for instance, by blocking the status quo allocation or because they envy the net trade of other coalitions) then an alternative improvement can be obtained through a perturbation of the initial improvement.

Sugar, Slavery, and Creative Destruction: World-Magnates and “Coreification” in the Longue-Durée

Recent literature in the world-systems perspective has refocused attention on questions of ‘core’ and ‘periphery’ in historical capitalism, yet rarely critically examines the underlying assumptions regarding these zones. Drawing on a developing dataset on the world’s wealthiest individuals (the World-Magnates Database), we trace the development and expansion of sugar circuits across the Atlantic world from the sixteenth through the eighteenth centuries to explain how the sugar commodity chain leads us to rethink some prevailing notions of core and periphery. Namely, we challenge the notion that these zones consist of geographical spaces that, since very early in the development of the world-economy, became permanently specialized in the production of raw materials (periphery) or more sophisticated manufactures (core); and that labor forces have been trans-historically relatively free/better-paid in core activities and coerced/poorly-paid in peripheral ones. We argue that, prior to the nineteenth century, the world-economy is not only characterized by the uneven and combined emergence of various forms of labor exploitation, as usually argued within a world-systems perspective, but also one in which core-like and peripheral activities (that is, those providing access to relatively greater or lesser wealth) were not yet as clearly bounded geographically as they would become in the nineteenth and twentieth centuries. We find that a longue-durée analysis of sugar production by enslaved labor illustrates not merely processes of peripheralization, but of what we call coreification.

The complexity of finding small separators in temporal graphs

Temporal graphs have time-stamped edges. Building on previous work, we study the problem of finding a small vertex set (the separator) whose removal destroys all temporal paths between two designated terminal vertices. Herein, we consider two models of temporal paths: those that pass through arbitrarily many edges per time step (non-strict) and those that pass through at most one edge per time step (strict). Regarding the number of time steps of a temporal graph, we show a complexity dichotomy (NP-completeness versus polynomial-time solvability) for both problem variants. Moreover, we prove both problem variants to be NP-complete even on temporal graphs whose underlying graph is planar. Finally, we introduce the notion of a temporal core (vertices whose incident edges change over time) and prove that the non-strict variant is fixed-parameter tractable when parameterized by the temporal core size, while the strict variant remains NP-complete, even for constant-size temporal cores.