Bilateral associated game: Gain and loss in revaluation

Hamiache introduces associated game to revalue each coalition’s worth, in which every coalition redefines his worth based on his own ability and the possible surpluses cooperating with other players. However, as every coin has two sides, revaluation may also bring some possible losses. In this paper, bilateral associated game will be presented by taking into account the possible surpluses and losses when revaluing the worth of a coalition. Based on different bilateral associated games, associated consistency is applied to characterize the equal allocation of non-separable costs value (EANS value) and the center-of-gravity of imputation-set value (CIS value). The Jordan normal form approach is the pivotal technique to accomplish the most important proof.

Phyllodic tumors of the breast: Frequency and anatomo-histoclinical aspects at Conakry University Teaching Hospital (CHU). Guinea

Objectives: Calculate the frequency of phyllodes tumors of the breast, describe the epidemiological profile and describe the anatomo-histoclinical aspects of phyllodes tumors of the breast at the Conakry University Teaching Hospital. Methodology: This was a retrospective descriptive type study lasting 10 years, from January 1, 2008 to December 31, 2018. It concerned all cases of breast lesions, the parts that were examined in the anatomo-pathological laboratory. All cases of mammary tumours were included for the diagnosis of phyllodes tumor which was histologically confirmed. All cases of breast lesions for which the diagnosis was histologically ruled out were excluded. We carried out an exhaustive examination of the data available in the registers of the anatomo-pathologies service of the Conakry University Teaching Hospital. . The limitations or constraints of the study were the absence of certain information on the pathological examination request forms and the absence of an immunohistochemical study. Results: The frequency of phyllodes tumors was 02.72% (n = 22) among benign and malignant breast pathologies (n = 807) and 1.65% among those of genital and breast pathologies (n = 1334). The epidemiologic profile was that of a woman in the age group 50-59 (27.27%), nulliparous (45.45%). Inflammation was the main reason for consultation (100%). The main presumptive clinical diagnosis was benign tumor (54.54%). Lumpectomy was the main surgical procedure (36.36%) followed by excised biopsies (27.27%). Cases of phyllodes with a consistency firm were the most observed (50%) followed by cases with associated consistency 6 cases (27.27%). Phyllodes tumours without rearrangements represented (63.63%) followed by cases with associated rearrangements (13.63%). Grade I constituted the majority of the histological grade found (54.54%) followed by grade II (22.73%). Phyllodes tumors with benign behavior constituted the majority of cases observed 17 (77.27%). Tumors resected in a healthy zone were the most represented (72.73%). The histologic types with good prognosis constituted the majority of our diagnosed cases (77.27%). Conclusion: Phyllodes tumours constitute of a particular histological type of fibroepithelial tumours of the breast. They constitute a predominantly benign tumor, its malignant forms consist of high-grade sarcomas, often with a poor prognosis. They affect all ages, but especially women between the third and fifth decade. Their diagnosis is exclusively histological, which makes it possible to assess to their behavior, grade and histological prognosis

Maximizing the Minimal Satisfaction—Characterizations of Two Proportional Values

A class of solutions are introduced by lexicographically minimizing the complaint of coalitions for cooperative games with transferable utility. Among them, the nucleolus is an important representative. From the perspective of measuring the satisfaction of coalitions with respect to a payoff vector, we define a family of optimal satisfaction values in this paper. The proportional division value and the proportional allocation of non-separable contribution value are then obtained by lexicographically maximizing two types of satisfaction criteria, respectively, which are defined by the lower bound and the upper bound of the core from the viewpoint of optimism and pessimism respectively. Correspondingly, we characterize these two proportional values by introducing the equal minimal satisfaction property and the associated consistency property. Furthermore, we analyze the duality of these axioms and propose more approaches to characterize these two values on basis of the dual axioms.

Characterizations of Three Linear Values for TU Games by Associated Consistency: Simple Proofs Using the Jordan Normal Form

This paper studies values for cooperative games with transferable utility. Numerous such values can be characterized by axioms of [Formula: see text]-associated consistency, which require that a value is invariant under some parametrized linear transformation [Formula: see text] on the vector space of cooperative games with transferable utility. Xu et al. [(2008) Linear Algebr. Appl. 428, 1571–1586; (2009) Linear Algebr. Appl. 430, 2896–2897] Xu et al. [(2013) Linear Algebr. Appl. 439, 2205–2215], Hamiache [(2010) Int. Game Theor. Rev. 12, 175–187] and more recently Xu et al. [(2015) Linear Algebr. Appl. 471, 224–240] follow this approach by using a matrix analysis. The main drawback of these articles is the heaviness of the proofs to show that the matrix expression of the linear transformations is diagonalizable. By contrast, we provide quick proofs by relying on the Jordan normal form of the previous matrix.