A new construction of the associahedron was recently given by Arkani-Hamed, Bai, He, and Yan in connection with the physics of scattering amplitudes. We show that their construction (suitably understood) can be applied to construct generalized associahedra of any simply-laced Dynkin type. Unexpectedly, we also show that this same construction produces Newton polytopes for all the F -polynomials of the corresponding cluster algebras.

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Background: In recent years, GATA-binding protein 3 (GATA3) has been indicated as a marker showing good prognosis in breast cancer. In luminal breast cancer, which has good a prognosis, it shows more significant elevation in small-sized and low-grade tumors. In contrast, Ki-67 is defined as a poor prognostic factor. The aim of this study was to emphasise the prognostic importance of GATA3 and the inverse relationship with Ki-67. Materials and Methods: In our study, 90 patients with invasive ductal breast cancer were immunohistochemically evaluated for Ki-67 and GATA3 expression. The relationship between GATA3 and Ki-67 expression was examined. In addition, the relationship between these two factors with estrogen, progesterone, human epidermal growth factor 2 receptor antibodies and other prognostic parameters such as disease-free survival and local recurrence was investigated. We accepted the level of ≥5% nüclear reaction as positive for GATA 3. A Ki-67 cut-off value of 20% was accepted as positive. Results: In GATA3 positive breast cancers, good prognostic parameters were seen including high estrogen receptor (ER) positivity, progesterone receptor (PR) positivity, small tumor size and low histological grade as well as low Ki-67 expression. In breast cancers showing high ER, PR, and GATA3 positivity

BACKGROUND: Appendix neoplasms are rare tumors of the gastrointestinal system. Appendiceal adenocarcinoma, appendiceal mucinous neoplasm, and neuroendocrine tumors (NETs) are the most encountered appendix-related neoplasms. The patients are usually got diagnosed after histopathological examination. This study aimed to explore the epidemiology, pathological subtypes, and treatment modalities of appendix neoplasms. METHODS:A retrospective examination was made with 2821 patients who underwent appendectomy between April 2010 and August 2020. Demographic, clinical, radiological, surgical findings, and histopathological results were collected from the patient files. RESULTS:Appendix neoplasms were detected in 1.06% of the patients included in the study. The mean age was 44.6±17.5 (17-83) years. Eight NETs, seven adenocarcinomas, fourteen mucinous neoplasms, and one neuroma were diagnosed with patients.CONCLUSION: Appendiceal neoplasms are generally asymptomatic and often diagnosed with postoperative histopathological examination. If the result is adenocarcinoma, right hemicolectomy recommends. Treatment of NETs depends on factors such as tumor size, location, mesoappendix invasion, and lymph node involvement. In the presence of mucinous neoplasm, surgical intervention is determined according to the pathological subtype and involvement of mesoappendix. The need for additional surgical intervention or medical treatment for patients with tumor, histopathological results must be followed carefully after appendectomy.