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There is an alleged connection between a much researched, yet unsolved math problem, the Collatz conjecture, and a quite common, damaging meteorological phenomenon: hailstorm. The relationship would be that, in sequences generated by Collatz algorithm, the way in which numbers rise and fall resembles hailstones going up and down inside a cloud, whence the name “Hailstone sequences”. The aim of this paper is two-fold: first, to use JavaScript to research on the Collatz conjecture with the perspective of a high-school student. Our algorithm tested a generalized form of the conjecture for multiple primes (3, 5, 7) and signs (+,). The Pearson correlation coefficient found between the initial value and, respectively, the total stopping time or the maximum value reached excluded any linear correlation. The second (and main) goal was to assess the hypothesis whether hailstones could indeed follow a Collatz-like function trajectory, studying the implication on the radii of them. Introducing the concept of conversion formula, we estimated the final radii for different functions (straight line, square-root, square, logarithmic, exponential), unit of measures (from Km to mm), and starting heights ranging from 4000m to 10000m, should the motion of hailstones behave like a Collatz function. In all but one case, we did not get radii believable in size, and reasonably randomly distributed. For the linear formula (in cm), the -test values between our estimated values and Nelson’s model values are above the critical values. Hence, we should reject the initial hypothesis.

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Background: Five years of adjuvant endocrine therapy (ET) including aromatase inhibitors (AIs) and tamoxifen (TAM) is considered the standard of care in hormone receptor–positive, human epidermal growth factor–negative (HR+/HER2−) early breast cancer (eBC). Clinical practice guidelines recommend the use of an AI or TAM depending on menopausal status and clinical risk stratification. Although TAM is generally recommended and more commonly used in premenopausal women, there is mixed evidence for different clinical outcomes. Patient-level meta-analyses conducted by the Early Breast Cancer Trialists’ Collaborative Group (EBCTCG) showed significantly lower rates of BC recurrence with AIs vs TAM. However, this was not specific to patients with HR+/HER2− eBC. This trial-level meta-analysis was conducted to compare AIs ± ovarian function suppression (OFS) vs TAM ± OFS in HR+/HER2−, pre- and postmenopausal patients with eBC. Methods: A systematic literature review (SLR) was conducted using key literature databases, ie, Embase, PubMed, and MEDLINE In-Process (from database inception to March 2022) and key conferences (2019-2021). Studies selected for the SLR were those that included either ≥80% of patients with HR+/HER2− eBC in the mixed patient population or subgroup data provided specifically for patients with HR+/HER2− eBC. Of these, randomized controlled trials (RCTs) investigating AI ± OFS vs TAM ± OFS and assessing disease-free survival (DFS) were included in the trial-level meta-analysis. This meta-analysis was conducted using the generic invariance method to obtain a pooled effect estimate (hazard ratio [HR]) together with its CI for DFS. This pooled estimate was calculated as a weighted average of the intervention effects estimated in the individual trials. Both fixed- and random-effect models (FEM, REM) were used to estimate the effect size. A base-case analysis was performed including all eligible trials. Three other scenario analyses were conducted: trials investigating only nonsteroidal AIs (NSAIs), assessing only premenopausal women, and assessing only postmenopausal women. Heterogeneity across the trials was assessed using I2 statistic. Results: A total of 5 RCTs comparing AI ± OFS vs TAM ± OFS were eligible for the meta-analysis (SOFT, HOBOE, BIG 1-98, N-SAS BC 03, Li 2019; additional information on rationale for exclusion of specific trials will be reported). Two studies assessing NSAI vs TAM included postmenopausal women, while 3 studies assessing AIs + OFS vs TAM ± OFS included premenopausal women. A total of 6623 patients were followed up for 34-97.2 months across these five trials. Heterogeneity was found to be low (I2 < 40%) across all scenarios. The base-case results (including all studies) using FEM significantly favored AIs ± OFS over TAM ± OFS, with a 29% reduction in risk of recurrence or death (pooled HR, 0.71 [95%CI, 0.64-0.80]). Similar results were observed with NSAIs ± OFS vs TAM ± OFS (HR, 0.73 [95% CI, 0.64-0.83]). Among premenopausal patients, the pooled HR for AIs + OFS vs TAM ± OFS was 0.66 (95% CI, 0.54-0.79). For postmenopausal women, the HR was 0.75 (95% CI, 0.65-0.87), favoring AIs over TAM. The findings for the base-case and different scenarios remained consistent when REM was used. Conclusions: This trial-level meta-analysis suggests significantly greater benefit with AIs than with TAM for HR+/HER2− eBC. Notably, AIs in combination with OFS are associated with a 34% reduction in risk of recurrence or death vs TAM ± OFS in premenopausal women; these results are aligned with the patient-level data findings of the EBCTCG. The findings indicate that AIs ± OFS are associated with a better DFS in the HR+/HER2− population, especially premenopausal women, than TAM ± OFS. Citation Format: Wolfgang Janni, Michael Untch, Nadia Harbeck, Joseph Gilgorov, William Jacot, Stephen K. Chia, Jean-Francois Boileau, Sina Haftchenary, Rhea Gupta, Namita Mishra, Purnima Pathak, Giuseppe Curigliano. Comparing the efficacy of aromatase inhibitors vs tamoxifen in hormone receptor-positive, human epidermal growth factor receptor 2-negative early breast cancer: a systematic review and trial-level meta-analysis [abstract]. In: Proceedings of the 2022 San Antonio Breast Cancer Symposium; 2022 Dec 6-10; San Antonio, TX. Philadelphia (PA): AACR; Cancer Res 2023;83(5 Suppl):Abstract nr P1-02-01.