Newton’s Unfinished Business: Uncovering the Hidden Powers of Eleven in Pascal’s Triangle

Sir Isaac Newton once observed that the first five rows of Pascal’s Triangle, when concatenated, yield the corresponding powers of eleven. He claimed without proof that subsequent rows also generate powers of eleven. Was he correct? While not all rows can simply be concatenated, the powers of eleven can still be easily derived from each. We have uncovered an algorithm the supports Newton’s claim and will prove its validity for all rows of the Triangle

Newton’s Unfinished Business: Uncovering the Hidden Powers of Eleven in Pascal’s Triangle

Sir Isaac Newton once observed that the first five rows of Pascal’s Triangle, when concatenated, yield the corresponding powers of eleven. He claimed without proof that subsequent rows also generate powers of eleven. Was he correct? While not all rows can simply be concatenated, the powers of eleven can still be easily derived from each. We have uncovered an algorithm the supports Newton’s claim and will prove its validity for all rows of the Triangle

Different Drought Tolerance Strategy of Wheat Varieties in Spike Architecture

Spike characteristics include spike length, total spikelet number per spike, number of fertile flowers, spike density, spike fertility, grain number, thousand kernel weight, the number of spikes per square meter, harvest index and the grain yield during the flowering and ripening stage. The six winter and one facultative variety differed in earliness, derived in part from the allele of the Ppd-D1 gene and phenological observation. The two sites significantly differed in the soil moisture, which varied during continual microclimate monitoring. The spike architecture of winter wheat was affected by drought. The plant samples from the site FIELD 2 (more drought stressed) showed a higher reduction in spike characteristics such as a lower spike length, total spikelet number, number of fertile flowers and spike fertility, leading to a lower yield than the site FIELD 1. Both early and late varieties possess compensatory abilities to create the grain yield during drought stress; however, the timing and duration of exposure to drought determine the application and success of the compensatory ability. In our experiment, the late varieties (photoperiod sensitive) performed better in yield than the early varieties during both growing seasons. That is at odds with the generally recommended "drought escape strategy" (early varieties) and suggests a possible direction for variety selection and breeding in arid areas in Central Europe.O

Teaching personal and social responsibility after school: A systematic review

Background: Teaching Personal and Social Responsibility (TPSR) has been studied and implemented through physical activity in different backgrounds for over three decades. However, there is no systematized review in the literature concerning the after-school context. Aim: Conducting a systematic review of literature on after-school interventions based on the TPSR model. Methods: This study was driven by the following research questions: Which were the conclusions regarding the implementation of TPSR in after-school settings? Which research methodologies have been used to assess TPSR in after-school time settings? Which results related to TPSR were reported in after-school time settings? Cochrane protocol guidelines were followed. Papers were selected by two independent researchers, with Cohen’s Kappa value of 81%. Results and discussion: Twenty-seven papers were selected, thirteen of which were reported with high scores. Most interventions were conducted in the USA on community-based after-school programs, lasting more than nine sessions, and led by school staff who prepared physical activities for youngsters from disadvantaged communities. Most of the reported studies resorted to qualitative methodologies. Some gaps were detected, such as lack of systematization of methods, lack of validity and reliability. Personal and social benefits were found. Other results were grouped into leadership, staff-youngsters relationship, values, transference, and impact on staff lives. We recommend future studies in the after-school context extend to extend to other countries, with more detailed descriptions of the specific used methods

Osteointegration of soft tissue grafts within the bone tunnels in anterior cruciate ligament reconstruction can be enhanced

Anterior cruciate ligament reconstruction with a soft tissue autograft (hamstring autograft) has grown in popularity in the last 10 years. However, the issues of a relatively long healing time and an inferior histological healing result in terms of Sharpey-like fibers connection in soft tissue grafts are still unsolved. To obtain a promising outcome in the long run, prompt osteointegration of the tendon graft within the bone tunnel is essential. In recent decades, numerous methods have been reported to enhance osteointegration of soft tissue graft in the bone tunnel. In this article, we review the current literature in this research area, mainly focusing on strategies applied to the local bone tunnel environment. Biological strategies such as stem cell and gene transfer technology, as well as the local application of specific growth factors have been reported to yield exciting results. The use of biological bone substitute and physical stimulation also obtained promising results. Artificially engineered tissue has promise as a solution to the problem of donor site morbidity. Despite these encouraging results, the current available evidence is still experimental. Further clinical studies in terms of randomized control trial in the future should be conducted to extrapolate these basic science study findings into clinical practice. © 2009 Springer-Verlag.postprin

The impact of surgical delay on resectability of colorectal cancer: An international prospective cohort study

AIM: The SARS-CoV-2 pandemic has provided a unique opportunity to explore the impact of surgical delays on cancer resectability. This study aimed to compare resectability for colorectal cancer patients undergoing delayed versus non-delayed surgery. METHODS: This was an international prospective cohort study of consecutive colorectal cancer patients with a decision for curative surgery (January-April 2020). Surgical delay was defined as an operation taking place more than 4 weeks after treatment decision, in a patient who did not receive neoadjuvant therapy. A subgroup analysis explored the effects of delay in elective patients only. The impact of longer delays was explored in a sensitivity analysis. The primary outcome was complete resection, defined as curative resection with an R0 margin. RESULTS: Overall, 5453 patients from 304 hospitals in 47 countries were included, of whom 6.6% (358/5453) did not receive their planned operation. Of the 4304 operated patients without neoadjuvant therapy, 40.5% (1744/4304) were delayed beyond 4 weeks. Delayed patients were more likely to be older, men, more comorbid, have higher body mass index and have rectal cancer and early stage disease. Delayed patients had higher unadjusted rates of complete resection (93.7% vs. 91.9%, P = 0.032) and lower rates of emergency surgery (4.5% vs. 22.5%, P < 0.001). After adjustment, delay was not associated with a lower rate of complete resection (OR 1.18, 95% CI 0.90-1.55, P = 0.224), which was consistent in elective patients only (OR 0.94, 95% CI 0.69-1.27, P = 0.672). Longer delays were not associated with poorer outcomes. CONCLUSION: One in 15 colorectal cancer patients did not receive their planned operation during the first wave of COVID-19. Surgical delay did not appear to compromise resectability, raising the hypothesis that any reduction in long-term survival attributable to delays is likely to be due to micro-metastatic disease

Promoting positive youth development through a values-bassed sport program

The increase in youth programming has been a response to societal concerns over the increase in school violence and juvenile drug abuse, incarceration, and prostitution. Since many of these problems have trickled into our schools teachers are found struggling to make sense of kids who are alienated to learning and disruptive in their classroom. Costs to the taxpayer to protect against the problems caused by "troubled youth" have further fueled the fires of public discontent. Some of these costs have supported the many "quick fixes" seen in our public schools (e.g., metal detectors, resource officers, stringent law enforcement, cameras in the hallways, zero tolerance policies, background checks). In essence these approaches have viewed youth as a nagging burdento the community. Fortunately, programs that focus on the strengths of youth, rather than their weaknesses, have begun to grow. Many of these programs include sport learning experiences that teach responsible behavior and citizenship to children and youth. This article describes one such program, Project Effort, that teaches personal social responsibility to underserved youth. The genesis of the program is profiled along with a description of Project Effort's: a) sport clubs, b) mentoring program, c) teacher and parent involvement, and d)Youth Leader Corps. We also suggest some strategies that have helped us move the club members forward within each of Project Effort's programs