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Exploring Hockey Stick Theorems: Proof of Results and References
Manage episode 425998942 series 3474373
محتوای ارائه شده توسط HackerNoon. تمام محتوای پادکست شامل قسمت‌ها، گرافیک‌ها و توضیحات پادکست مستقیماً توسط HackerNoon یا شریک پلتفرم پادکست آن‌ها آپلود و ارائه می‌شوند. اگر فکر می‌کنید شخصی بدون اجازه شما از اثر دارای حق نسخه‌برداری شما استفاده می‌کند، می‌توانید روندی که در اینجا شرح داده شده است را دنبال کنید.https://fa.player.fm/legal
This story was originally published on HackerNoon at: https://hackernoon.com/exploring-hockey-stick-theorems-proof-of-results-and-references.
Investigating hockey stick theorems in Pascal's and trinomial triangles, revealing patterns akin to ball trajectories in combinatorial mathematics.
Check more stories related to science at: https://hackernoon.com/c/science. You can also check exclusive content about #math, #pascal's-triangle, #trinomial-triangle, #hockey-stick-theorem, #combinatorial-mathematics, #mathematical-theorems, #pascal's-identity, #mathematical-patterns, and more.
This story was written by: @hockeystick. Learn more about this writer by checking @hockeystick's about page, and for more stories, please visit hackernoon.com.
In the proof of both theorems, we use induction. This paper is available on arxiv(https://arxiv.org/abs/1404.5106) under CC BY 4.0 DEED license. The hockey stick theorem in the trinomial triangles has been proved. It can be translated in Pascal pyramid as follows.
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Manage episode 425998942 series 3474373
محتوای ارائه شده توسط HackerNoon. تمام محتوای پادکست شامل قسمت‌ها، گرافیک‌ها و توضیحات پادکست مستقیماً توسط HackerNoon یا شریک پلتفرم پادکست آن‌ها آپلود و ارائه می‌شوند. اگر فکر می‌کنید شخصی بدون اجازه شما از اثر دارای حق نسخه‌برداری شما استفاده می‌کند، می‌توانید روندی که در اینجا شرح داده شده است را دنبال کنید.https://fa.player.fm/legal
This story was originally published on HackerNoon at: https://hackernoon.com/exploring-hockey-stick-theorems-proof-of-results-and-references.
Investigating hockey stick theorems in Pascal's and trinomial triangles, revealing patterns akin to ball trajectories in combinatorial mathematics.
Check more stories related to science at: https://hackernoon.com/c/science. You can also check exclusive content about #math, #pascal's-triangle, #trinomial-triangle, #hockey-stick-theorem, #combinatorial-mathematics, #mathematical-theorems, #pascal's-identity, #mathematical-patterns, and more.
This story was written by: @hockeystick. Learn more about this writer by checking @hockeystick's about page, and for more stories, please visit hackernoon.com.
In the proof of both theorems, we use induction. This paper is available on arxiv(https://arxiv.org/abs/1404.5106) under CC BY 4.0 DEED license. The hockey stick theorem in the trinomial triangles has been proved. It can be translated in Pascal pyramid as follows.
135 قسمت
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Science Tech Brief By HackerNoon
This story was originally published on HackerNoon at: https://hackernoon.com/thermodynamic-limits-around-m-dwarf-stars-acknowledgements . In this study, researchers explore the feasibility and potential characteristics of photosynthetic light-harvesting on exo-planets. Check more stories related to science at: https://hackernoon.com/c/science . You can also check exclusive content about #exoplanets , #thermodynamic-limits , #oxygenic-photosynthesis , #m-dwarf-stars , #light-harvesting , #low-mass-stars , #oxygenic-cyanobacteria , #nasa-exoplanet-archive , and more. This story was written by: @photosynthesis . Learn more about this writer by checking @photosynthesis's about page, and for more stories, please visit hackernoon.com . In this study, researchers explore the feasibility and potential characteristics of photosynthetic light-harvesting on exo-planets.…
This story was originally published on HackerNoon at: https://hackernoon.com/8-common-data-security-gaps-in-health-care . Health care data security is crucial but can be challenging. Here are the most common data security gaps to address. Check more stories related to science at: https://hackernoon.com/c/science . You can also check exclusive content about #healthcare , #data-security , #cybersecurity , #health-data , #data-storage , #medical-security , #third-party-risk-management , #it , and more. This story was written by: @zacamos . Learn more about this writer by checking @zacamos's about page, and for more stories, please visit hackernoon.com . The most common gaps in health care data security are adequately securing disparate data storage systems; enabling lateral movement with interconnected systems; brushing aside the need to revisit data sources; ignoring third-party vendors' roles in data security; minimizing medical wearable and implantable threats; improperly disposing of outdated data; viewing cybersecurity and data security as separate; and merging legacy and modern storage systems.…
This story was originally published on HackerNoon at: https://hackernoon.com/visualizing-colors-the-gradient-oscillation-hyperspace . Could we create a meta-computational space, for machine learning to sort concepts, and artificial intelligence to navigate them? Check more stories related to science at: https://hackernoon.com/c/science . You can also check exclusive content about #meta-computational-space , #hyperspace , #color-space , #gradient-oscillation , #hyper-labyrinth , #intuitive-movement , #rational-jumps , #hackernoon-top-story , and more. This story was written by: @damocles . Learn more about this writer by checking @damocles's about page, and for more stories, please visit hackernoon.com . The aim of this article is to present a colored hyperspace, in which the distance is not extracted using numerical values, but by using the color’s change (or oscillation). Imagine the inside of a sphere; randomly add the seven colors of the rainbow as dots within that sphere; and then expand all of them at once and at the same rate.…
This story was originally published on HackerNoon at: https://hackernoon.com/digital-health-and-ai-research-llms-for-prompt-and-quality-sleep . Postulates for sleep from theoretical neuroscience can explain some gaps around sleep, which could be provided with LLMs, towards prompt and quality sleep. Check more stories related to science at: https://hackernoon.com/c/science . You can also check exclusive content about #sleep , #digital-health , #ai , #llms , #theoretical-neuroscience , #computational-neuroscience , #ai-research , #brain , and more. This story was written by: @step . Learn more about this writer by checking @step's about page, and for more stories, please visit hackernoon.com . Why do humans sleep? Why might consistent lack of sleep result in physiological problems? Why do some people not take sleep seriously? How can the quality of sleep be improved? How can it be easier to fall asleep? What are the gaps in current understanding of sleep that conceptual brain science may postulate?…
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Science Tech Brief By HackerNoon
This story was originally published on HackerNoon at: https://hackernoon.com/defusing-emotionally-charged-conversations-4-steps-to-success . To defuse an emotionally charged conversation, follow these four practices. Check more stories related to science at: https://hackernoon.com/c/science . You can also check exclusive content about #emotional-intelligence , #the-expression-of-the-emotions , #anger-management , #work-culture , #leadership-skills , #emotionally-fit-founder , #entrepreneurs-mistakes , #effective-leadership , and more. This story was written by: @vinitabansal . Learn more about this writer by checking @vinitabansal's about page, and for more stories, please visit hackernoon.com . Emotionally charged conversations are often spontaneous and come out of nowhere. When you’re caught off-guard and expected to navigate complex interactions in real time without knowing how to handle them, you're most likely to act in self-defeating ways. To defuse an emotionally charged conversation, follow these four practices.…
This story was originally published on HackerNoon at: https://hackernoon.com/from-$0-to-$5000month-with-telegram-channels-my-story . I have several Telegram channels, in Russian and English. I earn about $5,000 a month from them. Check more stories related to science at: https://hackernoon.com/c/science . You can also check exclusive content about #solopreneur , #telegram , #telegram-channels , #telegram-based-marketing , #how-to-make-money-off-telegram , #telegram-channel-growth , #hackernoon-top-story , #telegram-monetization , and more. This story was written by: @marieintheworld . Learn more about this writer by checking @marieintheworld's about page, and for more stories, please visit hackernoon.com . I created my first Telegram channel in 2022 while working as a data analyst. The main goal was to share useful resources and my experiences. After a few months, it became an additional source of income. I have several Telegram channels, in Russian and English. I earn about $5,000 a month from them.…
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Science Tech Brief By HackerNoon
This story was originally published on HackerNoon at: https://hackernoon.com/ai-sleep-computational-neuroscience-dreams-loneliness-and-predictive-coding . How does the human mind regulate sleep and wakefulness? How does sleep include dreams sometimes? How is loneliness different from states of mind like emptiness? Check more stories related to science at: https://hackernoon.com/c/science . You can also check exclusive content about #sleep , #computational-neuroscience , #theoretical-neuroscience , #predictive-coding , #dreams , #ai , #loneliness , #predictive-processing , and more. This story was written by: @step . Learn more about this writer by checking @step's about page, and for more stories, please visit hackernoon.com . Could dreams provide companionship to an individual experiencing loneliness? Could dreams be distressful? What are all the benefits of dreaming? Are there differences between dreaming and imagination? Why do humans sleep? What does it mean to be lonely? How is this different from isolation? How does the human mind place all these experiences?…
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Science Tech Brief By HackerNoon
This story was originally published on HackerNoon at: https://hackernoon.com/from-san-francisco-to-london-a-designers-tale-of-two-tech-hubs . A designer's journey from big tech to small startups and working from San Francisco to London. Check more stories related to science at: https://hackernoon.com/c/science . You can also check exclusive content about #design , #san-francisco , #london , #startup , #startups , #careers , #career-development , #tech-hub , and more. This story was written by: @jwilburne . Learn more about this writer by checking @jwilburne's about page, and for more stories, please visit hackernoon.com .…
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Science Tech Brief By HackerNoon
This story was originally published on HackerNoon at: https://hackernoon.com/demystifying-genius-design-a-dive-into-big-techs-design-process . The tech industry is rife with romantic tales of "genius design" - a talented team huddled in a room birthing "eureka" moments. That's not the case in reality. Check more stories related to science at: https://hackernoon.com/c/science . You can also check exclusive content about #design , #big-tech , #startups , #startup-lessons , #branding , #product-design , #business , #genius-design , and more. This story was written by: @jwilburne . Learn more about this writer by checking @jwilburne's about page, and for more stories, please visit hackernoon.com . "Genius design" is a term that is as tantalizing as it is elusive. It suggests that innovative designs spring from a momentary spark of divine inspiration or from the prodigious talent of a solitary individual. This narrative has been popularized by stories in the media, films, and books that celebrate moments of individual brilliance, often overshadowing the gritty reality of the design process.…
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Science Tech Brief By HackerNoon
1 Human Touch in Legal Transcription Remains Irreplaceable (Or At Least Until AI Can Be Held Liable) 7:32
This story was originally published on HackerNoon at: https://hackernoon.com/why-human-touch-in-legal-transcription-remains-irreplaceable-or-at-least-until-ai-can-be-held-liabl . The role of human expertise in transcription services remains a topic of debate. Check more stories related to science at: https://hackernoon.com/c/science . You can also check exclusive content about #legaltech , #ai , #ai-in-criminal-courts , and more. This story was written by: @sarahevans . Learn more about this writer by checking @sarahevans's about page, and for more stories, please visit hackernoon.com . The role of human expertise in transcription services remains a topic of debate. Ben Walker, founder and CEO of DittoTranscripts, explains why the human touch is irreplaceable. Legal transcription services often offer more competitive pricing, usually 25-50% cheaper than traditional court reporters.…
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Science Tech Brief By HackerNoon
This story was originally published on HackerNoon at: https://hackernoon.com/present-your-way-to-success-key-tips-for-landing-a-product-design-job . Every design job interview I’ve ever done or given has had one thing in common, and that’s the portfolio presentation. Check more stories related to science at: https://hackernoon.com/c/science . You can also check exclusive content about #design , #product-design , #web-design , #ux-design , #job-interview , #tech-careers , #self-improvement , #optimization , and more. This story was written by: @jwilburne . Learn more about this writer by checking @jwilburne's about page, and for more stories, please visit hackernoon.com . Designers should put more focus on their portfolio presentation instead of their website. A well-designed presentation is crucial as it reflects your abilities as a designer. Here are some tips to help you create an impactful presentation. Use a consistent visual style throughout your presentation, including font choices, colors and layout.…
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Science Tech Brief By HackerNoon
This story was originally published on HackerNoon at: https://hackernoon.com/ask-these-10-questions-to-transform-your-leadership-approach . Discover key insights and strategies for leaders to tackle complex challenges, enhance team performance, and foster a healthy work environment Check more stories related to science at: https://hackernoon.com/c/science . You can also check exclusive content about #leadership-skills , #leadership-development , #engineering-leadership , #how-to-be-a-better-leader , #entrepreneurship , #startups-advice , #advice-for-ceos , #managing-technical-people , and more. This story was written by: @vinitabansal . Learn more about this writer by checking @vinitabansal's about page, and for more stories, please visit hackernoon.com . Leaders face increasing complexity and higher expectations as they climb the hierarchy. It's crucial to focus on leadership style, organizational structure, decision-making, and team well-being. Regular self-reflection and addressing key challenges like fostering creativity, psychological safety, and managing ambiguity can significantly improve leadership effectiveness and team performance.…
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Science Tech Brief By HackerNoon
This story was originally published on HackerNoon at: https://hackernoon.com/ask-these-10-questions-to-transform-your-leadership-approach . Discover key insights and strategies for leaders to tackle complex challenges, enhance team performance, and foster a healthy work environment Check more stories related to science at: https://hackernoon.com/c/science . You can also check exclusive content about #leadership-skills , #leadership-development , #engineering-leadership , #how-to-be-a-better-leader , #entrepreneurship , #startups-advice , #advice-for-ceos , #managing-technical-people , and more. This story was written by: @vinitabansal . Learn more about this writer by checking @vinitabansal's about page, and for more stories, please visit hackernoon.com . Leaders face increasing complexity and higher expectations as they climb the hierarchy. It's crucial to focus on leadership style, organizational structure, decision-making, and team well-being. Regular self-reflection and addressing key challenges like fostering creativity, psychological safety, and managing ambiguity can significantly improve leadership effectiveness and team performance.…
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Science Tech Brief By HackerNoon
This story was originally published on HackerNoon at: https://hackernoon.com/exploring-hockey-stick-theorems-abstract-introduction-and-description-of-results . Investigating hockey stick theorems in Pascal's and trinomial triangles, revealing patterns akin to ball trajectories in combinatorial mathematics. Check more stories related to science at: https://hackernoon.com/c/science . You can also check exclusive content about #math , #pascal's-triangle , #trinomial-triangle , #hockey-stick-theorem , #combinatorial-mathematics , #mathematical-theorems , #pascal's-identity , #mathematical-patterns , and more. This story was written by: @hockeystick . Learn more about this writer by checking @hockeystick's about page, and for more stories, please visit hackernoon.com . This paper is available on arxiv(https://arxiv.org/abs/1404.5106) under CC BY 4.0 DEED license. The big hockey stick theorem is a special case of a general theorem which our goal is to introduce it. We state a hockey Stick theorem in the trinomial triangle too.…
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Science Tech Brief By HackerNoon
This story was originally published on HackerNoon at: https://hackernoon.com/exploring-hockey-stick-theorems-proof-of-results-and-references . Investigating hockey stick theorems in Pascal's and trinomial triangles, revealing patterns akin to ball trajectories in combinatorial mathematics. Check more stories related to science at: https://hackernoon.com/c/science . You can also check exclusive content about #math , #pascal's-triangle , #trinomial-triangle , #hockey-stick-theorem , #combinatorial-mathematics , #mathematical-theorems , #pascal's-identity , #mathematical-patterns , and more. This story was written by: @hockeystick . Learn more about this writer by checking @hockeystick's about page, and for more stories, please visit hackernoon.com . In the proof of both theorems, we use induction. This paper is available on arxiv(https://arxiv.org/abs/1404.5106) under CC BY 4.0 DEED license. The hockey stick theorem in the trinomial triangles has been proved. It can be translated in Pascal pyramid as follows.…
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