* . *
  • About
  • Advertise
  • Privacy & Policy
  • Contact
Tuesday, September 23, 2025
Earth-News
  • Home
  • Business
  • Entertainment
    Caesars Entertainment (CZR): Assessing Valuation After Times Square Casino Setback and Mounting Investor Concerns – simplywall.st

    Caesars Entertainment Faces Times Square Casino Hurdles as Investor Concerns Mount

    Why Hilaria Baldwin Has Found the ‘DWTS’ Process ‘Embarrassing’ At Times – WFXG

    Hilaria Baldwin Opens Up About the Embarrassing Moments on Her ‘DWTS’ Journey

    Harvest Fest 2025 – yadkinripple.com

    Celebrate the Bounty: Harvest Fest 2025 is Coming!

    Fox News Entertainment Newsletter: Kate Middleton stuns during Trump state visit, Brett James dead at 57 – Fox News

    Kate Middleton Stuns During Trump State Visit; Remembering Brett James at 57

    Lara Beitz to headline Oshkosh show with top comedians at Time Community Theater Sept. 27 – Yahoo

    Lara Beitz to Headline Star-Studded Oshkosh Comedy Night on September 27

    Shakespeare (with a twist) in Grand Junction – Yahoo

    Experience Shakespeare Like Never Before in Grand Junction

  • General
  • Health
  • News

    Cracking the Code: Why China’s Economic Challenges Aren’t Shaking Markets, Unlike America’s” – Bloomberg

    Trump’s Narrow Window to Spread the Truth About Harris

    Trump’s Narrow Window to Spread the Truth About Harris

    Israel-Gaza war live updates: Hamas leader Ismail Haniyeh assassinated in Iran, group says

    Israel-Gaza war live updates: Hamas leader Ismail Haniyeh assassinated in Iran, group says

    PAP Boss to Niger Delta Youths, Stay Away from the Protest

    PAP Boss to Niger Delta Youths, Stay Away from the Protest

    Court Restricts Protests In Lagos To Freedom, Peace Park

    Court Restricts Protests In Lagos To Freedom, Peace Park

    Fans React to Jazz Jennings’ Inspiring Weight Loss Journey

    Fans React to Jazz Jennings’ Inspiring Weight Loss Journey

    Trending Tags

    • Trump Inauguration
    • United Stated
    • White House
    • Market Stories
    • Election Results
  • Science
  • Sports
  • Technology
    Agentic AI and the future of work: navigating technological promise and the risk of increased automation – Equal Times

    Agentic AI and the Future of Work: Embracing Innovation While Navigating Automation Challenges

    Technology alliance introduces system for stable recycling quality – RECYCLING magazine

    Innovative Technology Alliance Unveils Breakthrough System for Consistent Recycling Quality

    Pepper Pike council considers upgrading technology for streaming meetings, remote meeting participation – Cleveland.com

    Pepper Pike Council Explores Upgrading Technology for Enhanced Streaming and Remote Participation

    How Michelin Uses Technology to Rethink Tire Manufacturing: Interview – Motor1.com

    How Michelin’s Tech-Driven Revolution Is Transforming Tire Manufacturing

    Analysts Offer Insights on Technology Companies: Avnet (AVT), Nvidia (NVDA) and Atlassian (TEAM) – The Globe and Mail

    Experts Share Key Insights on Avnet, Nvidia, and Atlassian’s Future Prospects

    Top Technology Executives Recognized at the 2025 Carolina CIO ORBIE Awards – Yahoo Finance

    Celebrating Excellence: Top Technology Executives Honored at the 2025 Carolina CIO ORBIE Awards

    Trending Tags

    • Nintendo Switch
    • CES 2017
    • Playstation 4 Pro
    • Mark Zuckerberg
No Result
View All Result
  • Home
  • Business
  • Entertainment
    Caesars Entertainment (CZR): Assessing Valuation After Times Square Casino Setback and Mounting Investor Concerns – simplywall.st

    Caesars Entertainment Faces Times Square Casino Hurdles as Investor Concerns Mount

    Why Hilaria Baldwin Has Found the ‘DWTS’ Process ‘Embarrassing’ At Times – WFXG

    Hilaria Baldwin Opens Up About the Embarrassing Moments on Her ‘DWTS’ Journey

    Harvest Fest 2025 – yadkinripple.com

    Celebrate the Bounty: Harvest Fest 2025 is Coming!

    Fox News Entertainment Newsletter: Kate Middleton stuns during Trump state visit, Brett James dead at 57 – Fox News

    Kate Middleton Stuns During Trump State Visit; Remembering Brett James at 57

    Lara Beitz to headline Oshkosh show with top comedians at Time Community Theater Sept. 27 – Yahoo

    Lara Beitz to Headline Star-Studded Oshkosh Comedy Night on September 27

    Shakespeare (with a twist) in Grand Junction – Yahoo

    Experience Shakespeare Like Never Before in Grand Junction

  • General
  • Health
  • News

    Cracking the Code: Why China’s Economic Challenges Aren’t Shaking Markets, Unlike America’s” – Bloomberg

    Trump’s Narrow Window to Spread the Truth About Harris

    Trump’s Narrow Window to Spread the Truth About Harris

    Israel-Gaza war live updates: Hamas leader Ismail Haniyeh assassinated in Iran, group says

    Israel-Gaza war live updates: Hamas leader Ismail Haniyeh assassinated in Iran, group says

    PAP Boss to Niger Delta Youths, Stay Away from the Protest

    PAP Boss to Niger Delta Youths, Stay Away from the Protest

    Court Restricts Protests In Lagos To Freedom, Peace Park

    Court Restricts Protests In Lagos To Freedom, Peace Park

    Fans React to Jazz Jennings’ Inspiring Weight Loss Journey

    Fans React to Jazz Jennings’ Inspiring Weight Loss Journey

    Trending Tags

    • Trump Inauguration
    • United Stated
    • White House
    • Market Stories
    • Election Results
  • Science
  • Sports
  • Technology
    Agentic AI and the future of work: navigating technological promise and the risk of increased automation – Equal Times

    Agentic AI and the Future of Work: Embracing Innovation While Navigating Automation Challenges

    Technology alliance introduces system for stable recycling quality – RECYCLING magazine

    Innovative Technology Alliance Unveils Breakthrough System for Consistent Recycling Quality

    Pepper Pike council considers upgrading technology for streaming meetings, remote meeting participation – Cleveland.com

    Pepper Pike Council Explores Upgrading Technology for Enhanced Streaming and Remote Participation

    How Michelin Uses Technology to Rethink Tire Manufacturing: Interview – Motor1.com

    How Michelin’s Tech-Driven Revolution Is Transforming Tire Manufacturing

    Analysts Offer Insights on Technology Companies: Avnet (AVT), Nvidia (NVDA) and Atlassian (TEAM) – The Globe and Mail

    Experts Share Key Insights on Avnet, Nvidia, and Atlassian’s Future Prospects

    Top Technology Executives Recognized at the 2025 Carolina CIO ORBIE Awards – Yahoo Finance

    Celebrating Excellence: Top Technology Executives Honored at the 2025 Carolina CIO ORBIE Awards

    Trending Tags

    • Nintendo Switch
    • CES 2017
    • Playstation 4 Pro
    • Mark Zuckerberg
No Result
View All Result
Earth-News
No Result
View All Result
Home Science

Elliptic Curve ‘Murmurations’ Found With AI Take Flight

March 5, 2024
in Science
Elliptic Curve ‘Murmurations’ Found With AI Take Flight
Share on FacebookShare on Twitter

Almost immediately, the preprint garnered interest, particularly from Andrew Sutherland, a research scientist at MIT who is one of the managing editors of the LMFDB. Sutherland realized that 3 million elliptic curves weren’t enough for his purposes. He wanted to look at much larger conductor ranges to see how robust the murmurations were. He pulled data from another immense repository of about 150 million elliptic curves. Still unsatisfied, he then pulled in data from a different repository with 300 million curves.

“But even those weren’t enough, so I actually computed a new data set of over a billion elliptic curves, and that’s what I used to compute the really high-res pictures,” Sutherland said. The murmurations showed up whether he averaged over 15,000 elliptic curves at a time or a million at a time. The shape stayed the same even as he looked at the curves over larger and larger prime numbers, a phenomenon called scale invariance. Sutherland also realized that murmurations are not unique to elliptic curves, but also appear in more general L-functions. He wrote a letter summarizing his findings and sent it to Sarnak and Michael Rubinstein at the University of Waterloo.

“If there is a known explanation for it I expect you will know it,” Sutherland wrote.

They didn’t.

Explaining the Pattern

Lee, He and Oliver organized a workshop on murmurations in August 2023 at Brown University’s Institute for Computational and Experimental Research in Mathematics (ICERM). Sarnak and Rubinstein came, as did Sarnak’s student Nina Zubrilina.

Zubrilina presented her research into murmuration patterns in modular forms, special complex functions which, like elliptic curves, have associated L-functions. In modular forms with large conductors, the murmurations converge into a sharply defined curve, rather than forming a discernible but dispersed pattern. In a paper posted on October 11, 2023, Zubrilina proved that this type of murmuration follows an explicit formula she discovered.

“Nina’s big achievement is that she’s given a formula for this; I call it the Zubrilina murmuration density formula,” Sarnak said. “Using very sophisticated math, she has proven an exact formula which fits the data perfectly.”

Her formula is complicated, but Sarnak hails it as an important new kind of function, comparable to the Airy functions that define solutions to differential equations used in a variety of contexts in physics, ranging from optics to quantum mechanics.

Though Zubrilina’s formula was the first, others have followed. “Every week now, there’s a new paper out,” Sarnak said, “mainly using Zubrilina’s tools, explaining other aspects of murmurations.”

Jonathan Bober, Andrew Booker and Min Lee of the University of Bristol, together with David Lowry-Duda of ICERM, proved the existence of a different type of murmuration in modular forms in another October paper. And Kyu-Hwan Lee, Oliver and Pozdnyakov proved the existence of murmurations in objects called Dirichlet characters that are closely related to L-functions.

Sutherland was impressed by the significant dose of luck that had led to the discovery of murmurations. If the elliptic curve data hadn’t been ordered by conductor, the murmurations would have disappeared. “They were fortunate to be taking data from the LMFDB, which came pre-sorted according to the conductor,” he said. “It’s what relates an elliptic curve to the corresponding modular form, but that’s not at all obvious. … Two curves whose equations look very similar can have very different conductors.” For example, Sutherland noted that y2=x3 – 11x + 6 has conductor 17, but flipping the minus sign to a plus sign, y2=x3 + 11x + 6 has conductor 100,736.

Even then, the murmurations were only found because of Pozdnyakov’s inexperience. “I don’t think we would have found it without him,” Oliver said, “because the experts traditionally normalize ap to have absolute value 1. But he didn’t normalize them … so the oscillations were very big and visible.”

The statistical patterns that AI algorithms use to sort elliptic curves by rank exist in a parameter space with hundreds of dimensions — too many for people to sort through in their minds, let alone visualize, Oliver noted. But though machine learning found the hidden oscillations, “only later did we understand them to be the murmurations.”

Editor’s Note: Andrew Sutherland, Kyu-Hwan Lee and the L-functions and modular forms database (LMFDB) have all received funding from the Simons Foundation, which also funds this editorially independent publication. Simons Foundation funding decisions have no influence on our coverage. More information is available here.

>>> Read full article>>>
Copyright for syndicated content belongs to the linked Source : Quanta Magazine – https://www.quantamagazine.org/elliptic-curve-murmurations-found-with-ai-take-flight-20240305/

Tags: curveEllipticscience
Previous Post

Volvo Car Malaysia Hosts Inaugural Safety Driving Experience

Next Post

Ferdinand tips ‘fabulous’ Musiala as future Ballon d’Or winner

U.S. and Israel against the world as Palestine dominates UN week – Axios

U.S. and Israel against the world as Palestine dominates UN week – Axios

September 23, 2025
Global economic outlook weakens as policy uncertainty weighs on demand – OECD

Global economic outlook weakens as policy uncertainty weighs on demand – OECD

September 23, 2025
Caesars Entertainment (CZR): Assessing Valuation After Times Square Casino Setback and Mounting Investor Concerns – simplywall.st

Caesars Entertainment Faces Times Square Casino Hurdles as Investor Concerns Mount

September 23, 2025
AI Tool Predicts Health Problems in Patients 20 Years Before They Emerge – eWeek

AI Tool Detects Health Issues Two Decades Before Symptoms Appear

September 23, 2025
Germany’s €80B Rearmament Plan Sidelines US Weapons – politicstoday.org

Germany’s €80B Rearmament Plan Sidelines US Weapons – politicstoday.org

September 23, 2025
FOCUS | SCIO holds press conference on promoting high-quality development through high-level ecological & environmental protection – Xinhua

FOCUS | SCIO holds press conference on promoting high-quality development through high-level ecological & environmental protection – Xinhua

September 23, 2025
Researcher on Tylenol-Autism Connection: Not the Best Science – Managed Healthcare Executive

Researcher Questions the Science Behind Tylenol-Autism Link

September 23, 2025
Da Vinci’s Genetic Secrets May Soon Be Revealed by Ambitious DNA Project – ScienceAlert

Unlocking Da Vinci’s Genetic Mysteries: The Ambitious DNA Project Set to Reveal All

September 23, 2025
Eco-Chic Home & Lifestyle Design Market Is Booming Worldwide | Major Giants The Joinery, Emeco, Greenington – openPR.com

Eco-Chic Home & Lifestyle Design Market Is Booming Worldwide | Major Giants The Joinery, Emeco, Greenington – openPR.com

September 23, 2025
Agentic AI and the future of work: navigating technological promise and the risk of increased automation – Equal Times

Agentic AI and the Future of Work: Embracing Innovation While Navigating Automation Challenges

September 23, 2025

Categories

Archives

September 2025
MTWTFSS
1234567
891011121314
15161718192021
22232425262728
2930 
« Aug    
Earth-News.info

The Earth News is an independent English-language daily published Website from all around the World News

Browse by Category

  • Business (20,132)
  • Ecology (832)
  • Economy (853)
  • Entertainment (21,731)
  • General (17,194)
  • Health (9,896)
  • Lifestyle (865)
  • News (22,149)
  • People (855)
  • Politics (863)
  • Science (16,063)
  • Sports (21,352)
  • Technology (15,835)
  • World (837)

Recent News

U.S. and Israel against the world as Palestine dominates UN week – Axios

U.S. and Israel against the world as Palestine dominates UN week – Axios

September 23, 2025
Global economic outlook weakens as policy uncertainty weighs on demand – OECD

Global economic outlook weakens as policy uncertainty weighs on demand – OECD

September 23, 2025
  • About
  • Advertise
  • Privacy & Policy
  • Contact

© 2023 earth-news.info

No Result
View All Result

© 2023 earth-news.info

No Result
View All Result

© 2023 earth-news.info

Go to mobile version