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Tag: mathematics

  • Trump’s wind-down of the Education Department leaves schools fearing disruption

    WASHINGTON — The Trump administration says its plan to dismantle the Education Department offers a fix for the nation’s lagging academics — a solution that could free schools from the strictures of federal influence.

    Yet to some school and state officials, the plan appears to add more bureaucracy, with no clear benefit for students who struggle with math or reading.

    Instead of being housed in a single agency, much of the Education Department’s work now will be spread across four other federal departments. For President Donald Trump, it’s a step toward fully closing the department and giving states more power over schooling. Yet many states say it will complicate their role as intermediaries between local schools and the federal government.

    The plan increases bureaucracy fivefold, Washington state’s education chief said, “undoubtedly creating confusion and duplicity” for educators and families. His counterpart in California said the plan is “clearly less efficient” and invites disruption. Maryland’s superintendent raised concerns about “the challenges of coordinating efforts with multiple federal agencies.”

    “States were not engaged in this process, and this is not what we have asked for — or what our students need,” said Jill Underly, Wisconsin’s state superintendent. Underly urged the Trump administration to give states greater flexibility and cut down on standardized testing requirements.

    Education Secretary Linda McMahon said schools will continue receiving federal money without disruption. Ultimately, schools will have more money and flexibility to serve students without the existence of the Education Department, she said.

    Yet the department is not gone — only Congress has the power to abolish it. In the meantime, McMahon’s plan leaves the agency in a version of federal limbo. The Labor Department will take over most funding and support for the country’s schools, but the Education Department will retain some duties, including policy guidance and broad supervision of Labor’s education work.

    Similar deals will offload programs to the Department of Health and Human Services, the State Department and the Interior Department. The agreements were signed days before the government shutdown and announced Tuesday.

    Inking agreements to share work with other departments isn’t new: The Education Department already had dozens of such agreements before Trump took office. And local school officials routinely work with other agencies, including the U.S. Agriculture Department, which oversees school meals. What’s different this time is the scale of the programs offloaded — the majority of the Education Department’s funding for schools, for instance.

    Yet Virginia schools chief Emily Anne Gullickson, for one, said schools are accustomed to working with multiple federal agencies, and she welcomed the administration’s efforts to give states more control.

    Response to the plan has mostly been drawn along political lines, with Democrats saying the shakeup will hurt America’s most vulnerable students. Republicans in Congress called it a victory over bureaucracy.

    Yet some conservatives pushed back against the dismantling. U.S. Sen. Lisa Murkowski, an Alaska Republican, said on social media that moving programs to agencies without policy expertise could hurt young people. And Margaret Spellings, a former education secretary to Republican President George W. Bush, called it a distraction to a national education crisis.

    “Moving programs from one department to another does not actually eliminate the federal bureaucracy, and it may make the system harder for students, teachers and families to navigate and get the support they need,” Spellings said in a statement.

    There’s little debate about the need for change in America’s schooling. Its math and reading scores have plummeted in the wake of COVID-19. Before that, reading scores had been stagnant for decades, and math scores weren’t much better.

    McMahon said that’s evidence the Education Department has failed and isn’t needed. At a White House briefing Thursday, she called her plan a “hard reset” that does not halt federal support but ends “federal micromanagement.”

    Randi Weingarten, president of the American Federation of Teachers union and one of McMahon’s sharpest opponents, questioned the logic in her plan.

    “Why would you put a new infrastructure together, a new bureaucracy that nobody knows anything about, and take the old bureaucracy and destroy it, instead of making the old bureaucracy more efficient?” Weingarten said at a Wednesday event.

    The full impact of the shakeup may not be clear for months, but already it’s stoking anxiety among states and school districts that have come to rely on the Education Department for its policy expertise. One of the agency’s roles is to serve as a hotline for questions about complicated funding formulas, special education laws and more.

    The department has not said whether officials who serve that role will keep their jobs in the transition. Without that help, schools would have few options to clarify what can and can’t be paid for with federal money, said David Law, superintendent of Minnetonka Public Schools in Minnesota.

    “What could happen is services are not provided because you don’t have an answer,” said Law, who is also president of AASA, a national association of school superintendents.

    Some question whether other federal departments have the capacity to take on an influx of new work. The Labor Department will take over Title I, an $18 billion grant program that serves 26 million students in low-income areas. It’s going to a Labor office that now handles grants serving only 130,000 people a year, said Angela Hanks, who led the Labor office under former President Joe Biden.

    At best, Hanks said, it will “unleash chaos on school districts, and ultimately, on our kids.”

    In Salem, Massachusetts, the 4,000-student school system receives about $6 million in federal funding that helps support services for students who are low-income, homeless or still mastering English, Superintendent Stephen Zrike said. He fears moving those programs to the Labor Department could bring new “rules of engagement.”

    “We don’t know what other stipulations will be attached to the funding,” he said. “The level of uncertainty is enormous.”

    Other critics have noted the Education Department was created to consolidate education programs that were spread across multiple agencies.

    Rep. Bobby Scott, D-Va., the ranking member on the House Education and Workforce Committee, urged McMahon to rethink her plan. He cited the 1979 law establishing the department, which said dispersion had resulted in “fragmented, duplicative, and often inconsistent Federal policies relating to education.”

    ___

    AP education writers Moriah Balingit in Washington, Bianca Vázquez Toness in Boston and Makiya Seminera in Raleigh, N.C., contributed to this report.

    ___

    The Associated Press’ education coverage receives financial support from multiple private foundations. AP is solely responsible for all content. Find AP’s standards for working with philanthropies, a list of supporters and funded coverage areas at AP.org.

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  • The Hidden Math of Ocean Waves

    In 2011, Deconinck and Oliveras simulated different disturbances with higher and higher frequencies and watched what happened to the Stokes waves. As they expected, for disturbances above a certain frequency, the waves persevered.

    But as the pair continued to dial up the frequency, they suddenly began to see destruction again. At first, Oliveras worried that there was a bug in the computer program. “Part of me was like, this can’t be right,” she said. “But the more I dug, the more it persisted.”

    In fact, as the frequency of the disturbance increased, an alternating pattern emerged. First there was an interval of frequencies where the waves became unstable. This was followed by an interval of stability, which was followed by yet another interval of instability, and so on.

    Deconinck and Oliveras published their finding as a counterintuitive conjecture: that this archipelago of instabilities stretches off to infinity. They called all the unstable intervals “isole”—the Italian word for “islands.”

    It was strange. The pair had no explanation for why instabilities would appear again, let alone infinitely many times. They at least wanted a proof that their startling observation was correct.

    Bernard Deconinck and Katie Oliveras uncovered a strange pattern in computational studies of wave stability.

    Photograph: Courtesy of Bernard Deconinck

    The Hidden Math of Ocean Waves

    Photograph: Courtesy of Katie Oliveras

    For years, no one could make any progress. Then, at the 2019 workshop, Deconinck approached Maspero and his team. He knew they had a lot of experience studying the math of wavelike phenomena in quantum physics. Perhaps they could figure out a way to prove that these striking patterns arise from the Euler equations.

    The Italian group got to work immediately. They started with the lowest set of frequencies that seemed to cause waves to die. First, they applied techniques from physics to represent each of these low-frequency instabilities as arrays, or matrices, of 16 numbers. These numbers encoded how the instability would grow and distort the Stokes waves over time. The mathematicians realized that if one of the numbers in the matrix was always zero, the instability would not grow, and the waves would live on. If the number was positive, the instability would grow and eventually destroy the waves.

    To show that this number was positive for the first batch of instabilities, the mathematicians had to compute a gigantic sum. It took 45 pages and nearly a year of work to solve it. Once they’d done so, they turned their attention to the infinitely many intervals of higher-frequency wave-killing disturbances—the isole.

    First, they figured out a general formula—another complicated sum—that would give them the number they needed for each isola. Then they used a computer program to solve the formula for the first 21 isole. (After that, the calculations got too complicated for the computer to handle.) The numbers were all positive, as expected—and they also seemed to follow a simple pattern that implied they would be positive for all the other isole as well.

    Joseph Howlett

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  • Unpicking How to Measure the Complexity of Knots

    The duo kept their program running in the background for over a decade. During that time, a couple of computers from their ragtag collection succumbed to overheating and even flames. “There was one that actually sent out sparks,” Brittenham said. “That was kind of fun.” (Those machines, he added, were “honorably retired.”)

    Then, in the fall of 2024, a paper about a failed attempt to use machine learning to disprove the additivity conjecture caught Brittenham and Hermiller’s attention. Perhaps, they thought, machine learning wasn’t the best approach for this particular problem: If a counterexample to the additivity conjecture was out there, it would be “a needle in a haystack,” Hermiller said. “That’s not quite what things like machine learning are about. They’re about trying to find patterns in things.”

    But it reinforced a suspicion the pair already had—that maybe their more carefully honed sneakernet could find the needle.

    The Tie That Binds

    Brittenham and Hermiller realized they could make use of the unknotting sequences they’d uncovered to look for potential counterexamples to the additivity conjecture.

    Imagine again that you have two knots whose unknotting numbers are 2 and 3, and you’re trying to unknot their connect sum. After one crossing change, you get a new knot. If the additivity conjecture is to be believed, then the original knot’s unknotting number should be 5, and this new knot’s should be 4.

    But what if this new knot’s unknotting number is already known to be 3? That implies that the original knot can be untied in just four steps, breaking the conjecture.

    “We get these middle knots,” Brittenham said. “What can we learn from them?”

    He and Hermiller already had the perfect tool for the occasion humming away on their suite of laptops: the database they’d spent the previous decade developing, with its upper bounds on the unknotting numbers of thousands of knots.

    The mathematicians started to add pairs of knots and work through the unknotting sequences of their connect sums. They focused on connect sums whose unknotting numbers had only been approximated in the loosest sense, with a big gap between their highest and lowest possible values. But that still left them with a massive list of knots to work through—“definitely in the tens of millions, and probably in the hundreds of millions,” Brittenham said.

    For months, their computer program applied crossing changes to these knots and compared the resulting knots to those in their database. One day in late spring, Brittenham checked the program’s output files, as he did most days, to see if anything interesting had turned up. To his great surprise, there was a line of text: “CONNECT SUM BROKEN.” It was a message he and Hermiller had coded into the program—but they’d never expected to actually see it.

    Leila Sloman

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  • Trump says the US has secured $17 trillion in new investments. The real number is likely much less

    WASHINGTON (AP) — The economic boom promised by President Donald Trump centers on a single number: $17 trillion.

    That’s the sum of new investments that Trump claims to have generated with his tariffs, income tax cuts and aggressive salesmanship of CEOs, financiers, tech titans, prime ministers, presidents and other rulers. The $17 trillion is supposed to fund new factories, new technologies, more jobs, higher incomes and faster economic growth.

    “Under eight months of Trump, we’ve already secured commitments of $17 trillion coming in,” the president said in a speech last month. “There’s never been any country that’s done anything like that.”

    But based on statements from various companies, foreign countries and the White House’s own website, that figure appears to be exaggerated, highly speculative and far higher than the actual sum. The White House website lists total investments at $8.8 trillion, though that figure appears to be padded with some investment commitments made during Joe Biden’s presidency.

    The White House didn’t lay out the math after multiple requests as to how Trump calculated $17 trillion in investment commitments. But the issue goes beyond Trump’s hyperbolic talk to his belief that the brute force of tariffs and shaming of companies can deliver economic results, a strategy that could go sideways for him politically if the tough talk fails to translate into more jobs and higher incomes.

    Just 37% of U.S. adults approve of Trump’s handling of the economy, according to a September poll by The Associated Press-NORC Center for Public Affairs. That’s down from a peak of 56% in early 2020 during Trump’s first term — a memory he relied upon when courting voters in last year’s election.

    Adam Posen, president of the Peterson Institute of International Economics, said the public commitments announced by Trump do represent a “meaningful increase” — but one that amounts to hundreds of billions of dollars, not trillions. Even then, that comes with long-term costs as countries might be less inclined to invest with the U.S. after being threatened to do so.

    “It is a national security mistake because you’re turning allies into colonies of a sort — you’re forcibly extracting from them things that they don’t see as entirely in their interest,” Posen said. “Twisting the arms of governments to then twist the arms of their own businesses is not going to get you the payoff you want.”

    Trump banking on foreign countries making good on promises

    The Trump administration is betting that tariffs are an effective tool to prod other countries and international companies to invest in the United States, a big stick that other administrations failed to wield. Trump’s pitch to voters is that he will play a role in directly managing the investment commitments made by foreign countries — and that the allocation of that money starting next year will revive what has been a flagging job market.

    “The difference between hypothetical investments and ground being broken on new factories and facilities is good leadership and sound policy,” said White House spokesman Kush Desai.

    The White House said that Japan will invest $1 trillion, largely at Trump’s direction. The European Union will commit $600 billion. The United Arab Emirates made commitments of $1.4 trillion over 10 years. Qatar pledged $1.2 trillion. Saudi Arabia intends to pony up $600 billion, India $500 billion and South Korea $450 billion, among others.

    The challenge is the precise terms of those investments have yet to be fully codified and released to the public, and some numbers are under dispute, potentially fuzzy math or, in the case of Qatar, more than five times the annual gross domestic product of the entire country. The White House maintains that Qatar is good for the money because it produces oil.

    South Korea already has misgivings about its investment commitment, which is $100 billion lower than what the White House claims, after immigration agents raided a Hyundai plant under construction in Georgia and arrested Korean citizens. There are also concerns that an investment that large without a better way to exchange currencies with the U.S. could hurt South Korea’s economy.

    “From what I’ve seen, these commitments are worth about as much as the paper they’re not written down on,” said Jared Bernstein, who was the chairman of the Council of Economic Advisers in the Biden White House.

    As for the $600 billion committed by European companies, that’s based on those businesses having “expressed interest” and having stated “intentions” to do so through 2029 rather than an overt concession, according to European Union documents.

    Still too soon to see any investment impact in overall economy

    So far, there has yet to be a notable boost in business investment as a percentage of U.S. gross domestic product. As a share of the overall economy, business investment during the first six months of Trump’s presidency has been consistently bouncing around 14%, just as it was before the pandemic.

    But economists also note that Trump is double-counting and relying on investments that were initially announced during the Biden administration or investments that were already likely to occur because of the artificial intelligence build out.

    For example, the White House lists a $16 billion investment by computer chipmaker Global Foundries. But of that sum, more than $13 billion was announced during the Biden administration and supported by $1.6 billion in grants by the 2022 CHIPS and Science Act, as well as other state and federal incentives.

    Similarly, the White House is banking on $200 billion being invested by the chipmaker Micron, but at least $120 billion of that was announced during the Biden era.

    ‘The tariffs played a big role’

    For their part, White House officials largely credit Trump’s tariffs — like those imposed on Oct. 1 on kitchen cabinets, large trucks and pharmaceutical drugs — for forcing companies to make investments in the U.S., saying that the risk of additional import taxes if countries and companies fail to deliver on their promises will ensure that the promised cash comes into the economy.

    On Tuesday, Pfizer CEO Albert Bourla endorsed this approach after his pharmaceutical drug company received a three-year grace period on tariffs and announced $70 billion in investments in the U.S.

    “The president was absolutely right,” Bourla said. “Tariffs is the most powerful tool to motivate behaviors.”

    “The tariffs played a big role,” Trump added.

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  • Trump says US has secured $17T in new investments. The number is likely much less.

    WASHINGTON — WASHINGTON (AP) — The economic boom promised by President Donald Trump centers on a single number: $17 trillion.

    That’s the sum of new investments that Trump claims to have generated with his tariffs, income tax cuts and aggressive salesmanship of CEOs, financiers, tech titans, prime ministers, presidents and other rulers. The $17 trillion is supposed to fund new factories, new technologies, more jobs, higher incomes and faster economic growth.

    “Under eight months of Trump, we’ve already secured commitments of $17 trillion coming in,” the president said in a speech last month. “There’s never been any country that’s done anything like that.”

    But based on statements from various companies, foreign countries and the White House’s own website, that figure appears to be exaggerated, highly speculative and far higher than the actual sum. The White House website lists total investments at $8.8 trillion, though that figure appears to be padded with some investment commitments made during Joe Biden’s presidency.

    The White House didn’t lay out the math after multiple requests as to how Trump calculated $17 trillion in investment commitments. But the issue goes beyond Trump’s hyperbolic talk to his belief that the brute force of tariffs and shaming of companies can deliver economic results, a strategy that could go sideways for him politically if the tough talk fails to translate into more jobs and higher incomes.

    Just 37% of U.S. adults approve of Trump’s handling of the economy, according to a September poll by The Associated Press-NORC Center for Public Affairs. That’s down from a peak of 56% in early 2020 during Trump’s first term — a memory he relied upon when courting voters in last year’s election.

    Adam Posen, president of the Peterson Institute of International Economics, said the public commitments announced by Trump do represent a “meaningful increase” — but one that amounts to hundreds of billions of dollars, not trillions. Even then, that comes with long-term costs as countries might be less inclined to invest with the U.S. after being threatened to do so.

    “It is a national security mistake because you’re turning allies into colonies of a sort — you’re forcibly extracting from them things that they don’t see as entirely in their interest,” Posen said. “Twisting the arms of governments to then twist the arms of their own businesses is not going to get you the payoff you want.”

    The Trump administration is betting that tariffs are an effective tool to prod other countries and international companies to invest in the United States, a big stick that other administrations failed to wield. Trump’s pitch to voters is that he will play a role in directly managing the investment commitments made by foreign countries — and that the allocation of that money starting next year will revive what has been a flagging job market.

    “The difference between hypothetical investments and ground being broken on new factories and facilities is good leadership and sound policy,” said White House spokesman Kush Desai.

    The White House said that Japan will invest $1 trillion, largely at Trump’s direction. The European Union will commit $600 billion. The United Arab Emirates made commitments of $1.4 trillion over 10 years. Qatar pledged $1.2 trillion. Saudi Arabia intends to pony up $600 billion, India $500 billion and South Korea $450 billion, among others.

    The challenge is the precise terms of those investments have yet to be fully codified and released to the public, and some numbers are under dispute, potentially fuzzy math or, in the case of Qatar, more than five times the annual gross domestic product of the entire country. The White House maintains that Qatar is good for the money because it produces oil.

    South Korea already has misgivings about its investment commitment, which is $100 billion lower than what the White House claims, after immigration agents raided a Hyundai plant under construction in Georgia and arrested Korean citizens. There are also concerns that an investment that large without a better way to exchange currencies with the U.S. could hurt South Korea’s economy.

    “From what I’ve seen, these commitments are worth about as much as the paper they’re not written down on,” said Jared Bernstein, who was the chairman of the Council of Economic Advisers in the Biden White House.

    As for the $600 billion committed by European companies, that’s based on those businesses having “expressed interest” and having stated “intentions” to do so through 2029 rather than an overt concession, according to European Union documents.

    So far, there has yet to be a notable boost in business investment as a percentage of U.S. gross domestic product. As a share of the overall economy, business investment during the first six months of Trump’s presidency has been consistently bouncing around 14%, just as it was before the pandemic.

    But economists also note that Trump is double-counting and relying on investments that were initially announced during the Biden administration or investments that were already likely to occur because of the artificial intelligence build out.

    For example, the White House lists a $16 billion investment by computer chipmaker Global Foundries. But of that sum, more than $13 billion was announced during the Biden administration and supported by $1.6 billion in grants by the 2022 CHIPS and Science Act, as well as other state and federal incentives.

    Similarly, the White House is banking on $200 billion being invested by the chipmaker Micron, but at least $120 billion of that was announced during the Biden era.

    For their part, White House officials largely credit Trump’s tariffs — like those imposed on Oct. 1 on kitchen cabinets, large trucks and pharmaceutical drugs — for forcing companies to make investments in the U.S., saying that the risk of additional import taxes if countries and companies fail to deliver on their promises will ensure that the promised cash comes into the economy.

    On Tuesday, Pfizer CEO Albert Bourla endorsed this approach after his pharmaceutical drug company received a three-year grace period on tariffs and announced $70 billion in investments in the U.S.

    “The president was absolutely right,” Bourla said. “Tariffs is the most powerful tool to motivate behaviors.”

    “The tariffs played a big role,” Trump added.

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  • Parents Are Freaking Out Over These New Teaching Styles — And Experts Have Thoughts

    Across the country, parents are discovering that what their children bring home from school looks very little like what they once learned. It isn’t just math — reading lessons, writing expectations, even how science and history are taught have shifted. What once relied heavily on memorization has given way to conceptual thinking, inquiry and skills tied to the future workplace.

    Educators say these changes are not random or trendy. They’re the product of research, shifts in workforce demands and national policy decisions that have reshaped the classroom over the last few decades. But for parents, the changes often arrive without much explanation, leaving them feeling lost.

    To understand why classrooms look so different today, it helps to trace how teaching methods have evolved. From the rise of “new math” to the renewed focus on phonics, the story of modern education is one of pendulum swings, policy mandates and, above all, an ongoing debate about how kids learn best.

    From Memorization To Meaning

    “Some of the major changes in teaching practices are a direct result of the standards and now Common Core, with a shift from rote memorization to conceptual thinking and problem-solving,” Yolanda Carlos, an early childhood education professor at Pacific Oaks College, said.

    Where students once filled in worksheets with multiplication tables or copied definitions from a chalkboard, today’s lessons aim for depth. Teachers want students to make connections between ideas, explain their reasoning and apply skills to real-world scenarios.

    Michaela LeRoy, education and development specialist at the Haven Collection, a comprehensive family care center, described it as: “Twenty to 30 years ago, subjects like reading, writing and science were often taught through textbooks and rote memorization. Today, subjects are more integrated and inquiry-based, encouraging students to ask questions, investigate and apply concepts to real-world situations.”

    This doesn’t mean facts have disappeared. Kids still memorize math facts and spelling patterns. But the goal is less about storing knowledge and more about understanding why it works, a skill researchers say better prepares students for a rapidly changing economy.

    Young female teacher working with her students on a writing lesson in school

    Why ‘New Math’ Sparks Old Frustrations

    If one subject embodies the clash between old and new, it’s math. The phrase “new math” has become shorthand for parental exasperation.

    “Parents can become uncomfortable with changes they do not understand and therefore feel they cannot support their child’s required learning activities,” Carlos said. “Most parents’ understanding of mathematics is based on recalling facts, procedures and formulas. Today’s math requires thinking, reasoning, collaboration and problem-solving, the very skills employers want in the workforce.”

    To many parents, breaking apart numbers, drawing arrays, or showing multiple solution methods feels unnecessary. But teachers argue it helps kids develop number sense and flexibility, making them better problem-solvers long term.

    Dr. Geillan Aly, a math educator and researcher at CUNY, calls this recurring debate “the cycle of benign neglect”: “Every few decades, we swing from procedural to conceptual math learning. But parents and teachers are often left without enough support, creating frustration and what I call ‘math trauma.’”

    And that trauma is real. A parent who struggled with math in school may feel defeated when they can’t help their child. A child sensing that frustration may internalize it. And soon, math becomes a source of tension rather than growth, Aly adds.

    Phonics vs. Sight Words — The ‘New Math’ Debate For The Humanities

    Math isn’t the only battleground. Reading instruction has seen its own pendulum swings.

    For much of the late 20th century, schools leaned on whole language and sight word memorization, encouraging children to recognize words by sight and read through context. Critics argued that this left struggling readers behind, unable to decode new words.

    The pendulum has swung back toward phonics, or explicit instruction in letter-sound relationships. But most researchers agree the answer isn’t either/or, it’s both.

    “Reading is not innate,” Carlos said. “The science of reading shows a strong correlation between word recognition and language comprehension. Good readers have both decoding skills and strong word recognition.”

    “Research undeniably shows that systematic phonics instruction is the most effective for the majority of kids,” Beth Gaskill, an educator, learning specialist and the founder of Big City Readers, told HuffPost. “Sight word lists gave them a handful of memorized answers. Phonics gives them the key to unlock every word.”

    And Zack Barnes, a literacy professor at Austin Peay State University, explained that this “science of reading” movement has influenced policy in dozens of states. Many now require screenings for dyslexia, additional teacher training and curricula that emphasize phonics while also supporting comprehension.

    The Policy Legacies Of ‘No Child Left Behind’ And Common Core

    If there’s one federal policy that parents and teachers alike remember most vividly, it’s No Child Left Behind (NCLB). Signed into law in 2001 under President George W. Bush, the sweeping legislation reshaped the fabric of American education almost overnight.

    Its premise was straightforward: hold schools accountable for student achievement, with the promise that every child — regardless of ZIP code, race or socioeconomic status — would receive a “high-quality education.”

    The way it measured that promise, however, was through standardized testing. Annual assessments in reading and math for students in grades three through eight, plus once in high school, became the yardstick by which schools were judged. Funding and even school survival were tied to performance. Schools that failed to make “adequate yearly progress” (AYP) faced escalating consequences, from mandated tutoring to state takeovers.

    For policymakers, the law was about equity, closing the achievement gap and ensuring transparency. Classrooms increasingly revolved around test prep. Curriculum narrowed as subjects like art, social studies and even science were sidelined in favor of boosting reading and math scores.

    “Teachers were teaching kids how to pass a test, not how to think.”

    – Sarah Seitz, founder of The Enrichery tutoring center

    “Teachers moved toward graphic organizers, project-based learning and a heavy reliance on technology, not always because it was best practice but because it was the most efficient way to hit testing goals,” Carlos said.

    Sarah Seitz, founder of The Enrichery tutoring center, described how the legislation made classrooms test-driven. “Creative subjects were squeezed out aside,” she said. “Teachers were teaching kids how to pass a test, not how to think.”

    And yet, some positive legacies remained. LeRoy said one of the law’s most enduring shifts was how data was reported. For the first time, schools had to break down performance by subgroup — by race, by disability, by English learner status. That meant you couldn’t just hide behind an average anymore. Every child counted.

    Still, the tradeoffs were hard to ignore. Barnes said the over-testing was real, but so was the insight: “I think NCLB ushered in a reliance on over-testing our students, but also allowed us to dive into the data to figure out where schools and states were doing poorly.”

    By the late 2000s, bipartisan consensus had emerged: the law’s intentions were noble, but its implementation was deeply flawed. That realization eventually paved the way for its replacement in 2015 with the Every Student Succeeds Act (ESSA), which gave states more flexibility and attempted to balance accountability with a broader view of what student success could look like.

    How Parents Can Help Without Losing Their Minds

    So where does this leave parents trying to support their kids?

    Carlos suggests parents focus less on mastering the new methods and more on modeling curiosity: “Read to your children, model reading yourself and set aside a quiet study space. Take them to the library, have regular conversations and limit device time. Small daily habits make a big difference.”

    Seitz cautioned against undermining teachers: “One of the biggest mistakes is saying, ‘This is how I learned it. Let me show you a better way.’ Kids hate that. The best thing you can do is ask your child to walk you through their method. When parents mirror the teacher’s approach, kids gain confidence and homework fights drop dramatically.”

    Jamie Hendrickson, principal at the Meyer Levin Middle School for the Performing Arts in Brooklyn, New York, echoed the importance of partnership: “Review the curriculum, attend Curriculum Night and use resources like Khan Academy. Partnering with schools turns confusion into collaboration.”

    Education Will Keep Evolving

    If today’s classrooms already feel foreign, tomorrow’s may feel even more so. Experts predict that artificial intelligence will act as a personalized tutor, adjusting lessons in real time. Competency-based education could replace letter grades, with students advancing as they master skills. Social-emotional learning may be woven into daily lessons, teaching resilience, teamwork and empathy, while global collaboration may become routine, with students working virtually with peers across the world.

    “Parents may be surprised to see less rote work and more whole-child, brain-based learning,” said Gaskill. “Social-emotional skills will sit side by side with reading and math.”

    For parents, that may mean the kitchen-table homework battles of the future won’t be about long division at all, but about how to ask the kinds of questions that no textbook yet has the answers to.

    “With AI everywhere, kids won’t be judged on how many answers they know,” Seitz said. “They’ll be judged on how well they can frame the right questions.”

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  • Girls fell behind boys in math during the pandemic

    IRVING, Texas — Crowded around a workshop table, four girls at de Zavala Middle School puzzled over a Lego machine they had built. As they flashed a purple card in front of a light sensor, nothing happened.

    The teacher at the Dallas-area school had emphasized that in the building process, there is no such thing as mistakes. Only iterations. So the girls dug back into the box of blocks and pulled out an orange card. They held it over the sensor and the machine kicked into motion.

    “Oh! Oh, it reacts differently to different colors,” said sixth grader Sofia Cruz.

    In de Zavala’s first year as a choice school focused on science, technology, engineering and math, the school recruited a sixth grade class that’s half girls. School leaders are hoping the girls will stick with STEM fields. In de Zavala’s higher grades — whose students joined before it was a STEM school — some elective STEM classes have just one girl enrolled.

    Efforts to close the gap between boys and girls in STEM classes are picking up after losing steam nationwide during the chaos of the COVID-19 pandemic. Schools have extensive work ahead to make up for the ground girls lost, in both interest and performance.

    In the years leading up to the pandemic, the gender gap nearly closed. But within a few years, girls lost all the ground they had gained in math test scores over the previous decade, according to an Associated Press analysis. While boys’ scores also suffered during COVID, they have recovered faster than girls, widening the gender gap.

    As learning went online, special programs to engage girls lapsed — and schools were slow to restart them. Zoom school also emphasized rote learning, a technique based on repetition that some experts believe may favor boys, instead of teaching students to solve problems in different ways, which may benefit girls.

    Old practices and biases likely reemerged during the pandemic, said Michelle Stie, a vice president at the National Math and Science Initiative.

    “Let’s just call it what it is,” Stie said. “When society is disrupted, you fall back into bad patterns.”

    In most school districts in the 2008-2009 school year, boys had higher average math scores on standardized tests than girls, according to AP’s analysis, which looked at scores across 15 years in over 5,000 school districts. It was based on average test scores for third through eighth graders in 33 states, compiled by the Educational Opportunity Project at Stanford University.

    A decade later, girls had not only caught up, they were ahead: Slightly more than half of districts had higher math averages for girls.

    Within a few years of the pandemic, the parity disappeared. In 2023-2024, boys on average outscored girls in math in nearly nine out of 10 districts.

    A separate study by NWEA, an education research company, found gaps between boys and girls in science and math on national assessments went from being practically non-existent in 2019 to favoring boys around 2022.

    Studies have indicated girls reported higher levels of anxiety and depression during the pandemic, plus more caretaking burdens than boys, but the dip in academic performance did not appear outside STEM. Girls outperformed boys in reading in nearly every district nationwide before the pandemic and continued to do so afterward.

    “It wasn’t something like COVID happened and girls just fell apart,” said Megan Kuhfeld, one of the authors of the NWEA study.

    In the years leading up to the pandemic, teaching practices shifted to deemphasize speed, competition and rote memorization. Through new curriculum standards, schools moved toward research-backed methods that emphasized how to think flexibly to solve problems and how to tackle numeric problems conceptually.

    Educators also promoted participation in STEM subjects and programs that boosted girls’ confidence, including extracurriculars that emphasized hands-on learning and connected abstract concepts to real-life applications.

    When STEM courses had large male enrollment, Superintendent Kenny Rodrequez noticed girls losing interest as boys dominated classroom discussions at his schools in Grandview C-4 District outside Kansas City. Girls were significantly more engaged after the district moved some of its introductory hands-on STEM curriculum to the lower grade levels and balanced classes by gender, he said.

    When schools closed for the pandemic, the district had to focus on making remote learning work. When in-person classes resumed, some of the teachers had left, and new ones had to be trained in the curriculum, Rodrequez said.

    “Whenever there’s crisis, we go back to what we knew,” Rodrequez said.

    Despite shifts in societal perceptions, a bias against girls persists in science and math subjects, according to teachers, administrators and advocates. It becomes a message girls can internalize about their own abilities, they say, even at a very young age.

    In his third grade classroom in Washington, D.C., teacher Raphael Bonhomme starts the year with an exercise where students break down what makes up their identity. Rarely do the girls describe themselves as good at math. Already, some say they are “not a math person.”

    “I’m like, you’re 8 years old,” he said. “What are you talking about, ‘I’m not a math person?’”

    Girls also may have been more sensitive to changes in instructional methods spurred by the pandemic, said Janine Remillard, a math education professor at the University of Pennsylvania. Research has found girls tend to prefer learning things that are connected to real-life examples, while boys generally do better in a competitive environment.

    “What teachers told me during COVID is the first thing to go were all of these sense-making processes,” she said.

    At de Zavala Middle School in Irving, the STEM program is part of a push that aims to build curiosity, resilience and problem-solving across subjects.

    Coming out of the pandemic, Irving schools had to make a renewed investment in training for teachers, said Erin O’Connor, a STEM and innovation specialist there.

    The district last year also piloted a new science curriculum from Lego Education. The lesson involving the machine at de Zavala, for example, had students learn about kinetic energy. Fifth graders learned about genetics by building dinosaurs and their offspring with Lego blocks, identifying shared traits.

    “It is just rebuilding the culture of, we want to build critical thinkers and problem solvers,” O’Connor said.

    Teacher Tenisha Willis recently led second graders at Irving’s Townley Elementary School through building a machine that would push blocks into a container. She knelt next to three girls who were struggling.

    They tried to add a plank to the wheeled body of the machine, but the blocks didn’t move enough. One girl grew frustrated, but Willis was patient. She asked what else they could try, whether they could flip some parts around. The girls ran the machine again. This time, it worked.

    “Sometimes we can’t give up,” Willis said. “Sometimes we already have a solution. We just have to adjust it a little bit.”

    ___

    Lurye reported from Philadelphia. Todd Feathers contributed reporting from New York.

    ___

    The Associated Press’ education coverage receives financial support from multiple private foundations. AP is solely responsible for all content. Find AP’s standards for working with philanthropies, a list of supporters and funded coverage areas at AP.org.

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  • Google DeepMind’s Game-Playing AI Tackles a Chatbot Blind Spot

    Google DeepMind’s Game-Playing AI Tackles a Chatbot Blind Spot

    Several years before ChatGPT began jibber-jabbering away, Google developed a very different kind of artificial intelligence program called AlphaGo that learned to play the board game Go with superhuman skill through tireless practice.

    Researchers at the company have now published research that combines the abilities of a large language model (the AI behind today’s chatbots) with those of AlphaZero, a successor to AlphaGo also capable of playing chess, to solve very tricky mathematical proofs.

    Their new Frankensteinian creation, dubbed AlphaProof, has demonstrated its prowess by tackling several problems from the 2024 International Math Olympiad (IMO), a prestigious competition for high school students.

    AlphaProof uses the Gemini large language model to convert naturally phrased math questions into a programming language called Lean. This provides the training fodder for a second algorithm to learn, through trial and error, how to find proofs that can be confirmed as correct.

    Earlier this year, Google DeepMind revealed another math algorithm called AlphaGeometry that also combines a language model with a different AI approach. AlphaGeometry uses Gemini to convert geometry problems into a form that can be manipulated and tested by a program that handles geometric elements. Google today also announced a new and improved version of AlphaGeometry.

    The researchers found that their two math programs could provide proofs for IMO puzzles as well as a silver medalist could. Out of six problems total, AlphaProof solved two algebra problems and a number theory one, while AlphaGeometry solved a geometry problem. The programs got one problem in minutes but took up to several days to figure out others. Google DeepMind has not disclosed how much computer power it threw at the problems.

    Google DeepMind calls the approach used for both AlphaProof and AlphaGeometry “neuro-symbolic” because they combine the pure machine learning of an artificial neural network, the technology that underpins most progress in AI of late, with the language of conventional programming.

    “What we’ve seen here is that you can combine the approach that was so successful, and things like AlphaGo, with large language models and produce something that is extremely capable,” says David Silver, the Google DeepMind researcher who led work on AlphaZero. Silver says the techniques demonstrated with AlphaProof should, in theory, extend to other areas of mathematics.

    Indeed, the research raises the prospect of addressing the worst tendencies of large language models by applying logic and reasoning in a more grounded fashion. As miraculous as large language models can be, they often struggle to grasp even basic math or to reason through problems logically.

    In the future, the neural-symbolic method could provide a means for AI systems to turn questions or tasks into a form that can be reasoned over in a way that produces reliable results. OpenAI is also rumored to be working on such a system, codenamed “Strawberry.”

    There is, however, a key limitation with the systems revealed today, as Silver acknowledges. Math solutions are either correct or incorrect, allowing AlphaProof and AlphaGeometry to work their way toward the right answer. Many real-world problems—coming up with the ideal itinerary for a trip, for instance—have many possible solutions, and which one is ideal may be unclear. Silver says the solution for more ambiguous questions may be for a language model to try to determine what constitutes a “right” answer during training. “There’s a spectrum of different things that can be tried,” he says.

    Silver is also careful to note that Google DeepMind won’t be putting human mathematicians out of jobs. “We are aiming to provide a system that can prove anything, but that’s not the end of what mathematicians do,” he says. “A big part of mathematics is to pose problems and find what are the interesting questions to ask. You might think of this as another tool along the lines of a slide rule or calculator or computational tools.”

    Updated 7/25/24 1:25 pm ET: This story has been updated to clarify how many problems AlphaProof and AlphaGeometry solved, and of what type.

    Will Knight

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  • 50-year teacher & Lehigh Valley Math Team score championship victory

    50-year teacher & Lehigh Valley Math Team score championship victory

    BETHLEHEM, Pennsylvania (WPVI) — With 50 years of teaching experience, coach Don Davis led the Lehigh Valley Math Team to a victory at the 2024 American Regions Mathematics League contest.

    Students practiced hard throughout the spring, devoting countless hours to mastering their individual skills and streamlining their teamwork.

    The finals took place on June 1st, featuring over 100 teams with over 1,000 students competing from the United States, Canada, China and South Korea.

    Davis formed the math team in 1993. Over the years, it has grown to include students from the Lehigh Valley, Greater Philadelphia Area, and New Jersey.

    Davis plans on retiring from his post at Lehigh University this year, but will continue to coach the math team for the foreseeable future.

    To learn more about the Lehigh Valley Math Team, watch the video above and visit their website.

    RELATED: Pa. student, Irish dancing star brings trophy home from Ireland

    17-year-old Zachariah McLaughlin’s fast-tapping feet were heard across the world when he competed in a recent Irish dancing world championship.

    Copyright © 2024 WPVI-TV. All Rights Reserved.

    Matteo Iadonisi

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  • Peter Van Ness writes a new life chapter

    Peter Van Ness writes a new life chapter

    Former Gloucester resident Peter Van Ness’s debut novel, a tech thriller called “The Faithful” has arrived, and it is very ambitious indeed.

    Van Ness, who now lives in Florida, says he has always been fascinated by the intersection of science and spirituality/religion. Add to that the confluence of 21st century technology, and you are inside the mind of John Welles, a brilliant and ambitious MIT graduate who is not just the central character but absolutely central to the novel, as much of the book takes place in his mind.

    We first meet John when, as a precocious and curious child, he questions the very existence of reality. Little John recalls in a first-person introductory narrative that he observes the world as a place he can only think to call “pretend.” He can escape it by entering a secret portal in the hallway into infinity where he can time travel at will.

    As the son of a prominent Presbyterian minister, Van Ness himself developed an early interest in spirituality and religion, and their link to the metaphysical. Likewise, as a natural math whiz, science was second nature to him. His mind, he says, was ready made for the 21st century, and his tech resume began in high school when he programed computers connected to the ARPANET, the first operational computer network that became the foundation of the modern internet. Later, he’d go on to co-found a software company “that made his investors rich.”

    Anyone who knows Van Ness from his entrepreneurial 25 years in Gloucester, knows he marches to his own drum. He skipped college, and became a student of world religions, with a special inclination toward Buddhism.

    All of this — science, technology, religion, spirituality, mysticism, not to mention Van Ness’s passion for music — comes home to roost in “The Faithful,” as John’s tech brilliance gets him and his equally brilliant girlfriend Emily swept up in a struggle between two opposing secret religious sects, the Faithful versus the Disciples.

    Van Ness describes “The Faithful” sect as representing those wanting “to protect people from all the dangers of the world. They are absolutely sure they are right and committed to their mission, whatever it takes.” The Disciples, on the other hand, “are endlessly curious, seek adventure … constantly question whether they are doing the right thing, and are always adjusting their plans to adapt to current conditions.”

    When John and Emily stumble upon evidence of an undiscovered energy field that is, to make a long story short, the key to life itself, they become targets of an ensuing Dan Brownish conspiracy reminiscent of a high tech “The Da Vinci Code,” plunging the reader “into the minds and psyches of the couple as they each embark on a personal journey of self-discovery.”

    Ten years in the writing, “The Faithful” evolved with today’s rapidly changing technology and came to include new advances in artificial intelligence. Suffice to say, this is not a tale for tech luddites. But is you are a 21st century digital citizen, then fasten your seatbelts, you’re in for a ride.

    Tech aside, at its heart, “The Faithful” remains deeply humanitarian, even romantic. John, like Van Ness himself, loves music, and music weaves its magic throughout “The Faithful.” John hears it in everything, including the glug, glug, glug of fine wine decanting. Then there is “the maestro” — a beloved conductor revered by his musical students, one of whom is John. Van Ness creates in the relationship between the maestro and his students what sounded to this reader as a metaphor for the relationship between the all-seeing God orchestrating life itself.

    Van Ness, who, with his wife Vicky, was well known in Gloucester as a mover and shaker in downtown community creative and cultural initiatives. From the summer block parties to Discover Gloucester, they were on the launching pads. But they were best known as promoters of local live music. As founders of Gimme Music and Beverly’s “intimate listening room” 9 Wallis, they were — until the COVID-19 pandemic hit — major players on the North Shore’s live music scene.

    One door closes, another opens. In his new home in Florida, Van Ness says he loves swimming daily in the ocean. and as anyone who knows him will not be surprised to hear, in between riding the waves, he’s already writing a sequel. Stay tuned.

    Joann Mackenzie may be contacted at 978-675-2707 or jmackenzie@northofboston.com.

    By Joann Mackenzie | Staff Writer

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  • Beverly library announces teen poetry contest winners

    Beverly library announces teen poetry contest winners

    BEVERLY — The Beverly Public Library has announced the winners of the 28th annual Teen Poetry Contest.

    Winners in the Middle School Division were Sydney Brown, first place for “What Shall I Say”; Katie Daniels, second place for “A CD considers its music”; and James Daoust, third place for “some random poem I made part 2.”

    In the High School Division, the winners were Johnny Sheridan, first place for “Elegy for the Impermanent”; Michael Towne-Smith, second place for “Pupa”; and Sheridan, third place for “Sweet Dreams.”

    The library received over 450 poems for the contest. The poems were judged by a panel of local poets — Kevin Carey, coordinator of creative writing at Salem State University; Liz Ciampa, founder of the Winter Street Writers group; and Aly Pierce, author of “The Visible Plants and Cryptids.”

    The following students all won honorable mentions:

    Emma Conway for “Forgettable”; Charlie Cook for “Through my Telescope”; Liana for “A Woman”; Rory Horan for “The phantom cat”; Lequontavious Jarmanious Jaquan Lamar Quandale Lapaix III for “The boy from Rosario”; Bianca Loiacano for “Series of haikus”; Cornelia Sollins for “I Hate It Just As Much As You”; Cornelia Sollins for “Ode to Pointe”; Miya Tsuji for “An Ode to Soccer Fields”; Destiny Albanese for “My Mother, My Father”; Skyler Bickmore for “The M&M Not Taken”; Arianna B. for “Ballad of Nicole Duennebier’s ‘Still Life With Meat Pile’”; Amy Cai for “MATH”; Sabela de Haro Borras for “Dichotomy”; Scarlett for “A Photo Of Us”; Claire Fitzgerald for “learning”; Riley E. Michael for “The Bathroom Girls”; JJ Niemann for “The Dreamer”; Colin Vellante for “Wood Doves.”

    The poetry contest is supported by the Friends of the Beverly Public Library; Joan Nelson; and all of the parents, teachers and school librarians who encouraged their students to enter. Further questions about the Annual Teen Poetry Contest or any of the library’s Teen events can be directed to Katie Nelson, the head of Teen Services, at knelson@noblenet.org.

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  • Trahan pushing to protect nonprofit hospitals

    Trahan pushing to protect nonprofit hospitals

    METHUEN — In the wake of ongoing issues with Steward Health Care System, the U.S. House of Representatives is looking to pass a bill to provide additional funding to “fill the gaps” for struggling community health systems, according to Rep. Lori Trahan, D-Westford.

    Trahan. D-Westford, introduced the Reinforcing Essential Health Systems for Communities Act with Rep. David Valadao, R-California, to provide more federal funding and support to the safety net hospitals.

    “Essential health systems serve the most vulnerable families in cities and towns across the nation, and these facilities deserve the funding and support necessary to maintain and expand their lifesaving services,” Trahan said.

    Trahan recently called out potentially “dangerous” outcomes with Steward Health Care’s system “private equity playbook,” which could affect her own delegation. She was also a signature with other reps to Steward Health Care System about possible closures, violations of Medicare rules and reports of missing payments.

    While Steward Health Care System announced it would not be closing Massachusetts hospitals, the effects could still be detrimental to patients.

    “Steward-owned hospitals would not be eligible for federal assistance through this designation because of their for-profit, private equity model,” Trahan said.

    “However, if Holy Family Hospital was sold to a nonprofit health system as part of the agreement that Steward recently announced but has provided no details on, the facility could then be eligible to receive additional federal funding and resources under this legislation to better support the patient population in the Merrimack Valley.”

    The act targets over 1,000 hospitals throughout the nation. Trahan said this would designate about 18 hospitals in Massachusetts as “essential health systems,” including Lowell General Hospital and Lawrence General Hospital.

    “Creating an essential health system designation acknowledges the vital role these systems play in improving the health, well-being of vulnerable populations that rely on them, and potentially reducing the disparities in their financial underpinnings,” said Abha Agrawal, president and CEO of Lawrence General Hospital.

    Lawrence General’s Dr. Eduardo Haddad shared staff concerns with Gov. Maura Healey and the Public Health Council on Wednesday about the news surrounding Steward Health Care System’s Holy Family Hospitals in Methuen and Haverhill, while stressing his hospital’s commitment to support patients in need.

    With the Essential Health Systems legislation, Trahan continues to work to support Merrimack Valley health care.

    “Private equity hospitals like Steward put profits over patients, and communities like Haverhill and Methuen are the ones who are forced to pay the price,” Trahan said.

    “This legislation is designed to deliver additional funding to nonprofit safety-net hospitals that are often forced to fill the gaps left when corporations like Steward move on.”

    Essential health systems often serve disproportionately higher numbers of Medicaid, low-income Medicare and uninsured patients.

    The hospitals often provide five times more uncompensated care compared to other hospitals, according to Trahan. Yet, they are historically underfunded and often limited in their ability to maintain and expand the critical health services they offer to patients, she added.

    “We must ensure hospitals in our rural and underserved communities have the resources they need to provide high-quality care,” said Valadao. “The Reinforcing Essential Health Systems for Communities Act will clearly identify the hospitals that serve our most vulnerable communities, allowing critical federal resources to be more easily directed toward them.”

    Hospitals qualify as “essential health systems” if they have a disproportionate patient percentage of Medicaid and low-income Medicare patients. The hospital could also serve a high percentage of Medicaid and low-income patients, or it could help capture the costs of care delivered to uninsured individuals.

    “Safety-net providers are vital to improving the health of our community and addressing the health needs of at-risk and medically underserved populations,” said Amy Hoey, president of Lowell General Hospital.

    Follow Monica on Twitter at @MonicaSager3

    Follow Monica on Twitter at @MonicaSager3

    By Monica Sager | msager@eagletribune.com

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  • Some mosquitoes like it hot

    Some mosquitoes like it hot

    Newswise — Certain populations of mosquitoes are more heat tolerant and better equipped to survive heat waves than others, according to new research from Washington University in St. Louis.

    This is bad news in a world where vector-borne diseases are an increasingly global health concern. Most models that scientists use to estimate vector-borne disease risk currently assume that mosquito heat tolerances do not vary. As a result, these models may underestimate mosquitoes’ ability to spread diseases in a warming world.

    Researchers led by Katie M. Westby, a senior scientist at Tyson Research Center, Washington University’s environmental field station, conducted a new study that measured the critical thermal maximum (CTmax), an organism’s upper thermal tolerance limit, of eight populations of the globally invasive tiger mosquito, Aedes albopictus. The tiger mosquito is a known vector for many viruses including West Nile, chikungunya and dengue.

    “We found significant differences across populations for both adults and larvae, and these differences were more pronounced for adults,” Westby said. The new study is published Jan. 8 in Frontiers in Ecology and Evolution.

    Westby’s team sampled mosquitoes from eight different populations spanning four climate zones across the eastern United States, including mosquitoes from locations in New Orleans; St. Augustine, Fla.; Huntsville, Ala.; Stillwater, Okla.; St. Louis; Urbana, Ill.; College Park, Md.; and Allegheny County, Pa.

    The scientists collected eggs in the wild and raised larvae from the different geographic locations to adult stages in the lab, tending the mosquito populations separately as they continued to breed and grow. The scientists then used adults and larvae from subsequent generations of these captive-raised mosquitoes in trials to determine CTmax values, ramping up air and water temperatures at a rate of 1 degree Celsius per minute using established research protocols.

    The team then tested the relationship between climatic variables measured near each population source and the CTmax of adults and larvae. The scientists found significant differences among the mosquito populations.

    The differences did not appear to follow a simple latitudinal or temperature-dependent pattern, but there were some important trends. Mosquito populations from locations with higher precipitation had higher CTmax values. Overall, the results reveal that mean and maximum seasonal temperatures, relative humidity and annual precipitation may all be important climatic factors in determining CTmax.

    “Larvae had significantly higher thermal limits than adults, and this likely results from different selection pressures for terrestrial adults and aquatic larvae,” said Benjamin Orlinick, first author of the paper and a former undergraduate research fellow at Tyson Research Center. “It appears that adult Ae. albopictus are experiencing temperatures closer to their CTmax than larvae, possibly explaining why there are more differences among adult populations.”

    “The overall trend is for increased heat tolerance with increasing precipitation,” Westby said. “It could be that wetter climates allow mosquitoes to endure hotter temperatures due to decreases in desiccation, as humidity and temperature are known to interact and influence mosquito survival.”

    Little is known about how different vector populations, like those of this kind of mosquito, are adapted to their local climate, nor the potential for vectors to adapt to a rapidly changing climate. This study is one of the few to consider the upper limits of survivability in high temperatures — akin to heat waves — as opposed to the limits imposed by cold winters.

    “Standing genetic variation in heat tolerance is necessary for organisms to adapt to higher temperatures,” Westby said. “That’s why it was important for us to experimentally determine if this mosquito exhibits variation before we can begin to test how, or if, it will adapt to a warmer world.”

    Future research in the lab aims to determine the upper limits that mosquitoes will seek out hosts for blood meals in the field, where they spend the hottest parts of the day when temperatures get above those thresholds, and if they are already adapting to higher temperatures. “Determining this is key to understanding how climate change will impact disease transmission in the real world,” Westby said. “Mosquitoes in the wild experience fluctuating daily temperatures and humidity that we cannot fully replicate in the lab.”

    Washington University in St. Louis

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  • Mathematical framework for evolutionary developmental dynamics (evo-devo).

    Mathematical framework for evolutionary developmental dynamics (evo-devo).

    Newswise — Natural selection acts on phenotypes constructed over development, which raises the question of how development affects evolution. Classic evolutionary theory indicates that development affects evolution by modulating the genetic covariation upon which selection acts, thus affecting genetic constraints. However, whether genetic constraints are relative, thus diverting adaptation from the direction of steepest fitness ascent, or absolute, thus blocking adaptation in certain directions, remains uncertain. This limits understanding of long-term evolution of developmentally constructed phenotypes. Here we formulate a general, tractable mathematical framework that integrates age progression, explicit development (i.e., the construction of the phenotype across life subject to developmental constraints), and evolutionary dynamics, thus describing the evolutionary and developmental (evo-devo) dynamics. .The framework yields simple equations that can be arranged in a layered structure that we call the evo-devo process, whereby five core elementary components generate all equations including those mechanistically describing genetic covariation and the evo-devo dynamics. The framework recovers evolutionary dynamic equations in gradient form and describes the evolution of genetic covariation from the evolution of genotype, phenotype, environment, and mutational covariation. This shows that genotypic and phenotypic evolution must be followed simultaneously to yield a dynamically sufficient description of long-term phenotypic evolution in gradient form, such that evolution described as the climbing of a fitness landscape occurs in “geno-phenotype” space. Genetic constraints in geno-phenotype space are necessarily absolute because the phenotype is related to the genotype by development. Thus, the long-term evolutionary dynamics of developed phenotypes is strongly non-standard: (1) evolutionary equilibria are either absent or infinite in number and depend on genetic covariation and hence on development; (2) developmental constraints determine the admissible evolutionary path and hence which evolutionary equilibria are admissible; and (3) evolutionary outcomes occur at admissible evolutionary equilibria, which do not generally occur at fitness landscape peaks in geno-phenotype space, but at peaks in the admissible evolutionary path where “total genotypic selection” vanishes if exogenous plastic response vanishes and mutational variation exists in all directions of genotype space. Hence, selection and development jointly define the evolutionary outcomes if absolute mutational constraints and exogenous plastic response are absent, rather than the outcomes being defined only by selection. Moreover, our framework provides formulas for the sensitivities of a recurrence and an alternative method to dynamic optimization (i.e., dynamic programming or optimal control) to identify evolutionary outcomes in models with developmentally dynamic traits. These results show that development has major evolutionary effects.

    University of St. Andrews

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  • Topology, Algebra, and Geometry Give Math Respect in Data Science

    Topology, Algebra, and Geometry Give Math Respect in Data Science

    By John Roach

    Newswise — In the computer vision field of object detection, deep learning models are trained to identify objects of interest within an image of a scene. For example, such models can be trained to detect viruses in microscopy images or pick out airplanes parked on tarmacs in overhead aerial imagery.

    “In many cases, like microscopy or overhead images, a user would want to ensure that the objects are found regardless of their orientation,” said Tegan Emerson, a senior data scientist and leader of the mathematics, statistics, and data science group at Pacific Northwest National Laboratory (PNNL). “However, this property is not inherent in all deep learning models.”

    In some cases, the deep learning model can pick out the airplanes with noses pointed north but fail to detect the airplanes pointed south, for instance.

    Emerson and her colleagues explored solutions to address this problem by applying the algebraic concept of group action to a deep learning model for object detection. Group action describes how things are changed under a collection of operations such as rotation. With these algebra-based architecture changes applied to the model, objects are more reliably detected in imagery no matter their orientation.

    “If you constrain the model to have this type of mathematical invariance to it, you’re able to maintain your ability to detect and appropriately identify the objects within your scene, which makes this a much more trustworthy tool for people to use,” Emerson said. “That matters in operational environments where a lot of our algorithms are going to be deployed.”

    Giving math respect in data science

    In recent years, mathematicians were pushed to the sidelines in data science disciplines as computer power and datasets used to train machine learning (ML) models grew exponentially and led to a step-change in capabilities such as artificial intelligence (AI) systems that can generate fluid prose in natural language, noted Timothy Doster, a senior data scientist at PNNL.

    “The mathematics community felt a little behind the time as massive amounts of funding went into these computer science fields,” he said. “But now they’re seeing research around explainability or dependability of these algorithms and that’s where math can really come in and address these areas.”

    In 2022, Doster, Emerson, and PNNL data scientist colleague Henry Kvinge co-founded the Topology, Algebra, and Geometry in Data Science (TAG-DS) community to help spur interest in the application of math to address specific topics in data science and ML.

    The community hosts workshops and conferences as well as provides publishing opportunities to drive awareness of mathematically principled solutions to data science problems. Most recently, the team hosted the second annual TAG in ML workshop at the International Conference on Machine Learning (ICML) on July 28, 2023, in Honolulu, Hawaii, and attracted more than 200 participants.

    Part of the interest in the TAG-DS community stems from the growing complexity of ML systems, which operate on high-dimensional, complex datasets using models that have thousands to billions of learnable parameters, noted Kvinge.

    “Such settings transcend human intuition which begins to quickly degrade beyond three dimensions,” he said. “Modern topology, algebra, and geometry were designed to allow mathematicians to understand exotic spaces, making them natural toolboxes to investigate when studying state-of-the-art machine learning.”

    Proof of math in data science

    In some cases, the application of math to data science can improve the rigor of AI models trained with massive datasets and computer power. For example, the mathematical study of symmetry, or representation theory, is used in some of the models capable of predicting how proteins fold and twist into their three-dimensional shapes, according to Kvinge.

    Protein folding models help scientists understand the structure of proteins, which are the building blocks of life—they are molecular machines that play a fundamental role in the structure, function, and regulation of nearly every biological process.

    “We know that how a protein folds should not depend on its location in space nor its orientation, and consequently a deep learning model should ignore these factors of variation when processing representations of proteins,” he explained. “Building model architectures can be done far more accurately when you understand how to capture the symmetries intrinsic to three-dimensional space.”

    In other cases, mathematics techniques can improve data used in more niche data science tasks such as using topological data analysis to extract shape-based features for ML models used to understand the structure and properties of materials such as the metal rods, tubes, and cubes that provide cars and trucks their shape, strength, and fuel economy.

    “Topology is the study of shape and there is a widely used quote from a leader in the field that states, ‘Data has shape, shape has meaning’ and what shape means for different formats of data can be nuanced,” noted Emerson.

    In one study, researchers applied topology to scanning electron microscopy images that were used to support research and development in advanced manufacturing. In this case, white precipitates, or solid materials, that formed during a metal manufacturing process were visible throughout the image. By looking at the topology of the precipitates at multiple threshold values, the team was able to capture physically meaningful features, summarize the information, and use it as input to the ML model.

    “Part of the difference in the paradigm for TAG-DS both at PNNL and in the scientific community is that you’re not just trying to train a model. What you’re trying to do is build a solution,” said Emerson. “You want something that actually addresses a need or a way to support a human who is involved in the processing pipeline.”

    Growing the TAG-DS community

    Engagement with the TAG-DS community has more than doubled in its first year of existence, according to Doster. For example, the TAG-ML workshop at ICML in 2022 had about 40 published submissions. This year’s workshop received more than 90 submissions and included four keynotes by world leaders in geometric and topological deep learning, two poster sessions, six spotlight talks, and other activities.

    Looking forward, the group is planning to host more workshops at computer science and mathematics conferences and is aiming to host a standalone TAG-DS conference in 2025.

    According to Emerson, the ability of TAG-DS to increase the rigor, trustworthiness, and explainability of AI systems will only grow in importance as technologies such as generative AI become widespread.

    “From a national laboratory’s perspective with our interest for the nation, but also for the average person in daily life, the mathematical rigor that the TAG-DS community can bring to understanding the ways these tools can support you, when they will work, how they will fail, and when they are not an appropriate technique to be using is critical,” she said.

    ###

    About PNNL

    Pacific Northwest National Laboratory draws on its distinguishing strengths in chemistry, Earth sciences, biology and data science to advance scientific knowledge and address challenges in sustainable energy and national security. Founded in 1965, PNNL is operated by Battelle for the Department of Energy’s Office of Science, which is the single largest supporter of basic research in the physical sciences in the United States. DOE’s Office of Science is working to address some of the most pressing challenges of our time. For more information, visit https://energy.gov/science. For more information on PNNL, visit PNNL’s News Center. Follow us on Twitter, Facebook, LinkedIn and Instagram.

    Pacific Northwest National Laboratory

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  • Scalise faces a key math problem as he struggles to collect 217 votes for speaker | CNN Politics

    Scalise faces a key math problem as he struggles to collect 217 votes for speaker | CNN Politics



    CNN
     — 

    Majority Leader Steve Scalise is scrambling to lock down the votes to become the next House speaker, but protracted opposition to the Louisiana Republican inside the GOP conference and the numerical realities of the narrowly divided chamber could ultimately derail his bid.

    Several senior Republicans see little path to 217 votes, after Scalise won just 113 votes in the GOP conference, which includes three delegates who don’t have a vote on the House floor. Making up that deficit in just a matter of days is an extremely tall order – plus a number of hard-right Republicans say they are dead-set against Scalise, when he can only afford to lose four GOP votes on the floor. At least 12 GOP lawmakers have said publicly they’ll oppose Scalise’s nomination and more have expressed frustration or skepticism about his leadership, more than enough to sink his bid.

    House GOP members will huddle behind closed doors Thursday afternoon, according to two sources familiar. No phones will be allowed in the meeting.

    Republicans are worried that Scalise is facing grim prospects of becoming speaker, an impasse that threatens to prolong the GOP’s leadership crisis that has left the House paralyzed and unable to move on any legislation.

    Late Wednesday, members of the conference were beginning to weigh how they would handle the potential collapse of his bid, with several GOP sources saying they believe they’d have to consider a new candidate who has yet to run for the speakership.

    Scalise spent Wednesday after the vote meeting individually with GOP members as he and his whip operation tried to convince the holdouts to come around, the sources said. He found some success in the outreach, but it’s not yet clear whether he can win over enough Republicans to overcome the razor-thin GOP House majority.

    Scalise or any other Republican candidate for speaker needs 217 votes to win the speaker’s gavel, a majority of the entire House, meaning they can only afford to lose four Republicans if every member is voting.

    Rep. Jim Jordan, who lost the vote for speaker to Scalise on Wednesday, 113-99, said Thursday he wants Republicans to unite around Scalise. “I do and I’ve been clear about that since yesterday,” Jordan said.

    But pressed on if he would rule out taking the job if Scalise can’t get there, Jordan didn’t give a clear answer. “I will nominate Steve on the floor and I hope we can unite around a speaker,” the Ohio Republican said.

    The opposition to Scalise inside his party has thrown into doubt how Republicans will get out of their speaker conundrum that’s left them simply unable to govern.

    While there was some belief on Capitol Hill that the brutal assault on Israel over the weekend might prompt Republicans to quickly select a leader – House lawmakers were given a classified briefing on Israel Wednesday before the conference vote for speaker – the deep divisions in the conference that led to Kevin McCarthy’s removal last week have now left the quest for a new speaker at a standstill.

    Anger inside the conference is rising.

    “These folks are destroying our conference and apparently want to be in the minority,” said Rep. Don Bacon, who represents a swing Nebraska district. “They don’t respect the customs of the House that have gone on for over two centuries.”

    The House gavels back in at noon Thursday, but there’s no indication Republicans will be ready to vote on a speaker.

    Scalise is facing broad skepticism inside the far-right House Freedom Caucus, a key bloc of Republicans who mostly supported the Trump-backed Jordan for speaker, multiple sources told CNN, citing a general lack of trust with Republican leadership. Scalise has been in leadership years, although he is more conservative than McCarthy.

    Jordan, who chairs the Judiciary Committee, threw his weight behind Scalise following Wednesday’s vote, saying he was encouraging his supporters to do the same. “We need a speaker and Steve is the guy for that. Like I said, I have offered to give a nominating speech for him,” the Ohio Republican told reporters Wednesday afternoon.

    But there was a cohort of lawmakers who expressed staunch opposition to voting for Scalise on the House floor.

    “Well, Leader Scalise won, and it’s not over. I’m still throwing my support behind Jim Jordan for speaker. I’m not going to change my vote now or any time soon on the House floor,” said GOP Rep. Max Miller of Ohio.

    Scalise’s individual outreach did peel off at least one holdout. Rep. Anna Paulina Luna, who initially said Wednesday that she would vote for Jordan on the floor, met with Scalise and said afterward she felt “comfortable” enough to support his speaker nomination.

    While she said he did not make specific commitments, he did assure her that he’ll allow her to “aggressively” do her job on the Oversight Committee, which is part of the impeachment inquiry into President Joe Biden.

    But Luna said she would only back Scalise for the speakership on the first ballot. If it went to multiple ballots, she said, “we must find a candidate” the conference can unite behind.

    Still, a number of Republicans don’t think that Jordan could be a viable alternative given that he lost to Scalise in the nominating contest, and some Republicans were irritated when he didn’t immediately close ranks behind Scalise.

    “If Scalise were not to make it, the next person got less votes,” Rep. Mario Diaz-Balart of Florida said of Jordan. “And by the way, I think, more controversial. So that would not be a good thing for this place.”

    Rep. Erin Houchin of Indiana said she doesn’t know if “it will be Jordan or Scalise or even someone else at this point. … I think we’re in uncharted territory, and it’s gonna be very hard to predict.”

    Another GOP member said that it would have to be a new candidate altogether, something that would take longer to sort out.

    “Steve is nowhere near 217,” said the Republican member.

    Leaving the floor without a vote Wednesday, interim Speaker Patrick McHenry tried to be optimistic the House GOP conference would solve the impasse soon.

    Asked if there could be a floor vote Thursday, the North Carolina Republican said, “That’s the hope.”

    Could anyone get the 217 votes required? He had the same response: “That’s the hope.”

    This story and headline have been updated to include additional developments.

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  • New tools for teachers to address math learning loss

    New tools for teachers to address math learning loss

    BYLINE: Molly Blancett

    Newswise — University of Oregon researchers have developed research-based programs to identify students who struggle with numbers in kindergarten, provide support at the whole-class level and equip families with home-based interventions. The new programs are needed to help youngsters who struggle with numbers. The pandemic compounded math learning loss and left many students further behind than their pre-pandemic peers.

    Those programs include:

    ROOTs: Interventions that start in kindergarten    

    The transition to kindergarten comes at a critical juncture. Missed foundational skills can cause learning problems to intensify and persist over time. To ensure all children are supported and able to start on an upward curve of learning math, UO researchers developed a program called ROOTS.

    The 50-lesson kindergarten program focuses on understanding and working with whole numbers and is designed to teach students at risk for difficulties in math.   

    “Our work focuses on developing programs that can be easily used by educators in the field to quickly intervene and provide critical math skills that enable all students to access the increasingly complex math content they encounter as they advance through school,” said Ben Clarke, professor of school psychology and director of the Center on Teaching and Learning in the College of Education.  

    ROOTS and its follow-up program, Fusion, which continues the work in first grade, have undergone rigorous trials in Massachusetts, Texas and Oregon. Results have been strong for a range of learners, especially students who enter school with the greatest level of risk and those learning English as a second language.    

    Whole-class interventions   

    Districts across the nation are struggling to meet the academic and behavioral needs of an increasingly high-needs student population. Jessica Turtura, research associate at the Center on Teaching and Learning, recently received a $4 million grant from the U.S. Department of Education to modify the ROOTs intervention to be delivered at the whole-class level.

     The whole-class intervention also will blend in techniques designed to teach students behaviors that will support long-term learning.     “The program will bridge the gap between effective early mathematics instruction and positive behavior support and provide an evidence-based approach for kindergarten teachers to comprehensively support the needs of students,” Turtura said.    

    Home-based interventions   

    Researchers also are extending the interventions to include a home-based component for students with physical and developmental disabilities. Children with such disabilities often enter school with lower mathematics skills compared to their typically developing peers and require supplemental support in mathematics. 

    “To date, many home-based math intervention studies have excluded children with disabilities,” said Gena Nelson, a research assistant professor in the Center on Teaching and Learning. “Our team is taking a unique approach to home-math interventions by engaging parents of young children with disabilities as co-designers of the activities. Our ultimate goal is to design home-based math activities that are feasible and accessible for all types of children and families.” 

    While many caregivers are comfortable in supporting early literacy skills, fewer realize that they can engage children in math activities as well. Targeted home interventions offer the opportunity for students to practice and extend the concepts they are learning in school and further build their foundation for a strong start in math. 

    This research was funded by the U.S. Department of Education and the National Science Foundation.

    About the College of Education   
    The College of Education at the University of Oregon is a community of leading researchers and practitioners dedicated to transformational scholarship, integrated teaching, and collaborative practice designed to enhance individual lives and systems. The College of Education is UO’s highest-ranking and largest research-contributing college known for its innovative teaching and research in special education, counseling psychology, human services, education, and prevention science. The college is a leader in culturally responsive Indigenous and bilingual teacher preparation programs as well as community-based research.  
    https://education.uoregon.edu/ 

    University of Oregon

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  • Making sense of life’s random rhythms

    Making sense of life’s random rhythms

    Newswise — CLEVELAND–Life’s random rhythms surround us–from the hypnotic, synchronized blinking of fireflies…to the back-and-forth motion of a child’s swing… to slight variations in the otherwise steady lub-dub of the human heart.

    But truly understanding those rhythms—called stochastic, or random, oscillations—has eluded scientists. While researchers and clinicians have some success in parsing brain waves and heartbeats, they’ve been unable to compare or catalogue an untold number of variations and sources.

    Gaining such insight into the underlying source of oscillations “could lead to advances in neural science, cardiac science and any number of different fields,” said Peter Thomas, a professor of applied mathematics at Case Western Reserve University.

    Thomas is part of an international team that says it has developed a novel, universal framework for comparing and contrasting oscillations–regardless of their different underlying mechanisms—which could become a critical step toward someday fully understanding them.

    Their findings were recently published in Proceedings of the National Academy of Sciences.

    “We turned the problem of comparing oscillators into a linear algebra problem,” Thomas said. “What we have done is vastly more precise than what was available before. It’s a major conceptual advance.”

    The researchers say others can now compare, better understand—and even manipulate—oscillators previously considered to have completely different properties.

    “If your heart cells aren’t synchronized, you die of atrial fibrillation,” Thomas said. “But if your brain cells synchronize too much, you have Parkinson’s disease, or epilepsy, depending on which part of the brain the synchronization occurs in. By using our new framework, that heart or brain scientist may be able to better understand what the oscillations could mean and how the heart or brain is working or changing over time.”

    Swaying skyscrapers and brain waves

    Thomas said the researchers—who included collaborators from universities in France, Germany and Spain—found a new way to use complex numbers to describe the timing of oscillators and how “noisy,” or imprecisely timed, they are.

    Most oscillations are irregular to some extent, Thomas said. For example, a heart rhythm is not 100% regular. A natural variation of 5-10% in the heartbeat is considered healthy. 

    Thomas said the problem with comparing oscillators can be illustrated by considering two markedly different examples: brain rhythms and swaying skyscrapers.

    “In San Francisco, modern skyscrapers sway in the wind, buffeted by randomly shifting air currents—they’re pushed slightly out of their vertical posture, but the mechanical properties of the structure pull them back,” he said. “This combination of flexibility and resilience helps high-rise buildings survive shaking during earthquakes. You wouldn’t think this process could be compared with brain waves, but our new formalism lets you compare them.”

    How their findings might help either discipline—mechanical engineering and neuroscience—may be unknown right now, Thomas said, comparing the conceptual advance to when Galileo discovered Jupiter’s orbiting moons.

    “What Galileo realized was a new point of view, and while our discovery is not as far-reaching as Galileo’s, it is similarly a change in perspective,” he said. “What we report in our paper is an entirely new point of view on stochastic oscillators.”

     

                ###

    Case Western Reserve University is one of the country’s leading private research institutions. Located in Cleveland, we offer a unique combination of forward-thinking educational opportunities in an inspiring cultural setting. Our leading-edge faculty engage in teaching and research in a collaborative, hands-on environment. Our nationally recognized programs include arts and sciences, dental medicine, engineering, law, management, medicine, nursing and social work. About 6,000 undergraduate and 6,300 graduate students comprise our student body. Visit case.edu to see how Case Western Reserve thinks beyond the possible.

     

     

     

    Case Western Reserve University

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  • Free energy principle predicts self-organized learning in neurons

    Free energy principle predicts self-organized learning in neurons

    Newswise — An international collaboration between researchers at the RIKEN Center for Brain Science (CBS) in Japan, the University of Tokyo, and University College London has demonstrated that self-organization of neurons as they “learn” follows a mathematical theory called the free energy principle. The principle accurately predicted how real neural networks spontaneously reorganize to distinguish incoming information, as well as how altering neural excitability can disrupt the process. The findings thus have implications for building animal-like artificial intelligences and for understanding cases of impaired learning. The study was published August 7 in Nature Communications.

    When we learn to tell the difference between voices, faces, or smells, networks of neurons in our brains automatically organize themselves so that they can distinguish between the different sources of incoming information. This process involves changing the strength of connections between neurons, and is the basis of all learning in the brain. Takuya Isomura from RIKEN CBS and his international colleagues recently predicted that this type of network self-organization follows the mathematical rules that define the free energy principle. In the new study, they put this hypothesis to the test in neurons taken from the brains of rat embryos and grown in a culture dish on top of a grid of tiny electrodes.

    Once you can distinguish two sensations, like voices, you will find that some of your neurons respond to one of the voices, while other neurons respond to the other voice. This is the result of neural network reorganization, which we call learning. In their culture experiment, the researchers mimicked this process by using the grid of electrodes beneath the neural network to stimulate the neurons in a specific pattern that mixed two separate hidden sources. After 100 training sessions, the neurons automatically became selective—some responding very strongly to source #1 and very weakly to source #2, and others responding in the reverse. Drugs that either raise or lower neuron excitability disrupted the learning process when added to the culture beforehand. This shows that the cultured neurons do just what neurons are thought to do in the working brain.

    The free energy principle states that this type of self-organization will follow a pattern that always minimizes the free energy in the system. To determine whether this principle is the guiding force behind neural network learning, the team used the real neural data to reverse engineer a predictive model based on it. Then, they fed the data from the first 10 electrode training sessions into the model and used it to make predictions about the next 90 sessions. At each step, the model accurately predicted the responses of neurons and the strength of connectivity between neurons. This means that simply knowing the initial state of the neurons is enough to determine how the network would change over time as learning occurred.

    “Our results suggest that the free-energy principle is the self-organizing principle of biological neural networks,” says Isomura. “It predicted how learning occurred upon receiving particular sensory inputs and how it was disrupted by alterations in network excitability induced by drugs.”

    “Although it will take some time, ultimately, our technique will allow modelling the circuit mechanisms of psychiatric disorders and the effects of drugs such as anxiolytics and psychedelics,” says Isomura. “Generic mechanisms for acquiring the predictive models can also be used to create next-generation artificial intelligences that learn as real neural networks do.”

    RIKEN

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  • New center merges math, AI to push frontiers of science

    New center merges math, AI to push frontiers of science

    Newswise — ITHACA, N.Y. — With artificial intelligence poised to assist in profound scientific discoveries that will change the world, Cornell is leading a new $11.3 million center focused on human-AI collaboration that uses mathematics as a common language.

    The Scientific Artificial Intelligence Center, or SciAI Center, is being launched with a grant from the Office of Naval Research and is led by Christopher J. Earls, professor of civil and environmental engineering at Cornell Engineering. Co-investigators include Nikolaos Bouklas, assistant professor of mechanical and aerospace engineering at Cornell Engineering; Anil Damle, assistant professor of computer science in the Cornell Ann S. Bowers College of Computing and Information Science; and Alex Townsend, associate professor of mathematics in the College of Arts and Sciences. All of the investigators are field faculty members of the Center for Applied Mathematics.

    With the advance of AI systems – built with tangled webs of algorithms and trained on increasingly large sets of data – researchers fear AI’s inner workings will provide little insight into its uncanny ability to recognize patterns in data and make scientific predictions. Earls described it as a situation at odds with true scientific discovery.

    “Scientific theories are explanatory stories that offer mechanistic insights into how the universe works,” Earls said. “These theories offer reasoning behind what has been observed, but also, they predict that which has yet to be observed. Such extrapolatory power is entirely beyond anything standard AI can achieve. Our new center will pioneer radically new AI approaches for scientific discovery.”

    The SciAI Center will use mathematics as a common language between humans and machines because, Townsend said, math is how scientists have modeled the world for hundreds of years.

    “Instead of getting AI to predict the future using data from a physical system, we will get AI to speak in the language of calculus and derive the underlying differential equations that govern a physical system,” Townsend said. “We are trying to develop an AI-human collaboration that can become our science teacher, revealing patterns of the natural world.”

    The SciAI Center will have four intellectual thrusts – scientific data, operator learning, closure models and complex systems. Its three application areas of focus will be materials, turbulence and autonomy.

    “By blending machine learning techniques with physics-informed algorithms, we can accelerate computational methods to aid in the understanding of materials and molecular systems,” said Damle, who added that Cornell’s fostering of interdisciplinary research makes it a natural home for such a center, enabling researchers from a broad set of areas to contribute.

    Aside from its research goals, the center will be committed to helping populations underrepresented in science and engineering gain access to emerging AI tools through a series of student pathway programs that prepare young researchers to work in new industries.

    Other institutions participating include the United States Naval Academy; the University of California, Santa Cruz; the California Institute of Technology; the University of Cambridge; Brown University; the University of California, Berkeley; and Integer Technologies.

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    Cornell University

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