sciencehabit shares a report from Science.org: Addition and subtraction must be hard for fish, especially because they don't have fingers to count on. But they can do it -- albeit with small numbers -- a new study reveals. By training the animals to use blue and yellow colors as codes for the commands "add one" and "subtract one," respectively, researchers showed fish have the capacity for simple arithmetic. To make the find, researchers at the University of Bonn adopted the design of a similar experiment conducted in bees. They focused on bony cichlids (Pseudotropheus zebra) and cartilaginous stingrays (Potamotrygon motoro), which the lab uses to study fish cognition. In the training phase, the scientists showed a fish in a tank an image of up to five squares, circles, and triangles that were all either blue or yellow. The animals had 5 seconds to memorize the number and color of the shapes; then a gate opened, and the fish had to choose between two doors: one with an additional shape and the other with one fewer shape. The rules were simple: If the shapes in the original image were blue, head for the door with one extra shape; if they were yellow, go for the door with one fewer. Choosing the correct door earned the fish a food reward: pellets for cichlids, and earthworms, shrimp, or mussels for stingrays. Only six of the eight cichlids and four of the eight stingrays successfully completed their training. But those that made it through testing performed well above chance, the researchers report today in Scientific Reports.

Read more of this story at Slashdot.

An anonymous Slashdot reader summarizes some important news from the web page of Jason Donenfeld (creator of the open-source VPN protocol WireGuard): The Linux kernel's random number generator has seen its first set of major improvements in over a decade, improving everything from the cryptography to the interface used. Not only does it finally retire SHA-1 in favor of BLAKE2s [in Linux kernel 5.17], but it also at long last unites '/dev/random' and '/dev/urandom' [in the upcoming Linux kernel 5.18], finally ending years of Slashdot banter and debate: The most significant outward-facing change is that /dev/random and /dev/urandom are now exactly the same thing, with no differences between them at all, thanks to their unification in random: block in /dev/urandom. This removes a significant age-old crypto footgun, already accomplished by other operating systems eons ago. [...] The upshot is that every Internet message board disagreement on /dev/random versus /dev/urandom has now been resolved by making everybody simultaneously right! Now, for the first time, these are both the right choice to make, in addition to getrandom(0); they all return the same bytes with the same semantics. There are only right choices. Phoronix adds: One exciting change to also note is the getrandom() system call may be a hell of a lot faster with the new kernel. The getrandom() call for obtaining random bytes is yielding much faster performance with the latest code in development. Intel's kernel test robot is seeing an 8450% improvement with the stress-ng getrandom() benchmark. Yes, an 8450% improvement.

Read more of this story at Slashdot.

Pamela Burdman, the executive director of Just Equations, a policy institute focused on the role of math in education equity, writes in an op-ed for Scientific American: All routes to STEM (science, technology, engineering and mathematics) degrees run through calculus classes. Each year, hundreds of thousands of college students take introductory calculus. But only a fraction ultimately complete a STEM degree, and research about why students abandon such degrees suggests that traditional calculus courses are one of the reasons. With scientific understanding and innovation increasingly central to solving 21st-century problems, this loss of talent is something society can ill afford. Math departments alone are unlikely to solve this dilemma. Several of the promising calculus reforms highlighted in our report Charting a New Course: Investigating Barriers on the Calculus Pathway to STEM , published with the California Education Learning Lab, were spearheaded by professors outside of math departments. It's time for STEM faculty to prioritize collaboration across disciplines to transform math classes from weed-out mechanisms to fertile terrain for cultivating a diverse generation of STEM researchers and professionals. This is not uncharted territory. In 2013, life sciences faculty at the University of California, Los Angeles, developed a two-course sequence that covers classic calculus topics such as the derivative and the integral, but emphasizes their application in a biological context. The professors used modeling of complex systems such as biological and physiological processes as a framework for teaching linear algebra and a starting point for teaching the basics of computer programming to support students' use of systems of differential equations. Creating this course, Mathematics for Life Scientists, wasn't easy. The life sciences faculty involved, none of whom had a joint appointment with the math department, said they resorted to designing the course themselves after math faculty rebuffed their overture. The math faculty feared creating a "watered-down" course with no textbook (though after the course was developed, one math instructor taught some sections of the class). Besides math, the life sciences faculty said they experienced "significant pushback" from the chemistry and physics departments over concerns that the course wouldn't adequately prepare students for required courses in those disciplines. But the UCLA course seems to be successful, and a textbook based on it now exists. According to recently published research led by UCLA education researchers, students in the new classes ended up with "significantly higher grades" in subsequent physics, chemistry and life sciences courses than students in the traditional calculus course, even when controlling for factors such as demographics, prior preparation and math grades. Students' interest in the subject doubled, according to surveys.

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Pi day is here — 3/14. And to celebrate, NASA released their ninth annual NASA Pi Day Challenge — "some math problems related to current and future NASA missions." MIT Bloggers released a videogame-themed video to welcome the class of 2026. If you Google "pi day" (or Pi), you're given an interactive doodle that (when you click the pi symbol in the upper-left) presents a Simon-like game challenging you to type in approximations of pi to an ever-increasingnumber of digits. Guinness World Records points out that the most accurate value of pi is 62,831,853,071,796 digits, "achieved by University of Applied Sciences (Switzerland) in Chur, Switzerland, on 19 August 2021." (Note: the number of digits looks suspiciously significant....) And USA Today published an article which shares the history of how Pi Day got started. Former physicist Larry Shaw, who connected March 14 with 3.14, celebrated the first Pi Day at the Exploratorium with fruit pies and tea in 1988. The museum said Shaw led Pi Day parades there every year until his passing in 2017. In 2009, the U.S. House of Representatives passed a resolution marking March 14 as National Pi Day. The date is significant in the world of science. Albert Einstein was born on this day in 1879. The Exploratorium said it added a celebration of Einstein's life as part of its Pi Day activities after Shaw's daughter, Sara, realized the coincidence. March 14 also marks the death of renowned theoretical physicist Stephen Hawking, who passed away in 2018. And "For those who don't enjoy math, you get pie," the article quips, noting that numerous pizza chains and restaurants are offering appropriately-adjusted one-day sale prices on pizza (and fruit) pies. Instacart has even released a list showing which pie flavors enjoy the highest popularity over the national average in each of America's 50 states. ("New York — Boston Cream Pie. Washington — Marionberry Pie....")

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As Ukrainian researchers have feared for their lives and careers after Russia's invasion of Ukraine, mathematicians have been grappling over what to do about a prominent mathematical conference that was set to be held in Saint Petersburg, Russia, in July. From a report: The International Congress of Mathematicians (ICM) is "the largest and most significant conference on pure and applied mathematics as well as one of the world's oldest scientific congresses," according to the Web site of the 2022 conference. The meeting, which is run by the Germany-based International Mathematical Union (IMU), is held only once every four years. When the nine-day 2018 ICM was held in Rio de Janeiro, Brazil, it drew 10,506 attendees. On Saturday conference organizers announced the event would be fully virtual and hosted outside of Russia this year. The executive committee of the meeting released a statement saying, "We strongly condemn the actions by Russia. Our deepest sympathy goes to our Ukrainian colleagues and the Ukrainian people. Given this situation, it is impossible for the IMU to host the ICM and the GA [general assembly] as traditional in-person events in Russia." The Fields Medal -- one of the most prestigious honors in mathematics -- is traditionally awarded at the event. According to the recent decision, this year's prize ceremony and general assembly will be held in person but at an undecided location outside of Russia.

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An anonymous reader shares a report: We often think of multiplication and division as calculations that need to be taught in school. But a large body of research suggests that, even before children begin formal education, they possess intuitive arithmetic abilities. A new study published in Frontiers in Human Neuroscience argues that this ability to do approximate calculations even extends to that most dreaded basic math problem -- true division -- with implications for how students are taught mathematical concepts in the future. The foundation for the study is the approximate number system (ANS), a well-established theory that says people (and even nonhuman primates) from an early age have an intuitive ability to compare and estimate large sets of objects without relying upon language or symbols. For instance, under this non-symbolic system, a child can recognize that a group of 20 dots is bigger than a group of four dots, even when the four dots take up more space on a page. The ability to make finer approximations -- say, 20 dots versus 17 dots -- improves into adulthood.

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joshuark shares a report from Popular Mechanics: A mathematician from Harvard University has (mostly) solved a 150-year-old Queen's gambit of sorts: the delightful n queens puzzle. In newly self-published research (meaning it has not yet been peer-reviewed), Michael Simkin, a postdoctoral fellow at Harvard's Center of Mathematical Sciences and Applications, estimated the solution to the thorny math problem, which is based loosely on the rules of chess. The queen is largely understood to be the most powerful piece on the board because she can move in any direction, including diagonals. So how many queens can fit on the chess board without falling into each other's paths? The logic at play here is similar to a sudoku puzzle, dotting queens on the board so that they don't intersect. Picture a classic chess board, which is an eight-by-eight matrix of squares. The most well-known version of the puzzle matches the board because it involves eight queens -- and there are 92 solutions in this case. But the "n queens problem" doesn't stop there; that's because its nature is asymptotic, meaning its answers approach an undefined value that reaches for the infinite. Up until now, experts have explicitly solved for all the natural numbers (the counting numbers) up to 27 queens in a 27-by-27 board. However, there is no solution for two or three, because there's no possible positioning of queens that satisfies the criteria. But what about numbers above 27? Consider this: for eight queens, there are just 92 solutions, but for 27 queens, there are over 200 quadrillion solutions. It's easy to see how solving the problem for numbers higher than 27 becomes extremely unwieldy or even impossible without more computing power than we have at the moment. That's where Simkin's work enters the arena. His work approached the topic through a sharp mathematical estimate of the number of solutions as n increases. Ultimately, he arrived at the following formula: (0.143n)n. In other words, there are approximately (0.143n)n ways that you can place the queens so that none are attacking one another on an n-by-n chessboard.

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A group of Brown University physicists has developed a technique that can potentially generate millions of random digits per second by harnessing the behavior of skyrmions -- tiny magnetic anomalies that arise in certain two-dimensional materials. Phys.Org reports: Their research, published in Nature Communications, reveals previously unexplored dynamics of single skyrmions, the researchers say. Discovered around a half-decade ago, skyrmions have sparked interest in physics as a path toward next-generation computing devices that take advantage of the magnetic properties of particles -- a field known as spintronics. [...] Skyrmions arise from the "spin" of electrons in ultra-thin materials. Spin can be thought of as the tiny magnetic moment of each electron, which points up, down or somewhere in between. Some two-dimensional materials, in their lowest energy states, have a property called perpendicular magnetic anisotropy -- meaning the spins of electrons all point in a direction perpendicular to the film. When these materials are excited with electricity or a magnetic field, some of the electron spins flip as the energy of the system rises. When that happens, the spins of surrounding electrons are perturbed to some extent, forming a magnetic whirlpool surrounding the flipped electron -- a skyrmion. Skyrmions, which are generally about 1 micrometer (a millionth of a meter) or smaller in diameter, behave a bit like a kind of particle, zipping across the material from side to side. And once they're formed, they're very difficult to get rid of. Because they're so robust, researchers are interested in using their movement to perform computations and to store data. This new study shows that in addition to the global movement of skyrmions across a material, the local behavior of individual skyrmions can also be useful. For the study, which was led by Brown postdoctoral fellow Kang Wang, the researchers fabricated magnetic thin films using a technique that produced subtle defects in the material's atomic lattice. When skyrmions form in the material, these defects, which the researchers call pinning centers, hold the skyrmions firmly in place rather than allowing them to move as they normally would. The researchers found that when a skyrmion is held in place, they fluctuate randomly in size. With one section of the skyrmion held tightly to one pinning center, the rest of the skyrmion jumps back and forth, wrapping around two nearby pinning centers, one closer and one farther away. The change in skyrmion size is measured through what's known as the anomalous Hall effect, which is a voltage that propagates across the material. This voltage is sensitive to the perpendicular component of electron spins. When the skyrmion size changes, the voltage changes to an extent that is easily measured. Those random voltage changes can be used to produce a string of random digits. The researchers estimate that by optimizing the defect-spacing in their device, they can produce as many as 10 million random digits per second, providing a new and highly efficient method of producing true random numbers.

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In 1992 John Conway raised a question about the patterns in his famous mathematical Game of Life: "Is there a Godlike still-life, one that can only have existed for all time (apart from things that don't interfere with it)?" Conway closed his note by adding "Well, I'm going out to get a hot dog now..." And then, nearly 30 years later, a mathematical blog reports: Ilkka Törmä and Ville Salo, a pair of researchers at the University of Turku in Finland, have found a finite configuration in Conway's Game of Life such that, if it occurs within a universe at time T, it must have existed in that same position at time T-1 (and therefore, by induction, at time 0)... The configuration was discovered by experimenting with finite patches of repeating 'agar' and using a SAT solver to check whether any of them possess this property. The blogger also shares some other Game of Life-related news: David Raucci discovered the first oscillator of period 38. The remaining unsolved periods are 19, 34, and 41.Darren Li has connected Charity Engine to Catagolue, providing approximately 2000 CPU cores of continuous effort and searching slightly more than 10^12 random initial configurations per day.Nathaniel Johnston and Dave Greene have published a book on Conway's Game of Life, featuring both the theoretical aspects and engineering that's been accomplished in the half-century since its conception. Unfortunately it was released slightly too early to include the Törmä-Salo result or Raucci's period-38 oscillator. Thanks to Slashdot reader joshuark for sharing the story.

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How many red and blue beads can you string together without making a big evenly spaced sequence of the same color? Using a semi-structured pattern of squashed circles, a mathematician shattered the previous record for how long you can keep stringing beads. From a report: The mathematician Ben Green of the University of Oxford has made a major stride toward understanding a nearly 100-year-old combinatorics problem, showing that a well-known recent conjecture is "not only wrong but spectacularly wrong," as Andrew Granville of the University of Montreal put it. The new paper shows how to create much longer disordered strings of colored beads than mathematicians had thought possible, extending a line of work from the 1940s that has found applications in many areas of computer science. The conjecture, formulated about 17 years ago by Ron Graham, one of the leading discrete mathematicians of the past half-century, concerns how many red and blue beads you can string together without creating any long sequences of evenly spaced beads of a single color. (You get to decide what "long" means for each color.) This problem is one of the oldest in Ramsey theory, which asks how large various mathematical objects can grow before pockets of order must emerge. The bead-stringing question is easy to state but deceptively difficult: For long strings there are just too many bead arrangements to try one by one.

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Slashdot reader DevNull127 writes: It's a newspaper puzzle that's like Sudoku, except it's impossible. [Sort of...] They call it "The Challenger" puzzle — but when the newspaper leaves out a crucial instruction, you can end up searching forever for a unique solution which doesn't exist! "If you're thinking 'This could be a 9 or an 8....' — you're right!" complains Lou Cabron. "Everyone's a winner today! Just start scribbling in numbers! And you'd be a fool to try to keep narrowing them down by, say, using your math and logic skills. A fool like me..." (Albeit a fool who once solved a Sudoku puzzle entirely in his head.) But two hours of frustration later — and one night of bad dreams — he's stumbled onto the web page of Dr. Robert J. Lopez, an emeritus math professor in Indiana, who's calculated that in fact Challenger puzzles can have up to 190 solutions... and there's more than one solution for more than 97% of them! At the end of the day, it becomes an appreciation for the local newspaper, and the puzzles they run next to the funnies. But with a friendly reminder "that they ought to honor and respect that love — by always providing the complete instructions."

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"A team of researchers has finally created a long-sought locally testable code that can immediately betray whether it's been corrupted..." reports Quanta magazine. "Many thought local testability would never be achieved in its ideal form." Now, in a preprint released on November 8, the computer scientist Irit Dinur of the Weizmann Institute of Science and four mathematicians, Shai Evra, Ron Livne, Alex Lubotzky and Shahar Mozes, all at the Hebrew University of Jerusalem, have found it. "It's one of the most remarkable phenomena that I know of in mathematics or computer science," said Tom Gur of the University of Warwick. "It's been the holy grail of an entire field." Their new technique transforms a message into a super-canary, an object that testifies to its health better than any other message yet known. Any corruption of significance that is buried anywhere in its superstructure becomes apparent from simple tests at a few spots. "This is not something that seems plausible," said Madhu Sudan of Harvard University. "This result suddenly says you can do it." Most prior methods for encoding data relied on randomness in some form. But for local testability, randomness could not help. Instead, the researchers had to devise a highly nonrandom graph structure entirely new to mathematics, which they based their new method on. It is both a theoretical curiosity and a practical advance in making information as resilient as possible.... To get a sense of what their graph looks like, imagine observing it from the inside, standing on a single edge. They construct their graph such that every edge has a fixed number of squares attached. Therefore, from your vantage point you'd feel as if you were looking out from the spine of a booklet. However, from the other three sides of the booklet's pages, you'd see the spines of new booklets branching from them as well. Booklets would keep branching out from each edge ad infinitum. "It's impossible to visualize. That's the whole point," said Lubotzky. "That's why it is so sophisticated...." [A] test at one node can reveal information about errors from far away nodes. By making use of higher dimensions, the graph is ultimately connected in ways that go beyond what we typically even think of as connections... It establishes a new state of the art for error-correcting codes, and it also marks the first substantial payoff from bringing the mathematics of high-dimensional expanders to bear on codes... Practical and theoretical applications should soon follow. Different forms of locally testable codes are now being used in decentralized finance, and an optimal version will allow even better decentralized tools.

Read more of this story at Slashdot.

あるAnonymous Coward 曰く、

朝日新聞の記事によると、NTTは、純粋数学のみを取り扱う新研究組織を設けたそうだ。

新組織「基礎数学研究センタ」は、神奈川県厚木市にある既存のNTTの研究所内に設けられ、若手研究者約15人で構成されるらしい。純粋数学のみを扱うのが特徴で、未解決問題にも取り組むようだ。企業が数学の研究所を設けるのは世界的にも珍しいそうだ。NTTは、研究結果を基に、新しい暗号方式の発明等、社会や経済を変える技術革新に繋げたいそうだ。

日本では基礎研究がないがしろにされているとしばしば指摘されているが、基礎研究の最たる純粋数学のみを研究対象とする組織の設置は今後に期待したいところだ。

すべて読む | サイエンスセクション | サイエンス | 教育 | 数学 |

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プログラミング言語を一つ学んだら別の言語も簡単に習得できるという考えは正しいのか？ 2021年06月29日

After decades of effort, mathematicians now have a complete understanding of the complicated equations that model the motion of free boundaries, like the one between ice and water.

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An anonymous reader quotes a report from Phys.Org: Researchers have developed a mathematical model that can predict the optimum exercise regime for building muscle. The researchers, from the University of Cambridge, used methods of theoretical biophysics to construct the model, which can tell how much a specific amount of exertion will cause a muscle to grow and how long it will take. The model could form the basis of a software product, where users could optimize their exercise regimes by entering a few details of their individual physiology. The results, reported in the Biophysical Journal, suggest that there is an optimal weight at which to do resistance training for each person and each muscle growth target. Muscles can only be near their maximal load for a very short time, and it is the load integrated over time which activates the cell signaling pathway that leads to synthesis of new muscle proteins. But below a certain value, the load is insufficient to cause much signaling, and exercise time would have to increase exponentially to compensate. The value of this critical load is likely to depend on the particular physiology of the individual. In 2018, the Cambridge researchers started a project on how the proteins in muscle filaments change under force. They found that main muscle constituents, actin and myosin, lack binding sites for signaling molecules, so it had to be the third-most abundant muscle component -- titin -- that was responsible for signaling the changes in applied force. Whenever part of a molecule is under tension for a sufficiently long time, it toggles into a different state, exposing a previously hidden region. If this region can then bind to a small molecule involved in cell signaling, it activates that molecule, generating a chemical signal chain. Titin is a giant protein, a large part of which is extended when a muscle is stretched, but a small part of the molecule is also under tension during muscle contraction. This part of titin contains the so-called titin kinase domain, which is the one that generates the chemical signal that affects muscle growth. The molecule will be more likely to open if it is under more force, or when kept under the same force for longer. Both conditions will increase the number of activated signaling molecules. These molecules then induce the synthesis of more messenger RNA, leading to production of new muscle proteins, and the cross-section of the muscle cell increases. This realization led to the current work. [The researchers] set out to constrict a mathematical model that could give quantitative predictions on muscle growth. They started with a simple model that kept track of titin molecules opening under force and starting the signaling cascade. They used microscopy data to determine the force-dependent probability that a titin kinase unit would open or close under force and activate a signaling molecule. They then made the model more complex by including additional information, such as metabolic energy exchange, as well as repetition length and recovery. The model was validated using past long-term studies on muscle hypertrophy. "Our model offers a physiological basis for the idea that muscle growth mainly occurs at 70% of the maximum load, which is the idea behind resistance training," said [one of the paper's authors]. "Below that, the opening rate of titin kinase drops precipitously and precludes mechanosensitive signaling from taking place. Above that, rapid exhaustion prevents a good outcome, which our model has quantitatively predicted." [...] The model also addresses the problem of muscle atrophy, which occurs during long periods of bed rest or for astronauts in microgravity, showing both how long can a muscle afford to remain inactive before starting to deteriorate, and what the optimal recovery regime could be.

Read more of this story at Slashdot.

円周率の世界記録が更新されたと16日に発表された。記録を更新したのはスイスのグラウビュンデン応用科学大学の研究チームによるもので、スーパーコンピューター1台を使って円周率を62兆8000億桁まで計算したとしている。計算には108日9時間を要したという。これまでの「最も正確な円周率の値」は50兆桁だったそう。なお最後の10桁は「7817924264」であるそうだ。同大学の説明によれば、円周率の計算に関しては、数兆桁の知識を得ること自体よりも、この数列を正確に計算できるようにする手法が重要であるとしている（グラウビュンデン応用科学大学リリース、グラウビュンデン応用科学大学の専門ページ、AFPBB News）。

すべて読む | サイエンスセクション | サイエンス | 数学 |

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OneHundredAndTen writes: Pi is now known to 62.8 trillion decimal digits. Motherboard adds: Researchers in Switzerland broke the world record for the most accurate value of pi over the weekend, the team announced on Monday. They calculated the first 62.8 trillion digits, surpassing the former record by 12.8 trillion decimal points. Calculation first started in late April at the Competence Center for Data Analysis, Visualization and Simulation (DAViS) at the University of Applied Sciences in Graubünden, Switzerland. The calculated data was then backed up onto the high-performance computer where a Y-cruncher wrote it into the hexadecimal notation. It was then converted into the decimal system and verified by a mathematical algorithm

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Long-time Slashdot reader Pieroxy is working on a new open source project, a web-based version of the system-monitoring software Conky. The ultimate goal is send the data to an HTML interface "to find some use for the old iPads/tablets/laptops we all have lying around. You can put them next to your screen and have your metrics displayed there...!" There's just one problem: "I had to come up with a way for users to format a number." I needed a small string the user could write to describe exactly what they want to do with their number. Some examples can be: write it as a 3-digit number suffixed by SI prefixes when the numbers are too big or too small, display a timestamp as HH:MM string, or just the day of week, eventually cut to the first three characters, do the same with a timestamp in milliseconds, or nanoseconds, display a nice string out of a number of seconds to express a duration ("3h 12mn 17s"), pad the number with spaces so that all numbers are aligned (left or right), force a fixed number of digits after the decimal point, etc. In other words, I was looking for a "universal" way of formatting numbers and failed to find any kind of standard online. Do Slashdot readers know of such a thing or should I create my own?

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An Australian mathematician has discovered what may be the oldest known example of applied geometry, on a 3,700-year-old Babylonian clay tablet. Known as Si.427, the tablet bears a field plan measuring the boundaries of some land. From a report: The tablet dates from the Old Babylonian period between 1900 and 1600 BCE and was discovered in the late 19th century in what is now Iraq. It had been housed in the Istanbul Archaeological Museum before Dr Daniel Mansfield from the University of New South Wales tracked it down. Mansfield and Norman Wildberger, an associate professor at UNSW, had previously identified another Babylonian tablet as containing the world's oldest and most accurate trigonometric table. At the time, they speculated the tablet was likely to have had some practical use, possibly in surveying or construction. That tablet, Plimpton 322, described right-angle triangles using Pythagorean triples: three whole numbers in which the sum of the squares of the first two equals the square of the third -- for example, 3^2 + 4^2 = 5^2.

Read more of this story at Slashdot.