There may be a mathematical reason why crossword puzzles seem to get easier as you solve them. Credit: Deposit Photos / Jordan FeegShareWhats a 11-letter concept shared by crossword puzzles and avalanches, and starts with the letter P? According to one physicist, the answer is simple: Percolation.When a statistical physicist looks at a partially solved crossword puzzle, she or he sees immediately a percolation problem: Is there a spanning path consisting of fully solved words? writes the University of Oldenburgs Alexander Hartmann in a recent paper published in Physical Review E.Percolation is ubiquitous in all fields of sciences like physics, mathematics, computer science, social sciences, or biology, he adds.Percolation, in this sense, relates to what is known as percolation theory. In mathematics and statistical physics, percolation theory concerns the behavior of a network model as additional points, nodes, or links are added to the overall system. At a certain point, these interconnected frameworks undergo a geometric version of a phase transition, suddenly becoming a much larger, new formation with novel properties.Think of it like a tea bag so saturated by water droplets that it begins to leak out of its mesh container, the snowflake that shifts a mound of frozen powder into an avalanche. Or, as Hartmann describes, the letters and words that suddenly make a formerly difficult crossword puzzle much easier to solve.Hartmann, a crossword fan, was recently curious if he could generate a single block of letters that created words in every direction, minus the puzzles trademark black spacer squares. He soon realized, however, that he was encountering a variation on a percolation problem. In mathematics and statistical physics, percolation theory concerns the behavior of a network model as additional points, nodes, or links are added to the overall system. Hartmann then devised percolation-based calculations to illustrate the concept.In the present work, crossword-puzzle percolation is introduced, where letters or words are occupied with independent or neighbor-dependent probabilities. In the model, letters correspond to sites and words to segments of sites, bordered by black sites, he explains. But Hartmann noticed something after graphing his crossword-centric formula. Get the Popular Science newsletter Breakthroughs, discoveries, and DIY tips sent every weekday. By signing up you agree to our Terms of Service and Privacy Policy.[I]t appears that crossword-puzzle percolation comprises a new type of universal behavior, he writes. This means Hartmanns new formula is unique among all other known percolation problems.The physicist theorizes one potential explanation may be that the uncertainty one feels while staring at a largely blank crossword puzzle changes as you make progress.Since solving a word leads to an increase of the probability of solving neighboring words, this leads to further iterations, i.e., avalanches of solving words, writes Hartmann.Hartmann believes this concept can be studied further to explore relations between these abstract phase transition concepts and their physical counterparts. In the meantime, crossword puzzlers can be comforted that physics now implies that as difficult a puzzle may seem, its often darkest before the dawn. All it often takes is one letter or word to bring a puzzle to its percolation point.

Nature, Published online: 08 January 2025; doi:10.1038/s41586-024-08391-zA foundation model learns transcriptional regulatory syntax from chromatin accessibility and sequence data across a range of cell types to predict gene expression and transcription factor interactions, with generalizability to unseen cell types.

Nature, Published online: 08 January 2025; doi:10.1038/d41586-024-03852-xArtificial intelligence is already used extensively to infer outcomes from tables of data, but this typically involves creating a model for each task. A one-size-fits-all model just made the process substantially easier.

Nature, Published online: 08 January 2025; doi:10.1038/d41586-024-04106-6Electrochemical reactions for organic synthesis typically require intricate, specialized equipment, slowing progress in this field. Minuscule electric generators now enable faster reaction discovery and development.

We'll be exploring the Vortex Solo's capabilities to determine its effectiveness for birding, outdoor activities and basic astronomy.

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Monkey Palace Lego Strategy Board Game $26 (was $40) See at Amazon See at Walmart Earlier this week, Amazon and Walmart dropped a limited-time deal on the new Lego board game, and now that deal is even better. The family-friendly strategy game Lego Monkey Palace is on sale for only $25.56, which is over 35% off its $40 list price. Considering the retailer says it has sold over 10,000 copies of Monkey Palace over the past month, we wouldn't be surprised if it sold out soon. The Lego Store recently sold through its stock at full price. Monkey Palace Lego Strategy Board Game $26 (was $40) Monkey Palace turns building Lego into a fast-paced and varied strategy game for 2-4 players. It isn't the first officially licensed Lego board game, but it is the only one still in print at the moment. Older Lego board games tend to sell for rather high prices, so it'd be wise to add Monkey Palace to your collection sooner rather than later. See at Amazon See at Walmart What happens when a monkey stumbles upon an ancient palace in the jungle but decides to redecorate their new home? The entire place collapses, of course, so now you and up to three other players need to rebuild the structure from scratch.To help the monkey live large again, humans take turns adding Lego pieces to makeshift staircases. Each piece is worth a certain number of Monkey Credits, which are exchanged for Monkey Cards. The Monkey Card you choose to play determines which brick type(s) you use to make and decorate the staircases. As you build, you rack up Banana Points, which are counted at the end of the game to determine the winner. Games last roughly 45 minutes.Continue Reading at GameSpot

As part its delay of Assassin's Creed Shadows, Ubisoft has announced that it's putting plans in place to pursue "various transformational strategic and capitalistic options" to help put itself in the best possible financial situation. Ubisoft said it has appointed an advisory team to do this.Ubisoft said it will continue to "drive significant cost reductions" as part of this plan, though the company did not say if more layoffs are coming. Ubisoft added that it will take a "highly selective approach to investments" during this period. In total, Ubisoft said it expects to see a reduction of 200 million ($206 million USD) as part of this plan.Looking ahead, Ubisoft said it expects Q3 FY2024-25 revenue to be less than what it originally forecast, due in part to lower-than-expected game sales during the holiday, mainly due to an underperformance of Star Wars Outlaws. The downturn is also attributed in part to the discontinuation of XDefiant. Continue Reading at GameSpot

Ubisoft has delayed Assassin's Creed Shadows once again, moving the game from its planned February 14 launch date to March 20. Ubisoft says that it made the decision to provide an additional month of development to Assassin's Creed Shadows as part of its "renewed focus" on gameplay quality."This additional time will allow the team to better incorporate the player feedback gathered over the past three months and help create the best conditions for launch by continuing to engage closely with the increasingly positive Assassins Creed community," Ubisoft explained in a press release. Interestingly, this new date pushes Assassin's Creed Shadows almost out of Ubisoft's current financial year, which ends on March 31. With the company reportedly in talks with Tencent and other financial partners to potentially fund a "management-led buyout," poor sales of the game could potentially hurt the value of its share prices. In a financial call following news of the delay, Ubisoft declined to comment on the Tencent reports but it did mention that it is "exploring different options," adding, "We can't say more."Continue Reading at GameSpot

The acclaimed 2016 action RPG Hyper Light Drifter won players over with its visual style, compelling themes and storytelling, and striking audio. Developer Heart Machine is looking to deliver this experience all over again with Hyper Light Breaker, which launches in Early Access in just a few days. Hyper Light Breaker is very different from Hyper Light Drifter, however, transitioning to 3D, opting for open-world roguelike gameplay, and otherwise going further back in its lore.