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Li and his colleagues measured their sample’s resistivity, and found no sign of superconductivity. But they couldn’t explain the sharp resistivity drop seen by the South Korean team. Perfect Solved play can be generalized to non-perfect information games, as the strategy that would guarantee the highest minimal expected outcome regardless of the strategy of the opponent.

Imagine everyone in your network or even outside of it could be seamlessly connected, work and provide opportunities for each other in one online tool. An essential round-up of science news, opinion and analysis, delivered to your inbox every weekday. For Leslie Schoop, a solid-state chemist at Princeton University in New Jersey, who co-authored the flat-bands study, the lesson about premature calculations is clear. “Even before LK-99, I have been giving talks about how you need to be careful with DFT, and now I have the best story ever for my next summer school,” she says.

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Multiple unverified videos of LK-99 levitating subsequently circulated on social media, but none of the researchers who initially tried to replicate the findings observed any levitation. Whether a game is solved is not necessarily the same as whether it remains interesting for humans to play. Even a strongly solved game can still be interesting if its solution is too complex to be memorized; conversely, a weakly solved game may lose its attraction if the winning strategy is simple enough to remember (e.g., Maharajah and the Sepoys).

The researchers tested two samples — the first heated in a vacuum, which resulted in 5% Cu2S content, and the second in air, which gave 70% Cu2S content. On 7 August, the Peking University team reported3 that this “half-levitation” appeared in its own LK-99 samples because of ferromagnetism. “It’s exactly like an iron-filing experiment,” says team member Yuan Li, a condensed-matter physicist. The pellet experiences a lifting force, but it’s not enough for it to levitate — only for it to balance on one end. Perhaps the most striking evidence for LK-99’s superconductivity was a video taken by the South Korean team that showed a coin-shaped sample of silvery material wobbling over a magnet. The researchers said that the sample was levitating because of the Meissner effect — a hallmark of superconductivity in which a material expels magnetic fields.

Initial theoretical attempts using an approach called density functional theory (DFT) to predict LK-99’s structure had hinted at interesting electronic signatures known as flat bands. But these calculations were based on unverified assumptions about LK-99’s structure. By contrast, “strong” proofs often proceed by brute force—using a computer to exhaustively search a game tree to figure out what would happen if perfect play were realized. The resulting proof gives an optimal strategy for every possible position on the board. However, these proofs are not as helpful in understanding deeper reasons why some games are solvable as a draw, and other, seemingly very similar games are solvable as a win. For every one part that it makes of copper-doped lead phosphate crystal — pure LK-99 — it produces 17 parts copper and 5 parts sulfur.

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As an example, a perfect player in a drawn position would always get a draw or win, never a loss. If there are multiple options with the same outcome, perfect play is sometimes considered the fastest method leading to a good result, or the slowest method leading to a bad result. The conclusion dashes hopes that LK-99 — a compound of copper, lead, phosphorus and oxygen — would prove to be the first superconductor that works at room temperature and ambient pressure.

• But these calculations were based on unverified assumptions about LK-99’s structure.
• The pellet experiences a lifting force, but it’s not enough for it to levitate — only for it to balance on one end.
• Multiple unverified videos of LK-99 levitating subsequently circulated on social media, but none of the researchers who initially tried to replicate the findings observed any levitation.
• If there are multiple options with the same outcome, perfect play is sometimes considered the fastest method leading to a good result, or the slowest method leading to a bad result.

Jain points to the importance of old, often overlooked data — the crucial measurements that he relied on for the resistivity of Cu2S were published in 1951. Clearly, the innocent eyes of children can sometimes see possibilities that even the most learned scientists cannot. In 2004, she saw an interview with Roger Mason where he discussed his story of the fossil’s discovery. In 2007, Negus was invited to celebrate the 50th anniversary of the plant’s identification, where she was finally included as a co-discoverer. Thanks to the discovery of Charnia, as well as improved dating techniques, paleontologists around the world were finally able to look at old fossils with new eyes. Lifeforms that were once assumed to live in the Cambrian were now turning out to be much older.

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But the second sample’s resistivity plunged near 112 ºC (385 K) — closely matching the South Korean team’s observations. Given the rules of any two-person game with a finite number of positions, one can always trivially construct a minimax algorithm that would exhaustively traverse the game tree. Many algorithms rely on a huge pre-generated database and are effectively nothing more. Jain, a copper-sulfide specialist, remembered 104 ºC as the temperature at which Cu2S undergoes a phase transition. Below that temperature, the resistivity of air-exposed Cu2S drops dramatically — a signal almost identical to LK-99’s purported superconducting phase transition. “I was almost in disbelief that they missed it,” says Jain, who published a preprint7 on the important confounding effect.

While additional murders took place in the area in the years following 1888, they were never conclusively linked back to the original summer-of-1888 investigation, leading some to believe that Jack the Ripper’s killing spree only lasted one summer. The end of that summer matches when Hyams was scooped up by police for his degrading mental state, and later moved to the Colney Hatch Lunatic Asylum in North London. She also used his violent history, location of his work and home, medical records, and even police interactions to fill in details.

A few months after Ford published his findings, for instance, scientists in Australia published a discovery of another Charnia frond from the Precambrian. A year later, in 1957, three teenage boys were playing near the same rock face when they, too, noticed the same fossil. One of these teens, fifteen-year-old Roger Mason, took a pencil rubbing of the impression so that his father could pass along the design to a local university lecturer. But as a budding geologist, Negus knew these 600 million year old rocks were too old to host such a plant. According to the established fossil record, the first complex species of flora wouldn’t appear for at least another sixty million years, following the event known as the Cambrian explosion. IPG Health is home to the world’s most celebrated and awarded health marketing agencies.

In game theory, perfect play is the behavior or strategy of a player that leads to the best possible outcome for that player regardless of the response by the opponent. Perfect play for a game is known when the game is solved.[1] Based on the rules of a game, every possible final position can be evaluated (as a win, loss or draw). By backward reasoning, one can recursively evaluate a non-final position as identical to the position that is one move away and best valued for the player whose move it is. Thus a transition between positions can never result in a better evaluation for the moving player, and a perfect move in a position would be a transition between positions that are equally evaluated.

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Tangentially, she also found that she herself was related to an original officer on the case during her Jack the Ripper research. There are several actions that could trigger this block including submitting a certain word or phrase, a SQL command or malformed data. As evidence of complex life prior to the Cambrian explosion, it was everything Darwin and his successors had been searching for. Many researchers are reflecting on what they’ve learnt from the summer’s superconductivity sensation. Several red flags popped out to Derrick VanGennep, a former condensed-matter researcher at Harvard University in Cambridge, Massachusetts, who now works in finance but was intrigued by LK-99.

An ultra-weak solution (e.g., Chomp or Hex on a sufficiently large board) generally does not affect playability. Making conclusive statements about LK-99’s properties is difficult, because the material is unpredictable and samples contain varying impurities. “Even from our own growth, different batches will be slightly different,” says Li. But he argues that samples that are close enough to the original are sufficient for checking whether LK-99 is a superconductor in ambient conditions. The first sample’s resistivity increased smoothly as it cooled, as did samples from other replication attempts.

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A video made by VanGennep shows that his disc — made of non-superconducting, ferromagnetic materials — mimicked LK-99’s behaviour. All previously confirmed superconductors function only at very low temperatures and extreme pressures. Scientific detective work has unearthed evidence that the material is not a superconductor, and clarified its actual properties.

Although some commentators have pointed to the LK-99 saga as a model for reproducibility in science, others say that it involved an unusually swift resolution of a high-profile puzzle. “Often these things die this very slow death, where it’s just the rumours and nobody can reproduce it,” says Fuhrer. Today, scientists have found a variety of Precambrian life forms in England, Australia, North America, Greenland, South Africa, parts of Asia, and Russia. Like Negus, it turns out that several other people had noticed similar fossils in the past, although they had been ignored by the scientific establishment.

Half-baked levitation

A solved game is a game whose outcome (win, lose or draw) can be correctly predicted from any position, assuming that both players play perfectly. This concept is usually applied to abstract strategy games, and especially to games with full information and no element of chance;
solving such a game may use combinatorial game theory and/or computer assistance. To better understand the material, the US–European group5 performed precision X-ray imaging of its samples to calculate LK-99’s structure.

• For every one part that it makes of copper-doped lead phosphate crystal — pure LK-99 — it produces 17 parts copper and 5 parts sulfur.
• One of these teens, fifteen-year-old Roger Mason, took a pencil rubbing of the impression so that his father could pass along the design to a local university lecturer.
• While additional murders took place in the area in the years following 1888, they were never conclusively linked back to the original summer-of-1888 investigation, leading some to believe that Jack the Ripper’s killing spree only lasted one summer.
• A solved game is a game whose outcome (win, lose or draw) can be correctly predicted from any position, assuming that both players play perfectly.
• On 7 August, the Peking University team reported3 that this “half-levitation” appeared in its own LK-99 samples because of ferromagnetism.

As part of IPG Health’s collective of over 45 agencies and 6,000+ people across six continents, SOLVE(D) is able to offer a seamless, integrated offering to both new and existing clients across the network. “During the most difficult period of the pandemic, our goal, after securing urgent needs, was to create an aid application that can work in the long term and where donors can connect with applicants. Today, the Solved Together platform helps to connect people who have never met before and provide targeted assistance where it is needed. Together with Solved, we created an application using their platform helping Slovakia today.” The opportunity to set-up our platform super-quickly is a testament to its functional nature and purpose.

In the video, one edge of the sample seemed to stick to the magnet, and it seemed delicately balanced. By contrast, superconductors that levitate over magnets can be spun and even held upside down. “None of those behaviours look like what we see in the LK-99 videos,” VanGennep says. The only further confirmation would come from the South Korean team sharing its samples, says Michael Fuhrer, a physicist at Monash University in Melbourne, Australia.