Kremlin spokesman Dmitry Peskov said the exhibition was a &;quot;brilliant idea&;quot;

I don't know what's cooler ... this &;quot;cosmic&;quot; idea or the name &;quot;Tri-City Chili Peppers&;quot;

'We are not running daycare centers at our universities‚ we’re running universities'

'export and import transactions related to Israel have been stopped‚ covering all products'

A new study conducted by Pet Range‚ an online pet store‚ reveals the 10 popular human food that are affecting our dogs weight negatively.

The 'Two State' Solution Is Insane

The European Space Agency’s Solar Orbiter has observed the incredible behavior in the Sun’s lower atmosphere like never before. The Sun's corona is an ever-changing landscape with a range of fascinating features‚ from &;quot;moss&;quot; to &;quot;rain&;quot;. The new footage is providing a front seat to the currently active Sun.In previous videos of the Sun‚ we have seen spectacular eruptions release huge quantities of particles out into the Solar System. In September last year‚ Solar Orbiter spotted a more modest eruption – although it was still taller than our whole planet – as well as coronal moss‚ coronal rain‚ and spicules all in amazing detail‚ which has just been released.                         So‚ what are we looking at in this video&;#63;On the solar horizon we can see spicules‚ spires of plasma that reach up from the chromosphere into the solar corona above. They extend up to 10‚000 kilometers (6‚200 miles) into the higher levels of the solar atmosphere. We can also see coronal &;quot;moss&;quot;‚ lace-like patterns of plasma found at the base of coronal loops‚ the arch-like structures seen extending well above the surface of the Sun.Those loops create another effect: coronal rain. The loops are very bright because they are very hot‚ around 1 million °C. Some of the plasma cools and‚ thanks to gravity‚ comes back down in darker high-density clumps known as &;quot;rain&;quot;. These clumps are still hot but less scorching at probably less than 10‚000 °C (18‚000 °F). They are easier to see as they are much darker than the intensely hot coronal loops. This is the Sun in extreme ultraviolet.Solar Orbiter took the video on September 27‚ 2023. Just a few days later‚ on October 7‚ it was at its closest distance from the Sun: 43 million kilometers (26.7 million miles). That’s less than one-third of the Earth-Sun distance. On the same day the video was taken‚ NASA’s Parker Solar Probe was just 7.26 million kilometers (4.51 million miles) from the Sun‚ so the space agencies teamed up. Parker measures the particles and magnetic field in the Sun's corona and the solar wind‚ so Solar Orbiter observed the region from where the solar wind came to flow past Parker. Together‚ the spacecrafts are providing important insights into the Sun and how it works.

We live in (or at least‚ perceive‚ with various branches of string theory including up to 26 dimensions) a universe with three dimensions (plus time)‚ and there are reasons to suspect why we find ourselves in a 3D world. Scientists and mathematicians have suggested universes with more than three dimensions would be unpredictable and unstable &;quot;dead worlds&;quot; devoid of all life and observers. The three body problem is unpredictable in a 3D world‚ but even a two body problem – describing and predicting the orbit of two bodies – becomes too chaotic in higher dimensions‚ and no stable orbits are possible. &;quot;This means that such a world cannot contain any objects that are stable over time‚&;quot; one paper on the topic explains‚ &;quot;and thus probably cannot contain stable observers&;quot;.&;quot;In a space with more than three dimensions‚ there can be no traditional atoms and perhaps no stable structures‚&;quot; the paper adds.As such‚ we should not be surprised that we find ourselves in a 3D (plus time) universe – you can only live in universes where life is possible. There are suggestions that life could not take place in a 2D (plus time) universe‚ meanwhile‚ because of insufficient complexity. The main argument‚ which would make 2D universes a non-starter‚ is that two-dimensional universes would not allow for gravity‚ making the complex mix required for life impossible.But that may not be the case‚ according to physicist James Scargill. In a 2020 paper‚ Scargill showed that scalar gravitational fields could exist in two dimensions.     &;quot;I have presented a purely scalar theory of gravity which allows stable orbits around point sources‚ and has a not-obviously-fatal (though unusual) cosmology; it could potentially be improved by making the whole metric dynamical‚&;quot; Scargill writes in the paper. &;quot;One could also imagine a brane-world scenario in which the massless graviton is not localized to the brane‚ thus allowing two-dimensional life to enjoy fully four-dimensional gravity.&;quot;Gravity and stable orbits are not the only requirements for life – or‚ more important when you are using anthropic reasoning to explain why we are in a 3D universe‚ for observers to exist. For instance‚ you could not have a digestive tract in an animal (at least not the kind we are used to) as it would split the organism in two. Scargill went on to look at whether a 2D universe (again‚ plus time) would be sufficiently complex to allow for complex life. In the paper‚ he looked at biological networks and created planar graphs which &;quot;seem to exhibit many of the properties which have been conjectured to be important for complex brains.&;quot; This‚ he writes‚ is suggestive that complex brains could exist in two dimensions‚ though more work would be needed to compare the planar graphs to real-world neural networks.&;quot;In particular‚ they are approximately ‘small-world‚’&;quot; he added‚ &;quot;they have a hierarchical and modular construction‚ and they show evidence of the stretching (in parameter space) of a critical point into a finite critical region for certain stochastic processes.&;quot;This is‚ of course‚ highly hypothetical‚ and more of a thought exercise than saying life in 2D universes is real. But it puts a bit of a constraint on arguments that we experience a 3D world because it is the only type that could sustain life‚ because – perhaps – life in 2D could be possible as well.The paper is published in Physical Research Review.

Check out the latest futuristic offering from the Defense Advanced Research Projects Agency‚ otherwise known as DARPA. From the people who brought you hypersonic air-breathing weapons‚ submarine-detecting shrimp‚ and robot jazz musicians comes a massive manta ray-inspired uncrewed submarine. Constructed by Northrop Grumman‚ the prototype just completed its first in-water test.The sub has been devised to carry large payloads over long distances underwater‚ with no humans onboard for support. During deployment‚ it can spend periods of time in “hibernation”‚ anchored to the seabed to conserve energy.When the project was announced in 2022‚ Northrop Grumman wrote that their design would be in service of DARPA’s vision to create “strategic surprise.” We think they can safely say they’ve achieved that goal.DARPA recently announced that a full-scale test of the prototype uncrewed underwater vehicle (UUV) had taken place off the coast of Southern California in February and March of this year.“Our successful‚ full-scale Manta Ray testing validates the vehicle’s readiness to advance toward real-world operations after being rapidly assembled in the field from modular subsections‚” said Dr Kyle Woerner‚ DARPA program manager for Manta Ray‚ in a statement. “The combination of cross-country modular transportation‚ in-field assembly‚ and subsequent deployment demonstrates a first-of-kind capability for an extra-large UUV.”That “extra-large” is about as detailed as we can get right now. New Atlas notes that DARPA and Northrop Grumman have so far kept most of the technical specifications of the craft to themselves‚ speculating that images released online appear to show shrouded propulsors‚ an antenna‚ water inlets‚ and possibly maneuvering thrusters.From the images we can get some sense of scale and see that its smooth contours really do resemble its namesake animal - and maybe the odd sci-fi creation too.  IFLScience is not responsible for content shared from external sites.There are hundreds of different species of manta rays found in waters across the globe. They’re sociable and intelligent creatures‚ with numerous reports of them seeming to interact with divers and snorkelers. But it was the manta rays’ graceful locomotion that really inspired the engineers behind the new UUV‚ continuing a long tradition of bioinspired design.“Once deployed‚ the vehicle uses efficient‚ buoyancy-driven gliding to move through the water‚” said Woerner.Dr Kyle Woerner (right) chats with a member of the Northrop Grumman team on top of Manta Ray.Image credit: DARPAAnother key advantage of the Manta Ray UUV‚ as highlighted both by DARPA and Northrop Grumman‚ is that it can be shipped in pieces and rapidly reassembled on-site. This is how the prototype was transported from the build location in Maryland to the opposite side of the country and could also be handy in the field.“Shipping the vehicle directly to its intended area of operation conserves energy that the vehicle would otherwise expend during transit‚” Woerner explained. DARPA says it’s currently working with the US Navy on the next steps for this technology – we’ll have to wait to find out when Manta Ray might be taking to the water for real.

For most of us here in the 21st century‚ our memories of learning the times tables have become something of a running joke. “You won’t have a calculator in your pocket every day as an adult‚” we were warned – well‚ shows what you know‚ Mrs Hickinbottom; these days‚ virtually 100 percent of us have not just a calculator in our pocket‚ but access to the entirety of collected human knowledge so far.Mathematicians and computer scientists‚ though‚ are not most people. Ever since at least the early 19th century‚ there’s been a new kind of multiplication in town: matrix multiplication – and even today‚ with all our technological prowess‚ it’s a real ballache.But does it have to be&;#63; A pair of new results – one from November 2023‚ and a second which was published in January – hint that the answer is “no” – or at least‚ “not as much as we previously thought.” The problems with matrix multiplicationSo‚ first question: what actually is a matrix&;#63; Unfortunately‚ the answer is way less cool than the movie adaptation made it seem.Put simply‚ a matrix is just a rectangular array of numbers – or other mathematical objects like symbols or expressions or even other matrices‚ because sometimes we all feel a bit masochistic – arranged in rows and columns. They have a really wide range of uses in math and science‚ so being able to manipulate them is… well‚ pretty important.A matrix.Image Credit: IFLScienceNow‚ multiply two matrices together‚ and you’ll get another matrix – so long as a few stipulations are satisfied. First of all‚ you can only multiply two matrices together if the number of columns in the left matrix is the same as the number of rows in the right matrix‚ like this:Two matrix multiplication problems.Image Credit: IFLScienceGetting that right is important because‚ unlike normal multiplication‚ the matrix operation is not commutative – that is to say‚ order matters. Given two matrices A and B‚ it’s completely possible that you might be able to work out the matrix product AB but not BA; even if both are possible‚ there’s no particular reason that they would give the same answer.Two matrix products showing the noncommutativity of matrix multiplication.Image Credit: IFLScienceSo‚ once we’ve got all these requirements out of the way‚ how do we actually go about finding the product of two matrices&;#63; In mathematical notation‚ the answer looks like this:Easy peasy.Image Credit: IFLScienceWhich‚ we admit‚ may not actually be too helpful. So let’s look at an example.First row‚ first column; first row‚ second column; second row‚ first column; second row‚ second column. It's much more complicated after 2-by-2 matrices though.Image Credit: IFLScienceYou might be getting the idea by now that matrix multiplication involves a lot more work than regular multiplication – and you’d be completely right. That’s one reason why having a computer program that could do it all for us would be such a boon – except as it turns out‚ even that is a problem.The slow march of progress“Ever since the dawn of the computer age‚ researchers have been trying to find an optimal way of multiplying matrices‚ a fundamental operation that is a bottleneck for many important algorithms‚” explained Sara Robinson for SIAM News in an article on the problem from 2005. “Faster matrix multiplication would give more efficient algorithms for many standard linear algebra problems‚ such as inverting matrices‚ solving systems of linear equations‚ and finding determinants‚” the article continues. “Even some basic graph algorithms run only as fast as matrix multiplication.”So the question becomes: just how fast is that&;#63; And the answer‚ sadly‚ is “not all that fast at all‚ historically.” Given a couple of matrices with‚ say 100 rows and columns each‚ you’ll need to perform 1‚000‚000 multiplications to find their product – and that number increases cubically‚ not linearly. In other words: increase those matrices by just a single row and column‚ and the number of multiplications needed to solve the problem goes up by more than 30‚000.Now‚ that’s not to say we can’t do it faster – and indeed‚ quite a lot of research has gone into figuring out ways to do so over the years. Most experts in the field think we’ll eventually top out at quadratic time: that it should be possible to multiply a pair of 100-by-100 matrices using 10‚000 steps‚ but not fewer. But exactly how to achieve that is still a major open problem in computer science.“The point of this work‚” Renfei Zhou‚ theoretical computer science student at Tsinghua University and co-author on the new papers‚ told Quanta Magazine earlier this year‚ “is to see how close to two you can come‚ and whether it can be achieved in theory.”We’ve made some headway. Since 1969‚ when mathematician Volker Strassen made the first inroad into a more efficient algorithm for matrix multiplication‚ that time exponent has gone from three down to below 2.4 – or to put it another way‚ requiring fewer than 64‚000 calculations to multiply those 100-by-100 matrices together. But it’s been tough going – and since the late eighties‚ improvements have been “small and […] extremely difficult to obtain‚” Nagoya University computer scientist Fran&;ccedil;ois Le Gall told Quanta.So‚ you may be thinking‚ why should we be excited about some new refinement&;#63; After all‚ from a purely numerical perspective‚ the gain isn’t even that notable.And yet‚ the breakthrough is “conceptually larger than other previous ones‚” Le Gall told Quanta. So what makes it so special&;#63;     Improving on the bestTo understand the hurdle that was cleared between November and January‚ we ought to take a look at the situation beforehand – and as it turns out‚ it was a bit of a hodgepodge.In 1986 and 1987‚ two major breakthroughs occurred: first‚ Volker Strassen – yes‚ him again – came up with what is now known as the laser method for matrix multiplication; then‚ a year later‚ computer scientist Shmuel Winograd and cryptographer Don Coppersmith developed an algorithm specifically designed to complement and improve upon Strassen’s work.The result of combining these two techniques is quite ingenious. Strassen’s original contribution‚ back in the ‘60s‚ was to notice that by rewriting matrices A and B in terms of block matrices – that is‚ considering them to be matrices whose elements are other matrices – their product AB = C can be found in fewer than n3 calculations as long as you perform the right calculations.Figuring out what you need to do‚ then‚ is where Coppersmith and Winograd come in. Their algorithm “tells me what to multiply and what to add and what entries go where‚” Virginia Vassilevska Williams‚ a computer scientist at the Massachusetts Institute of Technology and co-author of one of the new papers‚ told Quanta. “It’s just a recipe to build up C from A and B.”And this is where the laser method comes into play. While Coppersmith and Winograd’s algorithm is brilliant‚ it’s not perfect; it generally results in some redundancies‚ with various terms “overlapping” here and there. The laser is how computer scientists aim to “cut out” these duplicates: it “typically works very well‚” Le Gall said‚ “and generally finds a good way to kill a subset of blocks to remove the overlap.”But like an early-2000s beautician faced with a pair of natural eyebrows‚ sometimes you can laser away too much. “Being able to keep more blocks without overlap thus leads to […] a faster matrix multiplication algorithm‚” Le Gall told Quanta – and it’s precisely that realization upon which Duan’s team’s technique hinges.Rebalancing the scalesBy modifying the way the laser method assigns weight to the blocks in a matrix – how important it deems them‚ and therefore how likely they are to be kept rather than cut out – the team managed to reduce the calculation time for matrix multiplication by the most significant amount in more than a decade. Now‚ don’t get too excited – they only brought it down from 2.373 to 2.372. But that isn’t really the point: what’s got computer scientists excited isn’t the result achieved‚ but how the team did it. After close to forty years of infinitesimally small improvements on the same combination of algorithms‚ Le Gall told Quanta‚ “they found that‚ well‚ we can do better.”Just how much better remains to be seen – but if you’re wondering what practical applications you can expect to see these groundbreaking results being applied to‚ you might find yourself a little disappointed. The laser method itself is already what’s known as a “galactic algorithm” – so named because it’s never used for any problems on Earth – and barring some massive unforeseen change in the status of quantum computing‚ the same will inevitably be true for the new improved versions. “We never run the method‚” confirmed Zhou. “We analyze it.”