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[ [ "Mrs. <PERSON>\nI know I have been on record in the past saying that TV is “the least important artistic medium,” but then again, give me a show exploring the complexity and hypocrisy of Conservative propagandists to defeat progressive platforms, and of course I’m gonna vibe with it. Half my apartment is filled with books on subject. Throw a dart at any one of my reviews and take a guess how I felt watching this schadenfreude.\nDoes it suffer from the same issues of all television - a hodgepodge of writer’s tones, unbalanced character development, over-balanced character growth, plotting issues, and pacing issues, especially toward the end? Yes to all the above.\nBut do we love to ogle at our enemies? 555-come-on-now - of course we vibe.", "480" ] ]

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[ [ "Dilemma in race between muon and light\nI have a dilemma concerning my understanding of Special Relativity. Maybe I am understanding or calculating something wrong and would hear so.\nThe problem is based on muons created in the upper atmosphere by cosmic rays. Basically, what happens when we time the difference between such a muon and light created the same place at the same time.\nSince the muon travels at 0.994c, it arrives 301 nanoseconds later than the light. However this is from observation on earth. From the muon's observation, the point of creation and the destination on the earth's surface are moving at 0.994c and the distance is contracted from 15 Km to 1638 m, so the light arrives 33 nanoseconds earlier.\nFurther, from the muon's observation, a clock on earth will experience time dilation and should only record 3.6 nanoseconds of time. So how much time does the earth clock record?\nDetailed Description: In practice, identifying one muon and whether it would not decay in the journey would be problematic. Since we are using observations from the muon, replace it with a spaceship traveling at the (now arbitrary) velocity of 0.994c. If you do not like crashing the spaceship into the surface of the earth, or worry about general theory effects from the earth or sun, move the thought experiment to space, say the midpoint between Sol and Alpha Centauri.\nA point m, is 15.0 Km above a point on the surface of the earth, e. At point me is a space station, Muse.\nA space ship traveling at 298 m/μs constant velocity passes point m and then point e.\nWhen the spaceship passes point m, the Muse Space Station turns on a light. A photographic plate at point e collects light only from the Muse Space Station. This will be our clock, and we will measure how long an exposure to light is indicated by the photographic plate at the time where the space ship reaches point e.", "275" ], [ "(Perhaps when the space ship passes we close a shutter on the plate.)\nThe light takes 50.03461 μs to reach point e. The spaceship takes 50.03461 μs to reach point e, 301 nanoseconds later. So the photographic plate is exposed to light for 301 ns.\nHowever, from the space ship's reference, the space ship is not moving, but points m and e are moving at 298 m/μs constant velocity. When point m reaches the space ship, it turns on a light.\nBecause of length contraction predicted by special relativity, the distance between points m and e is 1637 m. The light from point m takes 5.49540 μs to reach point e. Point e reaches the (\"stationary\") space ship after 5.46254 μs. So the photographic plate is exposed to light for 32.9 ns.\nSo how much has the exposure to light darkened the photographic plate? As much as expected for 301 ns or 33 ns?\nFurther, since from the space ship's observation, the photographic plate at point e is moving at a speed close to c. So it should experience time dilation according to special relativity.\nIf instead of leaving the light on when point m passes the space station, the light at point m was only turned on for 1 nanosecond, the clock timing that nanosecond would be slower observed from the space station, and would be on for 9 ns. Then the 9 ns of light would only expose the plate at e as much as for 1 ns of light, because of the time dilation at point e. So, observed from the space ship for every 9 units of time that the plate at point e is exposed to light, it only reacts as much as for one unit of time. So the 33 ns of light when point e reaches the space ship, the plate should only show 3.6 ns of exposure.\nSince we are comparing times in microseconds, and subtracting to get a time difference in nanoseconds, to get four digit precision in our result, we need to start with and carry seven digit precision in our thought experiment, even when the input was arbitrary.\nEarth Observation:\nDistance of segment em: 15 000.000 000 m\nSpeed of muon space ship: 298.000 000 m/μs\nSpeed of Light: 299.792 458 m/μs\nTime for space ship to reach e 50.335 57 μs\nTime before light reaches e 50.034 61 μs\nTime of exposure of p-plate 301.0 ns\nMuon Space Ship Observation:\nDistance of segment em: <PHONE_NUMBER> m\nRel Speed of e & m to muon space ship:\n298.000 000 m/μs\nSpeed of Light: 299.792 458 m/μs\nTime for space ship to reach e 5.", "562" ] ]

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[ [ "A Very Good Girl\nfilms that try and claim to be campy fail so much because they don't get the formula just right and in a very good girl, this is the case. it tries to be a lot of things but the film never really found the right balance for all of these genres to work. maybe if the humor was drier... maybe if it fully embraced its darkness...", "269" ], [ "maybe if the script was developed for at least two more years... some of the creative decisions are a bit questionable too (its style sometimes can be off putting that it renders the story too dramatically than it needs). love that <PERSON> is now choosing these projects cause her and <PERSON> is as good as always. i just need them to be in a decent project (together and individually), that'll be enough.", "577" ] ]

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[ [ "Efimov states in general\nEfimov states are special states of three praticle systems. Their existence is a purely quantum effect, because \"size\" (i.e. cross-section) of these states can be much greater than the range of underlying particle-particle interaction. (1,2)\nFor each system having an <PERSON> state there are in fact infinitely many of such states. Some properties of Efimov states are universal and do not depend on the nature of underlying particle-particle interaction: (1,2)\n1) size of $n$-th <PERSON> state is $s_0 \\approx 22.7$ times the size of $(n-1)$-th state\n2) energy of $n$-th <PERSON> state is $s_0^2$ times the energy of $(n-1)$-th state\n$s_0$ is the solution of the following transcedental equation (3):\n$s_0 \\cosh(\\pi s_0/2) = \\frac{8}{\\sqrt{3}} \\sinh(\\pi s_0/6) $\nThere can be <PERSON> states, so bound three particle states, when there are no bound dimer states. This is often depicted with borromean rings, since if we take one of the praticles away, the resulting two particle state will be unbound.\n<PERSON> states and halo nuclei\nThe original <PERSON> work treated three identical bosons.", "469" ], [ "However, the particles need not be identical, they can have different mases. The <PERSON> theory can also be extended to describe fermions. (2)\nHalo nuclei, that can be viewed as <PERSON> states, are the nuclei with two-neutron halos:\nA two-neutron halo is exhibited by ${}^6He$, ${}^{11}Li$, ${}^{17}B$, ${}^{19}B$ and ${}^{22}C$. Two-neutron halo nuclei break into three fragments, never two, and are called Borromean because of this behavior (referring to a system of three interlocked rings in which breaking any ring frees both of the others). (Atomic nucleus-Wikipedia)\nThe two neutrons in the halo \"do not stick together\", so we indeed have a three-particle system. It is interesting, that\n[lithium-11] has an exceptionally large cross-section of 3.16 fm, comparable to that of ${}^{208}Pb$. (4)\nFor an introduction to halo nuclei and Efimov states see the presentation Halo world: The story according to <PERSON>,<PERSON> and <PERSON> by <PERSON>: http://www.boseinst.ernet.in/capss/talks/2011/IndranilMazumder.ppt\nI also advertise the freely available Physics.APS.org article on <PERSON> states: http://physics.aps.org/articles/v3/9", "1020" ] ]

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[ [ "Micro-Bit Arcade Machine\nIntroduction: Micro-Bit Arcade Machine\nIn this Instructable you will be hooking up a joystick to a Micro-bit and making a machine you find at arcades. Inspiration to make this project came when I decided to figure out how to add parts onto Micro-bits, like joysticks. Once I completed my original goal, I decided to go further and instead of a Micro-bit, Joystick, and a million messy wires in between, I challenged myself to make an Arcade style box to put it in and I hope you will too!\nSupplies\nYou will need:\n* A light cardboard box (see step 1)\n* A hole puncher\n* A Micro-bit with some sort of extension board\n* A battery pack and USB cable\n* 4 Micro-bit buttons\n* 4 connector wires, 1 black, 1 red, and 2 random\n* A computer (pretty sure you have one!)\nStep 1: Measuring the Box\nFirst let's get some cardboard,\nThis arcade machine should be made out of light cardboard, slightly thicker then a cereal box, but not corrugated. The end result should be about the width and length of your micro-bit extension board.\nFor this project I will be using the measurements for this extension board (in the kit). Most extension boards that are smaller then 3.25 inches should work though.\nNow you can use the pictures as a guide to measure your box, clicking them enlarges the pictures.\nStep 2: Cutting and Adding to the Box\nNow that we have box measured, it is time to cut it. Simply cut it out along the edge of the boarder,\nAlso looking at the pictures for text boxes.\nLet us begin to measure holes to put things in.\n1.", "997" ], [ "Starting with the hole for the Micro-Bit, outline the uppermost part of the box upside down with your Micro-Bit, as in the pictures.\n2. Now use a hole puncher to make a hole right were the battery pack is going to go through.\n3. Finally, make a hole on the end of the box just big enough to fit your joystick.\nStep 3: Micro-Bit Side\nFirst let us download the code that we are using for this project.\nUse a USB to plug in your micro-bit into your computer, then download the code to your computer using the download below this step, then download it to your Micro-Bit using its file (found in your computer's files)\nOnce completed, your Micro-Bit should light up \"A\" on its screen.\nOnce you put your Micro-bit into the extension board, you should look for four pins on it, the Ground pin, 3V(volts) pin, pin 1, and pin 2.\nStart putting in your connector wires, connect one end of the black connector to ground, the red connector to 3V, and the two random ones to pins 1 and 2.\nFinally, take the other ends of each and put the black connector to Ground on the joystick, the red to 5V, pin 1 to VRX, and pin 2 to VRY.\nVRX makes an output between 0 and 1023, depending on the x position of the joystick(or horizontal position) VRY outputs the Y position (or vertical position).\nNow we will be putting on the Micro-bit to the arcade box.\nDownload Here\nStep 4: Gluing the Box\nStart by using hot-glue to glue the Micro-bit extension board onto the box, as shown in the picture. then push your joy-stick into the hole you made earlier, then gluing it in place.\nAt this point you should have cut out the box and put on the Micro-bit. You are now ready to glue the box together\nput glue on one of the tabs, like in the picture. Then fold that tab into another side, so that it folds up the box.\nrepeat this until you have all the tabs folded in, making sure that all the electronical parts don't move in the middle of it.\nOnce you have glued the whole box together, the last step is to plug in the battery to the Micro-bit and try it out!", "259" ] ]

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[ [ "Calculating vertex factor for scalar field theory\nI am practising basic QFT and am having some trouble with calculating the vertex factor of an interacting theory involving two real scalar fields, $\\phi_{1}$ and $\\phi_{2}$.\nIf I create a generic Lagrangian with interaction terms:\n$$\\mathcal{H}{\\text{int}}=g\\phi{1}^{2}\\phi_{2} + q\\phi_{1}^{2}\\phi_{2}^{2}$$\nI want to calculate the vertex factors associated with these interactions. So to calculate the $\\phi_{1}^{2}\\phi_{2}$ vertex, I calculate the three-point Green's function:\n$$G^{(3)}(x,y,z)=\\langle\\Omega|T\\phi_{1}(x)\\phi_{1}(y)\\phi_{2}(z)|\\Omega\\rangle = \\frac{\\langle0|T\\phi_{1}(x)\\phi_{1}(y)\\phi_{2}(z)\\exp\\left(-i\\int_{-\\infty}^{\\infty}\\mathcal{H}{\\text{int}}\\:\\mathrm{d}^{4}s\\right)|0\\rangle}{\\langle0|T\\exp\\left(-i\\int{-\\infty}^{\\infty}\\mathcal{H}_{\\text{int}}\\:\\mathrm{d}^{4}s\\right)|0\\rangle}$$\nWe can expand the exponential involving $\\mathcal{H}_{\\text{int}}$ to first order in $g$ and $q$:\n$$\\exp\\left(-i\\int_{-\\infty}^{\\infty}\\mathcal{H}{\\text{int}}\\:\\mathrm{d}^{4}s\\right)=1-ig\\int{-\\infty}^{\\infty}\\phi_{1}^{2}(s)\\phi_{2}(s)\\:\\mathrm{d}^{4}s-iq\\int_{-\\infty}^{\\infty}\\phi_{1}^{2}(s)\\phi^{2}_{2}(s)\\:\\mathrm{d}^{4}s$$\nClearly by <PERSON>'s theorem, any term without an even number of $\\phi_{1}$ or $\\phi_{2}$ terms will disappear, so the denominator will become:\n$$\\langle0|T\\exp\\left(-i\\int_{-\\infty}^{\\infty}\\mathcal{H}{\\text{int}}\\:\\mathrm{d}^{4}s\\right)|0\\rangle = 1-iq\\int{-\\infty}^{\\infty}\\langle0|\\phi_{1}^{2}(s)\\phi_{2}^{2}(s)|0\\rangle\\:\\mathrm{d}^{4}s = 1 - iq\\int_{-\\infty}^{\\infty}\\:\\mathrm{d}^{4}s\\Delta_{F}^{(1)}(0)\\Delta_{F}^{(2)}(0)$$\nWhere $\\Delta_{F}^{(1)}(z)$ is the Feynman propagator for $\\phi_{i}$.\nMy understanding is (from this other question I asked), that terms containing a tadpole diverenge ($\\Delta^{(i)}{F}(0)$) can be set to zero using the requirement that $\\langle \\phi{i}\\rangle = 0$, so the denominator evaluates to $1$.", "281" ] ]

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[ [ "A Modern Take on the Phenakistoscope\nIntroduction: A Modern Take on the Phenakistoscope\nThe Phenakistoscope is an early optical illusion device that uses static images to create the illusion of motion through the principle of persistence of vision. It is regarded as one of the first forms of moving media entertainment that paved the way for the motion picture industry.\nWe are not sure how big is the community currently interested in phenakistoscopes, however, from browsing through the internet, there seems to be quite a huge interest in this subject.\nIf you do not know how a phenakistoscope works, you may visit https://youtu.be/r4B3FHHt_k8 to see one in action.\nIt may be amazing to watch the mirror reflected images come to life by peeking through the slits or slots of phenakistoscopes, however, it can be quite tiresome when viewing for an extended period of time.\nIn this instructable, we are going to build a modern phenakistoscope. The phenakistoscope disc shall be mounted on a motor rotating at a speed that works with a strobing LED strip to make the images on the disc magically come to life when viewed with our naked eyes.\nA traditional phenakistoscope is normally used by a person at a time. Our design allows a few people to view the animation at the same time which should be much more fun.\nOur modern phenakistoscope can be controlled to rotate the disc in either clockwise or anti-clockwise direction, change the speed of rotation as well as vary the frequency of the strobe light. We will also be able to adjust the brightness of the strobe light for better viewing.\nTo build this project, basic electronics component soldering skill and some knowledge on using the Arduino are required.\nYou may like to view the following YouTube video to see what we are going to build for this project.\nCAUTION:\nFor a small percentage of people with epilepsy, exposure to flashing lights at certain intensities or to certain visual patterns can trigger seizures.\nThis project requires strobing of the LED strip lights. If you experience discomfort looking at the images on the rotating disc or the light from the LED strip, you should stop looking at them immediately.\nStep 1: Building the Electronic Circuit Board\nFor this project, we need a motor to spin at a consistent speed for the best visual effect.\nWe tested with cheap DC motors but they are not able to spin at a consistent speed over time.", "134" ], [ "Motor speed slowly drifts lower after running the motor for a while and this is quite noticeable for this project as we have to regularly compensate by adjusting the strobe light frequency in order to stabilize the animation. We may be able to mitigate this using PID motor control but this will require motor feedback and more elaborate program codes.\nWe have some faulty CDROM drives lying around and the salvaged CDROM Brushless DC (BLDC) motors from these drives work great for this project. We were able to drive these BLDC motors at a much consistent speed without using any feedback mechanism. The CDROM motor disc holder also allows us to easily mount a CD/DVD disc with a phenakistoscope image pasted onto it.\nWe will not be showing how to salvage the BLDC motors from CD or DVD drives as this information is readily found online such as the following Instructable\nhttps://www.instructables.com/Disassembling-a-CDDVD-reader-and-reusing-its-parts/\nand YouTube videos such as the following which also show where to connect to the 3 phases of the BLDC motor.\nhttps://www.youtube.com/watch?v=GntH4ZcVKPU&t=244s\nThe electronic circuit and program codes to drive the CDROM Brushless motor are adapted from the following two Instructables:\nhttps://www.instructables.com/Run-A-CDROM-Brushles...\nhttps://www.instructables.com/Arduino-CDROM-BLDC-M...\nWe will be using two L293D ICs for driving the CDROM BLDC motor and we will be using a DC to DC Step-down module to supply power to the motor.\nWe will be driving the BLDC motor in open-loop operation mode without the need for rotor position sensors since reliability is not critical here and also to simplify the electronic circuit.\nIn our design, we will need 2 potentiometers. One for strobe light frequency control and another for motor direction change as well as for motor speed change.\nA toggle switch will be used for the brightness control of the strobe light. Light will be brighter with each switch toggle and return to default brightness level after 10 brightness incremental steps.", "16" ] ]

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[ [ "I can point out a lot of reasons. But most of them are about the main character himself: <PERSON>.\n1. The most obvious reason is \"Humour\". <PERSON> can be a pretty complex character, but one thing that is certain about him is humour, which contributed greatly to his movie becoming a people's fave. He's not only making fictional humour, as in, humour that only applies in the movie. In the movie, he makes fun of even Marvel itself, and other superheroes/movies like Wolverine and Green Lantern. The character <PERSON> (<PERSON>), also played as another superhero in the movie Green Lantern, in which he had a green CGI animated suit. In the Movie <PERSON>, he says ***“don’t make the suit green or animated”***, referring to his superhero suit, and poking fun at the suit he (<PERSON>) wore in the movie Green Lantern. This makes him a different kind of superhero, not like the \"standard\" superheroes that are serious and uninteresting.\n2. The movie's length is just perfect. A lot of superhero movies feel the need to be over two hours long! This movie is just 1 hour 48 minutes. Just enough time to tell a story with some action and comedy without padding it out with pointless scenes\n3. Deadpool contains very little racial, political and social conspiracy theories. Most superhero movies seem to have hidden political translations.", "387" ], [ "An example is the X-Men Franchise. It draws deliberate parallels between the oppression of mutants and that of other marginalized groups, like the blacks and the LGBT community. But Deadpool doesn't contain any such content/tradition.\n4. The movie is balanced. It perfectly balances humour and drama/action, without completely overwhelming the audience with either. The movie gives you enough drama without being totally overwhelming. Most movies tend to bore out the viewers by over-emphasis of an event or plot. For example, <PERSON> suffered very much when he was experimented on. But his suffering is not forever showcased in the movie. every movie with <PERSON> (X-Men Character), who experienced the same suffering from the same types of experiments (from the same organisation too), is constantly darted with flashbacks and references to the times he suffered. In the end, it becomes depressing as the movie comes out to be a suffering story, rather than being an action feature.\nDeadpool went through so much and is no longer mentally well or sane but is ALLOWED to be funny by the movie. If Marvel had gone with the tradition of their other movies, Deadpool would either be a \"scary psychopath/sociopath\" with no feelings. Deadpool is a unique and even uplifting portrayal of someone with mental health problems\nIn conclusion, Deadpool is a likable, fun , compelling and even sympathetic character. And the movie is well crafted, and that's why people love it.", "387" ] ]

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[ [ "Why pilgrims from India and Nepal throng to see an orchid that blooms in April · Global Voices\nShrine dedicated to gardener sisters whom <PERSON> used to meet at the Salahesh fulbari in Siraha district of eastern Nepal. Image by <PERSON>.\nAn orchid that blooms around mid-April in a garden of historical and cultural significance in Siraha, eastern Nepal attracts hordes of pilgrims from both India and Nepal every year.\nThe locals in the area of the garden, known as the Salahesh Fulbari, believe that the flower blooms on the very first day of the year, 1st of Baishakh (the first month in the Nepali Calendar). According to legend, the orchid symbolizes the garland offered to the folk hero <PERSON> by his beloved malin (a Maithili word for a female gardener).\nअनौठो फूल !\nपूर्व–पश्चिम राजमार्गअन्तर्गत सिरहाको पडारिया चोकदेखि दक्षिणमा रहेको ऐतिहासिक तथा प्राचीन फूलबारीमा नयाँ वर्ष वैशाख १ गते मात्र फुल्ने फूल । ‘सल्हेस’ फूलबारी ‘हारमको’ रुखमा एकाबिहानै सुनाखरी आकारको फूल फुल्छ र साँझ ओइलाएर जान्छ । तस्वीर: रासस pic.twitter.com/SCRYHquX0I\n— Saral Patrika (@SaralPatrika) April 13, 2018\nStrange flower!\nA flower that blooms only on the New Year 1st of Baishakh at the historical and ancient garden located in the south of Siraha’s Padariya Chowk on the East-West Highway. The orchid blooms on the haram tree in the Salahesh Garden early in the morning and wilts in the evening. Photo: RSS (National News Agency)\nFascinating folklores, cultural demigod\nNot much has been written about <PERSON>, also known as <PERSON> (the king of mountains) and Jayavardhan. However, in the southern plains of eastern Nepal and adjoining states in Bihar of India, there are many folklore stories featuring <PERSON> and his adventures.", "765" ], [ "Different versions of folktales handed down from one generation to the other talk about <PERSON>’s bravery and his love for his malin.\nAccording to one legend, <PERSON> used to visit the Salahesh Fulbari to pick flowers for use in religious rituals after performing his ablutions. He would meet four sisters who were gardeners there, and in due course, he fell in love with one of them. The orchid which blooms in mid-April every year, according to locals, symbolizes that love. Young couples visit the garden on the Nepali New Year’s Day to receive blessings for their love and express hope that their love would last long just like that of <PERSON> and his gardener love.\nAccording to many stories about <PERSON>, he was a Dusadh, a member of the so-called untouchable community. He is also claimed, however, by the Danuwar community. But <PERSON> is worshipped by all, irrespective of caste and ethnicity. With time, he has evolved for several communities from a Dalit hero into a demigod.", "351" ] ]

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[ [ "There is actually a pion exchange between nucleons. This is the basis for the residual strong force.\nWhen a proton and neutron interact, one of the interactions we get is\n$$\\rm proton^+ +neutron \\rightarrow proton^++pion^-+proton^+ \\rightarrow neutron+proton^+$$\nSo the proton becomes a neutron and then the neutron becomes a proton by transferring a negative pion.\nEdits: <PERSON>: That's fair, my answer didn't really answer.\nThe proton and neutron aren't identical particles and so aren't limited by Pauli Exclusion between each other. They can have the same spin state and for some reason having parallel spins gives the combination a lower energy and so more stability.\nWhen I look for why parallel spins have a lower energy, I just see it stated as a fact or in better references, an equation that gives the details of the energy difference is given.\nWhat I haven't seen is a physical explanation for why parallel nuclear spins have lower energy.\nHere's my hunch (which I will try to verify). If it's correct then it's probably out there somewhere already.", "969" ], [ "If it's wrong, it's because I just thought the idea through myself.\nWhen a proton and neutron have all the same quantum numbers (and so their spins are parallel), then when a neutron transfers a negative pion to the proton, the final state is identical to the initial state. This means there are two different paths from the initial state to the final state: doing nothing and passing a negative pion both give you the same final state.\nIn quantum when two different events are possible because they both give the same initial and final state there is an interference term. For instance, in the collision of two identical atoms with identical spins states, colliding and not colliding can give the same final state, and so the two possibilities interfere.\nIn the case of a proton and a neutron with antiparallel spins, transferring a negative pion would give a different final state than the initial state. It could transfer back to then give the same final state, but (roughly speaking) every step a process needs makes the contribution of that process less important.\nIn the case of a diproton or dineutron, the transferring a neutral pion would also give the same final and initial state.\nSo I further suspect (again, all on me if it's wrong) that while the proton-neutron parallel pair has dominant exchanges of both neutral pions negative pions, the diproton and dineutron only has neutral pions giving the proton-neutron pair about twice the binding.\nSo the two key ideas I'll try to track down are: (1) Does a process having identical initial and final state make it more important? (2) Does having twice the number of similar interactions mean that there is about twice the binding energy involved?", "969" ] ]

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[ [ "Dances with Wolves\nThe majesty of a good epic is unlike anything else that cinema (or any art form, really) can offer, and this movie is a damn good example of that. Flaws aside, of which there are many, witnessing a journey as thoroughly as this and with as skilled a narrative hand as this can be deeply enlightening, here emphasizing just how meaningless almost any conflict is and how much potential the human race really has to love and care for one another. <PERSON> isn't the most captivating screen presence out there, but I'll be damned if the sheer scope doesn't more than account for that.\nGoodfellas is still better", "217" ] ]

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[ [ "Last Date.\nIntroduction: Last Date.\nMy father once told me <PERSON> song \"Last Date\" was playing at the time he asked my mother to marry him on their \"last date\" and, well, she said yes!\nThis model, \"Last Date\", is in remembrance of their \"last date\" and their forever marriage until their passing. We love and miss you both and wouldn't be here if not for your \"Last Date\"!\nAs usual I probably forgot a file or two or who knows what else, so if you have any questions, please do not hesitate to comment as I do make plenty of mistakes.\nDesigned using Autodesk Fusion 360, sliced using Ultimaker Cura 4.7.0, and 3D printed in PLA on Ultimaker S5s.\nSupplies\n* Soldering iron and solder.\n* Thick cyanoacrylate glue.\n* Sandpaper or emory cloth.\n* Lite machine oil.\n* AWG28 stranded wire.\n* Indelible ink pens (blue, red).\n* Double sided tape.\nStep 1: Parts.\nI acquired the following parts:\n* One N20 100RPM 6VDC gear motor.\n* One 2AAA battery holder with on/off switch.\n* Two AAA batteries.\n* One normally open momentary pushbutton switch (must fit a 13.00mm hole).\n* One micro lever switch (search for \"CYT1073\")\n* Thirty six inches of 1.15mm (3/64\") diameter music wire.\n* Two 3mm (diameter) by 1.5mm (thick) neodymium magnets.\n* Two 6mm (diameter) by 1.5mm (thick) neodymium magnets.\n* Four M2.5 by 16mm cap screws.\n* Four M2.5 nuts.\nThe attached file \"Parts.pdf\" contains the name, quantity, infill, layer height and support of all 3D printed parts I printed for this mechanism. Note parts with a \".3MF\" extension are dual extrusion prints.\nThis mechanism is a high precision print and assembly using at times very small precision 3D printed parts in confined spaces with highly precise alignment. I printed the gears, levers, arms, cams and wheels using the Ultimaker Cura 4.7.0 \"Engineering Profile\" on my Ultimaker S5s, which provides a highly accurate tolerance requiring minimal if any trimming, filing, drilling or sanding.", "654" ], [ "However, prior to assembly, I still test fitted and trimmed, filed, drilled, sanded, etc. all parts as necessary for smooth movement of moving surfaces, and tight fit for non moving surfaces. Depending on your slicer, printer, printer settings and the colors you chose, more or less trimming, filing, drilling and/or sanding may be required to successfully recreate this model. I carefully filed all edges that contacted the build plate to make absolutely certain that all build plate \"ooze\" is removed and that all edges are smooth using small jewelers files and plenty of patience to perform this step.\nThis mechanism also uses threaded assembly, so I used a tap and die set (6mm by 1, 8mm by 1.25) if required for thread cleaning.\nStep 2: Pushrods.\nTo create His pushrods, I performed the following tasks:\n* Cut a 160mm length of music wire.\n* Created a 90 degree bend, 15mm long, in one end of the cut length of music wire.\n* Placed the 15mm bend into the hole in \"Jig, His, Pushrod.stl\".\n* Created a 90 degree bend in the remaining end of the cut length of music wire.\n* Cut the last 90 degree bend to 5.5mm in length.\n* Removed the wire from the jig.\n* Sanded the cut ends smooth.\nTo create Her pushrod, I performed the following tasks:\n* Cut a 150mm length of music wire.\n* Created a 90 degree bend, 10mm long, in one end of the cut length of music wire.\n* Slid the straight end of this wire into the slot in \"Jig, Hers, Pushrod.stl\", then placed the 10mm bend in the hole in the jig.\n* Bent the straight end up 90 degrees.\n* Cut this bend to 3mm in length.\n* Removed the wire from the jig.\n* Sanded the cut ends smooth.\nStep 3: Base.\nTo assemble the base, I performed the following steps:\n* Attached the two micro lever switches to the base using the 2.5mm bolts and nuts.\n* Placed \"Arm, His, Pushrods.stl\" into the base assembly.", "784" ] ]

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[ [ "If I’m reading your question correctly, the answer really depends on what you choose for the characteristics of your engines and generators; their efficiency, waste products, energy requirements, operating lifetimes, and so on.\nIf your conversion process is fast, clean, efficient, and truly fuel-agnostic, then it doesn’t matter what you use - you won’t need much of it anyway. Depending on the service life of your generators, you might even buy one with a lifetime of fuel already built in. At 100% efficiency, 1kg of mass converts to 9e18 J using the usual formula. That’s more than a 2 gigaton nuclear bomb, which is a problem if you decide to crash at full speed, but that’s another discussion. Thermodynamics will most likely limit how much of that you can use for propulsion, but its still a ridiculous amount. The current annual world energy consumption could be produced by converting just 61kg of mass if you assume perfectly efficiency (1).\nYou mentioned a fueling infrastructure - tankers, stations and fuel deliveries. That implies that while people could use anything and everything as fuel, at least some people don’t. Somebody goes to the trouble and expense of operating a fleet of tankers and filling stations in a world where fuel is free, so we need a reason for that. The tankers also imply that this fuel comes from a limited number of locations and has to be transported rather than being manufactured everywhere it’s used - again, we need a reason.\nConsider a real-world example as a point of reference: A conventional 3000MW fission reactor converts pretty close to 1 kg of mass to energy every year (2). To accomplish this, it consumes 25 tons of enriched uranium fuel and produces 1 kg less than that in waste. That’s only 0.004% efficiency give or take, but it is genuine mass-energy conversion. The energy takes the form of heat, which we use to generate electricity. We could theoretically convert that same mass and generate that same heat using lots of other, cheaper processes, but we use uranium fission because it produces energy at a good rate, is a controllable reaction, it isn’t too short lived, isn’t too rare, and so on.", "435" ], [ "These same considerations could apply to your fuel. What characteristics could make a good fuel worth transporting if you can have other fuel for free?\n1) Performance: some materials could convert more efficiently than others. If it takes several tons of cheap junk to produce the same power as one gram of good stuff, it will be well worth it for anybody who needs better acceleration, longer flight times, or bigger payload capacities. 2) Safety: some materials might be riskier than others - maybe you can control the reaction rate better with some things than others, or maybe using the wrong thing risks damaging your generator or worse. Sure, you can save a few credits by connecting your generator to the san, but they used cheaper fuel rods at Chernobyl too and see where that got them. 3) Convenience: some materials could produce nastier waste products than others, making waste storage, handling and disposal a real show stopper. Perhaps pure rocket fuel converts cleanly and completely, while random junk will convert just fine and get you where you’re going, but it spews out loads of hard radiation in the process and leaves you with a residue of poisonous radioactive acid potion smeared all over the engine room. 4) Legality: Depending on your setting, smart devices and materials could be a consideration. Your generator might refuse to accept any other fuel than the genuine original manufacturer’s special blend. A government could even issue fuel that carried an encrypted signature so that your generator would only burn it while on a registered flight path. That might serve as a solution to the Kzinti Lesson(3) or the aforementioned 2 gigaton bomb problem as well.\nOn the other hand, maybe those tankers and fuel stations don’t really dispense fuel at all, and are called that for historic reasons. If those electric engines you mentioned are regular reaction engines you’ll need to take on reaction mass from time to time. That's what the tankers and stations are all about. For fuel, you just siphon off a few grams of reaction mass to feed your generator since you have tons of it with you anyway.\n(1) https://www.bp.com/en/global/corporate/energy-economics/statistical-review-of-world-energy.html\n(2) https://www.nuclear-power.com/nuclear-power-plant/nuclear-fuel/fuel-consumption-of-conventional-reactor/\n(3) http://www.projectrho.com/public_html/rocket/spacegunexotic.php#id--Propulsion_Systems", "435" ] ]

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[ [ "Light Bulb Base Repair\nIntroduction: Light Bulb Base Repair\nIntroduction\nHave you had a light bulb base oxidize and stop working? Furthermore, when you remove the bulb, the bulb comes out and the base remains in the socket? The reason for this instructable is to replace the base of an LED or CFL light bulb.\nThe Story:\nOne night the LED flood light stopped working. When I went to replace the bulb, it came out and the base stay behind. What a pain. Of course, it was supposed to be a simple twist out, twist in job. Not a repair to be done at night, so the next day I removed the base from the socket and inserted a new flood light.\nI started to think just because the base separated from the light, could the bulb still work? I attached the bulb to a power cord and Yes, it did work. Wow. Now I started to think could I replace the base? Yes, I think I could… Where do I find a base? It is not an item on Amazon. I removed the base from a burnt out CFL.", "854" ], [ "With a “replacement” base, I can solder it to the baseless LED Flood Light.\nA bulb without a base and means to repair.\nBecame another item trashed in despair.\nNow with solder and glue,\nthis bulb is made anew.\nNext Tools and Supplies\nStep 1: Tools and Supplies\nTools:\nSoldering Iron (More than 35 watts)\nSupplies:\nReplacement Light Bulb Base,\nSolder,\nJB Weld,\n100, 240 and 400 Grit Papers.\nLet’s go replace the Base.\nNext Replacement Base\nStep 2: Replacement Base\nAlign the replacement Base with the bulb wires.\nThe Hot wire to be aligned with the hole. The Ground wire is bent over the edge of the bulb and squeezed between the threads of the replacement Base and the threads of the bulb. See image with description.\nNext Solder\nStep 3: Solder\nBend the “Hot” wire and solder to the replacement Base.\nUse the Solder Iron and Solder to secure the replacement Base and Hot wire.\nThe highest Solder Iron I had, was 35 watts. It can be done, but will be easier with a higher wattage Solder Iron.\nNext Clean Solder\nStep 4: Clean Solder\nHere is where you will clean and smooth the soldered Base.\nI used 100, 240 and 400 Grit Papers.\nNext Secure Base\nStep 5: Secure Base\nHere is where you use the JB Weld to secure the replacement Base to the bulb.\n1) Mix enough JB Weld,\n2) Apply it where the replacement Base and bulb meet,\n3) Let dry,\n4) Insert bulb and test.\nNext Observations and Summary\nStep 6: Observations & Summary\nObservations\nI have found little information regarding how to prevent base oxidation, everyone knows it happens but there is not a consensus or easy solution on how to prevent this issue. This occurs because of heat and moisture.\nMy preventive intervention will be to loosen and tighten the bulb, monthly, at a minimum. In addition, after windy rains; take the bulb out and wipe the base and inside dry. The idea is to keep the bulb base and bulb socket dry, preventing the oxidation from building. Furthermore, removing the bulb should prevent any bonding from occurring. I will be exploring other options to replace my constant interaction.\nThe benefits of this design are:\n1) Removing repairable items from the waste stream,\n2) Reusing items saves money,\n3) Knowledge is a powerful tool.\nSummary\nI am satisfied with the results.", "819" ] ]

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[ [ "My First Ever Router Table!\nIntroduction: My First Ever Router Table!\nThis project has been inspired by Woodsmith Magazine. By far I think, is one of the best designs over the interweb, though I am not going to share exact dimensions, I want you to have a rough idea of what this design features so that you can make your own.\nI have a YouTube video that makes things way clearer and exciting.\nSupplies\n+Lumber (pine)\n+Router\n+Woodglue\n+3/8\" bolts, washers and nuts\n+Knobs\n+Outlet switch\nStep 1: Legs and Stretchers\nTo make the frame start by cutting half laps one on top and one on bottom. Do that by cutting on your table saw and remember that there are four legs and three stretchers, all of them made out of 2x4\"s. After that glue them forming two frames that are solid enough to stand alone, you can plane them if you want everything to sit flush.\nStep 2: Structure Assembly\nOnce you have two frames, make a template to drill the holes so that you can pass the bolt through and join the legs and stretchers, use a ratchet to adjust them and right after that, attach the angle brackets to fasten the table top.\nStep 3: Table Top\nI made the table top out of two tops that were prefab at the homecenter and glue them together to form a reliable top that is dead flat.\nThen I rounded the corners with a template to trace, rough cut with my jigsaw and flush trim with my router.\nStep 4: Insert\nThe insert is the part to attach your router to the main table.", "599" ], [ "I made this one out of acrylic because it is strong and transparent. Simply cut it to final depth and mark the position on the table top with a marking gauge. Drill 1\" holes for your fingers to pass through and holes to pass the screws for the router base.\nStep 5: Table Top Hole\nYou'll need to make a hole to sit the insert and router through. Drill a 1\" hole through the table top and rough cut the shaoe with a jigsaw, then use some straight edges to flush trim everything, including that you'll have to route a recess of the thickness of the insert to sit flush.\nStep 6: Groove and Safety Accesory\nUse your flush trim bit to route a groove so that you can slide jigs and sliders later. A safety accesory will prevent your hand from ever touching the bit, so temporarily clamp a piece of lumber to use it as a fence, and route two slots for height adjustment in a 1/2\" board, once done, use a template to make an acrylic semi-circle and finally screw them together.\nStep 7: Fence and T-Track\nRip cut two pieces to make the fence, using your table saw, cut some sort of mortises to pass the bolts for the sliders through and then attach both pieces.\nOn top of the fence the design features a T-Track that is used to place the hand safety device, feather boards and other type of jigs, to make it cut two identical boards route a 1/2\" groove and then make half a T with the table saw, then glue both of them together, and you have a T-Track, glue and clamp it on top of the fence and trim the excess.\nFinally cut an opening for the bit to pass through using the table saw.\nStep 8: Clamps and Knobs\nI made my own knobs with plywood, but you can purchase them.\nIf you want to DIY them, laser cut the template attached and stick it to the plywood with double-sided tape, then use your router table to free hand the shape using a flush trim bit with a bearing on top.\nMake a clamp of the thickness of the fence and drill a 3/8\" hole to pass a bolt through, the importance of making a kerf in it is to align it with the fence and hold it firmly.\nRepeat this with the knobs for the back as well and clamp everything to the table top.\nYou now have a router table.", "599" ] ]

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[ [ "Crimes and Misdemeanors\nI surely don't have time- to myself, or otherwise- to be sullenly rewatching <PERSON> movies (without even a monetizable work hook!) and yet here I am. I think this'll be the last one, after HUSBANDS AND WIVES last week and <PERSON> about a month ago - a trio that, taken together, but each in different ways, probably constitute the best directing he ever did. (The official over/under on \"Woody Allen: Ranked\" featurettes online when he eventually dies, sooner or later, is 0.5; the odds he'll somehow keep churning out movies post mortem, from a Hell presided over by <PERSON>, are slightly better).\nAnyway: CRIMES is spare and swift in a purposeful way, distinct from the more haphazard \"effortlessness\" of post-2000s, \"late style\" <PERSON>; MATCH POINT, which is basically a remake, isn't remotely as precise or effective despite its Highsmithian airs. The cutting in the sequence leading up to <PERSON> murder is maybe <PERSON> finest hour, a stately fugue of anticipatory dread synced perfectly to <PERSON>. And the image of <PERSON>'s dead, staring eyes -- crept up to by an uncharacteristically low-angled camera, which holds for a small eternity before scuttling away - is genuinely nightmarish, although I suppose it says something that a character given zero dimension beyond her status as an obstreperous plot point has her best onscreen moment as a corpse.\nThis was one of <PERSON> problems with <PERSON>'s \"film of ideas;\" that <PERSON>'s unfortunate <PERSON>, rubbed out by gangsters hired by her married, older lover after she threatens to bust up his marriage, inspires no sympathy - and thus no real sense of tragedy in the aftermath.", "698" ], [ "I think she's right about this, and that <PERSON>'s ominous line, \"I will not be destroyed by that neurotic woman,\" is probably one of the top ten jaw-droppers in <PERSON>'s filmography, category of \"veiled confessional,\" though of course this movie predates his major personal controversies - it'd have to with <PERSON> cast as the idealized object of his own character's affections. In a way, it's that precise *lack* of plausible, red-blooded, mammalian emotion - of feelings any deeper than fight-or-flight, the condition embodied perfectly in <PERSON>'s skilled, gestural acting- that makes CRIMES so bracing to me. <PERSON>'s movies, whether comedy or drama (the two modes juxtaposed so blatantly here in the titles and cross-cutting structure) are almost always chill, functional little edifices that instrumentalize their characters, so making that tendency explicit - in effect doubling and tripling down on it through parallel narratives in which evil prospers and idealism goes (literally) out the window - is a solid artistic choice; I sort of feel like this (and HUSBANDS, and I guess DECONSTRUCTING <PERSON>) feel like the last time this filmmaker was really *making* choices, instead of just flying on autopilot. None of this explains why I spent ninety minutes last night with a movie that I already know is pretty good, and yet isn't exactly likely to reveal new depths or meanings, or even provide much pleasure except as ambient audiovisual background noise (I watched it while revising a book proposal on something totally different). But I've been thinking of <PERSON>'s eyes - and the bride kissing her own blind father gratefully on the cheek - all afternoon, so I guess I don't regret it.", "698" ] ]

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[ [ "I seem to recall a ritualistic which <PERSON> was \"reborn\" a spirit without a body is for all intents and purposes dead. Reinhabiting a body... any body after being removed from your original body makes you undead. The use of powerful magics to bind the soul to an object before death seems (even in standard D&D Liches) to be a precursor to the Lichdom. If a wizard can't very well wait until they are already dead to create a Phylactary. We must ask ourselves, would <PERSON> EVER have died? If the answer is no, then he is clearly either divine, demonic, or undead. <PERSON> is how a Lich begins. An unnatural act to avoid death by a powerful Wizard. A d&d wizard who createds a Phylactary by whatever infernal magics puts their soul there. <PERSON> was not the first to do such a thing, he was the first to make multiple Phylacraries in the <PERSON> world. Nothing would stop a D&D Wizard from doing the same, provided he could find a way to divide his soul. Other clues that <PERSON> is undead are that he survives the destruction of his body.", "773" ], [ "A lich, once the body is destroyed, will reform after a time, just as <PERSON> did. Their soul will be protected (or trapped) by their Phylactery and they will experience exactly what <PERSON> describes. No death, especially not in the permanent sense, but also not really alive. <PERSON> is a Lich whose body was destroyed who reformed that Body (as Liches are want to do) and wasn't able to be defeated until his Phylacteries (Horcruxes) were destroyed... honestly it's a basic <PERSON> plot-line in D&D. The only debate here comes from <PERSON> fans who either want to idolize <PERSON>, saying she didn't have any inspiration or want to avoid admitting that <PERSON> is fantasy just like Lord of the Rings... btw, while we're at it, <PERSON> is where the fantasy genesis of the <PERSON> comes from his Phylactary is the One Ring. Remember in The Hobbit, he was merely called \"<PERSON>.\"\nIt all comes from LoTR, the granddaddy of D&D, Wheel of Time, the modern fantasy concept of elves and dwarves, Star Wars, and Harry Potter. Yep potterites, I guarantee you'd love picking up a Polyhedron and building your own Wizard. You'll recognize all the spells that are used in Harry Potter. Although I'd probably recommend more fireballs than disarming telekinesis... but that's up to you. Hey <PERSON> is a great PowerWord Kill, don't you think?", "773" ] ]

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[ [ "Hedges for Toy Farm / Model Farm\nIntroduction: Hedges for Toy Farm / Model Farm\nInexpensive model hedging for toy farm / model farm in 1/32 scale. When playing with a toy farm it is often useful to be able to mark out a field or two with some sort of model hedging. Field edging, hedging, fencing etc tends to be expensive. In the past I had made hedging using stained 1/4 inch plywood, but these proved to be a bit bulky to store and expensive to make. This instructable recycles plastic from plastic milk bottles and so is very low cost.\nI'm sure there are many ways to improve this project and look forward to your suggestions\nSupplies\nEmpty 4 pint plastic milk bottles (two bottles per 15 inch section of finished hedge)\nScissors\nCraft knife and steel ruler\ntwo pieces of scrap timber around 3/4 x 3/4 x 16 inches\nCraft heat gun\n2 small g clamps\nsmall piece of sandpaper\nAwl, embroidery silk and needle to fit\nCheap acrylic art paints in greens / browns and paintbrush to suit.\nSmall piece parcel tape\nStep 1: Design\nDesign stage\nAt 1/32 scale an 8 ft high hedge needs to be 3 inches tall. It also needs to have a base about 1 1/2 inches wide to stand unsupported.\nStep 2: Cut Up Milk Bottles\nRemove the labels from two four-pint plastic milk bottles. With a pair of scissors cut the top and bottom from the two bottles. Cut the remaining middle bands of the bottles vertically. This leaves you with two flat pieces of thin plastic, each approximately 5 inches by 15 inches, Trim these down with a craft knife and metal ruler to two rectangles 3.75 inches x 15 inches, With a pair of scissors cut a wavy edge along one long side of each piece of plastic. These wavy edges will become the top of the finished hedge.\nStep 3: Re-shape the Plastic\nThe plastic used in these milk bottles is HDPE (high density polyethylene) with a number 2 in the recycling triangle. This plastic melts at 125 degrees and with the application of a little heat below that temperature can, to some extent, be reshaped. Read up on this online and satisfy youtrself that this process can be tackled without safety risks. Essentially what we are going to do next is to put a right angled fold along the long edge of each piece of plastic. As a heat source I have used an inexpensive crafting heat gun.\nTo hold each piece of plastic while putting in the folds, clamp the plastic between a couple of pieces of scrap wood around 3/4 inches square and 16 inches long with 3/4 inch strip protruding. It would help to hold the whole arrangement in a vice. Apply a little heat to the protruding strip while pressing it down to make a right angled fold.", "401" ], [ "This needs a little experimentation gradually adding more heat until the fold is right. You are not trying to actually melt the plastic, just to warm it enough to enable it to be re-shaped. Be careful not to burn yourself with the heat gun.\nStep 4: Construction\nOnce you have put the folds in each piece of plastic use a small piece of sandpaper to rough up the surface of the plastic to enable paint to stick to it later. The two pieces of plastic now need sticking together back to back. The two 3/4 inch folds make the base of the model hedge. I thought that a glue gun would be the easiest way of sticking the pieces together. Unfortunately hot glue will not adhere to the plastic. Packaging tape might work but I have no idea how long it would last. Some sort of physical joining would be best. Staples or eyelets will work, but might leave sharp edges, not ideal for little fingers. Sewing works. Here I have used an awl and some embroidery silk. The curved needle was used because it was the only one I had with a large enough eye for the thread. Carefully done this sewing could outline wavy edges of the bushes or trees in the hedge. My sewing is rubbish. The pieces of parcel tape in the illustration temporarily hold the two pieces of plastic together during the sewing.\nStep 5: Painting\nThe final stage is to paint the plastic hedge. Cheap artists acrylic paint works OK and a mottling effect of greens and browns adds some realism.", "959" ] ]

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[ [ "Easy & Delicious Indian Flatbread (Paratha)\nIntroduction: Easy & Delicious Indian Flatbread (Paratha)\nMost flat breads from India are unleavened and made primarily from milled flour, usually Atta or Maida, and water. Some flatbreads, especially paratha, may be stuffed with vegetables and layered with either ghee or butter.\nToday, I will be sharing a family recipe for paratha as an entry in the Bread Speed Challenge.\nThis recipe is easy for beginners to make, with minimal ingredients and prep time.\nSupplies\nThe supplies are easy to find:\nIngredients:\n4 cups of wheat flour\n1.5 cups of water\n1 tsp of both salt and sugar\n0.5 cups of ghee or melted butter.\nUtensils:\nA large Bowl (to mix)\nA griddle\nA thin spatula for flipping (I will be using a steel one)\nA surface to roll out the dough\nA pastry brush\nAnd a rolling pin (Or a large dowel, about 1 inch in diameter)\nServing - Serves 2 people if served plain, 4 if served with accompaniments like yoghurt or a savory stew.\nStep 1: Get All Your Supplies Together.\nIt is always useful to assemble everything we need before starting.\nStep 2: Dough\nAdd the 4 cups of flour into our large bowl, along with 2 tbsp of ghee or butter and 1 tsp each of sugar and salt.\nStart mixing with your hands, adding small amounts of water till it starts coming together. Add more water and knead until it has a smooth texture. (Knead about 5 minutes).\nSet aside for 10 minutes to allow the dough to breathe and soften.\nStep 3: Roll Out the Dough\nAfter resting, roll into a large noodle, about 2 inches thick. Cut sections along the noodle, at intervals of 2 inches.\nCoat your hands with the ghee or melted butter and then roll the sections into small round balls.\nRoll the balls in the dry flour\nWith a rolling pin dusted in flour, roll out each ball into a 2 mm thick disk.\nBrush ghee or melted butter on the top of the disk and sprinkle some flour on it.\nStep 4: Fold Into a Paratha\nFirst place the griddle on low heat so it heats up while we fold our paratha.\nCoat your fingers with ghee or melted butter, so the dough will not stick to them. Then follow the following steps carefully\n1.", "863" ], [ "Fold each disc as shown in the above pictures, and brush with ghee or melted butter and sprinkle with flour.\nYou will now have a square piece of dough. dust with flour and roll out, keeping it in a squarish shape.\nStep 5: Cook the Paratha\nPlace the paratha on the griddle (that we already heated up in Step 4) to cook for about 2 minutes for each side. It should have golden brown (NOT black) spots. Brush ghee or melted butter on both sides. Take paratha off the heat and and put it to the side as you cook the others.\nStep 6: Serve\nServe your paratha plain, with stews, with yoghurt, or use it to wrap minced meat and vegetables. The possibilities are endless; it is up to you how you share it with others!", "702" ] ]

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[ [ "Image Courtesy of itiswonThis review continues my series of detailed reviews that attempt to be part review, part resource for anyone not totally familiar with the game. For this reason I expect readers to skip to the sections that are of most interest.\nSummary\nGame Type - Board Game (Tile)\nPlay Time: 80-90 minutes\nNumber of Players: 2-6\nMechanics – Set Collection, Tile Laying, Resource Management\nDifficulty – Moderate (Can be learnt in under 30 minutes)\nComponents - Excellent\nRelease - 2008\nDesigner <PERSON> -(All things Alhambra, Colonia, Eketorp, Granada, High Tide, Immortals, Metro, Neptun, The Rose King, Shogun, Show Manager,Speculation, Timbuktu, Wallenstein)\n+\n<PERSON> -(All 6 Alhambra Expansions, Flandern 1302, All things Fresco, Indus, LancasterExpansions, Lucky Loop, Maharani)\nThis is the fifth in a series of reviews that will analyse each of the 5 Alhambra expansions. I will outline each expansion on its own merits and then comment on how well it interacts with other expansions in the Alhambra Family.\nAs each Boxed Expansion for Alhambra includes 4 Mini-Expansions, I will refer to a box as an Expansion Set and each of the 4 additions within each box as Mini-Expansions. This will hopefully avoid confusion as I discuss each in turn.\nAt the end of this review is a series of links to help find my other Alhambra Reviews.\nNB - Since the time of writing this review initially, a 6th expansion (The Falconers) in this format has been released. I will look to get to this expansion in the near future.\n#17 – The New Score Cards\nComponents - This Mini-Expansion consists of two component types. First there is the Scoring Round Template, which essentially outlines the points available for each round (as per the original Reserve Tile Player Boards).\nImage Courtesy of Uncle G\nThis is essential now though due to the 2nd set of components, which are the alternate Scoring Tokens. There are 18 in all and they effectively randomize the relative values of each building type for each Scoring Round. These are of a size that allows them to sit snuggly into the brackets of the Scoring Round Template.\nImage Courtesy of Uncle G\nImpact – The New Score Cards have major implications for how a game of Alhambra will play out.", "581" ], [ "Randomising the scoring of each building type means that the building type that is king one moment, may be all but worthless in the next. What results is some careful analysis at the start of the game to calculate the relative value of each building type over the course of all 3 scoring rounds. This will appeal to some and not to others.\nThe other implication is the availability of each building type. The base game was deliberately designed to have fewer of the lower scoring buildings and more of the higher scoring ones. This meant that there was more competition to gain a majority for the high scoring Towers and Gardens and with a greater number on offer, there was less chance to miss out on them if you were in ‘the wrong place at the wrong time’ which Alhambra can suffer from.\nNow of course this is not the case and those 7 Pavillions and Seraglios (blue and red buildings) may now be worth major points. Heaven help the players that are just unlucky to see them come out and get purchased before they have a chance.\nStrategy – I’ll state it again, but it is imperative to know the relative values of each building type at the start of the game as this will help you to calculate which buildings are worth overbidding for and which ones are not.\nIt can also be quite important to gain ‘The Power of the Sultan’ (see Mini-Expansion summary below)!\nInteraction with other Expansion Sets – The Power of the Sultan is another Mini-Expansion in this Expansion Box that allows players to nab buildings of a given colour when they are added to the Market. Having one of more <PERSON> cards at your disposal can be crucial in gaining buildings that are in limited supply or are worth big points at scoring.\nNaturally the Vizier’s Favour is another very handy power to use at the right time.\nFeelings – Personally I am a little conflicted about the value of this expansion. Does it throw up an interesting set of considerations, which adds to the analysis and decision making required to play the game, or is it simply another level of randomness that could possibly throw the final result into total chaos and allow for score blowouts?", "755" ] ]

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[ [ "Easy DIY Pet Bandana\nIntroduction: Easy DIY Pet Bandana\nHi Y'all! Today I will be showing you how to sew a super easy dog bandana! I love making these because they take almost no time at all, and are effortless to make new ones for all the different holidays!\nSupplies\n1. 1/4 Yard of Cotton Fabric\n2. Iron\n3. Ironing Board/ Safe Place to Iron\n4. Scissors/ Rotary Cutter\n5. Cutting Mat/ Safe Place to Cut\n6. Sewing Machine\n7. Thread\n8. Dog/ Cat/ Pet\n9. OPTIONAL: Snap Buttons\nStep 1: Pick Your Fabric\nThis is the best part of the whole tutorial, in my opinion, because you get to go to a fabric/craft store and look around! I chose a simple <PERSON> fabric, in a standard quilting cotton weave. I would recommend using cotton, because for the purposes we will be using it, it better holds a crease and is much easier to sew with than knits or other thinner/ stretchy materials.\nStep 2: Iron Your Fabric\nThe next step is to iron your fabric completely flat. Make sure you are doing this on an iron safe surface. Also, be sure to turn your iron to a steam setting, as dry heat does not work well with cotton. Once you have ironed it flat, it is time to fold it in half. You can measure the circumference of your dogs neck and fold it accordingly- Say, if your dog's neck was 24\", you would fold it in half so that the top fabric equals 12\", or half of your dog's neck size- Or, you can eyeball the length based on what your dog looks like. Here, I just eyeballed it because I've made these a million times.", "316" ], [ "One tip is to make the length about 1/2\"-1\" longer to account for sewing. You can always wrap the fabric around your pet's neck, and add an inch to get an easy measurement too.\nStep 3: Cut Your Fabric\nNow it is time to cut your fabric!! Make sure you have the correct length/size because once you cut the fabric you can't go back!! If you are worried you might mess up, a good rule of thumb is to always cut bigger than you need- You can always cut fabric away, but you can't bring it back!!! I laid my fabric on a cutting board, and used a ruler and a rotary blade to cut a straight line from corner to corner, making sure that the folded end was on the side and the long edge was at the top. When you unfold your fabric you should have a big triangle.\nStep 4: Prep Your Fabric to Sew!\nAfter you have completed steps 1 through 3, it is time to return to your ironing board. Begin by ironing your piece flat once again, then iron down the longest part of your triangle about 1/4\". It doesn't have to be perfect! Start at one end, and slowly make your way across, folding down the edge evenly. Quick Tip!!!: Make sure that you have the right side of the fabric down, and that you are folding the right side back onto the wrong side. To ensure we make an even bandana, we will only be sewing one edge at a time.\nStep 5: Begin Sewing!\nYAY!! It is time to sew! Bring your bandana to your sewing machine and prepare the thread based on your specific machine. I chose to do a wide zig-zag stitch, but you can do whatever stitch you want! Turn your fabric right side up, and begin stitching down the very edge of the fabric. Although you can't see the backside where your fold is, since you are stitching directly on the edge you will still catch the fold and adhere it together. Sew directly down the edge in a straight line, and when you get to the end, feel free to backstitch. Once you remove it from your machine it should look something like this. Trim off the excess fabrics and head back to your ironing board!\nStep 6: Back to the Basics\nTime to repeat the step you just did. Chose one of the other two sides of the triangular bandana, and iron the edges down from the right side down to the wrong side about 1/4\" wide. Once you have your side ironed down, head back to your sewing machine and sew along the edge you just ironed, following the same ideas from the previous step.\nStep 7: Final Sew!\nNow that 2/3 side of your bandana have been sewn, it is time to finish sewing that final edge. Bring your bandana back to your ironing board and iron down the final side. This side is very important though, because it will be the finishing edge of the bandana.", "748" ] ]

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[ [ "How to find the trajectory of stationary action of a photon\nI am trying to work through a \"check your understanding\" question on p.393 of the textbook From Photon to Neuron by <PERSON>. The action functional S of a photon's trajectory is proposed to be\n$S [\\underline X^\\mu(\\xi),e(\\xi)] =\\frac{\\hbar}{2} \\int d\\xi (e^{-1}||\\dot {\\underline X}||^{2} )$\nwhere $\\mu$ = 0,1,2, or 3. $\\underline X^\\mu$ are spacetime coordinates; $\\underline X^0$ is $ct$. The parameter $\\xi$ is some index along the trajectory. The variable $e$ is described as a metric necessary so that different parameterizations of the same path give the same action.", "394" ], [ "The dot denotes differentiation with respect to $\\xi$ and $||\\dot {\\underline X}||^{2} $ is the Lorentz invariant interval $ -(c \\dot t)^2 + (\\dot r)^2 $.\nThe reader is asked to show that the equation above is stationary under any trajectory that satisfies\n$0 = e^{-2} ||\\dot {\\underline X}||^{2}$ and\n$e^{-1} \\dot {\\underline X} =$ constant.\nIt's not clear to me if the second equation is implying an <PERSON> summation.\nHere is what I have tried: I introduced a small variation in both the spacetime coordinates and metric along a path and examined the action of this new worldline:\n$S [\\underline X^\\mu+ \\Delta \\underline X^\\mu,e + \\Delta e] =\\frac{\\hbar}{2} \\int d\\xi \\bigl[(e +\\Delta e )^{-1}||\\dot {\\underline X}+\\Delta\\dot {\\underline X} ||^{2} \\bigr]$\n$\\approx \\frac{\\hbar}{2} \\int d\\xi (1 -\\frac{\\Delta e}{e} )\\bigl( ||\\dot {\\underline X}||^2+2 \\dot {\\underline X}\\Delta\\dot {\\underline X}^{2} + ||\\Delta\\dot {\\underline X}^{2}||\\bigr) $\nI then subtracted the action of the original worldline to get\n$ \\Delta S \\approx \\frac{\\hbar}{2} \\int d\\xi \\bigl(\\frac {2\\dot {\\underline X}\\Delta \\dot X}{e}\n+\\frac {{\\Delta \\dot X}^2}{e}\n$ $ +\\frac {2 \\dot X \\Delta \\dot X \\Delta e}{e^2} $ $ +\\frac {\\Delta \\dot X^2 \\Delta e}{e^2} $ $ + \\frac {|| \\dot X||^2 \\Delta e}{e^2} \\bigr) $\nI figured I could neglect terms that were second order in $\\Delta$. That leaves the first and last term in the equation above. The last term must equal zero; this satifies one of the two conditions I set out to show. But shouldn't the first also have to equal zero, not a constant?\nI am hoping someone can help me track down my error(s), explain if one must vary $e$ in addition to $X$, and clarify if the second condition stated above is an <PERSON> summation, i.e. if $ \\dot {\\underline X} = c \\dot t - \\dot r$. Thanks!", "955" ] ]

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[ [ "CONVERT OLD TOOTHBRUSHES INTO MINIATURE ELECTRIC SANDERS\nIntroduction: CONVERT OLD TOOTHBRUSHES INTO MINIATURE ELECTRIC SANDERS\nThis is a very simple Instructable on how to turn old or new electric toothbrushes and/or facial massages into small electric sanders.\nI make a lot of clay and plaster sculptures and sometimes they are so small or so detailed that using sanding paper is impossible. Dremel is usually great for small details, but it can be too powerful for fragile items. Converting an electric toothbrush into a sander can help with sanding or polishing small and difficult to access places.\nI used a regular electric, rotary toothbrush as well as \"disposable\" vibrating toothbrush. They provide a completely different set of motions. I also used an old electric facial massager/brush to create a sander with a bigger head.\nAll those devices are either powered by batteries or have the ability to be re-charged.", "98" ], [ "They are not very powerful compared to regular electric sanders or dremmel-like tools, but they can be a great help when you require light sanding on small or fragile items.\nStep 1: Supplies\n* electric toothbrushes and/or facial massager https://www.amazon.co.uk/Oral-B-Pro-Expert-Toothb...\n* Velcro (scratchy side) https://www.amazon.co.uk/Soneer-Adhesive-Sticky-R...\n* Gorilla glue epoxy https://www.amazon.co.uk/Gorilla-Glue-25ml-Epoxy/...\n* scalpel or very sharp knife\n* sanding pads for electric sanders(not sanding paper) https://www.amazon.co.uk/YoiYee-Detail-Sander-Sand...\nStep 2: Remove Bristles\nUse a very sharp scalpel to remove the bristles. Use your thumb to press the bristles down and slice them away bit by bit. Make sure they are cut as close to the surface as possible.\nStep 3: Attach Velcro\nUse scissors to cut velcro to fit each toothbrush head.\nMix small amount of Gorilla glue and use it to attach velcro pieces to the heads.\nStep 4: Prepare Sanding Pads\nAs mentioned before, use sanding pads with soft velcro backing. Cut them to fit the heads of the toothbrushes.\nStep 5: Attach Sanding Pads\nOnce the glue is dry, attach the sanding pads to the heads. If you want to replace used pads, simply peel them off and attach new pads.", "320" ] ]

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[ [ "How to add more theta parameters into my logistic regression?\nI am a complete beginner in machine learning and coding in python. I have been tasked with coding logistic regression from scratch in comparison with using sklearn. My question is, with my code below I believe I have set the number of thetas I want with:\n\"X = data[['texture_mean','perimeter_mean','smoothness_mean','compactness_mean','symmetry_mean', 'diagnosis']]\"\nbut I am unsure how to prove this is true with my code below and its definition of theta, if I added more parameters (e.g. all 31 variables of this dataset [https://www.kaggle.com/uciml/breast-cancer-wisconsin-data] which is for classifying tumours) would I just need to add them into this list above? Any help pointing me towards the right direction just to understand this better would be appreciated.\nX_train,X_test,Y_train,Y_test = train_test_split(X,Y,test_size=0.3)\nX = data[\"diagnosis\"].map(lambda x: float(x))\nX = data[['texture_mean','perimeter_mean','smoothness_mean','compactness_mean','symmetry_mean', 'diagnosis']]\nX = np.array(X)\nX = min_max_scaler.fit_transform(X)\nY = data[\"diagnosis\"].map(lambda x: float(x))\nY = np.array(Y)\ndef Sigmoid(z):\nif z < 0:\nreturn 1 - 1/(1 + math.exp(z))\nelse:\nreturn 1/(1 + math.exp(-z))\ndef Hypothesis(theta, x):\nz = 0\nfor i in range(len(theta)):\nz += x[i]*theta[i]\nreturn Sigmoid(z)enter preformatted text here\ndef Cost_Function(X,Y,theta,m):\nsumOfErrors = 0\nfor i in range(m):\nxi = X[i]\nhi = Hypothesis(theta,xi)\nerror = Y[i] * math.log(hi if hi >0 else 1)\nif Y[i] == 1:\nerror = Y[i] * math.log(hi if hi >0 else 1)\nelif Y[i] == 0:\nerror = (1-Y[i]) * math.log(1-hi if 1-hi >0 else 1)\nsumOfErrors += error\nconst = -1/m\nJ = const * sumOfErrors\nprint ('cost is: ', J )\nreturn J\ndef Cost_Function_Derivative(X,Y,theta,j,m,alpha):\nsumErrors = 0\nfor i in range(m):\nxi = X[i]\nxij = xi[j]\nhi = Hypothesis(theta,X[i])\nerror = (hi - Y[i])*xij\nsumErrors += error\nm = len(Y)\nconstant = float(alpha)/float(m)\nJ = constant * sumErrors\nreturn J\ndef Gradient_Descent(X,Y,theta,m,alpha):\nnew_theta = []\nconstant = alpha/m\nfor j in range(len(theta)):\nCFDerivative = Cost_Function_Derivative(X,Y,theta,j,m,alpha)\nnew_theta_value = theta[j] - CFDerivative\nnew_theta.append(new_theta_value)\nreturn new_theta\ndef Logistic_Regression(X,Y,alpha,theta,num_iters):\nm = len(Y)\nfor x in range(num_iters):\nnew_theta = Gradient_Descent(X,Y,theta,m,alpha)\ntheta = new_theta\nif x % 100 == 0:\nCost_Function(X,Y,theta,m)\nprint ('theta: ', theta)\nprint ('cost is: ', Cost_Function(X,Y,theta,m))\ninitial_theta = [0,1]\nalpha = 0.01\niterations = 1000\nLogistic_Regression(X,Y,alpha,initial_theta,iterations)", "422" ] ]

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[ [ "Use of Helmholtz free energy in problem involving spring-gas subsystem in thermal contact with a reservoir\nI have come across a problem from \"Biological Physics\" by <PERSON> (pg212) which involves finding the equilibrium position of a spring, $x_{eq}$, which is compressing an ideal gas whilst in contact with a heat reservoir of temperature, $T_{res}$. A diagram of the setup is shown below:\nI believe that solving it involves the minimisation of the system's free energy $F$:\n$$F = U - TS $$ $$dF = dU - TdS - SdT $$\nwhich simplifies to\n$$ dF = -SdT -pdV$$\nusing $dU = TdS - pdV$.\nSince the system is at thermal equilibrium with a head bath, $dT = 0$.", "474" ], [ "Also, the pressure and volume can be written in terms of the spring extension and constant: $V = A(L-x_{1})$ and $pA = \\frac{1}{2} kx^{2}$ (when at equilibrium) so that $dV = -Adx_{1}$ and $ dp = \\frac{k}{A}x$.\nHowever, setting the equilibrium condition $dF=0$ leaves me with\n$$ dF (=0) = dW = -pdV = \\frac{1}{2}kx^{3}dx $$\nwhich gives an extension of 0 as a (somewhat unhelpful) result.\nA second attempt involved writing $dW$ as\n$$ dW = fdx_{1} $$ where $f$ is the force on the compression plate so that\n$$ f(x_1) = \\frac{1}{2}x_{1}^{2} - pA $$\nwith the solutions of $f(x_1) = 0$ giving the equilibrium position of the plate assuming the ideal gas law $pV = pA(L-x_{1}) = nRT$. I believe this involves solving\n$$ x_{eq}^{3} - Lx_{eq}^{2} - \\frac{2nRT}{k} = 0 $$\nHowever, this solution appears to avoid all thermodynamic arguments, and just simplify to solving a simple mechanical problem assuming ideal gas behavior, which makes me believe I have make a mistake somewhere along the derivation.\nAny advice with the exercise, and on understanding the application of free energies to thermodynamic problems would be much appreciated.\n---------------------EDIT-----------------------\nI realise that I erred on the penultimate equation ( $f(x_{1}) = kx_{1} - pA$), which then leads to the equation $kx_{eq}(L - x_{eq}) = nRT$. This seems to suggest that the total internal energy of the system can be split into the energy of the spring, and the energy of the gas so that $$dU_{total} = dU_{gas} +dU_{spring} = -pdV + kxdx$$ It appears that my mistake was to treatthe spring as a seperate entity, and forgetting its energy addition to the total internal energy of the system", "37" ] ]

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[ [ "When using <PERSON> solvers to solve $\\mathbf A \\mathbf x = \\mathbf b$ systems, singularity in $\\mathbf A$ can be pretty benign as long as $\\mathbf b$ is consistent. Consider applying the conjugate gradient (CG) algorithm to a symmetric positive semidefinite $\\mathbf A$ (singular, but all non-zero eigenvalues still positive). Further assume $\\mathbf b$ is in the range of $\\mathbf A$, and we pick the initial guess to be $\\mathbf x = \\mathbf 0$. Then, the search vector/residual $\\mathbf r = \\mathbf b - \\mathbf A \\mathbf x$ will always be orthogonal to the nullspace of $\\mathbf A$ (because in CG, search vectors/residuals are always drawn by applying $\\mathbf A$ to previous residuals, and this multiplication by $\\mathbf A$ can't generate any component in the nullspace).", "768" ], [ "The algorithm can never \"sense\" the singularity of $\\mathbf A$, and will converge to the (unique!) $\\mathbf x$ such that $\\mathbf A \\mathbf x = \\mathbf b$ and $\\mathbf x \\perp \\mathrm {null}(\\mathbf A)$\nA short demo in matlab:\nclear all\nclose all\n% Form positive semidefinite A.\nN = 10;\n[Q,~] = qr(rand(N));\nD1 = linspace(1,N/2,N/2);\nD2 = zeros(1,N/2);\nD = diag([D1 D2]);\nA = Q*D*Q';\nkappa = cond(A) % infinite/singular\n% Form random b in range(A).\nb = A * rand(N,1);\n% Solve A*x=b using CG.\nx = pcg(A,b);\n% Check properties.\nresidual = norm(A*x-b)\nnullity = norm(x'*null(A))\nSimilar arguments can be made for other <PERSON> solvers, but I can't really speak to \"classical\" iterative solvers (Gauss-Seidel etc) .. I doubt they are as well-behaved.\nThere are preconditioning strategies (deflation) based entirely on this idea: find a basis for the eigenvectors of $\\mathbf A$ that are somehow problematic to the solver, then \"deflate\"/project them out (change the operator such that the corresponding eigenvalues are mapped to zero), then apply the same projection to $\\mathbf b$, and iterate away. For more information about deflation preconditioning (which involves convergence analysis for singular systems), I recommend:\n<PERSON>, <PERSON>, et al. \"A comparison of two-level preconditioners based on multigrid and deflation.\"\n<PERSON>, <PERSON>, and <PERSON>. \"Deflation and balancing preconditioners for <PERSON> subspace methods applied to nonsymmetric matrices.\"", "768" ] ]

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[ [ "The <PERSON>-Sham approach to density functional theory is based on a self-consistency scheme to obtain the ground-state electron density of the investigated material. As a starting point the scheme uses an input density that is some approximation to the ground-state density. It uses the density to determine the effective potential $V_\\text{eff}(\\mathbf{r})$ consisting of the Hartree potential, the exchange-correlation potential, and the external potential due to the atomic nuclei.\nWhen you have this the next step is the solving of the <PERSON>-Sham equations (here in Hartree atomic units) $$\\left. -\\frac{1}{2}\\nabla^2+V_\\text{eff}(\\mathbf{r}) \\middle| \\psi_i \\right\\rangle = \\left. \\epsilon_i \\middle| \\psi_i \\right\\rangle,$$ where the $\\psi_i(\\mathbf{r})$ are the Kohn Sham orbitals. The Kohn-Sham equations are eigenvalue equations that are typically approached by introducing some kind of basis functions $\\phi_i(\\mathbf{r})$ to get a formulation of the problem that can be solved with the tools of linear algebra. With the basis functions we obtain a Hamiltonian matrix $$H_{ij} = \\left\\langle \\phi_i \\middle| -\\frac{1}{2}\\nabla^2+V_\\text{eff}(\\mathbf{r}) \\middle| \\phi_j \\right\\rangle$$ and an overlap matrix $$S_{ij} = \\left\\langle \\phi_i \\middle| \\phi_j \\right\\rangle.$$ The Kohn-Sham equations thus become a generalized eigenvalue matrix problem. It can be solved by turning it into a standard eigenvalue problem and then diagonalizing the matrix for this problem with standard linear algebra methods.", "768" ], [ "In the end you obtain the orbital energies along with the eigenstates of the problem in terms of linear combinations of the basis functions.\nNext would be the determination of an output density with these eigenstates by occupying them with electrons. Then you have to guess an improved input density based on the last input densities and the output density. The loop is iterated again and again until the density is self-consistent, i.e., input and output densities are (nearly) the identical.\nYou mentioned in your question that you already have the electron density, but this is probably only an approximation to the self-consistent density that you obtain from the Kohn-Sham scheme. Otherwise you should have constructed the Kohn-Sham orbitals in the determination of your density.\nNote that the choice of the basis set $\\left\\lbrace\\phi_i\\right\\rbrace$ is critical to obtain reasonable results. If you want to include all electrons in your calculations the orbitals feature strong oscillatory behaviour near the atomic nuclei because of the singularity of the external potential at these points. You need a lot of intuition to design a basis that is capable to represent such orbitals. An example for a basis that is capable to do this is the linearized-augmented plane-wave (LAPW) basis.\nAnother approach would be the introduction of the pseudopotential approximation that cuts away the core electrons and replaces the real external potential by a pseudopotential that yields smooth valence electron eigenstates featuring (for a prototype system) the same energy eigenvalues as an all-electron calculation. These can be represented by a simple plane-wave basis but the transferability of the pseudopotential to materials deviating from the prototype system is not necessarily given.", "976" ] ]

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[ [ "The problem lies on the notation. The state $|\\psi\\rangle$ is not exactly equal to the eigenfunction $\\psi(x)$.\nThe eigenfunction $\\psi(x)$ is formally defined to be the projection of the state to the position basis $|x\\rangle$ i.e. $$ \\psi(x)=\\langle x|\\psi\\rangle $$\nTherefore the eigenstates $|\\psi\\rangle$ are not \"functions\" of position. Similarly, the operators can be represented as differential operators, but a more correct way of doing so is as follows. For this example I am using the momentum operator in the position representation:\nLet $|x\\rangle$ and $|y\\rangle$ be two orthonormal states in the position basis.", "66" ], [ "We note that $[X,P]=i\\hbar$, therefore $$ i\\hbar\\langle x|y\\rangle = \\langle x|[X,P]|y\\rangle=\\langle x|XP|y\\rangle-\\langle x|PX|y\\rangle=(x-y)\\langle x|P|y\\rangle $$ Since $\\langle x|y\\rangle=\\delta(x-y)$, then $$ \\langle x|P|y\\rangle=i\\hbar\\frac{\\delta(x-y)}{x-y}\\equiv i\\hbar\\frac{\\partial}{\\partial y}\\delta(x-y) $$ Which is a property of the Dirac delta i.e. $\\frac{\\partial}{\\partial y}\\delta(x-y) = \\frac{\\delta(x-y)}{x-y}$. Therefore we see that\n$$ \\langle x|P|\\psi\\rangle=\\int dy \\langle x|P|y\\rangle\\langle y|\\psi\\rangle=\\int dy \\bigg(i\\hbar\\frac{\\partial}{\\partial y}\\delta(x-y)\\bigg)\\langle y|\\psi\\rangle $$ $$ =\\int dy i\\hbar\\frac{\\partial}{\\partial y}\\delta(x-y)\\psi(y)=-i\\hbar\\frac{\\partial}{\\partial x} \\psi(x) $$ From this it is suitable to use the representation \\begin{equation} P\\longrightarrow -i\\hbar\\frac{\\partial}{\\partial x} \\end{equation} As you can see, the operator $P$ in a more general sense is not equal to $-i\\hbar\\frac{\\partial}{\\partial x}$, thus the arrow instead of an equality. It is mere a representation.\nNow that we have this information at hand, in truth when some books or lectures say $$ \\frac{d}{dx}|\\psi(x)\\rangle\\langle u(x)| $$ what they actually mean is $$ \\bigg(\\frac{d}{dx} \\psi(x)\\bigg)u(x) $$ Additional notes:\nWe can see the relationship of the momentum and the position bases states as $$ p\\langle x|p\\rangle=\\langle x|P|p\\rangle=-i\\hbar\\frac{\\partial}{\\partial x} \\langle x|p\\rangle $$ which is a first order partial differential equation, solving this gives $$ \\langle x|p\\rangle=\\frac{1}{\\sqrt{2\\pi\\hbar}}e^{\\frac{ipx}{\\hbar}} $$ i.e. the bases are Fourier transforms of each other $$ |p\\rangle=\\frac{1}{\\sqrt{2\\pi\\hbar}}\\int dx e^{\\frac{ipx}{\\hbar}}|x\\rangle $$ $$ |x\\rangle=\\frac{1}{\\sqrt{2\\pi\\hbar}}\\int dx e^{-\\frac{ipx}{\\hbar}}|p\\rangle $$", "955" ] ]

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[ [ "Belarus Catches Up to Russia With Its Own Pro-government ‘Troll Factory’ · Global Voices\nBelarusians are noticing suspiciously similar comments under news articles—are government trolls to blame? Images mixed by <PERSON>.\nAs the relations between Russia and the West soured over the ongoing crisis in Ukraine, Kremlin officials have been intensifying their information manipulation efforts. This summer for the first time the world found out about Russian troll factories—the secretive agencies that hire people to write and spread pro-Kremlin propaganda on the Internet.\nIt turns out, there is a online troll factory in Belarus as well. Several months ago local media detected accounts posting similar positive comments about the Belarusian ruble to US dollar exchange rate. The dollar exchange rate has soared almost six-fold during the last five years, with the Belarusian ruble heavily dependent on the state of neighboring Russia's economy, which is currently in deep trouble. At the end of August, 2015, the US dollar surpassed 17,000 Belarusian rubles—a record high. For reference, at the beginning of 2011 one US dollar cost 3,000 Belarusian rubles.\nIt was in August of this year that journalists of the opposition newspaper Nasha Niva (Our field) first noticed that some users were praising the ruble, at the time when it was so unstable. The suspected trolls would write that they “believed in ruble” and that Belarusians would overcome all temporary difficulties: “Don’t panic! Everything's gonna be alright!” Journalists dutifully copied all the “suspicious” comments and published a collection of them on their website (many original comments have since been deleted after the “unmasking.”)\nIn general, the Belarusian trolls are seen using three main tactics.", "564" ], [ "First, one should say that everything is alright and that any concerns about the issue are simply a sign of panic.\nРешили посеять панику? Зря. Валюты в обменниках хватает. Покупайте! И вообще-то, в стране все под контролем)))\nSo you decided to spread panic? It's no use. There is enough currency in exchange offices. Buy it! And, by the way, everything in the country is under control.\nSecond, one should mention that Belarusians don't need dollars, because they spend their money in Belarus, not in the US.\nНавошта мне гэтая амерыканская валюта!? Я усе свае дабро берагу у беларуских рублях. Я жыву у Беларуси, а не у Амерыцы\nWhat do I need this American currency for? I keep all my savings in Belarusian rubles. I live in Belarus, not in America.\nAnd thirdly, always blame the West.\nВсе мы понимаем, почему происходит падения рубля: сейчас это явно спровоцировано из вне. И если бы власть сегодня «показушно» сдерживала курс, то неизвестно к чему бы это привело к концу года.", "564" ] ]

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[ [ "Differential Thermal Analysis Using Arduino and PhyPhox\nIntroduction: Differential Thermal Analysis Using Arduino and PhyPhox\nWhen a solid substance is heated the increase in energy manifests itself in the form of an increase in temperature.\nIf the heating rate is constant the temperature increase is also constant as long as there is no change in the structure of the substance.\nAt the time when some kind of transition is initiated in the substance, for example fusion, change of crystal structure or other, the temperature will not increase at the same rate because part of the heating energy will be used in that change of state.\nIf we compare the temperature of the substance that is experiencing the change of state (Sample) with that experienced by another substance that remains stable (Reference) during heating under identical conditions and subtract a temperature value from another (Sample - Reference) we will be performing what is known as Differential Thermal Analysis (DTA).\nThe objective of this Instructable is to show the basics of the DTA using Arduino microprocessor, a home heater and a free access program (PhyPhox) that will allow us to obtain on our cell phones curves of Sample Temperature vs Difference (Sample Temperature - Reference temperature) known as thermograms.\nSupplies\n* Cell Phone (Android or iOS).\n* PhyPhox app (Google Play or AppStore).\n* 1 Plastic container with multiple compartments.\n* 2 Waterproof DS18B20 temperature sensor.\n* 2 Breadbord mini modular.\n* 1 Arduino Nano V3.0 CH340 with mini usb cable.\n* 1 Bluetooth Low Energy BLE CC2541 Bluetooth 4.0 UART.\n* 1 1k ohm resistance.\n* 1 2k ohm resistance.\n* 1 4,7k ohm resistance.\n* Male/Male jumpers wire.\n* Male/Female jumpers wire.\n* 1 Portable battery charger (6000 mAh 3.7V, Out 5V, Output Max. 2.4A).\n* 4 Glass test tubes (approximately 1 cm in diameter and 7.5 cm long)\n* Wooden base (circular or square of approximately 20 cm in diameter or side).\n* 1 Ceiling lampholder (E27).\n* 1 Incandescent light bulb of 25 Watts (E27).\n* 1 Rotary dimmer switch.\n* Approximately 1 m of electrical cable (two cores 0.4 mm thick).\n* 1 Two pin electric socket.\n* 1 Clothes dryer aluminum duct reducer (10.16 cm to 7.62 cm).\n* 2 Disposable circular aluminum plates of approximately 20 cm in diameter.\n* 2 Wire insulate screw cap.\n* Electrical tape.\n* Silicone or Epoxi glue.\n* Plastic fasteners.\nStep 1: Heating Device\nA DTA equipment basically consists of a furnace containing two containers, one for the Sample and one for the Reference and two sensors that measure the temperature of Sample and Reference simultaneously.\nThe temperature inside the furnace and its heating or cooling rate must be very well regulated so the construction of the furnace in professional equipment is an important factor in the design of a DTA apparatus, however for the illustrative purposes of this Instructable it was chosen to make a rather modest design using homemade materials (see supplies list) as indicated below :\n* Fix on a wooden base a ceiling lampholder (E27) provided with two core electrical cable with two pin electric socket.\n* Section one of the cores of the electrical cable and connect a rotatory dimmer switch, using wire insulate screw cap or electrical tape to reestablish the cable connection.\n* Screw an incandescent light bulb (25 Watts, E27) into the ceiling lampholder.\n* With the help of glue, fix on the surface of the ceiling lampholder a clothes dryer aluminum duct reducer (10.16 cm to 7.62 cm) so that the end of smaller diameter is like a chimney around the incandescent light bulb (Caution: Once the bulb is turned on this surface will be hot so there will be a danger of burn).\n* Fold the surface of a disposable circular aluminum plates in such a way as to form a concavity that fits on the chimney formed by the clothes dryer aluminum duct reducer (see video in Step 3).\n* Using another plate repeat the previous operation forming a concavity that fits on the first and in which two holes near the top of the concavity but separated from each other will be drilled, with a diameter that allows to receive the test tubes (approximately 1 cm in diameter and 7.5 cm long) of Sample and Reference.\n* Insert the Sample and Reference test tubes into the drilled holes by pushing until only about 1 cm is left outside. Deform the surface of the aluminum sheet in such a way that they fit on the surface of the test tubes and fix them.", "152" ] ]

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[ [ "A first problem is that there is in GR no such thing as \"an observers frame\", except in sloppy speech. There are various systems of coordinates. Two systems of coordinates may agree for an observer as much as one likes but differ elsewhere. And all the systems of coordinates are on equal foot, none is preferred.\nWhat could replace the \"observer's frame\"? The most plausible candidate seems to be the use of harmonic coordinates - they really essentially simplify the <PERSON> equations, are used in the Newtonian limit and in the PPN formalism (see here) or in <PERSON> local existence and uniqueness proof, roughly the only reasonable candidate for preferred coordinates. To define harmonic coordinates, one need some initial values, because the harmonic condition is only an evolution equation $\\square X^\\mu = 0$ for them, but this is given by the <PERSON> coordinates before the collapse.", "578" ], [ "This gives, roughly, the Schwarzschild time coordinate, thus, it would be such a system of coordinates where the material of the collapsing star never reaches the horizon.\nFrom point of view of classical GR, the only objection is that these coordinates would not cover the complete solution.\nIf one includes Hawking radiation into the consideration, one should care about the trans-Planckian problem (to derive that Hawking radiation lasts more than a second after the collapse, one has to presuppose that semiclassical theory remains valid for distances of $10^{-1000}$ of Planck length or so). The mainstream way to solve this problem is to rely on some results of <PERSON> and others that some Hawking radiation remains if one considers various regularizations. The problem is that these regularizations break covariance, thus, require preferred coordinates, and they obtain <PERSON> radiation only if the preferred coordinates are those related with the infalling observers. If they are stationary, there will be no <PERSON> radiation. And if one wants to rely on modifications of GR with preferred coordinates, see above for candidates.\nIf one ignores this and assumes Hawking radiation, then one can publish the idea that the BH evaporates before being formed even in Phys.Rev., as done by <PERSON>, PRD 14, 1479 (1976), and get citations by standard textbooks like <PERSON>, <PERSON>, quantum fields in curved spacetime, so it is close enough to being tenable.", "469" ] ]

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[ [ "It’s Emancipation Day in Trinidad & Tobago — but is the country free? · Global Voices\nRedemption Song Statue, Emancipation Park, Jamaica. Photo by <PERSON>, used with permission.\nAugust 1 is celebrated in many Caribbean territories as Emancipation Day, marking the freedom of enslaved Africans who were victims of the transatlantic slave trade.\nTrinidad and Tobago was the first country in the world to declare a national holiday to mark the abolition of slavery, but 34 years after that first public holiday was instituted and 185 years after the Slavery Abolition Act first came into effect, great discussion continues over whether or not the twin-island republic is emancipated.\nSpeaking about the issue on July 27, 2019, Prime Minister Dr. <PERSON> observed that among Trinidad and Tobago's diverse population, people of African descent “are not doing as well as we expected”. <PERSON> said that rising levels of violence which are part of the black, urban youth experience, should be inspiring citizens to “focus, reflect and have serious conversations about where we are as a nation”.\nChairman of the country's Emancipation Support Committee, <PERSON>, agreed.\nSome letters to the editor gave examples of modern slavery to make the point that true emancipation still seems a long way off, while others tried to make the occasion a political one, by criticising certain social services and a culture of “handouts.”\nThe Trinidad Express chose to feature an opinion on Emancipation Day which suggested that <PERSON>, <PERSON>, and activist <PERSON> were wrong about why some Afro-Trinbagonians may be underperforming:\nIt is easy for a dominant group to create a system that discriminates and subjugates. Those who do not measure up to that system are categorised as under-performers and relegated to second class or worse. […]\nSo many of our systems, education the leader, put people unfairly in a caste and they are not given a second chance. Every system has a rating and the further away it is from the top, the lower the ranking. Those who find themselves on the bottom rung have great difficulty coping with the elevated systems.", "678" ], [ "Self-esteem is low and in their perceived helplessness may even drive them to employ violence to counter-punch suppression.\nCommentator <PERSON> lauded the country's “commendable history of maturity” when it comes to discussing race-related issues, but he also suggested the problem lay deeper, within the system itself, and suggested the prime minister's message should motivate citizens to examine how institutional racism continues to be a restrictive force.\nSocial media users shared their musings as well. In a public post, Facebook user <PERSON> said:\nOn this day we remember and commemorate the freedom of our ancestors from the physical bondage of slavery.\nToday, many generations later, we the decendants [sic] of slaves struggle with the legacies left by colonialism.\nLegacies which thrive and are perpetuated by stereotypes: We are not savage, we are not violent, we are not predators, we are not just thugs and gangsters. We are leaders, revolutionary thinkers, visionaries, philosophers. We are <PERSON>, <PERSON>, <PERSON>, <PERSON>, <PERSON>. […]\nLet us recognize that colourism is an inherited tool used to divide us […]\nLet us call out respectability politics: a culture of dilution; stop playing down blackness to make it palatable to the masses […] Let us celebrate the rediscovery of our faith and belief systems. They took away the religion of our ancestors, they took away a belief system and sense of values. In today's world of information access you owe it to yourself to explore the belief systems of our ancestors, the reverence and honouring of the elders, the owning of one's actions […] an emphasis on choice and consequence, there is belief in the family, the extended family, the village, the community.\nThis emancipation embrace the fullness and richness of who you are, where you came from, the blood and history that's in your veins. Own with pride who you are, your culture, your identity.", "127" ] ]

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[ [ "I've been also looking for the answer of this question, and I give my different view of Gumbel softmax just because I think this is a good question.\nFrom a general point of view: We use softmax normally because we need a so-called score, or a distribution $\\pi_1 .. \\pi_n$ for representing n probabilities of categorical variable with size n; We use Gumbel-softmax to sample an one hot sample [0..1..0] from this distribution.\nIn more concrete examples: Normally in networks for NLP(which categorize outputs into different word tokens), softmax is used to calculate the distribution of different, say, 5000 word choices at current text position. the cross entropy loss, gives a measure about the difference between the softmax predicted distribution and the real word distribution; For Gumbel-softmax, it is normally used to generate a sample one-hot vector for the constructing the following network, like in some VAE-based models. That's why the temperature factor $\\tau$ is a must for Gumbel-softmax, and in most cases not needed in softmax.\nAt this point, we know the difference of their uses cases, now comes the confusing part: the two formulas are so similar, why they are doing the different things?\nThe first key factor: What makes the difference is the $g_i$ term in the Gumbel-softmax formula. It represents a point sampled from the distribution $Gumbel(0, 1)$. the adding term $log(\\pi_i)$ and the scaling term $\\tau$ is just used to reparameterize it to $Gumbel(log(\\pi_i), \\tau)$ (reparameterization trick is for making it differentiable). This Gumbel distribution is the key distribution for sampling a categorical variable in Gumbel-max method(hard and not differentiable since there is a argmax), and this is also where the name Gumbel comes from in Gumbel-softmax. Every time we use Gumbel-softmax, we need to randomly sample from $Gumbel(0,1)$ and do the reparameterization trick, this is the most different part from softmax.\nI would rather name it soft-Gumbel-max, to indicate it is motivated to make a soft version of Gumbel-max, instead of just intending to add a Gumbel term to softmax.\nThe second most significant difference: is the use of $\\tau$. In most neural networks, softmax is not coupled with this term. Since we normally need a distribution, not a nearly one-hot vector. What's more, in some cases, like beam search, we need to get the second or third most probable choices to explore global optimal searches.", "915" ], [ "In softmax, $\\tau$ is normally added with some domain-specific knowledges to make the distribution steeper. Smaller $\\tau$ not always means better, we need to tune it to best fit the model. For Gumbel-softmax however, in the later stage of the model training, we need the Gumbel-softmax as close to one-hot vector as possible. That's why we need to anneal it smaller and smaller during training.(the $\\tau$ is not too small at the beginning of training for this makes the training more stable). In some implementation like torch.nn.functional.gumbel_softmax, it uses the straight through trick hard - (detached soft) + soft to maintain the output value a one-hot vector as in hard Gumbel-max but with well-defined gradients as in soft differentiable Gumbel-softmax.\nThe most part I disagree with the previous answer is that, Gumbel-softmax will not give you the exact one-hot vector. It is still an estimation of one-hot vector. Even for straight-through, the forward pass is Gumbel-max and only the backward pass is Gumbel-softmax.\nThat's almost all how I understand Gumbel-softmax, Gumbel-max and softmax. Please comment if there is anything unclear or incorrect.\nMORE If you still confuse\nAfter writing this answer, I found that, although the use cases of softmax and Gumbel-softmax are different, but we can still force to apply softmax in the place where Gumbel-softmax is applied without getting any arithmetic problem, and vice versa. Because both of them are soft and not exact, and both of them are differentiable. To make clearer why this is a problem. let's make two very gross examples of misuse.\nSuppose there is a network needing a sample but not a distribution of a categorical variable, e.g.", "915" ] ]

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