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When trying to find the next branch of a decision tree, is it necessary to calculate the cost of every possible split, in every possible feature?

Itplicated. For typical decision trees the answer is not quite. It depends on the of feature For discrete ordered variables you can simply check each point (e.g. you have to check 3 if say temperature is cool warm hot). For discrete unordered variables you can take one of two approaches find a split into subsets (which is nasty because it O(n^2) in the number of possible values) or you can take a it X or not X approad. For continuous values you only need to look at some cut points (basically the points along the axis where the class labels change). Fayyad and Irani ( ) proved this in 1993. However for ensembles especially italic random forest approaches they deliberately limit the set of features considered at each node. That how they get the diversity of trees.

Is 1q2w3e4r a safe password?

Disclosure I work for AgileBits the makers of 1Password It certainly isn't safe now that you've posted it but it never was a good password. 1q2w3e4r appears 872 times italic in Mark Burnett's collection of 1 million passwords. Keyboard patterns nAutomated password cracking systems (such as John the Ripper and Hashcat) have long include keyboard patterns among their cracking rule sets. More recently (212) this has been formally studied and appears in this paper (PDF) by Hsieh-Cheng Chou and colleagues Here is part of the abstract of that paper. ... Onemonly used trick is to use keyboard patterns i.e. key patterns on a keyboard to create passwords that conform to theplex rules. This paper proposes an efficient and effective method to attack passwords generated from some special keyboard patterns. We create a framework to formally describe themonly used keyboard patterns of adjacent keys and parallel keys called AP patterns to generate password databases. Our simuation results show that the password space generated using AP patterns is about 2^ times smaller than that generated for a brute-force attack. ... tttt Here is figure 6 from their papern n Clever tricks are a bad idea nMore importantly you should keep in mind that people who crack passwords know more about the clever tricks that peoplee up with than the peopleing up with them. Cleverness typically reduces italic the search space. Remember the goal isn't to reach somebination of letters digits and symbols. The goal is to produce something that is hard to guess italic by automated systems built by people who've looked at millions of passwords. Real randomness is required n What you need instead is randomness. As I disclosed up top I work for apany that makes a password manager. The idea is that almost all of the passwords that you use should be truly random gibberish generated by aputer. But because all of those can't be remembered a password manager remembers them for you. For the small handful of passwords such as the Master Password for your password manager you do need to create strong memorable passwords. The scheme for creating good Master Passwords that I described four years ago is something that I think still holds up Toward Better Master Passwords s

Why did the Greeks invent mermaids?

Well they didn quite invent mermaids as such. The Ancient Greeks invented sirens who were bird-women rather than fish-women and who seduced seafarers to their doom as featured in the Odyssey Spencer Alexander McDaniel's answer to Were the sirens of Greek mythology actually intended to be bird-women not mermaids? answer aid 15176115 The Modern Greeks have a mermaid figure and the Greek folklorist Dimitris Loukopoulos account from 1926 ( PDF pager s ) speaks of the Mermaid as a woman with fish tails. But she is not a cute cuddly Ariel figure ue la Hans Christian Andersen. (Then again neither were mermaids in the rest of European folklore) There one of them in Greek folklore not multiples of them. In fact Greek Wikipedia distinguishes between the singular Mermaid s(u3bbu3b1u3bfu3b3u3c1u3b1u3c6u3afu3b1) as the Greek folklore figure and the plural Mermaids s(u3bbu3b1u3bfu3b3u3c1u3b1u3c6u3afu3b1) as pretty much all the other folklores figures. The Mermaid causes hurricanes drags sailors off boats and sinks ships. The Mermaid is Alexander the Great sister who has drunk the immortal water and so will never die. She lives in the Black Sea (which is notoriously stormy) butes down to the Aegean often. She often appears midnight on Saturdays. The Mermaid challenges sailors with the questions Is King Alexander alive? If you answer no you drown. If you answer yes the sea will calm and she will play you sweet music; sweet enough that Greeks had the proverbial expression He learned that song from the Mermaid. (Yes she is a Siren.) A clever and quick woman was called in Greece a Mermaid; a clever and quick child and indeed a clever and quick beast of burden was called with the neuter of Mermaid. The Modern Greek Mermaid is called a name straight out of Greek mythology. No not Seiru113na italic . Gorgona italic from the Gorgon - Wikipedia s While descriptions of Gorgons vary and occur in the earliest examples of Greek literature the termmonly refers to any of three sisters who had hair made of living venomous snakes s as well as a horrifying visage that turned those who beheld her to stone s . Traditionally while two of the Gorgons were immortal Stheno s and Euryale s(Gorgon) their sister Medusa s was not and she was slain by the demigod and hero Perseus s . The swiftness of the Modern Greek Gorgona italic is folk etymology the Ancient word gorgos italic meant grim and the word gorgos italic had already changed in meaning by the Koine to lively and in Modern Greek to swift. So the Ancient Greek Mermaid is a Siren and the Modern Greek Mermaid is a Medusa (with a lot inmon with Sirens). They were both invented because the sea was a scary place and folklore and mythology (which after all are the same thing) personalised that scariness through predatory monsters. The fact that the Modern Gorgona lives in the treacherous Black Sea is not a coincidence. The Ancient Sirens were more birds than women; the Modern Gorgona is an intriguingbination of fear of the sea and awe of Ancient Greece (Alexander the Great). Manatees s live nowhere near the Mediterranean by the way so they are not the inspiration for Greek Mermaid figures (and they weren behind the Sirens). The Modern Greek Mermaid may have a fish tail because of sighting seals but people knew full well what seals were in Greece so I don buy that. I surmise they stuck a tail on the Mermaid so she could be both human (sister of Alexander) and able to navigate from the Black Sea to the Aegean.

Astronauts on NASA's 1969 mission to the moon landed there during the daytime. Since the moon has no atmosphere, daytime temperatures can reach 100 degrees C and there is only a space suit for protection and life support. How did they manage?

Temperature is a tricky thing in space. Temperature is actually a measure of the kinetic energy of the atoms in some solid liq or gas so in a vacuum where there are no atoms - there is no such thing as temperature - it a meaningless thing even to talk about. But how hot some material object bes depends on its reflectivity. If an object is very light in colour itll reflect most of the sunlight and stay fairly cool - but dark objects that absorb most of the iing light will get very hot. Youll notice that the Apollo moon suits are white in colour - and that large areas of the LEM were wrapped in reflective gold foil and the remainder painted white. The moon has fairly dark grey rocks - so without an atmosphere and with 14 day-long days and 14 day-long nights - the daytime temperature of the ground might reach way over 1 degrees C - so the astronauts wore thick boots and heavily insulated suit and gloves when outside the LEM. But it a bit moreplicated even than that. Areas that are in shadow don get any direct sunlight at all and with insignificant lighting from the sky (unlike here on Earth in daytime) - objects would be quite cold if they were in shadow for long periods. The atmosphere also helps to even out temperature - it gets heated and cooled by other objects - which tends to cause objects to converge on some average temperature everywhere - no matter whether they are in sun or shade. But without an atmosphere - there can be DRASTIC differences in temperature between sunlit and shadowed objects. For things like space suits - this isn such a problem because the astronauts weren standing still for hours on end - so the heating and cooling of the suits would tend to even out. However in that big back-pack that they carried was a system to circulate fl through tubes in the suit to keep them at afortable temperature all the time. For the LEM however it was going to be parked on the moon for several days - and one side would be continuously in sunlight and the other continuously dark. So the craft had to be engineered to handle those kinds of temperature variations.

Why isn't there a text editor that combines a WYSIWYG editor with a LaTeX editor, like Dreamweaver does for HTML?

I realize it's been several years since you asked this but BaKoMa TeX is exactly what you're looking for. It's unfortunately not free but the developer has to make a living somehow. I've been using BaKoMa for 8 years and have produced several hundred pages of papers using it. BaKoMa TeX Site- The Home of TeXWord The website unfortunately looks terrible and some of the documentation and tooltips are not perfect--the developer is very much Russian. But the software works beautifully far better than anything else I've seen. Essentially the document rpiles itself after every keystroke. There is good error correction to predict how to close open mathematical expressions so that the preview will appear reasonable even when your TeX is not syntactially sound. This is important so that the expression We calculate the integral $int_^x (without the closing $ for instance) will actually show up as We calculate the integral int_^x math instead of just crashing. BaKoMa makes setting long expressions very easy. To illustrate how much this software changed how I use TeX when I was in college I used WinEdt with Miktex to do all my problem sets. When I tried BaKoMa I was so blown away by it that my poor college self scraped together $7 to buy a license. This software will change the way you work throw the developer some money. (You can try out a reasonably full-featured demo before paying anything.) As far as I know the closest alternative is LyX which is vastly inferior since it does not display real LaTeX output. The output from BaKoMa is the dvi exactly as Miktex wouldpile it. The other disadvantage of BaKoMa used to be that it was Windows-only but this no longer appears to be the case; I can only vouch for the Windows version though.

What program will turn a PDF into a Word document?

There are quite a few programs that can turn a PDF into a Word document. Some of them can convert native searchable PDFs to editable Word and some are more powerful with the ability to convert both native and scanned PDF files to editable Word and othermon file s. If you are a Mac user PDF Converter OCR s is the best choice. Its supported input formats include native PDF scanned (JPG PNG BMP TIFF GIF) Its supported output formats include Word (searchable) PDF Excel PowerPoint RTFD EPUB HTML Pages Key JPG BMP PNG GIF and more To convert PDF to Word using PDF Converter OCR you only need to drag PDFs into the app select DOCX as the output format and click the Convert button. It that easy. One of the greatest things about this app is that it can keep the original formatting layout hyper table of contents s 812 132 master_ s zoomable PDFs you can also click the gear icon to preview and manually adjust OCR recognition areas. PC users can check out Nitro PDF to Word Converter. It alsoes with the OCR function so it is able to deal with scanned documents. If you want to do the conversion for free Calibre is the best choice. It cross-platform and free to use. It performs well when ites to PDF files with simple formatting. It also possible to convert PDF to Word using web-based apps.

Is there any general algorithm to obtain a representation of any finite group, over a general linear group over complex numbers?

Yes in principle. If G math is a finite group the not-necessarilymutative ring CG math known as the group algebra of G math consists of formal linearbinations of elements of G math with coefficients in C math . It dposes into matrix algebras corresponding to the irreducible representations of G math over C math . Another way to think of it is that G math acts on the space of functions from G math to C math which contains d math copies of any irreducible representation of G math where d math is the dimension of the representation. The sum of the d^2 math for the irreducible representations is the order of the group. By the unitary trick each representation is equivalent to a unitary representation. For a finite group over theplex numbers the representation can always be taken to be over the algebraic numbers. The character of a representation is the representationposed with the trace (which takes a matrix to the sum of its diagonal elements). The trace has the property that the trace of AB math equals the trace of BA math when both are square. That is a fairly simple calculation. As a result the character is always constant on conjugacy classes of the group. The number of irreducible representations is the number of conjugacy classes; their characters form an orthonormal basis for the right choice of inner product. Finding the representations often is taken to mean finding the irreducible ones; finding the irreducible ones often is treated as amounting to finding the character table for the group (the matrix of characters of irreducible representations). The Wikipedia page for representations of finite groups walks you through these relationships in more detail. I haven really said how you can find the irreducible representations within the group algebra. The Dixon-Schneider algorithm forputing the character table of a finite group is described in these slides (this is a PDF ~hiss ~hiss ). It is implemented in GAP which is freely available. ( Representations and Characters of Groups s ) GAP has other methods for finding the character table of a finite group some using auxiliary information and clever tricks. The GAP web site says Theputation of irreducible characters of very large groups may take quite some time.