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u = exp ( x ) ; m = u - 1. 0 ; if ( m = = 0. 0 ) { / / x very close to zero m = x ; } else if ( fabs ( x ) < 1. 0 ) { / / x somewhat close zero u = log ( u ) ; m = m * x ; m = m / u ; } return m ; } | https://api.stackexchange.com |
the choice of whether to write binary hydrides with the hydrogen first or second depends on whether that hydrogen is considered acidic, with water marking the delineation point. by convention, if a binary hydride is more acidic than water, then they are written in the form $ \ ce { h } _ { \ text { n } } \ ce { x } $. ... | https://api.stackexchange.com |
it is not true that an infinite, non - repeating decimal must contain ‘ every possible number combination ’. the decimal $ 0. 011000111100000111111 \ dots $ is an easy counterexample. however, if the decimal expansion of $ \ pi $ contains every possible finite string of digits, which seems quite likely, then the rest o... | https://api.stackexchange.com |
the common saying is a hold over from when stp was defined to be $ \ pu { 273. 15 k } $ and $ \ pu { 1 atm } $. however, iupac changed the definition in 1982 so that $ \ pu { 1 atm } $ became $ \ pu { 1 bar } $. i think the main issue is a lot of educators didn't get the memo and went right along either teaching stp as... | https://api.stackexchange.com |
i found online the claim ( which we may as well accept for this purpose ) that there are $ 32241 $ words in hamlet. figuring $ 5 $ characters and one space per word, this is $ 193446 $ characters. if the character set is $ 60 $ including capitals and punctuation, a random string of $ 193446 $ characters has a chance of... | https://api.stackexchange.com |
the reason that it's so hard to understand what physicists mean when they talk about " gauge freedom " is that there are at least four inequivalent definitions that i've seen used : definition 1 : a mathematical theory has a gauge freedom if some of the mathematical degrees of freedom are " redundant " in the sense tha... | https://api.stackexchange.com |
\ bf b } $ fields without losing any physical information. however, in the case of a vector in a quantum hilbert space, there's no simple derivative operation that removes the phase freedom without losing anything else. definition 2 : the same as definition 1, but with the additional requirement that the redundant degr... | https://api.stackexchange.com |
x ) + \ partial _ \ mu \ lambda ( x ) $ over all possible $ \ lambda ( x ) $ for some particular $ a _ \ mu ( x ). $ see terry tao's blog post for a great explanation of this second sense of gauge symmetry from a more mathematical perspective. definition 3 : a lagrangian is sometimes said to posses a " gauge symmetry "... | https://api.stackexchange.com |
surely it would be even more beneficial for plants to be black instead of red or green, from an energy absorption point of view. and solar cells are indeed pretty dark. but, as rory indicated, higher energy photons will only produce heat. this is because the chemical reactions powered by photosynthesis require only a c... | https://api.stackexchange.com |
your question is a bit like asking for which screwdriver to choose depending on the drive ( slot, phillips, torx,... ) : besides there being too many, the choice also depends on whether you want to just tighten one screw or assemble a whole set of library shelves. nevertheless, in partial answer to your question, here ... | https://api.stackexchange.com |
specific problem. here are some general remarks : if you really need ( close to ) machine precision for your solution, or if your matrix is small ( say, up to $ 1000 $ rows ), it is hard to beat direct methods, especially for dense systems ( since in this case, every matrix multiplication will be $ \ mathcal { o } ( n ... | https://api.stackexchange.com |
for references in the comments, here are some textbooks and review papers to get you started. ( neither of these - nor the set - is comprehensive ; this question is much too broad, and depends too much on your particular problem. ) golub, van loan : matrix computations ( still the classical reference on matrix algorith... | https://api.stackexchange.com |
yes, this is a beautiful question. as you said, in lower rows of the periodic table, there are relativistic effects for the electrons. that is, for core electrons in gold, the electrons are traveling at a significant fraction of the speed of light ( e. g., ~ 58 % for $ \ ce { au } $ $ \ mathrm { 1s } $ electrons ). thi... | https://api.stackexchange.com |
this is a very interesting question. provided that the materials used in making papers aren't the same around the globe, this is a very broad case of study. however, a study has been conducted in which the main goal was to identify the compounds that are the cause of the smell ; vocs : [ 1 ] volatile organic compounds ... | https://api.stackexchange.com |
short answer : cold is pleasant only when your are not already freezing and cold might satiate thirst better because it acts as enhancer of the " water intake flow meter ". is cold water more tasty than warm water? no, it is actually the reverse as detailed in my footnote. cold is pleasant when your body is over - heat... | https://api.stackexchange.com |
and " sensation " signals use completely different paths to reach the brain - namely, the facial and glossopharyngeal nerves for the former and the trigeminal nerve for the latter. is the temperature affecting basic taste perceptions? the answer is yes. how this happens is quite simple if you understand the fundamental... | https://api.stackexchange.com |
i've sorted the visualisation out. here are three alternative representations of repetitive structures for the same sequence : these were generated using the same r script, callable from the command line : $ repaver. r - style dotplot - prefix dotplot maoa _ chrx _ 43645715 - 43756016. fa $ repaver. r - style profile -... | https://api.stackexchange.com |
so, i decided to try it out. i used audacity to record ~ 5 seconds of sound that resulted when i dropped a penny, nickel, dime, and quarter onto my table, each 10 times. i then computed the power spectral density of the sound and obtained the following results : i also recorded 5 seconds of me not dropping a coin 10 ti... | https://api.stackexchange.com |
, i used the following coins : penny : 1970 nickel : 1999 dime : 1991 quarter : 1995 edit : scaling collapse following floris, we can check to see how accurate the model $ f \ sim e ^ { 1 / 2 } m ^ { - 1 / 3 } \ eta ^ { - 1 } $ is. we will use the data provided, and plot our observed power density versus a scaled frequ... | https://api.stackexchange.com |
the area of $ \ triangle abc $ is $ \ frac { 1 } { 2 } \ sin ( x ) $. the area of the colored wedge is $ \ frac { 1 } { 2 } x $, and the area of $ \ triangle abd $ is $ \ frac { 1 } { 2 } \ tan ( x ) $. by inclusion, we get $ $ \ frac { 1 } { 2 } \ tan ( x ) \ ge \ frac { 1 } { 2 } x \ ge \ frac { 1 } { 2 } \ sin ( x )... | https://api.stackexchange.com |
adorable. frankly, the little bits kit is way overkill and incredibly expensive. if your goal is to make a simple sensor that detects pressure and turns on a light bulb, that can be done using stuff you probably have around the house. here's a basic idea that might be " good enough " for this year. next year may requir... | https://api.stackexchange.com |
another perspective on " efficiency " is that polynomial time allows us to define a notion of " efficiency " that doesn't depend on machine models. specifically, there's a variant of the church - turing thesis called the " effective church - turing thesis " that says that any problem that runs in polynomial time on on ... | https://api.stackexchange.com |
typical nuclear power reactions begin with a mixture of uranium - 235 ( fissionable, with a half - life of 700 myr ) and uranium - 238 ( more common, less fissionable, half - life 4 gyr ) and operate until some modest fraction, 1 % - 5 %, of the fuel has been expended. there are two classes of nuclides produced in the ... | https://api.stackexchange.com |
{ u } $ atoms of cobalt - 60. i've changed by population size by a factor of two, but i've changed the decay rate by a factor of a billion. the ratio of the half - lives $ t _ \ text { u - 238 } / t _ \ text { pu - 240 } $ is roughly a factor of a million. so if a typical fuel cycle turns 0. 1 % of the initial u - 238 ... | https://api.stackexchange.com |
hydrofluoric acid is toxic and corrosive, but actually isn't that strong of an acid compared to other hydrohalic acids ; the fluorine has a very good orbital overlap with hydrogen and is also not very polarizable, therefore it resists donating its proton, unlike other hydrohalic acids which are good proton donators. it... | https://api.stackexchange.com |
what does it mean when you refer to $. 99999 \ ldots $? symbols don't mean anything in particular until you've defined what you mean by them. in this case the definition is that you are taking the limit of $. 9 $, $. 99 $, $. 999 $, $. 9999 $, etc. what does it mean to say that limit is $ 1 $? well, it means that no ma... | https://api.stackexchange.com |
there is no necessary relation between the implementation of the compiler and the output of the compiler. you could write a compiler in a language like python or ruby, whose most common implementations are very slow, and that compiler could output highly optimized machine code capable of outperforming c. the compiler i... | https://api.stackexchange.com |
python and both of these implementations run the same python language. what we'll find is that if we run our compiler on cpython, then run it on pypy, then compile the same fortran source with gfortran, we'll get exactly the same machine code all three times, so the compiled program will always run at around the same s... | https://api.stackexchange.com |
programming languages evolve and are improved with time ( innovation ). people take ideas from different languages and combine them into new languages. some features are improved ( inheritance mechanisms, type systems ), some are added ( garbage collection, exception handling ), some are removed ( goto statements, low ... | https://api.stackexchange.com |
to their particular domain. without evolution in programming language design, we'd all still be using assembly language or c + +. as for knowing a functional programming language : functional languages allow you to express computations differently, often more concisely than using other programming languages. consider a... | https://api.stackexchange.com |
in my view the central question that you should ask yourself is what is the end goal of your studies. as an example, american college life as depicted in film is hedonistic and certainly not centered on actual studies. your example is the complete opposite - you describe yourself as an ascetic devoted to scholarship. m... | https://api.stackexchange.com |
##aggerating, viewing the situation from a romantic, heroic perspective. it's best therefore to talk to people who know you personally. even better, talk to people who're older than you and in the next stage of " life ". they have a wider perspective on your situation, which they of their acquaintances have just still ... | https://api.stackexchange.com |
what a great question - it's a chance to show how one would inspect the drawbacks and assumptions of any statistical method. namely : make up some data and try the algorithm on it! we'll consider two of your assumptions, and we'll see what happens to the k - means algorithm when those assumptions are broken. we'll stic... | https://api.stackexchange.com |
^ 2 $ - and yet at a glance we can see that only one of them, i, is appropriate for linear regression. in ii it suggests the wrong shape, in iii it is skewed by a single outlier - and in iv there is clearly no trend at all! one could say " linear regression is still working in those cases, because it's minimizing the s... | https://api.stackexchange.com |
other problematic situations easily, and that's just in two dimensions. when you're clustering 16 - dimensional data, there's all kinds of pathologies that could arise. lastly, i should note that k - means is still salvagable! if you start by transforming your data into polar coordinates, the clustering now works : tha... | https://api.stackexchange.com |
from! when netflix recommends movies to you, it's assuming that if you like one movie, you'll like similar ones ( and vice versa ). imagine a world where that wasn't true, and your tastes are perfectly random - scattered haphazardly across genres, actors and directors. their recommendation algorithm would fail terribly... | https://api.stackexchange.com |
originally, " differentials " and " derivatives " were intimately connected, with derivative being defined as the ratio of the differential of the function by the differential of the variable ( see my previous discussion on the leibnitz notation for the derivative ). differentials were simply " infinitesimal changes " ... | https://api.stackexchange.com |
are no longer ratios, instead they are limits. integrals are no longer infinite sums of infinitesimally thin rectangles, now they are limits of riemann sums ( each of which is finite and there are no infinitesimals around ), etc. the notation is left over, though, because it is very useful notation and is very suggesti... | https://api.stackexchange.com |
on the floor, and then says " which reduces it to a previously solved problem. " ) where were we? ah, yes. having to translate all those informal manipulations that work so well and treat $ dx $ and $ dy $ as objects in and of themselves, into formal justifications that don't treat them that way is a real pain. it can ... | https://api.stackexchange.com |
the practical difference, though? you'll probably be disappointed to hear " not much ". except one thing : when your functions represent actual quantities, rather than just formal manipulation of symbols, the derivative and the differential measure different things. the derivative measures a rate of change, while the d... | https://api.stackexchange.com |
original conception. | https://api.stackexchange.com |
to elaborate on my intuition here, the thing i consider " impressive " about classical computers is their ability to simulate other systems, not just themselves. when setting up a classical circuit, the question we want to answer is not " which transistors will be lit up once we run a current through this? " we want to... | https://api.stackexchange.com |
recently, there has been a lot of discussion of bent's rule ( see for example " what is bent's rule? " ) here in se chem. simply stated, the rule suggests that $ \ mathrm { p } $ - character tends to concentrate in orbitals directed at electronegative elements. why does $ \ ce { f } $ replace an axial bond in $ \ ce { ... | https://api.stackexchange.com |
^ 3 } $ or whatever is appropriate ) and each of these orbitals contains one electron for bonding. this is our 3 - center - 4 - electron bond and its mo diagram is pictured below. notice how the four electrons are distributed - there are two electrons in the homo which is a non - bonding m. o., so the bond order in thi... | https://api.stackexchange.com |
division is an iterative algorithm where the result from the quotient must be shifted to the remainder using a euclidean measure, see 2 ; whereas, multiplication can be reduced to a ( fixed ) series of bit manipulation tricks. | https://api.stackexchange.com |
the main division is between bjts and fets, with the big difference being the former are controlled with current and the latter with voltage. if you're building small quantities of something and aren't very familiar with the various choices and how you can use the characteristics to advantage, it's probably simpler to ... | https://api.stackexchange.com |
. | https://api.stackexchange.com |
to define the two terms without using too much technical language : an estimator is consistent if, as the sample size increases, the estimates ( produced by the estimator ) " converge " to the true value of the parameter being estimated. to be slightly more precise - consistency means that, as the sample size increases... | https://api.stackexchange.com |
4 ( n - 1 ) } { n ^ 2 } $ $ from these facts we can informally see that the distribution of $ \ hat { \ sigma } ^ 2 $ is becoming more and more concentrated at $ \ sigma ^ 2 $ as the sample size increases since the mean is converging to $ \ sigma ^ 2 $ and the variance is converging to $ 0 $. ( note : this does constit... | https://api.stackexchange.com |
short answer blue color is not only rare in edible organisms - blue color is rare in both the animal and plant kingdoms in general. in animals, blue coloring is generated through structural optic light effects, and not through colored pigments. in the few blue - colored plants, the blue color is generated by blue pigme... | https://api.stackexchange.com |
the equation you're solving does not permit right - going solutions, so there is no such thing as a reflecting boundary condition for this equation. if you consider the characteristics, you'll realize that you can only impose a boundary condition at the right boundary. you are trying to impose a homogeneous dirichlet b... | https://api.stackexchange.com |
first off, gold does react. you can form stable gold alloys and gold compounds. it's just hard, mostly for reasons explained by the other answer the reason bulk gold solid is largely unreactive is because the electrons in gold fall at energies which few molecules or chemicals match ( i. e., due to relativistic effects ... | https://api.stackexchange.com |
the concept is based on the convolution theorem, which states that for two signals $ x ( t ) $ and $ y ( t ) $, the product of their fourier transforms $ x ( f ) $ and $ y ( f ) $ is equal to the fourier transform of the convolution of the two signals. that is : $ $ \ mathcal { f } \ { x ( t ) * y ( t ) \ } = \ mathcal... | https://api.stackexchange.com |
} \ { x ( t ) \ } \ left ( \ mathcal { f } \ { y ( t ) \ } \ right ) ^ * $ $ and it is very easy to see that for real signals, cross correlation and convolution are equivalent if we flip one of the signals in time. in this case the convolution operation flip in time domain is compensated with another flip in $ y ( t ) ... | https://api.stackexchange.com |
the phenomenon in question is probably related to geotropism. if the hill soil is " on the move " it will cause the bend on the trees - if the soil in a slope is moving downward, the trees on this slope will tip downward. as the tree continues to try to grow upward, the trunk will show a curve. the degree of bending co... | https://api.stackexchange.com |
according to the bcftools man page, it is able to produce statistics using the command bcftools stats. running this myself, the statistics look like what you're asking for : # this file was produced by bcftools stats ( 1. 2 - 187 - g1a55e45 + htslib - 1. 2. 1 - 256 - ga356746 ) and can be plotted using plot - vcfstats.... | https://api.stackexchange.com |
0 t > g 0 # dp, depth distribution # dp [ 2 ] id [ 3 ] bin [ 4 ] number of genotypes [ 5 ] fraction of genotypes ( % ) [ 6 ] number of sites [ 7 ] fraction of sites ( % ) dp 0 > 500 0 0. 000000 333 100. 000000 this is annotating what is explicitly in the vcf file, and that's snvs ( and indels ). if you want a structura... | https://api.stackexchange.com |
this is a special case of a selection algorithm that can find the $ k $ th smallest element of an array with $ k $ is the half of the size of the array. there is an implementation that is linear in the worst case. generic selection algorithm first let's see an algorithm find - kth that finds the $ k $ th smallest eleme... | https://api.stackexchange.com |
for biopython 1. 70, there is a new seq. count _ overlap ( ) method, which includes optional start and end arguments : > > > from bio. seq import seq > > > seq ('aaaa'). count _ overlap ('aa') 3 > > > seq ('aaaa'). count _ overlap ('aa ', 1, 4 ) 2 this method is also implemented for the mutableseq and unknownseq classe... | https://api.stackexchange.com |
here are those i understand so far. most of these work best when given values between 0 and 1. quadratic cost also known as mean squared error, this is defined as : $ $ c _ { mst } ( w, b, s ^ r, e ^ r ) = 0. 5 \ sum \ limits _ j ( a ^ l _ j - e ^ r _ j ) ^ 2 $ $ the gradient of this cost function with respect to the o... | https://api.stackexchange.com |
gradient computes a vector and then multiplies it by $ c _ { exp } $. hellinger distance $ $ c _ { hd } ( w, b, s ^ r, e ^ r ) = \ frac { 1 } { \ sqrt { 2 } } \ sum \ limits _ j ( \ sqrt { a ^ l _ j } - \ sqrt { e ^ r _ j } ) ^ 2 $ $ you can find more about this here. this needs to have positive values, and ideally val... | https://api.stackexchange.com |
} { a ^ l } $ $ generalized kullback – leibler divergence from here. $ $ c _ { gkl } ( w, b, s ^ r, e ^ r ) = \ sum \ limits _ j e ^ r _ j \ log \ frac { e ^ r _ j } { a ^ l _ j } - \ sum \ limits _ j ( e ^ r _ j ) + \ sum \ limits _ j ( a ^ l _ j ) $ $ the gradient of this cost function with respect to the output of a... | https://api.stackexchange.com |
language designers face many choices. ken kennedy emphasized two : ( 1 ) better abstractions and ( 2 ) higher - or lower - level ( less or more machine - like ) code. while functional languages like haskell and scheme focus on the former, traditional scientific - computing languages like fortran and c / c + + focused o... | https://api.stackexchange.com |
first, here are some quick comments : the $ p $ - values of a kolmogorov - smirnov - test ( ks - test ) with estimated parameters can be quite wrong because the p - value does not take the uncertainty of the estimation into account. so unfortunately, you can't just fit a distribution and then use the estimated paramete... | https://api.stackexchange.com |
35. 60, 45. 34, 43. 37, 54. 15, 42. 77, 42. 88, 44. 26, 27. 14, 39. 31, 24. 80, 16. 62, 30. 30, 36. 39, 28. 60, 28. 53, 35. 84, 31. 10, 34. 55, 52. 65, 48. 81, 43. 42, 52. 49, 38. 00, 38. 65, 34. 54, 37. 70, 38. 11, 43. 05, 29. 95, 32. 48, 24. 63, 35. 33, 41. 34 ) now let's use descdist : descdist ( x, discrete = false... | https://api.stackexchange.com |
##t. weibull $ estimate [ " scale " ] ) $ statistic ) } ) the ecdf of the simulated ks - statistics looks as follows : plot ( ecdf ( stats ), las = 1, main = " ks - test statistic simulation ( cdf ) ", col = " darkorange ", lwd = 1. 7 ) grid ( ) finally, our $ p $ - value using the simulated null distribution of the ks... | https://api.stackexchange.com |
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - # plot pdf # - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - par ( bg = " white ", las = 1, cex = 1. 2 ) plot ( xs, boot. ... | https://api.stackexchange.com |
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - par ( bg = " white ", las = 1, cex = 1. 2 ) plot ( xs, boot. cdf [, 1 ], type = " l ", col = rgb (. 6,. 6,. 6,. 1 ), ylim = range ( boot. cdf ), xlab = " x ", ylab = " f ( x ) " ) for ( i ... | https://api.stackexchange.com |
$, which is the penalty for the gaic. in the example below, i set the parameter $ k = 2 $ which means that the " best " distribution is selected according to the classic aic. you can set $ k $ to anything you like, such as $ \ log ( n ) $ for the bic. library ( gamlss ) library ( gamlss. dist ) library ( gamlss. add ) ... | https://api.stackexchange.com |
" weibull type 2 " ) call : gamlssml ( formula = y, family = dist [ i ], data = sys. parent ( ) ) fitting method : " nlminb " coefficient ( s ) : estimate std. error t value pr ( > | t | ) eta. mu - 24. 3468041 2. 2141197 - 10. 9962 < 2. 22e - 16 * * * eta. sigma 1. 8661380 0. 0892799 20. 9021 < 2. 22e - 16 * * * accor... | https://api.stackexchange.com |
understanding $ p $ - value suppose, that you want to test the hypothesis that the average height of male students at your university is $ 5 $ ft $ 7 $ inches. you collect heights of $ 100 $ students selected at random and compute the sample mean ( say it turns out to be $ 5 $ ft $ 9 $ inches ). using an appropriate fo... | https://api.stackexchange.com |
if $ p < 0. 05 $. | https://api.stackexchange.com |
it's called chip - on - board. the die is glued to the pcb and wires are bonded from it to pads. the pulsonix pcb software i use has it as an optional extra. the main benefit is reduced cost, since you don't have to pay for a package. | https://api.stackexchange.com |
proof by contradiction is often used to show that a language is not regular : let $ p $ a property true for all regular languages, if your specific language does not verify $ p $, then it's not regular. the following properties can be used : the pumping lemma, as exemplified in dave's answer ; closure properties of reg... | https://api.stackexchange.com |
summary : i find a formula for the diameter of a bubble large enough to support one human and plug in known values to get $ d = 400 \, { \ rm m } $. i'll have a quantitative stab at the answer to the question of how large an air bubble has to be for the carbon dioxide concentration to be in a breathable steady state, w... | https://api.stackexchange.com |
assumed to be constant. then $ $ \ nabla \ phi ( a ) = - \ frac { ( \ phi ( \ text { inside } ) - \ phi ( \ text { far } ) ) a } { a ^ 2 } = - \ frac { \ phi ( \ text { inside } ) - \ phi ( \ text { far } ) } { a } $ $ yielding $ $ j = d \ frac { \ phi ( \ text { inside } ) - \ phi ( \ text { far } ) } { a }. $ $ next ... | https://api.stackexchange.com |
} _ 2 \ approx 4 \ % $, lung capacity $ \ approx 500 \, { \ rm ml } $ and breath rate $ \ approx \ frac { 1 } { 5 } \, { \ rm s } ^ { - 1 } $ ) i get $ d \ approx 400 \, { \ rm m } $. it's interesting to note that this is independent of pressure : i've neglected pressure dependence of $ d $ and human resilience to carb... | https://api.stackexchange.com |
i would also recommend to take a look at pomegranate, a nice python package for probabilistic graphical models. it includes solvers for hmms and much more. under the hood it uses cythonised code, so it's also quite fast. | https://api.stackexchange.com |
this effect is known as inharmonicity, and it is important for precision piano tuning. ideally, waves on a string satisfy the wave equation $ $ v ^ 2 \ frac { \ partial ^ 2 y } { \ partial x ^ 2 } = \ frac { \ partial ^ 2 y } { \ partial t ^ 2 }. $ $ the left - hand side is from the tension in the string acting as a re... | https://api.stackexchange.com |
your model of what you do mentally is incorrect. in fact, you operate in two steps : eliminate all points that are too far, in $ o ( 1 ) $ time. measure the $ m $ points that are about as close, in $ \ theta ( m ) $ time. if you've played games like petanque ( bowls ) or curling, this should be familiar — you don't nee... | https://api.stackexchange.com |
for the points that are closest to $ ( x _ 0, y _ 0 ) $ and the cell that contains this point contains at most one other point, then it is sufficient to check the containing cell and the 8 neighboring cells. the total number of points in these 9 cells is $ m $. this model respects some key properties of the human model... | https://api.stackexchange.com |
for more than two, the moving knife is a nice solution. somebody takes a knife and moves it slowly across the sandwich. any player may say " cut ". at that moment, the sandwich is cut and the piece given to the one who said " cut ". as he has said that is an acceptable piece, he believes he has at least $ \ frac 1n $ o... | https://api.stackexchange.com |
to add to rightskewed answer : while it is true that : gencode is an additive set of annotation ( the manual one done by havana and an automated one done by ensembl ), the annotation ( gtf ) files are quite similar for a few exceptions involving the x chromosome and y par and additional remarks in the gencode file ( se... | https://api.stackexchange.com |
t be interchangeable between themselves either in most cases ). however, you can easily translate most [ 1 ] of your refseq ids to ensembl ids and vice - versa with tools as for example ( there are devoted libraries / api as well like biocondutor : biomart [ 1 ] most as sometimes, they might be annotated in one of the ... | https://api.stackexchange.com |
i wrote this handout as a complement to oppenheim and willsky. please take a look at table 4. 1 on page 14, reproduced below. ( click for larger image. ) i wrote that table specifically to answer questions such as yours. note the similarities and differences among the four operations : " series " : periodic in time, di... | https://api.stackexchange.com |
it is a theorem of liouville, reproven later with purely algebraic methods, that for rational functions $ f $ and $ g $, $ g $ non - constant, the antiderivative of $ $ f ( x ) \ exp ( g ( x ) ) \, \ mathrm dx $ $ can be expressed in terms of elementary functions if and only if there exists some rational function $ h $... | https://api.stackexchange.com |
i'll try to give a succinct answer to some of your questions. please bear in mind that this is not strictly my field of research, so some of my info may be outdated / incorrect. there are many tools that are specifically designed to formally prove properties of java and c + +. however i need to make a small digression ... | https://api.stackexchange.com |
, and automatic theorem provers are known to occasionally have soundness bugs which make them less trustworthy. this is an area where coq shines in comparison ( but it is not automatic! ). if you want to generate ocaml code, then definitely write in coq ( gallina ) first, then extract the code. however, coq is terrible... | https://api.stackexchange.com |
a modified implementation of vivek's answer. peddy is a python package that samples an input. vcf at ~ 25000 sites and projects onto a principal component space built on 2504 thousand genome samples. the author has extensive documentation of the tool's features and a link to the preprint. i downloaded the. vcf and. vcf... | https://api.stackexchange.com |
( note : the full desciption is a bit complex, and has several subtleties which i prefered to ignore. the following is merely the high - level ideas for the qtm model ) when defining a quantum turing machine ( qtm ), one would like to have a simple model, similar to the classical tm ( that is, a finite state machine pl... | https://api.stackexchange.com |
each time step, the state of the qtm evolves according to some unitary $ u $ $ $ | \ psi ( i + 1 ) \ rangle = u | \ psi ( i ) \ rangle $ $ note that the state at any time $ n $ is given by $ | \ psi ( n ) \ rangle = u ^ n | \ psi ( 0 ) \ rangle $. $ u $ can be any unitary that " changes " the tape only where the head i... | https://api.stackexchange.com |
real signals are " mirrored " in the real and negative halves of the fourier transform because of the nature of the fourier transform. the fourier transform is defined as the following - $ $ h ( f ) = \ int h ( t ) e ^ { - j2 \ pi ft } dt $ $ basically it correlates the signal with a bunch of complex sinusoids, each wi... | https://api.stackexchange.com |
, the magnitude of their response will be the same, but the correlation phase will be different. edit : specifically, the negative frequency correlation is the conjugate of the positive frequency correlation ( due to the inverted imaginary sine component ) for real signals. in mathematical terms, this is, as dilip poin... | https://api.stackexchange.com |
here ’ s one to get things started. let $ u $ be a non - empty open subset of $ \ bbb r $. for $ x, y \ in u $ define $ x \ sim y $ iff $ \ big [ \ min \ { x, y \ }, \ max \ { x, y \ } \ big ] \ subseteq u $. it ’ s easily checked that $ \ sim $ is an equivalence relation on $ u $ whose equivalence classes are pairwise... | https://api.stackexchange.com |
with the topology generated by the subbase of open rays $ ( \ leftarrow, x ) $ and $ ( x, \ to ) $ : if $ u $ is a non - empty open subset of $ x $, then $ u $ is the union of a family of pairwise disjoint open order - convex sets. ( a set $ c \ subseteq x $ is order - convex if whenever $ u, v \ in c $ and $ u < x < v... | https://api.stackexchange.com |
( background : i have a chronic pain condition, and it is extremely painful for me to do any sort of repetitive fine motor activity, including writing and typing. i earned an undergraduate degree in math with quite little handwriting, and i'm currently a graduate student. ) unfortunately, i've never been able to find a... | https://api.stackexchange.com |
spending time on it while i'm preparing for comprehensive exams! ). the big advantage to a dictation system like this is that you get to go through the process of formally presenting your work, which is really helpful for checking understanding and practicing proof writing. disadvantages include a steep learning curve ... | https://api.stackexchange.com |
to computer algebra systems is that you can do all of the numerical calculations and tedious symbolic manipulations without needing to ever write down a single number. the disadvantage is that hiding all of the details can sometimes hinder your conceptual understanding. those are the main strategies i use. i hope somet... | https://api.stackexchange.com |
##latex input ( dictated with dragon ) begin theorem [ monotone convergence theorem ] let " left curly brace f sub n right curly brace sub { n equals one } to the infinity " be a sequence of nonnegative measurable functions with " f sub one less than or equal to f sub two less than or equal to low dots less than or equ... | https://api.stackexchange.com |
simula 67 is generally considered the first object - oriented language and predates smalltalk by a number of years. it also used the this keyword for the same concept, which can be seen in this book chapter extract : class linker ; begin ref ( linker ) next, sex, employment ; text id ; procedure add _ to _ list ( lhead... | https://api.stackexchange.com |
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