2 ) & = \ operatorname { cov } ( x ( t _ 1 ), x ( t _ 2 ) ) \ \ & = e [ ( x ( t _ 1 ) - \ mu _ x ( t _ 1 ) ) ( x ( t _ 2 ) - \ mu _ x ( t _ 2 ) ) ] \ \ & = e [ x ( t _ 1 ) x ( t _ 2 ) ] - \ mu _ x ( t _ 1 ) \ mu _ x ( t _ 2 ), \ end { align } is a function only of $ t _ 1 - t _ 2 $ and not of the individual values of $ t _ 1 $ and $ t _ 2 $. ( notice the absence of any claim that the mean is a constant ). since for a wss process, $ $ c _ x ( t _ 1, t _ 2 ) = r _ x ( t _ 1, t _ 2 ) - \ mu _ x ( t _ 1 ) \ mu _ x ( t _ 2 ) = r _ x ( t _ 1 - t _ 2 ) - \ mu _ x ^ 2 $ $ is a function only of $ t _ 1 - t _ 2 $, we see that every wss process is a covariance - stationary process. in fact, the prototypical covariance - stationary process is of the form $ $ \ { x ( t ) \ colon t \ in { \ mathbb t } \ } = \ { y ( t ) + s ( t ) \ colon t \ in { \ mathbb t } \ } $ $ where $ \ { y ( t ) \ colon t \ in { \ mathbb t } \ } $ is a zero - mean wss process. it is a model for a deterministic signal $ s ( t ) $ observed in the noise $ y ( t ) $. the verification of the claim that the prototypical process is indeed a covariance - stationary process is left as an exercise for the reader. finally, suppose that a stochastic process is assumed to be a gaussian process ( " proving " this with any reasonable degree of confidence is not a trivial task ). this means that for each $ t $, $ x ( t ) $ is a gaussian random variable and for all positive integers $ n \ geq 2 $ and choices of $ n $ time instants $ t _ 1 $, $ t _ 2 $, $ \ ldots


, t _ n $, the $ n $ random variables $ x ( t _ 1 ) $, $ x ( t _ 2 ) $, $ \ ldots, x ( t _ n ) $ are jointly gaussian random variables. now a joint gaussian density function is completely determined by the means $ e [ x ( t _ i ) ] = \ mu _ x ( t _ i ) $, variances \ begin { align } \ operatorname { var } ( x ( t _ i ) ) & = e [ ( x ( t _ i ) - \ mu _ x ( t _ i ) ) ^ 2 ] \ \ & = e [ ( x ( t _ i ) ^ 2 ] - ( \ mu _ x ( t _ i ) ) ^ 2 \ \ & = r _ x ( t _ i, t _ i ) - ( \ mu _ x ( t _ i ) ) ^ 2, \ end { align } and covariances \ begin { align } \ operatorname { cov } ( x ( t _ i ), x ( t _ j ) ) & = e [ ( x ( t _ i ) - \ mu _ x ( t _ i ) ] ) ( x ( t _ j ) - \ mu _ x ( t _ j ) ) ] \ \ & = e [ x ( t _ i ) x ( t _ j ) ] - \ mu _ x ( t _ i ) \ mu _ x ( t _ j ) \ \ & = r _ x ( t _ i, t _ j ) - \ mu _ x ( t _ i ) \ mu _ x ( t _ j ) \ end { align } of the random variables. thus, knowing the mean function $ \ mu _ x ( t ) = e [ x ( t ) ] $ ( it need not be a constant as is required for wide - sense - stationarity ) and the autocorrelation function $ r _ x ( t _ 1, t _ 2 ) = e [ x ( t _ 1 ) x ( t _ 2 ) ] $ for all $ t _ 1, t _ 2 $ ( it need not depend only on $ t _ 1 - t _ 2 $ as is required for wide - sense - stationarity ) is sufficient to determine the statistics of the process completely. if a gaussian process is a wss process, then it is also a strictly stationary gaussian process. fortunately for engineers and


signal processors, many physical noise processes can be well - modeled as wss gaussian processes ( and therefore strictly stationary processes ), so that experimental observation of the autocorrelation function readily provides all the joint distributions. furthermore since gaussian processes retain their gaussian character as they pass through linear systems, and the output autocorrelation function is related to th input autocorrelation function as $ $ r _ y = h * \ tilde { h } * r _ x $ $ so that the output statistics can also be easily determined, wss process in general and wss gaussian processes in particular are of great importance in engineering applications.


the answer to this question is simple and requires only sr, not gr or quantum mechanics. in units with $ c = 1 $, we have $ m ^ 2 = e ^ 2 - p ^ 2 $, where $ m $ is the invariant mass, $ e $ is the mass - energy, and $ p $ is the momentum. in terms of logical foundations, there is a variety of ways to demonstrate this. one route starts with einstein's 1905 paper " does the inertia of a body depend upon its energy - content? " another method is to start from the fact that a valid conservation law has to use a tensor, and show that the energy - momentum four - vector is the only tensor that goes over to newtonian mechanics in the appropriate limit. once $ m ^ 2 = e ^ 2 - p ^ 2 $ is established, it follows trivially that for a photon, with $ m = 0 $, $ e = | p | $, i. e., $ p = e / c $ in units with $ c \ ne 1 $. a lot of the confusion on this topic seems to arise from people assuming that $ p = m \ gamma v $ should be the definition of momentum. it really isn't an appropriate definition of momentum, because in the case of $ m = 0 $ and $ v = c $, it gives an indeterminate form. the indeterminate form can, however, be evaluated as a limit in which $ m $ approaches 0 and $ e = m \ gamma c ^ 2 $ is held fixed. the result is again $ p = e / c $.


to determine what can and cannot be proved by contradiction, we have to formalize a notion of proof. as a piece of notation, we let $ \ bot $ represent an identically false proposition. then $ \ lnot a $, the negation of $ a $, is equivalent to $ a \ to \ bot $, and we take the latter to be the definition of the former in terms of $ \ bot $. there are two key logical principles that express different parts of what we call " proof by contradiction " : the principle of explosion : for any statement $ a $, we can take " $ \ bot $ implies $ a $ " as an axiom. this is also called ex falso quodlibet. the law of the excluded middle : for any statement $ a $, we can take " $ a $ or $ \ lnot a $ " as an axiom. in proof theory, there are three well known systems : minimal logic has neither of the two principles above, but it has basic proof rules for manipulating logical connectives ( other than negation ) and quantifiers. this system corresponds most closely to " direct proof ", because it does not let us leverage a negation for any purpose. intuitionistic logic includes minimal logic and the principle of explosion classical logic includes intuitionistic logic and the law of the excluded middle it is known that there are statements that are provable in intuitionistic logic but not in minimal logic, and there are statements that are provable in classical logic that are not provable in intuitionistic logic. in this sense, the principle of explosion allows us to prove things that would not be provable without it, and the law of the excluded middle allows us to prove things we could not prove even with the principle of explosion. so there are statements that are provable by contradiction that are not provable directly. the scheme " if $ a $ implies a contradiction, then $ \ lnot a $ must hold " is true even in intuitionistic logic, because $ \ lnot a $ is just an abbreviation for $ a \ to \ bot $, and so that scheme just says " if $ a \ to \ bot $ then $ a \ to \ bot $ ". but in intuitionistic logic, if we prove $ \ lnot a \ to \ bot $, this only shows that $ \ lnot \ lnot a $ holds. the extra strength in classical logic is that the law of the excluded middle shows that $ \ lnot \ l


##not a $ implies $ a $, which means that in classical logic if we can prove $ \ lnot a $ implies a contradiction then we know that $ a $ holds. in other words : even in intuitionistic logic, if a statement implies a contradiction then the negation of the statement is true, but in classical logic we also have that if the negation of a statement implies a contradiction then the original statement is true, and the latter is not provable in intuitionistic logic, and in particular is not provable directly.


i think if you look at this animation and think about it long enough, you'll understand : why circles and right - angle triangles and angles are all related. why sine is " opposite over hypotenuse " and so on. why cosine is simply sine but offset by $ \ frac { \ pi } { 2 } $ radians.


there are a couple elements i look for when i consider something " publication - quality " in either my own work, or what i'm considering when looking at others. they are : high resolution, and preferably vector - based. this one should be fairly obvious by now, but you'd be surprised. a lack of clutter. i should be able to see what's happening in your figure, and see it quickly. there's few things i hate more than someone trying to take the " high ink : paper ratio " guidance and using it to try to cram an entire manuscript in a single figure. prints well. this is the one that's actually most important for me, and when i'm reviewing papers, one i always test. " do the figures print? " more than once, i've hit figures whose points are completely obfuscated when printed in grayscale, which renders them worthless for my purposes ( i don't read on screens ). evidence that the creator knows how to use graphics settings. no odd - ball axis choices, tick marks in the right place, etc. combined with # 2, a lack of " flourish " that's entirely graphical in nature. shadows, needless 3 - d, etc. that really do nothing but waste the readers time. most of those are honestly creator - specific, rather than program specific. i've seen terrible plots done in r, and excellent plots done in excel.


there are models that take into account compositional heterogeneity both under the maximum likelihood and bayesian frameworks. although the substitution process is not time - reversible, the computations are simplified by assuming that the instantaneous rate matrix can be decomposed into an " equilibrium frequency vector " ( non - homogeneous ) and a symmetric, constant exchange rate matrix. i guess all your suggestions are also valid, and i remember recoding being used successfully to reduce the gc - content bias ( examples in the references above and here ).


there are many good reasons not to use the 1968 - vintage lm741 : - minimum recommended power supply rails are + / - 10 volts modern op - amps have power supplies that can be as low as 0. 9 volts. input voltage range is typically from - vs + 2 volt to + vs - 2 volt modern op - amps can be chosen that are rail - to - rail input offset voltage is typically 1 mv ( 5 mv maximum ) modern op - amps can easily be as low as a few micro volts and have low drift. input offset current is typically 20 na ( 200 na maximum ) modern op - amps are commonly available that are less than 100 pa input bias current is typically 80 na ( 500 na maximum ) modern op - amps are commonly less than 1 na input resistance is typically 2 mω ( 300 kω minimum ) modern input resistance starts at hundreds of mω typical output voltage swing is - vs + 1 volt to + vs - 1 volt many cheap rail - to - rail op - amps get to their supplies within a few mv guaranteed output voltage swing is - vs + 3 volt to + vs - 3 volt supply current is typically 1. 7 ma ( 2. 8 ma maximum ) modern op - amps with this current consumption are ten times faster and better in many other ways too. noise is 60 nv / sqrt ( hz ) for lm348 ( quad version of 741 ) gbwp is 1 mhz with a slew rate of 0. 5 v / us the lm741a is slightly better but still a dinosaur in most areas. things of importance that the 741 data sheet does not appear to list ( and that may depend on the age and manufacturer ) : - input offset voltage drift versus temperature input offset current drift versus temperature common mode rejection ratio versus frequency output resistance ( closed or open loop ) phase margin likeliness of latchup ( and gain reversal ) i can't think of any valid reasons to use the 741 other than " that's all i will ever have or own ". common reasons why they are still used in actual devices appear to be : - someone had a design that they didn't want to change from the 70s someone had millions of them lying around and wanted to put them to use someone actually determined that all the parameters are fine for their design, and at that moment the 741 was the cheapest to acquire and in millions of units it saved a few thousand dollars


in total. i've been an electronics designer since 1980 and i have never used or specified a 741 in any design i've been associated with. maybe i'm missing out on something?


first we must assume that eve is only passive. by this, i mean that she truthfully sends the card to bob, and whatever she brings back to alice is indeed bob's response. if eve can alter the data in either or both directions ( and her action remains undetected ) then anything goes. ( to honour long - standing traditions, the two honest parties involved in the conversation are called alice and bob. in your text, you said " you ". my real name is not " alice ", but i will respond just as if you wrote that alice wants to verify bob's phone number. ) the simple ( but weak ) answer is to use a hash function. alice writes on the card : " return to me the sha - 256 hash of your phone number ". sha - 256 is a cryptographic hash function which is believed to be secure, as far as hash functions go. computing it by hand would be tedious but still doable ( that's about 2500 32 - bit operations, where each operation is an addition, a word shift or rotate, or a bitwise combination of bits ; bob should be able to do it in a day or so ). now what's weak about that? sha - 256, being a cryptographic hash function, is resistant to " preimages " : this means that given a hash output, it is very hard to recover a corresponding input ( that's the problem that eve faces ). however, " very hard " means " the easiest method is brute force : trying possible inputs until a match is found ". trouble is that brute force is easy here : there are not so many possible phone numbers ( in north america, that's 10 digits, i. e. a mere 10 billions ). bob wants to do things by hand, but we cannot assume that eve is so limited. a basic pc can try a few millions sha - 256 hashes per second so eve will be done in less than one hour ( less than 5 minutes if she uses a gpu ). this is a generic issue : if bob is deterministic ( i. e. for a given message from alice, he would always return the same response ), eve can simulate him. namely, eve knows everything about bob except the phone number, so she virtually runs 10 billions of bobs, who differ only by their assumed phone number ; and she waits for one of the virtual bobs to return whatever the real bob actually returned. the flaw affects many kinds of " smart


" solutions involving random nonces and symmetric encryption and whatsnot. it is a strong flaw, and its root lies in the huge difference in computing power between eve and bob ( now, if bob also had a computer as big as eve's, then he could use a slow hash function through the use of many iterations ; that's more or less what password hashing is about, with the phone number in lieu of the password ; see bcrypt and also this answer ). hence, a non - weak solution must involve some randomness on bob's part : bob must flip a coin or throw dice repeatedly, and inject the values in his computations. moreover, eve must not be able to unravel what bob did, but alice must be able to, so some information is confidentialy conveyed from bob to alice. this is called asymmetric encryption or, at least, asymmetric key agreement. the simplest algorithm of that class to compute, but still reasonably secure, is then rsa with the pkcs # 1 v1. 5 padding. rsa can use $ e = 3 $ as public exponent. so the protocol goes thus : alice generates a big integer $ n = pq $ where $ p $ and $ q $ are similarly - sized prime integer, such that the size of $ n $ is sufficient to ensure security ( i. e. at least 1024 bits, as of 2012 ). also, alice must arrange for $ p - 1 $ and $ q - 1 $ not to be multiples of 3. alice writes $ n $ on the card. bob first pads his phone number into a byte sequence as long as $ n $, as described by pkcs # 1 ( this means : 00 02 xx xx... xx 00 bb bb.. bb, where'bb'are the ten bytes which encode the phone number, and the'xx'are random non - zero byte values, for a total length of 128 bytes if $ n $ is a 1024 - bit integer ). bob interprets his byte sequence as a big integer value $ m $ ( big - endian encoding ) and computes $ m ^ 3 \ mathrm { \ mod \ } n $ ( so that's a couple of multiplications with very big integers, then a division, the result being the remainder of the division ). that's still doable by hand ( but, there again, it will probably take the better part of


a day ). the result is what bob sends back to alice. alice uses her knowledge of $ p $ and $ q $ to recover $ m $ from the $ m ^ 3 \ mathrm { \ mod \ } n $ sent by bob. the wikipedia page on rsa has some reasonably clear explanations on that process. once alice has $ m $, she can remove the padding ( the'xx'are non - zero, so the first'bb'byte can be unambiguously located ) and she then has the phone number, which she can compare with the one she had. alice's computation will require a computer ( what a computer does is always elementary and doable by hand, but a computer is devilishly fast at it, so the " doable " might take too much time to do in practice ; rsa decryption by hand would take many weeks ). ( actually we could have faster by - hand computation by using mceliece encryption, but then the public key - - what alice writes on the card - - would be huge, and a card would simply not do ; eve would have to transport a full book of digits. )


here's one key difference between the cases. suppose we add to the reals an element $ i $ such that $ i ^ 2 = - 1 $, and then include everything else you can get from $ i $ by applying addition and multiplication, while still preserving the usual rules of addition and multiplication. expanding the reals to the complex numbers in this way does not enable us to prove new equations among the original reals that are inconsistent with previously established equations. suppose by contrast we add to the reals a new element $ k $ postulated to be such that $ k + 1 = k $ and then also add every further element you can get by applying addition and multiplication to the reals and this new element $ k $. then we have, for example, $ k + 1 + 1 = k + 1 $. hence - - assuming that old and new elements together still obey the usual rules of arithmetic - - we can cheerfully subtract $ k $ from each side to " prove " $ 2 = 1 $. ooops! adding the postulated element $ k $ enables us to prove new equations flatly inconsistent what we already know. very bad news! now, we can in fact add an element like $ k $ consistently if we are prepared to alter the usual rules of addition. that is to say, if we not only add new elements but also change the rules of arithmetic at the same time, then we can stay safe. this is, for example, exactly what happens when we augment the finite ordinals with infinite ordinals. we get a consistent theory at the cost e. g. of having cases such as $ \ omega + 1 \ neq 1 + \ omega $ and $ 1 + 1 + \ omega = 1 + \ omega $.


in matlab, the ‘ \ ’ command invokes an algorithm which depends upon the structure of the matrix a and includes checks ( small overhead ) on properties of a. if a is sparse and banded, employ a banded solver. if a is an upper or lower triangular matrix, employ a backward substitution algorithm. if a is symmetric and has real positive diagonal elements, attempt a cholesky factorization. if a is sparse, employ reordering first to minimize fill - in. if none of criteria above is fulfilled, do a general triangular factorization using gaussian elimination with partial pivoting. if a is sparse, then employ the umfpack library. if a is not square, employ algorithms based on qr factorization for undetermined systems. to reduce overhead it is possible to use the linsolve command in matlab and select a suitable solver among these options yourself.


just look up a fractional inch to mm conversion chart. then break out the drill bits. 5 / 64 inch = 1. 9844 mm 3 / 32 inch = 2. 3813 mm 7 / 64 inch = 2. 7781 mm a 5 / 64 bit will fit the 2. 1mm barrel but not a 3 / 32 a 3 / 32 bit will fit the 2. 5mm barrel but not a 7 / 64


if you are in the us, there are several thousand institutions of higher learning, and at many of them there is very little " pressure to publish ". at others, the " pressure to publish " can be met by publishing a textbook or some work of scholarship that does not require proofs of interesting ( original ) results. high schools also need qualified mathematics teachers. consider staying in academia, just moving to a different part of it, as an option for using your powers to do good. i suspect, but cannot be sure, that much of what i've written applies outside the us as well.


i keep resistors in drawers organized by the first digits of value. r - 1, r - 12, r - 15, r - 18, r - 22 and so on. ( same for capacitors ) r - 1 contains 100ohm, 1k, 10k... r - 22 contains 22ohm, 220ohm, 2. 2k, 22k...


the felis catus genome has been published, annotated, and updated quite a bit since 1996, including spans of so - called intergenic regions, which are basically scaffolding and other structures, along with perhaps some unidentified genes, pseudogenes, regulatory sequences, etc. basically, pretty much the entire dna sequence is available now, not just the gene sequence of the mitochondrial genome, which was what was published in the 1996 paper you referenced. mitochondria are the power plants of the cell, but are just an organelle that happens to contain its own dna ; they are separate from the chromosomal dna in the nucleus. all of this is available for free ( if you know where to look ) at the national center for biotechnology information ( ncbi ), part of the national library of medicine ( nlm ) at the national institutes of health ( nih ) in the united states. other sites are also available, such as ensembl, a joint project between the european bioinformatics institute ( embl - ebi ), part of the european molecular biology laboratory ( embl ), and the wellcome trust sanger institute ( wtsi ). both institutes are located on the wellcome trust genome campus in the united kingdom. so, to the genome. genomic sequences can be searched in a couple of different ways, depending on what you're looking for, but the most common way is to use blast, the basic local alignment and search tool. as the name implies, it takes sequences as input and searches one against the other, aligning the results as best as possible using certain algorithms that the user can define and tweak. the blast web interface to the cat genome is here. you don't need to worry about any of the other options here except the " enter query sequence " box. fasta format is just using the single - letter abbreviations for nucleotides ( agct ), all strung together. the genome we're searching is of an abyssinian cat named cinnamon : cinnamon, the cat which was chosen to be the definitive genetic model for all cats in the feline genome project. image courtesy of the college of veterinary medicine at the university of missouri. to start with, i typed in catcatcatcat and to my surprise got back over 200 hits, covering every chromosome the cat has. so, i doubled the length of the input to 8 cats, and got back the same result set. unfortunately, 12 cats was too many


( and really, it is too many ), so i worked backwards. the final results are here ( sorry, link expires 10 / 13 / 16. to regenerate, go to blast link above and enter catcatcatcatcatcatcatcatcatcat ). apparently, popular wisdom is incorrect, and felis catus chromosomes really contain 10 cats each, one more than is needed for their 9 lives. no word yet as to why this may be, but scientists are presumably working on it.


brian hayes wrote a very interesting article from a mathematical point of view : especially the " reality intrudes " section. basically people had created fancy mathematical reasons why it has to be exactly 20. nature, being nature, does not follow the reasoning, but has its own ideas. in other words there was nothing especially special about 20. in fact there seems to be a slow grafting of a 21st amino acid, selenocysteine using the codon uga. also pyrrolysine is considered the 22nd. the last section suggests that the code was originally doublet, so coded for < 16 amino acids. this can partly explain why the third base in each codon is not as discriminating. so perhaps in the year 2002012 someone will be asking on biology. stackexchange why there are only 40 amino acids.


you are referring to the landau notation. they are not different symbols for the same thing but have entirely different meanings. which one is " preferable " depends entirely on the desired statement. $ f \ in \ cal { o } ( g ) $ means that $ f $ grows at most as fast as $ g $, asymptotically and up to a constant factor ; think of it as a $ \ leq $. $ f \ in o ( g ) $ is the stricter form, i. e. $ < $. $ f \ in \ omega ( g ) $ has the symmetric meaning : $ f $ grows at least as fast as $ g $. $ \ omega $ is its stricter cousin. you can see that $ f \ in \ omega ( g ) $ is equivalent to $ g \ in \ cal { o } ( f ) $. $ f \ in \ theta ( g ) $ means that $ f $ grows about as fast as $ g $ ; formally $ f \ in \ cal { o } ( g ) \ cap \ omega ( g ) $. $ f \ sim g $ ( asymptotic equality ) is its stronger form. we often mean $ \ theta $ when we use $ \ cal { o } $. note how $ \ cal { o } ( g ) $ and its siblings are function classes. it is important to be very aware of this and their precise definitions - - which can differ depending on who is talking - - when doing " arithmetics " with them. when proving things, take care to work with your precise definition. there are many definitions for landau symbols around ( all with the same basic intuition ), some of which are equivalent on some sets on functions but not on others. suggested reading : what are the rules for equals signs with big - o and little - o? sorting functions by asymptotic growth how do o and ω relate to worst and best case? nested big o - notation definition of $ \ theta $ for negative functions what is the meaning of $ o ( m + n ) $? is o ( mn ) considered " linear " or " quadratic " growth? sums of landau terms revisited what does big o mean as a term of an approximation ratio? any other question about asymptotics and landau - notation as exercise. if you are interested in using landau notation in a rigorous and sound manner, you may be interested in recent work by rutanen et al. [ 1 ]. they


formulate necessary and sufficient criteria for asymptotic notation as we use them in algorithmics, show that the common definition fails to meet them and provide a ( the, in fact ) workable definition. a general definition of the o - notation for algorithm analysis by k. rutanen et al. ( 2015 )


the question is relatively broad and one should take into account that the brain not only consists of neurons, but also glial cells ( supportive cells ) and pre - mitotic neuronal stem cells. furthermore, as critical fellow - scientists have indicated, developmental stage is very important, as the developing embryonic brain is very different from the adult brain. however, after sifting through various publications, the answer to the question is actually remarkably simple : yes, brain cells migrate. in the adult brain glial cells migrate in the brain ( klambt, 2009 ). glial cells are involved in a myriad of functions, but a notable example of migrating glial cells are the oligodendrocytes that migrate relative long distances to find their target axons onto which they wrap themselves to form the insulating myelin sheath ( tsai and miller, 2002 ). neuronal stem cells migrate over long distances in response to injury ( imitola et al., 2004 ) and they migrate from specific stem - cell locations ( e. g., hippocampus and subventricular zone ) to other regions ( clarke, 2003 ). post - mitotic, but non - differentiated neurons have been shown to migrate in the adult brain in fish ( scott et al., 2012 ), and in mammals and non - human primates as well ( sawada et al., 2011 ). not surprisingly, glial cells, stem cells and neurons also migrate during embryonic development. most notably, post - mitotic neurons destined to fulfill peripheral functions have to migrate over relatively long distances from the neural crest to their target locations ( neuroscience, 2nd ed, neuronal migration ).


interesting question! the cause of tears and itching is the chemicals produced by onion ( allium cepa ). lets go into some details. onions, coming from the family liliaceae ( also containing garlic, chives, scallions and leeks ) store compounds known as amino acid sulfoxides, and the one we are talking about here is s - 1 - propenyl - l - cysteine sulfoxide ( abbreviated as prencso ), also calles isoalliin ( due to its similarity with alliin found in garlic ). when onion is damaged ( cut, chewed, etc. ), an enzyme alliinase converts prencso into 1 - propenyl sulfenic acid. this compound is then converted into propanethial - s - oxide by an enzyme lachrymatory factor synthase ( earlier this reaction was considered spontaneous ). the reaction looks like this : propanethial - s - oxide is the major cause of the flavor and aroma of onion. however, it is a volatile compound i. e. vaporizes very quickly. when its vapors reach the eye, it causes tears because of being a lachrymator ( aka tear gas ) i. e. as soon as it comes in contact with cornea, it triggers a nervous response which leads to activation of lachrymal ( tear ) glands. ps : when propanethial - s - oxide comes in contact with cornea, a small amount of it reacts with water to form sulfuric acid. this sulfuric acid is the cause of itching and irritation in eyes due to onion. also, scientists are now trying to genetically either modify or stop the production of lachrymatory factor synthase enzyme to produce tearless onions. this ( modification ) has even been achieved to a high efficiency, as another answer discusses. however, making tearless onions could prove harmful to the crop in several ways, as discussed here. edit : as asked in comments, i will add some details about how the sulfuric acid is produced from the reaction between propanethial - s - oxide and water. the only resource i could find giving some details about this was marta corzo - martinez, 2014. they summarize the complete pathway in the following diagram : after applying some common chemistry principles, the concerned reaction turns out to be : $ \ ce { 4 ~ c _ 3h _ 6so ~ + ~ 4 ~ h _ 2o \ rightarrow 4 ~


c _ 3h _ 6o ~ + ~ h _ 2so _ 4 ~ + ~ 3 ~ h _ 2s } $ as you see, one of the products of hydrolysis of propanethial - s - oxide is hydrogen sulfide ( $ \ ce { h _ 2s } $ ). just like $ \ ce { h _ 2so _ 4 } $, $ \ ce { h _ 2s } $ also causes irritation in the eyes ( its effect on eyes has been well documented, see lambert et al, 2006 as an example ). thus, the produced $ \ ce { h _ 2s } $ only increases the irritation and itching in the eyes caused due to $ \ ce { h _ 2so _ 4 } $. bonus : another interesting point here is runny nose. propanethial - s - oxide is actually the compound responsible for the smell and flavor of onions. but, it causes tears by exciting the lachrymal glands i. e. reflexive lachrymation. propanethial - s - oxide excites the trigeminal nerve ( the fifth cranial nerve ) causing activation of lachrymal glands. interestingly, the nerve endings of trigeminal nerve are also present in the nose, along with the eyes. so, this compound can also activate the lachrymal glands from your nose, and since the lachrymal duct is joined from eyes to nose, you can also experience runny nose along with tears and irritation in eyes. references : propanethial - s - oxide | university of bristol alliin | wikipedia tear gas | wikipedia timothy william lambert, verona marie goodwin, dennis stefani, lisa strosher, hydrogen sulfide ( $ \ ce { h _ 2s } $ ) and sour gas effects on the eye. a historical perspective, science of the total environment, volume 367, issue 1, 15 august 2006, pages 1 - 22, issn 0048 - 9697, encyclopedia of perception, volume 1 - e. bruce goldstein, sage, 2010 the neurology of lacrimation – how an ear infection can cause dry eye - by noelle la croix, dvm, dip. acvo


do they exist? yes what are they called? marilyn roossinck calls them viral mutualistic symbiotes. she has an excellent review here. what are some examples? my personal favorite is gb - virus c, or hepatitis g, which appears to slow the progression of hiv using a number of different mechanisms : box 1. summary of the effects of gbv - c infection in hiv - positive individuals gbv - c infection downregulates hiv entry co - receptors ccr5 and cxcr4, and increases secretion of their ligands rantes, mip - 1α, mip - 1β and sdf - 1. in vitro gbv - c ns5a and e2 proteins inhibit x4 - and r5 - tropic hiv replication, and ns5a protein downregulates cd4 and cxcr4 gene expression. hiv - infected individuals positive for gbv - c e2 antibodies have survival benefit over hiv - infected individuals with neither gbv - c viremia nor e2 antibodies ; in vitro gbv - c e2 antibodies immunoprecipitate hiv particles and inhibit x4 - and r5 - tropic hiv replication. gbv - c induces activation of interferon - related genes and pdcs. gbv - c promotes th1 polarization and the ns5a protein contributes to this effect. gbv - c infection reduces surface expression of activation markers on t lymphocytes, suggesting its role in t cell activation signaling pathways. gbv - c protects the t cell from fas - mediated apoptosis and as a result of its effect on immune activation may also play a role in protecting lymphocytes from activation - induced cell death. gbv - c viremia reduces il - 2 - mediated t cell proliferation suggesting a significant interaction between gbv - c, il - 2 and il - 2 signaling pathways. endogenous retroviruses as @ mbrig recalls in the comments, there are a number of retroviruses that have inserted themselves into the germ line. those are called endogenous retroviruses, and they interact with the host genome in a number of ways. some are even translated : proteins produced from erv env genes have also been demonstrated to function as restriction factors against exogenous retroviral infection


here are the $ \ ce { h - x - h } $ bond angles and the $ \ ce { h - x } $ bond lengths : \ begin { array } { lcc } \ text { molecule } & \ text { bond angle } / ^ \ circ & \ text { bond length } / \ pu { pm } \ \ \ hline \ ce { h2o } & 104. 5 & 96 \ \ \ ce { h2s } & 92. 3 & 134 \ \ \ ce { h2se } & 91. 0 & 146 \ \ \ hline \ end { array } the traditional textbook explanation would argue that the orbitals in the water molecule is close to being $ \ ce { sp ^ 3 } $ hybridized, but due to lone pair - lone pair electron repulsions, the lone pair - x - lone pair angle opens up slightly in order to reduce these repulsions, thereby forcing the $ \ ce { h - x - h } $ angle to contract slightly. so instead of the $ \ ce { h - o - h } $ angle being the perfect tetrahedral angle ( $ 109. 5 ^ \ circ $ ) it is slightly reduced to $ 104. 5 ^ \ circ $. on the other hand, both $ \ ce { h2s } $ and $ \ ce { h2se } $ have no orbital hybridization. that is, the $ \ ce { s - h } $ and $ \ ce { se - h } $ bonds use pure $ \ ce { p } $ - orbitals from sulfur and selenium respectively. two $ \ ce { p } $ - orbitals are used, one for each of the two $ \ ce { x - h } $ bonds ; this leaves another $ \ ce { p } $ - orbital and an $ \ ce { s } $ - orbital to hold the two lone pairs of electrons. if the $ \ ce { s - h } $ and $ \ ce { se - h } $ bonds used pure $ \ ce { p } $ - orbitals we would expect an $ \ ce { h - x - h } $ interorbital angle of $ 90 ^ \ circ $. we see from the above table that we are very close to the measured values. we could fine tune our answer by saying that in order to reduce repulsion between the bonding electrons in the two $ \ ce { x - h } $ bonds the angle opens up


a bit wider. this explanation would be consistent with the $ \ ce { h - s - h } $ angle being slightly larger than the corresponding $ \ ce { h - se - h } $ angle. since the $ \ ce { h - se } $ bond is longer then the $ \ ce { h - s } $ bond, the interorbital electron repulsions will be less in the $ \ ce { h2se } $ case alleviating the need for the bond angle to open up as much as it did in the $ \ ce { h2s } $ case. the only new twist on all of this that some universities are now teaching is that water is not really $ \ ce { sp ^ 3 } $ hybridized, the $ \ ce { sp ^ 3 } $ explanation does not fit with all of the experimentally observed data, most notably the photoelectron spectrum. the basic concept introduced is that " orbitals only hybridize in response to bonding. " so in water, the orbitals in the two $ \ ce { o - h } $ bonds are roughly $ \ ce { sp ^ 3 } $ hybridized, but one lone pair resides in a nearly pure p - orbital and the other lone pair is in a roughly $ \ ce { sp } $ hybridized orbital.


to my knowledge the pumping lemma is by far the simplest and most - used technique. if you find it hard, try the regular version first, it's not that bad. there are some other means for languages that are far from context free. for example undecidable languages are trivially not context free. that said, i am also interested in other techniques than the pumping lemma if there are any. edit : here is an example for the pumping lemma : suppose the language $ l = \ { a ^ k \ mid k ∈ p \ } $ is context free ( $ p $ is the set of prime numbers ). the pumping lemma has a lot of $ / $ quantifiers, so i will make this a bit like a game : the pumping lemma gives you a $ p $ you give a word $ s $ of the language of length at least $ p $ the pumping lemma rewrites it like this : $ s = uvxyz $ with some conditions ( $ | vxy | ≤p $ and $ | vy | ≥1 $ ) you give an integer $ n≥0 $ if $ uv ^ nxy ^ nz $ is not in $ l $, you win, $ l $ is not context free. for this particular language for $ s $ any $ a ^ k $ ( with $ k≥p $ and $ k $ is a prime number ) will do the trick. then the pumping lemma gives you $ uvxyz $ with $ | vy | ≥1 $. do disprove the context - freeness, you need to find $ n $ such that $ | uv ^ nxy ^ nz | $ is not a prime number. $ $ | uv ^ nxy ^ nz | = | s | + ( n - 1 ) | vy | = k + ( n - 1 ) | vy | $ $ and then $ n = k + 1 $ will do : $ k + k | vy | = k ( 1 + | vy | ) $ is not prime so $ uv ^ nxy ^ nz \ not \ in l $. the pumping lemma can't be applied so $ l $ is not context free. a second example is the language $ \ { ww \ mid w \ in \ { a, b \ } ^ { \ ast } \ } $. we ( of course ) have to choose a string and show that there's no possible way


it can be broken into those five parts and have every derived pumped string remain in the language. the string $ s = a ^ { p } b ^ { p } a ^ { p } b ^ { p } $ is a suitable choice for this proof. now we just have to look at where $ v $ and $ y $ can be. the key parts are that $ v $ or $ y $ has to have something in it ( perhaps both ), and that both $ v $ and $ y $ ( and $ x $ ) are contained in a length $ p $ substring - so they can't be too far apart. this string has a number of possibilities for where $ v $ and $ y $ might be, but it turns out that several of the cases actually look pretty similar. $ vy \ in a ^ { \ ast } $ or $ vy \ in b ^ { \ ast } $. so then they're both contained in one of the sections of continguous $ a $ s or $ b $ s. this is the relatively easy case to argue, as it kind of doesn't matter which they're in. assume that $ | vy | = k \ leq p $. if they're in the first section of $ a $ s, then when we pump, the first half of the new string is $ a ^ { p + k } b ^ { p - k / 2 } $, and the second is $ b ^ { k / 2 } a ^ { p } b ^ { p } $. obviously this is not of the form $ ww $. the argument for any of the three other sections runs pretty much the same, it's just where the $ k $ and $ k / 2 $ ends up in the indices. $ vxy $ straddles two of the sections. in this case pumping down is your friend. again there's several places where this can happen ( 3 to be exact ), but i'll just do one illustrative one, and the rest should be easy to figure out from there. assume that $ vxy $ straddles the border between the first $ a $ section and the first $ b $ section. let $ vy = a ^ { k _ { 1 } } b ^ { k _ { 2 } } $ ( it doesn't matter precisely where the $ a $ s and $ b $ s are in $ v $ and $


y $, but we know that they're in order ). then when we pump down ( i. e. the $ i = 0 $ case ), we get the new string $ s'= a ^ { p - k _ { 1 } } b ^ { p - k _ { 2 } } a ^ { p } b ^ { p } $, but then if $ s'$ could be split into $ ww $, the midpoint must be somewhere in the second $ a $ section, so the first half is $ a ^ { p - k _ { 1 } } b ^ { p - k _ { 2 } } a ^ { ( k _ { 1 } + k _ { 2 } ) / 2 } $, and the second half is $ a ^ { p - ( k _ { 1 } + k _ { 2 } ) / 2 } b ^ { p } $. clearly these are not the same string, so we can't put $ v $ and $ y $ there. the remaining cases should be fairly transparent from there - they're the same ideas, just putting $ v $ and $ y $ in the other 3 spots in the first instance, and 2 spots in the second instance. in all cases though, you can pump it in such a way that the ordering is clearly messed up when you split the string in half.


let the real values data matrix $ \ mathbf x $ be of $ n \ times p $ size, where $ n $ is the number of samples and $ p $ is the number of variables. let us assume that it is centered, i. e. column means have been subtracted and are now equal to zero. then the $ p \ times p $ covariance matrix $ \ mathbf c $ is given by $ \ mathbf c = \ mathbf x ^ \ top \ mathbf x / ( n - 1 ) $. it is a symmetric matrix and so it can be diagonalized : $ $ \ mathbf c = \ mathbf v \ mathbf l \ mathbf v ^ \ top, $ $ where $ \ mathbf v $ is a matrix of eigenvectors ( each column is an eigenvector ) and $ \ mathbf l $ is a diagonal matrix with eigenvalues $ \ lambda _ i $ in the decreasing order on the diagonal. the eigenvectors are called principal axes or principal directions of the data. projections of the data on the principal axes are called principal components, also known as pc scores ; these can be seen as new, transformed, variables. the $ j $ - th principal component is given by $ j $ - th column of $ \ mathbf { xv } $. the coordinates of the $ i $ - th data point in the new pc space are given by the $ i $ - th row of $ \ mathbf { xv } $. if we now perform singular value decomposition of $ \ mathbf x $, we obtain a decomposition $ $ \ mathbf x = \ mathbf u \ mathbf s \ mathbf v ^ \ top, $ $ where $ \ mathbf u $ is a unitary matrix ( with columns called left singular vectors ), $ \ mathbf s $ is the diagonal matrix of singular values $ s _ i $ and $ \ mathbf v $ columns are called right singular vectors. from here one can easily see that $ $ \ mathbf c = \ mathbf v \ mathbf s \ mathbf u ^ \ top \ mathbf u \ mathbf s \ mathbf v ^ \ top / ( n - 1 ) = \ mathbf v \ frac { \ mathbf s ^ 2 } { n - 1 } \ mathbf v ^ \ top, $ $ meaning that right singular vectors $ \ mathbf v $ are principal directions ( eigenvectors ) and


that singular values are related to the eigenvalues of covariance matrix via $ \ lambda _ i = s _ i ^ 2 / ( n - 1 ) $. principal components are given by $ \ mathbf x \ mathbf v = \ mathbf u \ mathbf s \ mathbf v ^ \ top \ mathbf v = \ mathbf u \ mathbf s $. to summarize : if $ \ mathbf x = \ mathbf u \ mathbf s \ mathbf v ^ \ top $, then the columns of $ \ mathbf v $ are principal directions / axes ( eigenvectors ). columns of $ \ mathbf { us } $ are principal components ( " scores " ). singular values are related to the eigenvalues of covariance matrix via $ \ lambda _ i = s _ i ^ 2 / ( n - 1 ) $. eigenvalues $ \ lambda _ i $ show variances of the respective pcs. standardized scores are given by columns of $ \ sqrt { n - 1 } \ mathbf u $ and loadings are given by columns of $ \ mathbf v \ mathbf s / \ sqrt { n - 1 } $. see e. g. here and here for why " loadings " should not be confused with principal directions. the above is correct only if $ \ mathbf x $ is centered. only then is covariance matrix equal to $ \ mathbf x ^ \ top \ mathbf x / ( n - 1 ) $. the above is correct only for $ \ mathbf x $ having samples in rows and variables in columns. if variables are in rows and samples in columns, then $ \ mathbf u $ and $ \ mathbf v $ exchange interpretations. if one wants to perform pca on a correlation matrix ( instead of a covariance matrix ), then columns of $ \ mathbf x $ should not only be centered, but standardized as well, i. e. divided by their standard deviations. to reduce the dimensionality of the data from $ p $ to $ k < p $, select $ k $ first columns of $ \ mathbf u $, and $ k \ times k $ upper - left part of $ \ mathbf s $. their product $ \ mathbf u _ k \ mathbf s _ k $ is the required $ n \ times k $ matrix containing first $ k $ pcs. further multiplying the first $ k


$ pcs by the corresponding principal axes $ \ mathbf v _ k ^ \ top $ yields $ \ mathbf x _ k = \ mathbf u _ k ^ \ vphantom \ top \ mathbf s _ k ^ \ vphantom \ top \ mathbf v _ k ^ \ top $ matrix that has the original $ n \ times p $ size but is of lower rank ( of rank $ k $ ). this matrix $ \ mathbf x _ k $ provides a reconstruction of the original data from the first $ k $ pcs. it has the lowest possible reconstruction error, see my answer here. strictly speaking, $ \ mathbf u $ is of $ n \ times n $ size and $ \ mathbf v $ is of $ p \ times p $ size. however, if $ n > p $ then the last $ n - p $ columns of $ \ mathbf u $ are arbitrary ( and corresponding rows of $ \ mathbf s $ are constant zero ) ; one should therefore use an economy size ( or thin ) svd that returns $ \ mathbf u $ of $ n \ times p $ size, dropping the useless columns. for large $ n \ gg p $ the matrix $ \ mathbf u $ would otherwise be unnecessarily huge. the same applies for an opposite situation of $ n \ ll p $. further links what is the intuitive relationship between svd and pca - - a very popular and very similar thread on math. se. why pca of data by means of svd of the data? - - a discussion of what are the benefits of performing pca via svd [ short answer : numerical stability ]. pca and correspondence analysis in their relation to biplot - - pca in the context of some congeneric techniques, all based on svd. is there any advantage of svd over pca? - - a question asking if there any benefits in using svd instead of pca [ short answer : ill - posed question ]. making sense of principal component analysis, eigenvectors & eigenvalues - - my answer giving a non - technical explanation of pca. to draw attention, i reproduce one figure here :


there is still a lot to be learned about the roles introns play in biological processes, but there are a couple of things that have been pretty well established. introns enable alternative splicing, which enables a single gene to encode multiple proteins that perform different functions under different conditions. for example, a signal the cell receives could cause an exon that is normally included to be skipped, or an intron that is normally spliced out to be left in for translation ( the wikipedia article on the subject has a basic overview of the possibilities ). this would not be possible, or at least would be much more difficult, without the presence of introns. in recent years, we have discovered that rna molecules ( especially small rnas such as sirnas and mirnas ) are much more involved in regulating gene expression than previously thought. often the small regulatory rnas are derived from spliced introns. there is probably more, but essentially introns enable a finer level of regulatory control. biological complexity is often not the result of having a larger complement of genes, but of having additional layers of regulation to turn genes on and off at the right times. prokaryotic genes are often organized into operons, and a single polycistronic mrna will often encode multiple proteins from multiple adjacent genes. since the biological processes required to sustain microbial life are much less complicated than those required to sustain eukaryotic life, they can get away with much less regulatory control.


this is a very interesting question. basically ( and this is the short answer ), geckos possess a unique self - cleaning mechanism in their feet which synthetic nano tapes do not have. this capability allows geckos to maintain their adhesive properties even in dusty environments. gecko feet mechanism gecko feet are covered with millions of microscopic hair - like structures called setae, which branch into thousands of even smaller spatulae. these structures allow geckos to adhere to surfaces through van der waals forces, which are weak intermolecular forces that become significant at the nanoscale. when a gecko walks, the lateral movement of its feet creates friction that dislodges larger dirt particles, while smaller particles fall into the folds of their skin, effectively cleaning the setae as they move. the self - cleaning ability of gecko feet is attributed to the hierarchical structure of the setae and spatulae, which allows them to dislodge contaminants efficiently. experimental studies show that geckos can regain about 80 % of their adhesive strength after just a few steps on contaminated surfaces, thanks to this mechanism ( see references 1, 2 and 3 for more details ). synthetic nano - tape comparison in contrast, synthetic nano - tapes inspired by gecko feet often lack the same level of self - cleaning efficiency. while they can mimic the adhesive properties of gecko feet, they typically do not perform well in dusty conditions. the synthetic versions may rely on larger microhairs that do not effectively roll off dirt particles, leading to a significant loss of adhesive strength after contact with contaminants. moreover, many synthetic adhesives use glue, which can degrade over time and lose adhesion, unlike gecko feet that remain sticky without any additional substances. although some synthetic tapes have been developed to replicate the self - cleaning effect, they have not yet matched the natural efficiency of gecko feet in real - world conditions. conclusion in summary, the fundamental difference lies in the gecko's natural ability to maintain adhesion through a sophisticated self - cleaning mechanism facilitated by its unique micro - and nano - structured feet, whereas synthetic nano - tapes often struggle with dirt retention and adhesive longevity due to their reliance on larger structures and glue - based adhesion methods ( see references 4 and 5 for more details ). references : robust self - cleaning and micromanipulation capabilities of gecko spatulae and their bio - mimics gecko adhesion : evolutionary nanotechnology dynamic self -


cleaning in gecko setae via digital hyperextension robust self - cleaning and micromanipulation capabilities of gecko spatulae and their bio - mimics carbon nanotube - based synthetic gecko tapes


fun question! as you pointed out, $ $ \ theta \ approx 1. 22 \ frac { \ lambda } { d } $ $ for a human - like eye, which has a maximum pupil diameter of about $ 9 \ \ mathrm { mm } $ and choosing the shortest wavelength in the visible spectrum of about $ 390 \ \ mathrm { nm } $, the angular resolution works out to about $ 5. 3 \ times10 ^ { - 5 } $ ( radians, of course ). at a distance of $ 24 \ \ mathrm { km } $, this corresponds to a linear resolution ( $ \ theta d $, where $ d $ is the distance ) of about $ 1. 2 \ \ mathrm m $. so counting mounted riders seems plausible since they are probably separated by one to a few times this resolution. comparing their heights which are on the order of the resolution would be more difficult, but might still be possible with dithering. does legolas perhaps wiggle his head around a lot while he's counting? dithering only helps when the image sampling ( in this case, by elven photoreceptors ) is worse than the resolution of the optics. human eyes apparently have an equivalent pixel spacing of something like a few tenths of an arcminute, while the diffraction - limited resolution is about a tenth of an arcminute, so dithering or some other technique would be necessary to take full advantage of the optics. an interferometer has an angular resolution equal to a telescope with a diameter equal to the separation between the two most widely separated detectors. legolas has two detectors ( eyeballs ) separated by about 10 times the diameter of his pupils, $ 75 \ \ mathrm { mm } $ or so at most. this would give him a linear resolution of about $ 15 \ \ mathrm { cm } $ at a distance of $ 24 \ \ mathrm { km } $, probably sufficient to compare the heights of mounted riders. however, interferometry is a bit more complicated than that. with only two detectors and a single fixed separation, only features with angular separations equal to the resolution are resolved, and direction is important as well. if legolas'eyes are oriented horizontally, he won't be able to resolve structure in the vertical direction using interferometric techniques. so he'd at the very least need to tilt his head sideways, and probably also jiggle it around a lot ( including


some rotation ) again to get decent sampling of different baseline orientations. still, it seems like with a sufficiently sophisticated processor ( elf brain? ) he could achieve the reported observation. lubos motl points out some other possible difficulties with interferometry in his answer, primarily that the combination of a polychromatic source and a detector spacing many times larger than the observed wavelength lead to no correlation in the phase of the light entering the two detectors. while true, legolas may be able to get around this if his eyes ( specifically the photoreceptors ) are sufficiently sophisticated so as to act as a simultaneous high - resolution imaging spectrometer or integral field spectrograph and interferometer. this way he could pick out signals of a given wavelength and use them in his interferometric processing. a couple of the other answers and comments mention the potential difficulty drawing a sight line to a point $ 24 \ rm km $ away due to the curvature of the earth. as has been pointed out, legolas just needs to have an advantage in elevation of about $ 90 \ \ mathrm m $ ( the radial distance from a circle $ 6400 \ \ mathrm { km } $ in radius to a tangent $ 24 \ \ mathrm { km } $ along the circumference ; middle - earth is apparently about earth - sized, or may be earth in the past, though i can't really nail this down with a canonical source after a quick search ). he doesn't need to be on a mountaintop or anything, so it seems reasonable to just assume that the geography allows a line of sight. finally a bit about " clean air ". in astronomy ( if you haven't guessed my field yet, now you know. ) we refer to distortions caused by the atmosphere as " seeing ". seeing is often measured in arcseconds ( $ 3600'' = 60'= 1 ^ \ circ $ ), referring to the limit imposed on angular resolution by atmospheric distortions. the best seeing, achieved from mountaintops in perfect conditions, is about $ 1'' $, or in radians $ 4. 8 \ times10 ^ { - 6 } $. this is about the same angular resolution as legolas'amazing interferometric eyes. i'm not sure what seeing would be like horizontally across a distance of $ 24 \ \ mathrm { km } $. on the one hand there is a lot more air than looking up vertically ; the atmosphere


is thicker than $ 24 \ \ mathrm { km } $ but its density drops rapidly with altitude. on the other hand the relatively uniform density and temperature at fixed altitude would cause less variation in refractive index than in the vertical direction, which might improve seeing. if i had to guess, i'd say that for very still air at uniform temperature he might get seeing as good as $ 1 \ rm arcsec $, but with more realistic conditions with the sun shining, mirage - like effects probably take over limiting the resolution that legolas can achieve.


there are several methods to do the conversion from finite automata to regular expressions. here i will describe the one usually taught in school which is very visual. i believe it is the most used in practice. however, writing the algorithm is not such a good idea. state removal method this algorithm is about handling the graph of the automaton and is thus not very suitable for algorithms since it needs graph primitives such as... state removal. i will describe it using higher - level primitives. the key idea the idea is to consider regular expressions on edges and then removing intermediate states while keeping the edges labels consistent. the main pattern can be seen in the following to figures. the first has labels between $ p, q, r $ that are regular expressions $ e, f, g, h, i $ and we want to remove $ q $. once removed, we compose $ e, f, g, h, i $ together ( while preserving the other edges between $ p $ and $ r $ but this is not displayed on this ) : example using the same example as in raphael's answer : we successively remove $ q _ 2 $ : and then $ q _ 3 $ : then we still have to apply a star on the expression from $ q _ 1 $ to $ q _ 1 $. in this case, the final state is also initial so we really just need to add a star : $ $ ( ab + ( b + aa ) ( ba ) ^ * ( a + bb ) ) ^ * $ $ algorithm l [ i, j ] is the regexp of the language from $ q _ i $ to $ q _ j $. first, we remove all multi - edges : for i = 1 to n : for j = 1 to n : if i = = j then : l [ i, j ] : = ε else : l [ i, j ] : = ∅ for a in σ : if trans ( i, a, j ) : l [ i, j ] : = l [ i, j ] + a now, the state removal. suppose we want to remove the state $ q _ k $ : remove ( k ) : for i = 1 to n : for j = 1 to n : l [ i, i ] + = l [ i, k ]. star ( l [ k, k ] ). l [ k, i ] l [ j, j ] + = l [ j, k ]. star ( l [ k, k ]


). l [ k, j ] l [ i, j ] + = l [ i, k ]. star ( l [ k, k ] ). l [ k, j ] l [ j, i ] + = l [ j, k ]. star ( l [ k, k ] ). l [ k, i ] note that both with a pencil of paper and with an algorithm you should simplify expressions like star ( ε ) = ε, e. ε = e, ∅ + e = e, ∅. e = ∅ ( by hand you just don't write the edge when it's not $ ∅ $, or even $ ε $ for a self - loop and you ignore when there is no transition between $ q _ i $ and $ q _ k $ or $ q _ j $ and $ q _ k $ ) now, how to use remove ( k )? you should not remove final or initial states lightly, otherwise you will miss parts of the language. for i = 1 to n : if not ( final ( i ) ) and not ( initial ( i ) ) : remove ( i ) if you have only one final state $ q _ f $ and one initial state $ q _ s $ then the final expression is : e : = star ( l [ s, s ] ). l [ s, f ]. star ( l [ f, s ]. star ( l [ s, s ] ). l [ s, f ] + l [ f, f ] ) if you have several final states ( or even initial states ) then there is no simple way of merging these ones, other than applying the transitive closure method. usually this is not a problem by hand but this is awkward when writing the algorithm. a much simpler workaround is to enumerate all pairs $ ( s, f ) $ and run the algorithm on the ( already state - removed ) graph to get all expressions $ e _ { s, f } $ supposing $ s $ is the only initial state and $ f $ is the only final state, then doing the union of all $ e _ { s, f } $. this, and the fact that this is modifying languages more dynamically than the first method make it more error - prone when programming. i suggest using any other method. cons there are a lot of cases in this algorithm, for example for choosing which node we should remove, the number of final states at the end, the fact that a final


state can be initial, too etc. note that now that the algorithm is written, this is a lot like the transitive closure method. only the context of the usage is different. i do not recommend implementing the algorithm, but using the method to do that by hand is a good idea.


you're the second person i have ever seen using ncbi " chromosome names " ( they're more like supercontig ids ). normally i would point you to a resource providing mappings between chromosome names, but since no one has added ncbi names ( yet, maybe i'll add them now ) you're currently out of luck there. anyway, the quickest way to do what you want is to samtools view - h foo. bam > header to get the bam header and then change each ncbi " chromosome name " to its corresponding ucsc chromosome name. do not reorder the lines! you can then use samtools reheader and be done. why, you might ask, would this work? the answer is that chromosome / contig names in bam files aren't stored in each alignment. rather, the names are stored in a list in the header and each alignment just contains the integer index into that list ( read group ids are similar, for what it's worth ). this also leads to the warning above against reordering entries, since that's a very convenient way to start swapping alignments between chromosomes. as an aside, you'd be well served switching to gencode or ensembl chromosome names, they're rather more coherent than the something _ random mess that's present in hg19 from ucsc. update : because i'm nice, here is the conversion between ncbi and ucsc. note that if you have any alignments to patches that there is simply no ucsc equivalent. one of the many reasons not to use ucsc ( avoid their annotations too ).


when the world was younger, and computers weren't all glorified pcs, word sizes varied ( a dec 2020 we had around here had 36 bit words ), format of binary data was a contentious issue ( big endian vs little endian, and even weirder orders of bits were reasonably common ). there was little consensus on character size / encoding ( ascii, ebcdic were the main contenders, our dec had 5 / 6 / 7 / 8 bits / character encodings ). arpanet ( the internet predecessor ) was designed to connect machines of any description. the common denominator was ( and still is ) text. you could be reasonably certain that 7 - bit encoded text wouldn't get mangled by the underlying means to ship data around ( until quite recently, sending email in some 8 - bit encoding carried a guarantee that the recipient would get mutilated messages, serial lines were normally configured as 7 - bit with one bit parity ). if you rummage around in e. g. the telnet or ftp protocol descriptions ( the first internet protocols, the network idea then was to connect remotely to a " supercomputer ", and shuffle files to and fro ), you see that the connection includes negotiating lots of details we take as uniform, yes, binary would be ( a bit ) more efficient. but machines and memories ( and also networks ) have grown enormously, so the bit scrimping of yore is a thing of the past ( mostly ). and nobody in their right mind will suggest ripping out all existing protocols to replace them with binary ones. besides, text protocols offer a very useful debugging technique. today i never install the telnet server ( better use the encrypted ssh protocol for remote connections ), but have to telnet client handy to " talk " to some errant server to figure out snags. today you'd probably use netcat or ncat for futzing around...


as requested i'm posting this an answer. i wrote a short sage script to check the primality of numbers of the form $ 10 ^ n + 333 $ where $ n $ is in the range $ [ 4, 2000 ] $. i found that the following values of $ n $ give rise to prime numbers : $ $ 4, 5, 6, 12, 53, 222, 231, 416. $ $ edit 3 : i stopped my laptop's search between 2000 and 3000, since it hadn't found anything in 20 minutes. i wrote a quick program to check numbers of the form $ 10 ^ n + 3 * 10 ^ i + 33 $. here are a couple 100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000300033 100000000000000000000000000000000000000000000000000000300000000000000000000000000000000000000033 100000000000000000000000000000000000000000000000030000000000000000000000000000000000000000000033 100000000000000000000000000000000000000000000030000000000000000000000000000000000000000000000033 10000000000000000000000000000000003000000033 10000000000000000000000000000030000000000033 10000000000000000000000030000000000000000033 10000000003000000000000000000000000000000033 there seemed to be plenty of numbers of this form and presumably i could find more if i checked some of the other possible forms as outlined by dr jimbob. note : i revised the post a bit after jimbob pointed out i was actually looking for primes that didn't quite fit the requirements. edit 4 : as requested here are the sage scripts i used. to check if $ 10 ^ n + 333 $ was prime : for n in range ( 0, 500


) : k = 10 ^ n + 333 if ( is _ prime ( k ) ) : print n and to check for numbers of the form $ 10 ^ n + 3 * 10 ^ i + 33 $ : for n in range ( 0, 500 ) : k = 10 ^ n + 33 for i in range ( 2, n ) : l = k + 3 * 10 ^ i if ( is _ prime ( l ) ) : print l


a couple of decades ago i was peripherally involved with some research on the properties of ice cream being done by the company walls in the uk. the work was on relating the consistency of the ice cream to the microstructure, so it was quite closely related to your question. anyhow, ice cream has a surprisingly complicated microstructure. it contains ice crystals, liquid sugar solution, fat globules and air bubbles ( the proportions of these change with the type and quality of the ice cream ). at temperatures from zero down to typical domestic freezer temperatures it is not frozen solid because the sugar depresses the freezing point of water and the concentrated sugar solution remains liquid. the amount of the liquid phase present decreases with decreasing temperature. if you imagine starting at zero c then as you lower the temperature crystals of ice form, which pulls water out of the fluid phase and increases the sugar concentration in the fluid phase. this depresses the freezing point until it matches the freezer temperature at which point the system is in equilibrium. lower the temperature further and this forms more ice crystals, increases the sugar concentration still further and depresses the freezing point of the liquid phase still further. and so on. the liquid phase doesn't disappear completely until you get down to very, very low temperatures at which point the remaining sugar solution freezes as a glass. it's this change in the amount of the liquid phase present that is causing the changes you have observed. as you warm the initially very cold ice cream you melt some of the ice crystals and get more fluid phase, plus the viscosity of the fluid phase decreases as it gets more dilute. both of these soften the ice cream. i should emphasise that this is a very simplified account of a very complicated rheological behaviour, but it should give you a basic idea of what is going on. the details are endlessly fascinating if you're a colloid scientist ( or just like ice cream ). for example sugar poisons the surface of the ice crystals and changes their morphology. in ice cream the crystals tend to be rounded blobs rather than the jagged crystals ice usually forms. this also affects the rheology since the rounded crystals flow over each other more easily.


it is commonly said, that a cyclopropane fragment behaves somewhat like a double bond. it can conjugate, and pass mesomeric effect similar to a double bond, but the donor orbital is $ \ sigma _ { \ ce { c - c } } $ instead of $ \ pi _ { \ ce { c = c } } $. cyclopropane can be considered as a complex of a carbene and an alkene, where the carbene $ \ mathrm { p } $ orbital interacts with the $ \ pi ^ * _ { \ ce { c = c } } $ orbital while the carbene $ \ mathrm { sp ^ 2 } $ orbital interacts with the $ \ pi _ { \ ce { c = c } } $ orbital, so this'virtual'double bond behaves somewhat like a normal double bond. on the other hand, the structure of the cyclopropylmethyl cation is downright weird. it is well known that both cyclopropylmethyl and cyclobutyl derivatives give very similar product mixture under $ \ mathrm { s _ n1 } $ hydrolysis conditions, resulting in both cyclopropylmethyl and cyclobutyl derivatives ( see, for example, j. am. chem. soc. 1951, 73 ( 6 ), 2509 – 2520 ). this is commonly described by the conjugation in following manner ( here, the 1 - cyclopropylethyl cation is depicted ) : here bonding of $ \ ce { c - 4 } $ with $ \ ce { c - 1 } $ and $ \ ce { c - 2 } $ can be roughly described as an interaction of the vacant $ \ mathrm { p } $ - orbital of $ \ ce { c - 4 } $ with filled orbital of $ \ pi $ - bond between $ \ ce { c - 1 } $ and $ \ ce { c - 2 } $. it does not matter much, where the original leaving group was - at $ \ ce { c - 2 } $ or $ \ ce { c - 1 } $. since the positive charge is more or less symmetrically distributed between three atoms and the small ring is somewhat relieved of its geometrical strain ( both cyclopropane and cyclobutane are very strained molecules, not only due to angle strain, but also considerable steric interactions between hydrogens


), the cation has remarkable stability. similar effects are common in the chemistry of small bicyclic systems, with norbornane derivitives being the chosen test subjects for decades with the 2 - norbornyl cation being probably the most well - known example. march's advanced organic chemistry, 7th ed., section 10. c. i discusses such nonclassical carbocations in great detail, with the cyclopropylmethyl system being described on pp 404 – 406. with further addition of multiple cyclopropyl groups, however, the full conjugation becomes sterically hindered, so extra groups beyond the first have less of an effect. of course, the stability of these cations is far below that of the tropylium cation, which has very little strain and also possesses aromatic character, distributing the positive charge over seven (! ) carbon atoms. in fact, the stability of the tropylium system is so high, that even the cyclooctatrienyl cation ( also known as the homotropylium cation ) adopts a similar structure.


bowtie2 is no longer the fastest aligner. as you point out, bwa is faster, despite being based on the same burrows - wheeler transform as bowtie2. as @ user172818 points out, bwa - aln will work better for very short sequences under 36bp. for transcript mapping, salmon and kallisto are much faster, but have been designed to optimise cdna - seq mapping. their speed is gained from avoiding a strict base - to - base alignment, but they can output mostly - aligned reads ( i. e. position - only, without local alignment ) as pseudo - alignments. see here for more details. both kallisto and salmon can do additional bootstrapping that is interpreted by sleuth ( and other downstream tools ) for improved performance in isoform detection. they can also output counts that are equivalent to read - level counts from other programs, which can then be used by other downstream gene - based differential expression analysis software ( e. g. deseq2 ). salmon has additional options that can correct mappings for sequence - level and gc bias. hisat2 is from the same group as bowtie2, and does the same sort of stuff, but with a few optimisations added on top. in particular, it's much better at working out split reads from rnaseq runs, while also working for genomic alignments. like bowtie2, it will do local alignment of reads. for quick genomic alignment of long reads, minimap2 works well. for high - accuracy alignment ( but comparatively slower ), last works well. there are two programs i have used that are specifically designed for long read transcript quantification that process minimap2 read mapping into isoform counts ( based on a provided reference transcriptome ) : bambu and oarfish. both seem to work reasonably well ; bambu is a native r package with nice isoform visualisation included ; oarfish produces salmon - like output that can be imported into r via tximport. most bioinformaticians seem to prefer star for things that bowtie2 was previously used for. i'm not yet convinced it's a better alternative, and currently prefer hisat2 for high accuracy short - read alignment. according to @ kasper - thystrup - karstensen, star is able to read chimeric alignments ( for detecting e. g. circular rna through custom coding ).


i'd like to throw a tentative explanation for the ortho effect into the ring : in the molecules in question, an interaction between the protons of the methyl group and the lone pair of the amine nitrogen and the negative charge on the carboxylate, respectively, can be assumed. in the first case, the electron density on the n atom is ( slightly ) reduced, and thus the basicity of o - toluidine. in the latter case, a similar interaction provides additional stabilisation of the carboxylate. as a result, o - toluic acid is more acidic than the isomers.


as pointed out by @ johnrobertson in bag of tricks for denoising signals while maintaining sharp transitions, total variaton ( tv ) denoising is another good alternative if your signal is piece - wise constant. this may be the case for the accelerometer data, if your signal keeps varying between different plateaux. below is a matlab code that performs tv denoising in such a signal. the code is based on the paper an augmented lagrangian method for total variation video restoration. the parameters $ \ mu $ and $ \ rho $ have to be adjusted according to the noise level and signal characteristics. if $ y $ is the noisy signal and $ x $ is the signal to be estimated, the function to be minimized is $ \ mu \ | { x - y } \ | ^ 2 + \ | { dx } \ | _ 1 $, where $ d $ is the finite differences operator. function denoise ( ) f = [ - 1 * ones ( 1000, 1 ) ; 3 * ones ( 100, 1 ) ; 1 * ones ( 500, 1 ) ; - 2 * ones ( 800, 1 ) ; 0 * ones ( 900, 1 ) ] ; plot ( f ) ; axis ( [ 1 length ( f ) - 4 4 ] ) ; title ('original') ; g = f +. 25 * randn ( length ( f ), 1 ) ; figure ; plot ( g,'r') ; title ('noisy') ; axis ( [ 1 length ( f ) - 4 4 ] ) ; fc = denoisetv ( g,. 5 ) ; figure ; plot ( fc,'g') ; title ('de - noised') ; axis ( [ 1 length ( f ) - 4 4 ] ) ; function f = denoisetv ( g, mu ) i = length ( g ) ; u = zeros ( i, 1 ) ; y = zeros ( i, 1 ) ; rho = 10 ; eigd = abs ( fftn ( [ - 1 ; 1 ], [ i 1 ] ) ). ^ 2 ; for k = 1 : 100 f = real ( ifft ( fft ( mu * g + rho * dt ( u ) - dt ( y ) ). / ( mu + rho * eigd ) ) ) ; v = d ( f ) + ( 1 / rho ) * y ; u = max ( abs


( v ) - 1 / rho, 0 ). * sign ( v ) ; y = y - rho * ( u - d ( f ) ) ; end function y = d ( x ) y = [ diff ( x ) ; x ( 1 ) - x ( end ) ] ; function y = dt ( x ) y = [ x ( end ) - x ( 1 ) ; - diff ( x ) ] ; results :


short answer yes. handedness ( or behavioral lateralization ) has been documented in numerous vertebrates ( mammals, reptiles and birds ) as well as invertebrates. this includes domestic cats ( see wells & millsopp 2009 ). long answer there have been numerous studies that have documented behavioral lateralization in many groups of animals including lower vertebrates ( fish and amphibians ), reptiles ( even snakes! ), birds and mammals. more recent work ( e. g., frasnelli 2013 ) has also shown that lateralization can also occur in invertebrates. in other words, " handedness " ( or pawedness, footedness, eyedness, earedness, nostriledness, toothedness, breastedness, gonadedness, etc. ) occurs rather extensively across the animal kingdom. these studies suggest that the evolution of brain lateralization, often linked to lateralized behaviors, may have occurred early in evolutionary history and may not have been the result of multiple independent evolutionary events as once thought. although this view of brain lateralization as a highly conserved trait throughout evolutionary history has gained popularity, it's still contested ( reviewed by bisazza et al. 1998 ; vallortigara et al. 1999 ). note : laterality of function may manifest in terms of preference ( frequency ) or performance ( proficiency ), with the former being far more often investigated. and no, right - handedness is not always dominant. but why? one hypothesis is that brain lateralization was the evolutionary result of the need to break up complex tasks and perform them with highly specialized neuronal units to avoid functional overlap ( i. e., to account for " functional incompatibility " ). in humans, many hypotheses have been developed including : division of labor, genetics, epigenetic factors, prenatal hormone exposure, prenatal vestibular asymmetry, and even ultrasound exposure in the womb. snake studies ( see below ) have suggested lateralization behavior can be dictated by environmental conditions ( specifically, temperature ). other work ( hoso et al. 2007 ) suggest that lateralization could be the result of convergent evolution. in this case, snakes developed feeding aparati that allow them to better consume more - common dextral species of snails. note : dextral ( meaning " clockwise " ) is a type of chirality - - another form of " handedness " reviews : lateralization in non - human primates : mcgrew & marchant


1997. lateralized behaviors in mammals and birds : bradshaw & rogers 1993 ; rogers & andrew 2002. lateralized behaviors in lower vertebrates : bisazza et al. 1998 ; vallortigara et al. 1999. some examples : invertebrates some spiders appear to favor certain appendages for prey handling and protection ( ades & novaes ramires 2002 ). octopi ( or octopodes ) preferably use one eye over the other ( byrne et al. 2002 ; with seemingly no preference for right / left at the population level : byrne et al. 2004 ) and also apparently have a preferred arm ( byrne et al. 2006 ). fish preferential ventral fin use in the gourami ( trichogaster trichopterus ). [ bisazza et al. 2001 ]. preferential eye use in a variety of fish species [ sovrano et al. 1999, 2001 ]. amphibians lateralization of neural control for vocalization in frogs ( rana pipiens ). [ bauer 1993 ]. preferential use of hindlimbs ( robins et al. 1998 ), forelimbs ( bisazza et al. 1996 ) and eyes ( vallortigara et al. 1998 ) in adult anurans. snakes preferential use of right hemipenis over left under warm conditions. [ shine et al. 2000 ]. coiling asymmetries were found at both the individual and population levels. [ roth 2003 ]. birds tendency for parrots to use left - feet when feeding. [ friedmann & davis 1938 ]. mammals pawdness in mice. [ collins 1975 ]. left forelimb bias in a species of bat when using hands for climbing / grasping. [ zucca et al. 2010 ] behavior experiments show domesticated cats show strong preference to consistently use either left or right paw and that the lateralized behavior was strongly sex related ( in their population : = left / = right ). [ wells & millsopp 2009 ]. non - human primates posture, reaching preference, tool use, gathering food, carrying, and many other tasks. see mcgrew & marchant ( 1997 ) for review. citations ades, c., and novaes ramires, e. ( 2002 ). asymmetry of leg use during prey handling in the spider scytodes globula ( scytodidae ). journal of insect behavior 15 : 563 – 570. bauer, r. h. ( 1993 )


. lateralization of neural control for vocalization by the frog ( rana pipiens ). psychobiology, 21, 243 – 248. bisazza, a., cantalupo, c., robins, a., rogers, l. j. & vallortigara, g. ( 1996 ). right - pawedness in toads. nature, 379, 408. bisazza, a., rogers, l. j. & vallortigara, g. ( 1998 ). the origins of cerebral asymmetry : a review of evidence of behavioural and brain lateralization in fishes, reptiles and amphibians. neuroscience and biobehavioral reviews, 22, 411 – 426. bisazza, a., lippolis, g. & vallortigara, g. ( 2001 ). lateralization of ventral fins use during object exploration in the blue gourami ( trichogaster trichopterus ). physiology & behavior, 72, 575 – 578. bradshaw, j. l. & rogers, l. j. ( 1993 ). the evolution of lateral asymmetries, language, tool use and intellect. san diego : academic press. byrne, r. a., kuba, m. and griebel, u. ( 2002 ). lateral asymmetry of eye use in octopus vulgaris. animal behaviour, 64 ( 3 ) : 461 - 468. byrne, r. a., kuba, m. j. and meisel, d. v. ( 2004 ). lateralized eye use in octopus vulgaris shows antisymmetrical distribution. animal behaviour, 68 ( 5 ) : 1107 - 1114. byrne, r. a., kuba, m. j., meisel, d. v., griebel, u. and mather, j. a. ( 2006 ). does octopus vulgaris have preferred arms?. journal of comparative psychology 120 ( 3 ) : 198. collins rl ( 1975 ) when left - handed mice live in righthanded worlds. science 187 : 181 – 184. friedmann, h., & davis, m. ( 1938 ). " left - handedness " in parrots. the auk, 55 ( 3 ), 478 - 480. hoso, m., asami, t., & hori, m. ( 2007 ). right - handed snakes : convergent


evolution of asymmetry for functional specialization. biology letters, 3 ( 2 ), 169 - 173. mcgrew, w. c., & marchant, l. f. ( 1997 ). on the other hand : current issues in and meta ‐ analysis of the behavioral laterality of hand function in nonhuman primates. american journal of physical anthropology, 104 ( s25 ), 201 - 232. robins, a., lippolis, g., bisazza, a., vallortigara, g. & rogers, l. j. ( 1998 ). lateralized agonistic responses and hindlimb use in toads. animal behaviour, 56, 875 – 881. rogers, l. j. & andrew, r. j. ( eds ) ( 2002 ). comparative vertebrate lateralization. cambridge : cambridge university press. roth, e. d. ( 2003 ). ‘ handedness ’ in snakes? lateralization of coiling behaviour in a cottonmouth, agkistrodon piscivorus leucostoma, population. animal behaviour, 66 ( 2 ), 337 - 341. shine, r., olsson, m. m., lemaster, m. p., moore, i. t., & mason, r. t. ( 2000 ). are snakes right - handed? asymmetry in hemipenis size and usage in gartersnakes ( thamnophis sirtalis ). behavioral ecology, 11 ( 4 ), 411 - 415. sovrano, v. a., rainoldi, c., bisazza, a. & vallortigara, g. ( 1999 ). roots of brain specializations : preferential left - eye use during mirror - image inspection in six species of teleost fish. behavioural brain research, 106, 175 – 180. sovrano, v. a., bisazza, a. & vallortigara, g. ( 2001 ). lateralization of response to social stimuli in fishes : a comparison between different methods and species. physiology & behavior, 74, 237 – 244. vallortigara, g., rogers, l. j., bisazza, a., lippolis, g. & robins, a. ( 1998 ). complementary right and left hemifield use for predatory and agonistic behaviour in toads. neuroreport, 9, 3341 – 334


##4. vallortigara, g., rogers, l. j. & bisazza, a. ( 1999 ). possible evolutionary origins of cognitive brain lateralization. brain research reviews, 30, 164 – 175. wells, d. l., & millsopp, s. ( 2009 ). lateralized behaviour in the domestic cat, felis silvestris catus. animal behaviour, 78 ( 2 ), 537 - 541. zucca, p., palladini, a., baciadonna, l. and scaravelli, d. ( 2010 ). handedness in the echolocating schreiber's long - fingered bat ( miniopterus schreibersii ). behavioural processes, 84 ( 3 ) : 693 - 695.


factor out the $ 2 ^ n $ and you get : $ 2 ^ n ( 100 + 20 + 8 ) = 2 ^ n 128 = 2 ^ { n + 7 } $ since $ 2 ^ 7 = 128 $


dilawar says in 2. that he knows linear dependence! so i will give a proof, similar to that of themachinecharmer, which uses linear independence. suppose each matrix is $ n $ by $ n $. we consider our matrices to all be acting on some $ n $ - dimensional vector space with a chosen basis ( hence isomorphism between linear transformations and $ n $ by $ n $ matrices ). then $ ab $ has range equal to the full space, since $ ab = i $. thus the range of $ b $ must also have dimension $ n $. for if it did not, then a set of $ n - 1 $ vectors would span the range of $ b $, so the range of $ ab $, which is the image under $ a $ of the range of $ b $, would also be spanned by a set of $ n - 1 $ vectors, hence would have dimension less than $ n $. now note that $ b = bi = b ( ab ) = ( ba ) b $. by the distributive law, $ ( i - ba ) b = 0 $. thus, since $ b $ has full range, the matrix $ i - ba $ gives $ 0 $ on all vectors. but this means that it must be the $ 0 $ matrix, so $ i = ba $.


zero padding allows one to use a longer fft, which will produce a longer fft result vector. a longer fft result has more frequency bins that are more closely spaced in frequency. but they will be essentially providing the same result as a high quality sinc interpolation of a shorter non - zero - padded fft of the original data. this might result in a smoother looking spectrum when plotted without further interpolation. although this interpolation won't help with resolving or the resolution of and / or between adjacent or nearby frequencies, it might make it easier to visually resolve the peak of a single isolated frequency that does not have any significant adjacent signals or noise in the spectrum. statistically, the higher density of fft result bins will probably make it more likely that the peak magnitude bin is closer to the frequency of a random isolated input frequency sinusoid, and without further interpolation ( parabolic, et. al. ). but, essentially, zero padding before a dft / fft is a computationally efficient method of interpolating a large number of points. zero - padding for cross - correlation, auto - correlation, or convolution filtering is used to not mix convolution results ( due to circular convolution ). the full result of a linear convolution is longer than either of the two input vectors. if you don't provide a place to put the end of this longer convolution result, fft fast convolution will just mix it in with and cruft up your desired result. zero - padding provides a bunch zeros into which to mix the longer result. and it's far far easier to un - mix something that has only been mixed / summed with a vector of zeros.


there are whole journals based primarily around publishing open source tools. the primary example of that is " bioinformatics ", where a lot of the open - source tools are published. we've also had luck publishing in the nucleic acids research yearly special webservers issue, since we make galaxy wrappers around our tools. you can also publish on tools in venues like nature methods, but it's vastly more difficult to get in there if your paper is purely on a tool and it's not something game - changing like salmon or kallisto. regarding what's actually needed to publish a tool, you will typically need the following : decent documentation. i ask for this as a reviewer and am asked about it when i submit things. easy installation. no one wants to spend two hours trying to compile your tool, so make sure there's a conda package or at least a docker container for it. test data. without this your reviewers and users will likely not be happy since they won't be able to try it out on something small. for the actual submission you'll tend to need comparisons to other tools. i'm generally not a big fan of this, but you will find that some reviewers will demand it ( assuming there are other tools that do something similarish to yours ).


blood clots inside the body have an unfortunate tendency to get into the bloodstream and cause blockages, leading to severe problems such as strokes or heart attacks this statement is primarily true only for blood clots within blood vessels, especially in the veins. when you are talking about bruising, you are talking about clots outside of the vasculature. when a blood clot occurs in an artery, it can block that artery or break off, flow downstream, and block some smaller distal vessel. these events are most severe when they affect crucial organs like the brain and heart ( " stroke " or " heart attack " ), though of course any organ can be damaged in this way. however, blood clots in arteries can't ever directly affect a tissue that is not distal from where the clot starts, because they can never pass through capillaries or travel backward. when a blood clot occurs in a vein and is dislodged, it can follow the increasingly larger venous system back to the heart, where it can cause a pulmonary embolism ( blockage in the lungs ) or, via a patent foramen ovale, travel to the left - side circulation and end up anywhere, including the coronary arteries or blood vessels of the brain. similarly, clots that form in the venous return from the lungs to the heart or in the left side of the heart itself can travel anywhere ( except the lungs ) and create a blockage. for a clot outside the vasculature, for it to have an effect somewhere else systemically it must re - enter the vasculature. this is simply not possible in most situations, because the vessels involved are very small, and during bleeding the blood is flowing out of vessels : there is no pressure gradient to push the clot back into the vessels. in more severe cases of injury where major vessels are involved, clotting in those major vessels can indeed be a problem, but not for common occurrences of bruising. ( see also @ anongoodnurse's answer that contains a good clarification of what exactly a bruise is, as well as how there are risks from very serious bruises but not the same way the original question implied )


every cell phone ( as well as laptop and nearly everything with a rechargeable battery ) uses liion / lipo ( essentially equivalent for the purposes of this discussion ). and you're right : in terms of actual incidences, lithium - ion and lithium - polymer are the safest battery chemistry to be in wide use, bar none. and the only reason this now ubiquitous chemistry hasn't murdered you and / or your family several times over is that these cells aren't charged unattended. you may not be attending it personally, but every single one of those lithium - ion batteries has a significant amount of protection and monitoring circuitry that is permanently integrated into the pack. it acts as the gatekeeper. it monitors every cell in a battery. it disconnects the output terminals and prevents them from being overcharged. it disconnects the output if they are discharged at too high a current. it disconnects the output if it is charged at too high a current. if any of the cells are going bad, the output is disconnected. if any cell gets too hot, it disconnects the output. if anyone of the cells is over - discharged, it disconnects the output ( and permanently - if you forget to charge a lithium - ion battery for too long, you will find that it will no longer charge. it is effectively destroyed, and the protection circuit will not permit you to charge the cells ). indeed, every single phone battery, laptop battery, * whatever battery that is a rechargeable lithium chemistry is the most closely monitored, scrutinized, and actively managed, the diametric opposite of'unattended'as one can get for a battery. and the reason so much extra trouble is done is because lithium - ion batteries are actually that dangerous. they need protection circuitry to be safe, and they are not even remotely safe without it. other chemistries such is nimh or nicad can be used relatively safely as bare cells, without any monitoring. if they get too hot, they can vent ( which has happened to me personally ), and it can be pretty startling, but it isn't going to burn down your house or land you an extended stay in a burn unit. lithium - ion batteries will do both, and that's pretty much the only outcome. ironically, lithium - ion batteries have become the safest packaged battery by being the most dangerous battery chemistry. you might be wondering what actually makes them so dangerous. other battery chemistries


, such as lead - acid or nimh or nicad, are not pressurized at room temperature, though heat does generate some internal pressure. they also have aqueous, non - flammable electrolytes. they store energy in the form of a relatively slow oxidation / reduction reaction, one whose rate of energy release is too low to, say, cause them to eject 6 - foot jets of flame. or any flame, really. lithium - ion batteries are fundamentally different. they store energy like a spring. that's not a metaphor. well, like two springs. lithium ions are forced between the atoms of covalently - bonded anode material, pushing them apart and'stretching'the bonds, storing energy. this process is called intercalation. upon discharge, the lithium ions move out of the anode and into the cathode. this is very much electromechanical, and both the anode and cathode experience significant mechanical strain from this. in fact, both anode and cathode alternatively increase or decrease in physical volume depending on the battery's state of charge. this change in volume is uneven however, so a fully charged lithium - ion battery is actually exerting nontrivial amounts of pressure on its container or other parts of itself. lithium - ion batteries are generally under a lot of internal pressure, unlike other chemistries. the other problem is their electrolyte is a volatile, extremely flammable solvent that will burn quite vigorously and easily. the complex chemistry of lithium - ion cells is not even completely understood, and there are a few different chemistries with different levels of reactivity and inherent danger, but the ones with high energy density all can undergo thermal runaway. basically, if they get too hot, lithium ions will begin reacting with oxygen stored as metal oxides in the cathode and release even more heat, which accelerates the reaction further. what inevitably results is a battery that self - ignites, sprays its highly flammable solvent electrolyte out of itself, and promptly ignites that as well, now that a fresh supply of oxygen is available. that's just bonus fire however, there is still a ton of fire from the lithium metal oxidizing with the ample store of oxygen inside. if they get too hot that happens. if they are overcharged, they become unstable and mechanical shock can make them go off like a grenade. if they are over - discharged, some of the metal in the cathode undergoes


an irreversible chemical reaction and will form metallic shunts. these shunts will be invisible, until charging expands part of the battery enough that the separating membrane is punctured by one of these shunts, creating a dead short, which of course results in fire, etc. : the lithium - ion failure mode we know and love. so, just to be clear, not only is overcharging dangerous, but so is over - discharging, and the battery will wait until you've pumped a ton of energy back into it before spectacularly failing on you, and without any warning or measurable signs. that covers consumer batteries. all this protection circuitry is less able to mitigate the danger of high drain applications, however. high drain generates no small amount of heat ( which is bad ) and more worrying, it causes huge amounts of mechanical stress on the anode and cathode. fissures can form and widen, leading to instability if you're unlucky, or just a shorter useful life if it is not too severe. this is why you see lipos rated in'c ', or how quickly they can be safely discharged. please, take those ratings seriously and derate it, both for safety and because many manufacturers simply lie about the c rating of their batteries. even with all that, sometimes an rc lipo will just burst into flame for no reason. you absolutely need to heed the warnings to never charge them unattended, and everything else. you should buy a safety bag to charge them in because it might prevent your house from burning down ( possibly with you or loved ones inside ). even if the risk is very low, the damage it can cause is vast, and the measures needed to mitigate most of that potential for damage are trivial. don't ignore everything you're being told - it's all spot on. it comes from people who have learned to respect lipos for what they are, and you should too. the thing you definitely want to avoid is having this lesson taught to you by a lithium - ion battery, instead of peers online and offline. the latter might flame you on a forum, but the former will literally flame you. let's see some videos of stuff exploding! let me go a little more into how they fail. i've discussed the mechanism, but what really happens? lithium - ion batteries really only have one failure mode, which is kind of exploding then shooting out a stunningly huge amount of fire


in a giant jet of flame for several seconds, and then continuing general burning - related activities for a bit after that. this is a chemical fire, so you cannot extinguish it ( lithium - ion batteries will still shoot out huge jets of fire even in the vacuum of space. the oxidizer is contained inside, it doesn't need air or oxygen to burn ). oh, and throwing water on lithium does nothing good, at least in terms of fire reduction. here is a'greatest hits'list of some good examples of failure. note that this does sometimes happen in high drain rc cases even with proper safety measures in place. comparing high drain applications to the much safer and lower currents of phones is not at all a valid one. hundreds of amperes = a few hundred milliamperes. rc plane failure. knife stabs smartphone - sized battery. overcharged lipo spontaneously explodes. laptop battery in a thermal runaway is lightly pressed on, making it explode.


for the first part of my question, i found this very useful comparison for performance of different linear interpolation methods using python libraries : below is list of methods collected so far. standart interpolation, structured grid : unstructured ( scattered ) grid : 2 large projects that include interpolation : ( parts of cgal, licensed gpl / lgpl ) ( university of illinois - ncsa license ~ = mit + bsd - 3 ) sparse grids : kriging ( gaussian process ) : general gpl licensed : tasmanian the toolkit for adaptive stochastic modeling and non - intrusive approximation - is a robust library for high dimensional integration and interpolation as well as parameter calibration. python binding for tasmanian : ( parts of cgal, licensed gpl / lgpl )