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I am doing a research project involving calculating k-mer frequencies and I am wondering if there is any standard file format for storing k-mer counts. | Not as far as I am aware. The Ray assembler used to (and possibly still does) store the kmers as FASTA files where the header was the count of the sequence, which I thought was a pretty neat bastardisation of the FASTA file format. It looks like this format is also used by Jellyfish when reporting kmer frequencies by t... | https://api.stackexchange.com |
There are a number of different libraries out there that solve a sparse linear system of equations, however I'm finding it difficult to figure out what the differences are.
As far as I can tell there are three major packages: Trilinos, PETSc, and Intel MKL. They can all do sparse matrix solves, they are all fast (as ... | There are many more out there, all with different goals and views of the problems. It really depends on what you are trying to solve. Here is an incomplete list of packages out there. Feel free to add more details.
Large Distributed Iterative Solver Packages
PETSc — packages focused around Krylov subspace methods a... | https://api.stackexchange.com |
From my layman understanding, animals that inject venom into the bloodstream by biting or poking are venomous. And ones that harm you when you eat them are poisonous.
Are there any animals (or plants) that fit both descriptions?
I'm guessing eating a venomous rattlesnake will give you an upset stomach but not cause en... | That is certainly an interesting question!
First, to clarify definitions:
To be considered venomous the toxic substance must be produced in specialized glands or tissue. Often these are associated with some delivery apparatus (fangs, stinger, etc.), but not necessarily.
To be poisonous, the toxins must be produced in ... | https://api.stackexchange.com |
What is the impact of mental activity on the energy consumption of the human brain?
I am most interested in intellectually demanding tasks (e.g., chess matches, solving a puzzle, taking a difficult exam) versus tasks with a similar posture but less demanding (e.g., reading a newspaper, watching TV).
I heard that energ... | The energy consumption doesn't vary that much between resting and performing tasks, as discussed in a review by Marcus Raichle and Mark A. Mintun:
In the average adult human, the brain represents approximately 2% of
the total body weight but approximately 20% of the energy consumed
(Clark & Sokoloff 1999), 10 times th... | https://api.stackexchange.com |
This has been one of the holes in my cheddar cheese block of understanding DSP, so what is the physical interpretation of having a negative frequency?
If you have a physical tone at some frequency and it is DFT'd, you get a result in both the positive and negative frequencies - why and how does this occur? What does it... | Negative frequency doesn't make much sense for sinusoids, but the Fourier transform doesn't break up a signal into sinusoids, it breaks it up into complex exponentials (also called "complex sinusoids" or "cisoids"):
$$F(\omega) = \int_{-\infty}^{\infty} f(t) \color{Red}{e^{- j\omega t}}\,dt$$
These are actually spirals... | https://api.stackexchange.com |
I am wondering how to choose a predictive model after doing K-fold cross-validation.
This may be awkwardly phrased, so let me explain in more detail: whenever I run K-fold cross-validation, I use K subsets of the training data, and end up with K different models.
I would like to know how to pick one of the K models, ... | I think that you are missing something still in your understanding of the purpose of cross-validation.
Let's get some terminology straight, generally when we say 'a model' we refer to a particular method for describing how some input data relates to what we are trying to predict. We don't generally refer to particular ... | https://api.stackexchange.com |
Right now I stuck with a problem. It seems to be really trivial one, but still it is hard for me to find an appropriate solution. The problem is:
One has two intervals and are to find the intersection of them.
For instance:
Intersection of [0, 3]&[2, 4] is [2, 3]
Intersection of [-1, 34]&[0, 4] is [0, 4]
Intersection ... | We can define a solution to this problem in the following way. Assume the input intervals can be defined as $I_{a} = [a_s, a_e]$ and $I_{b} = [b_s, b_e]$, while the output interval is defined as $I_{o} = [o_s, o_e]$. We can find the intersection $I_{o} = I_{a} \bigcap I_{b}$ doing the following:
if ( $b_s \gt a_e$ or $... | https://api.stackexchange.com |
I'm studying some DSP and I'm having trouble understanding the difference between phase delay and group delay.
It seems to me that they both measure the delay time of sinusoids passed through a filter.
Am I correct in thinking this?
If so, how do the two measurements differ?
Could someone give an example of a situ... | First of all the definitions are different:
Phase delay: (the negative of) Phase divided by frequency
Group delay: (the negative of) First derivative of phase vs frequency
In words that means:
Phase delay: Phase angle at this point in frequency
Group delay: Rate of change of the phase around this point in frequency... | https://api.stackexchange.com |
ERCC spike-in is a set of synthetic controls developed for RNA-Seq. I'm interested in using it to normalize my RNA-Seq samples. In particular, I'd like to use the spike-ins to remove technical bias and any variation that should not be part of my analysis.
The site doesn't give any details on how I can do that.
Q: What ... | You may consider using RUVSeq. Here is an excerpt from the 2013 Nature Biotechnology publication:
We evaluate the performance of the External RNA Control Consortium (ERCC) spike-in controls and investigate the possibility of using them directly for normalization. We show that the spike-ins are not reliable enough to b... | https://api.stackexchange.com |
Normally in algorithms we do not care about comparison, addition, or subtraction of numbers -- we assume they run in time $O(1)$. For example, we assume this when we say that comparison-based sorting is $O(n\log n)$, but when numbers are too big to fit into registers, we normally represent them as arrays so basic oper... | For people like me who study algorithms for a living, the 21st-century standard model of computation is the integer RAM. The model is intended to reflect the behavior of real computers more accurately than the Turing machine model. Real-world computers process multiple-bit integers in constant time using parallel har... | https://api.stackexchange.com |
Self driving cars rely on cameras, radar, and lidar to recognize the environment around them. Cameras of course don't interfere with each other, since they are passive sensors. Since a signal received directly from another transmitter is much stronger than a reflected signal from your own transmitter, what stops the ... | You'd be surprised.
This is actually topic of ongoing research, and of several PhD dissertations.
The question which radar waveforms and algorithms can be used to mitigate interference is a long-fought over one; in essence, however, this breaks down to the same problem that any ad-hoc communication system has.
Differe... | https://api.stackexchange.com |
This morning I found a really strange ice formation in my garden. I can't figure out how it appeared, because there was nothing above. The night was particularly cold (Belgium).
To give an idea, it has the size of a common mouse (5 cm of Height and 2 cm for the base of the inverted pyramid). | Congratulations, you found an inverted pyramid ice spike, sometimes called an ice vase!
The Bally-Dorsey model of how it happens is that first the surface of the water freezes, sealing off the water below except for a small opening. If the freezing rate is high enough the expansion of ice under the surface will increas... | https://api.stackexchange.com |
The Journal of Computational Physics has been an important outlet for computational science in the past, and I have published there before. For the benefit of those (like me) who have signed the Elsevier boycott, what non-Elsevier journals would be appropriate places to publish articles that could have been submitted ... | The SIAM Journals, especially SISC (Scientific Computing) and MMS (Multiscale Modeling and Simulation) are obvious established and high-quality choices. | https://api.stackexchange.com |
Why draw blood from veins rather than arteries? Is it more convenient or safer? | Veins have several advantages over arteries. From a purely practical standpoint, veins are easier to access due to their superficial location compared to the arteries which are located deeper under the skin. They have thinner walls (much less smooth muscle surrounding them) than arteries, and have less innervation, so ... | https://api.stackexchange.com |
It seems that a number of the statistical packages that I use wrap these two concepts together. However, I'm wondering if there are different assumptions or data 'formalities' that must be true to use one over the other. A real example would be incredibly useful. | Principal component analysis involves extracting linear composites of observed variables.
Factor analysis is based on a formal model predicting observed variables from theoretical latent factors.
In psychology these two techniques are often applied in the construction of multi-scale tests
to determine which items load... | https://api.stackexchange.com |
Hydrogen is flammable, and for any fire to burn it needs oxygen. Why does a compound made of hydrogen and oxygen put out fires instead of catalyzing them? I understand that hydrogen and water are chemically different compounds, but what causes water to be non-flammable? | You can think of water as the ash from burning hydrogen: it's already given off as much energy as possible from reacting hydrogen with oxygen.
You can, however, still burn it. You just need an even stronger oxidizer than oxygen. There aren't many of them, but fluorine will work,
$$
\ce{2F2 + 2H2O -> 4HF + O2}
$$
as ... | https://api.stackexchange.com |
The Fast Fourier Transform algorithm computes a Fourier decomposition under the assumption that its input points are equally spaced in the time domain, $t_k = kT$. What if they're not? Is there another algorithm I could use, or some way I could modify the FFT, to account for what is effectively a variable sampling rate... | There is a wide variety of techniques for non-uniform FFT, and the most efficient ones are all meant for exactly your case: quasi-uniform samples. The basic idea is to smear the unevenly sampled sources onto a slightly finer ("oversampled") uniform grid though local convolutions against Gaussians. A standard FFT can th... | https://api.stackexchange.com |
In non-relativistic QM, the $\Delta E$ in the time-energy uncertainty principle is the limiting standard deviation of the set of energy measurements of $n$ identically prepared systems as $n$ goes to infinity. What does the $\Delta t$ mean, since $t$ is not even an observable? | Let a quantum system with Hamiltonian $H$ be given. Suppose the system occupies a pure state $|\psi(t)\rangle$ determined by the Hamiltonian evolution. For any observable $\Omega$ we use the shorthand
$$
\langle \Omega \rangle = \langle \psi(t)|\Omega|\psi(t)\rangle.
$$
One can show that (see eq. 3.72 in Griffith... | https://api.stackexchange.com |
One can imagine that a particular organism would be improved if it were to acquire certain traits — perhaps those found in a different organism (e.g. flight, photosynthesis, nitrogen fixation). Or alternatively one might consider that the solutions certain organisms have evolved to problems they face are inferior to ot... | During the process of selection, individuals having disadvantageous traits are weeded out. If the selection pressure isn't strong enough then mildly disadvantageous traits will continue to persist in the population.
So the reasons for why a trait is not evolved even though it may be advantageous to the organism, are:
... | https://api.stackexchange.com |
Towels (and coats) are often stored on hooks, like this:
To the untrained eye, it looks like the towel will slide off from its own weight. The hook usually angles upwards slightly, but a towel does not have any "handle" to string around and hang on to the hook -- this makes it seem like it will simply slide off.
Yet t... | Since this is PhysicsSE, I am happy with an answer based purely on theoretical analysis of the forces involved.
Oh boy, time to spend way too much time on a response.
Lets assume the simple model of a peg that makes an angle $\alpha$ with the wall and ends in a circular cap of radius $R$. Then a towel of total length... | https://api.stackexchange.com |
I've read many years ago in books, that the brain has no nerves on it, and if someone was touching your brain, you couldn't feel a thing.
Just two days before now, I had a very bad migraine, due to a cold. It's become better now, but when I had it I felt my head was going to literally split in half, as the pain was lit... | Brain, indeed, cannot feel pain, as it lacks pain receptors (nociceptors). However, what you feel when you have a headache is not your brain hurting -- there are plenty of other areas in your head and neck that do have nociceptors which can perceive pain, and they literally cause the headaches.
In especially, many type... | https://api.stackexchange.com |
I've been reading about Lambda calculus recently but strangely I can't find an explanation for why it is called "Lambda" or where the expression comes from.
Can anyone explain the origins of the term? | An excerpt from History of Lambda-calculus and Combinatory Logic by F. Cardone and J.R. Hindley(2006):
By the way, why did Church choose the notation “$\lambda$”? In [Church, 1964, §2] he stated clearly that it came from the notation “$\hat{x}$” used for class-abstraction by Whitehead and Russell, by first modifying “... | https://api.stackexchange.com |
In the definition of standard deviation, why do we have to square the difference from the mean to get the mean (E) and take the square root back at the end? Can't we just simply take the absolute value of the difference instead and get the expected value (mean) of those, and wouldn't that also show the variation of the... | If the goal of the standard deviation is to summarise the spread of a symmetrical data set (i.e. in general how far each datum is from the mean), then we need a good method of defining how to measure that spread.
The benefits of squaring include:
Squaring always gives a non-negative value, so the sum will always be ze... | https://api.stackexchange.com |
I had this question from a graduate student yesterday, and I was stuck.
What should I say? Why use a CRAM instead of a BAM?
When is it a good idea to use a CRAM instead of a BAM?
When is it a bad idea? | Whenever you want to save space (this can be a substantial savings). Until quite recently (samtools/htslib 1.7), only CRAM supported long CIGAR strings.
If you need to guarantee that any random obscure downstream program will be able to handle it.
Uptake of CRAM has been pretty slow. Java programs using htsjdk (e.g., ... | https://api.stackexchange.com |
If I have a list of key values from 1 to 100 and I want to organize them in an array of 11 buckets, I've been taught to form a mod function
$$ H = k \bmod \ 11$$
Now all the values will be placed one after another in 9 rows. For example, in the first bucket there will be $0, 11, 22 \dots$. In the second, there will be ... | Consider the set of keys $K=\{0,1,...,100\}$ and a hash table where the number of buckets is $m=12$. Since $3$ is a factor of $12$, the keys that are multiples of $3$ will be hashed to buckets that are multiples of $3$:
Keys $\{0,12,24,36,...\}$ will be hashed to bucket $0$.
Keys $\{3,15,27,39,...\}$ will be hashed to... | https://api.stackexchange.com |
The SARS-Cov2 coronavirus's genome was released, and is now available on Genbank. Looking at it...
1 attaaaggtt tataccttcc caggtaacaa accaaccaac tttcgatctc ttgtagatct
61 gttctctaaa cgaactttaa aatctgtgtg gctgtcactc ggctgcatgc ttagtgcact
121 cacgcagtat aattaataac taattactgt cgttgacagg acacgagtaa ctcgtctatc
.... | Good observation! The 3' poly(A) tail is actually a very common feature of positive-strand RNA viruses, including coronaviruses and picornaviruses.
For coronaviruses in particular, we know that the poly(A) tail is required for replication, functioning in conjunction with the 3' untranslated region (UTR) as a cis-acting... | https://api.stackexchange.com |
I'm having trouble understanding the simple "planetary" model of the atom that I'm being taught in my basic chemistry course.
In particular,
I can't see how a negatively charged electron can stay in "orbit" around a positively charged nucleus. Even if the electron actually orbits the nucleus, wouldn't that orbit eve... | You are right, the planetary model of the atom does not make sense when one considers the electromagnetic forces involved. The electron in an orbit is accelerating continuously and would thus radiate away its energy and fall into the nucleus.
One of the reasons for "inventing" quantum mechanics was exactly this conundr... | https://api.stackexchange.com |
I'm not running any parallel code right now, but I anticipate running parallel code in the future using a hybrid of OpenMP and MPI. Debuggers have been invaluable tools for me when running serial projects.
Can anyone recommend a parallel debugger (or multiple debuggers) to use for debugging parallel software? Free soft... | There are basically two major, commercial choices out there: DDT from Allinea (which is what we use at TACC) and Totalview (as mentioned in the other comment). They have comparable features, are both actively developed, and are direct competitors.
Eclipse has their Parallel Tools Platform, which should include MPI and... | https://api.stackexchange.com |
My Geiger counter measures a background radiation level in my home of 0.09–0.11 μSv/h.
When I stick it inside the dryer right after it finishes a cycle (while the clothes are still inside), it registers a radiation level of 0.16–0.18 μSv/h.
What happens during the dryer cycle that accounts for this reading? From what I... | Uranium and thorium in heavy rocks have a decay chain which includes a three-day isotope of radon. If a building has materials with some chemically-insignificant mixture of uranium and thorium, such as concrete or granite, then the radon can diffuse out of the material into the air. This is part of your normal backgrou... | https://api.stackexchange.com |
Common saying. Diamond possesses:
ultra hardness, (10 on the Mohs scale; 10000 HV on Vicker's Hard Test (iron merely 30-80))
hyper thermal conductivity, ($2320~\mathrm{W\, m^{-1}\, K^{-1}}$, or over ten times better than the heatsink in your computer!)
extreme pressure resistance, (withstands a crushing 600 gigapasca... | how long would it take for this super-material to convert to the stuff
I scribble with?
No, despite the fact that James Bond said "Diamonds are Forever", that is not exactly the case. Although Bond's statement is a fair approximation of reality it is not a scientifically accurate description of reality.
As we will s... | https://api.stackexchange.com |
As I understand it, there are two major categories of iterative methods for solving linear systems of equations:
Stationary Methods (Jacobi, Gauss-Seidel, SOR, Multigrid)
Krylov Subspace methods (Conjugate Gradient, GMRES, etc.)
I understand that most stationary methods work by iteratively relaxing (smoothing) ... | In general, all Krylov methods essentially seek a polynomial that is small when evaluated on the spectrum of the matrix. In particular, the $n$th residual of a Krylov method (with zero initial guess) can be written in the form
$$ r_n = P_n (A) b $$
where $P_n$ is some monic polynomial of degree $n$ .
If $A$ is diagonal... | https://api.stackexchange.com |
I would like to know if there has been any work relating legal code to complexity. In particular, suppose we have the decision problem "Given this law book and this particular set of circumstances, is the defendant guilty?" What complexity class does it belong to?
There are results that have proven that the card game M... | It's undecidable because a law book can include arbitrary logic. A silly example censorship law would be "it is illegal to publicize any computer program that does not halt".
The reason results for MTG exist and are interesting is because it has a single fixed set of (mostly) unambiguous rules, unlike law which is eve... | https://api.stackexchange.com |
There are many methods to prove that a language is not regular, but what do I need to do to prove that some language is regular?
For instance, if I am given that $L$ is regular,
how can I prove that the following $L'$ is regular, too?
$\qquad \displaystyle L' := \{w \in L: uv = w \text{ for } u \in \Sigma^* \setminus ... | Yes, if you can come up with any of the following:
deterministic finite automaton (DFA),
nondeterministic finite automaton (NFA),
regular expression (regexp of formal languages) or
regular grammar
for some language $L$, then $L$ is regular. There are more equivalent models, but the above are the most common.
There ar... | https://api.stackexchange.com |
There are many applications where a pseudo random number generator is used. So people implement one that they think is great only to find later that it's flawed. Something like this happened with the Javascript random number generator recently. RandU much earlier too. There are also issues of inappropriate initial ... | Sure, you can combine PRNGs like this, if you want, assuming they are seeded independently. However, it will be slower and it probably won't solve the most pressing problems that people have.
In practice, if you have a requirement for a very high-quality PRNG, you use a well-vetted cryptographic-strength PRNG and you ... | https://api.stackexchange.com |
I have an R package on github which uses multiple Bioconductor dependencies, 'myPackage'
If I include CRAN packages in the DESCRIPTION via Depends:, the packages will automatically install upon installation via devtools, i.e.
devtools::install_github('repoName/myPackage')
This is discussed in Section 1.1.3 Package De... | As suggested, here’s an example showing the relevant lines from a DESCRIPTION file from a CRAN/GitHub hosted project that has Bioconductor dependencies (truncated):
Depends:
R (>= 3.3.0)
biocViews:
Imports:
methods,
snpStats,
dplyr
The relevant bit is the empty biocViews: declaration, which allows the ... | https://api.stackexchange.com |
I'm currently looking into parallel methods for ODE integration. There is a lot of new and old literature out there describing a wide range of approaches, but I haven't found any recent surveys or overview articles describing the topic in general.
There's the book by Burrage [1], but it's almost 20 years old and hence ... | I'm not aware of any recent overview articles, but I am actively involved in the development of the PFASST algorithm so can share some thoughts.
There are three broad classes of time-parallel techniques that I am aware of:
across the method — independent stages of RK or extrapolation integrators can be evaluated in pa... | https://api.stackexchange.com |
I've heard that the wonderful smell of a fresh rain is actually chemicals released from the trees and grass and other plants.
What is the process that allows these chemicals to be released?
What are the chemicals that create that smell?
How is it advantageous for the plant to release the chemicals rather than hold on... | That molecule is called Geosmin. It is mainly produced 1 by Actinomycetes such as Streptomyces which are filamentous bacteria that live in soil. Other organisms also produce geosmin:
Cyanobacteria
Certain fungi
An amoeba called Vanella
A liverwort
It is an intracellular metabolite and cell damage is the primary reaso... | https://api.stackexchange.com |
The 2023 Nobel Prize in Physics was announced today, and it was awarded to Pierre Agostini, Ferenc Krausz and Anne L’Huillier, for
“experimental methods that generate attosecond pulses of light for the study of electron dynamics in matter”.
The documents released by the Nobel Foundation along with the announcement (t... | What's the big deal?
When quantum mechanics was being discovered and formalized, in the 1920s and 1930s, our view of physics was deeply rooted in the macroscopic world. We understood that microscopic entities like atoms and molecules existed, and we arrived reasonably quickly at a good understanding of their basic stru... | https://api.stackexchange.com |
I've noticed lately that a lot of people are developing tensor equivalents of many methods (tensor factorization, tensor kernels, tensors for topic modeling, etc) I'm wondering, why is the world suddenly fascinated with tensors? Are there recent papers/ standard results that are particularly surprising, that brought ab... | This is not an answer to your question, but an extended comment on the issue that has been raised here in comments by different people, namely: are machine learning "tensors" the same thing as tensors in mathematics?
Now, according to the Cichoki 2014, Era of Big Data Processing: A New Approach via Tensor Networks and ... | https://api.stackexchange.com |
My biology teachers never explained why animals need to breathe oxygen, just that we organisms die if we don't get oxygen for too long. Maybe one of them happened to mention that its used to make ATP. Now in my AP Biology class we finally learned the specifics of how oxygen is used in the electron transport chain due t... | Superoxide, O2− is created by the immune system in phagocytes (including neutrophils, monocytes, macrophages, dendritic cells, and mast cells) which use NADPH oxidase to produce it from O2 for use against invading microorganisms. However, under normal conditions, the mitochondrial electron transport chain is a major so... | https://api.stackexchange.com |
In the highly-rated TV series, Breaking Bad, Walter White, a high school chemistry teacher recently diagnosed with cancer, takes to making the illicit drug, crystal meth (methamphetamine), by two main routes.
First, along with his RV-driving accomplice, Jessie Pinkman, Mr. White uses the common small-scale route starti... | Intriguing question.
First, the best yield would be achieved by selectively producing one enantiomer instead of the other. In this case, White wants D-methamphetamine (powerful psychoactive drug), not L-methamphetamine (Vicks Vapor Inhaler). Reaction processes designed to do this are known as "asymmetric synthesis" re... | https://api.stackexchange.com |
Often, when I try to describe mathematics to the layman, I find myself struggling to convince them of the importance and consequence of "proof". I receive responses like: "surely if Collatz is true up to $20×2^{58}$, then it must always be true?"; and "the sequence of number of edges on a complete graph starts $0,1,3,6... | I'll translate an entry in the blog Gaussianos ("Gaussians") about Polya's conjecture, titled:
A BELIEF IS NOT A PROOF.
We'll say a number is of even kind if in its prime factorization, an even number of primes appear. For example $6 = 2\cdot 3$ is a number of even kind. And we'll say a number is of odd kind if the nu... | https://api.stackexchange.com |
A common bioinformatics task is to decompose a DNA sequence into its constituent k-mers and compute a hash value for each k-mer. Rolling hash functions are an appealing solution for this task, since they can be computed very quickly. A rolling hash does not compute each the hash value from scratch with each k-mer: rath... | A rolling hash function for DNA sequences called ntHash has recently been published in Bioinformatics and the authors dealt with reverse complements:
Using this table, we can easily compute the hash value for the reverse-complement (as well as the canonical form) of a sequence efficiently, without actually reverse- co... | https://api.stackexchange.com |
HardOCP has an image with an equation which apparently draws the Batman logo. Is this for real?
Batman Equation in text form:
\begin{align}
&\left(\left(\frac x7\right)^2\sqrt{\frac{||x|-3|}{|x|-3}}+\left(\frac y3\right)^2\sqrt{\frac{\left|y+\frac{3\sqrt{33}}7\right|}{y+\frac{3\sqrt{33}}7}}-1 \right) \\
&\qquad \qqu... | As Willie Wong observed, including an expression of the form $\displaystyle \frac{|\alpha|}{\alpha}$ is a way of ensuring that $\alpha > 0$. (As $\sqrt{|\alpha|/\alpha}$ is $1$ if $\alpha > 0$ and non-real if $\alpha < 0$.)
The ellipse $\displaystyle \left( \frac{x}{7} \right)^{2} + \left( \frac{y}{3} \right)^{2} - 1 ... | https://api.stackexchange.com |
Diborane has the interesting property of having two 3-centered bonds that are each held together by only 2 electrons (see the diagram below, from Wikipedia). These are known as "banana bonds."
I'm assuming there is some sort of bond hybridization transpiring, but the geometry doesn't seem like it is similar to anyth... | Look carefully, it's (distorted) tetrahedral--four groups at nearly symmetrically positions in 3D space{*}. So the hybridization is $sp^3$.
As you can see, the shape is distorted, but it's tetrahedral. Technically, the banana bonds can be said to be made up of orbitals similar to $sp^3$ but not exactly (like two $sp^{... | https://api.stackexchange.com |
I am the resident Bioinfo Geek in a hospital academic lab that routinely employs NGS as well as CyTOF and other large volume data producing technologies. I am sick of our current "protocol" for metadata collection and association with the final products (miriad excel sheets and a couple poorly designed RedCap DBs).
I w... | The Global Alliance for Genomics and Health has been working on the issue of representing sequencing data and metadata for storage and sharing for quite some time, though with mixed results. They do offer a model and API for storing NGS data in their GitHub repository, but it can be a bit of a pain to get a high-level... | https://api.stackexchange.com |
There is a well-known result in elementary analysis due to Darboux which says if $f$ is a differentiable function then $f'$ satisfies the intermediate value property. To my knowledge, not many "highly" discontinuous Darboux functions are known--the only one I am aware of being the Conway base 13 function--and few (non... | What follows is taken (mostly) from more extensive discussions in the following sci.math posts:
[23 January 2000]
[6 November 2006]
[20 December 2006]
Note: The term interval is restricted to nondegenerate intervals (i.e. intervals containing more than one point).
The continuity set of a derivative on an open interv... | https://api.stackexchange.com |
The help pages in R assume I know what those numbers mean, but I don't.
I'm trying to really intuitively understand every number here. I will just post the output and comment on what I found out. There might (will) be mistakes, as I'll just write what I assume. Mainly I'd like to know what the t-value in the coefficien... | Five point summary
yes, the idea is to give a quick summary of the distribution. It should be roughly symmetrical about mean, the median should be close to 0, the 1Q and 3Q values should ideally be roughly similar values.
Coefficients and $\hat{\beta_i}s$
Each coefficient in the model is a Gaussian (Normal) random vari... | https://api.stackexchange.com |
It's one of my real analysis professor's favourite sayings that "being obvious does not imply that it's true".
Now, I know a fair few examples of things that are obviously true and that can be proved to be true (like the Jordan curve theorem).
But what are some theorems (preferably short ones) which, when put into laym... | Theorem (false):
One can arbitrarily rearrange the terms in a convergent series without changing its value. | https://api.stackexchange.com |
I am looking for a tool, preferably written in C or C++, that can quickly and efficiently count the number of reads and the number of bases in a compressed fastq file. I am currently doing this using zgrep and awk:
zgrep . foo.fastq.gz |
awk 'NR%4==2{c++; l+=length($0)}
END{
print "Number... | It's difficult to get this to go massively quicker I think - as with this question working with large gzipped FASTQ files is mostly IO-bound. We could instead focus on making sure we are getting the right answer.
People deride them too often, but this is where a well-written parser is worth it's weight in gold. Heng Li... | https://api.stackexchange.com |
I've done some search in Internet and other sources about this question. Why the name ring to this particular object? Just curiosity.
Thanks. | The name "ring" is derived from Hilbert's term "Zahlring" (number ring), introduced in his Zahlbericht for certain rings of algebraic integers. As for why Hilbert chose the name "ring", I recall reading speculations that it may have to do with cyclical (ring-shaped) behavior of powers of algebraic integers. Namely, if ... | https://api.stackexchange.com |
I need to determine the KL-divergence between two Gaussians. I am comparing my results to these, but I can't reproduce their result. My result is obviously wrong, because the KL is not 0 for KL(p, p).
I wonder where I am doing a mistake and ask if anyone can spot it.
Let $p(x) = N(\mu_1, \sigma_1)$ and $q(x) = N(\mu_2,... | OK, my bad. The error is in the last equation:
\begin{align}
KL(p, q) &= - \int p(x) \log q(x) dx + \int p(x) \log p(x) dx\\\\
&=\frac{1}{2} \log (2 \pi \sigma_2^2) + \frac{\sigma_1^2 + (\mu_1 - \mu_2)^2}{2 \sigma_2^2} - \frac{1}{2} (1 + \log 2 \pi \sigma_1^2)\\\\
&= \log \frac{\sigma_2}{\sigma_1} + \frac{\sigma_1^2 + ... | https://api.stackexchange.com |
Many numerical approaches to CFD can be extended to arbitrarily high order (for instance, discontinuous Galerkin methods, WENO methods, spectral differencing, etc.). How should I choose an appropriate order of accuracy for a given problem? | In practice, most people stick to relatively low orders, usually first or second order. This view is often challenged by more theoretical researchers that believe in more accurate answers . The rate of convergence for simple smooth problems is well documented, for example see Bill Mitchell's comparison of hp adaptivi... | https://api.stackexchange.com |
Reading this question, Why are there no wheeled animals?, I wondered why no organisms seem to make use of the tensile and other strengths of metal, as we do in metal tools and constructions. I am obviously not talking about the microscopic uses of metal, as in human blood etc.
Why are there no plants with metal thorns?... | There are some cases of bio-metallic materials, as hinted at by the comments. But these are relatively small amount of metal.
It's not that there is a lack of metal available. Iron in particular is the fourth most common element in the earth's crust. Most soil that has a reddish color has iron in it. There are several... | https://api.stackexchange.com |
I am currently using an SVM with a linear kernel to classify my data. There is
no error on the training set. I tried several values for the parameter $C$
($10^{-5}, \dots, 10^2$). This did not change the error on the test set.
Now I
wonder: is this an error caused by the ruby bindings for libsvm I am using
(rb-libsv... | In a SVM you are searching for two things: a hyperplane with the largest minimum margin, and a hyperplane that correctly separates as many instances as possible. The problem is that you will not always be able to get both things. The c parameter determines how great your desire is for the latter.
I have drawn a small e... | https://api.stackexchange.com |
LEDs are an old technology, why did the industries take so long to put them into light bulbs? Was there any technological gap missing? | It is not possible to produce white light without an efficient blue LED, either using RGB LEDs or a blue LED + yellow phosphor.
The breakthrough was the invention of the high-brightness Gallium-Nitride blue LED by Shuji Nakamura at Nichia
in the early 1990s.
It still took a while to get the overall efficiency up to the... | https://api.stackexchange.com |
We use electromagnetic communication everywhere these days. Cell phones, wifi, old-school radio transmissions, television, deep space communication, etc.
I'm curious about some of the possible reasons we have never seen biological systems having evolved to use electromagnetic, i.e. radio, for communication. The one obv... | There is a very different mechanism for generation (and detection) of ultraviolet, visible and infrared light vs radio waves.
For the first, it is possible to generate it using chemical reactions (that is, chemiluminescence, bioluminescence) with a typical energy of order of 2 eV (electronovolts). Also, it is easy to d... | https://api.stackexchange.com |
Are there any free open source software tools available for simulating Oxford Nanopore reads? | Simulators designed specifically for Oxford Nanopore:
NanoSim
NanoSim-H
SiLiCO
ReadSim
DeepSimulator
General long read simulators:
Loresim
Loresim 2
FASTQsim
LongISLND
For an exhaustive list of existing read simulators, see page 15 of my thesis, Novel computational techniques for mapping and
classifying Next-Genera... | https://api.stackexchange.com |
From my understanding of light, you are always looking into the past based on how much time it takes the light to reach you from what you are observing.
For example when you see a star burn out, if the star was 5 light years away then the star actually burnt out 5 years ago.
So I am 27 years old, if I was 27 light year... | Yes, you can. And you do not even need to leave the Earth to do it.
You are always viewing things in the past, just as you are always hearing things in the past. If you see someone do something, who is 30 meters away, you are seeing what happened $(30\;\mathrm{m})/(3\times10^8\;\mathrm{m}/\mathrm{s}) = 0.1\;\mu\mat... | https://api.stackexchange.com |
I have come across many sorting algorithms during my high school studies. However, I never know which is the fastest (for a random array of integers). So my questions are:
Which is the fastest currently known sorting algorithm?
Theoretically, is it possible that there are even faster ones? So, what's the least complex... | In general terms, there are the $O(n^2)$ sorting algorithms, such as insertion sort, bubble sort, and selection sort, which you should typically use only in special circumstances; Quicksort, which is worst-case $O(n^2)$ but quite often $O(n\log n)$ with good constants and properties and which can be used as a general-p... | https://api.stackexchange.com |
There is probably some reason for this, but I can't figure out what it is. I agree that it probably doesn't happen 100% of the time, but most all of the time, the cream is clinging to just one of the cookie sides. | The "stuff" sticks to itself better than it sticks to the cookie. Now if you pull the cookies apart, you create a region of local stress, and one of the two interfaces will begin to unstick. At that point, you get something called "stress concentration" at the tip of the crack (red arrow) - where the tensile force conc... | https://api.stackexchange.com |
What is the difference between minimum spanning tree algorithm and a shortest path algorithm?
In my data structures class we covered two minimum spanning tree algorithms (Prim's and Kruskal's) and one shortest path algorithm (Dijkstra's).
Minimum spanning tree is a tree in a graph that spans all the vertices and total... | You are right that the two algorithms of Dijkstra (shortest paths from a single start node) and Prim (minimal weight spanning tree starting from a given node) have a very similar structure. They are both greedy (take the best edge from the present point of view) and build a tree spanning the graph.
The value they minim... | https://api.stackexchange.com |
The power spectrum of a signal can be calculated by taking the magnitude squared of its Fourier transform. Being an audio person, the signal of interest for me would be a time series.
How does this representation differ from a PSD (power spectral density), and importantly, in what practical situations should one use a ... | The power spectral density describes the density of power in a stationary random process $X(t)$ per unit of frequency. By the Wiener-Khinchin theorem, it can be calculated as follows for a wide-sense stationary random process:
$$
S_{xx}(f) = \int_{-\infty}^{\infty} r_{xx}(\tau) e^{-j2\pi f \tau} d\tau
$$
where $r_{xx}(... | https://api.stackexchange.com |
Air is 1% argon. Argon is heavier than air.
Why doesn't the argon concentrate in low-lying areas, choking out life there? | It does. You would find the average percentage of the atmosphere that is argon is very slightly higher at the floor of valleys. However, bear in mind first of all it wouldn't be anywhere near a complete stratification -- a layer of pure argon, then another of pure N2, and so on. A mixture of nearly ideal gases doesn... | https://api.stackexchange.com |
Why is it that when you look in the mirror left and right directions appear flipped, but not the up and down? | Here's a video of physicist Richard Feynman discussing this question.
Imagine a blue dot and a red dot. They are in front of you, and the blue dot is on the right. Behind them is a mirror, and you can see their image in the mirror. The image of the blue dot is still on the right in the mirror.
What's different is th... | https://api.stackexchange.com |
In most audio processing tasks, one of the most used transformations is MFCC (Mel-frequency cepstral coefficients).
I mostly know the math that's behind the MFCC: I understand both the filterbank step and the Mel frequency scaling.
What I don't get is the DCT (Discrete Cosine Transform) step: What kind of information d... | You can think of the DCT as a compression step. Typically with MFCCs, you will take the DCT and then keep only the first few coefficients. This is basically the same reason that the DCT is used in JPEG compression. DCTs are chosen because their boundary conditions work better on these types of signals.
Let's contrast t... | https://api.stackexchange.com |
There are mathematical proofs that have that "wow" factor in being elegant, simplifying one's view of mathematics, lifting one's perception into the light of knowledge, etc.
So I'd like to know what mathematical proofs you've come across that you think other mathematicians should know, and why. | Here is my favourite "wow" proof .
Theorem
There exist two positive irrational numbers $s,t$ such that $s^t$ is rational.
Proof
If $\sqrt2^\sqrt 2$ is rational, we may take $s=t=\sqrt 2$ .
If $\sqrt 2^\sqrt 2$ is irrational , we may take $s=\sqrt 2^\sqrt 2$ and $t=\sqrt 2$ since $(\sqrt 2^\sqrt 2)^\sqrt 2=(\sqrt... | https://api.stackexchange.com |
I'm still a student, but the same books keep getting named by my tutors (Rudin, Royden).
I've read Baby Rudin and begun Royden though I'm unsure if there are other books that I "should" be working on if I want to study beyond Masters. I'm not there yet as I'm on a four year course and had a gap year between Years 3 and... | EDIT: I now think that this list is long enough that I shall be maintaining it over time--updating it whenever I use a new book/learn a new subject. While every suggestion below should be taken with a grain of salt--I will say that I spend a huge amount of time sifting through books to find the ones that conform best t... | https://api.stackexchange.com |
Just like this guy's, the color of my stove's flames were affected by the humidifier as well.
Why does this happen?
Is it a good thing or a bad thing ? | OK, this question appears to have generated some controversy. On the one hand is the answer by niels nielsen (currently accepted), which implies that the orange color is from sodium. On the other hand is the answer by StessenJ, which implies that the orange is normal black body radiation from the soot. Plus there are l... | https://api.stackexchange.com |
One of the major issues that we have to deal with in molecular simulations is the calculation of distance-dependent forces. If we can restrict the force and distance functions to have even powers of the separation distance $r$, then we can just compute the square of the distance $r^2 = {\bf r \cdot r}$ and not have to ... | As an extension to moyner's answer, the on-chip sqrt is usually an rsqrt, i.e. a reciprocal square root that computes $a \rightarrow 1/\sqrt{a}$. So if in your code you're only going to use $1/r$ (if you're doing molecular dynamics, you are), you can compute r = rsqrt(r2) directly and save yourself the division. The re... | https://api.stackexchange.com |
We have a lot of Illumina sequenced exome data. Currently we are using spring for its great lossless compression, but we are looking if there is anything better (and most preferably opensource) which can let us compress our fastq files.
We also want to compress or reduce file size of BAM, but using CRAM in lossless mod... | EDIT: I am rewriting the answer in response to updates to the original question.
TL;DR: use CRAM
Background 1: quality binning and FASTQ compression
In the old days, base callers outputted base quality at full resolution – you could see quality from Q2 to Q40 in full range. As a result, quality strings were like semi-r... | https://api.stackexchange.com |
A thought experiment: Imagine the Sun is suddenly removed. We wouldn't notice a difference for 8 minutes, because that's how long light takes to get from the Sun's surface to Earth.
However, what about the Sun's gravitational effect? If gravity propagates at the speed of light, for 8 minutes the Earth will continue to... | Since general relativity is a local theory just like any good classical field theory, the Earth will respond to the local curvature which can change only once the information about the disappearance of the Sun has been communicated to the Earth's position (through the propagation of gravitational waves).
So yes, the Ea... | https://api.stackexchange.com |
Principal component analysis (PCA) can be used for dimensionality reduction. After such dimensionality reduction is performed, how can one approximately reconstruct the original variables/features from a small number of principal components?
Alternatively, how can one remove or discard several principal components from... | PCA computes eigenvectors of the covariance matrix ("principal axes") and sorts them by their eigenvalues (amount of explained variance). The centered data can then be projected onto these principal axes to yield principal components ("scores"). For the purposes of dimensionality reduction, one can keep only a subset o... | https://api.stackexchange.com |
Yesterday I was debugging some things in R trying to get a popular Flow Cytometry tool to work on our data. After a few hours of digging into the package I discovered that our data was hitting an edge case, and it seems like the algorithm wouldn't work correctly under certain circumstances.
This bug is not neccessarily... | I prefer to treat software tools and computers in a similar fashion to laboratory equipment, and in some sense biology in general. Biologists are used to unexpected things happening in their experiments, and it's not uncommon for a new discovery to change the way that people look at something. Things break down, cells ... | https://api.stackexchange.com |
I'm interested in finding all tennis courts (and other similar well defined features like basketball courts) in my county, and I have aerial imagery of good (but varying) resolution, but I'm not sure of the best way to find them. Here are two examples of the imagery:
I've looked at the various methods, and I think te... | You have some very strong color and geometry cues you can leverage. I would try the following:
Extract the Green channel & apply watershed type algorithm on it, followed by connected components. Subsequently compute component statistics (area & bounding box) for each component. Retain only the components with area ~= ... | https://api.stackexchange.com |
Experiment description:
In Lagrange interpolation, the exact equation is sampled at $N$ points (polynomial order $N - 1$) and it is interpolated at 101 points. Here $N$ is varied from 2 to 64. Each time $L_1$, $L_2$ and $L_\infty$ error plots are prepared. It is seen that, when the function is sampled at equi-spaced po... | The problem with equispaced points is that the interpolation error polynomial, i.e.
$$ f(x) - P_n(x) = \frac{f^{(n+1)}(\xi)}{(n+1)!} \prod_{i=0}^n (x - x_i),\quad \xi\in[x_0,x_n] $$
behaves differently for different sets of nodes $x_i$. In the case of equispaced points, this polynomial blows up at the edges.
If you use... | https://api.stackexchange.com |
If I have highly skewed positive data I often take logs. But what should I do with highly skewed non-negative data that include zeros? I have seen two transformations used:
$\log(x+1)$ which has the neat feature that 0 maps to 0.
$\log(x+c)$ where c is either estimated or set to be some very small positive value.
Are... | No-one mentioned the inverse hyperbolic sine transformation. So for completeness I'm adding it here.
This is an alternative to the Box-Cox transformations and is defined by
\begin{equation}
f(y,\theta) = \text{sinh}^{-1}(\theta y)/\theta = \log[\theta y + (\theta^2y^2+1)^{1/2}]/\theta,
\end{equation}
where $\theta>0$. ... | https://api.stackexchange.com |
How is using a 1:1 transformer safer than using the mains straight off? Is it because you can limit the current coming from the transformer whereas straight from the mains its not current limited? I fail to see how its "safer" when playing with electricity is dangerous. Could someone please explain why it is considered... | Without a transformer the live wire is live relative to ground.
If you are at "ground" potential then touching the live wire makes you part of the return path.
{This image taken from an excellent discussion here
With a transformer the output voltage is not referenced to ground - see diagram (a) below. There is no "ret... | https://api.stackexchange.com |
I'm supposed to calculate:
$$\lim_{n\to\infty} e^{-n} \sum_{k=0}^{n} \frac{n^k}{k!}$$
By using WolframAlpha, I might guess that the limit is $\frac{1}{2}$, which is a pretty interesting and nice result. I wonder in which ways we may approach it. | The probabilistic way:
This is $P[N_n\leqslant n]$ where $N_n$ is a random variable with Poisson distribution of parameter $n$. Hence each $N_n$ is distributed like $X_1+\cdots+X_n$ where the random variables $(X_k)$ are independent and identically distributed with Poisson distribution of parameter $1$.
By the centr... | https://api.stackexchange.com |
I have a series of data points $(x_i,y_i)$ which I expect to (approximately) follow a function $y(x)$ that asymptotes to a line at large $x$. Essentially, $f(x) \equiv y(x) - (ax + b)$ approaches zero as $x \to \infty$, and the same can probably be said of all the derivatives $f'(x)$, $f''(x)$, etc. But I don't know wh... | It's a rather rough algorithm, but I'd use the following procedure for a crude estimate: if, as you say, the purported $f(x)$ that represents your $(x_i,y_i)$ is already almost linear as $x$ increases, what I'd do is to take differences $\dfrac{y_{i+1}-y_i}{x_{i+1}-x_i}$, and then use an extrapolation algorithm like th... | https://api.stackexchange.com |
What is your favorite statistical quote?
This is community wiki, so please one quote per answer. | All models are wrong, but some are useful. (George E. P. Box)
Reference: Box & Draper (1987), Empirical model-building and response surfaces, Wiley, p. 424.
Also: G.E.P. Box (1979), "Robustness in the Strategy of Scientific Model Building" in Robustness in Statistics (Launer & Wilkinson eds.), p. 202. | https://api.stackexchange.com |
What causes the noise when you crack a joint? Is joint cracking harmful? | The exact mechanism is unclear. Here are some possible causes:
rapid collapsing of cavities inside the joint [1];
rapid ligament stretching [1];
breaking of intra-articular adhesions [1];
escaping gases from synovial fluid [2];
movements of joints, tendons and ligaments [2];
mechanic interaction between rough surfaces... | https://api.stackexchange.com |
Here is how I have understood nested vs. crossed random effects:
Nested random effects occur when a lower level factor appears only within a particular level of an upper level factor.
For example, pupils within classes at a fixed point in time.
In lme4 I thought that we represent the random effects for nested da... | (This is a fairly long answer, there is a summary at the end)
You are not wrong in your understanding of what nested and crossed random effects are in the scenario that you describe. However, your definition of crossed random effects is a little narrow. A more general definition of crossed random effects is simply: not... | https://api.stackexchange.com |
What is the difference between data mining, statistics, machine learning and AI?
Would it be accurate to say that they are 4 fields attempting to solve very similar problems but with different approaches? What exactly do they have in common and where do they differ? If there is some kind of hierarchy between them, what... | There is considerable overlap among these, but some distinctions can be made. Of necessity, I will have to over-simplify some things or give short-shrift to others, but I will do my best to give some sense of these areas.
Firstly, Artificial Intelligence is fairly distinct from the rest. AI is the study of how to c... | https://api.stackexchange.com |
When I pet my cat, and then touch her on the nose, I get a little shock. Sometimes, when she walks up to something, her nose sparks and she jumps back and puffs out. I was wondering how I might go about measuring the capacitance of my cat.
So how many micro-farads does my cat have? I don't think I can just attach the b... | "Touch Not The Cat, Bot a Glove"
DTTAH / ACNR / IANAL / YMMV *
Equipment:
High impedance voltmeter / oscilloscope with HV probe.
High voltage low capacitance capacitors (1 10 100 1000 pF) x 2 of each.
Pretest - charge capacitors to some semi known high voltage and measure with voltmeter to determine measurement ab... | https://api.stackexchange.com |
If you watched the last Olympics like me you probably also observed that most medallists in running events were black. Why is that? I discussed this with university grad friends and researchers and we only came up with hypotheses but nobody had an actual explanation. Is it cultural, genetic, other reasons or nobody rea... | It's an interesting question and one that has been asked before. NPR did a story in 2013 on this topic, but their question was a bit more focused than just "why are so many black people good runners?"
The observation that led to their story wasn't just that black people in general were over-represented among long-dist... | https://api.stackexchange.com |
Why does evolution not make life longer for humans or any other species?
Wouldn't evolution favour a long life? | Why do we age is a classical question in Evolutionary Biology. There are several things to consider when we think of how genes that cause disease, aging, and death to evolve.
One explanation for the evolution of aging is the mutation accumulation (MA) hypothesis. This hypothesis by P. Medawar states that mutations caus... | https://api.stackexchange.com |
Maybe the concept, why it's used, and an example. | First, we need to understand what is a Markov chain. Consider the following weather example from Wikipedia. Suppose that weather on any given day can be classified into two states only: sunny and rainy. Based on past experience, we know the following:
$P(\text{Next day is Sunny}\,\vert \,\text{Given today is Rainy)}=0.... | https://api.stackexchange.com |
I'm learning Haskell and I'm fascinated by the language. However I have no serious math or CS background. But I am an experienced software programmer.
I want to learn category theory so I can become better at Haskell.
Which topics in category theory should I learn to provide a good basis for understanding Haskell? | In a previous answer in the Theoretical Computer Science site, I said that category theory is the "foundation" for type theory. Here, I would like to say something stronger. Category theory is type theory. Conversely, type theory is category theory. Let me expand on these points.
Category theory is type theory
In a... | https://api.stackexchange.com |
I'm studying pattern recognition and statistics and almost every book I open on the subject I bump into the concept of Mahalanobis distance. The books give sort of intuitive explanations, but still not good enough ones for me to actually really understand what is going on. If someone would ask me "What is the Mahalanob... | Here is a scatterplot of some multivariate data (in two dimensions):
What can we make of it when the axes are left out?
Introduce coordinates that are suggested by the data themselves.
The origin will be at the centroid of the points (the point of their averages). The first coordinate axis (blue in the next figure) ... | https://api.stackexchange.com |
This is a basic question, but I'm thinking that $O(m+n)$ is the same as $O(\max(m,n))$, since the larger term should dominate as we go to infinity? Also, that would be different from $O(\min(m,n))$. Is that right? I keep seeing this notation, especially when discussing graph algorithms. For example, you routinely see: ... | You are right. Notice that the term $O(n+m)$ slightly abuses the classical big-O Notation, which is defined for functions in one variable. However there is a natural extension for multiple variables.
Simply speaking, since
$$ \frac{1}{2}(m+n) \le \max\{m,n\} \le m+n \le 2 \max\{m,n\},$$
you can deduce that $O(n+m)$ an... | https://api.stackexchange.com |
...assuming that I'm able to augment their knowledge about variance in an intuitive fashion ( Understanding "variance" intuitively ) or by saying: It's the average distance of the data values from the 'mean' - and since variance is in square units, we take the square root to keep the units same and that is called stand... | Sometimes we can "augment knowledge" with an unusual or different approach. I would like this reply to be accessible to kindergartners and also have some fun, so everybody get out your crayons!
Given paired $(x,y)$ data, draw their scatterplot. (The younger students may need a teacher to produce this for them. :-) E... | https://api.stackexchange.com |
It seems that every website on sexual health advises against using oil-based lubricants with condoms. It is claimed that "oil breaks down latex". One source claimed that a latex condom completely breaks down in only 60 seconds. It made me curious, so I made an experiment.
I took a piece of rubber latex condom and soake... | First off, may I say that I applaud your decision to test this through an experiment. It's rare to see that than I would like.
Now, on to the matter at hand. It's fairly well known from industrial chemistry that non-polar solvents degrade latex quite heavily.
I work with latex seals a lot, and the hexanes we use routin... | https://api.stackexchange.com |
These formulae are used if the molecule has a possible plane of symmetry. One such example would be:
Here the carbons marked with an asterisk are stereogenic centres (the asterisk is not used to mark isotopes). We can clearly see that if carbon number 2 (in the entire longest chain) and the carbon number 4 have opposi... | I managed to crack the formula for optical isomers with odd chiral centers, so I'll share my attempt here. Hopefully others may innovate on it and post solutions for other formulae.
Pseudo-chiral carbon atoms - an introduction
The Gold Book defines pseudo-chiral/pseudo-asymmetric carbon atom as:
a tetrahedrally coord... | https://api.stackexchange.com |
What is the Fourier transform? What does it do? Why is it useful (in math, in engineering, physics, etc)?
This question is based on the question of Kevin Lin, which didn't quite fit in Mathoverflow. Answers at any level of sophistication are welcome. | The ancient Greeks had a theory that the sun, the moon, and the planets move around the Earth in circles. This was soon shown to be wrong. The problem was that if you watch the planets carefully, sometimes they move backwards in the sky. So Ptolemy came up with a new idea - the planets move around in one big circle,... | https://api.stackexchange.com |
I need to get started using Finite Element Methods. I am about to start reading Numerical solutions of partial differential equations by the finite element method by Claes Johnson, but it's dated 1987.
Two questions:
1) What newer good resources/textbooks/e-books/lecture notes on this subject are out there?
2) How mu... | There are lots of modern finite element references, but I will just comment on a few books that I think are practical and relevant to applications, plus one containing more comprehensive analysis.
Wriggers Nonlinear Finite Element Methods (2008) is a good general reference, but will be most relevant to those concerned... | https://api.stackexchange.com |
This particular question has been of a great deal of interest to me, especially since it dives at the heart of abiogenesis. | In 2010, Dr. Craig Venter actually used a bacterial shell and wrote DNA for it.
Scientists have created the world's first synthetic life form in a landmark experiment that paves the way for designer organisms that are built rather than evolved.
(Snip)
The new organism is based on an existing bacterium that causes mast... | https://api.stackexchange.com |
The Mersenne Twister is widely regarded as good. Heck, the CPython source says that it "is one of the most extensively tested generators in existence." But what does this mean? When asked to list properties of this generator, most of what I can offer is bad:
It's massive and inflexible (eg. no seeking or multiple stre... | The initial Mersenne-Twister (MT) was regarded as good for some years, until it was found out to be pretty bad with the more advanced TestU01 BigCrush tests and better PRNGs.
This page lists the Mersenne-Twister features in detail:
Positive Qualities
Produces 32-bit or 64-bit numbers (thus usable as source of random b... | https://api.stackexchange.com |
I'm learning DSP slowly and trying to wrap my head around some terminology:
Question 1: Suppose I have the following filter difference equation:
$$y[n] = 2 x[n] + 4 x[n-2] + 6 x[n-3] + 8 x[n-4]$$
There are 4 coefficients on the right-hand side. Are the "number of taps" also 4? Is the "filter order" also 4?
Question 2... | OK, I'll try to answer your questions:
Q1: the number of taps is not equal the to the filter order. In your example the filter length is 5, i.e. the filter extends over 5 input samples [$x(n), x(n-1), x(n-2), x(n-3), x(n-4)$]. The number of taps is the same as the filter length. In your case you have one tap equal to z... | https://api.stackexchange.com |
As a novice electronics hobbyist, I have heard these terms and more being thrown around everywhere. At its root, I understand that they are all based on communication between devices, computers, peripherals, etc.
I have a basic understanding of how all of them work, but I get confused when I see so many of them and am ... | Serial is an umbrella word for all that is "Time Division Multiplexed", to use an expensive term. It means that the data is sent spread over time, most often one single bit after another. All the protocols you're naming are serial protocols.
UART, for Universal Asynchronous Receiver Transmitter, is one of the most us... | https://api.stackexchange.com |
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