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What is a decoupling capacitor (or smoothing capacitor as referred to in the link below)?
How do I know if I need one and if so, what size and where it needs to go?
This question mentions many chips needing one between VCC and GND; how do I know if a specific chip is one?
Would an SN74195N 4-bit parallel access shift... | Power supplies are slow...they take roughly 10 us to respond (i.e. bandwidth up to 100 kHz). So when your big, bad, multi-MHz microcontroller switches a bunch of outputs from high to low, it will draw from the power supply, causing the voltage to start drooping until it realizes (10 us later!) that it needs to do some... | https://api.stackexchange.com |
fast5 is a variant of HDF5 the native format in which raw data from Oxford Nanopore MinION are provided. You can easily extract the reads in fast5 format into a standard fastq format, using for example poretools.
Say I have aligned these reads in fastq format to an external reference genome, resulting in a SAM file. S... | NOTICE:
I have altered my answer slightly from the original as I have turned the original script into a pip installable program (with tests) and have updated the links and code snippets accordingly. The essence of the answer is still exactly the same.
This is something I have been meaning to get around to for a while,... | https://api.stackexchange.com |
You need 4 channels to determine your position (including elevation), and I can understand that a few extra channels increase accuracy. However, there are maximum 12 satellites in view at any time, so why have receivers with more channels? I've seen receivers with 50 or even 66 channels, that's more than the number of ... | The answer is complex due to the way the GPS system operates, so I'm going to simplify a number of things so you understand the principle, but if you are interested in how it's really implemented you'll need to go find a good GPS reference. In other words, what's written below is meant to give you an idea of how it wor... | https://api.stackexchange.com |
What is the difference between a latch and a flip-flop?
What I am thinking is that a latch is equivalent to a flip-flop since it is used to store bits and is also equivalent to a register which is also used to store data. But after reading some articles on the internet I found differences between latches and flip-flops... | A flip flop is built from two back to back latches with opposite polarity clocks, which form a master slave topology.
The type of latch is irrelevant (JK, SR, D, T) to this constraint, but it is important that the transparency is controlled by some pin (call it clock or enable or whatever you like).
SR latches throw e... | https://api.stackexchange.com |
How can $\ce{CO2}$ be converted into carbon and oxygen?
$$\ce{CO2 -> C + O2}$$
Alternatively:
$$\ce{CO2 + ? -> C + O2}$$
I'm aware that plants are capable of transforming $\ce{CO2 + H2O}$ to glucose and oxygen via photosynthesis, but I'm interested in chemical or physical means rather than biological. | In my opinion, the catalytic, solar-driven conversion of carbon dioxide to methanol, formic acid, etc. is much more interesting and promising, but since Enrico asked for the conversion of carbon dioxide to carbon itself:
The group around Yutaka Tamaura was/is active in this field. In one of their earlier publications,[... | https://api.stackexchange.com |
MATLAB's filtfilt does a forward-backward filtering, i.e., filter, reverse the signal, filter again and then reverse again. Apparently this done to reduce phase lags? What are the advantages/disadvantages of using such a filtering (I guess it would result in an effective increase in filter order).
Would it be preferabl... | You can best look at it in the frequency domain. If $x[n]$ is the input sequence and $h[n]$ is the filter's impulse response, then the result of the first filter pass is
$$X(e^{j\omega})H(e^{j\omega})$$
with $X(e^{j\omega})$ and $H(e^{j\omega})$ the Fourier transforms of $x[n]$ and $h[n]$, respectively. Time reversal c... | https://api.stackexchange.com |
What is the importance of eigenvalues/eigenvectors? | Short Answer
Eigenvectors make understanding linear transformations easy. They are the "axes" (directions) along which a linear transformation acts simply by "stretching/compressing" and/or "flipping"; eigenvalues give you the factors by which this compression occurs.
The more directions you have along which you under... | https://api.stackexchange.com |
At school, I really struggled to understand the concept of imaginary numbers. My teacher told us that an imaginary number is a number that has something to do with the square root of $-1$. When I tried to calculate the square root of $-1$ on my calculator, it gave me an error. To this day I still do not understand i... | Let's go through some questions in order and see where it takes us. [Or skip to the bit about complex numbers below if you can't be bothered.]
What are natural numbers?
It took quite some evolution, but humans are blessed by their ability to notice that there is a similarity between the situations of having three apple... | https://api.stackexchange.com |
Saw this bird outside my apartment in College Station, Texas and have never seen anything like it before!
It is about the size of a hand. | It is American Woodcock, Scolopax minor.
Superbly camouflaged against the leaf litter, the brown-mottled American Woodcock walks slowly along the forest floor, probing the soil with its long bill in search of earthworms. Unlike its coastal relatives, this plump little shorebird lives in young forests and shrubby old ... | https://api.stackexchange.com |
In Computer Science a De Bruijn graph has (1) m^n vertices representing all possible sequences of length n over m symbols, and (2) directed edges connecting nodes that differ by a shift of n-1 elements (the successor having the new element at the right).
However in Bioinformatics while condition (2) is preserved, what... | Several papers have made this distinction, and a few indeed use different terms to distinguish between them. For example, Kazaux et al. (2016) acknowledge that:
These constraints favour the use of a version of the de Bruijn Graph (dBG) dedicated to genome assembly – a version which differs from the combinatorial struc... | https://api.stackexchange.com |
The results obtained by running the results command from DESeq2 contain a "baseMean" column, which I assume is the mean across samples of the normalized counts for a given gene.
How can I access the normalized counts proper?
I tried the following (continuing with the example used here):
> dds <- DESeqDataSetFromMatrix(... | The normalized counts themselves can be accessed with counts(dds, normalized=T).
Now as to what the baseMean actually means, that will depend upon whether an "expanded model matrix" is in use or not. Given your previous question, we can see that geno_treat has a bunch of levels, which means that expanded models are not... | https://api.stackexchange.com |
Why do the names of most chemical elements end with -um or -ium for both primordial and synthetic elements? | To expand on @BelieveInvis's answer -- in the early 19th century, when the Royal Society was really in the swing of things, the dominant language of scholarship was still Latin. Since Latin didn't have words for the new metallic elements, new words were coined from the existing terms for the substances and given Latina... | https://api.stackexchange.com |
I have a single ~10GB FASTA file generated from an Oxford Nanopore Technologies' MinION run, with >1M reads of mean length ~8Kb. How can I quickly and efficiently calculate the distribution of read lengths?
A naive approach would be to read the FASTA file in Biopython, check the length of each sequence, store the lengt... | If you want something quick and dirty you could rapidly index the FASTA with samtools faidx and then put the lengths column through R (other languages are available) on the command line.
samtools faidx $fasta
cut -f2 $fasta.fai | Rscript -e 'data <- as.numeric (readLines ("stdin")); summary(data); hist(data)'
This out... | https://api.stackexchange.com |
The approximation $$\sin(x) \simeq \frac{16 (\pi -x) x}{5 \pi ^2-4 (\pi -x) x}\qquad (0\leq x\leq\pi)$$ was proposed by Mahabhaskariya of Bhaskara I, a seventh-century Indian mathematician.
I wondered how much this could be improved using our computers and so I tried (very immodestly) to see if we could do better using... | One simple way to derive this is to come up with a parabola approximation. Just getting the roots correct we have
$$f(x)=x(\pi-x)$$
Then, we need to scale it (to get the heights correct). And we are gonna do that by dividing by another parabola $p(x)$
$$f(x)=\frac{x(\pi-x)}{p(x)}$$
Let's fix this at three points (thus ... | https://api.stackexchange.com |
One of the commonest mistakes made by students, appearing at every level of maths education up to about early undergraduate, is the so-called “Law of Universal Linearity”:
$$ \frac{1}{a+b} \mathrel{\text{“=”}} \frac{1}{a} + \frac{1}{b} $$
$$ 2^{-3} \mathrel{\text{“=”}} -2^3 $$
$$ \sin (5x + 3y) \mathrel{\text{“=”}} \si... | I think this is a symptom of how students are taught basic algebra. Rather than being told explicit axioms like $a(x+y)= ax+ay$ and theorems like $(x+y)/a = x/a+y/a,$ students are bombarded with examples of how these axioms/theorems are used, without ever being explicitly told: hey, here's a new rule you're allowed to ... | https://api.stackexchange.com |
Lots of new batteries (for mobile devices, MP3 players, etc) have connectors with 3 pins.
I would like to know what is the purpose of this and how should I use these three pins?
They are usually marked as (+) plus, (-) minus, and T. | The third pin is usually for an internal temperature sensor, to ensure safety during charging. Cheap knock-off batteries sometimes have a dummy sensor that returns a "temp OK" value regardless of actual temperature.
Some higher-end batteries have internal intelligence for charge control and status monitoring, in which ... | https://api.stackexchange.com |
I found this confusing when I use the neural network toolbox in Matlab.
It divided the raw data set into three parts:
training set
validation set
test set
I notice in many training or learning algorithm, the data is often divided into 2 parts, the training set and the test set.
My questions are:
what is the differen... | Training set
A set of examples used for learning: to fit the parameters of the classifier
In the Multilayer Perceptron (MLP) case, we would use the training set to find the “optimal” weights with the back-prop rule
Validation set
A set of examples used to tune the hyper-parameters of a classifier
In the MLP case, we wo... | https://api.stackexchange.com |
I have finally built up a lab to design electronics in. I have quite a few designs I would like to test. I have tried the printer toner/iron technique a few times but have found that I cannot create small pitch sizes as they tear off while removing the printer paper. A few people have mentioned that this is due to usin... | For one-offs or prototypes I use:
Press-n-Peel transfer film with a laser printer (the blue one)
Steel wool and detergent to clean the PCB blank, then a short etch in ammonium persulphate: that gives a very clean surface, important for a good transfer from the film
A laminator to transfer the pattern to the PCB; I mod... | https://api.stackexchange.com |
I am confused with this! How does a capacitor block DC?
I have seen many circuits using capacitors powered by a DC supply. So, if capacitor blocks DC, why should it be used in such circuits?
Also, the voltage rating is mentioned as a DC value on the capacitor. What does it signify? | I think it would help to understand how a capacitor blocks DC (direct current) while allowing AC (alternating current).
Let's start with the simplest source of DC, a battery:
When this battery is being used to power something, electrons are drawn into the + side of the battery, and pushed out the - side.
Let's attach... | https://api.stackexchange.com |
I keep seeing the term "Aqua" in the ingredient labels on several shampoo varieties, but I really don't see why it should be there in the first place.
I mean, if the manufacturers just wanted to say it contains water, couldn't they've printed out "Water" instead?
Or could it be that "Aqua" is slang for purified wate... | In most countries, cosmetic product labels use the International Nomenclature of Cosmetic Ingredients (INCI) for listing ingredients.
The INCI name “AQUA” indeed just describes water (which is used as a solvent). | https://api.stackexchange.com |
I am interested in the time complexity of a compiler. Clearly this is a very complicated question as there are many compilers, compiler options and variables to consider. Specifically, I am interested in LLVM but would be interested in any thoughts people had or places to start research. A quite google seems to bring l... | The best book to answer your question would probably be: Cooper and Torczon, "Engineering a Compiler," 2003. If you have access to a university library you should be able to borrow a copy.
In a production compiler like llvm or gcc the designers make every effort to keep all the algorithms below $O(n^2)$ where $n$ is t... | https://api.stackexchange.com |
A bit of a historical question on a number, 30 times coverage, that's become so familiar in the field: why do we sequence the human genome at 30x coverage?
My question has two parts:
Who came up with the 30x value and why?
Does the value need to be updated to reflect today's state-of-the-art?
In summary, if the 30x v... | The earliest mention of the 30x paradigm I could find is in the original Illumina whole-genome sequencing paper: Bentley, 2008. Specifically, in Figure 5, they show that most SNPs have been found, and that there are few uncovered/uncalled bases by the time you reach 30x:
These days, 30x is still a common standard, but... | https://api.stackexchange.com |
I’m using the RepBase libraries in conjunction with RepeatMasker to get genome-wide repeat element annotations, in particular for transposable elements.
This works well enough, and seems to be the de facto standard in the field.
However, there are two issues with the use of RepBase, which is why I (and others) have bee... | Dfam has recently launched a sister resource, Dfam_consensus, whose stated aim is to replace RepBase. From the annoucement:
Dfam_consensus provides an open framework for the community to store both seed alignments (multiple alignments of instances for a given family) and the corresponding consensus sequence model.
Bo... | https://api.stackexchange.com |
I recently encountered a formulation of the meta-phenomenon: "two is easy, three is hard" (phrased this way by Federico Poloni), which can be described, as follows:
When a certain problem is formulated for two entities, it is relatively easy to solve; however, an algorithm for a three-entities-formulation increases in ... | One example that appears in many areas of physics, and in particular classical mechanics and quantum physics, is the two-body problem. The two-body problem here means the task of calculating the dynamics of two interacting particles which, for example, interact by gravitational or Coulomb forces. The solution to this p... | https://api.stackexchange.com |
I was going to add a bit of information to my post on a previous day using schematics and some instructions. What programs are being employed for this purpose?
I mostly want to see what others are using and that I can easily use to give descriptive schematics.
In a perfect world, and I know this is a case of me wishing... | Try KiCAD. Now it even does SPICE simulations, ngspice specifically, and it handles pretty much everything else. Other than that, if you wish, KiCAD has also the tools to design printed circuit boards, and even has a 3D viewer and exporter for the boards!
KiCAD runs on Windows, Linux and Apple OS X.
There is also a pro... | https://api.stackexchange.com |
I am working with a small dataset (21 observations) and have the following normal QQ plot in R:
Seeing that the plot does not support normality, what could I infer about the underlying distribution? It seems to me that a distribution more skewed to the right would be a better fit, is that right? Also, what other conc... | If the values lie along a line the distribution has the same shape (up to location and scale) as the theoretical distribution we have supposed.
Local behaviour: When looking at sorted sample values on the y-axis and (approximate) expected quantiles on the x-axis, we can identify from how the values in some section of ... | https://api.stackexchange.com |
I know that there's big controversy between two groups of physicists:
those who support string theory (most of them, I think)
and those who oppose it.
One of the arguments of the second group is that there's no way to disprove the correctness of the string theory.
So my question is if there's any defined experiment t... | One can disprove string theory by many observations that will almost certainly not occur, for example:
By detecting Lorentz violation at high energies: string theory predicts that the Lorentz symmetry is exact at any energy scale; recent experiments by the Fermi satellite and others have shown that the Lorentz symmetr... | https://api.stackexchange.com |
A former colleague once argued to me as follows:
We usually apply normality tests to the results of processes that,
under the null, generate random variables that are only
asymptotically or nearly normal (with the 'asymptotically' part dependent on some quantity which we cannot make large); In the era of
cheap ... | It's not an argument. It is a (a bit strongly stated) fact that formal normality tests always reject on the huge sample sizes we work with today. It's even easy to prove that when n gets large, even the smallest deviation from perfect normality will lead to a significant result. And as every dataset has some degree of ... | https://api.stackexchange.com |
When something gets wet, it usually appears darker. This can be observed with soil, sand, cloth, paper, concrete, bricks...
What is the reason for this? How does water soaking into the material change its optical properties? | When you look at a surface like sand, bricks, etc, the light you are seeing is reflected by diffuse reflection.
With a flat surface like a mirror, light falling on the surface is reflected back at the same angle it hit the surface (specular reflection) and you see a mirror image of the light falling on the surface. How... | https://api.stackexchange.com |
I was just thinking what can be the last atomic number that can exist within the range of permissible radioactivity limit and considering all other factors in quantum physics and chemical factors. | Nobody really knows. Using the naive Bohr model of the atom, we run into trouble around $Z=137$ as the innermost electrons would have to be moving above the speed of light. This result is because the Bohr model doesn't take into account relativity. Solving the Dirac equation, which comes from relativistic quantum mecha... | https://api.stackexchange.com |
This question is based on a discussion with a 10-year old. So if it is not clear how to interpret certain details, imagine how a 10-year old would interpret them.
This 10-year old does not know about relativistic issues, so assume that we are living in a Newtonian universe.
In this model, our universe is homogenous and... | There are about $10^{23}$ stars in the observable universe. Thanks to the expansion of the universe, those stars are currently spread over a sphere that is about $d=2.8\times 10^{10}$ parsecs across.
Of course some stars will have died whilst their light has been travelling towards us, but others will have been born, s... | https://api.stackexchange.com |
Is a stochastic process completely described by its autocorrelation function?
If not, which additional properties would be needed? | What is meant by a complete description of a stochastic process? Well, mathematically, a stochastic process is a collection $\{X(t) \colon t \in {\mathbb T}\}$ of random variables, one for each time instant $t$ in an index set $\mathbb T$, where usually $\mathbb T$ is the entire real line or the positive real line, an... | https://api.stackexchange.com |
As an explanation of why a large gravitational field (such as a black hole) can bend light, I have heard that light has momentum. This is given as a solution to the problem of only massive objects being affected by gravity. However, momentum is the product of mass and velocity, so, by this definition, massless photons ... | 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 Ei... | https://api.stackexchange.com |
Are there some proofs that can only be shown by contradiction or can everything that can be shown by contradiction also be shown without contradiction? What are the advantages/disadvantages of proving by contradiction?
As an aside, how is proving by contradiction viewed in general by 'advanced' mathematicians. Is it a ... | 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 o... | https://api.stackexchange.com |
Since I'm not that good at (as I like to call it) 'die-hard-mathematics', I've always liked concepts like the golden ratio or the dragon curve, which are easy to understand and explain but are mathematically beautiful at the same time.
Do you know of any other concepts like these? | 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. | https://api.stackexchange.com |
I've heard people say that plots produced by ORIGIN tend to look polished and "professional," whereas plots produced by Mathematica do not. However, most plot-creation programs are quite configurable and it stands to reason that with the right settings for things like tick location and labeling, font and color choices,... | 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 ... | https://api.stackexchange.com |
Let's say I want to construct a phylogenetic tree based on orthologous nucleotide sequences; I do not want to use protein sequences to have a better resolution. These species have different GC-content.
If we use a straightforward approach like maximum likelihood with JC69 or any other classical nucleotide model, conser... | 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"... | https://api.stackexchange.com |
Simple enough question. Why not use a 741 op-amp in a target circuit or anyone's target circuit? What are the reasons not to use it? What might be the reasons to still choose this part? | 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 ... | https://api.stackexchange.com |
You need to check that your friend, Bob, has your correct phone number, but you cannot ask him directly. You must write the question on a card which and give it to Eve who will take the card to Bob and return the answer to you. What must you write on the card, besides the question, to ensure Bob can encode the message ... | 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, th... | https://api.stackexchange.com |
Before, the concept of imaginary numbers, the number $i = \sqrt{-1}$ was shown to have no solution among the numbers that we had. So we declared $i$ to be a new type of number. How come we don't do the same for other "impossible" equations, such as
$x = x + 1$, or $x = 1/0$?
Edit:
OK, a lot of people have said that a n... | 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 i... | https://api.stackexchange.com |
I was comparing a few of my codes to "stock" MATLAB codes. I am surprised at the results.
I ran a sample code (Sparse Matrix)
n = 5000;
a = diag(rand(n,1));
b = rand(n,1);
disp('For a\b');
tic;a\b;toc;
disp('For LU');
tic;LULU;toc;
disp('For Conj Grad');
tic;conjgrad(a,b,1e-8);toc;
disp('Inv(A)*B');
tic;inv(a)*b;toc;
... | 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... | https://api.stackexchange.com |
Spring cleaning, and I'm trying to get power supplies for all my devices with missing power supplies. They're all the typical barrel power connector, and I'm having a dickens of a time trying to figure out the pin/hole diameter.
I ordered the power supplies I needed based on outside diameter (e.g., 5.5mm in my exampl... | 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 | https://api.stackexchange.com |
I hesitate to ask this question, but I read a lot of the career advice from MathOverflow and math.stackexchange, and I couldn't find anything similar.
Four years after the PhD, I am pretty sure that I am going to leave academia soon. I do enjoy teaching and research, but the alpha-maleness, massive egos and pressure t... | 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 scho... | https://api.stackexchange.com |
I did a big cleanup of my collection of parts today and I now have a big pile of parts on my desk (the majority of which is resistors). My previous method of finding the resistor value I wanted was to look through my little box and read the colour codes. Unfortunately I now have a lot of resistors, making an individua... | 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... | https://api.stackexchange.com |
In Hofstadter's Gödel, Escher, Bach: An Eternal Golden Braid (GEB), the following claim appears:
...in the species Felis catus, deep probing has revealed that it is indeed possible to read the phenotype directly off the genotype. The reader will perhaps better appreciate this remarkable fact after directly examining t... | 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 seque... | https://api.stackexchange.com |
This question got me thinking about amino acids and the ambiguity in the genetic code. With 4 nucleotides in RNA and 3 per codon, there are 64 codons. However, these 64 codons only code for 20 amino acids (or 22 if you include selenocysteine and pyrrolysine), so many of the amino acids are coded by multiple codons.
Is ... | 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 es... | https://api.stackexchange.com |
In most introductory algorithm classes, notations like $O$ (Big O) and $\Theta$ are introduced, and a student would typically learn to use one of these to find the time complexity.
However, there are other notations, such as $o$, $\Omega$ and $\omega$. Are there any specific scenarios where one notation would be prefer... | 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 a... | https://api.stackexchange.com |
I was discussing this with my brother. I'm pretty sure I read somewhere that they can move.
Thanks
EDIT: By movement I mean long distance migration (preferably within the brain only). | 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 ... | https://api.stackexchange.com |
Why does cutting onions cause tears? From a couple of sites, I found that it is because of sulfuric acid produced by onions. But I could not find more details. What is the biochemical pathway by which onions cause tears? Also, which compound is responsible for it? If it is enzyme-catalyzed reaction, can we just stop t... | 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-pr... | https://api.stackexchange.com |
Typically, people call viruses some kind of organic compounds that cannot reproduce autonomously and which lower the fitness of their hosts. Even the word "virus" means "venom" in Latin.
But from the perspective of natural selection, one would expect those organic compounds that cannot reproduce autonomously, but which... | 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 ef... | https://api.stackexchange.com |
I know that bond angle decreases in the order $\ce{H2O}$, $\ce{H2S}$ and $\ce{H2Se}$. I wish to know the reason for this. I think this is because of the lone pair repulsion but how? | 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 tha... | https://api.stackexchange.com |
We learned about the class of context-free languages $\mathrm{CFL}$. It is characterised by both context-free grammars and pushdown automata so it is easy to show that a given language is context-free.
How do I show the opposite, though? My TA has been adamant that in order to do so, we would have to show for all gramm... | 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 interes... | https://api.stackexchange.com |
Principal component analysis (PCA) is usually explained via an eigen-decomposition of the covariance matrix. However, it can also be performed via singular value decomposition (SVD) of the data matrix $\mathbf X$. How does it work? What is the connection between these two approaches? What is the relationship between SV... | 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 = \m... | https://api.stackexchange.com |
We touched on introns and exons in my bio class, but unfortunately we didn't really talk about why Eukaryotes have introns. It would seem they would have to have some purpose since prokaryotes do not have them and they evolved first chronologically, but I could easily be wrong. Did the junk sections of DNA just evolve ... | 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... | https://api.stackexchange.com |
Setup:
The way a gecko's feet function has been a captivating but now relatively well understood phenomenon. They have many small spatula on the feet that exploit electromagnetic van-der-Waals forces on the walls to which they stick.
This concept has been developed in "nano-tape" a product which is adhesive the same wa... | 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... | https://api.stackexchange.com |
The video “How Far Can Legolas See?” by MinutePhysics recently went viral. The video states that although Legolas would in principle be able to count $105$ horsemen $24\text{ km}$ away, he shouldn't have been able to tell that their leader was very tall.
I understand that the main goal of MinutePhysics is mostly educa... | 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, o... | https://api.stackexchange.com |
Converting regular expressions into (minimal) NFA that accept the same language is easy with standard algorithms, e.g. Thompson's algorithm. The other direction seems to be more tedious, though, and sometimes the resulting expressions are messy.
What algorithms are there for converting NFA into equivalent regular expre... | 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... | https://api.stackexchange.com |
I have a set of BAM files that are aligned using the NCBI GRCh37 human genome reference (with the chromosome names as NC_000001.10) but I want to analyze it using a BED file that has the UCSC hg19 chromosome names (e.g. chr1). I want to use bedtools to pull out all the on-target and off-target reads.
Are NCBI and UCSC... | 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... | https://api.stackexchange.com |
From what I have found, a very large amount of protocols that travel over the internet are "text-based" rather than binary. The protocols in question include, but are not limited to HTTP, SMTP, FTP (I think this one is all text-based?), WHOIS, IRC.
In fact, some of these protocols jump through some hoops whenever they ... | 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/encod... | https://api.stackexchange.com |
My son Horatio (nine years old, fourth grade) came home with some fun math homework exercises today. One of his problems was the following little question:
I am thinking of a number...
It is prime.
The digits add up to $10.$
It has a $3$ in the tens place.
What is my number?
Let us assume that the problem refers... | 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... | https://api.stackexchange.com |
What would seem to be a silly question actually does have some depth to it. I was trying to scoop out some of my favorite soft name-brand ice cream when I noticed it was frozen solid, rather than its usual creamy consistency. After leaving it out for 10 minutes, it was nice and creamy again.
Notably, that amount of tim... | 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 complic... | https://api.stackexchange.com |
Can someone explain this to me by drawing resonance structures for the cyclopropylmethyl carbocation please?
Also one more question, is the tricyclopropylmethyl carbocation more stable than tropylium ion? | 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... | https://api.stackexchange.com |
Bowtie2 is probably the most widely used aligner because of it's speed. Burrow-wheeler (BW) algorithms (including bwa) tend to be faster. However, they have limitations when it comes to aligning very short reads (e.g. gRNA). Also, setting maximum number of mismatches allowed is complicated by the seed length, overlaps ... | 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... | https://api.stackexchange.com |
When comparing o,m,p-toluidine basicities, the ortho effect is believed to explain why o-toluidine is weaker. But when comparing o,m,p-toluic acid basicities, the ortho effect is stated as a reason why o-toluic acid is stronger acid. I was told that the ortho effect is a phenomenon in which an ortho- group causes steri... | 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 o... | https://api.stackexchange.com |
I am fairly new to DSP, and have done some research on possible filters for smoothing accelerometer data in python. An example of the type of data Ill be experiencing can be seen in the following image:
Essentially, I am looking for advice as to smooth this data to eventually convert it into velocity and displacement.... | 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... | https://api.stackexchange.com |
I have been observing my cat and found that when confronted with an unknown item, she will always use her front left paw to touch it.
This has me wondering if animals exhibit handedness like humans do? (and do I have a left handed cat?)
One note of importance is that with an unknown item, her approach is always identic... | 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 man... | https://api.stackexchange.com |
My youngest son is in $6$th grade. He likes to play with numbers. Today, he showed me his latest finding. I call it his "Sum of Some" because he adds up some selected numbers from a series of numbers, and the sum equals a later number in that same series. I have translated his finding into the following equation:
$$(10... | Factor out the $2^n$ and you get: $2^n (100+20+8) = 2^n 128 = 2^{n+7}$ since $2^7 = 128$ | https://api.stackexchange.com |
If $A$ and $B$ are square matrices such that $AB = I$, where $I$ is the identity matrix, show that $BA = I$.
I do not understand anything more than the following.
Elementary row operations.
Linear dependence.
Row reduced forms and their relations with the original matrix.
If the entries of the matrix are not from a... | 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 transf... | https://api.stackexchange.com |
In an answer to a previous question, it was stated that one should
zero-pad the input signals (add zeros to the end so that at least half of the wave is "blank")
What's the reason for this? | 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... | https://api.stackexchange.com |
My colleague and I have developed a software tool intend to release it open-source. This tool is specifically for tasks in bioinformatics but we think it would be helpful for the wider community. Our institution will permit us to release it provided we get appropriate credit.
Thus we wish to publish it in peer-review. ... | 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.... | https://api.stackexchange.com |
Given the following:
bruises are caused by minor trauma which breaks blood vessels beneath the skin, causing bleeding
the mechanism by which bleeding stops is clotting
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... | 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... | https://api.stackexchange.com |
I've been trying to design a charging system for a small robot powered by a 2S 20C lithium polymer (LiPo) battery. Were I to trust everything I read online, I would believe that the LiPo will kill me in my sleep and steal my life savings. The common advice I read, if you are brave enough to use LiPo batteries, is "neve... | 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... | https://api.stackexchange.com |
What is the preferred and efficient approach for interpolating multidimensional data?
Things I'm worried about:
performance and memory for construction, single/batch evaluation
handling dimensions from 1 to 6
linear or higher-order
ability to obtain gradients (if not linear)
regular vs scattered grid
using as Interpol... | 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:
... | https://api.stackexchange.com |
Consider the question, "What is a photon?". The answers say, "an elementary particle" and not much else. They don't actually answer the question. Moreover, the question is flagged as a duplicate of, "What exactly is a quantum of light?" – the answers there don't tell me what a photon is either. Nor do any of the answe... | The word photon is one of the most confusing and misused words in physics. Probably much more than other words in physics, it is being used with several different meanings and one can only try to find which one is meant based on the source and context of the message.
The photon that spectroscopy experimenter uses to ex... | https://api.stackexchange.com |
The shift theorem says:
Multiplying $x_n$ by a linear phase $e^{\frac{2\pi i}{N}n m}$ for some integer m corresponds to a circular shift of the output $X_k$: $X_k$ is replaced by $X_{k-m}$, where the subscript is interpreted modulo N (i.e., periodically).
Ok, that works fine:
plot a
N = 9
k = [0, 1, 2, 3, 4, 5, 6, ... | If you want the shifted output of the IFFT to be real, the phase twist/rotation in the frequency domain has to be conjugate symmetric, as well as the data. This can be accomplished by adding an appropriate offset to your complex exp()'s exponent, for the given phase slope, so that the phase of the upper (or negative) ... | https://api.stackexchange.com |
As far as I can tell, the two big generic US Department of Energy computational science software frameworks are PETSc and Trilinos. They seem similar at first glance, beyond differences in language (C versus C++). What are the main differences between the two frameworks, and what factors should influence choosing one ... | There are huge differences in culture, coding style, and capabilities. Probably the fundamental difference is Trilinos tries to provide an environment for solving FEM problems and PETSc provides an environment for solving sparse linear algebra problems.
Why is that significant?
Trilinos will provide a large number o... | https://api.stackexchange.com |
I was very surprised when I started to read something about non-convex optimization in general and I saw statements like this:
Many practical problems of importance are non-convex, and most
non-convex problems are hard (if not impossible) to solve exactly in a
reasonable time. (source)
or
In general it is NP-har... | The misunderstanding lies in what constitutes "solving" an optimization problem, e.g. $\arg\min f(x)$. For mathematicians, the problem is only considered "solved" once we have:
A candidate solution: A particular choice of the decision variable $x^\star$ and its corresponding objective value $f(x^\star)$, AND
A proof o... | https://api.stackexchange.com |
How should I route USB Connector shield on PCB? Should it be connected to GND plane right where USB is placed, or should the shield be isolated from GND, or should it be connected to ground through ESD protection chip, high resistance resistor or fuse?
PS. Should I put the shield connections on schematic, or just rout... | For the shield to be effective, it requires as low impedance connection as possible to your shield ground. I think those recommending resistors, or not connecting it to ground at all, or strictly talking about your digital logic ground, and assuming you have a separate shield ground. If you have a metal enclosure, th... | https://api.stackexchange.com |
The recent news about a new supermassive virus being discovered got me thinking about how we define viruses as non-living organisms whilst they are bigger than bacteria, and much more complex than we first gave them credit for.
What biological differences between viruses and cellular organisms have made viruses be dee... | If this is a topic that really interests you, I'd suggest searching for papers/reviews/opinions written by Didier Raoult. Raoult is one of the original discoverers of the massive Mimivirus and his work will lead you to some truly fascinating discussions that I couldn't hope to reproduce here.
The main argument for why... | https://api.stackexchange.com |
I was trying to explain to someone that C is Turing-complete, and realized that I don't actually know if it is, indeed, technically Turing-complete. (C as in the abstract semantics, not as in an actual implementation.)
The "obvious" answer (roughly: it can address an arbitrary amount of memory, so it can emulate a RAM... | I'm not sure but I think the answer is no, for rather subtle reasons. I asked on Theoretical Computer Science a few years ago and didn't get an answer that goes beyond what I'll present here.
In most programming languages, you can simulate a Turing machine by:
simulating the finite automaton with a program that uses a... | https://api.stackexchange.com |
According to Wikipedia, if a system has $50\%$ chance to be in state $\left|\psi_1\right>$ and $50\%$ to be in state $\left|\psi_2\right>$, then this is a mixed state.
Now, consider the state
$$\left|\Psi\right>=\frac{\left|\psi_1\right>+\left|\psi_2\right>}{\sqrt{2}},$$ which is a superposition of the states $\left|\... | The state
\begin{equation}
|\Psi \rangle = \frac{1}{\sqrt{2}}\left(|\psi_1\rangle +|\psi_2\rangle \right)
\end{equation}
is a pure state. Meaning, there's not a 50% chance the system is in the state $|\psi_1\rangle$ and a 50% it is in the state $|\psi_2\rangle$. There is a 0% chance that the system is in either of thos... | https://api.stackexchange.com |
I have the following data of fragment counts for each gene in 16 samples:
> str(expression)
'data.frame': 42412 obs. of 16 variables:
$ sample1 : int 4555 49 122 351 53 27 1 0 0 2513 ...
$ sample2 : int 2991 51 55 94 49 10 55 0 0 978 ...
$ sample3 : int 3762 28 136 321 94 12 15 0 0 2181 ...
$ sample4 : int 4... | First off,
Don’t use RPKMs.
They are truly deprecated because they’re confusing once it comes to paired-end reads. If anything, use FPKMs, which are mathematically the same but use a more correct name (do we count paired reads separately? No, we count fragments).
Even better, use TPM (= transcripts per million), or an ... | https://api.stackexchange.com |
In this answer it is mentioned
A regular language can be recognized by a finite automaton. A context-free language requires a stack, and a context sensitive language requires two stacks (which is equivalent to saying it requires a full Turing machine).
I wanted to know regarding the truth of the bold part above. Is i... | Two bits to this answer;
Firstly, the class of languages recognised by Turing Machines is not context sensitive, it's recursively enumerable (context sensitive is the class of languages you get from linear bound automata).
The second part, assuming we adjust the question, is that yes, a two-stack PDA is as powerful as ... | https://api.stackexchange.com |
Given a real function of real variables, is there software available that can automatically generate numerically-accurate code to calculate the function over all inputs on a machine equipped with IEEE 754 arithmetic?
For example, if the real function to be evaluated were:
The software would consider catastrophic cance... | The best solution that I know of is to program the symbolic expressions in Mathematica, Maple, or SymPy; all of the links go directly to the code generation documentation. All of the programs above can generate code in C or Fortran.
None of the programs above mentions accuracy in IEEE 754 arithmetic; in general, it wou... | https://api.stackexchange.com |
Why are solderless protoboards called "breadboards"? I've used the term for decades but couldn't answer a student's question about the name. | This terminology goes waaaaay back to the days of vacuum tubes.
Generally, you would mount a number of tube-sockets on standoffs to a piece of wood (the actual "breadboard"), and do all the wiring with point-point wire and the components just hanging between the various devices.
If you needed additional connection poin... | https://api.stackexchange.com |
Rather basic, I'm afraid, but when would you use a relay, and when would you use a transistor? In a relay the contacts wear out, so why are relays used at all? | Relays offer complete isolation between the activating circuit and the load.
They can switch AC and DC, and be activated by AC or DC.
They can be very robust.
They also have the advantage that one can often see if the device is actuated, and one can even hear the actuation in many cases. | https://api.stackexchange.com |
In the calculus of variations, particularly Lagrangian mechanics, people often say we vary the position and the velocity independently. But velocity is the derivative of position, so how can you treat them as independent variables? | Unlike your question suggests, it is not true that velocity is varied independently of position. A variation of position $q \mapsto q + \delta q$ induces a variation of velocity $\partial_t q \mapsto \partial_t q + \partial_t (\delta q)$ as you would expect.
The only thing that may seem strange is that $q$ and $\partia... | https://api.stackexchange.com |
It is commonly asserted that no consistent, interacting quantum field theory can be constructed with fields that have spin greater than 2 (possibly with some allusion to renormalization). I've also seen (see Bailin and Love, Supersymmetry) that we cannot have helicity greater than 1, absenting gravity. I am yet to see ... | Higher spin particles have to be coupled to conserved currents, and there are no conserved currents of high spin in quantum field theories. The only conserved currents are vector currents associated with internal symmetries, the stress-energy tensor current, the angular momentum tensor current, and the spin-3/2 supercu... | https://api.stackexchange.com |
What can go wrong when using preconditoned Krylov methods from KSP (PETSc's linear solver package) to solve a sparse linear system such as those obtained by discretizing and linearizing partial differential equations?
What steps can I take to determine what is going wrong for my problem?
What changes can I make to succ... | Initial advice
Always run with -ksp_converged_reason -ksp_monitor_true_residual when trying to learn why a method is not converging.
Make the problem size and number of processes as small as possible to demonstrate the failure. You often gain insight by determining what small problems exhibit the behavior that is caus... | https://api.stackexchange.com |
I work in computational science, and as a result, I spend a non-trivial amount of my time trying to increase the scientific throughput of many codes, as well as understanding the efficiency of these codes.
Let's assume I have evaluated the performance vs. readability/reusability/maintainability tradeoff of the software... | First of all, as skillman and Dan have pointed out, profiling is essential. I personally use Intel's VTune Amplifier on Linux as it gives me a very fine-grained overview of where time was spent doing what.
If you're not going to change the algorithm (i.e. if there will be no major changes that will turn all your optimi... | https://api.stackexchange.com |
What is the difference between a matrix and a tensor? Or, what makes a tensor, a tensor? I know that a matrix is a table of values, right? But, a tensor? | Maybe to see the difference between rank 2 tensors and matrices, it is probably best to see a concrete example. Actually this is something which back then confused me very much in the linear algebra course (where we didn't learn about tensors, only about matrices).
As you may know, you can specify a linear transformati... | https://api.stackexchange.com |
In a book of word problems by V.I Arnold, the following appears:
The hypotenuse of a right-angled triangle (in a standard American examination) is $10$ inches, the altitude dropped onto it is 6 inches. Find the area of the triangle.
American school students had been coping successfully with this problem for over... | There is no such right triangle. The maximum possible altitude is half the hypotenuse (inscribe the triangle into a circle to see this), which here is $5$ inches. You would only get $30$ square inches if you tried to compute the area without checking whether the triangle actually exists. | https://api.stackexchange.com |
I know that bit-wise operations are so fast on modern processors, because they can operate on 32 or 64 bits on parallel, so bit-wise operations take only one clock cycle. However addition is a complex operation that consists of at least one and possibly up to a dozen bit-wise operations, so I naturally thought it will ... | Addition is fast because CPU designers have put in the circuitry needed to make it fast. It does take significantly more gates than bitwise operations, but it is frequent enough that CPU designers have judged it to be worth it. See
Both can be made fast enough to execute within a single CPU cycle. They're not equal... | https://api.stackexchange.com |
I read in some places that music is mostly sampled at 44.1 kHz whereas we can only hear up to 20 kHz. Why is it? | The sampling rate of a real signal needs to be greater than twice the signal bandwidth. Audio practically starts at 0 Hz, so the highest frequency present in audio recorded at 44.1 kHz is 22.05 kHz (22.05 kHz bandwidth).
Perfect brickwall filters are mathematically impossible, so we can't just perfectly cut off frequen... | https://api.stackexchange.com |
I'm not sure where this question should go, but I think this site is as good as any.
When humankind started out, all we had was sticks and stones. Today we have electron microscopes, gigapixel cameras and atomic clocks. These instruments are many orders of magnitude more precise than what we started out with and they r... | I work with an old toolmaker who also worked as a metrologist who goes on about this all day.
It seems to boil down to exploiting symmetries since the only way you can really check something is against itself.
Squareness:
For example, you can check a square by aligning one edge to the center of straight edge and tracin... | https://api.stackexchange.com |
I am looking for a tool to visualize very large directional link graphs.
I currently have ~2million nodes with ~10million edges. I have tried a few different things, but most take hours to even do 100k node graphs
What I have tried:
I spent a day with gephi, but 80K nodes take about an hour to add and the application b... | Graphviz should work. I believe that the images associated with the matrices in the University of Florida sparse matrix collection were visualized using sfdp, a force-directed graph visualization algorithm developed by Yifan Hu. Most of the matrices in the collection have a computational time associated with generating... | https://api.stackexchange.com |
Bit of a strange question, but what is it? My physics teacher said it was kind of like a "push" that pushes electrons around the circuit. Can I have a more complex explanation? Any help is much appreciated. | Your teacher was right.
Current is electric charges (usually electrons) moving. They don't do that by themselves for no reason, no more so than a shopping cart moves across the floor of a store by itself. In physics, we call the force that pushes charges the electromotive force, or "EMF". It is almost always express... | https://api.stackexchange.com |
The pH of pure liquid water depends on temperature. It is about pH = 7.0 at room temperature, pH = 6.1 at 100 °C, and pH = 7.5 at 0 °C. What happens to the pH (or to the ion product) of pure water when it freezes?
I assume that the proton transfer reactions
$$\ce{2H2O <=> H3O+ + OH-}$$
$$\ce{H3O+ + H2O <=> H2O + H3O+}... | According to Martin Chaplin's Water Dissociation and pH:
In ice, where the local hydrogen bonding rarely breaks to separate the constantly forming and re-associating ions, the dissociation constant is much lower (for example at $-4~\mathrm{^\circ C}$, $K_\mathrm{w} = 2 \times 10^{-20}~\mathrm{mol^2~L^{-2}}$).
So $[\... | https://api.stackexchange.com |
Does there exist a set of programming language constructs in a programming language in order for it to be considered Turing Complete?
From what I can tell from wikipedia, the language needs to support recursion, or, seemingly, must be able to run without halting. Is this all there is to it? | I always though that $\mu$-recursive functions nailed it. Here is what defines the whole set of computable functions; it is the smallest set of functions containing resp. closed against:
The constant $0$ function
The successor function
Selecting parameters
Function composition
Primitive Recursion
The $\mu$-operator (l... | https://api.stackexchange.com |
Reading discussions of the recent quantum supremacy experiment by Google I noticed that a lot of time and effort (in the experiment itself, but also in the excellent blog posts by Scott Aaronson and others explaining the results) is spent on verifying that the quantum computer did indeed compute the thing we believe it... | there exist problems that are hard to solve, but for which it is easy to verify the validity of a given solution: the so called NP problems.
This statement is wrong. There are many NP problems which are easy to solve. "NP" simply means "easy to verify". It does not mean hard to solve.
What you are probably thinking of... | https://api.stackexchange.com |
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