text:
# Tag Info

## Hot answers tagged performance

18

Post-quantum security: As you note, quantum attacks are not known to break lattice-based cryptosystems. But some other proposals like McEliece, as well as most symmetric primitives are not known to be poly-time breakable on a quantum computer. Security from worst case assumptions: In security proofs for cryptosystems we typically assume that some problem ...

16

Contrary to the other answer, I'll be assuming the hash function is of the password-oriented kind; and my answer will be: input size has almost no influence on speed in good practice, even for much longer input than in the question. Password-oriented (or entropy-stretching, key-stretching) hash functions are, for example, suitable to transform a (password, ...

16

There are two important differences between AES-128 and AES-256: AES-128 has 10 rounds, AES-256 has 14 The key expansion process (that is, how they generate subkeys) is different If your AES-128 encryption hardware just takes a plaintext block and a 128 bit key, and produces a ciphertext block, well, no, there's not much you can do. In this case, the ...

12

The security level of an elliptic curve group is approximately $\log_2{0.886\sqrt{2^n}}$. You can use this to approximate the security level of a $n$-bit key, eg: $\log_2{0.886\sqrt{2^{571}}} = 285.32537860389294$ The real computation (at least for curves over a finite field defined by a prime $p$) is $\log_2{\sqrt{\pi/4}\sqrt{ℓ}}$, where $ℓ$ is the ...

11

Bitslicing is a technique where a computation is Reduced to elementary operations (called gates) with two bit inputs (typically NOR, XOR, and similar like OR AND NAND NXOR), rather than operations on words or integers spanning several bits. Executed in parallel, with as many simultaneous instances (on a single CPU) as there are bits in some register kind, ...

9

The fastest block cipher is identity, which leaves input blocks completely unchanged. This is infinitely fast on all platforms; however, it is not secure. So maybe you want the fastest block cipher that still offers some given non-trivial level of security? Then it depends a lot on what you want to implement the block cipher on. With recent PC, you would ...

8

ECDSA should in general create signatures faster than RSA for the same cryptographic strength if you just look at the mathematics. In the end the modular exponentiation is performed for smaller numbers. However, ECDSA depends on a random number generator, so ECDSA speeds may be slower if the random number generator blocks for any reason (and not using a good ...

8

It depends. Specifically, it depends on the type of cipher, and on the way it's used. For stream ciphers like RC4, and for block ciphers like AES in CTR and OFB modes, decryption is effectively identical to encryption, and thus takes the exact same time. (Minor exception: encryption may require generating a unique nonce / IV, which might take a small ...

8

"Cycles" are CPU instruction cycles. Cycles per byte roughly measures how many instructions, in a given instruction set, are needed to produce each byte of output. They're a reasonably-good relative measure of the performance of different algorithms. Generally, when you measure an algorithm's cycles per byte, you use carefully controlled conditions. You ...

8

The basic idea of bitslicing, or SIMD within a register, involves two parts: expressing the cipher in terms of single-bit logical operations (AND, OR, XOR, NOT, etc.), as if you were implementing it in hardware, and carrying out those operations for multiple instances of the cipher in parallel, using bitwise operations on a CPU. That is, in a bitsliced ...

8

It depends how the “AES-128 encryption hardware units” you mention are actually defined. I've already encountered processors that allow to independently compute AES operations such as $\texttt{SubBytes}$ and $\texttt{MixColumns}$ – which are the same regardless the key size involved (128 or 256 bits). In that case: yes, it can speed up the calculation for ...

7

325 MB/s is already good, i.e. you will not get much more with another implementation. Also, SHA-1 is a sequential algorithm, so multiple cores or a GPU will not help you. Specialized hardware is probably your best bet to make SHA-1 faster. (Also, if SHA-1 is the bottleneck then you are able to move data around faster than that, which is impressive; usually,...

7

Yes, AES-128 is intended to be the standard block cipher for building a secure and efficient symmetric cryptosystem using some block cipher operating mode, like CTR for encryption or GCM for authenticated encryption; efficiency can be particularly good when there is hardware support for AES and GCM. There might be better choices in the case at hand, like ...

7

All hashes I know of are block oriented. The time required to calculate the hash scales with the number of blocks to be hashed. There is a small constant overhead dealing with the IV and, possibly, a finalization function.

7

Is Rijndael the fastest block cipher in the world? No. On an Intel 64 Sandy Bridge without AES-NI, AES (a subset of Rijndael) is outperfomed by ChaCha20 (and also likely by Threefish 512 which has about 6-7cpb cost on an older Intel Core 2 Duo with 64-bit ASM (link: original Skein paper PDF)) as opposed to AES' 11 cpb. (7.59 cpb on an Intel Core 2) ...

6

From the diagram on CTR mode you can notice that there are no dependencies between any of the phases of the pipeline. If you have more than one block-size worth of data, you can process each block-size chunk completely independently of the others by calculating $\mathrm{ciphertext}_i = E(\mathrm{key}, \mathrm{nonce} \, || \, \mathrm{counter}_i) \oplus \... 6 In RSA encryption as practiced (that is, to encipher a message which is a short symmetric key), the message size after padding is fixed and equal to the modulus size. Thus the size of the message has no impact on performance. Calculating a modular inverse is performed only during key generation, that is seldom. Also, it has low cost compared to generating ... 6 Computations on elliptic curves are more efficient. Roughly speaking, when the base field has size$n$(for DH/ElGamal/DSA, the size in bits of the modulus$p$; for elliptic curves, the size of the field for point coordinates) and a "security level"$t$(e.g.$t = 80$for "80-bit security" as can be expected when using a 160-bit subgroup and a 160-bit hash ... 6 Given the choice, it is preferable to use the block encryption operation of AES, since it often faster than block decryption (never slower AFAIK). For this reason, AES-CTR is defined to use the block encryption operation of AES exclusively; that's both for AES-CTR encryption and AES-CTR decryption, which are the same operation except for IV generation/input. ... 6 Dedicated stream ciphers typically are, or at least can be, somewhat faster than constructions based on block ciphers. (If they weren't, there would be no point in using them, since a block cipher can do everything a dedicated stream cipher can.) What you gain in speed (and possibly code size), however, you lose in versatility: A block cipher (in CTR / ... 6 The previous answer has the correct formula for estimating the security level of prime field elliptic curves. However, the table seems to just list the closest Koblitz curve sizes used, as Richie Frame points out. If you computed the actual security strength of the curves in question, you would not end up with exactly the values in the left column. For ... 6 If you are using the full HKDF each time, you could possibly save time by only using the Extract portion once and Expand once per derived key. That could even halve the total time taken, if you had a worst case situation. Another speedup possibility within HKDF is to use another hash. Either a faster hash or one that matches the required key length better. ... 5 A "general computer" simply doesn't exist, test for yourself with this command: openssl speed rsa As an example here is the output on a Mac Pro 2007 withIntel Xeon 5130: Doing 512 bit private rsa's for 10s: 67450 512 bit private RSA's in 9.95s Doing 512 bit public rsa's for 10s: 961891 512 bit public RSA's in 9.94s Doing 1024 bit private rsa's for 10s: ... 5 Predicting speed by looking at the assembly is hard, especially since processors do all sorts of tricks which have memory (e.g. branch prediction). So yes, this is all about measuring. There is an art to it; for instance, you would rather repeatedly encrypt the same relatively small buffer (4 or 8 kB) so as to avoid cache effects. One method is to do the ... 5 They measure it. Once upon a time, CPUs were simple enough that you really code compute the amount of time for a stretch of code by looking up the clocks per instruction in the manual, add them all together, and that'd be the total time. However, CPU manufacturers have added more and more optimizations and parallelism; this makes the CPUs run faster (for ... 5 Pretty much all modern encryption systems (including AES, in any standard mode) are data-agnostic: they are designed to encrypt any byte (or bit) stream regardless of its content, and their performance does not depend in any way on what the stream contains. Indeed, if this were not the case, that would open the encryption scheme to timing attacks — if ... 5 Bitslicing is a technique that allows multiple instructions/Data points to be encoded into a single register. The idea is that you encode several bitwise operations within a single register. So, instead of 32 bitwise OR operations in sequence, you could reduce the total number of operations by cramming the data into SIMD registers and executing in ... 5 Rabin-Williams signature verification with 3072 bit keys is much faster than EdDSA signature verification of comparable security (when done in software). How much depends on care of coding, hardware, EdDSA parameters. Two data points: in the eBATS benchmarks for a skylake CPU, ronald3072 signature verification (RSA with$e=3\$ as an OpenSSL wrapper, by ...

4

The performance bottleneck with RSA is the modular exponentiation operation. On the other hand, if you are interested in public key encryption performance, perhaps RSA is not the correct tool. RSA is actually fairly fast during its encryption operation; however it is quite slow during the decryption. If you care about decryption performance, you may want ...

4

For free software-based solutions on an x86_64, OpenSSL is the best around. Intel's IPP is purported to be 20% faster, and it's software-only, but it's not free (about 200USD, or 80USD for the academic version) and you have to fill out a form saying you're not from N. Korea, etc. There are hardware accelerators in the form of SSL cards/chips, but are ...

Only top voted, non community-wiki answers of a minimum length are eligible


text:
## Increased single-nucleotide discrimination of PCR by primer probes bearing hydrophobic 4'C modifications

2004
##### Authors
Strerath, Michael
Gaster, Jens
Journal article
##### Published in
ChemBioChem ; 5 (2004), 3. - pp. 333-339. - ISSN 1439-4227
##### Abstract
We report on significantly increased selectivity of real-time PCR through employment of primer probes that bear hydrophobic 4'C modifications at the 3'-terminal nucleotide. The primer probes were designed to bind the target sequences in such a way that the 3'-terminal nucleotide defines whether a matched or a single mismatched basepair is present depending on the respective target sequence. Several commercially available thermostable DNA polymerases belonging to different DNA polymerase families were tested for their efficacy in discriminating between PCR amplification of matched substrates and duplexes that contain a single mismatch. It turned out that, depending on the 4'C modification and the employed DNA polymerase, significantly increased differentiation between single matches and mismatches could be observed with real-time PCR. The degrees of the observed effects varied with the employed 4'C modification and the sequence context studied. The system is robust enough to work faithfully under several buffer conditions. Our approach should be useful for the direct diagnosis of single nucleotide variations within genes, like single nucleotide polymorphisms or mutations, by PCR without the need for further time- and cost-intensive post-PCR analysis.
540 Chemistry
##### Cite This
ISO 690STRERATH, Michael, Jens GASTER, Daniel SUMMERER, Andreas MARX, 2004. Increased single-nucleotide discrimination of PCR by primer probes bearing hydrophobic 4'C modifications. In: ChemBioChem. 5(3), pp. 333-339. ISSN 1439-4227. Available under: doi: 10.1002/cbic.200300757
BibTex
@article{Strerath2004-03-05Incre-351,
year={2004},
doi={10.1002/cbic.200300757},
title={Increased single-nucleotide discrimination of PCR by primer probes bearing hydrophobic 4'C modifications},
number={3},
volume={5},
issn={1439-4227},
journal={ChemBioChem},
pages={333--339},
author={Strerath, Michael and Gaster, Jens and Summerer, Daniel and Marx, Andreas}
}

RDF
<rdf:RDF
xmlns:dcterms="http://purl.org/dc/terms/"
xmlns:dc="http://purl.org/dc/elements/1.1/"
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:bibo="http://purl.org/ontology/bibo/"
xmlns:dspace="http://digital-repositories.org/ontologies/dspace/0.1.0#"
xmlns:foaf="http://xmlns.com/foaf/0.1/"
xmlns:void="http://rdfs.org/ns/void#"
xmlns:xsd="http://www.w3.org/2001/XMLSchema#" >
<dc:creator>Strerath, Michael</dc:creator>
<dcterms:issued>2004-03-05</dcterms:issued>
<dc:creator>Summerer, Daniel</dc:creator>
<dcterms:rights rdf:resource="https://rightsstatements.org/page/InC/1.0/"/>
<dcterms:bibliographicCitation>First publ. in: ChemBioChem : a European journal of chemical biology 5 (2004), 3, pp. 333–339</dcterms:bibliographicCitation>
<dcterms:abstract xml:lang="eng">We report on significantly increased selectivity of real-time PCR through employment of primer probes that bear hydrophobic 4'C modifications at the 3'-terminal nucleotide. The primer probes were designed to bind the target sequences in such a way that the 3'-terminal nucleotide defines whether a matched or a single mismatched basepair is present depending on the respective target sequence. Several commercially available thermostable DNA polymerases belonging to different DNA polymerase families were tested for their efficacy in discriminating between PCR amplification of matched substrates and duplexes that contain a single mismatch. It turned out that, depending on the 4'C modification and the employed DNA polymerase, significantly increased differentiation between single matches and mismatches could be observed with real-time PCR. The degrees of the observed effects varied with the employed 4'C modification and the sequence context studied. The system is robust enough to work faithfully under several buffer conditions. Our approach should be useful for the direct diagnosis of single nucleotide variations within genes, like single nucleotide polymorphisms or mutations, by PCR without the need for further time- and cost-intensive post-PCR analysis.</dcterms:abstract>
<bibo:uri rdf:resource="http://kops.uni-konstanz.de/handle/123456789/351"/>
<dspace:isPartOfCollection rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/52"/>
<dc:format>application/pdf</dc:format>
<dcterms:title>Increased single-nucleotide discrimination of PCR by primer probes bearing hydrophobic 4'C modifications</dcterms:title>
<void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/>
<dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2011-07-04T16:49:34Z</dcterms:available>
<dcterms:hasPart rdf:resource="https://kops.uni-konstanz.de/bitstream/123456789/351/1/Summerer.pdf"/>
<dc:contributor>Marx, Andreas</dc:contributor>
<foaf:homepage rdf:resource="http://localhost:8080/"/>
<dc:creator>Marx, Andreas</dc:creator>
<dc:contributor>Strerath, Michael</dc:contributor>
<dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2011-07-04T16:49:34Z</dc:date>
<dc:creator>Gaster, Jens</dc:creator>
<dspace:hasBitstream rdf:resource="https://kops.uni-konstanz.de/bitstream/123456789/351/1/Summerer.pdf"/>
<dcterms:isPartOf rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/52"/>
<dc:language>eng</dc:language>
<dc:contributor>Summerer, Daniel</dc:contributor>
<dc:contributor>Gaster, Jens</dc:contributor>
<dc:rights>terms-of-use</dc:rights>
</rdf:Description>
</rdf:RDF>

Yes

format: plain


text:
Courses
Courses for Kids
Free study material
Free LIVE classes
More

# An equilateral triangle has its side of $3\sqrt 3 cm$, then the radius of its circumcircle is:(A) $3cm$ (B) $4cm$ (C) $2\sqrt 3 cm$ (D) $2cm$

Last updated date: 31st Mar 2023
Total views: 308.7k
Views today: 6.85k
Hint: If $a$ is the side of the equilateral triangle, then the circumradius of the equilateral triangle is $\dfrac{a}{{\sqrt 3 }}$.
If $a$ is the side of the equilateral triangle then according to the question, the side of the equilateral triangle is given as $3\sqrt 3$.
$\Rightarrow a = 3\sqrt 3$.
$\therefore$ And we know that the circumradius of an equilateral triangle
is $\dfrac{a}{{\sqrt 3 }}$. If $R$ is the circumradius, then we’ll get:
$\Rightarrow R = \dfrac{a}{{\sqrt 3 }}, \\ \Rightarrow R = \dfrac{{3\sqrt 3 }}{{\sqrt 3 }}, \\ \Rightarrow R = 3 \\$
Therefore, the radius of the circumcircle of the given equilateral triangle is $3cm$.
Note: In an equilateral triangle circumcenter, the incenter and centroid lies at the same point. If $a$ is the side of the triangle, then $\dfrac{{a\sqrt 3 }}{2}$ is its altitude. And centroid divides the altitude in the ratio $2$: $1$. Larger divided part is circumradius and the smaller part is inradius. Thus:
Circumradius $= \dfrac{a}{{\sqrt 3 }}$ and inradius $= \dfrac{a}{{2\sqrt 3 }}$.


text:
#### Question

Solve the cube root equation

\sqrt[3]{x+4} - \sqrt[3]{x-4} = 2

Collected in the board: Cube root

Steven Zheng posted 5 months ago

Let

a = \sqrt[3]{x+4}
(1)
b = \sqrt[3]{x-4}
(2)

Then

a - b = 2
(3)

Difference of a and b raised to the power of 3 gives

a^3 - b^3 = 8
(4)

Factor LHS using difference of cubes formula

(a - b)(a^2+ab+b^2) = 8
(5)

Substitute (3) to (5) and simplify

a^2+ab+b^2 = 4
(6)

Square of equation (3) gives

(a -b )^2 = 4

Expand LHS

a^2 - 2ab +b^2 = 4
(7)

Substract (7) from (6) and solve for ab

ab = \dfrac{1}{3}(\dfrac{2\cdot 4}{2} - 2^2 ) = 0
(8)

Substituting ab to (6) gives

a^2+b^2 = 4 - ab = 4
(9)

Construct a perfect square binomial with (9) and (8)

(a+b)^2 = a^2+b^2+2ab
(a+b)^2 = 4 +2\cdot 0 = 4

Taking square root of both sides gives

a +b = \pm2
(10)

Now we get two systems of equations

Case 1

\begin{cases} a+b = 2 \\ a - b =2 \end{cases}

which gives

\begin{cases} a= 2 \\ b =1 \end{cases}

Then

x = a^3 - 4 = 2^3 - 4 = 4

Case 2

\begin{cases} a+b = -2 \\ a - b =2 \end{cases}

which gives

\begin{cases} a= 0 \\ b =-2 \end{cases}

Then

x = a^3 - 4 = 0^3 - 4 = -4

In summary, we get two solutions for x.

x = 4 \text{ or }x = -4

Steven Zheng posted 5 months ago

Scroll to Top


text:
# Divisibility Rule for 11 Using Identity

Using the following identity: $11 \vert (10^m + (-1)^{m+1}), m \in \mathbb{N}$

Prove the divisibility rule for $11$. (If $11$ divides the alternating sum of digits in a number $n$, then it divides $n$.)

I find this easy to do using modular arithmetic but am struggling in using this identity to prove it.

• That's what I used to prove it earlier but it doesn't make use of the identity, or at least I am missing how it does – Uq'''12wn1F12u2x3uW31H1JBk9m Mar 21 '17 at 21:10
• Is this the idendity ? : $$11|10^m+(-1)^{m+1}$$ – Peter Mar 21 '17 at 21:12
• yes that is, I think I will have to take the alternating series of digits and transform it somehow into the sum of digits multiplied with powers of 10 to get n – Uq'''12wn1F12u2x3uW31H1JBk9m Mar 21 '17 at 22:19
• Hmmph, I'm not sure why I'd believe the identity without proving it. But .. well, use induction. – fleablood Mar 21 '17 at 23:06
• @fleablood I proved the identity earlier using induction. Now I have to prove the divisibility rule for 11 using that identity! – Uq'''12wn1F12u2x3uW31H1JBk9m Mar 21 '17 at 23:17

## 1 Answer

So "If 11 divides the alternating sum of digits in a number n" means if

$n = \sum_{i=0}^m a_i10^i$ then this is saying:

$11| \sum_{i=0}^m a_i(-1)^i$

So that means $11|\sum_{i=0}^m a_i(-1)^i - a_m(10^m + (-1)^m)= \sum_{i=0}^{m-1}a_i(-1)^i - a_m10^m$.

So that means $11|\sum_{i=0}^{m-1}a_i(-1)^i - a_m10^m - a_{m-1}(10^{m-1} + (-1)^{m-1}) = \sum_{i=0}^{m-2}(-1)^i a_i - \sum_{i= m-1}^m a_i10^i$

And via induction:

$11|\sum_{i= 0}^{m-k-1}(-1)^ia_i - \sum_{i=m-k}^m a_i*10^i$.

Keep going to get:

$11|- \sum_{i=0}^m a_i10^i= -n$ and so $11|n$.

Of, course, I don't know why on earth I'd believe the identity without proving it first.


text:
# How to find the area of a region bounded by a simple closed curve?

I have the following equation:

$$\frac{p}{(a-x)^2+y^2}+\frac{1-p}{(b-x)^2+y^2}=1 \text{ where } 0\leq p\leq 1$$ Which represent a simple close curve. Obviously, when $$p=0,p=1$$ or $$a=b$$ we recover a unit circle. However the shape of the curve is more interesting in the other cases. Here is an example for $$p=0.2$$, $$a=1$$ and $$b=0$$:

The area inside the curve is supposed to represent an uniform distribution, thus I suspect the area to be equal to one (unless I did a mistake!). However I don't know how to compute it. My attempt was to shift to polar coordinates and compute a double integral. However I have trouble determining the boundaries of these integrals.

Any hints or general advice are appreciated !

• The problem is trivial whenever $a=b,$ so the interest is in the opposite case. Aug 11 '19 at 12:37
• Yes, whether $a=b$ or $p=0$ or $p=1$ we recover a unit circle. So I am more interested in the other cases
– Matt
Aug 11 '19 at 12:39
• Better state this in the body of the question, then. Aug 11 '19 at 12:41
• The problem with using polar coordinates is that one gets a nontrivial quartic in $r,$ which is a heck of a work in order to extract the limits for $r.$ Of course, the limits of $\phi$ are trivial. So polar coordinates cannot be the way. Have you tried using an algebra system like WA? Aug 11 '19 at 12:45
• Thanks! What is an algebra system?
– Matt
Aug 11 '19 at 12:53

The $$xy$$-integration is still easier than the polar coordinates for this problem.

Due to $$y$$-symmetry, the integration is between the two intersection points with the $$x$$-axis, which can be obtained by setting $$y = 0$$ in the curve equation (for $$a=1$$, $$b=0$$) $$\frac{p}{(1-x)^2}+\frac{1-p}{x^2}=1$$ or $$x^4-2x^3+2(1-p)x-(1-p)=0$$ Unfortunately, for general value of $$p$$, it has to be solved numerically. In your example of $$p=0.2$$, it has two real roots as expected. Let $$x_1$$ and $$x_2$$ be the two roots to be used as the integration bounds below.

The curve itself can be expressed as below by rearranging the original equation, $$y(x)= \left[ -x(x-1)+\sqrt{x^2+(1-p)(1-2x)} \right]^{1/2}$$ The area can then be integrated with, $$A = 2\int_{x_1}^{x_2}y(x)dx$$

It could not be done analytically, though. But, it is straightforward numerically. For the special case of $$p=1$$, the area integral reduces significantly and can be carried out by hand,

$$A_{p=1}=2\int_0^2 \sqrt{x(2-x)}=\pi$$ which is expected for a unit circle.

• The polynomial $x^4 - 2 x^2 + \cdots$ you write in $x$ is quartic, so its roots can be written in terms of radicals---it's just messy. Aug 11 '19 at 16:22
• Indeed. Numerical solutions maybe easier. Aug 11 '19 at 16:24

By clearing denominators, we see that our curve is a quartic $$p(x, y) = 0$$. For generic values of $$p, a, b$$, it is elliptic and so does not admit a rational parameterization. Probably the areas can be computed in terms of elliptic functions.

In the special case $$p = \frac{1}{2}$$, the curve is symmetric not only about the $$x$$-axis but also the line $$x = \frac{1}{2}(a + b)$$, and by translating our coordinate system we may as well assume $$b = -a$$, $$a > 0$$. The curve then can be written in the simple form $$x^4 + 2 x^2 y^2 + y^4 - (2 a^2 + 1) x^2 + (2 a^2 - 1) y^2 + a^2 (a^2 - 1) = 0 .$$ This is a biquadratic in, say, $$y$$, so we can solve for $$y$$ in terms of $$x$$ using two square root extractions: $$y = \pm F(x), \qquad F(x) := \frac{1}{2} \sqrt{2 - 4 (a^2 + x^2) + 2 \sqrt{16 a^2 x^2 + 1}} ,$$ and using the fourfold symmetry of the curve we find that the area it encloses is $$4 \int_{x_0}^{x_1} F(x) \,dx .$$ If $$b > 1$$ then $$F$$ has two positive roots, and we set $$x_0$$ to be the smaller root and $$x_1$$ the larger. If $$0 \leq b \leq 1$$ then $$F$$ has one positive root, and we take $$x_1$$ to be that root and take $$x_0 = 0$$.

Substituting $$x = \frac{t}{2 a (1 - t^2)}$$ gives an integrand without a nested radical: $$\int_{t_0}^{t_1} \frac{(t^2 + 1) \sqrt{-4 a^4 t^4 + (8 a^4 - 4 a^2 - 1) t^2 + 4 a^2 (1 - a^2)} \, dt}{(1 - t^2)^3} .$$ (NB if $$x_0 = 0$$ then $$t_0 = 0$$.) Generically the occurrence of the square root of quartic polynomial in an algebraic expression means that, at best, explicitly writing its antiderivative generically requires the use of elliptic functions, and trying a few parameter values for $$a$$ confirms this.

If the quartic has a multiple root, however, we can pull an even number of factors out of the radical, leaving at worst the square root of quadratic polynomial, and such integrals can often be evaluated using elementary techniques. The discriminant of the quartic is a constant multiple of $$(8 a^2 + 1)^2 a^6 (a^2 - 1)$$, so the only positive value of $$a$$ for which it has a multiple root is $$a = 1$$. For this parameter value the curve has genus $$0$$ and has a self-intersection at the origin, and the integral simplifies to $$\int_0^{\sqrt{3} / 2} \frac{(t^2 + 1) t \sqrt{3 - 4 t^2} \,dt}{(1 - t^2)^3} = \frac{2}{3} \pi + \sqrt{3} .$$

To illustrate how complicated the explicit expressions can be even for the case $$p = \frac{1}{2}, b = -a$$ for nonspecial values of $$a$$, Maple returns for $$a = 2$$ that the area is $${\frac {\left[6 \sqrt {2} \left( (136 + 8 \sqrt { 3}\sqrt {11} )\,\Pi \left( 1,2\,{\frac { \sqrt {3}\sqrt {11}}{111+\sqrt {3}\sqrt {11}}}, \omega \right) - (135 + 9\,\sqrt {3}\sqrt {11})K \left( \omega \right) +32\,\Pi \left( 1,2\,{\frac {\sqrt {3}\sqrt {11} }{\sqrt {3}\sqrt {11}+15}}, \omega \right) \right) \right] } {\sqrt {111+\sqrt {3}\sqrt {11}} \left( \sqrt {3}\sqrt {11}+15 \right) }},$$ where $$K$$ is the complete elliptic integral of the first kind, $$\Pi$$ is the incomplete elliptic integral of the third kind (but NB Maple's convention for these functions is different from Wikipedia's), and $$\omega := {\frac {\sqrt {2}\sqrt [4]{3}\sqrt [4]{11}}{\sqrt {111+\sqrt {3}\sqrt {11}}}}$$.

Numerically integrating, by the way, we find that the area of the interior of the example curve with parameters $$a = 1, b = 0, p = \frac{1}{5}$$ is $$3.56910\ldots$$, not $$1$$ as intended.


text:
# regular representation

Given a group $G$, the of $G$ over a field $K$ is the representation $\rho:G\longrightarrow\operatorname{GL}(K^{G})$ whose underlying vector space $K^{G}$ is the $K$–vector space of formal linear combinations of elements of $G$, defined by

 $\rho(g)\left(\sum_{i=1}^{n}k_{i}g_{i}\right):=\sum_{i=1}^{n}k_{i}(gg_{i})$

for $k_{i}\in K$, $g,g_{i}\in G$.

Equivalently, the regular representation is the induced representation on $G$ of the trivial representation on the subgroup $\{1\}$ of $G$.

Title regular representation RegularRepresentation 2013-03-22 12:17:40 2013-03-22 12:17:40 djao (24) djao (24) 5 djao (24) Definition msc 20C99


text:
My caption 😄

# phylopath: Easy phylogenetic path analysis in R

### Abstract

Confirmatory path analysis allows researchers to evaluate and compare causal models using observational data. This tool has great value for comparative biologists since they are often unable to gather experimental data on macro-evolutionary hypotheses, but is cumbersome and error-prone to perform. I introduce phylopath, an R package that implements phylogenetic path analysis (PPA) as described by von Hardenberg & Gonzalez-Voyer (2013). In addition to the published method, I provide support for the inclusion of binary variables. I illustrate PPA and phylopath by recreating part of a study on the relationship between brain size and vulnerability to extinction. The package aims to make the analysis straight-forward, providing convenience functions, and several plotting methods, which I hope will encourage the spread of the method.

Type
Publication
In PeerJ.
Date
More detail can easily be written here using Markdown and $\rm \LaTeX$ math code.


text:
Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Click to Chat

1800-1023-196

+91 7353221155

CART 0

• 0
MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping

he angle between the tangents to the parabola y^2=4ax at the points whrer ti intersects the line x-y=a

Jitender Singh IIT Delhi
7 years ago
Ans: 90
Sol:
Let P(t1, 2at1) & Q(t2, 2at2) be the points on the parabola where line intersects the parabola. Then slope of tangents at P & Q would be:
$\frac{1}{t_{1}}, \frac{1}{t_{2}}$
Angle between tangents:
$\frac{|t_{2}-t_{1}|}{1+t_{1}t_{2}}$
Since both points lie on the line, we have
$t_{1}^{2}-2t_{1}-1=0$
$t_{2}^{2}-2t_{2}-1=0$
t1, t2are the roots of the equation
$t^{2}-2t-1=0$
Product of the roots is -1,
$t_{1}t_{2}=-1$
Angle is 90.
Thanks & Regards
Jitender Singh
IIT Delhi


text:
# Reason for including the public key of the key agreement in the KDF

I found the following text when looking up KDFs:

In comparison, the so-called DHAES mode in IEEE 1363a mandates to use the binary representation of the sender’s public key as an input parameter.

where a quick lookup suggests that DHES and DHAES are simply earlier names for ECIES.

What would be the reason to include the sender's public key into the KDF as a parameter? Other ECDH based schemes do not seem to do this.

If the sender's public key is altered then the calculated shared secret $$Z$$ would be invalid and the KDF would fail to generate the correct key anyway. Is this just an additional spurious security measure or am I missing some significant reasoning?

• Can you put the link of the source? – kelalaka Feb 14 '19 at 9:32
• @kelalaka Adjusted. – Maarten Bodewes Feb 14 '19 at 14:42
• I suspect that the answer is in this or its references. But where? – fgrieu Feb 14 '19 at 15:49
• I don't think so. I went through it entirely and found a statement that it doesn't use any parameters. That's not so strange as it defines the KDF1-4 without parameters as well. Can't speak of the references yet of course - as there are 25 I presume it is in there though - if not it will be in the references of the references :P. – Maarten Bodewes Feb 14 '19 at 16:16
• I did a lot of looking into the references, but if it is there it has still escaped me. – Maarten Bodewes Apr 10 '19 at 22:35


text:
# American Institute of Mathematical Sciences

September  2015, 8(3): 413-441. doi: 10.3934/krm.2015.8.413

## Non-local kinetic and macroscopic models for self-organised animal aggregations

 1 Department of Mathematics, Imperial College, London, London SW7 2AZ 2 Division of Mathematics, University of Dundee, Dundee, DD1 4HN, United Kingdom 3 University of Cambridge, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA, United Kingdom

Received  November 2014 Revised  February 2015 Published  June 2015

The last two decades have seen a surge in kinetic and macroscopic models derived to investigate the multi-scale aspects of self-organised biological aggregations. Because the individual-level details incorporated into the kinetic models (e.g., individual speeds and turning rates) make them somewhat difficult to investigate, one is interested in transforming these models into simpler macroscopic models, by using various scaling techniques that are imposed by the biological assumptions of the models. However, not many studies investigate how the dynamics of the initial models are preserved via these scalings. Here, we consider two scaling approaches (parabolic and grazing collision limits) that can be used to reduce a class of non-local 1D and 2D models for biological aggregations to simpler models existent in the literature. Then, we investigate how some of the spatio-temporal patterns exhibited by the original kinetic models are preserved via these scalings. To this end, we focus on the parabolic scaling for non-local 1D models and apply asymptotic preserving numerical methods, which allow us to analyse changes in the patterns as the scaling coefficient $\epsilon$ is varied from $\epsilon=1$ (for 1D transport models) to $\epsilon=0$ (for 1D parabolic models). We show that some patterns (describing stationary aggregations) are preserved in the limit $\epsilon\to 0$, while other patterns (describing moving aggregations) are lost. To understand the loss of these patterns, we construct bifurcation diagrams.
Citation: José A. Carrillo, Raluca Eftimie, Franca Hoffmann. Non-local kinetic and macroscopic models for self-organised animal aggregations. Kinetic & Related Models, 2015, 8 (3) : 413-441. doi: 10.3934/krm.2015.8.413
##### References:
 [1] E. D. Angelis and B. Lods, On the kinetic theory for active particles: A model for tumor-immune system competition,, Math. Comp. Model., 47 (2008), 196. doi: 10.1016/j.mcm.2007.02.016. [2] A. Arnold, J. A. Carrillo, I. Gamba and C.-w. Shu, Low and high field scaling limits for the vlasov- and wigner-poisson-fokker-planck systems,, Transp. Theory Stat. Phys., 30 (2001), 121. doi: 10.1081/TT-100105365. [3] A. Barbaro and P. Degond, Phase transition and diffusion among socially interacting self-propelled agents,, Discrete Cont Dyn Syst B., 19 (2014), 1249. [4] M. Beekman, D. J. T. Sumpter and F. L. W. Ratnieks, Phase transitions between disordered and ordered foraging in pharaoh's ants,, Proc. Natl. Acad. Sci., 98 (2001), 9703. doi: 10.1073/pnas.161285298. [5] N. Bellomo, E. D. Angelis and L. Preziosi, Multiscale modeling and mathematical problems related to tumor evolution and medical therapy,, Journal of Theoretical Medicine, 5 (2003), 111. doi: 10.1080/1027336042000288633. [6] N. Bellomo, A. Bellouquid, J. Nieto and J.Soler, Multicellular biological growing systems: Hyperbolic limits towards macroscopic description,, Math Models Appl. Sci., 17 (2007), 1675. doi: 10.1142/S0218202507002431. [7] N. Bellomo, C. Bianca and M. Delitala, Complexity analysis and mathematical tools towards the modelling of living systems,, Physics of Life Reviews, 6 (2009), 144. doi: 10.1016/j.plrev.2009.06.002. [8] M. G. Bertotti and M. Delitala, Conservation laws and asymptotic behavior of a model of social dynamics,, Nonlinear Analysis RWA, 9 (2008), 183. doi: 10.1016/j.nonrwa.2006.09.012. [9] A. L. Bertozzi, J. A. Carrillo and T. Laurent, Blow-up in multidimensional aggregation equations with mildly singular interaction kernels,, Nonlinearity, 22 (2009), 683. doi: 10.1088/0951-7715/22/3/009. [10] A. Blanchet, J. Dolbeault and B. Perthame, Two-dimensional Keller-Segel model: Optimal critical mass and qualitative properties of the solutions,, Electron J. Diff. Eq., 44 (2006), 1. [11] M. Bodnar and J. J. L. Velazquez, Derivation of macroscopic equations for individual cell-based models: A formal approach,, Math. Meth. Appl. Sci., 28 (2005), 1757. doi: 10.1002/mma.638. [12] R. Breitwisch and G. Whitesides, {Directionality of singing and non-singing behaviour of mated and unmated Northern Mockingbirds, Mimus polyglottos},, Anim. Behav., 35 (1987), 331. [13] J. Buhl, D. J. T. Sumpter, I. D. Couzin, J. J. Hale, E. Despland, E. R. Miller and S. J. Simpson, From disorder to order in marching locusts,, Science, 312 (2006), 1402. doi: 10.1126/science.1125142. [14] P.-L. Buono and R. Eftimie, Analysis of Hopf/Hopf bifurcations in nonlocal hyperbolic models for self-organised aggregations,, Math. Models Methods Appl. Sci., 24 (2014), 327. doi: 10.1142/S0218202513400101. [15] P.-L. Buono and R. Eftimie, Codimension-two bifurcations in animal aggregation models with symmetry,, SIAM J. Appl. Dyn. Syst., 13 (2014), 1542. doi: 10.1137/130932272. [16] P.-L. Buono and R. Eftimie, Symmetries and pattern formation in hyperbolic versus parabolic models for self-organised aggregations,, J. Math. Biol., (2014), 1. doi: 10.1007/s00285-014-0842-3. [17] M. Burger, V. Capasso and D. Morale, On an aggregation model with long and short range interactions,, Nonlinear Analysis RWA, 8 (2007), 939. doi: 10.1016/j.nonrwa.2006.04.002. [18] J. A. Carrillo, M. R. D'Orsogna and V. Panferov, Double milling in self-propelled swarms from kinetic theory,, Kinetic and Related Models, 2 (2009), 363. doi: 10.3934/krm.2009.2.363. [19] J. A. Carrillo, M. Fornasier, J. Rosado and G. Toscani, Asymptotic flocking dynamics for the kinetic Cucker-Smale model,, SIAM J. Math. Anal., 42 (2010), 218. doi: 10.1137/090757290. [20] J. A. Carrillo, M. Fornasier, G. Toscani and F. Vecil, Particle, kinetic, and hydrodynamic models of swarming,, in Mathematical Modelling of Collective Behavior in Socio-Economic and Life Sciences (eds. G. Naldi, (2010), 297. doi: 10.1007/978-0-8176-4946-3_12. [21] J. A. Carrillo, T. Goudon, P. Lafitte and F. Vecil, Numerical schemes of diffusion asymptotics and moment closures for kinetic equations,, J. Sci. Comput., 36 (2008), 113. doi: 10.1007/s10915-007-9181-5. [22] J. A. Carrillo, Y. Huang and S. Martin, Explicit flock solutions for quasi-morse potentials,, European J. Appl. Math., 25 (2014), 553. doi: 10.1017/S0956792514000126. [23] J. A. Carrillo, A. Klar, S. Martin and S. Tiwari, Self-propelled interacting particle systems with roosting force,, Math. Models Methods Appl. Sci., 20 (2010), 1533. doi: 10.1142/S0218202510004684. [24] J. A. Carrillo and B. Yan, An asymptotic preserving scheme for the diffusive limit of kinetic systems for chemotaxis,, Multiscale Model. Simul., 11 (2013), 336. doi: 10.1137/110851687. [25] A. Chertock, A. Kurganov, A. Polizzi and I. Timofeyev, Pedestrian flow models with slowdown interactions,, Math Models Methods Appl. Sci., 24 (2014), 249. doi: 10.1142/S0218202513400083. [26] Y.-L. Chuang, M. R. D'Orsogna, D. Marthaler, A. L. Bertozzi and L. S. Chayes, State transitions and the continuum limit for a 2d interactiong, self-propelled particle system,, Physica D, 232 (2007), 33. doi: 10.1016/j.physd.2007.05.007. [27] P. Degond, G. Dimarco and T. Mac, Hydrodynamics of the Kuramoto-Vicsek model of rotating self-propelled particles,, Math Models Appl. Sci., 24 (2014), 277. doi: 10.1142/S0218202513400095. [28] P. Degond and S. Motsch, Macroscopic limit of self-driven particles with orientation interaction,, C.R. Acad. Sci. Paris Ser. I, 345 (2007), 555. doi: 10.1016/j.crma.2007.10.024. [29] P. Degond and S. Motsch, Large scale dynamics of the persistent turning awlker model of fish behaviour,, J. Stat. Phys., 131 (2008), 989. doi: 10.1007/s10955-008-9529-8. [30] R. Eftimie, Modeling Group Formation and Activity Patterns in Self-Organizing Communities of Organisms,, PhD thesis, (2008). [31] R. Eftimie, Hyperbolic and kinetic models for self-organized biological aggregations and movement: A brief review,, J. Math. Biol., 65 (2012), 35. doi: 10.1007/s00285-011-0452-2. [32] R. Eftimie, G. de Vries and M. A. Lewis, Complex spatial group patterns result from different animal communication mechanisms,, Proc. Natl. Acad. Sci., 104 (2007), 6974. doi: 10.1073/pnas.0611483104. [33] R. Eftimie, G. de Vries, M. A. Lewis and F. Lutscher, Modeling group formation and activity patterns in self-organizing collectives of individuals,, Bull. Math. Biol., 69 (2007), 1537. doi: 10.1007/s11538-006-9175-8. [34] R. Eftimie, G. de Vries and M. Lewis, Weakly nonlinear analysis of a hyperbolic model for animal group formation,, J. Math. Biol., 59 (2009), 37. doi: 10.1007/s00285-008-0209-8. [35] R. Fetecau, Collective behavior of biological aggregations in two dimensions: A nonlocal kinetic model,, Math. Model. Method. Appl. Sci., 21 (2011), 1539. doi: 10.1142/S0218202511005489. [36] E. Geigant, K. Ladizhansky and A. Mogilner, An integrodifferential model for orientational distributions of {F-actin} in cells,, SIAM J. Appl. Math., 59 (1998), 787. [37] P. Godillon-Lafitte and T. Goudon, A coupled model for radiative transfer: Doppler effects, equilibrium, and nonequilibrium diffusion asymptotics,, Multiscale Model. Simul., 4 (2005), 1245. doi: 10.1137/040621041. [38] T. Goudon, On Boltzmann equations and Fokker-Plank asymptotics: Influence of grazing collisions,, J. Stat. Phys., 89 (1997), 751. doi: 10.1007/BF02765543. [39] S.-Y. Ha and E. Tadmor, From particle to kinetic and hydrodynamic descriptions of flocking,, Kinetic and Related Models, 1 (2008), 415. doi: 10.3934/krm.2008.1.415. [40] C. K. Hemelrijk and H. Kunz, Density distribution and size sorting in fish schools: An individual-based model,, Behav. Ecol., 16 (2004), 178. doi: 10.1093/beheco/arh149. [41] H. Hildenbrandt, C. Carere and C. K. Hemelrijk, Self-organised complex aerial displays of thousands of starlings: A model,, Behavioral Ecology, 107 (2010), 1349. [42] T. Hillen and H. G. Othmer, The diffusion limit of transport equations derived from velocity jump process,, SIAM J. Appl. Math., 61 (2000), 751. doi: 10.1137/S0036139999358167. [43] E. E. Holmes, Are diffusion models too simple? A comparison with telegraph models of invasion,, Am. Nat., 142 (1993), 779. doi: 10.1086/285572. [44] A. Klar, An asymptotic-induced scheme for nonstationary transport equations in the diffusive limit,, SIAM J. Numer. Anal., 35 (1998), 1073. doi: 10.1137/S0036142996305558. [45] A. Klar, An asymptotic preserving numerical scheme for kinetic equations in the low Mach number limit,, SIAM J. Numer. Anal., 36 (1999), 1507. doi: 10.1137/S0036142997321765. [46] R. Larkin and R. Szafoni, Evidence for widely dispersed birds migrating together at night,, Integrative and Comparative Biology, 48 (2008), 40. [47] A. Mogilner and L. Edelstein-Keshet, A non-local model for a swarm,, J. Math. Biol., 38 (1999), 534. doi: 10.1007/s002850050158. [48] A. Mogilner, L. Edelstein-Keshet and G. B. Ermentrout, Selecting a common direction. II. Peak-like solutions representing total alignment of cell clusters,, J. Math. Biol., 34 (1996), 811. doi: 10.1007/s002850050032. [49] D. Morale, V. Capasso and K. Oelschläger, An interacting particle system modelling aggregation behavior: From individuals to populations,, J. Math. Biol., 50 (2005), 49. doi: 10.1007/s00285-004-0279-1. [50] I. Newton, The Migration Ecology of Birds,, Academic Press, (2008). [51] H. G. Othmer and T. Hillen, The diffusion limit of transport equations II: Chemotaxis equations,, SIAM J. Appl. Math., 62 (2002), 1222. doi: 10.1137/S0036139900382772. [52] R. D. Passo and P. de Mottoni, Aggregative effects for a reaction-advection equation,, J. Math. Biology, 20 (1984), 103. doi: 10.1007/BF00275865. [53] B. Pfistner, A one dimensional model for the swarming behaviour of Myxobacteria,, in Biological Motion (eds. W. Alt and G. Hoffmann), (1990), 556. [54] J. Saragosti, V. Calvez, N. Bournaveas, A. Buguin, P. Silberzan and B. Perthame, Mathematical description of bacterial traveling pulses,, PLoS Comput. Biol., 6 (2010). doi: 10.1371/journal.pcbi.1000890. [55] C. M. Topaz, A. L. Bertozzi and M. A. Lewis, A nonlocal continuum model for biological aggregation,, Bull. Math. Bio., 68 (2006), 1601. doi: 10.1007/s11538-006-9088-6. [56] F. Venuti, L. Bruno and N. Bellomo, Crowd dynamics on a moving platform: Mathematical modelling and application to lively footbridges,, Math. Comp. Model., 45 (2007), 252. doi: 10.1016/j.mcm.2006.04.007.

show all references

##### References:
 [1] E. D. Angelis and B. Lods, On the kinetic theory for active particles: A model for tumor-immune system competition,, Math. Comp. Model., 47 (2008), 196. doi: 10.1016/j.mcm.2007.02.016. [2] A. Arnold, J. A. Carrillo, I. Gamba and C.-w. Shu, Low and high field scaling limits for the vlasov- and wigner-poisson-fokker-planck systems,, Transp. Theory Stat. Phys., 30 (2001), 121. doi: 10.1081/TT-100105365. [3] A. Barbaro and P. Degond, Phase transition and diffusion among socially interacting self-propelled agents,, Discrete Cont Dyn Syst B., 19 (2014), 1249. [4] M. Beekman, D. J. T. Sumpter and F. L. W. Ratnieks, Phase transitions between disordered and ordered foraging in pharaoh's ants,, Proc. Natl. Acad. Sci., 98 (2001), 9703. doi: 10.1073/pnas.161285298. [5] N. Bellomo, E. D. Angelis and L. Preziosi, Multiscale modeling and mathematical problems related to tumor evolution and medical therapy,, Journal of Theoretical Medicine, 5 (2003), 111. doi: 10.1080/1027336042000288633. [6] N. Bellomo, A. Bellouquid, J. Nieto and J.Soler, Multicellular biological growing systems: Hyperbolic limits towards macroscopic description,, Math Models Appl. Sci., 17 (2007), 1675. doi: 10.1142/S0218202507002431. [7] N. Bellomo, C. Bianca and M. Delitala, Complexity analysis and mathematical tools towards the modelling of living systems,, Physics of Life Reviews, 6 (2009), 144. doi: 10.1016/j.plrev.2009.06.002. [8] M. G. Bertotti and M. Delitala, Conservation laws and asymptotic behavior of a model of social dynamics,, Nonlinear Analysis RWA, 9 (2008), 183. doi: 10.1016/j.nonrwa.2006.09.012. [9] A. L. Bertozzi, J. A. Carrillo and T. Laurent, Blow-up in multidimensional aggregation equations with mildly singular interaction kernels,, Nonlinearity, 22 (2009), 683. doi: 10.1088/0951-7715/22/3/009. [10] A. Blanchet, J. Dolbeault and B. Perthame, Two-dimensional Keller-Segel model: Optimal critical mass and qualitative properties of the solutions,, Electron J. Diff. Eq., 44 (2006), 1. [11] M. Bodnar and J. J. L. Velazquez, Derivation of macroscopic equations for individual cell-based models: A formal approach,, Math. Meth. Appl. Sci., 28 (2005), 1757. doi: 10.1002/mma.638. [12] R. Breitwisch and G. Whitesides, {Directionality of singing and non-singing behaviour of mated and unmated Northern Mockingbirds, Mimus polyglottos},, Anim. Behav., 35 (1987), 331. [13] J. Buhl, D. J. T. Sumpter, I. D. Couzin, J. J. Hale, E. Despland, E. R. Miller and S. J. Simpson, From disorder to order in marching locusts,, Science, 312 (2006), 1402. doi: 10.1126/science.1125142. [14] P.-L. Buono and R. Eftimie, Analysis of Hopf/Hopf bifurcations in nonlocal hyperbolic models for self-organised aggregations,, Math. Models Methods Appl. Sci., 24 (2014), 327. doi: 10.1142/S0218202513400101. [15] P.-L. Buono and R. Eftimie, Codimension-two bifurcations in animal aggregation models with symmetry,, SIAM J. Appl. Dyn. Syst., 13 (2014), 1542. doi: 10.1137/130932272. [16] P.-L. Buono and R. Eftimie, Symmetries and pattern formation in hyperbolic versus parabolic models for self-organised aggregations,, J. Math. Biol., (2014), 1. doi: 10.1007/s00285-014-0842-3. [17] M. Burger, V. Capasso and D. Morale, On an aggregation model with long and short range interactions,, Nonlinear Analysis RWA, 8 (2007), 939. doi: 10.1016/j.nonrwa.2006.04.002. [18] J. A. Carrillo, M. R. D'Orsogna and V. Panferov, Double milling in self-propelled swarms from kinetic theory,, Kinetic and Related Models, 2 (2009), 363. doi: 10.3934/krm.2009.2.363. [19] J. A. Carrillo, M. Fornasier, J. Rosado and G. Toscani, Asymptotic flocking dynamics for the kinetic Cucker-Smale model,, SIAM J. Math. Anal., 42 (2010), 218. doi: 10.1137/090757290. [20] J. A. Carrillo, M. Fornasier, G. Toscani and F. Vecil, Particle, kinetic, and hydrodynamic models of swarming,, in Mathematical Modelling of Collective Behavior in Socio-Economic and Life Sciences (eds. G. Naldi, (2010), 297. doi: 10.1007/978-0-8176-4946-3_12. [21] J. A. Carrillo, T. Goudon, P. Lafitte and F. Vecil, Numerical schemes of diffusion asymptotics and moment closures for kinetic equations,, J. Sci. Comput., 36 (2008), 113. doi: 10.1007/s10915-007-9181-5. [22] J. A. Carrillo, Y. Huang and S. Martin, Explicit flock solutions for quasi-morse potentials,, European J. Appl. Math., 25 (2014), 553. doi: 10.1017/S0956792514000126. [23] J. A. Carrillo, A. Klar, S. Martin and S. Tiwari, Self-propelled interacting particle systems with roosting force,, Math. Models Methods Appl. Sci., 20 (2010), 1533. doi: 10.1142/S0218202510004684. [24] J. A. Carrillo and B. Yan, An asymptotic preserving scheme for the diffusive limit of kinetic systems for chemotaxis,, Multiscale Model. Simul., 11 (2013), 336. doi: 10.1137/110851687. [25] A. Chertock, A. Kurganov, A. Polizzi and I. Timofeyev, Pedestrian flow models with slowdown interactions,, Math Models Methods Appl. Sci., 24 (2014), 249. doi: 10.1142/S0218202513400083. [26] Y.-L. Chuang, M. R. D'Orsogna, D. Marthaler, A. L. Bertozzi and L. S. Chayes, State transitions and the continuum limit for a 2d interactiong, self-propelled particle system,, Physica D, 232 (2007), 33. doi: 10.1016/j.physd.2007.05.007. [27] P. Degond, G. Dimarco and T. Mac, Hydrodynamics of the Kuramoto-Vicsek model of rotating self-propelled particles,, Math Models Appl. Sci., 24 (2014), 277. doi: 10.1142/S0218202513400095. [28] P. Degond and S. Motsch, Macroscopic limit of self-driven particles with orientation interaction,, C.R. Acad. Sci. Paris Ser. I, 345 (2007), 555. doi: 10.1016/j.crma.2007.10.024. [29] P. Degond and S. Motsch, Large scale dynamics of the persistent turning awlker model of fish behaviour,, J. Stat. Phys., 131 (2008), 989. doi: 10.1007/s10955-008-9529-8. [30] R. Eftimie, Modeling Group Formation and Activity Patterns in Self-Organizing Communities of Organisms,, PhD thesis, (2008). [31] R. Eftimie, Hyperbolic and kinetic models for self-organized biological aggregations and movement: A brief review,, J. Math. Biol., 65 (2012), 35. doi: 10.1007/s00285-011-0452-2. [32] R. Eftimie, G. de Vries and M. A. Lewis, Complex spatial group patterns result from different animal communication mechanisms,, Proc. Natl. Acad. Sci., 104 (2007), 6974. doi: 10.1073/pnas.0611483104. [33] R. Eftimie, G. de Vries, M. A. Lewis and F. Lutscher, Modeling group formation and activity patterns in self-organizing collectives of individuals,, Bull. Math. Biol., 69 (2007), 1537. doi: 10.1007/s11538-006-9175-8. [34] R. Eftimie, G. de Vries and M. Lewis, Weakly nonlinear analysis of a hyperbolic model for animal group formation,, J. Math. Biol., 59 (2009), 37. doi: 10.1007/s00285-008-0209-8. [35] R. Fetecau, Collective behavior of biological aggregations in two dimensions: A nonlocal kinetic model,, Math. Model. Method. Appl. Sci., 21 (2011), 1539. doi: 10.1142/S0218202511005489. [36] E. Geigant, K. Ladizhansky and A. Mogilner, An integrodifferential model for orientational distributions of {F-actin} in cells,, SIAM J. Appl. Math., 59 (1998), 787. [37] P. Godillon-Lafitte and T. Goudon, A coupled model for radiative transfer: Doppler effects, equilibrium, and nonequilibrium diffusion asymptotics,, Multiscale Model. Simul., 4 (2005), 1245. doi: 10.1137/040621041. [38] T. Goudon, On Boltzmann equations and Fokker-Plank asymptotics: Influence of grazing collisions,, J. Stat. Phys., 89 (1997), 751. doi: 10.1007/BF02765543. [39] S.-Y. Ha and E. Tadmor, From particle to kinetic and hydrodynamic descriptions of flocking,, Kinetic and Related Models, 1 (2008), 415. doi: 10.3934/krm.2008.1.415. [40] C. K. Hemelrijk and H. Kunz, Density distribution and size sorting in fish schools: An individual-based model,, Behav. Ecol., 16 (2004), 178. doi: 10.1093/beheco/arh149. [41] H. Hildenbrandt, C. Carere and C. K. Hemelrijk, Self-organised complex aerial displays of thousands of starlings: A model,, Behavioral Ecology, 107 (2010), 1349. [42] T. Hillen and H. G. Othmer, The diffusion limit of transport equations derived from velocity jump process,, SIAM J. Appl. Math., 61 (2000), 751. doi: 10.1137/S0036139999358167. [43] E. E. Holmes, Are diffusion models too simple? A comparison with telegraph models of invasion,, Am. Nat., 142 (1993), 779. doi: 10.1086/285572. [44] A. Klar, An asymptotic-induced scheme for nonstationary transport equations in the diffusive limit,, SIAM J. Numer. Anal., 35 (1998), 1073. doi: 10.1137/S0036142996305558. [45] A. Klar, An asymptotic preserving numerical scheme for kinetic equations in the low Mach number limit,, SIAM J. Numer. Anal., 36 (1999), 1507. doi: 10.1137/S0036142997321765. [46] R. Larkin and R. Szafoni, Evidence for widely dispersed birds migrating together at night,, Integrative and Comparative Biology, 48 (2008), 40. [47] A. Mogilner and L. Edelstein-Keshet, A non-local model for a swarm,, J. Math. Biol., 38 (1999), 534. doi: 10.1007/s002850050158. [48] A. Mogilner, L. Edelstein-Keshet and G. B. Ermentrout, Selecting a common direction. II. Peak-like solutions representing total alignment of cell clusters,, J. Math. Biol., 34 (1996), 811. doi: 10.1007/s002850050032. [49] D. Morale, V. Capasso and K. Oelschläger, An interacting particle system modelling aggregation behavior: From individuals to populations,, J. Math. Biol., 50 (2005), 49. doi: 10.1007/s00285-004-0279-1. [50] I. Newton, The Migration Ecology of Birds,, Academic Press, (2008). [51] H. G. Othmer and T. Hillen, The diffusion limit of transport equations II: Chemotaxis equations,, SIAM J. Appl. Math., 62 (2002), 1222. doi: 10.1137/S0036139900382772. [52] R. D. Passo and P. de Mottoni, Aggregative effects for a reaction-advection equation,, J. Math. Biology, 20 (1984), 103. doi: 10.1007/BF00275865. [53] B. Pfistner, A one dimensional model for the swarming behaviour of Myxobacteria,, in Biological Motion (eds. W. Alt and G. Hoffmann), (1990), 556. [54] J. Saragosti, V. Calvez, N. Bournaveas, A. Buguin, P. Silberzan and B. Perthame, Mathematical description of bacterial traveling pulses,, PLoS Comput. Biol., 6 (2010). doi: 10.1371/journal.pcbi.1000890. [55] C. M. Topaz, A. L. Bertozzi and M. A. Lewis, A nonlocal continuum model for biological aggregation,, Bull. Math. Bio., 68 (2006), 1601. doi: 10.1007/s11538-006-9088-6. [56] F. Venuti, L. Bruno and N. Bellomo, Crowd dynamics on a moving platform: Mathematical modelling and application to lively footbridges,, Math. Comp. Model., 45 (2007), 252. doi: 10.1016/j.mcm.2006.04.007.
 [1] Alina Chertock, Changhui Tan, Bokai Yan. An asymptotic preserving scheme for kinetic models with singular limit. Kinetic & Related Models, 2018, 11 (4) : 735-756. doi: 10.3934/krm.2018030 [2] Alina Chertock, Alexander Kurganov, Mária Lukáčová-Medvi${\rm{\check{d}}}$ová, Șeyma Nur Özcan. An asymptotic preserving scheme for kinetic chemotaxis models in two space dimensions. Kinetic & Related Models, 2019, 12 (1) : 195-216. doi: 10.3934/krm.2019009 [3] Felisia Angela Chiarello, Paola Goatin. Non-local multi-class traffic flow models. Networks & Heterogeneous Media, 2019, 14 (2) : 371-387. doi: 10.3934/nhm.2019015 [4] Thierry Goudon, Martin Parisot. Non--local macroscopic models based on Gaussian closures for the Spizer-Härm regime. Kinetic & Related Models, 2011, 4 (3) : 735-766. doi: 10.3934/krm.2011.4.735 [5] N. Bellomo, A. Bellouquid. From a class of kinetic models to the macroscopic equations for multicellular systems in biology. Discrete & Continuous Dynamical Systems - B, 2004, 4 (1) : 59-80. doi: 10.3934/dcdsb.2004.4.59 [6] Tadahisa Funaki, Hirofumi Izuhara, Masayasu Mimura, Chiyori Urabe. A link between microscopic and macroscopic models of self-organized aggregation. Networks & Heterogeneous Media, 2012, 7 (4) : 705-740. doi: 10.3934/nhm.2012.7.705 [7] Sanda Cleja-Ţigoiu, Raisa Paşcan. Non-local elasto-viscoplastic models with dislocations and non-Schmid effect. Discrete & Continuous Dynamical Systems - S, 2013, 6 (6) : 1621-1639. doi: 10.3934/dcdss.2013.6.1621 [8] Jan Friedrich, Oliver Kolb, Simone Göttlich. A Godunov type scheme for a class of LWR traffic flow models with non-local flux. Networks & Heterogeneous Media, 2018, 13 (4) : 531-547. doi: 10.3934/nhm.2018024 [9] Raffaella Servadei, Enrico Valdinoci. Variational methods for non-local operators of elliptic type. Discrete & Continuous Dynamical Systems - A, 2013, 33 (5) : 2105-2137. doi: 10.3934/dcds.2013.33.2105 [10] Guillaume Bal, Olivier Pinaud. Self-averaging of kinetic models for waves in random media. Kinetic & Related Models, 2008, 1 (1) : 85-100. doi: 10.3934/krm.2008.1.85 [11] Shixiu Zheng, Zhilei Xu, Huan Yang, Jintao Song, Zhenkuan Pan. Comparisons of different methods for balanced data classification under the discrete non-local total variational framework. Mathematical Foundations of Computing, 2019, 2 (1) : 11-28. doi: 10.3934/mfc.2019002 [12] Pierre Degond, Cécile Appert-Rolland, Julien Pettré, Guy Theraulaz. Vision-based macroscopic pedestrian models. Kinetic & Related Models, 2013, 6 (4) : 809-839. doi: 10.3934/krm.2013.6.809 [13] Tahir Bachar Issa, Rachidi Bolaji Salako. Asymptotic dynamics in a two-species chemotaxis model with non-local terms. Discrete & Continuous Dynamical Systems - B, 2017, 22 (10) : 3839-3874. doi: 10.3934/dcdsb.2017193 [14] Pierre Degond, Hailiang Liu. Kinetic models for polymers with inertial effects. Networks & Heterogeneous Media, 2009, 4 (4) : 625-647. doi: 10.3934/nhm.2009.4.625 [15] Seung-Yeal Ha, Doron Levy. Particle, kinetic and fluid models for phototaxis. Discrete & Continuous Dynamical Systems - B, 2009, 12 (1) : 77-108. doi: 10.3934/dcdsb.2009.12.77 [16] Qiyu Jin, Ion Grama, Quansheng Liu. Convergence theorems for the Non-Local Means filter. Inverse Problems & Imaging, 2018, 12 (4) : 853-881. doi: 10.3934/ipi.2018036 [17] Gabriel Peyré, Sébastien Bougleux, Laurent Cohen. Non-local regularization of inverse problems. Inverse Problems & Imaging, 2011, 5 (2) : 511-530. doi: 10.3934/ipi.2011.5.511 [18] Olivier Bonnefon, Jérôme Coville, Guillaume Legendre. Concentration phenomenon in some non-local equation. Discrete & Continuous Dynamical Systems - B, 2017, 22 (3) : 763-781. doi: 10.3934/dcdsb.2017037 [19] Dan Liu, Shigui Ruan, Deming Zhu. Bifurcation analysis in models of tumor and immune system interactions. Discrete & Continuous Dynamical Systems - B, 2009, 12 (1) : 151-168. doi: 10.3934/dcdsb.2009.12.151 [20] Cesare Tronci. Hybrid models for perfect complex fluids with multipolar interactions. Journal of Geometric Mechanics, 2012, 4 (3) : 333-363. doi: 10.3934/jgm.2012.4.333

2017 Impact Factor: 1.219


text:
### Particle, Astrophysics, And Nuclear Physics Seminar

Monday, November 30, 2020
2:00pm – 3:00pm

Storrs Campus
online

Prof. H.Haggard, Bard College

Why do so many black holes measured in gravitational waves have zero spin?

Black hole entropy is a robust prediction of quantum gravity with no established phenomenological consequences to date. We use the Bekenstein-Hawking entropy formula and general-relativistic statistical mechanics to determine the probability distribution of random geometries uniformly sampled in phase space. We show that this statistics (in the limit $$\hbar \to 0$$ ) is relevant to large curvature perturbations, resulting in a population of primordial black holes with zero natal spin. In principle, the identification of such a population at LIGO, Virgo, and future gravitational wave observatories could provide the first observational evidence for the statistical nature of black hole entropy.

Contact:

Prof. L. Jin

Physics Department (primary), College of Liberal Arts and Sciences, UConn Master Calendar


text:
# Inertial Twin Paradox with no acceleration, radio transmitted selfies and a third alien observer [closed]

I've seen many questions answered on the twin paradox but they hand-wave the problem away using non-inertial frames. "you must accelerate away and come back therefore we use the Rindler metric". But I'm not interested in that, I'm interested in this inertial situation:

I am in my spaceship, you are on the ISS. We are twins. I am already moving at $$86.6\%$$ of the speed of light. As I whizz past you, right next to the ISS, we both start our clocks.

I travel to andromeda. I do not accelerate, I do not decelerate.

We both wait $$1$$ year according to our clocks, then we take a selfie, and we both fire out a radio signal containing our selfie and the timestamp towards each other.

By happenstance, an alien is in a UFO and at the midpoint and is static relative to you when the two radio packets both arrive at the same position. He intercepts both simultaneously, and decrypts them, and looks at both selfies.

Who is younger in the selfie? In your frame of reference I was moving at $$0.866c$$, so:

$$t' = \frac{t}{\sqrt{1-0.866^2}} = 2t$$

But my frame of reference you were moving at $$-0.866c$$, so

$$t' = t' =\frac{t}{\sqrt{1-(-0.866)^2}} = 2t$$

So in my frame you should've aged at half speed but in your frame I should've aged at half speed.

So what does the alien see? whose selfie is older?

(I would've liked to have used the example that as soon as I reached andromeda I collapsed a quantum entangled particle and told you to take a selfie upon collapse and then we saw who was older but I guess someone would just say "you can't transfer information through entanglement" so I had to use the alien example).

• All twin paradox questions and confusions get resolved when you draw a spacetime diagram. Have you drawn a spacetime diagram? – Prof. Legolasov May 28 at 5:22
• We both wait 1 year according to our clocks, then we take a selfie...Who is younger in the selfie?" Seriously? If you were both 35 when you passed each other, you both waited 1 year according to your own clocks, then you took the selfies --- then you are both 36 in the selfies. Sometimes it pays to stop and think for a moment before you start writing down formulas. (In this case you wrote down the wrong formula for the Lorentz transformation, which depends on both $t$ and $x$, not just $t$.) – WillO May 28 at 5:30
• PS: @Prof.Legolasov gave you good advice re spacetime diagrams in general. But in this specific case, 30 seconds of thought would have sufficed. – WillO May 28 at 5:34
• " We both wait 1 year according to our clocks, then we take a selfie, and we both fire out a radio signal " Do you wait 1 year, from the moment of when clocks were set to 0 , or 1 year from the moment of passing andromeda ? If you are waiting 1 year from the moment of passing ISS, then why is andromeda part of the question ? Isnt it better to remove the andromeda part entirely ? – silverrahul May 28 at 6:24

There is only one correct resolution to the twin "paradox" regardless of your setup. There is no need for hand-waving or use a special set of coordinates (such as the Rindler coordinates OP mentions). No. The only real definition for the time elapsed on someone's person clock is the proper time of their world-line. I would go as far as to argue that the only real way to avoid confusing oneself with relativity is to try and think exclusively in terms of world lines and what they are doing.

To make this precise, suppose that in the coordinates $$x^\mu=\langle t,\vec x\rangle$$, the observer on Earth is simply sitting at the origin and time is elapsing for them. That is, the world-line (path through spacetime) of the person on Earth may be written $$x^\mu_E=\langle t,0\rangle$$, the subscript $$E$$ for Earth. We can also write the path traveled by the spaceship person (in the same coordinates!) as $$x^\mu_S=\langle t,\vec vt\rangle$$. Normally, physicist would say that this is the path through spacetime taken by the spaceship as seen by the Earth observer.

We then need to define the proper time, and to do so we must introduce the Minkowski metric: $$ds^2 = -dt^2+d\vec x^2=dx^\mu\eta_{\mu\nu}dx^\nu.$$ I am working in units where $$c=1$$ since the factors of $$c$$ aren't important for determining who's older. Note $$\eta_{\mu\nu}$$ is itself the Minkowski metric here, which is $$\text{diag}(-1,+1,+1,+1)$$. In this metric signature, a timelike curve will have negative length, so we define the proper time to be $$d\tau=\sqrt{- ds^2}$$, so $$\tau = \int_C\sqrt{-d s^2}$$ is the time elapsed on the personal clock of someone traveling along the curve $$C$$ through spacetime.

If the curve $$C$$ is parametrized by a function $$X(t) = \langle t,\vec x(t)\rangle$$, then the above integral can be computed in the same way we would compute the arclength of a curve in a calculus 3 class: $$\tau = \int_C\sqrt{-d x^\mu\eta_{\mu\nu} dx^\nu} = \int_{t_1}^{t_2}\sqrt{-\frac{dx^\mu}{dt}\eta_{\mu\nu}\frac{dx^\nu}{dt}}dt.$$ This last expression is just a regular 1D integral. Note that this makes no assumptions about the particular coordinates we are using (if you change to, for example, polar coordinates, you would need to also change the components of $$\eta$$, but it is what it is) and certainly makes no assumptions about what kind of path the person is taking through spacetime...so there is absolutely zero inhibition to thinking about accelerating observers.

So, let's see how this calculation works out for the Earth observer, starting their path at $$t=0$$ for sake of convenience. $$\tau_E=\int_0^T\sqrt{1+0}dt = T.$$ This should not be a surprise, they were just sitting there till their clock hit $$T$$. What about the spaceship person? $$\tau_S=\int_0^T\sqrt{1-v^2}dt = T\sqrt{1-v^2} = T/\gamma.$$ Again, this should not be surprising...we have two inertial observers and when the Earth observer finally sees the ship person reach their destination, they had to wait longer for the light of the spaceship at its destination to get back to Earth.

In the particular situation OP has described with an alien, I will first point out that saying the alien is "static" would seem to suggest OP has a preferential reference frame in mind. This of course cannot happen. But even that aside, OP has said that both people wait 1 year to take their selfie...so assuming they have followed their own instructions they will be indeed 1 year older in the selfie. The difference would come up in which selfie the alien receives first, and the answer to that would depend on exactly what the alien is doing. Again, there is no sense in which the alien can be "static."

When they take their selfies, both individuals will have aged by 1 year according to their local clocks. So the selfies will show them at the same age.

However, you have posed the question with a built in asymmetry. The alien observer is stationary with respect to the ISS and will see time elapse at the same rate as the twin on the ISS. He/she will however see time going at half that rate for the twin traveling to Andromeda. As a result, the alien will not receive the selfies simultaneously. The selfie from the ISS twin will arrive first and one year later the selfie from the Andromeda twin will arrive.

The asymmetry can be fixed by having the alien traveling towards Andromeda at half the speed. So he is always midway between the two twins. In this case he/she will simultaneously receive two selfies showing (as before) both twins at the same age.

You will each appear to have aged by one year. However, if you were to stop at Andromeda (I mean reduce your speed to 0 relative to your twin back on Earth) and ask someone there the date and time, you will find it to be much further ahead than your own watch and calendar would suggest. In other words, the people there will believe that your watch has been running slow since you synchronised it with your twin back on Earth.

The secret to all these supposed time dilation paradoxes is that a moving clock must be compared to two stationary clocks which the moving one passes in turn. The differences in the times shown by the two stationary clocks when the moving clock passes each of them is always less than the time that seems to have elapsed during the same period according to the moving clock. The discrepancy appears to be time dilation to the stationary clocks, but to the moving clock it seems to be due to the stationary clocks being out of synch.

In your example, suppose you had been trailed by another space ship moving at the same distance as you, and whose clock was synchronised with yours, and which was so far behind you that it arrived at Earth just at the same time as you arrive at Andromeda according to your clocks. From the perspective of you and your companion ship, you have both been stationary and it is your brother who has moved between you. The people on the companion ship will see that you brother has aged only one year, which will surprise them because their clocks will suggest it is a much longer time since your brother started his journey from you.

What happens is that the plane of simultaneity in your frame of reference is tilted from that in your brother's, so even if you synchronise your frame's clocks when you and your brother are together, the further out in your respective frames, time becomes increasingly out of synch.

To make that concrete, suppose you had also been accompanied by a third ship travelling at the same speed as you but so far ahead that they were already at Andromeda when you were just passing Earth (according to your clocks). For the forward companion ship the time would be the same as it is for you, but if they were to ask the Andromeda locals (in the same frame as your brother) they would have an entirely different view of the date and time.


text:
181 posts / 1 project
Finding a lightweight but powerful code editor for Linux
Edited by Dawoodoz on
It seems like all code editors available for Linux are either quirky command line tools where you cannot copy using Ctrl-C (because that would kill the program), or a bloated web application dynamically transpiling into JavaScript only so that it can sand-box itself inside of a full copy of a web browser taking up hundreds of megabytes and leaving old versions of the browser behind when it updates.

Just need a stable light-weight editor with multi-document tabs, syntax coloring, file browser on the side and recursive folder search and replace.
44 posts
Finding a lightweight but powerful code editor for Linux
I mainly use vim but occasionally use kate as a backup from time to time. It has most of the features you are asking for. If you happen to be running KDE the dependencies will be minimal.

Here is a small project worth keeping an eye on https://github.com/rxi/lite and additional plugins for it https://github.com/rxi/lite-plugins. Not sure if it has recursive search or not.
7 posts
Finding a lightweight but powerful code editor for Linux
Dawoodoz
It seems like all code editors available for Linux are either quirky command line tools where you cannot copy using Ctrl-C (because that would kill the program), or a bloated web application dynamically transpiling into JavaScript only so that it can sand-box itself inside of a full copy of a web browser taking up hundreds of megabytes and leaving old versions of the browser behind when it updates.

Just need a stable light-weight editor with multi-document tabs, syntax coloring, file browser on the side and recursive folder search and replace.

vim fits all that criteria. Even Ctrl-C if you feel that is the only right way to do it.

 1 2 3 inoremap "+pa vnoremap "+y vnoremap "+d
181 posts / 1 project
Finding a lightweight but powerful code editor for Linux
Dawoodoz
It seems like all code editors available for Linux are either quirky command line tools where you cannot copy using Ctrl-C (because that would kill the program), or a bloated web application dynamically transpiling into JavaScript only so that it can sand-box itself inside of a full copy of a web browser taking up hundreds of megabytes and leaving old versions of the browser behind when it updates.

Just need a stable light-weight editor with multi-document tabs, syntax coloring, file browser on the side and recursive folder search and replace.

vim fits all that criteria. Even Ctrl-C if you feel that is the only right way to do it.

 1 2 3 inoremap "+pa vnoremap "+y vnoremap "+d

I should try it then.
Mārtiņš Možeiko
2446 posts / 2 projects
Finding a lightweight but powerful code editor for Linux
There's also Sublime Text, Geany and CodeLite that fit these requirements.
181 posts / 1 project
Finding a lightweight but powerful code editor for Linux
mmozeiko
There's also Sublime Text, Geany and CodeLite that fit these requirements.

I'll try CodeLite next then.
7 posts
Finding a lightweight but powerful code editor for Linux
Dawoodoz
mmozeiko
There's also Sublime Text, Geany and CodeLite that fit these requirements.

I'll try CodeLite next then.

BTW, vim isn't a editor to "try" you pick it and use it for life. Isn't it easy to start, since it's too different of actual paradigm of "code editors".

But, IMHO is worth it.

There is also emacs...
69 posts
Professional programmer, working in the video games industry since 2012
Finding a lightweight but powerful code editor for Linux
I came here to also recommend rxi's lite, it's the cleanest and most user friendly text editor I found in a while.
Miles
130 posts / 4 projects
Finding a lightweight but powerful code editor for Linux
BTW, vim isn't a editor to "try" you pick it and use it for life. Isn't it easy to start, since it's too different of actual paradigm of "code editors".

In other words, vim is a cult for people who succumb easily to the sunk cost fallacy.
181 posts / 1 project
Finding a lightweight but powerful code editor for Linux
Guntha
I came here to also recommend rxi's lite, it's the cleanest and most user friendly text editor I found in a while.

The interface does look neat and Lua scripting sounds like a good middle ground between resource effective and flexible.
7 posts
Finding a lightweight but powerful code editor for Linux
notnullnotvoid
BTW, vim isn't a editor to "try" you pick it and use it for life. Isn't it easy to start, since it's too different of actual paradigm of "code editors".

In other words, vim is a cult for people who succumb easily to the sunk cost fallacy.

As emacs. But as you can see, Casey's productivity is far high using it. The same is applied to vim.

I have tried many simple/IDE editors and I always return to vim.
Miles
130 posts / 4 projects
Finding a lightweight but powerful code editor for Linux
As emacs. But as you can see, Casey's productivity is far high using it.

Nah, not really. His productivity with emacs isn't noticeably higher than any other programmer using any other common text editor.
Amin Mesbah
6 posts
Finding a lightweight but powerful code editor for Linux
Geany falls into neither the quirky command line nor the bloated javascript category. I find it comparable to notepad++.
19 posts
Finding a lightweight but powerful code editor for Linux
Edited by Aphetres on
notnullnotvoid
BTW, vim isn't a editor to "try" you pick it and use it for life. Isn't it easy to start, since it's too different of actual paradigm of "code editors".

In other words, vim is a cult for people who succumb easily to the sunk cost fallacy.

notnullnotvoid
As emacs. But as you can see, Casey's productivity is far high using it.

Nah, not really. His productivity with emacs isn't noticeably higher than any other programmer using any other common text editor.

Ow! I just cut myself on the edginess of your posts. lol

The reason vim is one of the most popular editors, is because you can find it on every platform. Cross platform programmers don't want to learn a new editor every time they switch platform. Some programmers are just passing ships in the night on the OS they use, so they learn the editors that will always be there. ed, vi, vim, if you know all three you will have a familiar editor on every platform.

As much as I try, I would never be as fast as Casey using any editor.

notnullnotvoid
BTW, vim isn't a editor to "try" you pick it and use it for life. Isn't it easy to start, since it's too different of actual paradigm of "code editors".

In other words, vim is a cult for people who succumb easily to the sunk cost fallacy.

As emacs. But as you can see, Casey's productivity is far high using it. The same is applied to vim.

I have tried many simple/IDE editors and I always return to vim.

Emacs I would advise against. Its default config gives people RSI. Vim does not give you RSI.

See this thread from an old emacs fan who damaged her hands:

I used vim for a couple of years, but found it too complicated and never got good with it. I was always thinking about what keys to push next. Then I got the simple bug due to the Handmade Hero influence and and moved to ed(1) which is vi's predecessor, vi is vim's predecessor. ed(1) is so simple it has just 8 man pages and no config file, by comparison to master vim, you must read > 2000 pages.

The reason ed(1) is so simple is because it doesn't replicate anything that is already offered by the OS. It has a filter command and with it all the programs that are installed on Unix/Linux become your IDE. This is good if you are on Linux and know it well or want to know it well. Not so good if you are on Windows I imagine.

Someone above said they don't like editors that won't die when you press Ctr-C. That is because of the filter command in ed, vi, vim, You can start programs running using the filter command in ed, vi, or vim, and if the program misbehaves, you can kill it without killing your editor.

Miles
130 posts / 4 projects
Finding a lightweight but powerful code editor for Linux
Aphetres
Ow! I just cut myself on the edginess of your posts.

My posts have about as much edge as safety scissors. If you manage to cut yourself on that, I can't be held liable.
Aphetres
The reason vim is one of the most popular editors, is because you can find it on every platform.

Indeed, the advantage of vim is that it's available out of the box on virtually every linux distro (barring maybe android/chromeos/etc.) and runs in the terminal so you can use it in headless environments. That's about where its advantages end. If you're not a sysadmin, or otherwise finding yourself doing that kind of work, there is literally no reason to ever touch vim.
Aphetres
As much as I try, I would never be as fast as Casey using any editor.

That sounds like a you problem.


text:
# Math Help - Sobel operator smoothing, why?

1. ## Sobel operator smoothing, why?

Why does the Sobel operator, as the Wikipedia article also concludes, smooth the image out (with a triangle filter) perpendicular to the derivative direction, before it applies the central difference operator? What is the purpose of that?

2. ## Re: Sobel operator smoothing, why?

Originally Posted by TriKri
Why does the Sobel operator, as the Wikipedia article also concludes, smooth the image out (with a triangle filter) perpendicular to the derivative direction, before it applies the central difference operator? What is the purpose of that?
Presumably to reduce the effects of image noise on the numerical derivative, which is known to be a noise amplifying process.

CB

3. ## Re: Sobel operator smoothing, why?

Yes, that might much likely be it. My thought was that it would have something to do with the rotational symmetry of the operator, which is mentioned very shortly in the Wikipedia article (but not explained). I have to figure out what that is though.


text:
# Radio group labelling and semantics

I can't seem to get fieldset's to react properly when using display:table and display:table-cell even if I reset the default values, it just reacts oddly in a variety of ways in different browsers/devices, so as a result I have actually removed all fieldset's and replaced them with div's.

Is this a semantically accurate method to label a radio group? or is there a better more semantic method aside from using fieldset/legend?

<form method="get" novalidate>

Pet Type

</form>

I've always approached it in this manner, but to avoid using flexbox and floats I used the above instead.

<form method="get" novalidate>
<fieldset class="table">

<legend for="r1-group">Pet Type</legend>

</fieldset>
</form>

Should I be bolstering this with Schema's microdata and aria to improve semantics instead?

• Why is this tagged CSS when there is no CSS here? Also tagged as HTML5 when there are no new HTML5 elements. – cimmanon Mar 4 '15 at 22:45
• The CSS is listed encase someone perhaps knows a work around to the CSS oddities with fieldset, and similarly if there are html5 elements that aren't being used that may fit this situation better. – darcher Mar 4 '15 at 23:18
• The complaint about rendering sounds like a Stack Overflow question. If you want to use a fieldset, but you can't get it to render the way you want, ask on SO, stating what your expected rendering is, how the actual result differs, what browsers you have tested. – 200_success Mar 4 '15 at 23:46
• On the other hand, the semantic judgement question is still on-topic on Code Review. I think that fieldset is probably overkill for a single radio choice. – 200_success Mar 4 '15 at 23:50
• @200_success yup, that was my thought, hence why I didn't ask about CSS question, just mentioned it as a reason this situation came to light, and tagged encase someone wanted to add input. – darcher Mar 5 '15 at 0:12

You can’t use the label element like that. Its for attribute may only refer to "labelable elements" (and div isn’t labelable).

### Semantic markup

(Assuming that you can’t use fieldset.)

You can ignore all the div elements (except their "meaningful" attributes, if any), because they are meaningless. So your markup is essentially this:

<form method="get" novalidate>

Pet Type

Cat

Dog

</form>

Having a label without associated form control is not wrong, but maybe uncommon. It "represents a caption in a user interface", so I guess you could keep it like that.

If you want more "structure", you could use the dl element. However, I think it might be overkill for such a simple case.

### Accessibility

WAI-ARIA recommends "that elements with role radio are explicitly grouped in order to indicate which ones affect the same value".

(In HTML5, input elements in the radio button state have the radio role by default.)

How to group them explicitly?

This is achieved by enclosing the radio elements in an element with role radiogroup.

So you should use the radiogroup role, e.g.:

<form method="get" novalidate>

Pet Type

(HTML5 recommends not to set role="radio" for the radio buttons explicitly, but you may do so if you want to.)


text:
Chapter 2 - Review Exercises - Page 95: 49

137 ft

Work Step by Step

The vertical height of the tree is a leg of a right triangle, (label it with $a)$. $a$ is opposite to the measured angle $A=70^{o}$ The other leg, ($b$=50 ft) is adjacent to A. (SOHCAHTOA) We use $\displaystyle \tan A=\frac{a}{b}$ and solve for $a$: $a=b\cdot\tan A$ $a=50\cdot\tan 70^{o}\approx$137.373870973, which, to the nearest foot is 137 ft

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.