text stringlengths 1 1.11k | source dict |
|---|---|
organic-chemistry, reaction-mechanism
To reduce the reactivity, the phenol is first mono-sulfonated ( some of the product which is substituted may also be used). The products are ortho- and para-isomers. The para-isomer is separated and then nitrated. The nitration is comparatively far smoother (easier to handle).
Ips... | {
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"tags": "organic-chemistry, reaction-mechanism",
"url": null
} |
python, python-2.x, regex, pygame, chess
funciones.py -> Line: 129
def move_back():
global pos, history
output = ''
if pos > 0:
pos -= 1
if history[pos][2] == 2:
statem = 'del lamesa.lista_'+history[pos][0][0]+'['+(str)(history[pos][0][1])+']'
exec statem
... | {
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"tags": "python, python-2.x, regex, pygame, chess",
"url": null
} |
everyday-chemistry, alcohols, combustion, materials, fuel
Down here in the south, where it's hot and humid most of the year, you hear a news story or two about this every year, usually when a gas station didn't properly purge its storage tank on a regular basis. The regular addition of thousands of gallons of fresh et... | {
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"tags": "everyday-chemistry, alcohols, combustion, materials, fuel",
"url": null
} |
Theorem.
# Columns that correspond to basic variables are linearly independent
The columns that correspond to basic variableslink are linearly independent.
Proof. By definitionlink, basic variables correspond to pivot columns. We know from theoremlink that the columns corresponding to pivot columns are linearly inde... | {
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"openwebmath_score": 0.7695202231407166,
"tags": n... |
Equations with Fourier Series and Boundary Value Problems answers. 3) with the coefficients (5. Here, the workflow for Fourier transforms is demonstrated by calculating the deflection of a beam due to a force. Introduction to Fourier Transforms Fourier transform as a limit of the Fourier series Inverse Fourier transform:... | {
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"lm_q1_score": 0.9850429120895838,
"lm_q1q2_score": 0.8007091966034915,
"lm_q2_score": 0.8128673246376009,
"openwebmath_perplexity": 765.7105353484437,
"openwebmath_score": 0.7930785417556763,
"tags... |
thermodynamics, material-science, physical-chemistry, phase-transition, phase-diagram
Title: Quenching of binary alloy: Concentration equilibrium I'm currently reading "Models for phase separation and their mathematics" by Paul C. Fife and there is a paragraph which I don't understand because I lack the necessary bac... | {
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"tags": "thermodynamics, material-science, physical-chemistry, phase-transition, phase-diag... |
collision
<link name="back_right_leg">
<collision name="collision">
<origin pose="-0.78 -0.38 0.34 0 0 0"/>
<geometry>
<cylinder radius="0.02" length="0.68"/>
</geometry>
</collision>
<visual name="visual">
<origin pose="-0.78 -0.38 0.34 0 0 0"/>
<geometry>
<cy... | {
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"tags": "collision",
"url": null
} |
classical-mechanics, lagrangian-formalism, reference-frames, coordinate-systems, centrifugal-force
Title: Centrifugal Force and Polar Coordinates In Classical Mechanics, both Goldstein and Taylor (authors of different books with the same title) talk about the centrifugal force term when solving the Euler-Lagrange equa... | {
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"tags": "classical-mechanics, lagrangian-formalism, reference-frames, coordinate-systems, ce... |
# Exercise 9.7.2
## Exercise statement
Let $f : [0,1] \to [0,1]$ be a continuous function. Show that there exists a real number $x$ in $[0,1]$ such that $f(x) = x$. This point $x$ is known as a fixed point of $f$, and this result is a basic example of a fixed point theorem, which play an important rôle in certain typ... | {
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"lm_q2_score": 0.8311430415844384,
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"openwebmath_score": 0.9872211217880249,
"tags": ... |
php, object-oriented, repository
$result = filter_var( $email , FILTER_VALIDATE_EMAIL );
if(!$result)
throw new \CustomException("Invalid Email");
$obj = $this->userRepo->getByEmail($email);
if(!is_null($obj))
throw new \CustomException("Email already found");
... | {
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"openwebmath_score": null,
"tags": "php, object-oriented, repository",
"url": null
} |
compilers, parsers
Title: Not getting the clear picture of Goto actions , reduce and shift actions in SLR Parsing I am going through the following lecture notes on LR parsing :
https://www3.nd.edu/~dthain/courses/cse40243/fall2016/chapter4b.pdf
For the following grammar :
The following LR automation has been done :
... | {
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"tags": "compilers, parsers",
"url": null
} |
And the formula to find the standard deviation of a sample (denoted as, Measures of Central Tendency: Definition & Examples. Measures of dispersion are used to describe the variability or spread in a sample or population. Relative Dispersion The actual variation or dispersion, determine from standard deviation or other... | {
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"lm_q1_score": 0.9585377272885904,
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"lm_q2_score": 0.8376199694135332,
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"openwebmath_score": 0.8919327259063721,
"... |
# Math Help - Integral (secx)^-1
1. ## Integral (secx)^-1
$/int sec^{-1}xdx$
How do I start?
2. Originally Posted by circuscircus
$/int sec^{-1}xdx$
How do I start?
Start by expressing the question clearly. Presumably you want:
integral arcsec(x) dx.
Start by putting u=arcsec(x), then sec(u)=x, or 1/cos(u)=x.
R... | {
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"openwebmath_score": 0.9901721477508545,
"tag... |
classical-mechanics, lagrangian-formalism, differential-geometry, coordinate-systems, covariance
Title: How does the Lagrangian transform when coordinates are changed? I'll talk of single particle Lagrangian in $n$ dimensions.
Suppose in a given coordinate system with the coordinates $(q_i)_{i=1}^n$, the Lagrangian is... | {
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astrophysics, astronomy, planets
This is similar to how asteroids fairly commonly pass closer than the distance of the Moon to Earth. It's interesting and notable, but not catastrophic, which makes me want to say based on intuition that your estimate is reasonable. | {
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"tags": "astrophysics, astronomy, planets",
"url": null
} |
ds.algorithms, reference-request
C_1={1,2,3}, C_2={ 4,5,6}, C_3={1,2,4}
v_fill = [ 1, 1, 1, 1, 1, 1, 2, 0 ]
v_C_1 = [ 1, 1, 1, 0, 0, 0,-1, 1 ]
v_C_2 = [ 0, 0, 0, 1, 1, 1,-1, 1 ]
v_C_3 = [ 1, 1, 0, 1, 0, 0,-1, 1 ]
v_clear= [ 3, 3, 3, 3, 3, 3, 3,-2 ] | {
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"tags": "ds.algorithms, reference-request",
"url": null
} |
general-relativity, special-relativity, black-holes, spacetime
The problem with the universe is that it has no outside. All observers are by definition inside it, and their attempts to measure it are always restricted by the sorts of problems with coordinates that I've just described. What General Relativity gives us ... | {
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"tags": "general-relativity, special-relativity, black-holes, spacetime",
"url": null
} |
c++, matrix, library
deter = (a + c) * (a + c) -4 * (a*c-b*b);
}else if(X == 3)
{
float determinant1 = (data[1][1] * data[2][2]) - (data[2][1] * data[1][2]);
float determinant2 = (data[1][0] * data[2][2]) - (data[2][0] * data[1][2]);
float determinant3 = (data[... | {
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"tags": "c++, matrix, library",
"url": null
} |
# Lindelof Exercise 2
The preceding post is an exercise showing that the product of countably many $\sigma$-compact spaces is a Lindelof space. The result is an example of a situation where the Lindelof property is countably productive if each factor is a “nice” Lindelof space. In this case, “nice” means $\sigma$-comp... | {
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"lm_q1q2_score": 0.8057260766037354,
"lm_q2_score": 0.822189134878876,
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"openwebmath_score": 0.9999508857727051,
"tags": n... |
There are more innovative ways to solve this question. A few of them have not been discussed here. Can you all think of any other way to solve it? Would love to see a few other methods!
I will post two more ways to solve this question tomorrow. In the mean time, expecting some more responses with other ways to solve t... | {
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"lm_q1_score": 0.9744347905312774,
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"lm_q2_score": 0.9196425377849806,
"openwebmath_perplexity": 1808.9536375803552,
"openwebmath_score": 0.7690556645393372,
"tags": ... |
# Limits and restrictions?
If we assume that the restrictions put on simplified forms of expressions to prevent evaluation at points undefined in the original unsimplified form are important why do we drop them when dealing with limits? For example, consider the following when trying to find the derivative of $f= x^2%... | {
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"openwebmath_score": 0.9446923136711121,
"tag... |
c#, performance, beginner
Ran on my machine in ~127s for maxVal = 100.
I really didn't put much effort into this, so it's not the nicest code ever, but should provide a clear example of how to do this without the explicit filtering stage and reduced opportunity for thread contention (though this clearly isn't a big de... | {
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We can put all of this together. The group $H_2(M,\mathbb{Z})$ is given by the quotient of the kernel of $F \to E$ by the image of $0 \to F$, i.e. $0/0 \cong 0$. The group $H_1(M,\mathbb{Z})$ is given by the quotient of the kernel of $E \to V$ by the image of $F \to E$, i.e. $\mathbb{Z}^2/\mathbb{Z} \cong \mathbb{Z}$. ... | {
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"lm_q1_score": 0.9744347905312772,
"lm_q1q2_score": 0.8162060275906882,
"lm_q2_score": 0.8376199572530448,
"openwebmath_perplexity": 179.18659594049885,
"openwebmath_score": 0.9441990852355957,
"ta... |
torque
I have been trying to answer this question, Z axis: Stepper motor and lead screw torque calculation, over on the 3D Printing site.
I obtained an equation for the raising torque from
Torque Required to Raise Load (TR) Calculation and the full equation, for both thread and collar, is given by:
$$T_R = \frac{Fd_m}... | {
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"tags": "torque",
"url": null
} |
homework-and-exercises, energy, work
I thought work would be given as $\int F_{ext} \cdot dx$, giving $mg \Delta h=(.5) g (3\times 10^{-3})$, but apparently it is $ \frac{mg \Delta h}{2}$.
The solution arrives at this by considering $W= \frac{yAl}{L} \frac{l}{2}$, which is the energy associated with Young's modulus an... | {
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"tags": "homework-and-exercises, energy, work",
"url": null
} |
Example 2 Every Cayley graph ${Cay(G,S)}$ is also a Schreier graph ${Sch(G,S)}$, using the obvious left-action of ${G}$ on itself. The ${k}$-regular graphs formed from ${l}$ permutations ${\pi_1,\ldots,\pi_l \in S_n}$ that were studied in the previous set of notes is also a Schreier graph provided that ${\pi_i(v) \neq ... | {
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"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9940889309686339,
"lm_q1q2_score": 0.8032906701740407,
"lm_q2_score": 0.8080672112416737,
"openwebmath_perplexity": 84.97322490766847,
"openwebmath_score": 0.9605917930603027,
"tags": ... |
kinematics, acceleration, definition, differentiation
$$
\frac{s}{t} = \frac{\frac{1}{2}at^2}{t} = \frac{1}{2}at \ ,
$$
whereas
$$
\frac{\Delta s}{\Delta t} = \frac{s(t+\Delta t)-s(t)}{\Delta t} = \frac{\frac{1}{2}a(t+\Delta t)^2-\frac{1}{2}at^2}{\Delta t}=\frac{at\Delta t+\frac{1}{2}a\Delta t^2}{\Delta t} \approx at ... | {
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"id": 70301,
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"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "kinematics, acceleration, definition, differentiation",
"url": null
} |
Beyond that, the coil and its integral. The GRE, Graduate Record Examination, is an integral part of the application process for many graduate or business schools. 2 The integral psychograph is based on the notion that human beings have multiple distinct interior ca-. Test your choice of u: (du/dx), or a constant multi... | {
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"lm_q1_score": 0.9752018426872777,
"lm_q1q2_score": 0.8105322318081508,
"lm_q2_score": 0.8311430478583168,
"openwebmath_perplexity": 729.8619265918579,
"openwebmath_score": 0.8300469517707825,
... |
You did not end up with power series yet: \begin{align*} \sum_{n=0}^{\infty} (n+1)x^n+\sum_{n=0}^{\infty} (n+1) x^{n+1} &=\sum_{n=0}^{\infty} (n+1)x^n+\sum_{n=1}^{\infty} n x^{n}\\ &=\sum_{n=1}^{\infty} (2n+1) x^{n} + 1\\ &=\sum_{n=0}^{\infty} (2n+1) x^{n}\\ \end{align*}
From here you can derive correct radius of conv... | {
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"openwebmath_perplexity": 510.9299508526779,
"openwebmath_score": 0.9994896054267883,
"tags... |
c++, linux, assembly, windows
Recent Intel (and, I believe, AMD) CPUs seem to have a special execution path that lets this run just about as fast as anything--if any more than a minuscule percentage of your data may be in main memory, it becomes difficult to measure the difference between this and the fastest code pos... | {
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"tags": "c++, linux, assembly, windows",
"url": null
} |
thermodynamics, phase-transition
I would like to calculate this temperature for:
$$\begin{align*}
T & = 300\;\mathrm{K} \\
RH & = 0.5 \\
P & = 1\;\mathrm{atm} \approx 10^5\;\mathrm{Pa}
\end{align*}
$$
where $RH$ is the relative humidity.
The vapor pressure under these conditions is about $P_V \approx 3.5 \times 10^3\;... | {
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"tags": "thermodynamics, phase-transition",
"url": null
} |
general-relativity, differential-geometry, ads-cft, boundary-conditions, differential-equations
Now I thought, did I have to include all possible $g_{\mu\nu}$? Well, that wouldn't make much sense, since all other terms of the background metric are zero, right? And even if I include them, I'll get more equations, and s... | {
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"tags": "general-relativity, differential-geometry, ads-cft, boundary-conditions, differenti... |
exclude only a small number of objects. Combinations and Permutations Calculator. I want to create all possible sequence of numbers with 10 digits by using numbers 0 to 9 . P(10,5)=10!/(10-5)!= 30,240 Possible Orders. For example, locks allow you to pick the same number for more than one position, e.g. The calculator p... | {
"domain": "blitsogiannis.gr",
"id": null,
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"lm_q1_score": 0.960361158630024,
"lm_q1q2_score": 0.810444082221903,
"lm_q2_score": 0.843895106480586,
"openwebmath_perplexity": 551.8044542757877,
"openwebmath_score": 0.616959810256958,
"tags... |
homework-and-exercises, statistical-mechanics
The autocorrelation function of $\eta(t)$ is written as:
\begin{equation}
<\eta(t) \eta(t+\tau)>=k\delta(\tau)
\end{equation}
What I understand from the term 'Gaussian noise' is that the function $\eta(t)$ will take random values at any time $t$, corresponding to a Gaussia... | {
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"url": null
} |
quantum-field-theory, hilbert-space
This is called second quantization. And, in very reductive terms, all we did is just rewriting a sum as a product, a bit like $\sum_{n_i} \prod_i a_{n_i,i} = \prod_i\sum_n a_{n,i}$
$$
\begin{aligned}
\bigoplus_{n_1,n_2,\ldots=0}^\infty \bigotimes_{i=1}^\infty \mathcal{H}_{\mbox{stat... | {
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${\displaystyle {\text{angle in degrees}}={\text{angle in radians}}\cdot {\frac {180^{\circ }}{\pi }}}$
For example:
${\displaystyle 1{\text{ rad}}=1\cdot {\frac {180^{\circ }}{\pi }}\approx 57.2958^{\circ }}$
${\displaystyle 2.5{\text{ rad}}=2.5\cdot {\frac {180^{\circ }}{\pi }}\approx 143.2394^{\circ }}$
${\display... | {
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"openwebmath_score": 0.9678522348403931,
"tags"... |
digital-filters, bandpass, scipy, baseband
Title: Complex Samples (IQ) - Baseband Filtering We are currently analyzing a large set of IQ samples in a desktop application and we are interested in implementing many different bandpass filters dynamically.
We realized, that working with scipy offers no suppport for comple... | {
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"tags": "digital-filters, bandpass, scipy, baseband",
"url": null
} |
with -854. Beginner’s Guide to Portfolio Optimization with Python from Scratch. Work involves mathematical modeling, statistical analysis, statistical computing, dimensional data analysis, pattern discovery for data. These optimizations can play an important role both in the cases of rebalancing as well as in the case ... | {
"domain": "freccezena.it",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9632305381464927,
"lm_q1q2_score": 0.8047632511380802,
"lm_q2_score": 0.8354835309589074,
"openwebmath_perplexity": 1894.8592761976015,
"openwebmath_score": 0.26045969128608704,
"t... |
c++, multithreading, callback, c++20
void runExample()
{
auto cb_simple_cookie = _broadcast.add_listener([&](auto fr_) noexcept { simpleCallback(fr_); });
_cb_oneShot_cookie = _broadcast.add_listener([&](auto fr_) noexcept { oneShotCallback(fr_); });
_cb_twostep_cookie = _broadcast.add_list... | {
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"tags": "c++, multithreading, callback, c++20",
"url": null
} |
python, python-3.x, classes, python-requests
SettingReader = create_SettingReader_class()
domain = "https://my_dummy_api.com"
headers = {"Authorization": "my_token"}
reader = SettingReader(domain, headers, 'my_device_serial')
result_A = reader.read_setting_A()
result_B = reader.read_setting_B()
result_C = reader.rea... | {
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"url": null
} |
group-theory, conventions, lie-algebra, trace
On a related note, some physics texts change the normalization by defining "the generators of the $\mathrm{SU}(3)$ group" as $T_i=\frac{1}{2}\lambda_i$. But these just fulfil $\mathrm{trace}(T_iT_j)=\frac{1}{2}\delta_{ij}$ which seems just as unnatural to me. (And the diff... | {
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"tags": "group-theory, conventions, lie-algebra, trace",
"url": null
} |
lagrangian-formalism, metric-tensor, field-theory, covariance, variational-calculus
Then
$$\partial_{\mu}\Bigg(\frac{\partial \mathcal{L}}{\partial (\partial_{\mu} \phi)}\Bigg) = \partial_{t} \partial^{t} \phi + \partial_{x} \partial^{x} \phi$$
We seem to missing a minus sign here. Where's the mistake... | {
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"tags": "lagrangian-formalism, metric-tensor, field-theory, covariance, variational-calculu... |
dataset, recommender-system, graphs
Problem is the pipe names change doesn't occur where there is a tank - they change name because historical reasons, size or connections...
So if I want to graphically show that S tank 2 is connected to pipeline 2 at point X and pipeline 2 connects to pipeline and the content goes to... | {
"domain": "datascience.stackexchange",
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"tags": "dataset, recommender-system, graphs",
"url": null
} |
As perhaps the most important special case, consider multiplying $$n \times k$$ matrix $$A$$ and $$k \times 1$$ column vector $$x$$
According to the preceding rule, this gives us an $$n \times 1$$ column vector
(2)$\begin{split}A x = \left[ \begin{array}{ccc} a_{11} & \cdots & a_{1k} \\ \vdots & \vdots & \vdots \\ a_... | {
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"openwebmath_score": 0.9709522724151611,
"tags":... |
python, dynamic-programming, memoization
def memoize(fn)
def inner(*args):
try:
return cache[args]
except IndexError:
cache[args] = fn(*args)
return cache[args]
return inner
# Natural abstracted algorithm.
@memoize
def lcs(s1, s2):
if not s1 or not s2:
... | {
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"tags": "python, dynamic-programming, memoization",
"url": null
} |
thermodynamics, visible-light, electromagnetic-radiation, experimental-physics, home-experiment
But your laser is such an open system that any scattering of photons off the hot gas molecules of the flame probably just dissipates the heat in all directions. It makes no sense then, to talk about an ensemble of photons w... | {
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"tags": "thermodynamics, visible-light, electromagnetic-radiation, experimental-physics, ho... |
neural-network, keras, cnn
Title: Why do people import weights for DenseNet when Keras includes them? In several Kaggle kernels I've seen that people often import their weights into Keras' DenseNet. In the following case, I believe the weights are sourced from this github repo and contain the pre-trained weights on th... | {
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"tags": "neural-network, keras, cnn",
"url": null
} |
ros, ardrone-autonomy
I really appreciate it if anyone can help with these issues.
Originally posted by z3391384 on ROS Answers with karma: 11 on 2014-08-21
Post score: 0
I know that it's been a while, but from what I know about the AR.Drone and ardrone_autonomy here's my input:
Is AR.Drone flying? If it's not, the... | {
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"url": null
} |
quantum-algorithms, quantum-gate, matrix-representation, teleportation, quirk
$|\psi\rangle = \begin{bmatrix} \alpha \\ \beta \end{bmatrix}$
the operations are as follows:
$H_2C_{2,1}C_{1,0}H_1
\left (
\begin{bmatrix} \alpha \\ \beta \end{bmatrix} \otimes \begin{bmatrix} 1 \\ 0\end{bmatrix} \otimes \begin{bmatrix} 1 ... | {
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"id": 504,
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"tags": "quantum-algorithms, quantum-gate, matrix-representation, teleportation, qui... |
c#, multithreading, .net, asynchronous, http
This is similar in some ways to working with a BackgroundWorker but seems less annoying.
OMDBSearcher is a request-type specific object that is a wrapper around a generic http request processor called HttpGetter. The interface OMDBSearcher uses to access HttpGetter is simil... | {
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"tags": "c#, multithreading, .net, asynchronous, http",
"url": null
} |
a. 35
b. 40
c. 45
d. 50
e. 55
The Common Formula is Average speed = Total distance / Total time.
However if the distances traveled with two different speeds are the same (as 30 in this case), we can calculate the average speed as per following rule.
ratio of two distinct speeds = 1:2
Difference of two distinct speeds ... | {
"domain": "gmatclub.com",
"id": null,
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"openwebmath_score": 0.8038458228111267,
"tags... |
gazebo-sensor, contact
Title: contact force sensing
It seems that there is a bump/force sensor that works for contact on a link. However, does this scale or is there another implemented sensor that would allow me to get contact forces all over a robot arm? Essentially, I'd like to simulate tactile sensing. I have ... | {
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"tags": "gazebo-sensor, contact",
"url": null
} |
microcontroller, gazebo, ros-hydro, camera
Originally posted by Marcus on ROS Answers with karma: 164 on 2014-03-20
Post score: 2
It appears the old way of using a PR2 controller manager is deprecated and does not work anymore in hydro (Example of a roll/pitch mount using that approach here).
Everything you need to k... | {
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"tags": "microcontroller, gazebo, ros-hydro, camera",
"url": null
} |
quantum-mechanics, hilbert-space, quantum-information, unitarity
Title: Is that possible to have some state-specific unitary operator to escape from the non-clone theorem? The non-clone theorem states that for arbitrary states, it is not possible to have a unitary transformation such that
$$
\hat{U} | \phi_A \rangle... | {
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"tags": "quantum-mechanics, hilbert-space, quantum-information, unitarity",
"url": null
} |
spectroscopy, ir-spectroscopy
But that $\pu{2727 cm-1}$ band seems of too weak intensity. Then the $\pu{2911 cm-1}$ band would be the $\ce{C-H}$ elongation from the methoxy group ($\ce{O-CH3}$) of vanillin.
So which is the right one? If neither, can aldehyde shows just one band at $\pu{2839 cm-1}$ instead of two (for ... | {
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"id": 17875,
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"tags": "spectroscopy, ir-spectroscopy",
"url": null
} |
everyday-chemistry, electrochemistry, materials, electricity
This discharging is probably not linear, and its rate would be decreasing. Also, consider it as illustrative number only. It may differ for different cell technologies and age. Discharge cutoff cuts the connection before a real 0% charge. So the effective 0%... | {
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"tags": "everyday-chemistry, electrochemistry, materials, electricity",
"url": null
} |
mathematics, textbook-and-exercises, trace-distance
$$
|\operatorname{Tr}(A^{\ast} B)|
= \biggl| \sum_{k} s_k \langle \psi_k | B | \phi_k\rangle \biggr| \leq \sum_k s_k |\langle \psi_k | B | \phi_k\rangle|
\leq \sum_k s_k \|B\| = \| A \|_{\text{tr}} \| B \|.
$$ | {
"domain": "quantumcomputing.stackexchange",
"id": 2059,
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"tags": "mathematics, textbook-and-exercises, trace-distance",
"url": null
} |
ros, pr2, grasping, tutorials
[INFO] [WallTime: 1313333963.061611] [3135.721000] controller manager: waiting for pr2_controller_manager/list_controllers to be there
[INFO] [WallTime: 1313333963.100582] [3135.728000] controller manager: pr2_controller_manager/list_controllers found
[INFO] [WallTime: 1313333963.313206] ... | {
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"url": null
} |
# What's the benefit of using strong induction when it's replaceable by weak induction?
Example of a proof of a theorem using weak(ordinary) induction
The two types of inductions have process of proving P(a) and "for all integers $n \ge b, P(n)$" as a result in common.
For example, in the proof of the following ques... | {
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"tags... |
c++, array, reinventing-the-wheel
// Phase 2: Mutate "ALL" your state to final state.
// You can not call anything that is not `noexcept`
// This limits you to very basic operations.
// Luckily swap method is `noexcept`
swap(copy);
// Phase 3: Clean u... | {
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"tags": "c++, array, reinventing-the-wheel",
"url": null
} |
quantum-chemistry, orbitals, molecular-orbital-theory
are only two electrons, only the bonding orbital is occupied, but because the Pauli exclusion principle tells us we can only have two electrons in a given orbital, if you add another electron (as in $\ce{He2+}$), it will occupy the higher-lying "anti bonding" orbit... | {
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"tags": "quantum-chemistry, orbitals, molecular-orbital-theory",
"url": null
} |
ros, rviz, laser, ros-melodic, fixed-frame
Title: Who publishes the map frame?
ROS Melodic, Ubuntu18, Gazebo9
Issue:
Not able to visualize laser scan data in rviz
Error:
No tf data. Actual error: Fixed Frame [map] does not exist
Steps to recreate:
Launch gazebo with ros
roslaunch gazebo_ros empty_world.launch
Insert... | {
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"tags": "ros, rviz, laser, ros-melodic, fixed-frame",
"url": null
} |
general-relativity, spacetime, metric-tensor, wormholes
Anyway, the claim is that this Einstein-Rosen bridge also has an event horizon, you passed through it and what is a finite time for you, but your light stops streaming back to a distant observer, and they see you appear to slow down as you slowly take forever to ... | {
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"tags": "general-relativity, spacetime, metric-tensor, wormholes",
"url": null
} |
quantum-information, history, specific-reference, bloch-sphere
Title: Which paper introduced the concept of the "Bloch sphere"? Everyone loves Bloch sphere, but which paper of Bloch was it introduced? The Wikipedia article on Bloch sphere (here), as of 17/May/2021 links to this paper of Bloch “Nuclear Induction” but i... | {
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"tags": "quantum-information, history, specific-reference, bloch-sphere",
"url": null
} |
electricity, voltage, short-circuits
Title: is the voltage drop of a battery that is being short circuited the same as the battery's advertised voltige So I know this is a pretty fundamental question, but I'll ask it any way. lets say you have a 12V battery, and the positive is connected to the negative directly by a ... | {
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"id": 3392,
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "electricity, voltage, short-circuits",
"url": null
} |
cosmology, universe, space-expansion, big-bang, popular-science
I might rephrase the question like this: What's the smallest size of the Universe for which we have substantial observational evidence in support of the standard big-bang picture?
People can disagree about what constitutes substantial evidence, but I'll n... | {
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"id": 1231,
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"tags": "cosmology, universe, space-expansion, big-bang, popular-science",
"url": null
} |
evolution, ecology
Title: Deciduous trees in tropical rainforest Some books says the dominant plant form in tropical rainforest biome is broad leaved evergreen trees. Other books say it is broad leaved evergreen trees and deciduous trees. What is the most accepted way (or the truth)? Also how do you explain the decidu... | {
"domain": "biology.stackexchange",
"id": 3229,
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"lm_name": null,
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "evolution, ecology",
"url": null
} |
newtonian-mechanics, forces, rotational-dynamics, centrifugal-force
Here, tension and weight are real forces (non fictitious) for an external observer (even for an observer on the ball surface). Weight is compensated by the $T_y$ component of tension.
Hence: what does compensate the $T_x$ component of the real tension... | {
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"tags": "newtonian-mechanics, forces, rotational-dynamics, centrifugal-force",
"url": nul... |
special-relativity, soft-question, notation
$$
T^{\mu_1...\mu_p}_{\nu_1...\nu_q} \partial_{\mu_1} \otimes ... \otimes \partial_{\mu_p} \otimes dx^{\nu_1}... dx^{\nu_q}
$$
where $\{\partial_\mu\}$ denotes a basis for your vector space and ${dx^\nu}$ denotes a basis for its dual vector space. (The notation I chose is f... | {
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"tags": "special-relativity, soft-question, notation",
"url": null
} |
quantum-mechanics, photons, momentum
$$
\frac{1}{\sqrt{2}}\big(\lvert +2p \rangle_M \lvert +p \rangle_{\gamma_1} \lvert -p \rangle_{\gamma_2} + \lvert +2p \rangle_M \lvert -p \rangle_{\gamma_1} \lvert +p \rangle_{\gamma_2} \big)
$$
That is, even after measurement the system is still in a superposition. This is because... | {
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"tags": "quantum-mechanics, photons, momentum",
"url": null
} |
gravitational-waves, statistics, ligo
In this case, the p-value is apparently $p(O|H)\approx2\times10^{-7}$. Also, apparently the only other plausible explanation is a BH-BH merger. In an earlier question we estimated the prior probability of this to be $\approx10^{-4} \text{ to } 10^{-1}$. If we suppose that is the o... | {
"domain": "physics.stackexchange",
"id": 28643,
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"lm_q2_score": null,
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"openwebmath_score": null,
"tags": "gravitational-waves, statistics, ligo",
"url": null
} |
human-biology, immunology, pharmacology, medicine, antibiotics
Phototoxic reaction
Phototoxic damage refers to the direct damage the photoactivated drug can cause to the tissue. Light leads to excitation of electrons and as they return, they can lead to formation of reactive oxygen species which damage the cell membra... | {
"domain": "biology.stackexchange",
"id": 5907,
"lm_label": null,
"lm_name": null,
"lm_q1_score": null,
"lm_q1q2_score": null,
"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "human-biology, immunology, pharmacology, medicine, antibiotics",
"url": null
} |
vcf, filtering, bcftools
1 841166 rs12124819 G A . . PR GT 0/1
1 858952 rs12127425 G . . . PR GT 0/0
1 866156 rs79373928 T . . . PR GT 0/0
1 880041 rs72888853 N . . . PR GT ./. First of all, bcftools might be a bit of overkill if you want one specific variant. Al... | {
"domain": "bioinformatics.stackexchange",
"id": 2295,
"lm_label": null,
"lm_name": null,
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"lm_q1q2_score": null,
"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "vcf, filtering, bcftools",
"url": null
} |
c, console, formatting, animation, unicode
while still being easy to use.
Here some examples that demonstrate what can be done with this library. These examples can also be found in examples.c:
I am already fairly happy with the implementation of my grid structure, that stores and accesses data in a very compact mann... | {
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"id": 39125,
"lm_label": null,
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "c, console, formatting, animation, unicode",
"url": null
} |
machine-learning, deep-learning, keras, regularization, dropout
Dropout also works as a form of regularisation, as it is penalising the model for its complexity, somewhat.
I would recommend having a read of the Dropout section in Michael Nielsen's Deep Learning book (freely available), which gives nice intuition and a... | {
"domain": "datascience.stackexchange",
"id": 7153,
"lm_label": null,
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"lm_q2_score": null,
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"tags": "machine-learning, deep-learning, keras, regularization, dropout",
"url": null... |
on 1. equations where you have a variable in an exponent 2. equations that are quite complicated and can be simplified using logarithms. Approximating a function with a polynomial by making the derivatives equal at f(0) Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medici... | {
"domain": "cmccintl.com",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9808759638081522,
"lm_q1q2_score": 0.8173880676218309,
"lm_q2_score": 0.8333245973817158,
"openwebmath_perplexity": 1750.0349962657733,
"openwebmath_score": 0.4318494498729706,
"tag... |
python, protein-structure, biopython
ATOM 30 CG TRP A 4 16.164 0.734 0.997 1.00 11.80 C
ATOM 31 CD1 TRP A 4 16.913 -0.218 1.669 1.00 12.50 C
ATOM 32 CD2 TRP A 4 15.535 0.036 -0.079 1.00 11.53 C
ATOM 33 NE1 TRP A 4 16.806 -1.43... | {
"domain": "bioinformatics.stackexchange",
"id": 1994,
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "python, protein-structure, biopython",
"url": null
} |
python, performance, beautifulsoup, python-requests
tag_keywords = ['python']
content_keywords = ['python'.casefold()]
res = []
with requests.Session() as sess:
for page_num in range(1):
new_questions_page_req = sess.get(f'https://stackoverflow.com/questions?tab=newest&page={page_num}')
soup = Be... | {
"domain": "codereview.stackexchange",
"id": 39845,
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "python, performance, beautifulsoup, python-requests",
"url": null
} |
general-relativity, spacetime, differential-geometry, metric-tensor, tensor-calculus
And the tetrad basis of the paper $[2]$ is given by:
\begin{cases}\hat{\textbf{e}}_{(0)} = \frac{1}{N}\frac{\partial}{\partial x^{0}} + \frac{\omega}{N}\frac{\partial}{\partial x^{3}}\\ \hat{\textbf{e}}_{(1)} = \sqrt{1-\frac{b(r,\the... | {
"domain": "physics.stackexchange",
"id": 69018,
"lm_label": null,
"lm_name": null,
"lm_q1_score": null,
"lm_q1q2_score": null,
"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "general-relativity, spacetime, differential-geometry, metric-tensor, tensor-calcul... |
quantum-electrodynamics, quantum-optics, density-operator, cavity-qed, open-quantum-systems
$$ \gamma(t) \to \gamma = \int_0^{\infty}\mathrm{d}s\; e^{i\epsilon s} \Gamma(s), $$
so that we effectively have a constant spontaneous emission rate over time, leading to pure exponential decay.
When does $\Gamma(s)$ decay rap... | {
"domain": "physics.stackexchange",
"id": 19478,
"lm_label": null,
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"openwebmath_score": null,
"tags": "quantum-electrodynamics, quantum-optics, density-operator, cavity-qed, open-quantu... |
ros, moveit, collision, transform
Originally posted by courrier on ROS Answers with karma: 454 on 2014-06-13
Post score: 3
You could subscribe to the "monitored_planning_scene" topic (which is what the RVIZ plugins do). This will publish the current planning scene, which includes changes to collision objects and atta... | {
"domain": "robotics.stackexchange",
"id": 18265,
"lm_label": null,
"lm_name": null,
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "ros, moveit, collision, transform",
"url": null
} |
$\alpha^3 = 2$ and $\alpha \in \Bbb R$
since $\sigma$ fixes $\Bbb Q$ taking $\sigma$ of both sides gives:
$(\sigma(\alpha))^3 = 2$
now that doesn't seem to help much, but at least it does tell us $\sigma(\alpha)$ is a root of $x^3 - 2$.
let's expand our investigation of $x^3 - 2$ a bit. suppose $\omega$ is a root o... | {
"domain": "mathhelpboards.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9433475715065793,
"lm_q1q2_score": 0.8127299843343267,
"lm_q2_score": 0.8615382165412808,
"openwebmath_perplexity": 178.1052126639129,
"openwebmath_score": 0.9436347484588623,
"ta... |
java, ai, connect-four
int i = Board.i;
int j = Board.j;
while(j < Boards[0].length-1 && Boards[i][j+1].piece == Piece.None)
j++;
switch(currentPlayer)
{
case 1:
Boards[i][j].setPiece(Piece.Blue);
break;
case 2:
... | {
"domain": "codereview.stackexchange",
"id": 23497,
"lm_label": null,
"lm_name": null,
"lm_q1_score": null,
"lm_q1q2_score": null,
"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "java, ai, connect-four",
"url": null
} |
c, parsing
Title: Classifying lexemes in a given C program Please review my code and tell where I can improve my program.
#include <stdio.h>
#include <string.h>
#include <ctype.h>
#include <stdlib.h>
#define BUFFER_SIZE 1024
#define TOKEN_SIZE 32
#define TRUE 1
#define FALSE 0
int isKeyword(const char* token)
{
... | {
"domain": "codereview.stackexchange",
"id": 15040,
"lm_label": null,
"lm_name": null,
"lm_q1_score": null,
"lm_q1q2_score": null,
"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "c, parsing",
"url": null
} |
homework-and-exercises, newtonian-mechanics, forces, vectors, free-body-diagram
It is possible, it is just not useful.
What is so special in the second case that we can't do the same for the first one? | {
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"tags": "homework-and-exercises, newtonian-mechanics, forces, vectors, free-body-diagram",
... |
$P(A\cap\overline{E}) = ?$
I know that the result should be $0,4545$
Also, what how do I calculate the probability for Adam to win, if the 6 was in the first 3 throws?
Thank you
• You should not calculate $P(A|E^c)$. That would be the probability that Adam wins given the fact that Eve didn't win and it is essential... | {
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"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9787126531738088,
"lm_q1q2_score": 0.8069113151834929,
"lm_q2_score": 0.8244619220634457,
"openwebmath_perplexity": 530.5672042046926,
"openwebmath_score": 0.9231860637664795,
"tag... |
arc of wire T At center of arc, φ→ arc's central angle in radians. The strength of the magnetic field is proportional to the number of turns. The Biot-savart\'s law is a general modification of. Reply Delete. Both laws can be used to calculate the net magnetic field produced at a point by various distributions of curre... | {
"domain": "aoly.pw",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9715639644850629,
"lm_q1q2_score": 0.8075086305677752,
"lm_q2_score": 0.8311430436757312,
"openwebmath_perplexity": 686.7284100631799,
"openwebmath_score": 0.8189038634300232,
"tags": null,
... |
complexity-theory, turing-machines, automata, finite-automata, space-complexity
It is a well-known fact that this problem is PSPACE-hard, but the only proof that I am aware of is not particularly trivial. I believe the first proof was given in:
Dexter Kozen. Lower Bounds for Natural Proof Systems. FOCS 1977: 254-266.... | {
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"tags": "complexity-theory, turing-machines, automata, finite-automata, space-complexity",
"ur... |
# How to show this obvious and basic property of abelian groups?
I have a question that is probably very silly, but let's go. Let $(G,+)$ be an abelian group. In that case we know that $+$ is associative and commutative. This leads us to the following: if $\{a_i \in G : i \in I_n\}$ with $I_n = \{i \in \mathbb{N} : 1 ... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9766692257588072,
"lm_q1q2_score": 0.892359748455787,
"lm_q2_score": 0.9136765292901317,
"openwebmath_perplexity": 389.432666711012,
"openwebmath_score": 0.9243401288986206,
"tags"... |
type-theory, dependent-type, semantics
Title: What's the categorical semantics of definitional equality? The categorical semantics of a dependent type theory is normally described as a CwA/CwF/CompCat/etc. and in these models, we can talk about propositional equality by interpreting an 'identity type'. So, what about ... | {
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"id": 5262,
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"lm_q2_score": null,
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"openwebmath_score": null,
"tags": "type-theory, dependent-type, semantics",
"url": null
} |
combinatorics, probability-theory, probabilistic-algorithms
\P_{a_0,\ldots,a_k}[C_0(a_0,\ldots,a_k)]
&= \frac{1}{k+1}\sum_{i=0}^k \P_{a_0,\ldots,a_k}[C_i(a_0,\ldots,a_k)] \\
&= \frac{1}{k+1}\sum_{i=0}^k \E_{a_0,\ldots, a_k} \I[C_i(a_0,\ldots, a_k)] \\
&= \frac{1}{k+1} \E_{a_0,\ldots, a_k} \sum_{i=0}^k \I[C_i(a_0... | {
"domain": "cs.stackexchange",
"id": 20505,
"lm_label": null,
"lm_name": null,
"lm_q1_score": null,
"lm_q1q2_score": null,
"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "combinatorics, probability-theory, probabilistic-algorithms",
"url": null
} |
thermodynamics, temperature
I am unable to figure out why would $x$ also necessarily increase. Obviously $r$ and $d$ are part of the same container so that would increase at the same rate. But it is not given that $x$ is made of the same material as the container. I am not saying that the rod wouldn’t increase at all.... | {
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"id": 44955,
"lm_label": null,
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"lm_q1q2_score": null,
"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "thermodynamics, temperature",
"url": null
} |
linear transformations. The zero In contrast, the zero linear substitution 8 >> >< >> >: y 1 = 0 y 2 = 0 y 3 = 0 y 4 = 0 destroys everything in sight by setting all variables zero. Properties of this matrix will imply properties of the linear transformation itself. A Matrix is an array of numbers: The determinant of th... | {
"domain": "shopnetplus.it",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.986571747626947,
"lm_q1q2_score": 0.801951925875367,
"lm_q2_score": 0.8128673133042217,
"openwebmath_perplexity": 351.95506445665274,
"openwebmath_score": 0.8326934576034546,
"tag... |
c++, object-oriented, neural-network
void NeuralNetwork::reduceLearnRate(double factor)
{
learnRate_ = learnRate_ / factor;
std::cout << "learnRate_ reduced to:\t" << learnRate_ << "\n";
}
void NeuralNetwork::storeResults()
{
/// Store essential parameters of the network: weights and biases
for (int i... | {
"domain": "codereview.stackexchange",
"id": 38019,
"lm_label": null,
"lm_name": null,
"lm_q1_score": null,
"lm_q1q2_score": null,
"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "c++, object-oriented, neural-network",
"url": null
} |
c++, linked-list, iterator
element<T> *prev = nullptr;
element<T> *next = nullptr;
T data;
int elem_ID = 0;
char t_flag = '\0';
element(T const& copy)
: data(copy)
{}
// In C++11 we introduced the concept of moving data
// rather than copying it (as in C++03). This is as
// ... | {
"domain": "codereview.stackexchange",
"id": 13004,
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"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "c++, linked-list, iterator",
"url": null
} |
ubuntu-trusty, ubuntu, ros-indigo
Comment by Nap on 2015-02-27:
ERROR: the following rosdeps failed to install apt: command [sudo -H apt-get install -y libgl1-mesa-dev] failed
Comment by Nap on 2015-02-27:
Perhaps there is another package that needs to be added to your list?
Comment by Spyri on 2015-03-06:
I have been... | {
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"id": 20957,
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"openwebmath_score": null,
"tags": "ubuntu-trusty, ubuntu, ros-indigo",
"url": null
} |
norm #define two vectors a = np.array([2, 6, 7, 7, 5, 13, 14, 17, 11, 8]) b = … There is nothing special about the Euclidean norm. Vector norms are any function that fulfil the following criteria: 1. JonnyJohnson May 29, 2013, 6:21am #1. euclidean_distances (X, Y = None, *, Y_norm_squared = None, squared = False, X_nor... | {
"domain": "ubbcluj.ro",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9658995703612219,
"lm_q1q2_score": 0.8491674804342325,
"lm_q2_score": 0.8791467627598856,
"openwebmath_perplexity": 353.12657717468664,
"openwebmath_score": 0.9066149592399597,
"tags"... |
php, mysql, pdo, authentication
$sqlQuery->execute(array(':username' => $username,
':password' => $password));
/**
* Note: I could have used PDO's rowCount() here but chose not to
* There's no particular reason why I did that
*/
... | {
"domain": "codereview.stackexchange",
"id": 9321,
"lm_label": null,
"lm_name": null,
"lm_q1_score": null,
"lm_q1q2_score": null,
"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "php, mysql, pdo, authentication",
"url": null
} |
idris
-- If l and m intersect at a point a, then they both contain a.
intersection_result : (l : line) ->
(m : line) ->
(a : point) ->
IntersectsAt l m a ->
(Contains l a, Contains m a)
-- For any two distinct points t... | {
"domain": "codereview.stackexchange",
"id": 31011,
"lm_label": null,
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "idris",
"url": null
} |
r, file-formats, phylogenetics
# Convert matrix to genind format (for adegenet package)
test <- df2genind(temp, ploidy = 4, sep = "")
test
# How to convert to STRUCTURE?
If anyone has input, please chime in! Thanks I ultimately found this function, which I used for the purpose of converting a genind to a STRUCTURE f... | {
"domain": "bioinformatics.stackexchange",
"id": 2212,
"lm_label": null,
"lm_name": null,
"lm_q1_score": null,
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "r, file-formats, phylogenetics",
"url": null
} |
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