text stringlengths 1 1.11k | source dict |
|---|---|
This method is how to kill a fly with a gun, anyway it's working. You need to find a primitive of $$xe^{6x}$$. Search it as $$p(x)e^{6x}$$ where $$p(x)$$ is a polynomial of first degree. This is justified by observing that if you have a function like $$f(x)=p(x)e^{kx}$$ it is $$f'(x)=(p'(x)+kp(x))e^{kx}$$ and $$q(x)=p'... | {
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ros, imu, navigation, robot-pose-ekf, sensor
Originally posted by bikram.adhikari on ROS Answers with karma: 3 on 2015-03-26
Post score: 0
You can publish the raw data to ROS and use the AHRS (madgwick's filter) in imu_tools to process the data on the PC side.
Originally posted by tonybaltovski with karma: 2549 on 2... | {
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$\begin{split}t_{0,1} = (0) 2 \pi \frac{1}{N} \\ t_{1,1} = (1) 2 \pi \frac{1}{N} \\ ... \\ t_{N-1,1} = (N-1) 2 \pi \frac{1}{N} \\\end{split}$
In general, because the sequence $$k 0,1,,N-1$$ is equal to the sequence $$n \in 0,1,\ldots,N-1$$, this means that the column sampling positions for row $$n \in t_{0, n}, t_{1, ... | {
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... |
c++, c++14
Assumptions on types
There's no reason to cast n to be an int. size_t is fine:
size_t n = std::distance(first, last) - 1;
Similarly, I would initialize element with auto. You take arbitrary iterators, what if we had a huge container of size_t? You'd overflow.
Also, avoid this construction:
auto current{fir... | {
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Integrate the rows of a matrix where the data has a nonuniform spacing.
Create a vector of x-coordinates and a matrix of observations that take place at the irregular intervals. The rows of `Y` represent velocity data, taken at the times contained in `X`, for three different trials.
```X = [1 2.5 7 10]; Y = [5.2 7.7 ... | {
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"tags": ... |
OpenStudy (anonymous):
It does. I didn't mind waiting. Thank you so much! So, would I do the same sort of thing for this type of problem? Which set of parametric equations represents the graph of the following rectangular equation using t = 1 - x. y = x2 + 2
jimthompson5910 (jim_thompson5910):
are you given a graph?... | {
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"openwebmath_score": 0.6164286136627197,
"tag... |
fluid-dynamics, aerodynamics, air, heat-engine, aircraft
Title: The suction and thrust of an aircraft engine Does only the air sucked in (not the air that is ejected at the back of the engine) by an airliner engine (turbofan engine) causes a thrust forward or in other words pull the engine forward? and why ?
If so how... | {
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I like this way of thinking about it because it does apply to rational roots of integers; it just gives a different conclusion (that they're integers, rather than that they're irrational).
-
+1 because that was actually another question I had -- is it true that all rational squares of integers are themselves integers.... | {
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"openwebmath_score": 0.8872660398483276,
"ta... |
quantum-mechanics, waves, wavefunction, fourier-transform, dispersion
Title: Derivation of group velocity using Fourier transform The aim is to determine the group velocity of a wave packet with the general form
$$\Psi\left(x,t\right)=\frac{1}{\sqrt{2\pi}}\int_{-\infty}^{\infty} \phi\left(x\right)e^{i\left(kx-\omega t... | {
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"tags": "quantum-mechanics, waves, wavefunction, fourier-transform, dispersion",
"url": n... |
java, beginner, object-oriented
Assignment Summary
In this exercise, you implement a dungeon game. In the game, the
player is in a dungeon full of vampires. The player has to destroy the
vampires before his lamp runs out of battery and the vampires can suck
his blood in the darkness. The player can see the vamp... | {
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classical-mechanics
Title: Complex part of the solution for physical values What's a physical meaning of, for example, complex part of the solution for coordinate change of the anharmonic oscillator? | {
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The partials are
$$\frac{\partial D}{\partial x} = \frac{x}{D};\frac{\partial D}{\partial y} = \frac{y}{D}$$
The change in the distance $D$ with respect to $x$ is negative at three o'clock, because of the motion and position of the hands. Likewise, the change in $D$ with respect to $y$ is positive. At three o'clock, ... | {
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"openwebmath_score": 0.9452716112136841,
"tag... |
finite-impulse-response, octave, least-squares
The results changed, but they are still wrong. Even so, the a(1) terms in the middle seem to need multiplying by a constant. I used the hammer a bit and ~2.25 seems to be a reasonable value. It doesn't change the fact that the results are wrong (or that the hammer is not ... | {
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"tags": "finite-impulse-response, octave, least-squares",
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} |
thermodynamics, temperature, energy-conservation, thermal-conductivity
Title: Would a warm cup with water and ice inside cool the water faster than if the cup was normal temperature? Imagine you pour water and ice inside a glass cup (assume that the water and cup are at ambient temperature). Now, suppose that you get ... | {
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"tags": "thermodynamics, temperature, energy-conservation, thermal-conductivity",
"url": ... |
floating-point, integers, number-formats
Title: Why are floats converted from different integers sometimes equal? I'm trying to understand the following algorithm:
int ubnd = Integer.MAX_VALUE
int lbnd = ubnd
while (fload)lbnd == (float)ubnd {
lbnd = lbnd - 1
}
lbnd = lbnd + 1
print "$lbnd..$ubnd" | {
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A is defined as - A T ij = A ji; Where 1 ≤ i ≤ m and 1 ≤ j ≤ n. Logic to find transpose of a matrix. Dimension also changes to the opposite. © Parewa Labs Pvt. The following is a C program to find the transpose of a matrix: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 2… So, taking transpo... | {
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"lm_q2_score": 0.8519528038477824,
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"openwebmath_score": 0.46098050475120544,
"tag... |
control, matlab
Now, I would like to use stepinfo() to obtain the performance of the system, hence:
clear all
clc
kp=7130;
kd=59.3880;
num=[kd kp];
den=[1 (kd+18) (kp+72)];
F=tf(num,den);
step(F)
stepinfo(F)
which yields this information (i.e. obviously wrong)
RiseTime: 0.0133
SettlingTime: 0.0910
SettlingMin:... | {
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homework-and-exercises, newtonian-mechanics, classical-mechanics
Physically, one of three things can happen, depending on $F$. If $F$ is small, you won't lift either mass off the ground, the tension in the string will be $\frac F2$ and masses will be motionless. If $F$ is somewhat larger, the heavy mass will stay on... | {
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"tags": "homework-and-exercises, newtonian-mechanics, classical-mechanics",
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c#, functional-programming
So, go ahead and shoot at it. Can it be improved?
(It's not that important that the Random generator might be predictable.)
If you need to get a value of a Dictionary<TKey, TValue> you shouldn't use ContainsKey() together with the Item property getter but TryGetValue(), because by using Con... | {
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python, programming-challenge
The power of a set of cubes is equal to the numbers of red, green, and blue cubes multiplied together. The power of the minimum set of cubes in game 1 is 48. In games 2-5 it was 12, 1560, 630, and 36, respectively. The solution involves summing up the power of the minimum set of cubes of ... | {
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Write the sum as $\sum_{k=1}^{n}\frac{1}{n+k} = \sum_{1}^{n}\left(\frac{1}{1 + \frac{k}{n}}\right)\cdot\frac{1}{n}.$ Reinterpret this as the sum of the area of rectangles, where each rectangle has base [k/n, (k+1)/n] and height 1/(1 + k/n). Consider the function f defined by f(x) = 1/(1+x) on the interval [0,1]. Partit... | {
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"lm_q2_score": 0.8539127529517043,
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"openwebmath_score": 0.8891925811767578,
"tags... |
operating-systems, deadlocks
The ordering and protocol is a global invariant. All code everywhere at all times needs to follow the protocol to avoid deadlock. In practice, this is pretty difficult to enforce in realistic code unless there's a manager that handles resource access. | {
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"tags": "operating-systems, deadlocks",
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electromagnetism, general-relativity, gravity, differential-geometry, kaluza-klein
3. Rainich-Misner-Wheeler theory. There is a way to obtain electromagnetism from geometry, in the 4d spacetime of General Relativity. Rainich was able to give in 1925 necessary and suficient conditions that spacetime is curved in a way ... | {
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|E|<=3|V|-6
But I am unsure how to connect the two. Given either edges or vertices I can solve for the other, but I don't know how to find these. Apparently the number of vertices is 12, but why?
I am also unsure if the number of faces should be 20 or 21. The hint given says 20, but that's 20 triangular faces, leavin... | {
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"lm_q1_score": 0.9896718496130619,
"lm_q1q2_score": 0.8310610749231956,
"lm_q2_score": 0.8397339736884712,
"openwebmath_perplexity": 109.23174160926102,
"openwebmath_score": 0.7838432192802429,
"ta... |
quantum-chemistry, energy, spectroscopy
In the real world, at least at normal pressures, this limiting case of a single band comprised of all bonding orbitals seems unlikely. Instead, some orbitals where the energy separation between them is large likely form separate bands. In this case, the HOMO would still broaden... | {
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"tags": "quantum-chemistry, energy, spectroscopy",
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java, algorithm, reinventing-the-wheel
That's it for now, I will keep updating the list if something comes to me later.
Ref: Algorithms readAllInts
This is a wishy washy name. What does it mean, "all ints"? In the universe? In my little black book of ints? Entered by the user on standard input? Aha!
It might be good t... | {
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"tags": "java, algorithm, reinventing-the-wheel",
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bash, jq
[[ -f $filename ]] || die "$filename is not a file or does not exist."
[[ -r $filename ]] || die "$filename is not readable."
The -r implies -f. I would simplify this to one line:
[[ -r $filename ]] || die "$filename is not a readable file."
Use echo when it's good enough
Instead of printf '\n%s:\n' "$f" ... | {
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"tags": "bash, jq",
"url": null
} |
newtonian-mechanics, newtonian-gravity, orbital-motion, earth, satellites
Title: Gravitation question I’d like to ask the following doubt that came to me after some exercises:
Is it possibile to exactly establish,given a satellite orbiting Earth with a certain $\vec v_{0}$ and distance $\vec R_{1}$ from earth, with $v... | {
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"tags": "newtonian-mechanics, newtonian-gravity, orbital-motion, earth, satellites",
"url... |
general-relativity, spacetime, coordinate-systems, time, observers
Since TCG is defined in terms of an observer at rest relative to the Earth's center it is not affected by special relativity time dilation due to Earth's rotation. The conversion from TCB to TAI is a simple linear equation, so TAI is also oblivious to ... | {
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"tags": "general-relativity, spacetime, coordinate-systems, time, observers",
"url": null... |
java, parsing, tex
for (int i = 0; i < text.length(); i++) {
int c = text.codePointAt(i);
if (braceLevel > 0) {
if ((char) c == '{') {
braceLevel++;
} else if ((char) c == '}') {
braceLevel--;
}
... | {
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"openwebmath_score": null,
"tags": "java, parsing, tex",
"url": null
} |
c++, algorithm, programming-challenge, matrix, graph
int main (int argc, char const* argv[])
{
int n;
std::cin >> n;
std::vector<std::vector<int> >matrix(n,std::vector<int>(n));
for(int i=0;i<n;i++){
for(int j=0;j<n;j++){
std::cin >> matrix[i][j];
}
}
int i ,j ,power... | {
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"tags": "c++, algorithm, programming-challenge, matrix, graph",
"url": null
} |
ros, navigation, teleop, joy
Title: joystick output not reliable
Using joystick to drive turtlesim, he goes a ways then stops. If I move the stick a bit, he'll start up again. This may be a similar problem to seeing the numbers zero out when I run a full robot stack, with ROS_controls, and echo cmd_vel output to the ... | {
"domain": "robotics.stackexchange",
"id": 29680,
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"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "ros, navigation, teleop, joy",
"url": null
} |
quantum-mechanics, quantum-entanglement, probability, bells-inequality
Title: What if we test three photons instead of two in Bell's paradox? I am not a physicist and do not know anything about quantum mechanics (except that it can be formulated using Hilbert spaces), but watching a vulgarization video about Bell's pa... | {
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"url": ... |
roslaunch, image-view
<arg name="stereo" default="multisense_sl/camera"/>
<arg name="image_view" default="image_rect_color"/>
<node name="stereo_cam" pkg="image_view" type="stereo_view" >
<remap from="stereo" to=$(stereo) />
<remap from="image" to=$(image_view) />
</node>
</launch>
Originally posted by ... | {
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"openwebmath_score": null,
"tags": "roslaunch, image-view",
"url": null
} |
optics, geometric-optics, software
Title: Intensity loss due to vignetting I was trying to get an expression for the loss of intensity due to vignetting in a simple optical system, and got a fairly complex integral. I was wondering if there's an easier way, or any book that does this calculation. I guess not, because ... | {
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"id": 1997,
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"openwebmath_perplexity": null,
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"tags": "optics, geometric-optics, software",
"url": null
} |
genetics, gene-expression, mrna, protein-expression, microarray
‘Level’ is not a scientific unit, and can only be used unambiguously
as a scientific term in its English sense in relation to liquids, e.g. “The level of mercury in the thermometer had
fallen.”, “The land is 10 metres above sea level.”
It is used by some ... | {
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monte-carlo
Thats what I tried. Lets pick an arbitrary index $i$ which make sense in $V$, then check if $x=V[i]$ and return true or false as the equality holds or not.
My doubt comes at the time of calculating the probability of a correct answer as the statement gives no more details. Is it even numerically doable wit... | {
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1 Answer
You have sequences $(a_n)$ and $(b_n)$ which satisfy recurrence relations $$a_{n}=f(a_{n-1})$$ with some function $f$ and $$b_n=b_{n-1}+a_n.$$ Moreover you found an index $k=4$ and a positive step size $d=20$ with $a_{k+d}=a_k$. It follows by induction that $a_{n+d}=a_n$ holds for all $n\ge k$. Therefore it i... | {
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"lm_q2_score": 0.8267117855317474,
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"tag... |
electromagnetism, magnetic-fields, maxwell-equations
In this way, it is very similar to the fact that an antiderivative is only determined up to some arbitrary integration constant. | {
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the concept of differentiating a function with the concept of integrating a function. As we know, Integration is a reverse process of differentiation, which is a process where we reduce the functions into smaller parts. a) In all states, the French model of state leadership: and state guarantee of railway bonds was fol... | {
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"lm_q1_score": 0.9871787830929848,
"lm_q1q2_score": 0.8410297302997354,
"lm_q2_score": 0.8519528019683105,
"openwebmath_perplexity": 561.1808117201255,
"openwebmath_score": 0.8674394488334656,
"ta... |
javascript, jquery, animation, dom
Title: Show and hide posts using setTimeout I have made an effect that has the h1 move and then reveals p using .addClass, .removeClass and CSS3 transition. It works perfectly but I think I am repeating too much of the code and I think there may be a way to write it better. I need po... | {
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"tags": "javascript, jquery, animation, dom",
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} |
# Number of 5-digit numbers such that the sum of their digits is even
I found the same question on this site and many others...where everywhere the answer $45000$ is written ...while I have no problem with this but I am having problems with the logical answer...as everywhere it is written since total numbers is $90000... | {
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"lm_q2_score": 0.8757869916479466,
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"openwebmath_score": 0.7157057523727417,
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programming-challenge, parsing, rust
The full story can be found on the website.
My solution
src/day_3.rs
use {
anyhow::{anyhow, bail, ensure, Result},
itertools::Itertools,
ndarray::prelude::*,
std::io::{self, prelude::*},
};
pub const PATH: &str = "./data/day_3/input";
#[derive(Clone, Copy, Debug, ... | {
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electromagnetism, potential, maxwell-equations
$\nabla \times \mathbf{H}_F = j\omega \epsilon \mathbf{E}_F$
and using superposition we have
$\mathbf{E} = \mathbf{E}_A+\mathbf{E}_F$
$\mathbf{H} = \mathbf{H}_A+\mathbf{H}_F$
Solving the electric current case, we use the usual magnetic vector potential $\mathbf{A}$, where... | {
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"url": null
} |
Equations Poisson equation 1D, 2D, and 3D Laplacian Matrices dimension grid n bands w memory complexity 1D N N 3 1 2N 5N 2D N ×N N2 5. The electric field is related to the charge density by the divergence relationship. Solving a 2D Poisson equation with Neumann boundary conditions through discrete Fourier cosine transf... | {
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"lm_q2_score": 0.8289388104343892,
"openwebmath_perplexity": 603.9435741108301,
"openwebmath_score": 0.814243495464325,
"tags"... |
python, python-3.x, csv, web-scraping, selenium
from selenium import webdriver
from selenium.webdriver.common.by import By
from selenium.webdriver.support.ui import WebDriverWait
from selenium.common.exceptions import TimeoutException
from selenium.webdriver.support import expected_conditions as EC
import csv | {
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• I've reduced it to $$2^{1/4} \int_0^{\infty} \frac{dv}{(v^2+8)^{1/4} (v^2+2)^{1/2}}$$ – Ron Gordon Jun 15 '15 at 19:01
• It is interesting to point out that Mathematica evaluates the equivalent $$\int_{0}^{1}\frac{dx}{x^{3/4}(1-x)^{1/2}(x+1/3)^{1/4}}$$ almost instantly. – Jack D'Aurizio Jun 15 '15 at 19:17
• may this... | {
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"lm_q2_score": 0.8333245973817158,
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"openwebmath_score": 0.8526572585105896,
"tag... |
c++, linked-list, pointers
template <class T>
typename SingleLinkedList<T>::const_iterator SingleLinkedList<T>::cbefore_begin() const {
return before_begin();
}
#endif /* SingleLinkedList_h*/
Here is the main.cpp file:
#include <iostream>
#include <iterator>
#include <memory>
#include <utility>
#include <random>... | {
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c++, c++20
Data(const char *str, size_t length = 0, bool copy = false) : _type(STRING)
#if INITIALIZE_COPY
,
_copy(copy ? vector<uint8_t>{reinterpret_cast<uint8_t *>(const_cast<char *>(st... | {
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machine-learning, python, k-means
#print(X)
km = KMeans(n_clusters=3)
#labels = km.fit_predict(vectorizer)
#print(labels)
X = vectorizer.fit_transform(token_dict).todense()
km.fit(X)
pca = PCA(n_components=2).fit(X)
data2D = pca.transform(X)
# ==========================================================================... | {
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"tags": "machine-learning, python, k-means",
"url": null
} |
beginner, c, strings, pointers
Title: string-length, structs, pointers in c So since I'm just new with learning C (this is the second day now), I'd be very happy if someone could review my code:
what I tried to do is:
create a structure containing a string- and a length-property
I want to create a function, that chec... | {
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"tags": "beginner, c, strings, pointers",
"url": null
} |
normalization
This is thought to be one reason why ResNet is so effective: even if values die to ReLU, there is still the skip connection for them to propagate through.
Despite all this, it is still probably more common to normalize images with respect to the statistics of the whole dataset. One problem with per-image... | {
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• the set $$\{\mathbf{v}_i\}$$ is an orthogonal basis for the domain of $$A$$, and
• the set $$\{A\mathbf{v}_i\}$$ is an orthogonal basis for the range of $$A$$.
Now we can define the SVD.
Theorem. Let $$A$$ be an $$m\times n$$ matrix with rank $$r$$. Then there exists an $$m\times n$$ matrix $$\Sigma$$ whose diagon... | {
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... |
for epoch in range(5):
l = loss(net(x_train, keys, values), y_train)
l.backward()
trainer.step(1)
print(f'epoch {epoch + 1}, loss {float(l.sum()):.6f}')
net = NWKernelRegression()
loss = nn.MSELoss(reduction='none')
trainer = torch.optim.SGD(net.parameters(), lr=0.5)
animator = d2l.Animator(xlabel='epoch', ylabel='los... | {
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"lm_q1_score": 0.9828232924970204,
"lm_q1q2_score": 0.8103003786612976,
"lm_q2_score": 0.8244619199068831,
"openwebmath_perplexity": 8879.337267077532,
"openwebmath_score": 0.6985899209976196,
"tags": null,
... |
video-processing, camera, hardware
Each of these interact with each other so it is often difficult to find the right trade off.
The sensor size and resolution are usually related. For example, it is hard to find sensors with resolution above 1024 * 1200 in a 1/3" sensor.
The resolution and thus sensor size will dicta... | {
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} |
ros, intel, ros-kinetic
Originally posted by songshan with karma: 36 on 2019-12-07
This answer was ACCEPTED on the original site
Post score: 2 | {
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gazebo, ros-groovy, ubuntu, xacro
Title: Catkin_make problem with xacro when installing gazebo
I encountered a problem of xacro when I am trying to install gazebo. which is
CMake Error at /opt/ros/groovy/share/catkin/cmake/catkinConfig.cmake:72 (find_package):
CMake Error at /opt/ros/groovy/share/catkin/cmake/catkinC... | {
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"tags": "gazebo, ros-groovy, ubuntu, xacro",
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} |
kinect, octomap, ros-kinetic, ur10, ur5
<link name="${prefix}wrist_3_link">
<visual>
<geometry>
<mesh filename="package://ur_description/meshes/ur10/visual/wrist3.dae"/>
</geometry>
<material name="LightGrey">
<color rgba="0.7 0.7 0.7 1.0"/>
</material>
<... | {
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"tags": "kinect, octomap, ros-kinetic, ur10, ur5",
"url": null
} |
Your question is "are we allowed to use the regular definition of harmonic numbers when our $$n$$ is not necessarily a natural number?" The answer is no, since the "regular definition" of a sum is $$a_1 + a_2 + ... + a_n$$. Here $$n$$ is the number of summands which can't be a non natural number.
But you can very well... | {
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"lm_q2_score": 0.8807970748488297,
"openwebmath_perplexity": 373.008033976001,
"openwebmath_score": 0.9237313270568848,
"tags... |
java, tic-tac-toe
Example 2:
startPosition = (11 / 5) * 5 == 10
Example 3:
startPosition = (12 / 5) * 5 == 10
So now we have a starting position for the horizontal checking loop we can add a method to check the horizontal line. In the loops body we will check if the current position of the board does not equal... | {
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} |
gazebo-plugin
Originally posted by wicked88 with karma: 38 on 2016-08-13
This answer was ACCEPTED on the original site
Post score: 2
Original comments
Comment by blastpower5 on 2016-08-17:
Thanks for the help! I have also found a plugin that I put in the sdf file of my robot's model: ''. It publishes messages of type... | {
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newtonian-mechanics, reference-frames, rotational-dynamics, definition
part of constraint used to define center of mass, the general constraint is that Centre of mass is a point, for which, If all mass is assumed to be concentrated , will follow same equation of forces as if a point particle of same mass will follow, ... | {
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"tags": "newtonian-mechanics, reference-frames, rotational-dynamics, definition",
"url": ... |
electric-circuits, electrical-resistance, capacitance
Title: Do all capacitors in a DC circuit reach steady state if so then why? I want to know if capacitors connected in DC circuits having any combination of capacitors and resistors ever reach a steady state(no current flows through the capacitor) If that is the cas... | {
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"tags": "electric-circuits, electrical-resistance, capacitance",
"url": null
} |
deep-learning, image-recognition
———
Footnotes
[1] P. Sermanet, D. Eigen, X. Zhang, M. Mathieu, R. Fergus, Y. LeCun, Overfeat: Integrated recognition, localization and detection using convolutional networks, arXiv preprint arXiv:1312.6229v4
[2] A. Krizhevsky, I. Sutskever, G. E. Hinton, Imagenet classification with de... | {
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"tags": "deep-learning, image-recognition",
"url": null
} |
c++, performance, beginner
case 7 : alphabet = "-0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ";
cout << endl << endl << "Couldn't find the password, increasing the searching level."<< endl << endl << "Testing lowercase, uppercase characters and numbers(0123456789abcde... | {
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} |
c, image, console
mallocedPtr = malloc(MALLOC_SIZE);
if (mallocedPtr) {
exitStatus = function(mallocedPtr, ...);
free(mallocedPtr);
mallocedPtr = NULL;
}
else
{
exitStatus = EXIT_FAILURE;
}
return exitStatus;
}
The free() function only deallocates the memory, i... | {
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"tags": "c, image, console",
"url": null
} |
whose four sides all have the same length. Hello!!! We now have the approximate length of side AH as 13.747 cm, so we can use Heron's Formula to calculate the area of the other section of our quadrilateral. The area of the rhombus can be found, also knowing its diagonal. [3] P = 4s P = 4(10) = 40 Yes, because a square ... | {
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"openwebmath_score": 0.8021650314331055,
"tags... |
# Linear operator $A$ on a finite -dimensional vector space
Let $A$ and $B$ be linear operators on a finite dimensional vector space $V$ over $\mathbb{R}$ such that $AB=(AB)^2$. If $BA$ is invertible then which of the following is true:
(a) $BA = AB$ on $V$
(b) $\operatorname{tr}(A)$ is non zero
(c) $0$ is an eigenva... | {
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"lm_q2_score": 0.8499711832583696,
"openwebmath_perplexity": 328.3039916831494,
"openwebmath_score": 0.9139401316642761,
... |
supersymmetry, group-theory, lie-algebra, supergravity
of vectors to scalar and spinors in a sigma model way) and the $28$ vector fields with their duals are assigned to $56$ pseudo-real representation of $E_{7(7)} $. So$ E_7$ which acts on scalar fields also act on vector fields through duality transformation a prope... | {
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"openwebmath_score": null,
"tags": "supersymmetry, group-theory, lie-algebra, supergravity",
"url": null
} |
human-biology, cell-biology, muscles, glucose, liver
Title: What does the term 'glycogen mobilisation' mean? I read that glycogen is a mobilised store of glucose:
Glycogen is a readily mobilized storage form of glucose. It is a very large, branched polymer of glucose residues (Figure 21.1) that can be broken down to ... | {
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"openwebmath_score": null,
"tags": "human-biology, cell-biology, muscles, glucose, liver",
"url": null
} |
quantum-mechanics, time
Title: How close are we to measure Planck time I know that Plack time is considered a fundamental time unit by some of the physicists. To test this we need to try to falsify it. I want to learn what the smallest time interval we can measure is. Planck time is about $10^{-44}$ s. The most accura... | {
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"tags": "quantum-mechanics, time",
"url": null
} |
acid-base, equilibrium, aqueous-solution, ph
Check $x$ is small approximation: $\frac{x}{0.122} = 9.081\times10^{-9}$ which is less than $5\ \%$, so the approximation is valid.
My question
The answer I got using both of these methods, $\mathrm{pH} = 8.92$, is not correct. The only conclusion I can come to is that I ha... | {
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"tags": "acid-base, equilibrium, aqueous-solution, ph",
"url": null
} |
quantum-mechanics, quantum-field-theory
The integrand is the spectral energy distribution we want. Note that it is called spectral because the spectral distribution of the radiation in frequency can be rewritten as a function of energy given the dispersion relation. Here $n(\epsilon, T)$ is the mean occupation number ... | {
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"tags": "quantum-mechanics, quantum-field-theory",
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computational-physics
So, to do this, we have to generate the random numbers y instead of the random numbers s. s is uniformly distributed between 0 and 20, so y should be uniformly distributed between arctan(-4) and arctan(20).
And that should be that. I hope you found this useful. | {
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"tags": "computational-physics",
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speed-of-light, gravitational-waves
Title: Why were the GW detections at Livingston and Hanford separated by 7 ms if the light travel time between them is 10 ms? How did a gravitational wave travel from Livingston, Louisiana to Hanford, Washington in 7 milliseconds, when they are separated by 10 milli-light seconds (3... | {
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"openwebmath_score": null,
"tags": "speed-of-light, gravitational-waves",
"url": null
} |
algorithms, greedy-algorithms
$L(n,m)=n(m+1)+m^2$ if $Q_0$ is last
$nk + m(m+1)$ if $Q_0$ is $k^{th}$
Clearly, if you want to not put $Q_0$ last, then you might as well put it first so that the cost is $F(n,m)=n + m(m+1)$.
Now $L(n,m)-F(n,m)=nm+n+mm-n-mm-m=nm-m=(n-1)m$ so that whenever $n>1$ and $m>0$, we'll have $L(... | {
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"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "algorithms, greedy-algorithms",
"url": null
} |
bond, hydrogen-bond
See also the Wikipedia article about hydrogen bonding
A hydrogen atom attached to a relatively electronegative atom will play the role of the hydrogen bond donor An electronegative atom such as fluorine, oxygen, or nitrogen will be the hydrogen bond acceptor, irrespective of whether it is bonded to... | {
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"tags": "bond, hydrogen-bond",
"url": null
} |
newtonian-mechanics, forces, momentum, conservation-laws
Now, "any force applied in one direction is split in the opposite direction" would be far more misleading. This is because forces are not 'split'. Instead, they are exactly what the Third law says they are: TWO different forces, acting on TWO different objects. ... | {
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"tags": "newtonian-mechanics, forces, momentum, conservation-laws",
"url": null
} |
python, matplotlib
v=v-(10.0/1.0)*x*h #k=10.0, m=1.0
x=x+v*h
t=t+h
Two things: firstly, what are k and m? It seems that they should be constants with comments explaining their physical significance.
Secondly, this isn't Euler's method. Euler's method is \$\vec{x}_{n+1} = \vec{x}_n + hf(t_n, \vec{x}_n)\$ wh... | {
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"tags": "python, matplotlib",
"url": null
} |
javascript, jquery
$.fn.marquee = function(method) {
// Method calling logic
if (methods[method]) {
return methods[method].apply(this, Array.prototype.slice.call(arguments, 1));
} else if (typeof method === 'object' || !method) {
return methods.init.apply(this, argument... | {
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"id": 2965,
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"openwebmath_score": null,
"tags": "javascript, jquery",
"url": null
} |
c++, performance, c++11, programming-challenge, combinatorics
My solution is not yet accepted because of performance constraints in that it should output answers for 5 input even numbers within 10 seconds. On my Intel dual core system by using O3 compiler optimization, it is taking 35 seconds and without optimization ... | {
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"openwebmath_score": null,
"tags": "c++, performance, c++11, programming-challenge, combinatorics",
"url": null
} |
newtonian-mechanics, friction
Title: How to identify whether the friction is kinetic or static? The body 'A' is moving forward with certain acceleration over the ground. The ground applies a kinetic friction force on 'A' in backward direction to oppose the relative motion. The block 'A' also applies an equal and oppos... | {
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"openwebmath_score": null,
"tags": "newtonian-mechanics, friction",
"url": null
} |
javascript, jquery
if(min_rem == 59 && first_load) { $('#minutes').data('easyPieChart').disableAnimation(); }
$("#minutes").data('easyPieChart').update((100/59)*min_rem);
if(min_rem == 59 && first_load) { $('#minutes').data('easyPieChart').enableAnimation(); }
if(sec_rem == 59 && f... | {
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"id": 14551,
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "javascript, jquery",
"url": null
} |
vectors, group-theory, rotation, rotational-kinematics, angular-velocity
Title: How is it that angular velocities are vectors, while rotations aren't? Does anyone have an intuitive explanation of why this is the case? This is a note on why angular velocities are vectors, to complement Matt and David's excellent expla... | {
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"tags": "vectors, group-theory, rotation, rotational-kinematics, angular-velocity",
"url"... |
thermodynamics
So, Boyle's law is talking about isothermal condition,right? But, what if temperature is not constant?
My thinking:
Suppose, there is a given gas in a frictionless cylinder fitted with a piston. Its initial temperature is $t_0$ and its pressure is $p_0$ . It is at equilibrium initially and hence the pi... | {
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"tags": "thermodynamics",
"url": null
} |
special-relativity, inertial-frames
\end{bmatrix}
\tag{A-17}
\end{equation}
\begin{align}
&\Bbb{L}(\rm{A}\mathbf{v})\cdot\Bbb{A}\cdot\Bbb{L}\left(-\mathbf{v}\right)=
\nonumber\\
&\begin{bmatrix}
&I+(\gamma-1)\rm{A} \mathbf{n}\mathbf{n}^{\rm{T}}\rm{A}^{\rm{T}} &\hspace{5mm} -\;\dfrac{\gamma \upsilon}{c}\rm{A}\... | {
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"tags": "special-relativity, inertial-frames",
"url": null
} |
ruby, elasticsearch
Things will break if the info hash doesn't have an attributes key - your code is assuming it's there. A way to avoid this is to use Hash#fetch to absorb nil values:
puts info['host'] if info.fetch('attributes', {})['master'] == 'true'
Since all you want is the master node, it'd be more expressive ... | {
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Another visual proof. Recently published in arXiv
Yet another line of thought would be this: \begin{align} e^{\pi} > \pi^e &\iff \pi \ln(e)>e\ln(\pi)\\ &\iff \pi >e\ln(\pi) \\ &\iff \ln(\pi)>\ln(e)+\ln (\ln (\pi)) \\ &\iff \ln(\pi)>1+\ln (\ln (\pi)) \end{align} By concavity of $\ln$, $x-1>\ln(x)$ for all $x\neq 1$. Wi... | {
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"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9683812318188366,
"lm_q1q2_score": 0.8172121789376514,
"lm_q2_score": 0.8438951025545426,
"openwebmath_perplexity": 323.2235854854502,
"openwebmath_score": 0.9777542948722839,
"tag... |
mathematical-physics, differential-geometry, mathematics, relativity, vectors
Title: In coordinate-free relativity, how do we define a vector? Relativity can be developed without coordinates: Laurent 1994 (SR), Winitzski 2007 (GR).
I would normally define a vector by its transformation properties: it's something whose... | {
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"tags": "mathematical-physics, differential-geometry, mathematics, relativity, vectors",
"... |
javascript, game, playing-cards
this.shuffle = function () {
var tempCard,
randomDeckIndex,
tempCardSuit = 1,
tempCardNumber = 1;
deckOfCards.length = 0;
// Populate deck with 52 cards in order
for (var i = 0; i < 52; i++) {
deckOfCards[i] = new Car... | {
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"id": 2946,
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"lm_name": null,
"lm_q1_score": null,
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"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "javascript, game, playing-cards",
"url": null
} |
quantum-mechanics, quantum-field-theory, field-theory
$$ a(p)=i\int d^3x\ e^{ipx}\overset{\leftrightarrow}{\partial_0}\phi(x),\ a^\dagger(p)=-i\int d^3x\ e^{-ipx}\overset{\leftrightarrow}{\partial_0}\phi(x)$$
where $g\overset{\leftrightarrow}{\partial_0}f:=g\partial_0f-(\partial_0 g)f$. This relation is always true (a... | {
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"tags": "quantum-mechanics, quantum-field-theory, field-theory",
"url": null
} |
python, beginner, algorithm, python-3.x, validation
Don't use the name bd - call it perhaps full_board, and pieces instead of pcs. temp needs a better name as well.
Later down, your piece dictionary should be pieces because it's a collection.
Range
hor should not use a manual tuple, and should instead use range(8, 0, ... | {
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"tags": "python, beginner, algorithm, python-3.x, validation",
"url": null
} |
error-correction, stabilizer-code
In this picture, the $k$ logical $X$ operators $\{\bar{X}_i\}$ are represented by a $k \times 2n$ matrix $L^X$. The $i$th operator will the $i$th row of the matrix $L^X_i$. Similarly, for the logical $Z$ operators. You have not mentioned in your question if the logical operators of yo... | {
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"tags": "error-correction, stabilizer-code",
"url": null
} |
thermodynamics, adiabatic, reversibility
Similarly we can't say all irreversible process are adiabatic but we can say most of them occurs adiabatically.
In practical all the changes in thermodynamics state supposed to occurs in quasistatic process. | {
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"tags": "thermodynamics, adiabatic, reversibility",
"url": null
} |
rospy
I don't remember why I got that impression but I really did believe it!
Well technically you could argue that since rospy.sleep(..) calls time.sleep(..) (one of its variants) it does allow Python to suspend that thread and allow other threads to become active.
Again, technically, you could describe that as "oth... | {
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"tags": "rospy",
"url": null
} |
human-biology
P.S.
Are there also more scientific names for these "finger lines" so that I can look it up somewhere? Googling "finger lines" brings up a lot of stuff about palm reading. I am not sure that this can be accurately estimated because the outer layer of skin is ill-defined in terms of cells and cell boundar... | {
"domain": "biology.stackexchange",
"id": 227,
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"openwebmath_score": null,
"tags": "human-biology",
"url": null
} |
fft, fourier-transform, dft, 3d
OK, so to then make the connection that is required to answer the questions, we need one more observation: The fact that the n-dimensional FFT is equivalent to the 1D FFT successively applied to each orthogonal dimension.
For the 2D FFT, we first perform an FFT along the X direction. Th... | {
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"tags": "fft, fourier-transform, dft, 3d",
"url": null
} |
c++, design-patterns, c++11, template, polymorphism
Doing it this way also gives the compiler better opportunities for optimizations.
I am not sure I would do release like that.
T* release() {
T* p = m_p;
m_p = 0;
return p;
}
You now have a pointer to an object with the ref-count incremented to +1. If you... | {
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"tags": "c++, design-patterns, c++11, template, polymorphism",
"url": null
} |
c++, c++11, reinventing-the-wheel, pointers
Ptr& operator-=(int i) {
check_range(index-i);
index -= i;
p -= i;
return *this;
}
Thus moving p during the lifetime of the object is not a good idea (because you must call delete on the pointer returned by new). So if you are going to move p you need to kee... | {
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"tags": "c++, c++11, reinventing-the-wheel, pointers",
"url": null
} |
machine-learning, predictive-modeling, statistics, logistic-regression, machine-learning-model
However, in case you observe $y$, and in case you don't have rasons to believ that there is a bias in $y$, you should be fine with a normal Logit. Here it would be really important for you to clarify what your problem actual... | {
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"tags": "machine-learning, predictive-modeling, statistics, logistic-regression, machine... |
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