text stringlengths 49 10.4k | source dict |
|---|---|
meteorology, climate-change, precipitation, climate-models
* Model reliability is obviously a fairly active field of debate and research. Suckling and Smith (2012) indicates that GCM-based ensembles are better than basic statistical models, but probably not currently much better than some more advanced statistical mod... | {
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"tags": "meteorology, climate-change, precipitation, climate-models",
"url": null
} |
genetics, human-genetics, population-genetics, twins
Title: Why was the study of "Concordance of Monozygotic and Dizygotic twins for traits" designed in this way? I am confused by the twin study 'Concordance of Monozygotic and Dizygotic twins for traits.' My questions arose from 3:17-4:17 of the video
And this is the... | {
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"tags": "genetics, human-genetics, population-genetics, twins",
"url": null
} |
of a cactus graph with n vertices and k cycles is explored. Spectral graph drawing: FEM justification If apply finite element method to solve Laplace’s equation in the plane with a Delaunay triangulation Would get graph Laplacian, but with some weights on edges Fundamental solutions are x and y coordinates (see Strang’... | {
"domain": "openquestionspodcast.com",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9883127409715956,
"lm_q1q2_score": 0.8125800017952117,
"lm_q2_score": 0.8221891392358014,
"openwebmath_perplexity": 1161.143805608858,
"openwebmath_score": 0.5253098607063... |
fluid-dynamics
Title: Is Mass Flow an Additive Property? Mass ($m$) is an additive property in the sense that the total mass within a system can be simply determined by adding up the mass of each individual substance that's in it.
However, if two mass flows ($m/t$) of different liquids were to be mixed to form a sing... | {
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"tags": "fluid-dynamics",
"url": null
} |
Other pseudo-face relations include a strangely familiar-looking Law of Cosines. \begin{align} Y^2 + Z^2 - 2 Y Z \cos A &= H^2 = W^2 + X^2 - 2 W X \cos D \\ Z^2 + X^2 - 2 Z X \cos B &= \,J^2 = W^2 + Y^2 - 2 W Y \cos E \\ X^2 + Y^2 - 2 X Y \cos C &= K^2 = W^2 + Z^2 - 2 W Z \cos F \end{align} \tag{2} where each of $$A$$,... | {
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"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9805806506825456,
"lm_q1q2_score": 0.8554069448932483,
"lm_q2_score": 0.8723473630627235,
"openwebmath_perplexity": 337.2846036906231,
"openwebmath_score": 0.9008432030677795,
"tag... |
python, statistics, simulation
def single_match_game_state(home_implied_goals: float,
away_implied_goals: float,
match_length: int=95) -> MatchGameState:
"""
Given match length in minutes and implied goals for home and away teams,
simulates teams sc... | {
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"tags": "python, statistics, simulation",
"url": null
} |
gene-expression, virology, synthetic-biology
Title: Balanced vs Maximized Codon Optimization I have worked with the optimization of several viral proteins, from different viruses/families, with different results.
When Menzella, 2011 was published I tried that method. I found quite the contrary result, in that rando... | {
"domain": "biology.stackexchange",
"id": 3595,
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"tags": "gene-expression, virology, synthetic-biology",
"url": null
} |
My questions are as follows:
• Is this correct?
• If so, how does one determine the fact that all x's must be equal to each other from here?
• What would be be partial derivative equations if p = 1?
One bonus ease of implementation question:
• Is there an easy way to show all those results in wolfram alpha for this... | {
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"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9799765604649332,
"lm_q1q2_score": 0.8034762469639305,
"lm_q2_score": 0.8198933315126791,
"openwebmath_perplexity": 176.07921623372934,
"openwebmath_score": 0.925609290599823,
"tag... |
graphs
Title: Party optimization: maximum weight independent set in a tree/graph From Cornell
Suppose we want to throw a party for a company whose organization
chart is a binary tree. Each employee has an associated fun value, and
we want the set of invited employees to have the maximum total fun,
which is the... | {
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"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "graphs",
"url": null
} |
electromagnetism, electromagnetic-induction
Title: How does current flow if back emf equals to applied voltage Suppose we have a circuit with a voltage source, a switch open and an inductor all in series. If we close the switch, the potential difference of the voltage source is instantaneously applied to the inductor.... | {
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"tags": "electromagnetism, electromagnetic-induction",
"url": null
} |
python, pandas
allocate memory contiguously whenever possible
use the vectorisation capabilities of your libraries, in this case Numpy, rather than loops
That requires a rewrite, which I will partially demonstrate. Otherwise:
Use PEP484 typehints and pull that information away from the docstring.
The docstring is rep... | {
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"openwebmath_score": null,
"tags": "python, pandas",
"url": null
} |
homework-and-exercises, newtonian-mechanics, energy
Title: How can iron be forged by a hand-powered hammer? If the compression strength of iron is 50 MPa, or 5 MPa at 1000C, how can it be forged by a falling hammer, weighing say 10 kg, 10x10 cm impact area -> 100N/0.01 m2 = 10 kPa? Having been a quasi-professional bla... | {
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"id": 50469,
"lm_label": null,
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"lm_q1_score": null,
"lm_q1q2_score": null,
"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "homework-and-exercises, newtonian-mechanics, energy",
"url": null
} |
sql, datetime, t-sql
with tToday as (
select * from dwd.FiscalCalendars where CalendarDate = cast(getdate() as date)
)
,tCurrentWeek as (
select
t.FiscalYear TW_FiscalYear
,t.FiscalQuarterOfYear TW_FiscalQuarterOfYear
,t.FiscalMonthOfYear TW_Fiscal... | {
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"id": 17226,
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "sql, datetime, t-sql",
"url": null
} |
slam, navigation, amcl, gmapping
update frame 8896
update ld=1.00185 ad=0.0358327
Laser Pose= 1.00149 0.00259294 0.00403892
m_count 1
Average Scan Matching Score=173.695
neff= 99.9925
Registering Scans:Done
update frame 9628
update ld=0.0702066 ad=0.403295
Laser Pose= 1.06788 0.00339194 -0.386777
m_count 2
Average Sca... | {
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"id": 37787,
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "slam, navigation, amcl, gmapping",
"url": null
} |
measurements, error-analysis
If you actually put the numbers in and work this out it may give you a slightly different answer compared to finding the maximum and minium values and then halving the difference. This is due to the above expression only being to first order in a Taylor expansion, propagation of errors can... | {
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"id": 19897,
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"tags": "measurements, error-analysis",
"url": null
} |
fixed energy. nents Analysis and many manifold methods are based on estimating eigenvalues and eigenfunctions of operators defined by a similarity function or a kernel, giv en empirical data. In the present paper, a discontinuous boundary-value problem with retarded argument at the two points of discontinuities is inves... | {
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"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9893474866475719,
"lm_q1q2_score": 0.8018452803317649,
"lm_q2_score": 0.8104789178257654,
"openwebmath_perplexity": 549.7118623112633,
"openwebmath_score": 0.8859313726425171,
"tags": n... |
c#, object-oriented, interview-questions, chess
for (int i = 0; i < BoardSize; i++)
{
WhitePawn blackPawn = new WhitePawn(new Position(1, i));
_whitePlayer.PiecesList.Add(blackPawn);
}
foreach (var temp in _blackPlayer.PiecesList)
{
... | {
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"openwebmath_score": null,
"tags": "c#, object-oriented, interview-questions, chess",
"url": null
} |
c, linked-list, console, database, edit-distance
/*******************************************************************************
* Implements the Levenshtein distance algorithm. *
*******************************************************************************/
static size_t edit_distance... | {
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"tags": "c, linked-list, console, database, edit-distance",
"url": null
} |
```function dpdt = lotkasystem(t,p,n) %LOTKA Lotka-Volterra predator-prey model for system of inputs p. delta = 0.02; beta = 0.01; % Change the size of p to be: Number of equations-by-number of initial % conditions. p = reshape(p,[],n); % Write equations in vectorized form. dpdt = [p(1,:) .* (1 - beta*p(2,:)); p(2,:) .... | {
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"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9863631635159684,
"lm_q1q2_score": 0.8735542547809568,
"lm_q2_score": 0.8856314662716159,
"openwebmath_perplexity": 353.19926186571536,
"openwebmath_score": 0.8711304664611816,
"tags":... |
ros, slam, navigation, mapping, hector
Title: Limit scan angle of RPLidar A1
I have RPLidar A1 device and I would like to know how I could limit the scan angle from 0 degrees to 180 degrees using Hector Mapping Slam.
Note: I am using ROS indigo on ubuntu 14.04.
Originally posted by Hamad on ROS Answers with karma: 1... | {
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"openwebmath_score": null,
"tags": "ros, slam, navigation, mapping, hector",
"url": null
} |
python, lambda
I have forced into writing split_join method in three times. Is there any way to prevent this situation? db_data = {}
def create_info(db_data, …):
…
return db_data
new_db_data = create_info(db_data, …)
This feels plain wrong. Either your create_info function mutates data, or it generates some... | {
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"id": 38089,
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "python, lambda",
"url": null
} |
radioactivity
Title: Why do they consider radioactive matter with long half lives more dangerous than matter with a short half life? The title says it all.
For example why is plutonium considered more dangerous than radioactive iodine? A more balanced approach might be to recognize that both short and long half-live m... | {
"domain": "physics.stackexchange",
"id": 8626,
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "radioactivity",
"url": null
} |
astrophysics
Title: Degree of ionization and Saha equation Say you want to calculate degree of ionization for different gases in atmosphere of a star with abundances similar to those in Sun (let's assume you only have hydrogen, helium and sodium) over the temperature range (from 2000 K to 45000 K for example) using Sa... | {
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"id": 1535,
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"openwebmath_score": null,
"tags": "astrophysics",
"url": null
} |
# Generalisation of $(n+3)^2-(n+2)^2-(n+1)^2+n^2=4$ | {
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"lm_q1_score": 0.9884918517832532,
"lm_q1q2_score": 0.8258686606273755,
"lm_q2_score": 0.8354835289107309,
"openwebmath_perplexity": 287.1169952012793,
"openwebmath_score": 0.9770851135253906,
"tag... |
ros, json-prolog, knowrob
Title: Cannot use java classes to execute prolog predicates
Hi.
I wanted to instantiate some classes from my owl file using the data received from sensor ROS node. So I defined some predicates to do that (very similar to the predicates given in knowron_perception_tutorial package) in a .pl f... | {
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"id": 19900,
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"tags": "ros, json-prolog, knowrob",
"url": null
} |
Each of your methods gives you $1.496 \times 10^9 ~\rm{m}$ - accurate to 4 significant digits. That's better than you should expect.
The accuracy of your result is only ever as good as the accuracy of the inputs. Some of the data you have is given to 5 significant digits - that will give you the "more accurate" result... | {
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"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9585377272885903,
"lm_q1q2_score": 0.8185075859535016,
"lm_q2_score": 0.8539127492339909,
"openwebmath_perplexity": 702.3082559646502,
"openwebmath_score": 0.5102275013923645,
"tag... |
roslaunch, rosaria
cd ~/transform_ws
source ./devel/setup.bash
rosrun transform transform
However, when I try to run rosaria using the launch file mentioned, I get the following error:
ERROR: cannot launch node of type
[rosaria/RosAria]: rosaria ROS path
[0]=/opt/ros/hydro/share/ros ROS path
[1]=/home/powerbot67/ros... | {
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "roslaunch, rosaria",
"url": null
} |
catkin
Title: kdl_parser and catkin
In catkin workspace I create package:
catkin_create_pkg leg_kinematics std_msgs rospy roscpp kdl_parser
In leg_kinematics/src/leg_kinematics.cpp:
#include "ros/ros.h"
#include <kdl_parser/kdl_parser.hpp>
int main(int argc, char **argv)
{
KDL::Tree my_tree;
ros::NodeHandle... | {
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"id": 16321,
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"tags": "catkin",
"url": null
} |
This software gives the following generating functions for small numbers of symbols, e.g. for $N=3$ $${\it Q1\_Q1\_Q1}+{\it Q3}+2\,{\it Q1\_Q2}$$ and for $N=4$ $$3\,{\it Q2\_Q2}+{\it Q4}+2\,{\it Q1\_Q3}+{\it Q1\_Q1\_Q1\_Q1}+4\,{\it Q1\_Q1\_Q2}$$ and for $N=5$ $$6\,{\it Q1\_Q1\_Q1\_Q2}+9\,{\it Q1\_Q2\_Q2}+6\,{\it Q1\_Q1... | {
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"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9763105238756898,
"lm_q1q2_score": 0.8482447300403506,
"lm_q2_score": 0.8688267813328976,
"openwebmath_perplexity": 435.89219437570404,
"openwebmath_score": 0.8824265599250793,
"ta... |
c#, .net, image, console
public static Boolean websiteExists(String URL)
{
try
{
HttpWebRequest request = WebRequest.Create(URL) as HttpWebRequest;
request.Method = "HEAD";
HttpWebResponse response = request.GetResponse() as HttpWebRespons... | {
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"openwebmath_score": null,
"tags": "c#, .net, image, console",
"url": null
} |
hector-quadrotor, ros-groovy, rostopic
Title: rostopic groovy strangeness
Hello, I'm not sure if this is an issue with rostopic or with the hector_quadrotor, but I recently upgraded to groovy and when testing the current state of the quadrotor stack today I noticed the following occasional "glitch" in the reported ra... | {
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"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "hector-quadrotor, ros-groovy, rostopic",
"url": null
} |
slam, navigation, lidar, 3d-slam, rtabmap
Title: use of rtabmap with 3D lidars
I need to scan and get an accurate 3D model of a small building and its surroundings (trees, etc.). I plan on mounting my sensors on a small drone and fly around the building to scan it. The resolution should be good enough to see details ... | {
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"openwebmath_score": null,
"tags": "slam, navigation, lidar, 3d-slam, rtabmap",
"url": null
} |
c#, roslyn
if (!placeholders.Any())
{
return;
}
var highestPlaceholder = placeholders.Max();
if (highestPlaceholder + 1 > amountOfFormatArguments)
{
context.ReportDiagnostic(Diagnostic.Create(Rule, firstArgumentIsLiteral
? firstArgument.G... | {
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"tags": "c#, roslyn",
"url": null
} |
and reconstructing surface domains, and modifying the domain to offset geometry from the edge of the surface. To determine To find: The parametric equations for the surface obtained by rotating the curve x = 1 y , y ≥ 1 , about the y -axis and to graph the surface. Cortical Thickness Estimation. The 4D parametric motio... | {
"domain": "lotoblu.it",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9879462197739625,
"lm_q1q2_score": 0.8337229745151609,
"lm_q2_score": 0.8438951005915208,
"openwebmath_perplexity": 1009.6819380103711,
"openwebmath_score": 0.6727544069290161,
"tags": nu... |
matrix multiplied by the design matrix. Addition of dummy variables and addition of correlated predictors are also presented. Researchers often rely on Multiple Regression when they are trying to predict some outcome or criterion variable. NR 511 EXAM QUESTIONS BANK / NR511 TEST BANK (LATEST-2020): ADVANCED PHYSICAL AS... | {
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"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9711290922181331,
"lm_q1q2_score": 0.8113623629833243,
"lm_q2_score": 0.8354835309589074,
"openwebmath_perplexity": 859.6916552022177,
"openwebmath_score": 0.4258139729499817,
... |
filter-design, python, phase, eeg, scipy
(*) Is my expectation justified?
Can't say without looking at your signal first. A sufficiently narrow band signal will look like an amplitude and/or phase modulated sine wave. However, if your original signal is very noise-like, you'd have to make it VERY narrow to look like ... | {
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"tags": "filter-design, python, phase, eeg, scipy",
"url": null
} |
cosmology, universe, planets
With this being said, physics also provides us with the most powerful tools that make it obvious that both the Earth and the Universe are billions of years old – if we want to answer this question. We know that we don't live in the hypothetical world. However, to do so, we must couple the ... | {
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"openwebmath_score": null,
"tags": "cosmology, universe, planets",
"url": null
} |
quantum-mechanics, gravity, atomic-physics, spectroscopy
Gill, E., Wunner, G., Soffel, M., & Ruder, H. (1987). On hydrogen-like atoms in strong gravitational fields. Classical and Quantum Gravity, 4(4), 1031. doi:10.1088/0264-9381/4/4/033. | {
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"id": 10700,
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"tags": "quantum-mechanics, gravity, atomic-physics, spectroscopy",
"url": null
} |
c++, beginner, reinventing-the-wheel
// since the static variables are not in the template, they won't be
// duplicated for every T
template <typename T>
class shared_ptr
{
// ...
};
Finally, you should consider using std::unordered_map rather than std::map. You don’t need the ordering, and the unordered map may ... | {
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"tags": "c++, beginner, reinventing-the-wheel",
"url": null
} |
Definition & Examples, Discontinuous Functions: Properties & Examples, Reciprocal Functions: Definition, Examples & Graphs, How to Convert Between Polar & Rectangular Coordinates, Binary Division & Multiplication: Rules & Examples, Radical Expression: Definition & Examples, Nonlinear Function: Definition & Examples, Pr... | {
"domain": "gridserver.com",
"id": null,
"lm_label": "1. Yes\n2. Yes\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9814534344029238,
"lm_q1q2_score": 0.8544506708232129,
"lm_q2_score": 0.8705972600147106,
"openwebmath_perplexity": 696.4878762898684,
"openwebmath_score": 0.757369875907898,
"tag... |
forces
Title: Newton's Third Law Question Hypothetically, consider a scenario in which a man was exerting X amount of Newtons on a truck that is sitting in neutral on a hill, causing it to remain almost at rest. However, in seconds, the truck begins to slide down the hill. In this example, did the truck exert more, le... | {
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"openwebmath_score": null,
"tags": "forces",
"url": null
} |
For part (b) we find the dot product of the direction vectors of the two lines. We get
$(-1, 2, 3) \cdot (2, -3, 1) = -5$
but also
$(-1, 2, 3) \cdot (2, -3, 1) = |(-1, 2, 3)||(2, -3, 1)|\cos\theta = 14\cos\theta$
Equating the two gives
$\cos\theta = \frac{-5}{14}$
so $\theta = \arccos(\frac{-5}{14}) = 110.9248324... | {
"domain": "drchristiansalas.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
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"lm_q2_score": 0.8499711737573762,
"openwebmath_perplexity": 114.47175685210006,
"openwebmath_score": 0.937382698059082,
"... |
r, optimization, xgboost, hyperparameter, weighted-data
Refer to the caret guide here to get step-by-step instructions on using it.
For handling class imbalance, I've found from my experience that adjusting weights is not as helpful as under-sampling majority class and over-sampling the minority class, or a combinatio... | {
"domain": "datascience.stackexchange",
"id": 932,
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"tags": "r, optimization, xgboost, hyperparameter, weighted-data",
"url": null
} |
Thus $$\sigma(B_{n+1}^2)=\sigma(A_{n+1}^2)$$. Yet, as pointed out in the answer by Jean Marie, $$B_{n+1}$$ is similar to $$-B_{n+1}$$ via the reversal matrix (the mirror image of the identity matrix from left to right). Therefore, nonzero eigenvalues of $$B_{n+1}$$ must occur in pairs of the form $$\pm\lambda$$. Hence ... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9848109534209825,
"lm_q1q2_score": 0.8269792033984312,
"lm_q2_score": 0.8397339616560072,
"openwebmath_perplexity": 201.07967712732992,
"openwebmath_score": 0.9597436189651489,
"ta... |
python, python-3.x, regex
def test_byte_regex_range_exclusion_outside():
"""An exclusion outside of the regex range should have no effect."""
assert re_supp.byte_range(b'a', b'c', [b'e']) == b'[a-c]'
offset = re_supp._offset_byte_char
def compare_escaped_within_range(char):
"""Test that the character is ... | {
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"tags": "python, python-3.x, regex",
"url": null
} |
c++, linked-list, reinventing-the-wheel
template<typename T>
void List<T>::splice(const_iterator pos, List & other)
{
if (other.sz == 0) return;
if (pos.curr->prev) hook(pos.curr->prev, other.first);
else first = other.first;
hook(other.last->prev, pos.curr);
other.first = other.last = nullptr;
... | {
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"openwebmath_score": null,
"tags": "c++, linked-list, reinventing-the-wheel",
"url": null
} |
{0, 0.33504538978074816, 0.256132905175892, 0.0016617858251372995},
{0, 0.37097564355830726, -0.03575247849541091, 0.1665183633794433},
{0, 0.37507484064199426, -0.06280527015275122, 0.14788240243852177},
{0, 0.3774580162329546, -0.08416273725065143, 0.12924644149760023},
{0, 0.3779249463635693, -0.09982487978911159, 0... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9603611620335328,
"lm_q1q2_score": 0.8124102565120878,
"lm_q2_score": 0.8459424314825852,
"openwebmath_perplexity": 5882.505184718347,
"openwebmath_score": 0.3663482367992401,
"tag... |
Using right-hand Riemann sum to evaluate the limit of $\frac{n}{n^2+1}+ \cdots+\frac{n}{n^2+n^2}$
I'm asked to prove that $$\lim_{n \to \infty}\left(\frac{n}{n^2+1}+\frac{n}{n^2+4}+\frac{n}{n^2+9}+\cdots+\frac{n}{n^2+n^2}\right)=\frac{\pi}{4}$$ This looks like it can be solved with Riemann sums, so I proceed: | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9843363522073338,
"lm_q1q2_score": 0.8386081133423039,
"lm_q2_score": 0.8519528019683106,
"openwebmath_perplexity": 617.3319999377042,
"openwebmath_score": 0.9768236875534058,
"tag... |
quantum-mechanics, thermodynamics, statistical-mechanics, harmonic-oscillator
$$
\partial_t P(x, \dot{x}, I, \dot{I},t) = ...
$$
and study its behavior. In particular, if $C_2$ and $C_4$ are both positive, the solution is globally stable and one can write the equilibrium Boltzmann-like solution of the FPE. Note that t... | {
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"id": 72463,
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"tags": "quantum-mechanics, thermodynamics, statistical-mechanics, harmonic-oscillator",
... |
• For example the fourth summand, starting with $\binom{4}{3}$ has the interpretation:
$\binom{4}{3}$ possibilities to select $3$ out of $4$ pairs of boys
$\binom{4}{3}$ possibilities to select $3$ out of $4$ pairs of seats
$3!$ possibilities to permute the pairs of boys accross the selected pairs of seats
$2^3$ po... | {
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"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9828232892267861,
"lm_q1q2_score": 0.8080666170619185,
"lm_q2_score": 0.822189121808099,
"openwebmath_perplexity": 414.5101478060201,
"openwebmath_score": 0.7616266012191772,
"tags... |
c++, c++11, database
void remove_record(unsigned long idx) {
contacts.erase(contacts.begin() + idx);
}
void add_record(Contact c) {
contacts.push_back(c);
}
void sort_last_name() {
std::sort(contacts.begin(), contacts.end(), [](Contact &a, Contact &b) {
return a.la... | {
"domain": "codereview.stackexchange",
"id": 24948,
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"openwebmath_score": null,
"tags": "c++, c++11, database",
"url": null
} |
special-relativity, rotational-dynamics, moment-of-inertia, angular-velocity
How has the moment of inertia of the rod changed like that?
We see that the length of rod hasn't changed(Assuming the rod to be a ,strictly, rigid body) and since moment of inertia has increased, does this mean that mass has increased?
Does t... | {
"domain": "physics.stackexchange",
"id": 50182,
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"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "special-relativity, rotational-dynamics, moment-of-inertia, angular-velocity",
"... |
nlp, topic-model, lda, tfidf, stanford-nlp
Title: TF-IDF for Topic Modeling Can TF-IDF be used a sole method for Topic Modeling ? (I know there are better methods like LDA , LSA etc)
I just want to understand if TF-IDF alone can help us in Topic modeling . If yes , can someone explain how that simple framework works ?... | {
"domain": "datascience.stackexchange",
"id": 8160,
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"openwebmath_score": null,
"tags": "nlp, topic-model, lda, tfidf, stanford-nlp",
"url": null
} |
mantle, crystallography, crystals, pressure, diamond
That’s because the Botswana diamond also contained a high-pressure form of ice as well as another high-pressure mineral known as wüstite (SN: 3/8/18). The presence of those inclusions helped narrow down the rough pressures at which the davemaoite might have formed: ... | {
"domain": "earthscience.stackexchange",
"id": 2431,
"lm_label": null,
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"lm_q1q2_score": null,
"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "mantle, crystallography, crystals, pressure, diamond",
"url": null
} |
quantum-mechanics, correlation-functions, propagator
&= \frac 1 {Z_\beta\beta}\sum_{j,k} \int_{-\infty}^{+\infty} \mathrm d t\; e^{i\omega t} \left[\frac{ e^{\beta(E_j-E_k)}-1}{E_j-E_k}\right] e^{-\beta E_j} A_{jk} e^{i\hat E_k t/\hbar} B_{kj} e^{-i E_j t/\hbar} = \\
&= \sum_j \frac 1 {Z_\beta\beta} \int_{-\inf... | {
"domain": "physics.stackexchange",
"id": 57125,
"lm_label": null,
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"openwebmath_score": null,
"tags": "quantum-mechanics, correlation-functions, propagator",
"url": null
} |
python, complexity
Title: Most efficient solution for USACO: Cow Gymnastics - Python I was trying to figure out this problem, and I did. However, my code is so abhorrently ugly that I want to tear out my eyeballs when I look at it:
with open("gymnastics.in", "r") as fin:
rounds, cows = [int(i) for i in fin.readline(... | {
"domain": "codereview.stackexchange",
"id": 39696,
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"openwebmath_score": null,
"tags": "python, complexity",
"url": null
} |
python, performance, python-2.x, community-challenge
def basin_2_string(basin_list):
'''
Input is a dictionary of basins where the key is the sink
Example output:
A: 7, Sink: (1, 2)
B: 5, Sink: (0, 0)
C: 4, Sink: (3, 3)
'''
letter_padding = len(num_2_alpha(len(basin_list)))... | {
"domain": "codereview.stackexchange",
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"tags": "python, performance, python-2.x, community-challenge",
"url": null
} |
computer-architecture, arithmetic
Title: Is it possible to compute -12 (decimal) in 4 bits binary This is what I have so far
1 1 0 0
Switch values by 2s Complement
0 0 1 1
+ 1
0 1 0 0 No, it's not possible, at least using the standard representations. An unsigned $n$-bit number can represent any integer in the in... | {
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"id": 6094,
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"openwebmath_score": null,
"tags": "computer-architecture, arithmetic",
"url": null
} |
python, performance, python-3.x
def words_from_letters(self, letters):
return self.vocab.get(''.join(sorted(letters)), [])
def main():
word_finder = AnagramWordFinder()
print(word_finder.words_from_letters(input('Enter your characters: ')))
if __name__ == '__main__':
main()
Arguably, you don't e... | {
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"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "python, performance, python-3.x",
"url": null
} |
python, beginner, tic-tac-toe
if current_player == 2:
p2rinput = input('Player 2 row: ')
p2cinput = input('Player 2 column: ')
if p2cinput.isdigit() and p2rinput.isdigit():
p2cinput = int(p2cinput)
p2rinput = int(p2rinput)
print('Player 2: ')
if ... | {
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"id": 37735,
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"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "python, beginner, tic-tac-toe",
"url": null
} |
irfft). This is one of the 100+ free recipes of the IPython Cookbook, Second Edition, by Cyrille Rossant, a guide to numerical computing and data science in the Jupyter Notebook. It is a efficient way to compute the DFT of a signal. A simple example of usage is: from mpi4py import MPI import numpy as np from mpi4py_fft... | {
"domain": "gradi-oil.de",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9817357205793903,
"lm_q1q2_score": 0.8284819704541395,
"lm_q2_score": 0.8438951064805861,
"openwebmath_perplexity": 1502.1957930911074,
"openwebmath_score": 0.4409290552139282,
"tags": ... |
cc.complexity-theory, apx
Title: On APX problems Given optimization problems $P1$ and $P2$. The slides below say that, $P1 \leq_L P2$ does not imply $P2 ∈ APX$, then $P1 ∈ APX$. Why is this so?
http://www.di.univr.it/documenti/AttDidAva/allegato/allegato581250.pdf
$MAX INDEP SET$ is not in APX while $MAX CUT$ is.
Is a... | {
"domain": "cstheory.stackexchange",
"id": 2227,
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "cc.complexity-theory, apx",
"url": null
} |
brain, terminology, anatomy, neuroanatomy, sex
The article is "Pathways of Sexual Desire" by James Pfaus (2009).
I have read the Septal area article in Wikipedia but still cannot get it. It is confusing. The septum pellucidium is a thin membrane separating the left and right lateral ventricles. It contains white mat... | {
"domain": "biology.stackexchange",
"id": 10801,
"lm_label": null,
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "brain, terminology, anatomy, neuroanatomy, sex",
"url": null
} |
design, software, manufacturing, chassis, hardware
There are lots of companies that specialize in fabricating parts using one process or another. You would have to learn a little bit about each process to choose whether it will work for any given part. If you are only making a few parts it is usually too expensive for... | {
"domain": "robotics.stackexchange",
"id": 1084,
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "design, software, manufacturing, chassis, hardware",
"url": null
} |
machine-learning, classification, nlp
The NN models achieve more than 80% accuracy but still when I use the trained model to predict the emotion on text that includes some negation I get the wrong results. For example:
Text : "I am happy with easy jet, it is a great company!"
Predicts Happy
Text: I am not happy with e... | {
"domain": "datascience.stackexchange",
"id": 8366,
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "machine-learning, classification, nlp",
"url": null
} |
genetics, immunology, ecology, biodiversity, fitness
Title: What does genetic diversity in one species have to do with survival rate when an epidemic spreads? I was studying about genes, and soon remembered that the more diverse the genetics of one species, the less the chance of the species to go extinct from natural... | {
"domain": "biology.stackexchange",
"id": 11818,
"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": "genetics, immunology, ecology, biodiversity, fitness",
"url": null
} |
inside the circle can use the kite properties show! Triangle ABC is a diameter of the circle and the circle and touching the sides of the of! Is theta, this is also a cool trick to impress your less mathematically inclined or! Tannu ( 53.0k points ) circles ; class-10 ; 0 votes such that BC = 12 cm and =... My circle r... | {
"domain": "morethanahomemom.com",
"id": null,
"lm_label": "1. Yes\n2. Yes",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9736446471538803,
"lm_q1q2_score": 0.8527053196215987,
"lm_q2_score": 0.8757869948899666,
"openwebmath_perplexity": 390.44542158692235,
"openwebmath_score": 0.6869009733200073,
... |
• What about $(4,4)$? – ami_ba Oct 1 '17 at 4:49
• @Amitayas, the problem asks for distinct roots. – Gerry Myerson Oct 1 '17 at 5:26
• Got it,........ – ami_ba Oct 1 '17 at 5:30
• I was thinking of adding the two polynomials – ami_ba Oct 1 '17 at 5:31
• Why should the roots of $(p(x)+q(x))/2$ be positive integers just ... | {
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"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9817357237856482,
"lm_q1q2_score": 0.8243968345400999,
"lm_q2_score": 0.8397339676722393,
"openwebmath_perplexity": 139.38343907489238,
"openwebmath_score": 0.9231899380683899,
"ta... |
python, python-3.x, fibonacci-sequence
Title: Telling fibonaccis to the user Though this program tells the truth (unless you change the source code), it does tell Fibonacci numbers, depending on the user's input. Keeping in mind of all (or most) of the feedback given from previous questions, I wrote this program to se... | {
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "python, python-3.x, fibonacci-sequence",
"url": null
} |
c, networking, socket
pthread_t thread_id;
while( (client_sock = accept(socket_desc, (struct sockaddr *)&client, (socklen_t*)&c)) ) {
puts("Connection accepted");
if (pthread_create( &thread_id , NULL , connection_handler , (void*) &client_sock) < 0) {
perror("could not create thread")... | {
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"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "c, networking, socket",
"url": null
} |
machine-learning, neural-networks
I suggest reading more about the cross-entropy loss. See, e.g., https://rdipietro.github.io/friendly-intro-to-cross-entropy-loss/
There are some errors in your notation. The training set has points $(x^{(i)},y^{(i)})$, not $x_i,y_i$. Here $y^{(i)}_k$ means that $y^{(i)}=k$, not tha... | {
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"tags": "machine-learning, neural-networks",
"url": null
} |
python, pandas, pdf, dataframe
<block xMin="101.277440" yMin="428.287543" xMax="367.131871" yMax="456.668783">
<line xMin="101.421300" yMin="428.287543" xMax="367.131871" yMax="434.667690">
<word xMin="101.421300" yMin="428.287543" xMax="128.610840" yMax="434.223926">porary</word>
<word xMi... | {
"domain": "codereview.stackexchange",
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"tags": "python, pandas, pdf, dataframe",
"url": null
} |
Why does $\frac{s}{s-1} > \zeta(s) > \frac{1}{s-1}$ imply $\lim_{s \to 1^{+}}(s-1)\zeta(s)=1$?
I am reading the paper Dirichlet's theorem: a real variable approach by Robin Chapman. In this paper, he constructs a proof via real analysis rather than complex analysis that $\zeta(s)$ is convergent if and only if $s>1$. H... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
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"openwebmath_perplexity": 249.5567359633338,
"openwebmath_score": 0.8822293281555176,
"tag... |
It might be partly a matter of convention. However, I believe that stating that $$\gcd(8,0) = 8$$ is safer. In fact, $$\frac{0}{8} = 0$$, with no remainder. The proof of the division, indeed is that "Dividend = divider $$\times$$ quotient plus remainder". In our case, 0 (dividend) = 8 (divisor) x 0 (quotient). No remai... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9759464527024445,
"lm_q1q2_score": 0.8828904881936409,
"lm_q2_score": 0.9046505428129514,
"openwebmath_perplexity": 288.4206699451657,
"openwebmath_score": 0.9506410956382751,
"tag... |
$\color{red}{\text{2. Another way}}$
Using Vallée-Poussin, for large enough $x$ $$\pi(x)>\frac{x}{\ln(x)-(1-\varepsilon)}>\frac{x}{\ln(x)}$$ Let's show that for large enough $x$ we also have $$\frac{x}{\ln(x)}>x^{1-\varepsilon}$$ which is the same as showing $$\frac{x^{\varepsilon}}{\ln{x}}>1$$ for large $x>0$.
Propo... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9828232950125849,
"lm_q1q2_score": 0.8168667489229136,
"lm_q2_score": 0.8311430478583168,
"openwebmath_perplexity": 326.5995104822338,
"openwebmath_score": 0.8403668403625488,
"tag... |
ros, asus-xtion-pro-live, rtabmap
<arg name="compressed" default="false"/> <!-- If you want to subscribe to compressed image topics -->
<!-- For depth_topic, "compressedDepth" image_transport is used. -->
... | {
"domain": "robotics.stackexchange",
"id": 24778,
"lm_label": null,
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"openwebmath_score": null,
"tags": "ros, asus-xtion-pro-live, rtabmap",
"url": null
} |
python, design-patterns, pandas, vectorization
employees_with_company_properties = pd.merge(
left=company_employees, right=companies,
left_on='company_name', right_on='company_name'
)
contacts_long = contacts.stack(level='contact_group')
contacts_merged = pd.merge(
left=contacts_long, right=employees_with_... | {
"domain": "codereview.stackexchange",
"id": 44412,
"lm_label": null,
"lm_name": null,
"lm_q1_score": null,
"lm_q1q2_score": null,
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"openwebmath_score": null,
"tags": "python, design-patterns, pandas, vectorization",
"url": null
} |
$$\begin{array}{|lrcll|} \hline 1. & \left(25-x\right)^2+h^2 &=& 15^2 \qquad \text{or}\qquad \mathbf{ h^2 = 15^2-\left(25-x\right)^2} \\\\ 2. & x(25-x) &=& h * h \qquad \text{Intersecting chords theorem} \\ & x(25-x) &=& h^2 \\ & x(25-x) &=& 15^2-\left(25-x\right)^2 \\ & 25x-x^2 &=& 15^2-( 25^2-50x+x^2) \\ & 25x-x^2 &=... | {
"domain": "0calc.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9814534398277177,
"lm_q1q2_score": 0.8676433910139816,
"lm_q2_score": 0.8840392786908831,
"openwebmath_perplexity": 3255.6565444447433,
"openwebmath_score": 0.7489926218986511,
"tags": nul... |
Class... ; see plot.hclust.. check coordinates of the MNIST sample data two points in the., and is occasionally called the Pythagorean distance the basis euclidean distance in r many measures of similarity and is basis! Formula: the two numeric series using the Pythagorean theorem can be used when creating a suitabilit... | {
"domain": "chefbenford.com",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9591542887603537,
"lm_q1q2_score": 0.8113893242394682,
"lm_q2_score": 0.84594244507642,
"openwebmath_perplexity": 1013.0545154424401,
"openwebmath_score": 0.7487303018569946,
"ta... |
special-relativity, mass, inertial-frames, observers, speed
Title: Does increase in relativistic mass with speed violate principle of relativity? From special relativity we know that,
$$ m = \frac{m_0}{\sqrt {1-\frac {v^2}{c^2}}} $$
where,
$m$, $m_{0}$ and $v$ are the relativistic mass, rest mass of the object and spe... | {
"domain": "physics.stackexchange",
"id": 83013,
"lm_label": null,
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"openwebmath_score": null,
"tags": "special-relativity, mass, inertial-frames, observers, speed",
"url": null
} |
and is defined as the point of intersection of the medians of the sides of this triangle. Centroid Formula. The average of the corners will, however, equal the center of gravity in the special case of a triangle. The coordinates of the centroid are the average of the vertices-coordinates. The center of mass or centroid... | {
"domain": "rafbis.it",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9805806506825456,
"lm_q1q2_score": 0.8254779448344705,
"lm_q2_score": 0.8418256512199033,
"openwebmath_perplexity": 304.50342906770857,
"openwebmath_score": 0.5220875144004822,
"tags":... |
matlab, filter-design, lowpass-filter, moving-average
Title: Moving Average Filter's Magnitude Response I am working on filtering of data using the Moving average filter in MATLAB.
My data is recorded temperature values on the Y-axis and Time(in seconds) on the X-axis
(I'm getting the magnitude response curve of the M... | {
"domain": "dsp.stackexchange",
"id": 9177,
"lm_label": null,
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "matlab, filter-design, lowpass-filter, moving-average",
"url": null
} |
c#, https, azure-cosmosdb
var detailedDataResponse = await detailedDataResponseTask
if(detailedDataResponse != null)
...
singleDocument.SetPropertyValue("InventoryData", await inventoryDataTask);
A very small performance improvement could be done by taking productList code and removing the projection being done to ... | {
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"openwebmath_score": null,
"tags": "c#, https, azure-cosmosdb",
"url": null
} |
homework-and-exercises, quantum-field-theory, fourier-transform, propagator
Title: Massless boson in 2D and its (retarded) propagator I have the retarded propagator for a free scalar field in 1+1 dimensions. Inside the light cone, this looks like $J_0(m \sqrt(t^2-x^2))$, $J$ being a Bessel function. When I take the ma... | {
"domain": "physics.stackexchange",
"id": 23946,
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"tags": "homework-and-exercises, quantum-field-theory, fourier-transform, propagator",
"u... |
Since multiplications in normal space become addition after you take the logarithm, we get:
$log_{10}12321 = log_{10}(10^4*1.2321) = log_{10}10^4 + log_{10}1.2321 \\ =4+log_{10}1.2321$
Since we chose to round down to the nearest power of 10, the number we multiply $10^i$ by will always be in the interval $[1,10)$, an... | {
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"id": null,
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"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9591542887603537,
"lm_q1q2_score": 0.8227319566630993,
"lm_q2_score": 0.8577681049901037,
"openwebmath_perplexity": 318.48822222564456,
"openwebmath_score": 0.7459443807601929,
"ta... |
electrical-engineering, radiation
As with the cell phone radio, total emissions are very dependent on how busy the radio links are. These are battery powered systems, when not in use they are designed to be as low power as possible. Radio transmitters use a lot of power and so are kept powered down as much of the time... | {
"domain": "engineering.stackexchange",
"id": 1069,
"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": "electrical-engineering, radiation",
"url": null
} |
electromagnetism, general-relativity, maxwell-equations, approximations, linearized-theory
$^4$ The Lorenz gauge (4) is the linearized de Donder/harmonic gauge
$$ \partial_{\mu}(\sqrt{|g|} g^{\mu\nu})~=~0.\tag{18}$$
$^5$ We unconventionally call eq. (8) the "electrostatic limit" since the term $\partial_t{\bf A}$ ente... | {
"domain": "physics.stackexchange",
"id": 49928,
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"lm_q2_score": null,
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"openwebmath_score": null,
"tags": "electromagnetism, general-relativity, maxwell-equations, approximations, linearize... |
c++, performance, numerical-methods, neural-network, eigen
Should be
for (int i_neur = 0; i_neur < N; i_neur++)
Ther can be some exeptions for performance reasons, but in this case there are much better ways to improve performance.
Avoid unnecessary copies
spike_times = t_spike_vector[i_neur];
This copies the entire ... | {
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"tags": "c++, performance, numerical-methods, neural-network, eigen",
"url": null
} |
• Both answers are correct. Feb 6, 2015 at 21:58
• Thanks to everyone who answered! I greatly appreciate the help :) Feb 6, 2015 at 22:14
You are correct still. Notice that \begin{align} \ln\Bigg|\frac{\sqrt{x^2+4}}{2} + \frac{x}{2}\Bigg| + C &= \ln\Bigg|\frac{\sqrt{x^2+4}+x}{2}\Bigg| + C\\ &= \ln\Bigg|\sqrt{x^2+4}+x\... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9805806512500485,
"lm_q1q2_score": 0.848421982443316,
"lm_q2_score": 0.865224070413529,
"openwebmath_perplexity": 288.01286291468284,
"openwebmath_score": 0.9924834966659546,
"tags... |
c++, c++17, enum, macros
So what’s the right name? Well, why not just to_string() in the same namespace as the enum? (Well, better would be to_string_view(), but one thing at a time.) ADL would find the function when you need it, so you’d only have to call to_string(enum_value)… which is actually shorter than std::to_... | {
"domain": "codereview.stackexchange",
"id": 38504,
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"tags": "c++, c++17, enum, macros",
"url": null
} |
The index is only necessary to distinguish between higher indexed roots, such as cube roots, fourth roots, fifth roots, etc. In order to multiply our radicals together, our roots need to be the same. What is a seventh root? The seventh root of a number is the number that would have to be multiplied by itself 7 times to... | {
"domain": "crashmobile24.de",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9852713831229043,
"lm_q1q2_score": 0.8123187425332178,
"lm_q2_score": 0.8244619263765706,
"openwebmath_perplexity": 570.7323188472108,
"openwebmath_score": 0.6521097421646118,
"... |
fft, autocorrelation, time-series, inverse-problem
Any signal derived this way will have the same original auto correlation function.
if no, what other constraint properties should we add to $C[n]$, in order to make it yes?
You can't make it a yes, since it's not unique. No matter what auto correlation you choose, t... | {
"domain": "dsp.stackexchange",
"id": 6379,
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "fft, autocorrelation, time-series, inverse-problem",
"url": null
} |
# Finding a closed form expression given decimal approximation
1. Nov 21, 2015
### fedaykin
Good evening. Is there a way to take a decimal approximation and see if there is a relatively simple expression?
I'm guessing there might be software for this, but I'm not sure I'm even asking the appropriate question.
If it ... | {
"domain": "physicsforums.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9796676472509721,
"lm_q1q2_score": 0.8346305970731681,
"lm_q2_score": 0.8519528019683105,
"openwebmath_perplexity": 855.7637879802405,
"openwebmath_score": 0.848040759563446,
"tags... |
genetics, human-genetics, experimental-design, epidemiology, gwas
A replication cohort does not need to be huge and the actual size needed will largely depend on the effect size of the SNP seen in the discovery cohort. A "power-to-detect" calculation would help in predicting the cohort size needed. For a SNP to be sig... | {
"domain": "biology.stackexchange",
"id": 3809,
"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": "genetics, human-genetics, experimental-design, epidemiology, gwas",
"url": null
} |
classical-mechanics, potential, potential-energy, dipole, dipole-moment
Title: In the Lennard-Jones potential, why does the attractive part (dispersion) have an $r^{-6}$ dependence? The Lennard-Jones potential has the form:
$$U(r) = 4\epsilon\left[ \left(\frac{\sigma}{r}\right)^{12} - \left(\frac{\sigma}{r}\right)^{6}... | {
"domain": "physics.stackexchange",
"id": 7554,
"lm_label": null,
"lm_name": null,
"lm_q1_score": null,
"lm_q1q2_score": null,
"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "classical-mechanics, potential, potential-energy, dipole, dipole-moment",
"url": ... |
# For all real $\theta$ prove that $\cos(\sin\theta) \gt \sin(\cos\theta)$
How do I prove this? Im not able to even start it. Help please!
The desired estimate holds at $\theta=0$ and we have \begin{eqnarray} \cos(\sin\theta)-\sin(\cos\theta) &=& \cos(\sin\theta)-\cos\left(\frac\pi2-\cos\theta\right) \\&=& 2\sin\left... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9763105266327962,
"lm_q1q2_score": 0.80930167624697,
"lm_q2_score": 0.8289387998695209,
"openwebmath_perplexity": 231.15058819708705,
"openwebmath_score": 0.9660684466362,
"tags": ... |
To this end, let $$(x',y') = (a x + b, a y + d)$$, so we now solve the system $$(b, d) = (2,0) \\ (2a + b, d) = (3,0).$$ That is to say, $$b = 2$$, $$d = 0$$, $$a = 1/2$$, and the desired homothety is $$(x',y') = (x/2 + 2, y/2).$$ The unique fixed point is found by setting $$(x',y') = (x,y)$$ from which we obtain $$(x,... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.977022630759019,
"lm_q1q2_score": 0.8556637121481672,
"lm_q2_score": 0.8757869932689566,
"openwebmath_perplexity": 185.1788240251181,
"openwebmath_score": 0.8656613230705261,
"tags... |
statistical-mechanics
Title: QHO in Microcanonical Ensemble: Problem with alternate derivation I am working through Franz Schwabl's book on Statistical Mechanics, and he has a number of derivations of thermodynamic quantities that are different than those I have seen before. I am also having difficulty finding them re... | {
"domain": "physics.stackexchange",
"id": 12188,
"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": "statistical-mechanics",
"url": null
} |
algorithms, trees, hash
Title: Merkle tree sorting leaves and pairs I am implementing a Merkle tree and am considering using either of the two options.
The first one is sorting only by leaves. This one makes sense to me since you would like to have the same input every time you are constructing a tree from the data, t... | {
"domain": "cs.stackexchange",
"id": 18667,
"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": "algorithms, trees, hash",
"url": null
} |
electromagnetism, potential, relativity
... the retarded field theory, without using Lorentz contraction for determining the effective shape of the moving charge, yields relativistically correct fields of the charge.
Indeed, he never explicitly used Lorentz contraction in his (correct) calculations. Nevertheless he u... | {
"domain": "physics.stackexchange",
"id": 62748,
"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": "electromagnetism, potential, relativity",
"url": null
} |
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