qid int64 1 4.65M | metadata listlengths 3 3 | prompt stringlengths 31 25.8k | chosen stringlengths 17 28.2k | rejected stringlengths 19 40.5k | domain stringclasses 28
values |
|---|---|---|---|---|---|
52,278 | [
"https://dba.stackexchange.com/questions/52278",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/15425/"
] | I am trying to connect my MySQL RDS from EC2. Under security groups I have made sure permissions are in place.
<pre><code>$ mysql -h xxx.xyz.ap-southeast-1.rds.amazonaws.com -P 3306 -p
Enter password:
</code></pre>
I am sure password is correct; because i reset it using AWS console. I am getting following error:
<p... | I am 99% sure that Amazon RDS does not give you a 'root' access. i.e. You can't create a user as 'root'@'localhost' or 'root'@''.
Can you confirm user you have used while launching Amazon RDS instance? and make sure that Password matches with user created.
| It looks like there is a bug in AWS console. Most likely you've provided a password with restricted characters for the master user. In this case, AWS console doesn't prevent it, but you will never manage to connect to the database, even you'll change a password (BTW here AWS console will not allow you to insert restric... | https://dba.stackexchange.com |
461,925 | [
"https://physics.stackexchange.com/questions/461925",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/217900/"
] | Perhaps there is another way to calculate the escape velocity, or perhaps light always has the same kinetic energy regardless of the energy of the light, but shouldn't the event horizon of a black hole be different distances from the singularity for different colors (and thus energies) of light?
The amount of potentia... | Although the existing answers are perfectly correct, I think they don't directly address the reason as to why OP thinks it is possible to have different effective horizon radii corresponding to different colors of light--despite the fact that OP seems to (somewhat contradictorily) understand that there would be a true ... | All wavelengths of light have exactly the same velocity in the vacuum surrounding a black hole. This means that a "purple hole" cannot form in the manner you propose.
| https://physics.stackexchange.com |
179,931 | [
"https://softwareengineering.stackexchange.com/questions/179931",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/75344/"
] | What is a better approach when it comes to performance and optimal resource utilization: accessing a database multiple times through AJAX to only get the exact information needed when it is needed, or performing one access to retrieve an object that holds all information that <strong>might</strong> be needed, with a hi... | There is no one correct answer to this; like any optimization it depends heavily on context / usage.
However, consider the following as a rule of thumb:
<pre><code>x
+: Data is stable / static
-: Data is dynamic / volatile
y
+: Data is frequently used
-: Data is infrequently used
++: fetch large chunks in the fewes... | Remember the first rule of optimization: <strong>measure, don't guess</strong>. Try both, instrument them with some sort of stopwatch code, and see what takes longer.
And also bear in mind the old joke that "there are only two difficult problems in computer science: cache invalidation and naming things well." If you... | https://softwareengineering.stackexchange.com |
645,832 | [
"https://electronics.stackexchange.com/questions/645832",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/328089/"
] | When we walk in one of our office rooms, our body gets static electricity. When we touch a metal object such as a window or the body of a laptop, the tips of our fingers spark due to the discharge of electric charge. This event is sometimes very annoying.
The floor of our room is wooden parquet and recently I have noti... | Get a 10Meg ohm resistor and put it in series with ground then touch the non-grounded end, might take longer to discharge your ESD but it should work. If that doesn't work you might need a few 1 mega ohm resistors in series because the spark is jumping the Gap inside the resistor.
| You don't need a "semiconductor."
<ol>
<li>Wear leather soled shoes.</li>
<li>Wear clothing (shirt, pants, socks) of cotton or linen.</li>
<li>Do <strong>not</strong> wear clothing made of wool, silk, or synthetic materials.</li>
</ol>
Instead of a metal bar, you can simply hold a key in your hand and touch i... | https://electronics.stackexchange.com |
186,874 | [
"https://dba.stackexchange.com/questions/186874",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/91148/"
] | Here is a same schema with data,
<pre><code>CREATE TABLE groups (
id int PRIMARY KEY,
name varchar(30)
);
CREATE TABLE emp (
id int PRIMARY KEY,
name varchar(50),
group_id int REFERENCES groups
);
INSERT INTO groups(id,name) VALUES
(1, 'Managers'),... | There is no "sites" field in your SQL statements.
I did the following to solve your problem:
(You'll notice that I've taken many more fields than are necessary to do the operation - it's so that you understand where the data is coming from. I often find it very helpful to include far more fields than required in my i... | You can use union operator to achieve this like below:
<pre><code>SELECT 'Site1' Site, COUNT(id) Employees FROM
(
SELECT * FROM emp
WHERE group_id IN (1,2)
GROUP By group_id,id
) AS q1
UNION
SELECT 'Site' || group_id - 1 Site, COUNT(id)
FROM emp
WHERE group_id NOT IN (1,2)
GROUP BY group_id,id
ORDER BY ... | https://dba.stackexchange.com |
75,144 | [
"https://mathoverflow.net/questions/75144",
"https://mathoverflow.net",
"https://mathoverflow.net/users/9317/"
] | A Sunday question for specialists of eigenverieties:
In their important paper "the eigencurve", Coleman and Mazur globalized the earlier construction of Coleman's families, constructing a beautiful eponymous rigid analytic space
that parametrizes all systems of Hecke eigenvalues of finite-slope overconvergent modular ... | This is something I've told people privately for a while, and now have enough ingredients written up (jointly with Liang Xiao) to claim on the web somewhere: the validity of the parity conjecture is constant in $p$-adic analytic families. (Fine print: the family must be symplectic self-dual, and be equipped with a sor... | On p. 4 of Kisin's paper "Overconvergent modular forms and the Fontaine-Mazur conjecture", he explains the possibility of proving modularity lifting theorems via "analytic continuation along the eigencurve". This seems to require a global point of view, since it's predicated on understanding (at the very least!) the co... | https://mathoverflow.net |
215,853 | [
"https://softwareengineering.stackexchange.com/questions/215853",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/102175/"
] | Suppose that I have project backlog item with effort of 40 hours. My sprint is 40 hours (1 week) and I have one developer in team.
So developer creates child task to pending backlog and estimates work to 40 hours. At the end of the sprint developer didn't succeed in resolving his task. Suppose that developer works onl... | I prefer to not recognize any of the effort in my velocity unless we've achieved "Done". My preference is to show velocity of value delivered, and a partially working but incomplete solution that doesn't achieve the goal of the story doesn't deliver the value that was estimated.
So the 'value' is the same, rolls over... | I would say your story is too big and would require cutting down into smaller tasks. Generally in agile teams I have worked with we tend to do as much as we can in the sprint, anything not finished just goes on the backlog to be re-prioritized for the next sprint, as you may not want to play them in the next sprint.
... | https://softwareengineering.stackexchange.com |
24,181 | [
"https://mathoverflow.net/questions/24181",
"https://mathoverflow.net",
"https://mathoverflow.net/users/2530/"
] | This may be total nonsense. But I need to know the answer quickly and I am too tired to think about it thoroughly. Let <span class="math-container">$k$</span> be a positive integer. Roe's "Elliptic Operators" claims that there is a 1-to-1 correspondence between:
<ul>
<li>representations of the Clifford algebr... | I'm not sure whether a representation of an algebra <span class="math-container">$A$</span> means a representation of the unit group of <span class="math-container">$A$</span>, or an <span class="math-container">$A$</span>-module. With the second interpretation, the statement is false.
Let's take <span class="math-cont... | Thanks to everyone who posted here. It is not "obvious" to me what I was thinking of here, and I'm embarrassed that this argument has stood unchanged in the book since the first edition in 1988 or so. I appreciate your pointing the issue out. There aren't any plans currently for a new edition of the book - I just dr... | https://mathoverflow.net |
2,359,559 | [
"https://math.stackexchange.com/questions/2359559",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/309041/"
] | Does the idiom
<blockquote>
Nothing implies everything.
</blockquote>
make sense?
If here the term <em>nothing</em> means empty set $\emptyset$ of premises, and <em>imply</em> means "semantically implication, $\vDash$"(or syntactically implication, $\vdash$; doesn't matter), then it is not true; since, for exampl... | I have never heard of 'nothing implies everything' ... are you sure it's idiom?
And I'm with you, it doesn't make sense; either it says that everything can be implied from the empty set, which you are are correct to say is clearly false, or it says that there isn't anything from which everything can be inferred, but... | One possible interpretation of the implication $P\vDash Q$ is that $S_P\subseteq S_Q$ where $S_P$ and $S_Q$ are the set of "objects" with property $P$ and property $Q$ respectively. So the idiom "nothing implies everything" is like saying that the empty set $\emptyset$ is a subset of any set.
| https://math.stackexchange.com |
437,865 | [
"https://softwareengineering.stackexchange.com/questions/437865",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/227698/"
] | From time to time you need to do technical updates, like:
<ul>
<li>Update versions of your dependencies</li>
<li>Update the version of your parent POM, you build tool etc.</li>
</ul>
Leave out those updates that have a firm deadline or directly induced by business needs. I mean the updates that are not urgent, but shou... | Feature branches are a general term that means "not the main branch" (or master). Don't get too complicated with this. Create a branch just to upgrade that dependency. This should capture any additional code or documentation changes necessary during the upgrade. Breaking changes should be noted in the commit ... | Ticket, like everything else. Also serves to account for time spent doing this and provides visibility to the team.
| https://softwareengineering.stackexchange.com |
1,563,717 | [
"https://math.stackexchange.com/questions/1563717",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/296591/"
] | <blockquote>
If $A$ and $B$ are finite sets, show $|A\cup B|= |A|+|B| \iff A\cap B = \emptyset$
</blockquote>
I want to prove via the route: Let $A=\{a_1,a_2,\dots,a_n\}$ and $B=\{b_1,b_2,\dots ,b_m\}$ and then using the properties of sets to come to a conclusion.
| Any method: By <strong>symmetry</strong> the integral is $0$.
| HINT:
Basic trigonometry tells us
$$x=r\cos(\theta)$$
$$y=r\sin(\theta)$$
$$r^2=x^2+y^2$$
So substituting these values will help find (a). Also for (a), keep note of the bounds for $r$ and $\theta$ when setting up the double integral. The bounds will most likely be the more difficult part.
For (b), they say <em>any me... | https://math.stackexchange.com |
30,863 | [
"https://physics.stackexchange.com/questions/30863",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/10138/"
] | Let's say you live at a moderate (temperate, in today's terms) latitude during the last glacial maximum. You're probably in some kind of steppe or taiga biome, even though you're at 40 degrees north, and you've never known hot weather. If you're outside on a sunny summer day, would you still get a suntan/sunburn like y... | Yes, of course, the suntan/sunburn depends on the overall energy in UV radiation coming from the Sun to one's skin and this quantity is virtually unchanged in the glaciation cycles, at least if you average it over seasons. What primarily matters is the angle between the Sun rays and the plane of the skin; and the angle... | Assuming it's a cloudless day, then yes you will get a sunburn just as you would today. Sunburn is caused by the intensity of ultraviolet light, and this didn't change (much) during the ice age. The external temperature makes no difference: it's just the uv intensity that matters. Any skier can tell you that :-)
Actua... | https://physics.stackexchange.com |
82,722 | [
"https://security.stackexchange.com/questions/82722",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/69326/"
] | There is a website I use at work, external to our own. They have just presented with every employee with their plain text password and username via our internal website which requires our own logins.
I was wondering if this should be viable for a professional company (Either the external website company or my internal... | Well-tested code helps to <em>reduce the risk</em>, but even PHP keeps issuing patches to remedy security issues.
The problem is not with "newcomers" but with appropriate protections and controls over any type service that you expose. PHP/Apache/etc. behave (and fail) in predictable ways, but we can predict their beh... | I would not be using node for production but that's a different topic.
The use of ngnix or Apache as a reverse proxy will provide little if no benefit security wise due to the fact that almost everything is being passed through transparently
| https://security.stackexchange.com |
9,561 | [
"https://dba.stackexchange.com/questions/9561",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/-1/"
] | I have a table with a lot of records (more than 15M) and i am executing an alter query to add 2 columns to the table.<br>
the query is taking around 1hr to finish executing.<br>
So my question is: How does an alter work? and why is it affected by the number of records?<br>
is it possible to speed up an alter query usin... | An ALTER TABLE operation that adds a column to a table should be a simple data dictionary only update. There is no reason for Oracle to visit all the blocks/rows in the table. So, the operation should be very fast. (sub-second response time.)
The only exception to this would be, if you're on a version of Oracle pri... | Every row in the table needs to be updated to add the new columns if you're specifying a default value. That's why it's affected by the number of records. Column indexes won't help, because indexes aren't involved in this operation.
| https://dba.stackexchange.com |
580,193 | [
"https://physics.stackexchange.com/questions/580193",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/265821/"
] | I got a Doubt that what if the spring has mass
I found the following question
When one end of a spring (of mass m and length l ) is pulled with velocity V1 and other and with velocity V2 then velocity of a point on spring at a distance x from first end is given by formula<br />
V1+ (x/l)×V2
I tried to prove this but I ... | The elongation (or compression) of a spring distributes itself linearly over the spring's length.
That can easily be explained. Let's assume for a moment, the right half of the spring elongates more than the left half. Then the right half pulls stronger than the left half, thus pulling stronger on the middle point than... | I'd say the formula is wrong. If you set x = L, then one end of the spring is moving at <span class="math-container">$v_1$</span> + <span class="math-container">$v_2$</span>. It should be <span class="math-container">$v_1$</span> + (x/L)(<span class="math-container">$v_2 - v_1$</span>).
| https://physics.stackexchange.com |
90,325 | [
"https://stats.stackexchange.com/questions/90325",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/39997/"
] | Suppose you have $\theta=\{1,2\}$ and the sample of (0,1,2) with the task of finding MLE:
\begin{array} {|c|c|c|}
\hline
x & p(x|\theta=1) & p(x|\theta=2) \\
\hline
0 & 1/2 & 1/4 \\
\hline
1 & 0 & 1/4 \\
\hline
2 & 1/3 & 0 \\
\hline
\end{array}
I can't compare $\prod_i p(x_i|\theta)$, ... | Now we have the original question, the mystery is no mystery.
In that question, a single observation will be consistent (to greater or lesser degree) with some of the $\theta$ values and inconsistent with others (the ones that have no chance of giving that observed value).
So for example, if we look at your probabil... | If $P(x=1|\theta = 1) = 0$, then (0,1,2) is impossible, since it has a 1 in it. If $P(x=2|\theta = 2) = 0$, then (0,1,2) is impossible, since it has a 2 in it. So, your likelihood calculation is telling it like it is. It is impossible to get that sample, given your probability distributions and thetas.
| https://stats.stackexchange.com |
58,083 | [
"https://softwareengineering.stackexchange.com/questions/58083",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/10021/"
] | Everything I've read about Hadoop seems like exactly the technology we need to make our enterprise more scalable. We have terabytes of raw data that is in non-relational form (text files of some kind). We're quickly approaching the upper limits of what our centralized file server can handle and everyone is aware of thi... | Why are you in favor of this move?
<ul>
<li>Does it make life easier for the team?</li>
<li>Does it help users in managing, accessing files?</li>
</ul>
Unless you have a technical person who is a decision maker chances are they don't care about who favours what. They care about:
<ul>
<li>ROI (Return on Investment) ... | <blockquote>
what steps can we take to get upper management to move forward with Hadoop despite the hesitation of one member of the team?
</blockquote>
Solve the problem.
You can't "convince" people of anything with argumentation or science or even facts established outside the organization.
You need to actually s... | https://softwareengineering.stackexchange.com |
86,381 | [
"https://mathoverflow.net/questions/86381",
"https://mathoverflow.net",
"https://mathoverflow.net/users/10400/"
] | Let $G$ be a locally compact group and let $K$ be a compact group. Let $(\tau, V_\tau)$ be an irreducible representation of $K$.
We consider the space of $Endo_K(\tau)$-valued, compactly supported continuous functions
$f$ on $G$<br>
with
$$ f(k_1 g k_2) = \tau(k_1) f(g) \tau(k_2), $$
which is an $*$ algebra under co... | These Hecke algebras are intensively studied in the field of "type theory" for reductive $p$-adic groups.
You have a nice summary of basic facts <em>with proofs</em> in chapter 4 of Bushnell and Kutzko's book "The admissible dual of ${\rm GL}(N)$ via compact open subgroups" (the chapter is entitled "Interlude with Hec... | A classical reference for twisted Gelfand pairs is J.R. Stembridge, On Schur's Q-functions and the primitive idempotents of a commutative Hecke algebra, J. Algebr. Comb. 1 (1992) 71–95, but I believe this paper considers only finite groups.
| https://mathoverflow.net |
3,375 | [
"https://engineering.stackexchange.com/questions/3375",
"https://engineering.stackexchange.com",
"https://engineering.stackexchange.com/users/2146/"
] | What type of a mechanical device can I use and program to apply a controllable force within the range of what a human can to an area about the size of a fingertip? It is desirable for the applied force to be precise and known.
| I agree the compressed air is the way to go. There are many vendors that sell small cylinders and even have bumpers available for the end of the actuator rod that could approximate a fingertip.
For control, you don't mention any requirements, but if they're simply manually controlled on/off application of force, a reg... | There are many possible options, but possibly this simplest would be a cylinder driven by compressed air. Since compressed air pressure is easy to measure, and your cylinder area will be constant, it is easy to know how much pressure is being applied. Compressed air is also nice because the amount of pressure can be ea... | https://engineering.stackexchange.com |
12,645 | [
"https://datascience.stackexchange.com/questions/12645",
"https://datascience.stackexchange.com",
"https://datascience.stackexchange.com/users/15064/"
] | How can I get the number of missing value in each row in Pandas dataframe.
I would like to split dataframe to different dataframes which have same number of missing values in each row.
Any suggestion?
| You can apply a count over the rows like this:
<pre><code>test_df.apply(lambda x: x.count(), axis=1)
</code></pre>
test_df:
<pre><code> A B C
0: 1 1 3
1: 2 nan nan
2: nan nan nan
</code></pre>
output:
<pre><code>0: 3
1: 1
2: 0
</code></pre>
You can add the result as a column like this:
<pre><c... | When using pandas, try to avoid performing operations in a loop, including <code>apply</code>, <code>map</code>, <code>applymap</code> etc. That's slow!
A DataFrame object has two axes: “axis 0” and “axis 1”. “axis 0” represents rows and “axis 1” represents columns.
If you want to count the missing values in each col... | https://datascience.stackexchange.com |
357,642 | [
"https://softwareengineering.stackexchange.com/questions/357642",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/119333/"
] | For example, I find myself using software X.
Software X has a github repository. I find that I can make a lot of serious refactoring changes that are <em>not small</em>, and reconfigure the entire repository to use a different software methodology. i.e. software X is written using procedural style non-object-oriente... | My impression is that you can, if you'd like, contact the author and see if they would be interested in the change. They will likely want to have an idea of what sort of changes you want to make and will probably want a small example of the refactoring. This is assuming they are even open to the idea. They may have rea... | You have actually write access to this repository?
The way to do this would be to make a change that is small enough to be reviewed, and then to post a pull request so that someone can review your change and merge it into the repository. And then you make the next change and so on.
Or you fork the repository. Take ... | https://softwareengineering.stackexchange.com |
187,681 | [
"https://mathoverflow.net/questions/187681",
"https://mathoverflow.net",
"https://mathoverflow.net/users/42326/"
] | Let $\Gamma$ be a prescribed $n-2$ dimensional set and assume $S \subset R^n$ is a minimal hyper-surface with respect to some smooth metric $g$ on $R^n$, and $\partial S= \Gamma$. Is $S$ is stable with respect to variations in the metric $g$? I believe the stability problem for minimal surfaces has to be well understoo... | Now that your comment has clarified your question, we can answer it: The answer is 'no'. There is the following well-known example:
Consider the following family of circles: $C_\lambda$ is defined as $x^2+y^2 = 1$ and $z = \lambda$. Let $\lambda>0$ be fixed and orient $C_{-\lambda}$ counterclockwise and orien... | The answer is (trivially) no.
The reason is that $S$ is never going to even be stationary for arbitrary changes in the metric*.
*Proof: If $\phi$ is a non-negative cutoff of compact support satisfying $0\leq \phi \leq 1$ and $\phi(p)=1$ for some $p\in S$ then $\frac{d}{dt}|_{t=0} Area_{(1+t\phi)g}(S)>0$
| https://mathoverflow.net |
350,351 | [
"https://softwareengineering.stackexchange.com/questions/350351",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/171920/"
] | I'm working on some code that checks for some invariants in the database. For example to check that an element is not repeated the code checks for a database error since the invariant is coded at database level.
Basically to enforce uniqueness for a certain set of key the code checks for the error:
<pre><code>if (sql... | That API belongs to your employer, not you. If you showed that to another potential employer, or even a recruiter, you'd be telling them that you can't be trusted not to share work that doesn't belong to you.
It really doesn't matter that you have only incomplete projects on GitHub. They still show your coding abiliti... | Absolutely not, unless that "private API" has some form of license you can comply with. If you wrote it for them, it is almost assuredly their intellectual property (I suppose this could vary depending on where you are, but it's unlikely to).
If you do show it, you could be liable for breach of NDA or other possible... | https://softwareengineering.stackexchange.com |
147,548 | [
"https://chemistry.stackexchange.com/questions/147548",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/106068/"
] | I came across three reactions while studying p-block compounds in inorganic chemistry.
<span class="math-container">$$\ce{2Al + 2NaOH + 6H2O -> 2 Na[Al(OH)4] + 3H2} \label{eq:1} \tag{1}$$</span>
<span class="math-container">$$\ce{Al2O3 + 2NaOH + 3H2O -> 2 Na[Al(OH)4]} \label{eq:2} \tag{2}$$</span>
<span class="m... | I will answer in a more general way to your question, because you have a specific one. Aluminium is absolutely a metal, but it can manifest peculiar features of non-metals. Its oxide, <span class="math-container">$\text{Al}_2\text{O}_3$</span> is very inert, while the hydroxide <span class="math-container">$\text{Al}(\... | The difference between <span class="math-container">$(2)$</span> and <span class="math-container">$(3)$</span> is the number of <span class="math-container">$\ce{NaOH}$</span> that has been used. If few <span class="math-container">$\ce{NaOH}$</span> is available, <span class="math-container">$\ce{Al2O3}$</span> reacts... | https://chemistry.stackexchange.com |
588,607 | [
"https://physics.stackexchange.com/questions/588607",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/277750/"
] | I read that bath scales measure body weight and not mass which means they measure m*g and not m.
<ol>
<li>If I got a reading of 50 kg, does that mean that my mass is nearly 5?
</li>
<li>Units of m*g aren't kg so why we say my weight is 50 kg? shouldn't it be called like my weight is 500 N?
</li>
</ol>
| Yes, typical bathroom scales measure weight <span class="math-container">$mg$</span>, not mass <span class="math-container">$m$</span>. But for convenience they are calibrated to show a reading in mass units, eg kilograms (or pounds).
So if the scales indicate that your "weight" is 50 kg that really means tha... | Typical bath scales do measure weight and report the weight in units of mass. These scales will report a lower weight for the same mass at the equator compared to the poles and at a high altitude compared to a low altitude. Usually these errors are far below the precision of the reported weight.
However, there are simi... | https://physics.stackexchange.com |
736,761 | [
"https://physics.stackexchange.com/questions/736761",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/156987/"
] | In Quantum Mechanics, path integrals are used to calculate the matrix element:
<span class="math-container">$$
\langle x_1, t_1|x_2, t_2\rangle_J=\int
e^{i(S[x(t)]+\int\!J x(t))/\hbar} d[x(t) ].\tag{1}$$</span>
If we naively try to extend this idea to QFT, we will naturally get:
<span class="math-container">$$\langle ... | They are in the same framework, but we usually use them in different ways, which explains the differences you are noticing.
In general, the path integral should include factors of the wavefunction to describe the initial and final states
<span class="math-container">\begin{equation}
Z = \int D \phi \Psi_{in}[\phi] \Psi... | Quantum mechanics is just a special case of QFT when the base manifold is one-dimensional. The path integral framework is the same.
Let me deal with a <span class="math-container">$d$</span>-dimensional base manifold, <span class="math-container">$Y$</span>, and some field <span class="math-container">$\phi\in\mathcal{... | https://physics.stackexchange.com |
26,042 | [
"https://scicomp.stackexchange.com/questions/26042",
"https://scicomp.stackexchange.com",
"https://scicomp.stackexchange.com/users/16799/"
] | In all the sources I have that discuss the elasticity equations, they start by saying that the strain tensor, $\epsilon$, is related to the displacement gradient, $\nabla u$, where $u$ is the (vector valued) displacement as
$$
\epsilon_{ij} = \frac{1}{2}\left(\frac{\partial u_j}{\partial x_i} + \frac{\partial u_i}{\pa... | In general, in the linearized theory of elasticity, it is only the displacement gradients that need to be small compared to unity. The displacements don't need to be small. (Note that when we say displacements are small, we usually mean displacements nondimensionalized with some quantity such as the characteristic leng... | Let us consider the uncoupled mechanical problem. Hence, we have 10 unknowns <span class="math-container">$\{\rho, \mathbf{v}, \underline{\underline{\sigma}}\}$</span>, assuming that the stress and strains are symmetric (this might not be true in Cosserat solids, for example). And we have 10 equations, namely:
<ul>
<l... | https://scicomp.stackexchange.com |
16,202 | [
"https://electronics.stackexchange.com/questions/16202",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/1270/"
] | I've got a 30V 2A isolated DC/DC supply. I need to be capable of outputting 1A for short periods of time (3 sec, exception condition only), so with temperature derating that's what I picked.
However, in normal operation the current draw is only 20-60mA. The poor efficiency of this is really bothering me. (It's like ... | As already asked - do you really care about the lost energy? Cost wise it's not liable to matter. Thermally it may.
You can easily enough achieve what you want, not by switching between supplies but instead by adding in a second supply when required. Your acceptable response time of "several hundred milliseconds" is 1... | Is efficiency when drawing 20-60mA really that important? You only say it's "bothering" you. Perhaps the answer is simply to get over it?
60mA at 30V is 1.8W. You say the supply is 10% efficient at that current, but that would imply a total input power of 18W. I find that hard to believe.
It is certainly possible... | https://electronics.stackexchange.com |
71,949 | [
"https://physics.stackexchange.com/questions/71949",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/22964/"
] | Consider the classical XOR Gate:
Given a 2 bit system: $G = [u_1, u_2]$
$$XOR(G) = (u_1 + u_2) \ mod \ 2$$
Is the following a good generalizaiton of a Quantum XOR Gate:
Given a 2-qubit system: $Q = a_1|00] + a_2|01] + a_3|10] + a_4|11]$
We now write:
$$XOR(Q) = a_1|0] + a_2|1] + a_3|1] + a_4|0] = (a_1 + a_4)|0... | Usually, a XOR quantum gate is implemented by the function :
$XOR(Q) = a_1|00 \rangle + a_2|01 \rangle + a_4|10\rangle + a_3|11 \rangle$
The first bit is conserved, while the second bit is the result of an XOR operation between the first and second bit.
For instance, if we have the combination $|11\rangle$, this ... | The XOR gate is almost always called the <strong>NOT gate</strong> in quantum information and computation. To implement the XOR gate unitarily one must do it in a <em>reversible way</em>, since unitary gates must be invertible; conversely, any reversible logic gate defines a physical unitary operation. The XOR gate is ... | https://physics.stackexchange.com |
72,061 | [
"https://electronics.stackexchange.com/questions/72061",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/24940/"
] | I'm building a custom Arduino compatible with an ATMEGA328P.
Would it be better to get a 5V power supply that plugs into the wall to power the project and gives me a barrel jack, then connect that directly to the uC, or should I instead use something like a 9V power supply, then use a 7805 to regulate down to 5V?
| You should go with the 5-V external supply and put a capacitor between 5 V and GND near the ATmega to reduce noise in the power. With the 9-V supply, you still need to have a wall wart but you also have an extra component on the board.
Also, don't use a linear regulator if you do decide to use 9 V. Since you're going ... | I'd prefer the external 5 volt supply - then I don't have to place a regulator on my board.
| https://electronics.stackexchange.com |
912,134 | [
"https://math.stackexchange.com/questions/912134",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/151558/"
] | If I have the numbers $0,1,2,3,4,5,6,7,8,9$ written down in that order, how many ways can the $10$ digits be written down so that no <em>even</em> digit is in its original position?
It would seem that I can move rewrite it starting from $0$ in $9!$ ways, and same with $2,4,6,8$, hence the answer is $5*9!=1814400$ is t... | Let $r(m,n)$ be the number of ways of placing $m$ objects, with $n$ of them constrained not to go in a particular position, where the $n$ particular positions are all different. Then we have $r(m,0)=m!$ (obviously), $r(m,1)=(m-1)(m-1)!$ (because we may place the constrained object in $m-1$ ways, and then the remainder ... | As suggested by Robert Israel, here is a solution using Inclusion-Exclusion:
Let S be the set of all arrangements of the digits, and for $1\le i\le5$
let $A_i$ be the set of arrangements with the $i$th even digit in its original position.
Then $|{A_1}^{c}\cap \cdots \cap {A_5}^{c}|=|S|-\sum|A_i|+\sum|A_i\cap A_j|-\... | https://math.stackexchange.com |
44,995 | [
"https://stats.stackexchange.com/questions/44995",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/17398/"
] | Should the likelihood be increasing in every step of the EM algorithm?
I wrote an EM algorithm recently and the number it arrived does not seem to be the maximum.
I know this because I used the optim function on R on the same problem and it arrived parameters which gave a bigger log-likelihood value.
But even when I... | The estimator may increase or decrease during each iteration however the likelihood must increase.
You should make sure your likelihood is increasing at each step and see if you are converging to the same value.
| Perhaps not relevant in this case but note that if the E-step is estimated, with Monte Carlo methods or another approximation, it is possible for the likelihood to decrease.
A thought that might be relevant is that the EM does not converge towards the global maxima but to a local.
For more details see section 3 of
"O... | https://stats.stackexchange.com |
2,114,606 | [
"https://math.stackexchange.com/questions/2114606",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/351797/"
] | I'm trying to show that
$$\lim_{(x,y)\to (0,0)} \frac{12x^3y^5+4x^4y^4}{x^6+4y^8}=0$$
I've used polar coordinates but when I do this I get the possibility of $\frac{0}{0}$ if $\cos(\theta)\to 0$ as $r\to 0$. So it must be that I need some sort of bound to make sense of this limit. But I'm not sure how to proceed.
| If we wish to use polar coordinates $(r,\theta)$, then we can write
$$\begin{align}
\frac{12x^3y^5+4x^4y^4}{x^6+4y^8}&=r^2\left(\frac{12\cos^3(\theta)\sin^5(\theta)+4\cos^4(\theta)\sin^4(\theta)}{\cos^6(\theta)+4r^2\sin^8(\theta)}\right)\\\\
&=r\left(3\sin(\theta)+\cos(\theta)\right)\left(\frac{4r\cos^3(\theta... | Hint: $u^2 + 4v^2 = (u-2v)^2 + 4uv \ge 4uv$, so:
$$x^6 + 4y^8 = (x^3)^2 + 4(y^4)^2 \ge 4x^3 y^4$$
<strong>Edit:</strong>
I pointed out in a comment that an argument by symmetry works.
A slightly better approach might be as follows:
$$\left| \frac{12x^3 y^5 + 4 x^4y^4}{x^6 + 4y^8} \right| \le 4\frac{3|x|^3 |y|^5 +... | https://math.stackexchange.com |
586,691 | [
"https://stats.stackexchange.com/questions/586691",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/366283/"
] | Suppose a student starts with test A, and will proceed to test B, then test C if he passes.
The probability for the student to pass test A is 30%.
The probability for the student to pass test B is 20%.
The probability for the student to pass test C is 10%.
The student has maximum 20 tries to attempt for the tests in TO... | This can be solved using Markov chains. First define your 4x4 transition matrix (A, B, C, F - final state), probabilities of passing from one state to the next. I am assuming there is only one direction of progression, forward, i.e. there is no rollback to previous tests upon failure. If this is not true then the matri... | No.
Since the probabilities are different at each time point, this data will not follow a geometric distribution.
I also don't quite understand when you say "The student has maximum 20 tries to attempt for the tests in TOTAL." bit, but that's not necessary to answer your question.
| https://stats.stackexchange.com |
8,544 | [
"https://softwareengineering.stackexchange.com/questions/8544",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/3262/"
] | For someone with .Net experience and wanting to develop for iPhone/iPod/iPad, is it worth learning Objective-C? Is MonoTouch a good alternative? What are some of the trade-offs when using MonoTouch vs coding in Objective-C?
| MonoTouch is a fantastic alternative. I've been using it for pretty much one year now, and I can't ever imagine going back to objective-c. Highlights: LINQ, LINQ to XML, LINQ, C#, LINQ, Garbage collector, LINQ, MonoTouch.Dialog, and a lot of other things.
Seriously, though.. nowadays most apps are always downloading d... | I'm a seasoned C, C++, Delphi & .NET developer and I recently needed to tackle an iOS application development project with a .NET back-end. I initially got very excited about MonoTouch and climbed into it only to find that the learning curve was not really the language but rather the design patterns.
I also noted ... | https://softwareengineering.stackexchange.com |
129,754 | [
"https://dba.stackexchange.com/questions/129754",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/87543/"
] | I'm drawing an ER diagram for an ecommerce site that I'm building, and noticed something: the diamond that I am drawing between two models (or entities), which I understand is meant to symbolize the relationship between the entities, seems irrelevant.
The diagram could be drawn without the diamonds, and it would still... | As James K already said, there is more than one set of rules for forming ERDs, and more than one answer to your question. But, to deal with your question from a generic point of view, here goes.
Sometimes the diamond is irrelevant. The line between two boxes depicts the relationship, and often says everything that n... | The answer to your question depends on the rules of the diagramatic representation implemented by the tool you're using.
One possibility is that you're looking at a logical view of an M:N relationship, and the diamond represents the physical table that will be generated to support that relationship. (From an ER poi... | https://dba.stackexchange.com |
507,771 | [
"https://physics.stackexchange.com/questions/507771",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/236248/"
] | Suppose we have a block of mass m which was at rest on a rough floor and is now given an impulse towards a wall.It is given that the collision with wall is perfectly elastic and no energy is lost in it.It is given that block comes to rest at its starting position after the collision.Friction does no work on the block a... | <blockquote>
Friction does no work on the block as displacement is 0.
</blockquote>
That is incorrect.
Friction is not a conservative force, like gravity. The work done by gravity depends only on the end points and not on the path traveled. The work done by friction is along the entire path of travel and therefo... | Firstly friction is a non conservative force, so it s path dependent, so the total work done is not zero, one more thing I want to add is here direction of friction is different in both the direction.
| https://physics.stackexchange.com |
644,819 | [
"https://physics.stackexchange.com/questions/644819",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/304102/"
] | Sorry if this question is dumb, but I don't seem to have a grasp on it.
Suppose you are on a rock in space, with no external forces acting. The rock attracts you with a force given by
<span class="math-container">$$F=G\frac{m_1m_2}{r^2},$$</span>
and you also attract the rock with an equal and opposite force. The groun... | Just like the ground exerts force on you stopping you from accelerating, your legs push the rock stopping it from accelerating.
| One way to look at is:
<ol>
<li>Newton’s laws (namely action and reaction) implies that both bodies feel the same force (in opposite directions).
</li>
<li>Both bodies are therefore accelerated, but in proportion to their respective masses <span class="math-container">$a = f/m $</span>., therefore the most massive will... | https://physics.stackexchange.com |
326,922 | [
"https://math.stackexchange.com/questions/326922",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/26728/"
] | <img src="https://i.stack.imgur.com/6BuAU.png" alt="enter image description here">
How did they justify
$$\left | \int_{a}^{b} x(t) dt \right| \leq (b - a)\max_{t \in J} x(t)$$
| Take <em>any</em> Riemann sum wrt <em>any</em> partition $\,\{a=t_0<t_1<\ldots <t_n=b\}\,$ of $\,[a,b]\,$ , and for any points $\,c_k\in [t_k-t_{k-1}]\,$:
$$\left|\sum_{k=1}^nx(c_k)(t_k-t_{k-1})\right|\le ||x||\sum_{k=1}^n(t_k-t_{k-1})=||x|| (b-a)$$
| Take the case where $x(t)\ge0$ for all $t$. Draw the graph of $x(t)$, and draw a box around it of length $b-a$ and height $\max x(t)$, and see the inequality geometrically. Then work out how to make this go through even if $x(t)$ is not non-negative.
| https://math.stackexchange.com |
2,288,909 | [
"https://math.stackexchange.com/questions/2288909",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/357933/"
] | <blockquote>
Given that $K$ is a vector subspace then $Sp(K)=K$.
</blockquote>
Can you please explain why?
I understand that $K$ spans $Sp(K)$, that is with the set of vectors $K$, for example {$(1,0), (0,1)$} we can span $\mathbb{R^2}$. So if anything $K \subseteq Sp(K)$. But $Sp(K)$ contains infinite number of ve... | For any subset $S$ of a vector space $V$, the span of $S$ is the smallest vector subspace of $V$ containing $S$. Therefore, if $S$ itself is a vector subspace of $V$, then the span of $S$ is $S$.
| Another way of thinking about this is the following:
Remember that $Sp(K)$ is the set of all finite linear combinations of vectors in $K$. Since vector spaces are closed under linear combination, each element of $Sp(K)$ must also be in $K$; that is, $Sp(K)\subseteq K$. You're right that $K\subseteq Sp(K)$, so $Sp(K) =... | https://math.stackexchange.com |
94,202 | [
"https://cs.stackexchange.com/questions/94202",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/90630/"
] | I'm reading about an operating system but some concept confuses me.
<strong>What doesn't confuse me:</strong>
When an interrupt or system call or processor exception occurs, it happens when user mode tries to switch to the kernel mode, the operating system uses PCB(process control block) to save needed stuff, namely... | To be in NPC a problem, C, has to be in NP, and every problem in NP has to be polynomial-time reducible to C.
If P=NP every problem in NP can be solved in polynomial time.
This means that if P=NP, we can for most problems in P define the following reduction to C; Solve the problem in polynomial time, if the instance ... | The premise of your question is false. If $P=NP$, then the middle drawing ("This is true...") is wrong and the third ("but why not this?") drawing is correct.
<blockquote>
Assuming P = NP, why should P be a subset of NPC?
</blockquote>
$P$ is not a subset of $NPC$, and this is unconditionally true.
There are two ... | https://cs.stackexchange.com |
543,953 | [
"https://stats.stackexchange.com/questions/543953",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/334261/"
] | I am trying to use Bayes formula to compute the likelihood of a given state given a collection of independent <strong>but not sequenced</strong> observations - knowing the priors and knowing the probabilities of being in the state given each observation.
In other words for pre-defined states <span class="math-container... | This is correct:
<span class="math-container">\begin{align}\mathbb P(S=S_i|\theta_1,\ldots,\theta_k) \propto \frac{\mathbb P(S=S_i|\theta_1)p(\theta_1)}{\pi_i}\cdots \frac{\mathbb P(S=S_i|\theta_k)p(\theta_k)}{\pi_i} \pi_i\\
\propto \mathbb P(S=S_i|\theta_1)\cdots \mathbb P(S=S_i|\theta_k) \pi_i^{-k+1}
\end{align}</spa... | It's a little bit confusing as at the beginning we define a relationship between the probability of a state given a single observation but now we are looking at a set of observations. Do we know with certainty that all observations come from the same state? Assuming that we do then the solution by Xi'an is correct.
Rep... | https://stats.stackexchange.com |
381,143 | [
"https://softwareengineering.stackexchange.com/questions/381143",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/229683/"
] | Say there is a single database table containing information about two different types of animals: land animals and sea animals.
I want to create two lists of animals, one list for each type of animal.
Is it better practice to query all animals from the database, iterate over the returned list of animals, and place th... | "Better" could have many meanings. This is a tricky question and the answer would require some assumptions. Anyway, I will throw in my 2 cents...
In your case, and index will not help. The optimizer will probably ignore it since you have 2 types only.
To execute the query on the server, you may consider 3 factors aff... | It is better to retrieve only what is required from the database rather than retrieve everything and then filter it down. If your table has millions of rows and <code>land</code> and <code>sea</code> only have a few hundred rows your query is going to return a million rows to be iterated over.
So changing your databas... | https://softwareengineering.stackexchange.com |
3,579,558 | [
"https://math.stackexchange.com/questions/3579558",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/758940/"
] | Given this function
<span class="math-container">$f(x) = (x^2 + 1)^{\sin(x)} $</span>
How would I establish its differentiability over the entire function? I understand how to establish differentiability at a point <span class="math-container">$c$</span>, by assessing the limit of the different quotient at <span clas... | Here's a plan:
(i) Prove that <span class="math-container">$x^2+1$</span> is differentiable.
(ii) Prove that if <span class="math-container">$\phi(x)$</span> is differentiable so is <span class="math-container">$\ln\phi(x)$</span>.
(iii) Prove that <span class="math-container">$\sin x$</span> is differentiable.
(iv... | You shouldn't use the definition of derivative, instead you should use a tricky technique:
<span class="math-container">$\displaystyle f(x)=(1+x^2)^{\sin x} \implies \ln(f(x)) = \ln\left( (1+x^2)^{\sin x} \right) = \sin x \ln(1+x^2)$</span>
<span class="math-container">$\displaystyle \implies \frac{d}{dx} \ln(f(x)) =... | https://math.stackexchange.com |
7,489 | [
"https://security.stackexchange.com/questions/7489",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/5091/"
] | While there is the possibility that this is just to prevent people from viewing offensive images against their will, somehow I don't think that's the reason why pretty much every email client defaults to making the user white list every single email address that sends them images. This level of paranoya screams "securi... | Several reasons:
<ul>
<li>The more content in the email that the client loads and interprets, the greater the possibility that the email will deliver a malicious payload. The relatively recent vulnerability in JPEG 2000 rendering code comes to mind -- merely displaying a malicious image could be dangerous.</li>
<li>Im... | I think there's two separate security risks that need to be addressed here:
<strong>Images which are actually <em>in</em> the e-mail.</strong> As some have touched on, there is inherently a direct correlation between the amount of content you allow your e-mail client to load and the attack surface of your computer wh... | https://security.stackexchange.com |
1,830,791 | [
"https://math.stackexchange.com/questions/1830791",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/338187/"
] | I read that a Matrix $A$ has the eigenvalue $0$ if and only if $\ker(A) \neq \{0\}$.
Why so?
<strong>Edit</strong> Okay actually I figured it out myself. If $0$ is an eigenvalue of a matrix $A$ then $\det(A)=0$ and then $A$ is not invertible, therefore the rows are not linearly independent: $\ker(A) \neq0$.
| $A$ has eigenvalue $0$ $\iff$ $\exists v \neq0$ such that $Av=0v=0$ $\Rightarrow 0\neq v\in \ker (A) \Rightarrow \ker (A) \neq\{0\} $ .
On the other hand : $\ker (A) \neq\{0\} \Rightarrow \exists v\neq0$ such that $v \in \ker (A)\Rightarrow \exists v\neq0$ such that $Av=0=0v$. So $0$ is eigenvalue of $A$.
| Because there exists non-trivial vector $x$ such that $Ax = 0$, so then $Ax = 0 *x$ and $0$ is an eigenvalue.
| https://math.stackexchange.com |
19,592 | [
"https://softwareengineering.stackexchange.com/questions/19592",
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] | Im really not getting the idea:
<ol>
<li>What is Detailed Design.</li>
<li>Why use Detailed Design.</li>
<li>Advantages/Disadvantage of using Detailed Design.</li>
<li>Any alternative methods other than using Detailed Design.</li>
</ol>
Could some one please guide/explain me ?
| 1) When most people talk about detailed design, they are referring to a process known as top-down design. In short, when you think about the problem you are trying to solve, you start at the highest level and then work yourself into the details. This approach works very well when you have an overall structure you wan... | A detailed design allows you to evaluate design options prior to actually <em>implementing</em> them. It can potentially save you a ton of needless work you would otherwise have spent on an implementation that was deeply flawed due to a high level design choice and had to be extensively rewritten.
| https://softwareengineering.stackexchange.com |
45,314 | [
"https://datascience.stackexchange.com/questions/45314",
"https://datascience.stackexchange.com",
"https://datascience.stackexchange.com/users/57214/"
] | I am using a dataset to practice for building a decision tree classifier.
Here is my code:
<pre><code>import pandas as pd
tdf = pd.read_csv('https://archive.ics.uci.edu/ml/machine-learning-databases/breast-cancer-wisconsin/breast-cancer-wisconsin.data', sep = ',', header=0)
tdf.info()
</code></pre>
The column has n... | For any dataframe, say df , you can add/modify column names by passing the column names in a list to the df.columns method:
For example, if you want the column names to be 'A', 'B', 'C', 'D'],use this:
<code>df.columns = ['A', 'B', 'C', 'D']</code>
In your code , can you remove <code>header=0</code>? This basically tel... | <pre><code>df = pd.read_csv("Price Data.csv", names=['Date', 'Price'])
</code></pre>
use the <code>names</code> field to add a header to your pandas dataframe.
| https://datascience.stackexchange.com |
276,182 | [
"https://electronics.stackexchange.com/questions/276182",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/7098/"
] | I need to power a Thermoelectric module with 10A maximum load current. I'm designing a card with a minimal design in order to change the current or the voltage across the load, given a standard voltage source.
I just need a minimal regulation of the load, which is, just be able to decrease the power of the thermoelect... | Your ripple requirement isn't that hard – what's more problematic is that your output voltage * output current = 300 W!
That's quite a lot. You would not want to burn a couple of volts at 20A over a linear regulator (which, by the way, makes no sense – that will convert the energy that you don't put inot your thermoel... | Just ask your favorite supplier or search engine for <strong>"Adjustable Power Resistors"</strong> and use one of those together with your load as a voltage divider.
Let's assume that your load is strictly ohmic. Your output specs require 300 W of output power, and you want to regulate (burn away) 10-20% of that. That... | https://electronics.stackexchange.com |
4,088 | [
"https://cstheory.stackexchange.com/questions/4088",
"https://cstheory.stackexchange.com",
"https://cstheory.stackexchange.com/users/189/"
] | Let $G$ be an edge-weighted DAG with a unique source $s$. The question is how to find out a maximum weight arborescence in $G$ rooted at $s$.
When all edge weights are positive then the required arborescence is also spanning and so we can use the directed minimum spanning tree algorithm (http://www.ce.rit.edu/~sjyeec/... | The problem is NP-complete by a reduction from the set cover problem.
<strong>Set cover</strong><br>
<em>Instance</em>: A finite set <i>U</i>, a family <i>C</i> of subsets of <i>U</i> and <i>k</i>∈ℕ.<br>
<em>Question</em>: Is there a cover <i>D</i> of <i>U</i> in <i>C</i> with at most <i>k</i> sets, that is, a subset ... | What about picking, for any vertex different from the source, an incoming arc with maximum weight ? Each vertex except the source is of indegree one, and you needn't worry about circuits as you are in a DAG.
| https://cstheory.stackexchange.com |
1,102,519 | [
"https://math.stackexchange.com/questions/1102519",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/183855/"
] | I am trying to integrate an equation of the form
\begin{equation}
\int_0^\pi \frac{\sin^2(x)}{\cos(x)+C}dx
\end{equation}
I can't think of a way to do it and Mathematica tells me that it is undefined at limits, is this impossible?
| Let $(e_1,\ldots,e_p)$ a basis for $W$ and we complete it on a basis $(e_1,\ldots,e_n)$ of $V$. Now define $g$ by
$$g(e_i)=f(e_i),\; i=1,\ldots,p$$
and for example
$$g(e_i)=0,\; i=p+1,\ldots,n$$
then $f$ and $g$ are equal on $W$ since they are equal on a basis of $W$.
| Hints:
Take any basis $\;\{u_1,...,u_k\}\;$ of $\;W\;$ and expand it to a basis $\;\{u_1,...,u_k,u_{k+1},...,u_n\}\;$ of V.
Use that any <em>linear</em> transformation is uniquely and completely determined by its values on any basis of the space.
Define now
$$g(u_i)=\begin{cases}f(u_i)&,\;\;1\le i\le k\\{}\\0&a... | https://math.stackexchange.com |
85,012 | [
"https://datascience.stackexchange.com/questions/85012",
"https://datascience.stackexchange.com",
"https://datascience.stackexchange.com/users/106706/"
] | I'm training a <strong>Unet</strong> model for tumor segmentation.
I have a dataset of <strong>400 patients</strong> for that.
The used images are CT scans (3D images) that I divide into 2D images (for a total of 30k 2D images).
I am actually splitting the dataset into:
10% test data, 18% validation data, 72% actual tr... | <strong>Generally numbers (percentages) do not matter.</strong>
What matters is that your Splitting (Train/test/Validation) does 2 things. Represent the real world sitatution and making sure the model can generalise given that ist evaluated on the holdout sets.
So what does that mean here exactly? You have 30k Images a... | Generally you should have a 60% train dataset and a 20% validation as well tests set. I'm not familiar with the tumor segmentation thing but as long as the images for the same pacient are different and with a relevant level of difference that must be enough.
| https://datascience.stackexchange.com |
1,847 | [
"https://scicomp.stackexchange.com/questions/1847",
"https://scicomp.stackexchange.com",
"https://scicomp.stackexchange.com/users/549/"
] | I have a set of equations of the form:
$$\begin{align*}
x_1&=(ax_0+c) \bmod (m)\\
x_2&=(ax_1+c) \bmod (m)\\
x_3&=(ax_2+c) \bmod (m)\\
&\vdots\\
x_{n}&=(ax_{n-1}+c) \bmod (m)
\end{align*}$$
I want to compute the sensitivity indices of each equation with respect to the parameters $a$, $c$, and $m$. ... | My explanation is getting long-winded here, but the answer is, attempting to use a continuous definition of sensitivity index is not going to be meaningful for your problem.
It is possible to find the sensitivity of a discontinuous function with respect to a parameter at a specific point of discontinuity, so if the pr... | The mod operation leads to a discontinuity in the function. That means of course that you can't take a derivative for values $x_i$ where $ax_i+c$ is a multiple of $m$. At all the other places, the mod-operation does nothing but shift its left operand so the derivative is as if the mod-operation wasn't there.
To see wh... | https://scicomp.stackexchange.com |
1,306,140 | [
"https://math.stackexchange.com/questions/1306140",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/-1/"
] | Well I have just started doing topology and I am doing open sets. So i thought of the following question:
Is there any set such that if if take any point in it and draw an open ball of some arbitrary radius It will always lie inside the set?
Well I asked my friend about it and said an example of such a set is $\Bbb{R... | (Why does your $f$ start with $a_2$ instead of $a_0$?)
All we know from $\alpha$ being algebraic is that an equality
$$\tag 1\sum_{k=0}^na_k\alpha^k=0$$
holds, where $a_k\in F$ and at least one $a_k$ is $\ne 0$. Since $\alpha\notin F$, certainly $\alpha\ne 0$ so that we obtain
$$\sum_{k=0}^na_{n-k}(1/\alpha)^k=\alpha... | Notice that $\frac{1}{\alpha}$ belongs to $F(\alpha)$ so $F(\frac{1}{\alpha}) \subseteq F(\alpha)$. Similarly $\alpha =\frac{1}{\frac{1}{\alpha}}$ so $F(\alpha)=F(\frac{1}{\alpha})$. Hence $[F(\frac{1}{\alpha}):F]=n$ So $\frac{1}{\alpha}$ is algebraic of degree n. (I hope I am not mistaken),
| https://math.stackexchange.com |
187,726 | [
"https://physics.stackexchange.com/questions/187726",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/68456/"
] | Suppose you have an ideal spring (constant of the spring $k$) attached to a uniform disc of radius $R$ as in the picture below:
<img src="https://i.stack.imgur.com/ru1S8.png" alt="enter image description here">
The force $F$ in red is from the spring.
My question is the following:
How should I decompose the force $F... | At L4 and L5, the object would stay in the same relative position because it is in the same orbit around the Sun as Earth. Any other points on the circle would not be in the same orbit as Earth. They would be in orbits of differing inclination and so, in the course of the orbit of that object about the Sun, it would ne... | <blockquote>
<em>This circle is the set of locations where the gravity of the sun and earth cancel out.</em>
</blockquote>
Uhm. No. They are neither co-linear nor the same magnitude. To get a zero "force" at the Lagrange points you have to work in a rotating frame of reference, implying a centrifugal pseudo-force w... | https://physics.stackexchange.com |
2,495 | [
"https://astronomy.stackexchange.com/questions/2495",
"https://astronomy.stackexchange.com",
"https://astronomy.stackexchange.com/users/1707/"
] | I'm writing a space game that I want to give a more "realistic" feel. When looking for a reference as to distribute elements in planets (for mining, etc) Instead of finding the more usual percentage tables, it seems that all elements are presented in a "normalized to Si 10 to the power 6", and furthermore, it seems tha... | The table you referenced is normalized so that the abundance of Silicon (Si) is exactly $10^6$, and all the other numbers are related to that.
"Abundance" in this table refers to the number of atoms.
Please note that this table is for the entire Solar System, taking into account the huge amounts of Hydrogen and Heliu... | It simply means that the scale is such that the relative abundance of silicon is $10^6$. For example, if you see a statement on this scale that in atom number $\mathrm{C} = 1.17\times 10^7$, that would tell you that carbon atoms are $11.7$ times as numerous as silicon ones.
What you're probably looking at is sometimes... | https://astronomy.stackexchange.com |
516,467 | [
"https://electronics.stackexchange.com/questions/516467",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/251503/"
] | i am trying to design an efficient cooling solution for my project.
I planned placing a IoT computer in an aluminum housing which is completely closed.
In this case, do I really need fins and large surface areas INSIDE the aluminium housing when my main goal is to dissipate the heat to the housing itself as fast as pos... | There are two power functions you need to be concerned with: instantaneous power dissipation, and long term power dissipation. A large thermal mass (finned or not) will prevent your IC overheating due to a quick spike of power. Over the longer term, the heat needs to be dissipated to the outside environment. Fins are o... | It depends on a few factors: what’s the maximum temp of the CPU die? What’s the surface area of the enclosure? What is it made from? What is the distance between the CPU and the surface you want to reach with this copper block? What is the ambient temperature? Do you expect solar heating?
Off the top of my head I’... | https://electronics.stackexchange.com |
69,233 | [
"https://mechanics.stackexchange.com/questions/69233",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/43607/"
] | My battery charger has a 2 A and 10 A option. What's the difference? If 10 A is more and faster, why not just put the 10 A option?
| You're right that 10 amperes is faster, by a factor of 5x.
Lead-acid batteries are charged in 3 stages, first by constant current (with voltage limit), then by constant voltage (with tapering current), then in the end during float charge the voltage is reduced to a float charge voltage level.
The 2 ampere and 10 ampe... | That battery charger has been designed to charge smaller, and larger, 12V batteries.
The ones on motorcycles or batteries having a smaller capacity need a lower charging rate.
However, if the charger is a quality one, then it will have a charge control circuit that will change the charging regime according to the sta... | https://mechanics.stackexchange.com |
39,594 | [
"https://electronics.stackexchange.com/questions/39594",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/17697/"
] | I'm making a safety disconnect for an experimental RC craft. It will be tethered to the ground, and if it goes out of control the tether will pull a plug disconnecting the power. I will make the plug from a male Deans connector (pictured below) looped to connect the positive and negative terminals. The female connec... | The lubricant does not need to be conductive - the contact pressure between connector halves will push the lubricant out of the way and ensure a good connection. A wide range of lubricants will work for your application. Try dielectric grease (sold for starter battery terminals), petroleum jelly, or WD-40 (wiped, not... | In marine applications silicone grease is used on all copper contacts for corrosion resistance: water-resistant, non-corrosive, etc.
| https://electronics.stackexchange.com |
299,990 | [
"https://physics.stackexchange.com/questions/299990",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/27939/"
] | Given a Hamiltonian how does one find the metric <strong>(or families of metrics)</strong> it obeys?
<h2>For example</h2>
Let's say for the Hamiltonian $H$:
$$ H = \frac{p^2}{2m} + V(x).$$
How do I show this follows the Euclidean metric?
| Sometimes it may not be possible to deduce the metric of the background a theory lives in. Consider for example Liouville theory, given by the action,
$$S = \frac{1}{4\pi}\int d^2 x \, \sqrt{g} \left(\frac{1}{2}g^{ab}\partial_a \phi \partial_b \phi + \frac{1}{\gamma} \phi \mathcal R + \frac{\mu}{2\gamma^2}e^{\gamma \p... | Two different metrics can have the same Hamiltonian, for instance for a conformally invariant scalar field and two conformally related metrics. Hence I do not believe it is generally possible to do.
| https://physics.stackexchange.com |
3,183,905 | [
"https://math.stackexchange.com/questions/3183905",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/53017/"
] | <blockquote>
Evaluate the limit:
<span class="math-container">$$
\lim_{x\to0}\frac{\pi - 4\arctan{1\over 1+x}}{x}
$$</span>
</blockquote>
I've been able to show the limit is equal to <span class="math-container">$2$</span> using L'Hopital's rule. After finding the derivative of the nominator the limits simply bec... | Set <span class="math-container">$\dfrac\pi4-\arctan\dfrac1{1+x}=y$</span>
<span class="math-container">$\dfrac1{1+x}=\tan\left(\dfrac\pi4-y\right)=\dfrac{1-\tan y}{1+\tan y}$</span>
<span class="math-container">$x=?$</span>
| Rewrite as
<span class="math-container">$$
-4\frac{\arctan(1/(1+x))-\pi/4}{x}
$$</span>
then it is of the form: <span class="math-container">$-4\,(f(x)-f(0))/(x-0)$</span> with <span class="math-container">$f(x)=\arctan(1/(1+x))$</span> which by definition tends to <span class="math-container">$-4\,f'(0)=2$</span>
| https://math.stackexchange.com |
697,025 | [
"https://physics.stackexchange.com/questions/697025",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/329461/"
] | Imagine I have a simple AC generator. I am providing energy to rotate the coil, which converts this to electrical energy. If I connect the ends to an electrical component such as motor, bulb, the power consumed would be equal to <span class="math-container">$P=V^2/R.$</span> Now if I instead connect the ends to a low-r... | You are right. In the limit of <em>infinite load resistance</em>, no current is exiting the AC generator (the load is an <em>open circuit</em>) and it takes no work to turn the armature (except for overcoming bearing friction, etc.).
As the load resistance is reduced, progressively more current can then flow out of the... | To expand just a bit on Niels' answer:
With less resistance in the load resistor, the higher the current in the coil. The higher the current in the coil, the higher the magnetic dipole moment of the coil. The higher the dipole moment of the coil, the greater the force between the coil and the magnet. The greater the fo... | https://physics.stackexchange.com |
258,267 | [
"https://dba.stackexchange.com/questions/258267",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/199744/"
] | I have a 3 node replica set that's been online since mid december. Last Friday (Jan 24), we added a 4th node in our disaster recovery data center.
We used the automatic initial sync procedure as our data set is relatively small. No problems here, after a while it's status switched to secondary and rs.printSlaveReplica... | I use to follow this path:
<ol>
<li>create all table, only structure (fields), without any Primary Keys nor Foreign Key, without any Index, the order doesn't matter</li>
</ol>
1.1 inject predefined (aka static) datas
<ol start="2">
<li>create Primary Keys & Indexes</li>
<li>create Constraints if any</li>
<li>fin... | Please follow the below steps that might help you to achieve your desired goal.
<ol>
<li>create parent tables(for foreign key reference) or any table and define primary keys.</li>
<li>create child tables(for foreign key) and define the foreign key and refer it from the column of parent table.</li>
<li>create indexes o... | https://dba.stackexchange.com |
63,756 | [
"https://electronics.stackexchange.com/questions/63756",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/20443/"
] | I have three devices which I'm working on and one of them needs to control i2c communication between the other two.
Each of the devices is based on an AtMega or AtTiny chip. The Controller (based on some external input not known to either the Master or Slave) needs to be able to decide whether or not to pass on the i2... | While pulling the clock line low might work for some instances, it highly depends on how the master and the slave are coded. It might result in failed arbitration attempts or freezing due to unexpected clock stretching.
There are two simple options. One, would be to connect the slave's Clock Line, through a transistor... | You'd be better off blocking the clock signal.
If you let the slave see the clock but not the data, it will still try to read bits from the data line each time the clock pulses. If you block the clock, the slave won't try reading the bus at all.
One simple, but somewhat crude, method would be to use an open collector ... | https://electronics.stackexchange.com |
149,552 | [
"https://electronics.stackexchange.com/questions/149552",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/37879/"
] | If a single wire is moving at \$v\$, inside a magnetic field \$B\$, with length \$L\$ then induced EMF is:$$\epsilon\ = -vBL$$
That is for a vertical wire that's motion is perpendicular to a magnetic field, the direction of induced \$I\$ is quite simple to find.
What about this diagram:
<img src="https://i.stack.img... | There are two approaches of the same phenomena. For an observer located inside the wire, the sources of magnetic field are moving, and therefore, an electric field appears according to Faraday's Law, generating an EMF \$\epsilon\$. On the other hand, an observer located outside the wire (in the same inertial frame of t... | The actual (physics) expression is v X B (where X is the cross product between the two vectors), So there is an angle in there v<em>B</em>l*sin (theta)... putting the angle at the top of your drawing.
| https://electronics.stackexchange.com |
64,084 | [
"https://dba.stackexchange.com/questions/64084",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/7326/"
] | Is there a way to copy maintenance plans from one SQL Server 2012 to another? Both servers are not accessible via the same copy of Management Studio at the same time (on different networks).
| Go to the server where the jobs exist, in Management Studio's Object Explorer go to Management > SQL Server Agent and highlight the Jobs folder. Hit <kbd>F7</kbd> (or View > Object Explorer Details). You should see multiple jobs in the right pane. Highlight the ones you want to copy, right-click, Script Job As > Create... | I found a more hacking way.
Every Execution Plan is one record in the <code>msdb.sysssispackages</code> table.
You can copy records from the <code>msdb.sysssispackages</code> table of source server to the <code>msdb.sysssispackages</code> table of the destination server.
Simply create a linked server on source serve... | https://dba.stackexchange.com |
393,215 | [
"https://mathoverflow.net/questions/393215",
"https://mathoverflow.net",
"https://mathoverflow.net/users/151406/"
] | Consider the closed interval <span class="math-container">$[0,1]$</span> and let <span class="math-container">$f \in C[0,1]$</span>. Let <span class="math-container">$g$</span> be a real valued function on <span class="math-container">$[0,1]$</span> such that <span class="math-container">$g \leq f$</span>.
<ol>
<li>Sup... | As I have commented, if <span class="math-container">$f,g:[0,1]\rightarrow\mathbb{R}$</span> are <span class="math-container">$C^{\infty}$</span> functions, and <span class="math-container">$c\in(0,1)$</span> is a real number with <span class="math-container">$f^{(n)}(c)=g^{(n)}(c)$</span> for each <span class="math-co... | Here is a purely real-analytic proof that is a bit simpler than my other answer and just relies on the Stone-Weierstrass theorem rather than complex analysis and Mergelyan's theorem.
<blockquote>
Theorem: Suppose that <span class="math-container">$f,g:[0,1]\rightarrow\mathbb{R}$</span> are functions
such that <span cla... | https://mathoverflow.net |
200,444 | [
"https://security.stackexchange.com/questions/200444",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/192173/"
] | I'm building a mobile application that transfers points between users via QRCode. I'm concerned about security and am looking for effective simple yes secure algorithm to use.
The scenario should be something similar to this.
<ol>
<li>User A wants to transfer X points to User B.</li>
<li>User A generates a QR code on ... | You are overcomplicating this. A counter of QR codes per day, daily salts, values that need to be synchronized...
I would simply design the application having an ECC keypair. When A wants to give N points, it makes a 'coin' with the information (timestamp, sourceUser, points, expiry), signed with its private key.
The... | Step 1: The auto incremented id implies you're worried someone would know the id one day. In that case they would know it on other days too.
Step 2: If the salt isn't long enough, someone can find it by brute force if they know their own id, and then they'll be able to use the id they got in step 1 to create the md5 w... | https://security.stackexchange.com |
93,899 | [
"https://dba.stackexchange.com/questions/93899",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/60306/"
] | I'm trying to write a stored procedure
So far I have this, but it always returns <code>1</code>
<pre><code>CREATE DEFINER=`root`@`localhost` PROCEDURE `USER_EXISTS`(IN `USERNAME` VARCHAR(64) CHARSET utf8mb4)
SELECT CASE WHEN MAX(user_id) IS NULL THEN '0' ELSE '1' END User_exists
FROM `dbname`.`tablename`
WHERE `us... | Perhaps doing a <code>COUNT</code> is better since it must be a number always
<pre><code>DELIMITER $$
DROP PROCEDURE IF EXISTS `USER_EXISTS` $$
CREATE DEFINER=`root`@`localhost` PROCEDURE `USER_EXISTS`
(IN `GIVEN_USERNAME` VARCHAR(64) CHARSET utf8mb4)
BEGIN
SET @User_exists = 0;
SELECT COUNT(1) INTO @found
... | This can be a one-liner: <code>RETURN EXISTS ( SELECT * FROM tbl WHERE ... )</code>. You get 0 or 1, not NULL.
At which point, why even create a function? The query to run without the function:
<code>SELECT EXISTS ( SELECT * FROM tbl WHERE ... )</code>
| https://dba.stackexchange.com |
232,869 | [
"https://physics.stackexchange.com/questions/232869",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/87129/"
] | Now this might be a very stupid question for many readers, but I am getting really confused.
I was reading about electricity and current, and I read this:
Suppose we connect a wire to the ends of a battery, and a bulb in the circuit, current flows and lights up the bulb. The battery is responsible for doing work on ... | In a copper wire there are copper ions with 28 bound electrons orbiting the nucleus. Approximately one electron per copper atom is free to roam throughout the metal and these electrons are called unbound or free electrons ans are responsible for electrical (and heat) conduction in copper. The positive copper ions are... | Positive charges are massive in relation to negative charges, so, what actually flow are negative charge carriers such as electrons or holes.
But due convention, we say that the current flows from positive to negative
| https://physics.stackexchange.com |
3,139 | [
"https://dba.stackexchange.com/questions/3139",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/1896/"
] | We have an "organic" environment, meaning people piled code on code for ten years with minimal oversight or documentation. The server I use has several databases which I believe are no longer being used; I'd love to delete them and leave just the three I actually use.
At the reckless extreme, I could disable these da... | You also want to make sure of the datetime stamps of every table. Search for any metadata in the system for every table, order such a list by datetime last updated, and display the output in desc order by datetime. You could also check the table size for even the slight change in size.
For example, in MySQL 5.x, you h... | You could try to set up a trace that only captures connections and to what database they connect to. I would leave this running for a bit and then make sure nothing is connecting to it.
One problem with that would be if you have some code opening up on the master db but calling another DB within the code. I'm not sure... | https://dba.stackexchange.com |
256,947 | [
"https://security.stackexchange.com/questions/256947",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/246544/"
] | I found an information leakage vulnerability on a company website and I found that the information includes all the usernames of the users.
I also observed that the application uses a lockout mechanism that locks out users after 5 attempts for 30 mins.
So will this lockout be considered a vulnerability?
Yes, account lo... | I would consider this a serious vulnerability. This can lead to an attack where the attacker can lock out every single user for 30 minutes.
Unless the company have a VPN in place, or other protection mechanism, it would be possible to download the entire user list, throw bogus passwords at all of them, and lock the ent... | I would look at it the other way around:
<blockquote>
Does knowing the list of users increase the severity of an attackable account lockout mechanism?
</blockquote>
Usernames are generally not random but based on people's names, so even without specific knowledge you can enumerate <em>likely</em> usernames (based on a ... | https://security.stackexchange.com |
56,110 | [
"https://softwareengineering.stackexchange.com/questions/56110",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/18063/"
] | There might be a situation where one of my clients won't pay for the web site that I've made. So I am wondering if it is possible to sell a web site? It is an internet shop, so there is no content that comes with it, but the source code is fully available, and it has a decent design. I've seen people trying to sell web... | You could try to sell it as a <em>platform</em>, and all it needs is a client to give it a some graphics and content. If enough clients want a similar site you could sell it again and again. You might have to work out some sort of hosting arrangement with each client but it can be done.
<strong>BUT</strong>... if the ... | I've seen a few people try, but unless it has a highly desirable domain name, I've never seen anyone sell one w/o a user base.
| https://softwareengineering.stackexchange.com |
607,702 | [
"https://physics.stackexchange.com/questions/607702",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/85871/"
] | An archer cannot throw an arrow as far as they can shoot it, nor would its penetrating power be as great.
The obvious explanation is that they have traded strength for speed. A slow draw stores energy in the bow that is then released quickly.
The problem is that, when an arrow strikes its target it has a lot of energy ... | Due to the physiology of the human arm, it's very difficult to throw an object much faster than 100mph. No matter what object is being thrown, it can't move faster than the hand that's holding it, so around 100mph is the upper speed limit of any thrown object.
A bow gets around this by using the elastic potential of th... | As you said, "A slow draw stores energy in the bow that is then released quickly."
The speed of the string, and therefore the speed of the arrow, is much faster than the archer's arm can move. The arrow's kinetic energy is proportional to the square of its speed.
Greater speed translates to greater range.
Gr... | https://physics.stackexchange.com |
268,798 | [
"https://mathoverflow.net/questions/268798",
"https://mathoverflow.net",
"https://mathoverflow.net/users/66131/"
] | Denote $[n]=\{1,2,\dots,n\}$. Assume $n\geq2$.
<blockquote>
<strong>Question.</strong> Is it true that given any $S_1,S_2,\dots,S_{2n}$ (repetition allowed) subsets of $[2n]$ with $a\in S_a$ and $\# S_a=n$ for all $1\leq a\leq 2n$, there exist $i, j, k\in[2n]$ (not all equal) such that
$$i\in S_j, \qquad j\in S_k... | For $n>2$ this is true. Consider a directed graphs with arrows from $a$ to $S_a\setminus a$. If it has arrows $a\to b$, $b\to a$, take $i=j=a$, $k=b$. If not, consider a vertex $a$ with maximal indegree, it is at least $n-1$ (since all outdegrees are equal to $n-1$). Let $B=\{i\ne a:a\in S_i\}$, $C=S_a\setminus a$. ... | If we take again $n=2$,
$S_1=\{1,2 \}$
$S_2=\{2,3 \}$
$S_3=\{3,4 \}$
$S_4=\{4,1 \}$
is a counterexample, right?
To see this label the vertices of an square clockwise with $1,2,3,4$. The $3-$distributed condition for this $n$ is equivalent to find a triangle in the graph with edges the $S_i's$.
| https://mathoverflow.net |
25,895 | [
"https://softwareengineering.stackexchange.com/questions/25895",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/1522/"
] | <ul>
<li>What will you use for a webpage layout? Percentage or pixels? </li>
<li>When should one use one over the
other?</li>
</ul>
| What unit you use depends entirely on what you want to accomplish. The units most used in web layouts are:
<ul>
<li>px - absolute; one pixel</li>
<li>pt - absolute; 1/72 inch, about 1.3px for screen media</li>
<li>em - relative to parent font size; 1.0em = size of a character (width of uppercase M)</li>
<li>% - relati... | I tend to use pixels for width declarations (which generally are fixed), but em's for height. That way the layout resizes vertically - but maintains horizontal consistency.
| https://softwareengineering.stackexchange.com |
21,427 | [
"https://cstheory.stackexchange.com/questions/21427",
"https://cstheory.stackexchange.com",
"https://cstheory.stackexchange.com/users/12280/"
] | A graph $G$ is chordal if it is the intersection graph of subtrees of a tree $T$. In particular $T$ can be chosen such that each node of $T$ corresponds to a maximal clique of $G$ and the subtrees $T_v$ consist of precisely those maximal cliques in $G$ that contain $v$. $T$ is then called the clique tree of $G$.
Now ... | Chordal graphs can be <strong>defined</strong> as intersection graph of subtrees of any tree. So the answer to your decision question is trivially YES. On the construction side, for each subtree $T_v$ of bags (it's convenient and conventional to call the nodes of the tree as bags), you'll have a unique new vertex $v$... | If I understood your question correctly, you want to know whether every tree $T$ is the clique tree of a chordal graph $G$. In this case, the answer is yes.
To see this, take the family of subtrees being the set of vertices and the set of edges of $T$.
To see that the vertices of $T$ correspond to the maximal cliques... | https://cstheory.stackexchange.com |
321,230 | [
"https://physics.stackexchange.com/questions/321230",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/68493/"
] | Consider the Lie algebra of $SU(2)$.
To find the infinitesimal generators we linearise about the identity $$U=I+i\alpha T$$ where $\alpha$ is some small parameter. To find the form of $T$ use the condition $\textrm{det}(U)=1$ to find $\textrm{Tr}(T)=0$ and also $U^{\dagger}U=I$ to give $T=T^{\dagger}$ Hermitian.
But ... | The factor of $i$ is generally a matter of convention. Essentially, it boils down to choosing what constant you'd like sitting in front of the defining equation,
$$[T^a,T^b] = f_{abc} T^c$$
of the structure constants $f_{abc}$ of the Lie group. We could have instead a factor of $i$ or any constant in our definition ... | Strictly speaking, the first convention is almost an abuse of notation, for there is no Hermitian matrix Lie algebra, at least with the usual matrix commutator as the Lie bracket. To understand this, do the:
<strong>Exercise</strong> <em>Prove that the Lie bracket of two Hermitian matrices</em> $X,\,Y$ <em>is</em> <st... | https://physics.stackexchange.com |
261,548 | [
"https://security.stackexchange.com/questions/261548",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/275693/"
] | In known wordlists like crackstation.lst there are random emails in the list. Why are they there?
| There are a few reasons (and often all three are in play):
<strong>Larger <em>wordlists</em> are often dirty.</strong> Unless the list is specifically filtered for likely noise / "junk" - such as the Crackstation "human" variant - then a variety of other plaintexts often find their way into lists, s... | Presumably it's just people using their email address as their password..
| https://security.stackexchange.com |
89,376 | [
"https://stats.stackexchange.com/questions/89376",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/17661/"
] | I am currently a PhD student in Biostatistics (finishing my 2nd year). My original goal when entering graduate school was to go into academia. Recently I have been debating this choice and wondering if perhaps industry will be a better fit.
I come from a strong programming background. I love using R because it is a l... | you have to figure what is that you're interested in:
<ol>
<li>programming statistics in R </li>
<li>programming statistics</li>
<li>statistics</li>
<li>programming</li>
</ol>
If your answer is 2-4, then it shouldn't matter which language you use. if you already know R and don't want to learn SAS, then get certified... | SAS is extremely expensive as an enterprise wide solution. It is used by some large organisations specially in banking and insurance. Many companies today are taking a different approach, looking for less expensive and scalable solutions. Open source is getting a lot of traction even in large organisations.
I would sta... | https://stats.stackexchange.com |
3,001 | [
"https://stats.stackexchange.com/questions/3001",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/1395/"
] | So let's say you have a distribution where X is the 16% quantile. Then you take the log of all the values of the distribution. Would log(X) still be the 16% quantile in the log distribution?
| Yes. Quantiles can be transformed under any monotonically increasing transformation.
To see this, suppose $Y$ is the random variable and $q_{0.16}$ is the 16% quantile. Then
$$
\text{Pr}(Y\le q_{0.16}) = \text{Pr}(\log(Y)\le\log(q_{0.16})) = 0.16.
$$
Generally, if $f$ is monotonic and increasing then
$$
\text{Pr}(Y\l... | Yes.
When you say that "X is the 16% quantile", what it means is that 16% of the sample have a lower value than X. The log of any number smaller than X is smaller than log(X) and the log of any number greater than X is greater than log(X), so the ordering is not changed.
| https://stats.stackexchange.com |
1,034,191 | [
"https://math.stackexchange.com/questions/1034191",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/194515/"
] | Do you know of a proof of $[a,b](a,b)=ab$ in $\mathbb Z$ that doesn't use prime factorization?
To be more precise let's strip all unnecessary properties and leave only the bare bones of divisibility: on a commutative monoid $M$ with the cancellation law and for which the g.c.d and l.c.m of two elements exists, does $[... | Use
$$\begin{align} (1-t)\sum_{k=0}^\infty{d+k-1\choose d-1}t^k&=\sum_{k=0}^\infty\left({d+k-1\choose d-1}-{d+k-2\choose d-1}\right)t^k\\&=\sum_{k=0}^\infty{d+k-2\choose d-2}t^k\end{align}$$
and
$$ \sum_{k=0}^\infty{k\choose 0}t^k=\sum_{k=0}^\infty t^k=\frac1{1-t}$$
| The number of ways you can color k identical objects with d colors is given by
$$\binom{d+k-1}{d-1}$$
To see this consider representing colorings as a string of the form oo|o|ooo|o|o|... where the "o" are the objects and the "|" are the separations between regions where the "o" get different colors. The number of dif... | https://math.stackexchange.com |
460,963 | [
"https://stats.stackexchange.com/questions/460963",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/247628/"
] | I was wondering if anyone could help explain to me why someone would use a two tailed hypothesis test? Let's say I am doing a t-test, presumably I know which mean was greater than the other and I am testing if that difference is statistically significant (i.e. a one tailed test). Given the formula for computing the t-s... | Actually, in the context of the test of mean differences, it tends to be the other way around --- it is almost never appropriate to use a <em>one-sided</em> test. The reason for this is that we need to specify our objects of inference (e.g., hypothesis tests, confidence intervals, etc.) prior to seeing the data, or we... | A one-tailed test is appropriate if you only want to test if there is a difference between your groups in a specific direction. You would use a two-tailed test if you want to determine if there is <em>any</em> difference between the two groups you're comparing.
As user <em>Mur1lo</em> says in their comment - you shou... | https://stats.stackexchange.com |
9,642 | [
"https://earthscience.stackexchange.com/questions/9642",
"https://earthscience.stackexchange.com",
"https://earthscience.stackexchange.com/users/7483/"
] | Ever since the 3rd grade, I've been troubled by the inability to remember if Latitude runs East/West or runs North/South. I would always stress out <strong>BIG TIME</strong> during my Geography class.
I'm <strong>much</strong> older now, and I still have trouble telling them apart...
"facepalm"
Are there any good t... | I also mixed <strong>Longitude</strong> and <strong>Latitude</strong> until I heard someone saying '<em>... at high latitudes.</em>' in a conference talk.
In my mind, the picture of the Earth shows the Earth with the North and South poles at the top and bottom (or reversed, doesn't matter). <em>High</em> describes a v... | The way I remember is pretty simple. When I think of <strong>LAT</strong>itude I stick my arms out <strong>LAT</strong>erally (metaphorically or literally). When I think of <strong>LON</strong>gitude I imagine stretching out a <strong>LON</strong>g ribbon or something vertically. Also, the "on" sound in longitude stret... | https://earthscience.stackexchange.com |
6,140 | [
"https://math.stackexchange.com/questions/6140",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/2333/"
] | Allow me to preface this by saying this is not a homework problem. If I had had this thought four years ago when I was taking calculus, I probably could do it...
I'm trying to calculate the limit as $n \to \infty$ of $1-\left(\frac{n-1}{n}\right)^n$ -
- it's a constant I'm inclined to call "natural chance of success"... | You are essentially trying to find the limit of $\left(1-\frac{1}{n}\right)^n$ as $n\to\infty$. Rewrite this as $e^{n\ln(1 - \frac{1}{n})}$. Since the exponential function is continuous, you have
$$\lim_{n\to\infty} e^{n\ln(1-\frac{1}{n})} = e^{\lim_{n\to\infty}(n\ln(1-\frac{1}{n})}.$$
To compute that limit, rewrite a... | If you know one of the definitions for the number $e$:
$$
e=\lim_{n\to\pm\infty}\Big(1+\frac{1}{n}\Big)^n,
$$
then you could calculate your limit in the following way:
$$
\lim_{n\to\infty}\Big(1-\frac{1}{n}\Big)^n =
\lim_{n\to\infty}\left[\Big(1+\frac{1}{-n}\Big)^{-n}\right]^{-1} =
\frac{1}{e}.
$$
| https://math.stackexchange.com |
331,915 | [
"https://softwareengineering.stackexchange.com/questions/331915",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/24987/"
] | I'm really struggling to come up with a design pattern for an Alerter I'm building. Here's a contrived example of what I'm trying to do:
A person wants to get an alert by weather type (rain, snow, sun, etc.). A person also has a choice of alert method (email, sms, slack channel, hipchat room, etc.)
I need to: have a ... | <pre><code>var people = PersonRepository.GetPeople(_weatherType);
</code></pre>
The first thing to note is that you are using a service locator here, which is widely recognised as an anti-pattern. So you could improve that by injecting an instance of <code>IPersonRepository</code> into the <code>Alerter</code> constru... | Since every user has its own prefered alert method (probably coming from some user settings), this information belongs to the user (= should be part of the user's internal state, as an attribute). <code>User</code> objects must be <strong>responsible</strong> for deciding how to send the alerts and it must be <strong>o... | https://softwareengineering.stackexchange.com |
177,589 | [
"https://electronics.stackexchange.com/questions/177589",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/16307/"
] | <img src="https://i.stack.imgur.com/ASmKN.gif" alt="enter image description here">
As seen in the figure above, a current regulator is providing a constant current looping through the series resistor Rshunt. Input impedance of data acquisition device is 10 GigaOhm. Can we say that almost no current passes through the ... | An equivalent circuit could be this one
<img src="https://i.stack.imgur.com/2ZdiY.png" alt="enter image description here">
<blockquote>
Can we say that almost no current passes through the probe resistance
Rcable(since input impedance is huge) and therefore there is no
voltage drop across the probe cables?
</bl... | @Lelesquiz has given you an answer that is applicable to low frequency changes in the signal, however to answer the question about current you really need to know the bias current of the amplifier, which (when modeled) appears as a constant current source at the ideal amplifier input.
The bias current can be much lar... | https://electronics.stackexchange.com |
3,717,275 | [
"https://math.stackexchange.com/questions/3717275",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/433136/"
] | Let <span class="math-container">$X$</span> is be a vector space over a field <span class="math-container">$\mathbf F$</span>, and <span class="math-container">$\{e_1, \dots ,e_k\}$</span> a basis for <span class="math-container">$X$</span>.
For <span class="math-container">$x,y \in X $</span> such that
<span class="ma... | I don't think the equality generally holds, specially by differentiating both sides we must have <span class="math-container">$$\sum_{i=1}^{\infty} {1\over (i+x)\cdot i}={1\over x}$$</span>which for <span class="math-container">$x\in\Bbb N-\{1\}$</span> means that <span class="math-container">$$\sum_{i=1}^{x}{1\over i}... | The correct result should be
<span class="math-container">$$ \prod_{i=1}^\infty \left( \frac{i+x}{i+1} \right)^{1/i} = \exp \left(\int_1^x \frac{\Psi(t+1)+\gamma}{t} \; dt\right) $$</span>
See my comment to Mostafa Ayaz's answer.
I don't know if this can be written in a more "closed-form" way than this, but i... | https://math.stackexchange.com |
106,191 | [
"https://datascience.stackexchange.com/questions/106191",
"https://datascience.stackexchange.com",
"https://datascience.stackexchange.com/users/128662/"
] | Hopefully a simple question, but it's a little unclear to me on how best to separate train/validate/test sets.
I have say 100 examples of class A. I'm classifying text into either class A, which I care about, or class B, which could be any text in the world (negative class). I have, obviously, far more examples of cl... | In the comments you wrote:
<blockquote>
I can't exclude it because it is related on an other feature
</blockquote>
If you mean <em>related</em> as in a function of two other features, you could add columns to explicitly show those relations, then delete the original column. E.g. add a column called <code>petal.width.pl... | As far as I know there would be only two ways to use a particular feature "less" than its normal use by the decision tree:
<ul>
<li>Remove the feature completely.</li>
<li>Modify the data so that the feature becomes less important compared to the others (don't do it, this is complex and pointless)</li>
</ul>
... | https://datascience.stackexchange.com |
364,351 | [
"https://stats.stackexchange.com/questions/364351",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/217378/"
] | I was wondering what is the difference between regression kNN model and classification kNN model. I tried Googling and no success. In presentation from lectures we only have graphs of errors of mentioned models and no description as to what these models are.
| I figured out that the difference is:
<ul>
<li><strong>regression</strong> model: codomain of model is a <strong>continuous</strong> space, e.g. $\mathbb{R}$</li>
<li><strong>classification</strong> model: codomain of model is a <strong>discrete</strong> space, e.g. $\{0,1\}$.</li>
</ul>
| The key differences are:
<ul>
<li><em>KNN regression</em> tries to predict the <strong>value</strong> of the output variable
by using a local average. </li>
<li><em>KNN classification</em> attempts to predict the <strong>class</strong> to which the output variable belong by computing the local probability.</li>
</ul>... | https://stats.stackexchange.com |
161,704 | [
"https://softwareengineering.stackexchange.com/questions/161704",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/8898/"
] | We have big enterprise projects they normally involve copying data from a source database to a destination database and then setting up a number of additional applications that sync this data etc.
The last project contained 250,000 items (rows of data). The next project will only contain 4,000 items. Project managers ... | Tell them it's like building a new four lane highway to a remote part of the country. Whether that road gets used by 100 cars a day or 1000 cars a day, the effort to create the road will be about the same.
Granted, if it's going to support 1,000,000 cars a day you'll have to make the road a little more robust, but re... | Give them a calculator and ask them to add 1238783423 to 9858238483, time how long it takes. then ask them to add 3423 to 8483 and tell them you expect the answer approximately 100000 time quicker.
You might also explain the amount of data (probably) effects the length of time the software will take to <em>run</em> no... | https://softwareengineering.stackexchange.com |
347,666 | [
"https://electronics.stackexchange.com/questions/347666",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/169864/"
] | My confusion stems from a an led that shows: Input(DC): 600mA-700mA / 3V-3.4V.
the product suggests a constant current led driver (same brand as LED) that shows: Output: Current 600mA (Constant) ; Voltage 18-34V
In researching I have read that excessive current will burn out the LED and over time as the battery drain... | The driver is inappropriate for the LED because the minimum voltage from the driver (18V) is greater than the minimum LED voltage at 600mA (3V). The driver is likely designed for LED arrays that have at least 6 dice in series, so 18V.
When you feed the particular LED die you mention with a constant current between 60... | An LED is a very simple device. It behaves according to:
$$I_{LED}=I_{SAT}\cdot\left(e^\frac{V_{LED}}{n \cdot V_T}-1\right)$$
Or, alternately,
$$V_{LED}=n\cdot V_T\cdot \operatorname{ln}\left(\frac{I_{LED}}{I_{SAT}}+1\right)$$
In the above examples, \$n\$ is the emission coefficient (some number that is 1 or larger... | https://electronics.stackexchange.com |
80,623 | [
"https://dsp.stackexchange.com/questions/80623",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/34744/"
] | Ever since I found out that coding gain allows you to receive a signal that is well below the noise floor I have been fascinated with the idea of covert radio signals (low probability of detection). You could imagine a clandestine scenario with spies or political dissidents where not only the content of the radio messa... | Just spreading the spectrum either with Direct Sequence Spread Spectrum (DSSS) or Frequency Hopping Spread Spectrum (FHSS) is not enough to ensure undetectability with over the air communications. We can always simply point a high gain antenna at the transmitter (or move closer to it) to the point where the signal powe... | I guess it depends on the channel. If you can occupy a large relative bandwidth and use really long spread sequences without fear of fading or doppler making the signal unreadable, then you can go very deep into the noise floor. Using the right key it is then trivial to dig the signal out of the noise floor. Most pract... | https://dsp.stackexchange.com |
367,697 | [
"https://electronics.stackexchange.com/questions/367697",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/185294/"
] | Good day guys. This is my first time posting, hope you can help me a bit with this.
My Sony Vaio laptop from 2009 has two damaged AO4433 MOSFETS near the power supply connector. I want to replace them, but I can't find this exact model in my city. I have an old laptop motherboard (for spare parts) that has some FDS667... | The FDS6679 has 1/2 the RdsOn at the same Vgs (-10) so it will run cooler yet have more gate capacitance, which may slow down the gate driver and increase VI SOA dissipation.
Not much to lose in trying, but try a low current limited lab supply source to bypass the FETs to investigate root cause.
Gate charge * RdsOn =... | They don't look all that similar to me, the proposed replacement has more than 2.5x the gate charge. Look for something with similar gate charge as well as voltage, current, Vgs(th) and Rds(on) ratings.
Those parts are obsolete but you may still be able to scare some up. Beware of dubious sources though (Ali, eBay et... | https://electronics.stackexchange.com |
627,336 | [
"https://physics.stackexchange.com/questions/627336",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/226310/"
] | I pose the following situation:
A paramagnetic solid, with dipoles that can only be parallel or antiparallel to a magnetic field, is at a small temperature (so most dipoles are parallel to the field). If the direction of the field is suddenly reversed, at the instant of inversion the dipoles would find themselves in a ... | If the field is aligned with the material, there is some potential energy <span class="math-container">$-U$</span>. When the field is reversed, before the spins have flipped back, the energy has become <span class="math-container">$+U$</span>. So whoever is flipping the field back and forth must do work in order to exe... | This is because negative "magnetic orientation temperatures" properly reflect the change in number of available magnetic states with energy increase, but only of the magnetic states. The entropy of the system as a whole remains on the increase as does the thermal temperature.
Your comment on "indefinite... | https://physics.stackexchange.com |
110,651 | [
"https://datascience.stackexchange.com/questions/110651",
"https://datascience.stackexchange.com",
"https://datascience.stackexchange.com/users/125747/"
] | If MLE (Maximum Likelihood Estimation) cannot give a proper closed-form solution for the parameters in Logistic Regression, why is this method discussed so much? Why not just stick to Gradient Descent for estimating parameters?
| Maximum likelihood is a method for estimating parameters.
Gradient descent is a numerical technique to help us solve equations that we might not be able to solve by traditional means (e.g., we can't get a closed-form solution when we take the derivative and set it equal to zero).
<strong>The two can coexist.</strong>
I... | I think you are comparing apples and oranges here. Maximum likelihood is a the maximum value of your likelihood function, which somehow describes your data generation process. Specifically likelihood gives you the probability of observing your data, given the data-generation model you imagine. It is similar to a loss m... | https://datascience.stackexchange.com |
143,625 | [
"https://electronics.stackexchange.com/questions/143625",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/61284/"
] | I still have a good old landline at home. But I miss the easiness of cell phones where you can just see a list of missed calls. I'm a MSP430 Launchpad hobbyist and I'm alway looking for some little projects. I wonder if there is a way to tap my own landline and listen for calls. This should be passive listening, so no ... | In the U.S., an incoming call would start with ringing, which is an AC signal of around 60V, then proceed to a modulated Caller ID signal after the first ring. It could be similar in Belgium.
So it would take some dedicated circuitry to handle and detect the 60V ringing and then decode the Caller ID. It is messy in th... | Well ring voltage is a pretty high ac voltage so you could run one conductor through a current transformer and measure with the msp430. Take a look for msp430 smart meter reference designs to get an idea of what it would take to do it.
Or look up the silabs proslic, they have a global reference design for interfacin... | https://electronics.stackexchange.com |
94,210 | [
"https://physics.stackexchange.com/questions/94210",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/37596/"
] | My Question goes like this:
If a mosquito inside the bus wants to move from back to front, will there be any difference if the bus is stationary or moving (ie extra effort in the latter case?)? Consider it as a closed bus & mosquito at a fixed point in bus, ie the air column will be constant throughout the process,... | Small insects and animals have to deal with the viscosity of the air. The motion of the train takes the air with it, the air does not accumulate at the back neither during acceleration or steady velocity. The effect will be small and only during acceleration. The air has the steady velocity of the vehicle and anything... | Using Galileo's Ship as an example:
"Shut yourself up with some friend in the main cabin below decks on some large ship, and have with you there some flies, butterflies, and other small flying animals. Have a large bowl of water with some fish in it; hang up a bottle that empties drop by drop into a wide vessel beneat... | https://physics.stackexchange.com |
20,703 | [
"https://ai.stackexchange.com/questions/20703",
"https://ai.stackexchange.com",
"https://ai.stackexchange.com/users/35896/"
] | People sometimes use 1st layer, 2nd layer to refer to a specific layer in a neural net. Is the layer immediately follows the input layer called 1st layer?
How about the lowest layer and highest layer?
| <blockquote>
People sometimes use 1st layer, 2nd layer to refer to a specific layer in a neural net. Is the layer immediately follows the input layer called 1st layer?
</blockquote>
The 1st layer should typically refer to the layer that comes after the input layer. Similarly, the 2nd layer should refer to the layer ... | Lowest layer generally refers to the layer closest to the input. This comes from the idea that layers closer to the input represent low-level features such as gradients and edges, while layers closer to the output represent high-level features such as parts and objects.
| https://ai.stackexchange.com |
473,693 | [
"https://physics.stackexchange.com/questions/473693",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/228374/"
] | If there is a spherical Gaussian surface and there are 2 point charges inside it and 3 point charges outside it (all of say (+1)coulomb) and we consider a point x "<strong>on</strong>" the Gaussian surface,
Does the electric field <em>intensity</em> depend on all of the charges or does it depend only on the charges ins... | The net electric field intensity <span class="math-container">$\vec E_{\rm net}(\vec r)$</span> at a position <span class="math-container">$\vec r$</span> is the vector sum of the electric field intensities produced at that point by each individual charge, <span class="math-container">$\vec E_{\rm net}(\vec r)= \vec E_... | Field intensity depends upon all charges in the surroundings and the presence of conductors too affects field intensity. However, flux at a "point" isn't quite meaningful I guess.
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