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
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|---|---|---|---|---|---|
343,290 | [
"https://electronics.stackexchange.com/questions/343290",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/170734/"
] | If we dont know the channel coefficients but assume that we are sending a bunch of training symbols how does the receiver estimate the channel coefficients and how often should we estimate these channel coefficients?
| The RAKE is essentially another form of diversity
combining, since the spreading code induces a path diversity on the transmitted signal so that
independent multipath components separated by more than a chip time can be resolved.
In order to study the behavior of RAKE receivers, assume a channel model with impulse
resp... | Simplifying somewhat (a lot, really) think of the training symbols as if we were sending a single pulse of a square wave. At the receiver, we receive a version of that that's been affected by multipath, so instead of a single pulse of the square wave, we receive several different versions of it, delayed by different am... | https://electronics.stackexchange.com |
461,593 | [
"https://math.stackexchange.com/questions/461593",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/60930/"
] | Is there a general family of curves $f(x,c)$ that satisfies the following conditions?
<ol>
<li>$f(x,c)$ is strictly increasing for $x \ge 0$</li>
<li>$f(0,c) = 0$</li>
<li>$f(1,c) = 1$</li>
<li>$f(x,c) \to \infty$ as $x \to \infty$</li>
<li>For every positive constant $0 < c < 1$,
$$
\int_{0}^{\infty} c^{f(x,c)}... | The naming and scaling of the parameter $c$ is irrelevant. We just want a family of strictly increasing functions $(f_q)_{q>0}$ such that for each $q$ we have
$$f_q(0)=0,\quad f_q(1)=1,\quad \lim_{x\to \infty}f_q(x)=\infty\ ,\tag{1}$$
and such that for a certain number $c=c(q)\in\ ]0,1[\ $ depending smoothly and inv... | Correct me if I am being stupid here, but I don't see that $x^a$ actually works. Let $a=1$ and then note that $$\int_0^\infty c^{x}dx = \frac{-1}{\ln(c)}$$ which is not always $1$. As for your question, the family is very large and one way to see this is by using the transformation $$f(x,c) = \log_c(g_c(x))$$ which int... | https://math.stackexchange.com |
54,770 | [
"https://softwareengineering.stackexchange.com/questions/54770",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/19258/"
] | I usually leave my email address as a courtesy in case someone wants to ask me a question about it later. Do other people leave more or less information than that? Does anyone leave a phone number??
| I almost never leave my name nor e-mail address :
<ul>
<li>It tends to get copy-pasted <em>(yeah, bad practice)</em> ; and I end up with people contacting me for code I didn't write</li>
<li>When the code is modified, the contact info is not removed nor update ; and I end up with people contacting me about code that h... | I use to be in the habit of leaving my name or initials in comment headers, with a revision number and a brief description of the change.
I've recently gotten out of that habit given the fact the this is redundant with version control, e.g. any one interested in who made what changes can see the entire history of the... | https://softwareengineering.stackexchange.com |
418,781 | [
"https://physics.stackexchange.com/questions/418781",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/195955/"
] | <blockquote>
If white light (sunlight) is passed through a spectrometer can we observe all 7 colors from it?
</blockquote>
I know that spectrometer is having a prism in it. And the prism has the capability to refract white to rainbow colors. But I have a dought if you observe any light ray from the equipment, you ca... | Even if you looked directly at the refracted white light coming out of a prism, you would not necessarily see all seven colors of rainbow.
If the source of (close to) white light is the sun or a white light bulb, the spectrum of the light is continuous and includes all seven colors of rainbow and everything in between... | A spectrometer is a measuring apparatus, so light goes to a detector, you can't see it.
I guess you're rather looking for a <strong>Monochromator</strong>. Spectrometers usually use a monocrhomator.
However, the prism has been long time superceeded by other separating techniques, such as difraction gratings, which wo... | https://physics.stackexchange.com |
64,292 | [
"https://chemistry.stackexchange.com/questions/64292",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/7757/"
] | My lecture notes state that
<blockquote>
Condensation reactions, like all biosynthetic reactions, are endergonic.
</blockquote>
I am unsure as to why this would be the case. I thought bond formation was an exothermic reaction, so you would get a negative enthalpy change from the bond being formed. I appreciate that... | One of the most simple biosynthetic reactions that generates ‘oligomers’ from ‘monomers’ (between inverted commas because that description is not fully correct here) is the ester formation used to synthesise lipids. It can be broken down to:
$$\ce{R-O-H + H'-O'-C(=O)-R' -> R-O-C(=O)-R' + H'-O'-H}$$
With each impor... | That all condensation reactions are endergonic is certainly not true. And as can be seen by the Helmholtz equation $\Delta G = \Delta H - T\cdot \Delta S$, this also depends on the employed temperature. One example is cupper(II)sulfate penta hydrate that spontaneously releases water upon heating, so there you have an e... | https://chemistry.stackexchange.com |
39,973 | [
"https://electronics.stackexchange.com/questions/39973",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/12197/"
] | I want to control a 2 digit 7-segment LED with a MSP430 micro controller. The display has 8 input pins per digit (8th pin is the dot, which I do not need) and two ground pins (common cathode). The idea is to connect the first 7 pins from the µc to the 7 segments of both digits and then use another pin (the control pin)... | You are right about the NPN transistor, that is what you need in order to achieve that behaviour, however, since the µC would have to control the cathode of one of the displays, that would be a problem since most µC can only source / sink a few mA. Assuming each segment needs 10mA that would require the pin to sink 70 ... | The first answer is a reasonable starting idea. There are some things to keep in mind while implementing this.
Where the seven anodes of each LED module connect over to the MCU port pins it will be needed to insert series resistors in each line to limit the current to a safe value for the individual segments. The res... | https://electronics.stackexchange.com |
583,817 | [
"https://math.stackexchange.com/questions/583817",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/93671/"
] | I wonder if anyone can provide me with a simple step-by-step proof in hyperbolic geometry of a fact that does not hold in Euclidean geometry.
I imagine an answer to be a series of statements, such that later statements follow from earlier ones. It is not strictly necessary to get back to axioms, so it is possible to u... | Here's a sample theorem, then, which astonished me when I first realized it. I'll do the hyperbolic argument and leave the spherical case to you.
<blockquote>
THEOREM: Given two triangles $\triangle ABC$ and $\triangle A'B'C'$ in the hyperbolic plane. If $\angle A = \angle A'$, $\angle B = \angle B'$, and $\angle C ... | Regular hyperbolic tilings exist in H2, H3, and H4, and with points on the horizon as far as H9. There are an infinite number of archimedean tilings, but even more quasi-regular tilings.
A very famous tiling is the 'Not Knot' poster, which shows a very detailed projection of the right-angled dodecahedron, tiling H3 s... | https://math.stackexchange.com |
100,440 | [
"https://electronics.stackexchange.com/questions/100440",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/25255/"
] | I have two transformers (220v to 110v) which has a nominal power of 300VA. I want more than that for a specific application. Can I use both together to supply more current like this (?):
<img src="https://i.stack.imgur.com/qklCS.gif" alt="enter image description here">
Any chance of going wrong or anything that I sho... | That won't hurt anything (until you put a load on there) but it also won't work so well. As you can see, the same current is going through both coils. The lower voltage on the primaries and secondaries means that the core is going to be less utilized, so they might be a bit more efficient, but basically you'll be stuck... | Who is to say the two transformers will be exactly identical? The primary inductanc eon one will not necessarily be the same as the other. For instance, with no-load on the secondary, the primary takes a small current because basically it acts like a big inductor across the AC voltage. It might be 10 henries and at 50H... | https://electronics.stackexchange.com |
152,520 | [
"https://math.stackexchange.com/questions/152520",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/16886/"
] | I am struggling to understand the behavior of the Fourier transform (in the <span class="math-container">$x$</span> variable) of initially smooth solutions of the hyperbolic Burgers' equation in 1-D,
<span class="math-container">$ \partial_t u + u~ \partial_x u =0$</span> .
I start with a smooth and rapidly decaying... | Hint:
<ul>
<li>$\sin^{2}{x} \cdot \cos^{3}(x) = \sin^{2}{x} \cdot \bigl(1-\sin^{2}(x)\bigr) \cdot \cos{x}$</li>
<li>Now put $t = \sin(x)$. The integral you have has the form $t^{2} \cdot (1-t^{2}) = t^{2}-t^{4}$.</li>
</ul>
| Noting that: $\int \sin^2{x}\cos^3{x}dx= \int\sin^2{x}\cos{x}dx-\int\sin^4{x}\cos{x}dx$ by the substitution $\cos^2{x}=1-\sin^2{x}$.
Then, make the substitution $u=\sin{x} \implies du=\cos{x}dx$ and the integral should be easy to calculate from there :)
(i.e. you should get $\int u^2 du - \int u^4 du$)
| https://math.stackexchange.com |
775,294 | [
"https://math.stackexchange.com/questions/775294",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/139697/"
] | <blockquote>
Define:$T_a:G\to G,T_a(x)=ax$,$L_a:G\to G,L_a(x)=xa^{-1}$. Show that if $V\in A(G)$ is such tath $T_aV=VT_a$ for all $a\in G$, then $V=L_a$ for some $b\in G$. (Hint: Acting on $e\in G$, find out what $b$ should be.) $A(G)$: the symmetrict group for $G$
</blockquote>
I tried this:
$\forall x\in G, T_eV(x... | First apply AM-GM inequality: $(a+b+c)^3 \geq 27abc$, then you need to prove: $abc \geq (a+b-c)(b+c-a)(c+a-b)$, and this follows from:
$a^2 \geq a^2 - (b-c)^2$
$b^2 \geq b^2 - (c-a)^2$
$c^2 \geq c^2 - (a-b)^2$.
by multiply all three inequalities and taking square root.
| Using $s=\frac{a+b+c}2$, this transforms to:
$$s^3\geqslant27(s-a)(s-b)(s-c)$$
Which is true by AM GM,
$$[(s-a)(s-b)(s-c)]^{1/3}\leqslant\frac{3s-a-b-c}{3}=\frac s 3$$
| https://math.stackexchange.com |
23,811 | [
"https://cs.stackexchange.com/questions/23811",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/4911/"
] | In section 9.2 of CLRS (<em>Introduction to Algorithms; page 185 in the 2nd edition and page 215 in the 3rd edition</em>), a randomized selection algorithm is presented.
For its analysis, $T(n)$ is a random variable denoting the time required on an input array $A[p \cdots r]$ of $n$ elements and $X_k$ is an indicator... | The two random variables <span class="math-container">$X_k$</span> and <span class="math-container">$T(\max(k-1, n-k))$</span> are independent because in each recursive call to RANDOMIZED-SELECT() we invoke RANDOMIZED-PARTITION(), a pivot is randomly selected, and the choice of the pivot in one recursive call is <em>in... | Apparently it seems that "<span class="math-container">$X_k$</span> and <span class="math-container">$T(\max(k-1,n-k)$</span> are independent" is counter-intuitive, as at glimpse it seems that the value of <span class="math-container">$X_k$</span> depends on <span class="math-container">$k$</span> and so does... | https://cs.stackexchange.com |
36,689 | [
"https://electronics.stackexchange.com/questions/36689",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/10412/"
] | Recently my old amplifier in car has got a defective contact on one of the switches, so I decided to unsolder the old one and solder a new one. Unfortunately the amplifier caused a short as I connected it to the battery again (I don't know how this could happen, maybe I damaged some component or something, or maybe the... | At this low frequency it doesn't really matter whether they are routed as a transmission line on the PCB or not. The more important issue is capacitive coupling from other traces that could inject noise. You are only looking for a little over 10 bit accuracy, so nothing out of the ordinary needs to be done.
Some low... | Double sided PTH PCB having proper ground layer below the input tracks and having ground shield tracks- guard tracks & small caps at the input side will be helpful for proper operation.
| https://electronics.stackexchange.com |
142,789 | [
"https://physics.stackexchange.com/questions/142789",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/59523/"
] | I was going through one of the examples in Griffith's Quantum book and there was a few things in Example 3.3 that I didn't understand that I was hoping to get some clarification on.
For instance, we first find that the eigenfunctions of the position operator x, have to be
Starting from the eigenvalue equation
$xg_{... | The $\delta$ function has the following property:
$$
\int \text{d}x\; f(x)\delta(a-x)=f(a)
$$
This actually answers both of your questions. First, the non-square-integrability:
$$
\int \text{d}x\;\delta(x-y)\delta(x-y)=\delta(y-y)=\delta(0)=\infty
$$
according to the rule above if you choose one of the $\delta$'s to be... | <blockquote>
The integral without delta square would converge to 1, but squaring
the function somehow breaks it?
</blockquote>
Yes. Recall the sifting property:
$$\int_{-\infty}^{\infty}f(x)\delta(x - a)dx = \int_{-\infty}^{\infty}f(a)\delta(x - a)dx = f(a)$$
Then, it follows formally that
$$\int_{-\infty}^{\i... | https://physics.stackexchange.com |
167,632 | [
"https://chemistry.stackexchange.com/questions/167632",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/126999/"
] | Are all the individual 133,845 molecules of QM9 drug-like molecules?
Can other drug-like molecules be made from the these 133,845 molecules by some combination or permutation which are not part of QM9?
| <blockquote>
For points 1 and 3, if they're both agreed to be true then <span class="math-container">$\Delta S_{\text{total}} = 0=R\ln K \implies K = 1$</span>, no matter the reaction.
</blockquote>
The entropy change of a reaction is concentration-dependent:
<span class="math-container">$$\Delta S = \Delta S^\circ - R... | (1) The entropy reaches a maximum at equilibrium, thus any change will depart from equilibrium, but this cannot happen if we are at equilibrium unless some other parameter changes such a temperature or pressure thus any change in entropy is zero.
If the reaction is <span class="math-container">$A+B\rightleftharpoons C$... | https://chemistry.stackexchange.com |
481,090 | [
"https://stats.stackexchange.com/questions/481090",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/99099/"
] | What can you say about your linear regression if the residuals are uniformly distibuted (and not normal)? I would like to consider the case I have a histogram showing residuals which are uniformly distributed between -1 and 1.
We still have errors that are symmetrically distributed around 0, so I would have thought tha... | There are a few things we can say about this situation
<ul>
<li>the condition of normality of residuals only needs to hold <em>approximately</em>. If the sample size is small then it can be difficult to distiguish a uniform from a normal distribution, and it is reasonable in such circumstances to assess the residuals a... | A classic linear regression model works under the assumption that the data can be modeled as
<pre><code>y = Ax + b + eta
</code></pre>
where <code>eta ~ N(0,sigma)</code> .
if your residuals are uniformly distributed, it means that the above assumptions doesn't hold.
However, this linear regression can still work for y... | https://stats.stackexchange.com |
525,059 | [
"https://physics.stackexchange.com/questions/525059",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/249204/"
] | When light travels in a perpendicular path from one medium to another medium of different optical density, is Snell’s law valid?
<span class="math-container">$\sin i$</span> and <span class="math-container">$\sin r$</span> are both 0, right?
So it isn’t valid.
Is this correct?
| In this case where the incident angle is <span class="math-container">$0^\circ$</span> to the interface and thus from <span class="math-container">$$ n_{1}\sin{\theta_1}=n_2\sin{\theta_2}$$</span> we get that <span class="math-container">$\theta_1 = \theta_2$</span> I'd simply instead reason and say that Snell's law is... | Let me first give an example from Newton's laws. If there is no net force acting on an object, then it will not be accelerating. Therefore, the equation of Newton's second law <span class="math-container">$F=ma$</span> is a valid equation, as we have <span class="math-container">$0=m\cdot 0=0$</span>. But what if we we... | https://physics.stackexchange.com |
81,753 | [
"https://mathoverflow.net/questions/81753",
"https://mathoverflow.net",
"https://mathoverflow.net/users/2097/"
] | <strong>Edit:</strong> Even though there is an accepted answer, the problem isn't solved. I only accepted the answer, because there was a bounty on the question so I had to accept an incomplete answer.
I was working on a problem in discrete matematics, and reduced it to a more analytical problem. I was hoping that we... | Just writing down for the record why the best answer can't beat $2/3$.
Look at the plane $z=0$. From $f(0,1,0,0) \leq 1$ and $f(1/2, 0, 1/2, 0) \leq 1/2$, we see that $f(1/3,1/3,1/3,0) \leq 2/3$. Similar arguments show that all cyclic permutations of $(1/3,1/3,1/3,0)$ also have $f \leq 2/3$.
Look at the plane $y=z$.... | This answer is to record a sequence of upper bounds which I have been building. I am coming to believe that the correct answer is $2/3$, but I don't have a construction which achieves it.
Looking at the line segment from $(1,0,0,0)$ to $(0,1/2,0,1/2)$, at a point of the form $(u,v,0,v)$ with $u+2v=1$, the function $f... | https://mathoverflow.net |
214,811 | [
"https://physics.stackexchange.com/questions/214811",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/75324/"
] | To implement real quantum cryptography in the real world, does the physical link layer from Point A to Point B be an optical link for all parts? Is there any links or whitepaper containing prototypes of technical implementations over varying lengths and distances and types of networks?
Can QC be implemented over a WAN... | In order to implement quantum cryptography, you need a link which allows to send <em>quantum</em> states, i.e., some kind of object/particle which carries a quantum degree of freedom. These particles should travel as freely as possible along their way. This is most easily accomplished using a single photon, thus the op... | Any quantum channel will work, even if it involves temporarily holding the qubits or routing them through some convoluted path. As long as the qubits stay coherent through the trip (i.e. aren't measured or perturbed by errors), quantum encryption should work fine.
As an example of how flexible this could be, imagine a... | https://physics.stackexchange.com |
228,758 | [
"https://softwareengineering.stackexchange.com/questions/228758",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/43587/"
] | We are using some utility methods in our company to simplify programming.
So we have following string extension:
<pre><code>public static bool IsNoE(this string s)
{
return string.IsNullOrEmpty(s);
}
</code></pre>
This is just for convenience and the intention of this question is not to discuss the sense or sens... | The first naming is just plainly wrong. Want a proof? What does the next piece of code do?
<pre><code>if (this.ah == PcX.Def)
{
this.Z.SecN.Coll();
}
</code></pre>
The second naming is ok. It's explicit enough, but not too long. It's the one which is used by .NET Framework, so other developers won't be lost.
Thi... | I actually use <code>NullOrEmpty</code> (on strings) as well as eg. <code>JoinWith</code> (an alias for <code>String.Join</code>).
<blockquote>
The argument for the first naming is:
<ul>
<li>It would not make sense to make extensions if they are not shorter to write</li>
</ul>
</blockquote>
Extension meth... | https://softwareengineering.stackexchange.com |
115,633 | [
"https://security.stackexchange.com/questions/115633",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/90589/"
] | Someone is using a client's commerce site to check the validity of lots of credit cards.
After dropping IP addresses based on usage whoever is behind it throttled their requests down to 1 request every 20 seconds and only using the same ip for about 15 requests then switching IPs.
So for the last few months or so I... | Reporting this to local law enforcement sound like the right thing to do. Hopefully they will have access to people who are competent enough to make use of the information you can provide without you getting into trouble.
You should also contact whoever you are using for processing credit card transactions. Ideally th... | If you're in the USA, contact your local FBI office. They will likely have one or two cyber crime investigators who will likely be very interested in finding an active hacker's watering hole.
| https://security.stackexchange.com |
77,483 | [
"https://electronics.stackexchange.com/questions/77483",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/20250/"
] | The upper resistor is bootstrapped: \$i_\text{small signal} = \dfrac{v_{in} - v_{out}}{R} = 0\$. According to The Art of Electronics (p. 97) said resistor is a current source (with \$i=0\$A ?). Why is it replaced with a current source instead of an open circuit?
Another thing is the return-to-ground of the ac coupled... | Lets see what we're trying to implement here:
<ol>
<li>AC follower (A = 1 for frequencies of interest)</li>
<li>AC coupled (A = 0 for DC)</li>
<li>High input impedance</li>
</ol>
We get the desired results by the following means :
<ol>
<li>AC follower - \$V_{out}\$ and \$V_-\$ are shorted</li>
<li>AC coupled - a se... | For dc conditions the resistor is there "biasing" the V+ input to 0V and at low frequencies inputted this resistor is there representing the ac input impedance.
For normal (mid range to high frequency) ac conditions, the ac voltage on the output is virtually the same as the input and this ac voltage is very nearly the... | https://electronics.stackexchange.com |
292,775 | [
"https://physics.stackexchange.com/questions/292775",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/135806/"
] | Can terminal potential difference be greater than EMF? If so, how?
Upto my knowledge and my research, during charging it can happen but the question remains same: how it happens. What is the basic principal behind this concept? By doing this, do we violate the principle of conservation of energy?
| Yes it can, for example when a cell is being recharged the terminal pd is $V = {\mathcal E} + IR$ where $\mathcal E$ is the emf of the cell, $I$ is the current passing through the cell from positive to negative terminal and $R$ is the internal resistance of the cell.
Power is being supplied from an external source $VI... | Yes, it can be.
We know that $V=E-IR$. When the current $I$ becomes negative, the equation becomes $V=E+IR$ i.e. $E$ is less than $V$
Now we have to know when $I$ becomes negative. When another cell with higher emf (electromotive force) is connected in opposite direction with the main battery the new battery produc... | https://physics.stackexchange.com |
18,650 | [
"https://quantumcomputing.stackexchange.com/questions/18650",
"https://quantumcomputing.stackexchange.com",
"https://quantumcomputing.stackexchange.com/users/16800/"
] | I read an article that claims, QRNG can produce a true random number. So I wonder, how could they prove that this is a true random numbers generator? In fact, imagine I look at my memory state and took a bit of that and claims that I generate a true random number. If we want to prove this, we need a perfect theoretical... | There is certainly a very valid concern in your question. Yes, there are physical processes which, assuming quantum mechanics to be true, give us perfect randomness that is completely unpredictable to anyone. It's as simple as a beamsplitter that can perform a 50:50 split of photons into two different directions.
The i... | "our knowledge of quantom behavior is not that perfect" -- I would disagree.
Sometimes, the fact that quantum behavior "can't be predicted", or some of the claims in popular media ("entanglement is <em>spooky</em>!" / "<em>Mysterious</em> quantum process...!") lead people to thin... | https://quantumcomputing.stackexchange.com |
59,796 | [
"https://stats.stackexchange.com/questions/59796",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/25997/"
] | I have following variables in my dataset:
<ol>
<li>Working hours (numerical:ordinal)</li>
<li>Effectiveness (categorical:ordinal ; 4 values-> (poor,average,good,best))</li>
<li>Satisfaction (categorical:ordinal ; 4 values-> (poor,average,good,best))</li>
</ol>
I want to cluster the data on the basis of how good is m... | Regardless of clustering, there is a simple graph within reach.
Form a 16-category variable from effectiveness and satisfaction. (Naturally, not all joint categories are guaranteed to be present in your data.)
Then you can plot work hours against that. If you have multiple observations with exactly the same values,... | I don't use SAS but I can give you the sketch of one approach that could work when you want to cluster categorical data.
The first step is to convert <code>working hour</code> into categorical data (by dividing in class, 4 classes is ok here) and apply a Multicorrespondance Analysis (MCA) to your data.
In a second st... | https://stats.stackexchange.com |
269,434 | [
"https://physics.stackexchange.com/questions/269434",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/122237/"
] | In <em>Spacetime and Geometry</em>, Sean Carroll defines the Riemann tensor in terms of the commutator of covariant derivatives:
<span class="math-container">$$R^\rho_{\sigma\mu\nu}V^\sigma = [\nabla_\mu, \nabla_\nu]V^\rho + T^\lambda_{\mu\nu}\nabla_\lambda V^\rho$$</span>
At first I interpret this (the commutator part... | The quote you give from Carroll about the covariant derivative is right: it quantifies the rate of change of a tensor <em>field</em> relative to parallel transport. The covariant derivative of a tensor at a point doesn't make sense. However, the commutator of covariant derivatives acting on a point does.
The situation... | Consider a region in the manifold where a tensor field is everywhere well defined. Consider a point $x$ and a neighbouring point $x+dx$. The tensor field, say $V^\mu$ is given at both points as $V^\mu(x)$ and $V^\mu(x+dx)$. We can parallel transport the tensor(vector in this case) from $x$ to $x+dx$. This parallel tran... | https://physics.stackexchange.com |
212,449 | [
"https://dba.stackexchange.com/questions/212449",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/156471/"
] | Assuming one has about 1k requests per second that require an insert.
Now, there are a lot of answers to this on the internet... but they're technically wrong in this specific context. Yes, pretty much any RDBMS can handle 1k inserts per second on standard hardware but IF AND ONLY IF you drop ACID guarantees. It's su... | My simple RAID 10 array running on old hardware with 300GB SAS disks can handle 200-300 inserts per second without any trouble; this is with SQL Server running on a VM, with a lot of other VMs running simultaneously.
With just a consumer grade SSD, you can expect 3,000 to 5,000 or more 4K I/Os per second.
What exactl... | This
<blockquote>
This essentially means that if you have a forum with 100 posts per
second... you can't handle that with such a setup.
</blockquote>
Is simply incorrect. What you're missing is that multiple users can enqueue changes in each log flush. So while each log flush takes, say 10ms, it can harden doze... | https://dba.stackexchange.com |
116,286 | [
"https://cs.stackexchange.com/questions/116286",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/58433/"
] | I am trying to find the fastest algorithm to find all the possible paths of length <span class="math-container">$N$</span> from a given node in a directed graph.
My solution is to do a modification of breadth first search from the given node for <span class="math-container">$N$</span> iteration. Its time complexity i... | This problem is NP-hard, since the Hamiltonian Path problem is a special case of this problem where we set N=n and check whether the answer is strictly greater than zero.
This problem is actually #P-hard wich is believed to be strictly harder than NP.
The version of the problem where you only look for the existence o... | The above answer considers the version of this problem where vertices cannot be visited multiple times. However it seems that the intention of the question is that vertices could be visited multiple times.
The number of such paths can be exponential in |V| and |E|, so they cannot be listed in polynomial time.
The pro... | https://cs.stackexchange.com |
105,064 | [
"https://electronics.stackexchange.com/questions/105064",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/13366/"
] | What is the usage of theses negative voltages? Are they there only for backward compatibility?
In nowadays PC power supplies, we have:
<ul>
<li>+12V</li>
<li>+5V</li>
<li>+3.3V</li>
</ul>
but also:
<ul>
<li>-12V</li>
<li>-5V</li>
</ul>
But the current rating of the negative rails are much smaller than the positive... | PCs are stuffed with requirements which relate to backwards compatibility - and -Ve rails are part of that. I'm not sure about -5V, but there's a -12V line on the original PCI bus, so if you want to provide proper PCI sockets, then you need a -12V rail, even if the last person making a PCI card which needed -12V died ... | Although –12 V and –5 V are supplied to the motherboard via the power supply connectors, the motherboard normally uses only the +3.3 V, +5 V, and +12 V. If present, the –5 V is simply routed to the ISA bus on pin B5 so any ISA cards can use it, even though very few ever have. However, as an example, the analog data sep... | https://electronics.stackexchange.com |
190,119 | [
"https://physics.stackexchange.com/questions/190119",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/77786/"
] | I wonder whether it is even possible to find the answer. <em>If it is impossible to find out, why?</em>
<strong>Do moles of neutrons basically look like a neutron star? If so, what does one look like?</strong>
<strong>How about moles and moles of protons and electrons gathered together? What would be their electromag... | If you had a mole of electrons and a mole of protons and put them together, they would make hydrogen. The transition from ions to ground-state atoms would release 13.6 eV/atom or about 1300 kJ/mol.
This mole of hydrogen would have a mass of one gram. For comparison, combustion of 1 kg of gasoline releases about 44 M... | I assume that what you're getting at is something like "what would it look like if we created something the size and mass of a basketball, made of only neutrons?" If this is what you're getting at, you should consider what is meant by what something "looks like". This generally means how does visible wavelength light i... | https://physics.stackexchange.com |
127,243 | [
"https://cs.stackexchange.com/questions/127243",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/122365/"
] | Almost every time I see an article about time or space complexity, people are expressing the complexity with Big O, whereas it should be <span class="math-container">$\Theta$</span>.
From the book "Cracking the coding interview":
<blockquote>
"In industry (and therefore in interviews), people seem to have merge Θ
... | Here is an answer from reddit that I found the most useful:
<blockquote>
I guess I would say, if someone says, "what's O of insertion sort?", you want to say "it's <span class="math-container">$O(n^2)$</span>". Sure it's not precisely the same thing as saying that it's "<span class="math-contai... | I think its fine. It just shows the interviewer you actually know what the real meaning of big-O and theta are. Just make sure its actually true (the <span class="math-container">$\Omega$</span> part) when you have a complicated algorithm and you have used some inequality for big-O complexity proof.
| https://cs.stackexchange.com |
330,127 | [
"https://mathoverflow.net/questions/330127",
"https://mathoverflow.net",
"https://mathoverflow.net/users/23542/"
] | Before asking my question I like to admit that i am not an expert in the foundation of mathematics and I am interested in this issue more from a philosophical perspective. So my question may be competently naive. If we assume <span class="math-container">$ZFC$</span> and the negation of the continuum hypothesis, what... | By a theorem of Solovay, <span class="math-container">$|\mathbb R|$</span> can consistently be <span class="math-container">$\aleph_\alpha$</span> for any ordinal number <span class="math-container">$\alpha>0$</span> that does not have countable cofinality. Then the set <span class="math-container">$\{|A|:A\subseteq... | It depends. Do you care about naming or describing such sets?
In the system you propose, you may be able prove the existence of more than finitely many of them, but in a countable (non-infinitary, since you mention a small extension of ZFC) language, you will only be able to describe countable many of these sets or eq... | https://mathoverflow.net |
112,352 | [
"https://cs.stackexchange.com/questions/112352",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/108124/"
] | As title.
I consider finding a specific L to fulfill the condition stated to prove the statement, however, I have no luck in finding one.
A senior gave me a hint that Lagrange's four square theorem might help, but I don't see how I can utilize it.
Thanks.
| Let us prove a more general result:
<blockquote>
For each <span class="math-container">$m \geq 2$</span> there is a language <span class="math-container">$L$</span> such that <span class="math-container">$L,L^2,\ldots,L^{m-1}$</span> are not regular but <span class="math-container">$L^m$</span> is regular.
</blockqu... | Unless you must deal with unary regular languages, there is no need for complex math ...
Just pick an irregular language that is able to "capture and mask" the concatenation of itself; e.g. over <span class="math-container">$\Sigma = \{a,b \}$</span>
<span class="math-container">$L = \{ (a^ib^j) (a^n b^n) \mid i, j \... | https://cs.stackexchange.com |
1,129,299 | [
"https://math.stackexchange.com/questions/1129299",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/210818/"
] | Find $\lim_\limits{n\to\infty}\sin(\pi\sqrt[3]{n^3+1})$. I am trying to find it using <strong>Taylor series.</strong>
What I did so far is: $\sqrt[3]{z+1}=1+O(z)$ (I really can't tell when I should be done developing it, and what is valid or not.) I get that $(\pi\sqrt[3]{n^3+1})=1+O(n^3)$. What do I do with that $O(... | $\sqrt[3]{z+1}=1+O(z)$ holds for $z\to0$, but $n\to\infty$. You should use
$$
\sqrt[3]{n^3+1}=n\sqrt[3]{1+n^{-3}}=n(1+O(n^{-3}))=n+O(n^{-2}),
$$
$$
\pi\sqrt[3]{n^3+1}=n\pi+O(n^{-2}),
$$
And the formula for the $\sin$ of a sum.
| Your error term looks too big (you are probably doing your expansion around zero instead of infinity). Try to show that
$$
(1+n^3)^{1/3}=n+O(1/n^2),\quad\text{as}\quad n\to+\infty
$$
for example by making the Maclaurin expansion
$$
(1+t)^{1/3}=1+O(t),\quad\text{as}\quad t\to 0,
$$
(with $t=1/n^3$).
| https://math.stackexchange.com |
339,039 | [
"https://softwareengineering.stackexchange.com/questions/339039",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/124070/"
] | I mean, it's a matter of choosing words more than there is any difference between function and constructor call. The thing which is named "constructor of an object" can also be named "function with name <code>object</code> returning type <code>object</code>".
One could argue that C++ does not allow one to have the sa... | A constructor is basically a method, yes, but it is a special method.
For example, in C++ a constructor isn't simply a function that returns a new instance of that type. If it was, inheritance wouldn't work. You couldn't call into the base constructors, because they'd return a new instance as well. You'd end up with a... | No, a constructor of <code>object</code> is very different from a function called <code>object</code> and returning <code>object</code>. A constructor has no name, but that is largely a technicality. The more important differences are that a constructor has no return type and that it cannot be called directly.
A const... | https://softwareengineering.stackexchange.com |
1,820,855 | [
"https://math.stackexchange.com/questions/1820855",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/227385/"
] | So I have to prove $\lim\limits_{x \to 2} \frac{x-1}{x^2}$= $\frac{1}{4}$.
So I need to find $0<|x-2|<\delta$, such that $\left\vert\frac{x-1}{x^2}-\frac{1}{4}\right\vert<\epsilon$.
So $\left\vert\frac{x-1}{x^2}-\frac{1}{4}\right\vert=\frac{(x-2)^2}{4x^2}$.
Now I try to set $\delta=1$, so $0<|x-2|<1... | Looks good, because you can use $\color{blue}{4<4x^2}<36$ to say:
$$|f(x)-L|=\frac{(x-2)^2}{4x^2} \le \frac{(x-2)^2}{4}$$
And since $|x-2| < \delta$, this means:
$$\frac{(x-2)^2}{4} < \frac{\delta^2}{4}$$
You want this under $\varepsilon$, so:
$$\frac{\delta^2}{4} < \varepsilon \iff \delta < 2\sqrt{\v... | May be you set $\delta$ to 1,and $0<|x-2|<1$, so $ 4 x^2 $ will between 4 and 36, that is $ 1/4 x^2<1/4 $. Then we can get $ (x-2)^2/(4 x^2)< \frac{1}{4} (x-2)^2 $. Set $ \frac{1}{4} (x-2)^2 < \epsilon $, then $ |x-2|<2 \sqrt{ \epsilon} $.
Let $ \delta = Min \{ 2\sqrt \epsilon ,1 \} $
| https://math.stackexchange.com |
22,679 | [
"https://mechanics.stackexchange.com/questions/22679",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/10905/"
] | One thing that bugs me about my car is that the fuel pump noise is fairly inconsistent. Turning on the lights, aircon, defroster, etc. lowers the fuel pump speed and gives a lower pitched noise. It also dips for a second when the RPM gets too low, sometimes when accelerator is released and clutch is pushed in, sometime... | It sounds very much like your alternator is not delivering a constant voltage. It should be able to cope with a change in demand. Check the voltage at the battery with different loads turned on, the alternator should be able to keep a voltage of around 14v
Alternatively you could have a slightly bad connection from ... | Your issues may be beyond the fuel pump.
The telling sign of this is that a change in engine load is inducing a change in the noise of the fuel pump.
I assume that your fuel supply system is a "return"-style fuel system in which the fuel flow provided by the pump is constant, regardless of load; the pressure regulato... | https://mechanics.stackexchange.com |
25,974 | [
"https://security.stackexchange.com/questions/25974",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/18067/"
] | I'm trying to weigh the benefits of not allowing users to create their own passwords, but must pick out of a generated selection. Are there any examples of sites that use this approach?
Workflow adjustments for such a site would be along the lines of:
Registration: user is prompted to pick of the generated passwords ... | Generating passwords for user means that you will get good passwords. However, security is an all-encompassing thing; you also need the users to remember the passwords, and not store them insecurely (the traditional stick-up note under the keyboard), and, generally speaking, you need the user to <strong>cooperate</stro... | I think it might be worth it for some business critical apps, banking apps, maybe even hosting control panels. But I think some consumers and others will get annoyed by it and might not want to signup. Maybe you should do a UI where you have auto generated good passwords and notes about them on the left, the non the ri... | https://security.stackexchange.com |
482,600 | [
"https://math.stackexchange.com/questions/482600",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/84064/"
] | I am reading Donald Knuth's Concrete Mathematics (2nd Edition) and I am on chapter 2 (Sums).
I have problems in understanding his some notations on multiple sums. I quote his explanations I can't understand from his book.
<blockquote>
$$\sum_{j\in J}\sum_{k\in K(j)}a_{j,k}=\sum_{k\in K'}\sum_{j\in J'(k)}a_{j,k}$$
... | Here's some intuition (but not a rigorous proof).
If $A$ is hermitian (with entries in $\mathbb C$), you can easily show that the eigenvalues of $A$ are real and that eigenvectors corresponding to distinct eigenvalues are orthogonal.
Typically, all the eigenvalues of $A$ are distinct. (It is in some sense a huge coi... | Suppose the ground field is $\mathbb C$. It is immediate then that every square matrix can be triangulated. Now, symmetry certainly implies normality ($A$ is normal if $AA^t=A^tA$ in the real case, and $AA^*=A^*A$ in the complex case). Since normality is preserved by similarity, it follows that if $A$ is symmetric, the... | https://math.stackexchange.com |
35,558 | [
"https://cs.stackexchange.com/questions/35558",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/20461/"
] | <blockquote>
$T(n+1)=T(n)+\lfloor \sqrt{n+1} \rfloor$ $\forall n\geq 1$ <br>
$T(1)=1$<br><br>
The value of $T(m^2)$ for m ≥ 1 is?
<br>
</blockquote>
Clearly you cannot apply master theorem because it is not of the form $T(n)=aT(\frac{n}{b})+f(n)$<br><br>
So I tried Back Substitution:<br>
$T(n)=T(n-1)+\lfloor\s... | Your problem is that you're ignoring the floors. Make sure that you know what $\lfloor x \rfloor$ means.
It is not hard to check that
$$ T(n) = \sum_{k=1}^n \lfloor \sqrt{k} \rfloor. $$
Therefore
$$
\begin{align*}
T(m^2-1) &= \sum_{k=1}^{m^2-1} \lfloor \sqrt{k} \rfloor \\ &=
\sum_{r=1}^{m-1} \sum_{\ell=r^2}^{(... | For a slightly different way to look at his problem, consider your original equation,
$$
T(n) = T(1)+\lfloor\sqrt2\rfloor+\lfloor\sqrt3\rfloor+\dotsb+\lfloor\sqrt n\rfloor
$$
Now the key here is to group the terms with the same values of $\lfloor\sqrt k\rfloor$:
$$\begin{align}
T(n) &= (T(1)+\lfloor\sqrt2\rfloor+\l... | https://cs.stackexchange.com |
105,396 | [
"https://electronics.stackexchange.com/questions/105396",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/33411/"
] | I'm having difficulty working out required values of resistors \$R_C\$ and \$R_E\$ in the circuit below. Can't seem to find any formulas on the web.
<img src="https://i.stack.imgur.com/B7NIl.png" alt="schematic1![][1]">
I know how to find \$R_1\$ and \$R_2\$:
$$R_1 = (\frac{R_2}{V_B} \times V_{CC})-R_2$$
$$R_2 = \f... | You have 4 resistors and thus, 4 degrees of freedom. You need four independent and consistent design constraints to find a unique set of four resistor values.
Some of the possible design constraints are:
(1) input impedance
(2) output impedance
(3) AC gain
(4) DC collector current
The input impedance is approxim... | <strong>Warning</strong> - rules of thumb being used!!
I always try and get about 0.5 to 1V on the emitter (lets say 0.75V). This means the base will be at about 1.45V and this allows you to calculate R1 and R2 (but be prepared to revise those values should the base current drawn be a little high).
You want 10mA thru... | https://electronics.stackexchange.com |
2,881,353 | [
"https://math.stackexchange.com/questions/2881353",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/552998/"
] | <blockquote>
What is the probability of occurrence of at least two of the three
events if $P(A) = 0.38, P(A \cap B \cap C) = 0.1, P(A \cap B' \cap C')
= 0.17$ and $ P(A'\cap B \cap C) = 0.12 $
</blockquote>
I'm guessing this question is based on some sort of formula from sets I'm not aware of. Can anyone help?
| While the article you refer to correctly defines the concept of confidence interval (your highlighted text) it does not correctly treat the case of a normal distribution with unknown standard deviation. You may want to search "Neyman confidence interval" to see an approach that produces confidence intervals with the pr... | Let me address your question item by item:
<blockquote>
<ol>
<li>If I transfer my population distribution to Z standard deviation, then 95% area occurs at $Z= \pm 1.96$. Since $Z = \dfrac {Y-\mu}{\sigma}$, in original population distribution, 95% data points fall within $Y = \mu \pm 1.96\sigma$. $$ \color{blue}{\... | https://math.stackexchange.com |
435,475 | [
"https://softwareengineering.stackexchange.com/questions/435475",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/261048/"
] | I am in two minds about sharing client / server errors codes. We are writing both ends of the system, if our API was external this would not be possible, but that requirement is very unlikely.
So an idea would be to have some shared directory between client and server and then on the server:
<pre class="lang-js prettyp... | If your frontend and your backend
<ul>
<li>are developed in the same programming language (typically Javascript)
</li>
<li>are developed by the same team
</li>
</ul>
then there is nothing generally wrong in having shared libraries for both, especially when there are things you want to keep in sync between frontend and ... | If you want to communicate specific error situations from the server to the client, they need to agree on their encoding. Effectively, it becomes part of the interface.
So, I'd place the error codes specification along the other interface definition parts (maybe you're using OpenAPI, then you can specify the error code... | https://softwareengineering.stackexchange.com |
41,408 | [
"https://physics.stackexchange.com/questions/41408",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/4435/"
] | Let us suppose this gedanken experiment:
A man isolated into a room asks if he is made of matter or antimatter.
Could he set some experiments to see if he is made of matter or antimatter instead?
Is it possible to have a universe similar to ours but 'inverted' in the sense that this new universe would be made of anti-a... | To do this, the man needs to build a particle accelerator and measure Kaon decays, or some other process involving higher quark flavors. Everything else is CP invariant, so he wouldn't know for sure.
| Being the egocentrics, we typically define <em>matter</em> to be the stuff we are made of, and <em>antimatter</em> to be the stuff we are not. So from a semantic point of view, the man will always conclude that he is made of matter.
| https://physics.stackexchange.com |
102,930 | [
"https://physics.stackexchange.com/questions/102930",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/30632/"
] | We studied electric fields due to point charges. The magnitude of these fields decreases with the square of the distance from the point charge.
It seems to me that we could treat the positive terminal of a battery as a point charge. So, I would conclude that the magnitude of the electric field set up by the positive t... | You are absolutely correct, the electric field <em>does</em> fall off with distance from the battery. However, this is only true during the transient state (the state of the field when the battery is first connected). In fact not only are the magnitudes inconsistent, but so is the direction of the field. The field does... | The battery terminal appears "small" when you hold it in your hand.
But from the perspective within the wire, close to the terminal, the battery terminal appears large. The electric field close to a large object like this is roughly constant (pitcure the constant field between capacitor plates).
Further away from the ... | https://physics.stackexchange.com |
29,714 | [
"https://cs.stackexchange.com/questions/29714",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/12441/"
] | I'm almost sure I understand $o(1)$ (a class of functions that converge to zero in their limit), but the way I understand it, that would seem to imply that functions in $n^{o(1)}$ converge to 1 (after all, $n^0=1$ )
Certainly the limit of $n^{1/n}$ is 1.
But it can't mean that, because the next question (and yes, th... | Your error is to assume that the convergence from the exponent will always dominate the divergence of the base.
As an instructive example, consider the composition $f^g$, where $f(n) = a^n$, $a>1$ and $g(n) = \frac 1n$. As in your example, $f$ diverges and $g$ converges to 0. So your reasoning would imply that $f^g... | <blockquote>
$n^{o(1)}$ converge to 1 (after all, $n^0=1$ )
</blockquote>
You can't take the limit of one part without taking the limit of the other part, that doesn't give any useful information. If you take the limit of both parts, you get $\infty^0$, which is an indeterminate form.
It's easier to reason about ex... | https://cs.stackexchange.com |
22,959 | [
"https://ai.stackexchange.com/questions/22959",
"https://ai.stackexchange.com",
"https://ai.stackexchange.com/users/40196/"
] | I recently read some introductions to AI alignment, AIXI and decision theory things.
As far as I understood, one of the main problems in <em>AI alignment</em> is how to define a <em>utility function</em> well, not causing something like the paperclip apocalypse.
Then a question comes to my mind that whatever the utilit... | Actually, there is usually an upper bound for inputs of transformers, due to the inability of handling long-sequence. Usually, the value is set as 512 or 1024 at current stage.
However, if you are asking handling the various input size, adding padding token such as [PAD] in BERT model is a common solution. The position... | The accepted answer is wonderful; this answer provides an alternative approach for dealing with variable length inputs. More specifically, what might be done when the input is longer than the maximum sequence length supported by the transformer you have built.
We have found it useful to wrap our transformer in a class... | https://ai.stackexchange.com |
23,694 | [
"https://cs.stackexchange.com/questions/23694",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/16703/"
] | In my first lecture of "Theory of Automata", after giving some concepts of Alphabet, Language, transition function etc. and a couple of simple automata of an electric circuit with one and two switches, is this question.
<img src="https://i.stack.imgur.com/WIYoO.png" alt="enter image description here">
I understand wh... | Yes, there are procedures that help you draw a DFA.
One of them is to draw first an NFA (Non deterministic finite automaton), if we cannot draw instantly a DFA. We humans cannot with ease draw a DFA, especially for a complex language as you've seen. So we draw a NFA which is closer to our understanding. Then, rules ar... | Do not confuse defining an automaton and drawing an automaton.
The drawing is intended as a support for better intuition, and because
it can often be read more easily in a single look. That is what
drawing are usually for.
However, you are supposed to actually (be able to) give a formal
definition, with the mathemati... | https://cs.stackexchange.com |
98,136 | [
"https://dba.stackexchange.com/questions/98136",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/63605/"
] | Say I have a <code>product</code> table with the following columns:
<pre><code>product
--------
product_id
name
</code></pre>
And I have another table to record the transaction (IN/OUT) for each product
<pre><code>product_transaction
--------------------
transaction_id
transaction_date
product_id
type
quantity
</cod... | Like many things, the answer to this question is "it depends". In this case, what it depends on is how many transactions each product will get.
With low to moderate volumes of transactions, it will be very fast to compute the running total on the fly and you don't have to write lots of code to compute, store and maint... | Actually, in case of correct indexes existence, you will receive the data calculated in the relatively small time. In this case you don't need to perform the data manipulations relevant for storage of running sums and so on. The indexes will increase the insert time, but influence will be very small (almost slight). Fo... | https://dba.stackexchange.com |
642,214 | [
"https://electronics.stackexchange.com/questions/642214",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/305610/"
] | I'm trying to measure current on a cheap multimeter. It has an unfused 20A port and a fused 200mA port.
I'm using a simple circuit with an LED, a resistor and 5V DC and setting the multimeter dial to read maximum of 20mA DC input.
If I use the fused mA port I get the correct reading of about 2mA. If I use the same sett... | The lower current settings usually only read the current through the fused, low current jacks.
If you want to use the 20A jack, you have to set the meter to the 20A setting.
You probably won't be able to get a good reading for the LED current when using the 20A setting. 2mA is probably too low to register on the 20A s... | Assuming a 3.5 digit DMM, the lowest digit would be 10mA (19.99A FS), so you would expect it to read zero with 2mA.
Also some newer chipsets for low-end DMMs are not quite as good from an accuracy pov as the older ones based on the ICL7106 (and its many clones) and have more nonlinearity etc. but require fewer and chea... | https://electronics.stackexchange.com |
662,575 | [
"https://physics.stackexchange.com/questions/662575",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/312771/"
] | Can someone help me in understanding why there is no centripetal force acting on a vehicle while taking a turn?
Basically, my physics teacher used a non-inertial frame where the frame was at the centre of the turn but if the observer was from ground frame, then he would have seen that the car is rotating and would have... | The centripetal force from the road doesn't vanish in either frame. The difference is that there's another force in the rotating frame that cancels it out.
Suppose we have a car driving in a circle on a flat track at a uniform speed. In the ground frame, there is a force of friction pushing the car towards the center... | I think the confusion is more general. About what those two forces are:
<h2>Centripetal</h2>
When a truck is going around a curve at constant speed, its velocity is changing. Velocity is speed <em>and</em> direction. Therefore direction changing... is velocity changing. Changing velocity is acceleration.
So, it takes a... | https://physics.stackexchange.com |
602 | [
"https://stats.stackexchange.com/questions/602",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/-1/"
] | Do you know any good heuristics for finding optimal value of ν in case of ν-SVM classification? In this particular problem I have a radial basis kernel, if it helps.
| For optimisation, you don't need to perform a grid search; a Nelder-Mead simplex(fminsearch in MATLAB) approach is just as effective and generally much faster, especially if you have a lot of hyper-parameters to tune. Alternatively you can use gradient descent optimisation - if your implementation doesn't provide grad... | There are no general heuristics, you should make a grid search, especially since the value of nu must be between 0-1.
| https://stats.stackexchange.com |
4,298,381 | [
"https://math.stackexchange.com/questions/4298381",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/636226/"
] | If <span class="math-container">$X\times Y$</span> is compact then <span class="math-container">$X,Y$</span> are compact spaces
<hr />
Let <span class="math-container">$X\times Y$</span> be non-empty compact space <span class="math-container">$U_i, i\in \{1,2,...\}$</span> be an open cover for <span class="math-conta... | Let <span class="math-container">$\{U_{\alpha}\}_{\alpha\in A}\,$</span> and <span class="math-container">$\{W_{\beta}\}_{\beta\in B}\,$</span> be covers of <span class="math-container">$X$</span> and <span class="math-container">$Y$</span>. Where <span class="math-container">$A$</span> and <span class="math-container"... | If neither <span class="math-container">$X$</span> nor <span class="math-container">$Y$</span> is empty and if <span class="math-container">$X$</span> is not compact, let <span class="math-container">$C$</span> be an open cover of <span class="math-container">$X$</span> with no finite sub-cover. Then <span class="math-... | https://math.stackexchange.com |
17,985 | [
"https://quantumcomputing.stackexchange.com/questions/17985",
"https://quantumcomputing.stackexchange.com",
"https://quantumcomputing.stackexchange.com/users/16312/"
] | Let <span class="math-container">$\sigma$</span> be a fixed positive semidefinite matrix (edit: need unit trace too as pointed out if we want trace nonincreasing). Is the map
<span class="math-container">$$N:H\rightarrow\mathbb{C}$$</span>
given by <span class="math-container">$N(\rho) = Tr(\sigma\rho)$</span> complete... | I assume for <span class="math-container">$\rho$</span> and <span class="math-container">$\sigma$</span>, you meant to write <span class="math-container">$\rho = \sum_i p(i) \vert i\rangle\langle i\vert \otimes \rho_i$</span> and <span class="math-container">$\sigma = \sum_i q(i)\vert i\rangle\langle i\vert\otimes\sigm... | Observe that, for any collection of matrices <span class="math-container">$A_i$</span>, we have
<span class="math-container">$$\sqrt{\sum_i |i\rangle\!\langle i|\otimes A_i}
= \sum_i |i\rangle\!\langle i|\otimes \sqrt{A_i}, \\
{\rm Tr}\left(\sum_i |i\rangle\!\langle i|\otimes A_i\right)
= \sum_i {\rm Tr}(A_i).$$</span>... | https://quantumcomputing.stackexchange.com |
118,626 | [
"https://softwareengineering.stackexchange.com/questions/118626",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/4705/"
] | I hope this is the right forum for this ... Well, in C, the standard library uses usually <code>(void* buffer, int size)</code> when referring to some data buffer. I wonder if there is a rationale for this order instead of <code>(int size, void* buffer)</code>. I couldn't think of any good reason, and it seems to be an... | In C you can't do <code>object->method(value)</code>, so it's idiomatic to put the "object"—the thing whose state you're changing—as the first parameter, and prefix the function name with the "class." The C standard library makes a lot more sense when you think about it that way. For example, <code>str... | Generally you prefer the data parameters first and then the const values.
There is also a preference for the result first eg strcpy(dest,src) memcpy(dest,src)
In c++ it's useful because you can have default parameters at the end.
| https://softwareengineering.stackexchange.com |
35,304 | [
"https://physics.stackexchange.com/questions/35304",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/11220/"
] | I have a rather trivial question. I am looking for the decomposition of $1/2\otimes 1/2\otimes 1/2$. It should give, $0,1/2$ and $3/2$. I thought one must get as the overall dimension of this space 8, but counting, I just get 7. Does one have 2 singlets?
| From where did you get the idea that one can get a spin zero representation? The product of an even/odd number of Fermion representations always gives a Boson/Fermion representation.
In your particular case, repeated use of $$1/2 \otimes s = (s-1/2) \oplus (s+1/2)$$ gives $$1/2 \otimes 1/2 \otimes 1/2=(0\oplus 1) \ot... | With the caveat that I'm 30+ years rusty at this stuff: <em>Two</em> 1/2's and <em>one</em> 3/2 (and <em>no</em> singlet) does have dimension 8. And <em>Mathematica's</em> Clebsch-Gordon routines affirm this decomposition.
| https://physics.stackexchange.com |
336,175 | [
"https://softwareengineering.stackexchange.com/questions/336175",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/144461/"
] | So I will be creating a feature to a php application that does the following:
<ul>
<li>Create a session that expires after 30 minutes.</li>
<li>After 30 minutes, if there is no user activity in the application (including typing to a textbox, moving a mouse throughout the page), the session will be destroyed and the sy... | Your second solution is best solution. I believe this because it should fundamentally be the clients responsibility to inform the server that they are still active. The server can then do as it must from there.
This gives the server all the control over what happens. The only control the client has is to designate if ... | You shouldn't rely on Javascript as the only solution. The PHP should track the session expiration with the Javascript class handling the updates on the page. If no updates from the JS, then the PHP should expire the session automatically on the next request. There are lots of reasons why the JS would not update the pa... | https://softwareengineering.stackexchange.com |
3,813,303 | [
"https://math.stackexchange.com/questions/3813303",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/344488/"
] | I start by apologizing for my English, please correct if you find a typo.
I am stuck with this problem; I know the answer should normally be yes, but I am not able to prove it.
Please can somebody help (or give a counter example)?
Suppose <span class="math-container">$f$</span> is a monotone and bounded function and <s... | The assumption is not true
Counterexample
Let <span class="math-container">$f(x) = \begin{cases}
1,& \text{if } x < 0 \\
e^{-\lambda x}, & x \geq 0
\end{cases}$</span>
Then <span class="math-container">$f$</span> is bounded and monotone and <span class="math-container">$$ \lim_{x\rightar... | How about the piecewise function:
<span class="math-container">$$f(x) = \begin{cases} 1 \quad \text{ for } x < 0\\ e^{-\lambda x} \text{ for } x \ge 0\end{cases}$$</span>
It is bounded and non-increasing, satisfies the limit property at <span class="math-container">$+\infty$</span>, and the integral diverges.
| https://math.stackexchange.com |
155,469 | [
"https://mathoverflow.net/questions/155469",
"https://mathoverflow.net",
"https://mathoverflow.net/users/36688/"
] | To what extent, the following types of Lie algebras are classified :
<blockquote>
Those Lie algebras $L$ such that every Lie Group $G$ with $Li(G)\sim L$, is necessarily compact.
</blockquote>
| They are exactly the semi-simple Lie algebras which admit a positive definite invariant bilinear form (or equivalently, for which the Killing form is negative definite). An excellent reference for this is the first section of Bourbaki, <em>Lie groups and Lie algebras</em>, Chapter 9 (you need very little background to ... | They are the compact Lie algebras. Note that are two different definitions in the literature. One is that a compact Lie algebra is the Lie algebra of a compact Lie group. This includes tori, and the Killing form then is negative semidefinite. The Lie algebra is not necessariliy semisimple, but <em>reductive</em>. The o... | https://mathoverflow.net |
176,371 | [
"https://electronics.stackexchange.com/questions/176371",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/5814/"
] | I am planning to buy some MOSFETs for testing and playing around, to decide if I would use one instead of a BC338 transistor (see my intended application below).
My "filtering algorithm" would be:
<ol>
<li>Small package (TO-92 preferrably);</li>
<li>Small power dissipation (less heat = more light!);</li>
<li>Saturate... | Don't be shy about spec'ing your own part from a distributor's website. It's not as hard as you'd think, once you learn which parameters are important in which situations. Based on the information you've provided, I'll guide you through selecting a usable MOSFET on Digikey.
Note that I am not validating your schematic... | I think your problem is that you don't know what you don't know - you don't understand the many various parameters of MOSFETs & how they might apply to your needs, and so you've dismissed several of the best & easiest ways to find a MOSFET for one's needs: Digikey, Mouser, Parts.io, Element14/Farnell/Newark, Ra... | https://electronics.stackexchange.com |
37,242 | [
"https://softwareengineering.stackexchange.com/questions/37242",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/4091/"
] | Most people seem to treat debugging as an art, rather than a science. For those here which treat it as a science, rather than an art - what process(es) do you normally use when faced with a new issue/bug/problem?
| In very general terms, what I do is:
<ol>
<li>Try to isolate the problem. Think of what has changed when the bug first appeared. What where you working on? What part of the code were you changing? 99% of my bugs are
solved this way. It's usually something silly.</li>
<li>If I have a guess about where the problem is, ... | There are a number of definitions for the word science, but it sounds like you are possibly referring to what may be more accurately termed the "<em>scientific method</em>". The scientific method might be summarized as observing some phenomena (presumably a bug or unexpected program behavior), formulating a hypothesis ... | https://softwareengineering.stackexchange.com |
2,194,143 | [
"https://math.stackexchange.com/questions/2194143",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/369955/"
] | let $X=Y=\mathbb R$ and $\mu=\nu=$Lebesgue measure, and $\mu*\nu$ is a two dimensional Lebesgue measure on $X*Y=R^2$. Then Show that
For each measurable subset $E$ of $\mathbb R$, the set $\sigma(E)=$$\{(x,y):x-y\in E\}$ is a measurable subset of $\mathbb R^2$. If $f$ is measurable function on $\mathbb R$, then functi... | $F_n \equiv t^n \mod m$ is a solution if $t$ is a root of the characteristic polynomial mod $m$. In this case ($m = 31$, characteristic polynomial $p(x) = x^2 - x - 3$) the characteristic polynomial has no root in the field $\mathbb F_{31}$, so you go to an extension field where you get your two roots.
Alternatively... | Yes, the shift map sends the pair $(F_i, F_{i+1})$ to $(F_{i+1}, 3 F_{i+1} + F_i),$ so the corresponding matrix is
$$\begin{pmatrix}0 & 1\\ 3 & 1\end{pmatrix}.$$ Now, you need to raise this matrix to power $2999,$ and then apply it to the vector $\begin{pmatrix}1 \\ 1 \end{pmatrix}.$ You can raise the matrix t... | https://math.stackexchange.com |
208,886 | [
"https://mathoverflow.net/questions/208886",
"https://mathoverflow.net",
"https://mathoverflow.net/users/62680/"
] | I am reading about 'Exponential Sums' in the book 'Analytic Number Theory' by Iwaniec and Kowalski. On page 199 they mention the bound:
$$|S_f(N)|^2 \le N +2N^2q^{-1}+4(N+q)\log q \tag{1}$$
where, $\displaystyle S_f(n) = \sum\limits_{n=1}^{N} e^{2\pi i(\alpha n^2 +\beta n)}$ and $1 \le q \le 2N$ satisfies $\displays... | Regarding your first question, observe that (2) is equivalent to
$$ |S_f(N)|^2 \le 4N^2q^{-1}+4N\log q+q\log^2 q. $$
Hence, by (1), it suffices to show
$$ N +2N^2q^{-1}+4N\log q + 4q\log q \le 4N^2q^{-1}+4N\log q+q\log^2 q,$$
which in turn is equivalent to
$$ N+4q\log q \le 2N^2q^{-1}+q\log^2 q.$$
Here we have $N\leq 2... | If $\log(q)\ge4$, then the fact that $N\le2N^2q^{-1}$ and $4q\log(q)\le q\log(q)^2$ show that
$$
N+2N^2q^{-1}+4(N+q)\log(q)\le\overbrace{4N^2q^{-1}+q\log(q)^2+4N\log(q)}^{\left(2Nq^{-1/2}+q^{1/2}\log(q)\right)^2}
$$
This shows that $(1)\implies(2)$.
<hr>
If $q\le4$, then
$$
N^2\le4N^2q^{-1}+q\log(q)^2+4N\log(q)
$$
Th... | https://mathoverflow.net |
16,987 | [
"https://physics.stackexchange.com/questions/16987",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/5504/"
] | Basically, the book is Brian Cox's <em>Why Does $E=mc^2$?: (And Why Should We Care?)</em>.
I just finished Chapter 5, where we derived the spacetime momentum vector (energy-momentum four vector, as he establishes the physics jargon).
Let $\gamma=\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}$
So, as we found out, the vector's s... | Dimensional analysis is enough to see that $mc^2$ has the same units as energy while $\gamma mc$ or $mc$ doesn't.
Concerning the components of a 4-vector, special relativity unifies the spatial and temporal components. But the 4 components of a 4-vector with "uniform units" do not necessarily enjoy the same normalizat... | Uh, because $mc$ is not energy? And what do you mean "time component"? Your $\gamma mc$ is momentum.
| https://physics.stackexchange.com |
4,387,024 | [
"https://math.stackexchange.com/questions/4387024",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/623979/"
] | We have <span class="math-container">$X_1, ..., X_n \sim U[0, \theta]$</span> and estimator <span class="math-container">$\phi^*(X_{[n]}) = X_{(n)}$</span>. <span class="math-container">$X_{(n)}$</span> here stands for <span class="math-container">$\max_iX_i$</span>.
I need to made this estimator <strong>unbiased</stro... | Given <span class="math-container">$X_i$</span> are iid, it would be easy enough to obtain the CDF of the standardized estimator (we assume it is <span class="math-container">$n^\alpha$</span>-consistent):
<span class="math-container">$$P\left(n^\alpha \left(\frac{n+1}{n}X_{(n)}-\theta \right)\leq x\right)=P\left(X_{(n... | First of all, your approach to this problem is flawed. To check if a sequence <span class="math-container">$Y_1,Y_2,\dots,$</span> of variables is asymptotically normal, you need to show that <span class="math-container">$$\frac{Y_n-E[Y_n]}{\sqrt{\text{Var}(Y_n)}}\to N(0,1).$$</span> In your case, <span class="math-con... | https://math.stackexchange.com |
11,546 | [
"https://softwareengineering.stackexchange.com/questions/11546",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/175/"
] | Take the example of the recent ASP.NET (and Java Server Faces) vulnerability disclosure at a Hacker conference in Brazil. It's my understanding that the poet tool was demonstrated before Microsoft was even aware of the issue.
Are there laws to protect legitimate customers from people who encite the hacker community t... | None that I know of, and there probably shouldn't be, either.
<blockquote>
<em>Who knows how many legitimate businesses were compromised between when the tool was demoed and the patch was applied to the server.</em>
</blockquote>
Who knows how many legitimate business were compromised before the tool was demoed? Y... | Where would the laws apply? If the tool was demoed in Brazil, presumably it would have to be Brazilian law that is applied. So even if there <em>was</em> a U.S. law that protected companies, it wouldn't have helped because you can't prosecute someone in Brazil for violating a U.S. law.
You might be able to get a law l... | https://softwareengineering.stackexchange.com |
220,239 | [
"https://softwareengineering.stackexchange.com/questions/220239",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/41780/"
] | I'm currently doing an application design that involves sale of service. The application will ultimately be used internationally and will need to adjust prices based on user location.
Is it a good idea to store / work with all prices in an absolute unit? For example - credits. And I can specify conversion rules like 1... | You're both over and under-complicating it. You're over-complicating it for the users, who now have to convert things between credits and their local currency in their head, and under-complicating it for yourself. Things are not priced identically around the world, even once you account for exchange rates. Heck, things... | I don't think you can do this with an artificial currency.
At some point your application needs to interact with the "real" world of accounting, and the transactions need to be auditable ... in terms of an actual currency. The tax man wants his cut of the action ... in a particular currency. And people need to pay... | https://softwareengineering.stackexchange.com |
544,819 | [
"https://physics.stackexchange.com/questions/544819",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/206319/"
] | A symmetry transformation is a transformation on the states that can be seen as <span class="math-container">$$|\phi\rangle'=\hat U |\phi\rangle$$</span> Then imagine we have an observable <span class="math-container">$\hat A$</span> and a state <span class="math-container">$|\phi\rangle$</span> such that <span class="... | If I have a device that measures horizontal distance, I can rotate it <span class="math-container">$90^\circ$</span> to obtain a device that measures vertical distance.
An "observable" can be regarded as an abstract representation of a measuring device, specifying only what it measures, without specifying any details... | After a <span class="math-container">$\frac\pi2$</span> rotation along the <span class="math-container">$z$</span> axis, the <span class="math-container">$x$</span> axis coincides with the <span class="math-container">$y$</span> axis. Note that we are considering a passive transformation, that is, we are just changing ... | https://physics.stackexchange.com |
148,061 | [
"https://dba.stackexchange.com/questions/148061",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/98646/"
] | I need to monitor the local admins on my SQL Server systems for auditing. Is there a way to use a stored procedure with powershell to accomplish that?
| You can use this stored procedure to collect the local admins on the system as long as it runs under the context of a member of the sysadmin role.
<pre><code>SET ANSI_NULLS ON
GO
SET QUOTED_IDENTIFIER ON
GO
Create procedure [dbo].[usp_CollectLocalAdmins]
as
-- list all members of Local Administrators group
set nocount... | You don't need to use Powershell for this, which would require xp_cmdshell in a stored procedure. Just use xp_logininfo. As long as you add the group to SQL Server (you don't have to give it any permissions), you can query the members of it.
<pre><code>EXEC master.dbo.xp_logininfo 'Builtin\Administrators', 'members'
<... | https://dba.stackexchange.com |
11,118 | [
"https://robotics.stackexchange.com/questions/11118",
"https://robotics.stackexchange.com",
"https://robotics.stackexchange.com/users/15206/"
] | I'm working on Graph SLAM to estimate robot poses (x, y, z, roll, pitch, yaw). Now I want to integrate GPS measurement (x, y, z, of course no angles).
I implemented GPS as pose's prior. But I have a problem.
<ul>
<li>Position(x, y, z) is perfectly corrected by graph optimization</li>
<li>But orientaiton(roll, pitch, ... | You can use a very low information matrix value at the orientation elements of your state, given that the information matrix is the inverse of the covariance matrix.
The covariance matrix represents the uncertainty about the measurement, and the information matrix the certainty about it.
So, the GPS constraints wo... | Frankly speaking, I don't have any experience with implementing a SLAM algorithm. That said, GPS gives you a position and SLAM gives you a position. My advice would be to use a data fusion technique, such as a Kalman filter or maybe even the Madgwick filter, to combine the position estimates.
| https://robotics.stackexchange.com |
18,033 | [
"https://dba.stackexchange.com/questions/18033",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/8823/"
] | I have a database with about 40-50 tables. All but 5 are part of a giant hierarchy of 1:M relationships that all point back to one solitary parent (call it "Project"). Each table is joined to its direct parent using a foreign key to the parent's primary key, which is an identity field. Some branches go as many as 6 ... | We do something similar with client id. Yes it can improve performance if you don't need to go through all those intervening tables in every query. However, and it's an important however, this is best done only if you are using a surrogate key that never changes. Otherwise a change of the project id could require a cas... | A cascading key structure would work well if you are interested in optimizing key access to the children, as the children will include the parent key. The cascading key would not be a denormalization. This also works well if you have a large amount of data and wish to partition on a high order key as now that high or... | https://dba.stackexchange.com |
9,902 | [
"https://dba.stackexchange.com/questions/9902",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/4846/"
] | I Have a table <code>articles</code> with following data
<pre><code>mysql> select * from articles;
+----+-----------------------+------------------------------------------+
| id | title | body |
+----+-----------------------+---------------------------------------... | It probably seems that <code>following</code> is in the <code>stop words</code> list.<br>
you should check the stop words to see is that the case.
| @John.Locke's answer hits the nail on the head. +1 on your answer.
@DTest's comment confirmed it. +1 on your comment.
Here is how to get around it:
Step 01) Create an empty stopword list
<pre><code>$ echo -n > /var/lib/mysql/stopwords.txt
</code></pre>
Optional : Make the stopword list have articles (no pun int... | https://dba.stackexchange.com |
297,102 | [
"https://softwareengineering.stackexchange.com/questions/297102",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/196326/"
] | I'm a volunteer for a non-profit organization and am helping them develop a free open source Android application that will be licensed under GPLv3.
We are going to use the logo and some other graphics files from the organization and are wanting to use licensing of this artistic work to protect ourselves from anyone do... | I have gotten help from FSF licensing and <strong>they suggest using the GPLv3 to license the art as well as the code</strong>.
After asking this question:
<blockquote>
i'm a volunteer for a non-profit organization and am helping them
develop a free open source Android app that i hope will be licensed
under GPL... | For copyright purposes, the code of an application and the resources (images, sounds, etc.) used by the application are considered to be separate works. This means that they can have completely separate license terms.<br>
For your Android app, you can license the code under GPLv3 and the logos under a non-free license ... | https://softwareengineering.stackexchange.com |
93,178 | [
"https://mathoverflow.net/questions/93178",
"https://mathoverflow.net",
"https://mathoverflow.net/users/21090/"
] | Jacobson's theorem states that
If $R$ is a ring, and for every $x\in R$, there exists $n(x)\geq 2$ such that $x^{n(x)}=x$. Then
$R$ is commutative.
I wonder if the following stronger assertion(in case $R$ has unity) is true.
Let $R$ be a ring with unity. For every $x$ in $R$, there exists $n(x)\geq 2$ such that
$x... | Yes, this is true.
By Jacobson's theorem, $R$ is commutative. Now the radical of $R$ is the intersection of all primes $P$ of $R$. Hence we have an embedding
$$\phi: R/rad(R) \to \prod_P R/P.$$
For each $x \in R/P, x \neq 0$ there is $n \ge 1$ such that $x(x^n-1)=0$ and since $R/P$ is a domain, $x^n =1$, i.e. $x$ is... | This is true. Let $R$ be a ring satisfying your property. Then $R$ has no nilpotent element since if $x^a=0$, then for $b$ an integer such that $n(x)^b > a$ we have $x=x^{n(x)^b}=0$.
So the radical of $R$ is $0$, and since the radical is the intersection of all
prime ideals of $R$, we see that the natural map $R \m... | https://mathoverflow.net |
161,797 | [
"https://electronics.stackexchange.com/questions/161797",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/70914/"
] | What is the mechanism by which Triodes in audio tube amps generate harmonic distortion?
It is my understanding that the distortion is generated by means of electron bunching. That is, when the grid voltage swings negative and is larger than the cathode voltage, it blocks off electron flow from the cathode to the anode... | All the effects you mention are much faster than relevant to audio signals, so have nothing to do with audio distortion.
The dynamic characteristic of a triode makes it look sortof like a variable resistor with a variable voltage offset once you get to some minimum current level. Both these are controlled by the grid... | When you're talking electron bunches and stuff, that's device physics, and it happens on a timescale much faster than audio signals. (Generally you have to get up to microwave frequencies to make use of collective electron effects.) However you are right that it does matter; the device physics explains why the 'macrosc... | https://electronics.stackexchange.com |
189,867 | [
"https://electronics.stackexchange.com/questions/189867",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/86205/"
] | Current flows through a conductor connecting points at different potentials.
Leaving aside multi-phase details, common/conventional AC systems use a 3-wire setup:
<ul>
<li>Wire-1: a line/live/hot/phase wire presenting a point that oscillates between 2 potentials.</li>
<li>Wire-2: a neutral wire presenting a point of ... | If wires were 100% reliable and had zero resistance, there would be no difference between the neutral (groundED conductor) and the safety ground (groundING conductor). Neither condition applies, however.
Even if the neutral-grounded and safety-grounding conductors are connected at the breaker panel, a current-drawing... | TL;DR:
The ground wire is a safety feature to keep you safe in case things aren't working right.
You have a neutral wire as a current conducting wire to provide power.
You have the ground wire as a safe ground point for equipment with conductive (metal) housings and as a safe short circuit path for current when thi... | https://electronics.stackexchange.com |
29,902 | [
"https://physics.stackexchange.com/questions/29902",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/9787/"
] | Why is the center-of-mass of 2 bodies (which interact only via Newtonian gravity) located at a focus of each of the elliptical orbits?
I know that when there are no external forces, the center of mass moves at a constant speed, but that doesn't explain it.
| I'm going to assume that Omer is specifically asking why the centre of mass is at the focus (well, one of the foci) of the orbits. Omer, if this isn't what you meant please ignore what follows because it's completely irrelevant!
If you have a body moving in a central field (i.e. the force is always pointing towards th... | This actually follows from Newton's laws (and it only holds true for an isolated system).
For simplicity we'll consider <em>an isolated system</em> of two bodies on a line. Call their masses $m_1$ and $m_2$ and put them at $x_1$ and $x_2$. Now computer their center of mass:
$$X = \frac{\sum_i m_i x_i}{\sum_i m_i} = \f... | https://physics.stackexchange.com |
9,575 | [
"https://electronics.stackexchange.com/questions/9575",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/2830/"
] | note and question
<pre><code>* Is it an alternator or dynamo?
</code></pre>
I am not an electrical engineer and neither have any core knowledge but, this is a simple procedure of car battery charging using a dynamo, which is present in all cars and bicycles. But what i don't understand is how can a battery be utilise... | In short, it can't. If the battery is being charged then current is flowing <em>into</em> it, so it can't be powering anything. It is the charger/dynamo/alternator that is powering the components whilst charging. In the case of a dynamo or alternator, if the output drops below the open-circuit terminal voltage of the b... | The battery is only being used when the alternator is not running. While the alternator is running (delivering power), the battery is essentially just another load like lights, radio, etc.
For most of the time, the alternator is just maintaining the battery charge and thus supply little actual current into the battery.... | https://electronics.stackexchange.com |
3,914,643 | [
"https://math.stackexchange.com/questions/3914643",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/449018/"
] | I have to solve the equation <span class="math-container">$\vec x\times\vec a=\vec b-\vec x$</span> , where <span class="math-container">$\vec x, \vec a,\vec b$</span> are vectors and the last two are known.
I have proven that <span class="math-container">$\vec a\cdot \vec x=\vec a\cdot\vec b$</span>, but that is al... | You wrote as if <span class="math-container">$B$</span> is the finite-dimensional one, so I'll stick with that.
Let <span class="math-container">$\gamma$</span> be a C<span class="math-container">$^*$</span>-norm on <span class="math-container">$A\otimes M_n(\mathbb C)$</span> (one certainly exists, because we can repr... | The point is that <span class="math-container">$A \odot B$</span> is closed in <span class="math-container">$A \otimes B$</span>. To see this, choose a basis <span class="math-container">$\{e_i\}_{i=1}^n$</span> for <span class="math-container">$A$</span> and suppose that <span class="math-container">$\{x_k\}_{k=1}^\in... | https://math.stackexchange.com |
671,253 | [
"https://physics.stackexchange.com/questions/671253",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/102243/"
] | In nearly every webpage that I read on the topic, it is recommended to not let a house cool down over the day (even if nobody is there), but to instead keep a constant temperature.
This is reasoned by the sentence "It takes more energy to heat up the house again, than you would save by not heating it for a certain... | <strong>Spherical horse in vacuum</strong><br />
The obvious answer that constant heat losses exceed the energy expenditure for warming up the house from a lower temperature is based on many simplifying assumptions that <em>may or may not</em> hold in real life - depending on the climate (typical temperatures, huminity... | It is incorrect indeed. The house is losing heat at a rate <span class="math-container">$\dot q = k(T_i-T_o)$</span>, in a simplified point of view, so the higher the difference between inner and outer temperature the higher the heating cost. From this point of view it is better to keep it at a lower temperature. As lo... | https://physics.stackexchange.com |
120,844 | [
"https://electronics.stackexchange.com/questions/120844",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/28592/"
] | Say I have a very simple program that functions perfectly fine on a ARM Cortex M0+ processor. How much will I need to change in order for it to work on an ARM Cortex M4 processor, assuming they are both made by the same company and I have imported the new cores header.
I just can't think of any reason it wouldn't wor... | The CPU should not give you any problems, as you say the instruction set of an M4 is a superset of the M0/M0+ instruction set. Note that the timing might be different, so busy-wait based timing might not work the same.
Peripherals can be a PITA, I would not assume they are the same unless the datasheets read the same.... | If your software is in ASM/compiled format it will work (as Cortex M4 is superset of Cortex M0), but it will be suboptimal.
If your software is in C/C++ (essentially it can be recompiled), you will have to choose:
<ul>
<li>compile for M0 (and do not use more powerful instructions),</li>
<li>compile for M4 and ensure ... | https://electronics.stackexchange.com |
145,746 | [
"https://stats.stackexchange.com/questions/145746",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/72711/"
] | I am familiar with the basics of how to present a problem to a machine learning algorithm using binary encodings. I am also familiar with, but still learning about, feature selection/extraction and construction. However, <strong>I am wondering if there is a term or keyword for the way in which you deicde to encode your... | As far as I can tell from the comments on the original post, analyzing a 2 x 2 contingency table doesn't make sense for these data. Instead you would want to compare the count of <em>c1</em> out of the total observed count, and compare that to 0.10.
You might use an exact binomial test or a chi-square test goodness... | As far as I know you can use chi-square throughout, unless the expected counts are less than five in which case you can use Fisher's exact test. I'm not sure but I think Fisher's Exact Test is slightly more conservative in its resulting p-value, i.e., it's slightly less likely to show statistical significance (but I'm... | https://stats.stackexchange.com |
42,994 | [
"https://cs.stackexchange.com/questions/42994",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/9670/"
] | In Constraint programming we have Variables and their Domains and then all the constraints, but if you at the concept of a domain of a variable it is nothing but another type of constraint, you are saying that this variable can take all these values.
Is there any particular reason why domain is defined as a different c... | As you observe, restricting the domain of a variable has exactly the same effect as applying a unary constraint to it.
One situation where you might prefer to use unary constraints rather than restricted domains is when you want to control very tightly the relations that are allowed to be used in constraints. For exam... | Even though a domain may be considered just another type of constraint, there do exist good reasons to keep them separated, and it may be easier to think of them from a pure mathematical standpoint. Domains should in a sense be seen as the definition of the variable in terms of Type - e.g. Integer or Real etcetera. The... | https://cs.stackexchange.com |
436,729 | [
"https://physics.stackexchange.com/questions/436729",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/209226/"
] | In thermal energy transfer, why does the total combined energy of all particles remain constant?
| Your result is correct. You have a function <span class="math-container">$\psi(x)$</span> whose mean is <span class="math-container">$x_0$</span>. So the function <span class="math-container">$\psi(x+x_0)$</span> is the original function shifted by an amount <span class="math-container">$|x_0|$</span> towards <span cla... | If you have an integral over the interval <span class="math-container">$[-\infty, \infty]$</span>, yes, that's correct.
The wave function <span class="math-container">$\psi'$</span> is simply displaced by <span class="math-container">$-x_0$</span>, so the Position expectation value does Change exactly this amount. For... | https://physics.stackexchange.com |
175,789 | [
"https://softwareengineering.stackexchange.com/questions/175789",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/70219/"
] | So here's the confusion, let's say I declare an array of characters
<pre><code>char name[3] = "Sam";
</code></pre>
and then I declare another array but this time using pointers
<pre><code>char * name = "Sam";
</code></pre>
What's the difference between the two? I mean they work the same way in a program. Also how ... | The first option only consumes the necessary space in memory for a 3 char string + the termination character.
EDIT: Thanks for pointing that out in the comments. This option will actually give out an error because you only have 3 positions to fill, meaning there is no space for the termination character.
The second o... | <ol>
<li><code>char name[3] = "Sam";</code><br>
define an array named "name" (of course, you can use <code>name[]</code> rather than <code>[3]</code>), and<br>
<code>name[0] = 'S', name[1] = 'a', name[2] = 'm', name[3] = '\0';</code></li>
<li><code>char * name = "Sam";</code><br>
define a pointer pointed to the address... | https://softwareengineering.stackexchange.com |
170,500 | [
"https://softwareengineering.stackexchange.com/questions/170500",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/51940/"
] | What is the difference of delegator and dispatcher?
I am not quite sure of either concept.
| Delegation is assigning a responsibility to some other object. For example, if I am invited to a meeting and I assign it to a junior colleague, I am delegating. The point to note here is that it is the junior colleague who will attend the meeting and there is no intermediary between him and me.
Dispatching is not del... | <strong>Dispatcher</strong>
<ul>
<li>The dispatcher can be considered as a <strong>Queue</strong> where the events are sent. </li>
<li>A dispatcher runs on the <strong>UI thread</strong> and executes events for the UI. </li>
<li>In windows, <strong>UI controls may only be modified by the thread that created t... | https://softwareengineering.stackexchange.com |
695,887 | [
"https://physics.stackexchange.com/questions/695887",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/318925/"
] | There are huge tidal forces at work around a black hole. But the larger the hole, the smaller the tidal effects near the horizon. So the differences between nearby local forces is small.
What about the force itself? How strong must a rocket be to stay just above the horizon? The horizon grows linearly with M, the mass ... | <blockquote>
Is there a formula that relates the force we need to let a rocket stay stationary above its horizon?
</blockquote>
Yes. The gravitational acceleration is given by
<span class="math-container">$a = \frac{G\cdot M}{r^2 \cdot \sqrt{1-r_s/r}}$</span>
which means that the force you are mentioning approaches inf... | The force required to hover at radius <span class="math-container">$r$</span> goes to infinity as <span class="math-container">$r$</span> approaches the Schwarzschild radius
| https://physics.stackexchange.com |
42,875 | [
"https://dsp.stackexchange.com/questions/42875",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/30099/"
] | I am aware of applying edge detector on rb images by first converting rgb2gray...In my work i need output of edge detector in RGB and not in grayscale....Is there any way to get output in RGB.?
| Perform the edge detection channel wise and then add up the individual output.
<pre><code>im0 = imread(filename);
imR = im0(:,:,1);
imG = im0(:,:,2);
imB = im0(:,:,3);
%DO YOUR DETECTION HERE
res=im0;
res(:,:,1)=resR; %putting R resultant in result image
res(:,:,2)=resG; %putting G resultant in result image
re... | As suggested, do edge detection (whichever algorithm) on different channels separately, and merge then together to get back the RGB. That could be a solution.
| https://dsp.stackexchange.com |
42,404 | [
"https://mathoverflow.net/questions/42404",
"https://mathoverflow.net",
"https://mathoverflow.net/users/2672/"
] | Assuming that one needs $k$ quantifiers to express that a graph contains an $k$-cycle, $\lfloor n/2 \rfloor$ counting quantifiers suffice to express that a graph is an $n$-cycle:
<em>G has exactly $n$ nodes, each node has exactly 2 neighbors, and G doesn't contain a 3-cycle, a 4-cycle, ... and an $\lfloor n/2 \rfloor$... | The previous answer showed that quantifier rank $\log_2(k) \pm 1$ is sufficient and necessary for expressing "A is a $k$-cycle". This implies a lower bound of at least $\log_2(k)$ quantifiers, but not an upper bound since quantifier rank counts nesting-depth of quantifiers and not the number of quantifiers. However, it... | If A and B are cycles of length m, n, then the duplicator can win the k-long Ehrenfeucht-Fraisse game iff m, n > 2^(k-1).
Basically, whatever player I moves in A, player II choose an arbitrary element in B. The rest of the strategy is the same as for linear orders.
This means that A and B are elementarily equivalent ... | https://mathoverflow.net |
78,963 | [
"https://dba.stackexchange.com/questions/78963",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/49120/"
] | This is my current structure of my matches table:
<pre><code>id, title, description, max_players, host_username, host_ip
</code></pre>
and there's another table called matches_players:
<pre><code>match_id, player_username
</code></pre>
This requires two queries to get the matches list and the player count of each o... | WAMPServer is primarily designed for use on a single machine i.e. a developer writing and testing code locally on that PC.
So to protect the beginner from his/her self the Apache & MySQL configuration by default is setup so no access can be made to the Apache or MySQL server form anywhere but the PC running Apache... | If you are access PHPMyAdmin from another LAN location then the Apache server needs to be able and willing to accept connections from other than localhost. This will probably mean simply ensuring that the port (80 by default) is open to the LAN and that Apache is likewise willing to serve to remote addresses (which I w... | https://dba.stackexchange.com |
94,697 | [
"https://stats.stackexchange.com/questions/94697",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/44261/"
] | The 'conventional' configuration of RBMs are Binary-Binary and Gaussian-Binary (and sometimes Binary-Gaussian) units.
Although it is possible for both the visible and hidden units to be gaussian, wouldn't a Gaussian-Gaussian RBM just resemble a linear model, since there is no non-linearity in the networks units anymor... | First, notice that you can fix the variance of the hidden units to 1, since the weight matrix will scale them arbitrarily.
Then:
<ul>
<li>If you learn the variance of each visible unit, you get factor analysis</li>
<li>If the variance of the visible units is tied, you get is PPCA (of the demeaned data)</li>
<li>If yo... | Yes, with just the means (without the covariances) being transmitted, it is a linear model. Gaussian nodes are useful when representing Gaussian inputs. I don't think they are useful as latent variables.
| https://stats.stackexchange.com |
102,235 | [
"https://datascience.stackexchange.com/questions/102235",
"https://datascience.stackexchange.com",
"https://datascience.stackexchange.com/users/115551/"
] | So I have the task of classifying sentences based on their level of 'change talk' shown. Change talk is a psychology term used in counseling sessions to express how much the client wants to change their behavior.
So let's say there are two classes: change talk; and non-change talk.
An example of change talk is: "I... | Your problem as you said is a high level of syntax overlapping between your sentences. take a look at these two sentences:
Work to live versus live to work. The earlier that you can allow yourself to enjoy other things in life, aside from your job while the latter means obtaining resources so that you can be a function... | Often it is not clear at beginning of a project how difficult a task is and which elements will have biggest impact. One approach is to setup a machine learning system to systematically evaluate options and empirically explore the problem.
First setup the simplest possible text classification pipeline where the raw tex... | https://datascience.stackexchange.com |
548 | [
"https://dsp.stackexchange.com/questions/548",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/471/"
] | If I sample sound with a microphone and find the absolute square of the (non-normalized) DFT, I get the discrete power spectrum (correct me if I'm wrong). Which unit does it have?
| This depends a little on how thorough you want to be. Your microphone measures pressure and not actual power. That means your time domain signal has the units of Pascal and the spectrum has Pascal squared per Hz. In order to turn that into Intensity you would have to normalize by the free field impedance of air which i... | Power is measured in Watts ($W$). For a power spectrum the indiviudal bins have units of $W / Hz$.
However unless you calibrate you microphone/ADC input and eliminate other scaling factors (e.g. window compensation, factor of N / 2 in your FFT, implicit scaling in integer sample values, etc) then there is an arbitrary... | https://dsp.stackexchange.com |
323,792 | [
"https://mathoverflow.net/questions/323792",
"https://mathoverflow.net",
"https://mathoverflow.net/users/124254/"
] | given polish space <span class="math-container">$(X,d)$</span>, consider weak* topology of probability. optimal transport of probability <span class="math-container">$u,v$</span> is defined by <span class="math-container">$\pi(u,v)$</span> such that <span class="math-container">$\pi(u,v)$</span> minimizes:
<span class... | Of course not! This is hopeless if <span class="math-container">$X$</span> has unbounded diameter.
As a counterexample, consider <span class="math-container">$X=\mathbb Z$</span> with the standard metric; <span class="math-container">$\mu_k=(1-\frac 1k)\delta_0+\frac 1k\delta_k$</span>; and <span class="math-containe... | Anthony's example is based on the well-known fact that in the non-compact case the transportation distance does not actually metrize the weak topology unless one imposes additional moment conditions on the considered measures. However the actual point of this question is, in my opinion, that, to begin with, "the" optim... | https://mathoverflow.net |
80,742 | [
"https://dba.stackexchange.com/questions/80742",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/7169/"
] | I'm trying to start the server and then fix the root user by
<pre><code>$ mysql -u root mysql
$mysql> UPDATE user SET Password=PASSWORD('my_password') where USER='root';
$mysql> FLUSH PRIVILEGES;
</code></pre>
But the server can't be started:
<pre><code>$ mysqld --skip-grant-tables
2014-10-21 07:18:24 0 [Warni... | The entire folder should be owned by mysql
<pre><code>cd /usr/local/mysql-5.6.21-osx10.8-x86_64/data/
chown -R mysql:mysql *
</code></pre>
Then go restart mysql
Give it a Try !!!
| I find another reason for the same error. I use homebrew to install mysql.
The server could not be stopped by simply use the command:
<pre><code>mysql.server stop
</code></pre>
The mysql process will automatically restart. The only way to stop that is using this command:
<pre><code>brew services stop mysql
</code><... | https://dba.stackexchange.com |
16,273 | [
"https://chemistry.stackexchange.com/questions/16273",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/5084/"
] | I am told that para-dichlorobenzene exhibits <em>two</em> proton NMR <em>signals</em>. This doesn't jibe with me; all the protons on the molecule are equivalent. Here is a book claiming the same thing. Am I wrong, or is the person who told me that para-dichlorobenzene has two signals on its proton NMR wrong?
<img src... | Be very careful with how you interpret this molecule. Although the 1H NMR spectrum appears as a single line, this is actually an AA'A''A''' system, meaning that, although chemically equivalent, all four protons are magnetically non-equivalent, but have coincidental chemical shift. The coupling between all protons is d... | P-dichlorobenzene only has 1 type of H (check the symmetry) and thus appears as a singlet in the HNMR.
However, it is not an AA'A"A"' system as another responder implies, it is an A4 system because there is only 1 type of nuclei in the spin system.
| https://chemistry.stackexchange.com |
157,538 | [
"https://electronics.stackexchange.com/questions/157538",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/68854/"
] | I have a footprint file for a component (.mod). There doesn't seem to be an option to import it though. How to do it?
<img src="https://i.stack.imgur.com/hiHEZ.png" alt="">
Also the left-hand menu here doesn't seem to do anything.
<img src="https://i.stack.imgur.com/aZS4Z.png" alt="">
| You are in the right place when looking at the library table. Click Append Library and you get a new line in the table. Fill out the table with the location of your .mod file in the Library Path and make the Plugin Type = Legacy. Click OK
If you want to save changes to a library, you have to save it as a .pretty w... | Open CvPCB and Click on Preference->Option. This should show a window to import custom MOD file. Select your file and save the project.
P.S. remember to remove the Footprint filter if you don't see your footprints.
Screenshot of the process attached.
<img src="https://i.stack.imgur.com/3DJMo.jpg" alt="Step 1">
<i... | https://electronics.stackexchange.com |
480,420 | [
"https://physics.stackexchange.com/questions/480420",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/237684/"
] | I am currently in high-school, currently working on a physics research on the normalization of the Schrodinger's equation. I was quite interested on how we can mathematically explain preservation of the SE's normalization with the evolution of time. I was wondering if anyone can help me understand the physical and math... | Special relativity addresses the null result of the Michelson-Morley experiment, which failed to measure motion relative to an assumed ether.
I wouldn't say time is moving at all. Rather, measured time and space intervals collected by pairs of observers will only match if their is no relative uniform motion between... | Instead of trying to sort out the details, I'll offer a perspective that can help the details fall into place:
<ul>
<li>In general relativity (GR), the geometry of spacetime is dynamic (reacts to its contents) and can therefore be curved.</li>
<li>In special relativity (SR), the geometry of spacetime is neither dynami... | https://physics.stackexchange.com |
81,567 | [
"https://dsp.stackexchange.com/questions/81567",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/872/"
] | Of course this is not about converting an RGB to grayscale.
In most photo-editing software like Photoshop and Affinity etc, there is an option to go from a regular color photo to a black and white photo. Often this is done by a control like the image below that allows you to control the contribution of each color group... | You've already shown that the real part of <span class="math-container">$F(\omega)$</span> is zero. And the imaginary part is odd because <span class="math-container">$\sin(\omega t)$</span> is an odd function, i.e., <span class="math-container">$\sin(\omega t)=-\sin(-\omega t)$</span>. Done.
You should also know that ... | A suggestion that is helpful for such parity (even, odd) properties is to remember that every function <span class="math-container">$f(t)$</span> can be decomposed into an even and an odd part:
<span class="math-container">$$ h(t) = \frac{1}{2}\left(h(t)+h(-t)\right) + \frac{1}{2}\left(h(t)-h(-t)\right)$$</span>
Simply... | https://dsp.stackexchange.com |
337,608 | [
"https://stats.stackexchange.com/questions/337608",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/191014/"
] | Is stochastic gradient descent basically the name given to mini-batch training where batch size = 1 and selecting random training rows? i.e. it is the same as 'normal' gradient descent, it's just the manner in which the training data is supplied that makes the difference?
One thing that confuses me is I've seen people... | Standard gradient descent and batch gradient descent were originally used to describe taking the gradient over all data points, and by some definitions, mini-batch corresponds to taking a small number of data points (the mini-batch size) to approximate the gradient in each iteration. Then officially, stochastic gradien... | <blockquote>
Is stochastic gradient descent basically the name given to mini-batch
training where batch size = 1 and selecting random training rows?
</blockquote>
Yes. Though shuffling the rows isn't necessarily implied.
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19,768 | [
"https://datascience.stackexchange.com/questions/19768",
"https://datascience.stackexchange.com",
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] | I am trying to implement Python's <strong><em>MLPClassifier</em></strong> with <strong><em>10 fold</em></strong> cross-validation using <strong><em>gridsearchCV</em></strong> function. Here is a chunk of my code:
<pre><code>parameters={
'learning_rate': ["constant", "invscaling", "adaptive"],
'hidden_layer_sizes': [(1... | A tuple of the form $(i_1, i_2, i_3, ... , i_n)$ gives you a network with $n$ hidden layers, where $i_k$ gives you the number of neurons in the $k$th hidden layer.
If you want three hidden layers with $10,30$ and $20$ neurons, your tuple would need to look like $(10,30,20)$.
$(100,1)$ would mean that the second hidd... | You can implement MLPClassifier with GridSearchCV in scikit-learn as follows (other parameters are also available):
<pre><code>GRID = [
{'scaler': [StandardScaler()],
'estimator': [MLPClassifier(random_state=RANDOM_SEED)],
'estimator__solver': ['adam'],
'estimator__learning_rate_init': [0.0001],
... | https://datascience.stackexchange.com |
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