keras categorical CNN prediction always output [[ 0. 0. 0. 0. 0. 0. 1. 0.]] No probability for other classes?
Keras - no prediction probability for multiple output models?
Show $x^p-t$ has no root in the field $\mathbb{F}_p(t)$ I don't think I fully understand.  Let's say there is a root $x_0 \in K=\mathbb{F}_p(t)$, where $p$ is a prime number.  Then $x_0 = \frac{P(t)}{Q(t)}$ for some polynomials $P,Q \in \mathbb{F}_p[t]$. We can assume $\gcd(P,Q)=1$  and $x_0^p-t= \frac{(P(t))^p}{(Q(t))^p}-t= \frac{P(t)^p-tQ(t)^p}{Q(t)^p} =0$, so coefficients of $P(t)^p, tQ(t)^p$ must be identical, which contradicts $\gcd(P,Q)=1$,   hence such $x_0$ does not exist and the polynomial has no root in $K$.   am I about right?    anyway, I would appreciate an explanation about $\mathbb{F}_p(t)$, what is $t$? what is the meaning of a variable which does not belong to any specific "world"? I cannot use $t$ as if it was a member of $\mathbb{F}_p$ and hence cannot assume $t^{p-1} = 1 \pmod p$... What is the best way to clean the sensor on a interchangeable lens camera (mirrorless or digital SLR)? Is there an efficient method of converting an integer into the written numbers, for example:  string Written = IntegerToWritten(21);   would return "Twenty One".  Is there any way of doing this that doesn't involve a massive look-up table? Prove that $n=\dfrac{5^{125}-1}{5^{25}-1}$ is a composite number   My attempt,  Let $x=5^{25}$, so that $5^{125}-1=x^5-1=(x-1)(x^4+x^3+x^2+x+1)$  $=(x^4+9x^2+1+6x^3+6x+2x^2-5x^3-10x^2-5x)(x-1)$  $=((x^2+3x+1)^2-5x(x+1)^2)(x-1)$  I'm stuck at this point and don't know how to continue anymore. Hope someone can provide a detailed solution. Thanks a lot. My boss gave me a task with completion date suppose 31 March, 2017and I completed on 28 February, 2017. Is it in time or before time. How often do publishers sue researchers for copyright infringement for putting their articles on a personal website? I know that some publishers sometimes send copyright infringement emails to researchers putting their articles on a personal website. How often do publishers actually sue researchers for copyright infringement for putting their articles on a personal website? (assuming the authors didn't have the legal right to do so)  I am mostly interested in United States-based authors, but I am curious about other countries as well. Meta duplicates don't require an answer. Don't suggest there is one when that's not true This request was sparked . The vote to close as a duplicate on meta, in contrast to the main site, does not require for the duplicate to have an answer. Yet, the closure message still says:     This question has been asked before and already has an answer.    ...even when this is not the case. Perhaps we should either only show this particular sentence if there is indeed an answer, or remove this altogether for meta.   Note: I fear this might be a duplicate request, but I was unable to find one. (Not even one without an answer :) ) When is the finalize() method called in Java? I have a command that I want to have run again automatically each time it terminates, so I ran something like this:  while [ 1 ]; do COMMAND; done;   but if I can't stop the loop with Ctrl-c as that just kills COMMAND and not the entire loop.  How would I achieve something similar but which I can stop without having to close the terminal? I want to compute the Galois group of some polynomials, but I want to see some examples first. For example this proposition could be helpful. I don't know how to prove it &lt;.&lt;  Let's consider a polynomial $f(x)= x^4+ax^2+b \in \mathbb{Z} $. Let $ \pm\alpha , \pm\beta$ denote the roots of $f(x)$. Note that $f$ is irreducible iff $\alpha^2, \alpha\pm\beta \notin \mathbb{Q}$. So let's suppose that $f(x)$ is irreducible. Let's denote $G$ the galois group of $f$ (the Galois group of the splitting field $\mathbb{Q}(\alpha,\beta)/\mathbb{Q}$)  $i)$ $G\cong V$ the Klein 4-group iff $\alpha\beta \in \mathbb{Q}$  $ii)$ $G\cong \mathbb{Z}_4$ iff $\mathbb{Q}(\alpha\beta)=\mathbb{Q}(\alpha^2)$  $iii)$ $G\cong D_8$ the dihedral group of order 8, iff $\alpha\beta \notin \mathbb{Q}(\alpha^2)$  I need help with the proofs of this propositions... Well I'm very lost with the computation of Galois group, some care must be exercised, I don't have it. For example I know that Galois group acts transitively, in the sense that $u\in K/F$ a galois extension, the other roots of the minimal polynomial of $m_u(x)\in F[x]$ are precisely the elements $ \sigma(u)$ , where $\sigma \in Gal(K/F)$. And clearly any automorphism, is determined by only the value of a basis. In this case we are working on $\mathbb{Q}(\alpha,\beta)$, so I have to know the values of both. But I have to respect the algebraic relations involving $\alpha , \beta$ I proved that in $i),ii)$ $\mathbb{Q}(\alpha,\beta) = \mathbb{Q}(\alpha) $ So I have to know the values on $\alpha$.   My first question is: If in both cases $i),ii)$, I have an extension of degree 4 (so $|G|=4$) I have to map $\alpha$ to determine the automorphism, but I have also to map $\alpha$ to all of it's four roots. Why the galois group in this case are different?  My second question is about $iii)$ I have no idea How to attack it. Is $G^{(X, Y)} = (G^X)^Y?$ ($A^B$ just means that $B$ is mapped to $A$) I have to prove that $$\lim_{n\to\infty} \left(1+n^2\right)^{\frac1n}$$ converges and give its limit. What I did was the following: $$\lim_{n\to\infty} \left(1+n^2\right)^\frac{1}{n} = \lim_{n\to\infty}(n^2)^{\frac1n}\lim_{n\to\infty}\left(\frac1{n^2} + 1\right)^\frac1n= \lim_{n\to\infty}(n^2)^{\frac1n}$$ Now that is where I am stuck - how to I continue with $\lim_{n\rightarrow\infty}(n^2)^{\frac{1}{n}}$? I really don't have any ideas left... Thank you very much! FunkyPeanut SQL - Query to get server's IP address How can I create my own Action using Photoshop? Can anyone guide me with a simple example? EL expressions not evaluated in JSP Ways to put numbered balls in boxes no box being empty I know the formula for putting $n$ identical balls in $r$ different boxes such that each box has at least 1 ball, but what is the formula for putting $n$ different balls in $r$ different boxes, no box being empty?  Thanks! PCB opaque coating for anti reverse engineering? Im trying to find a coating for my PCB in order to protect it from reverse engineering. I want it opaque, non-conductive and with a low thermal resistance.  Basically I do not want that someone replicates my circuit easily. I´ve beens searching a lot on coatings but did't find anything that suits to all my requirement. Anyone with an idea? How to remove "phone style" Gnome swipe to unlock I need to remove the annoying new "locking" screen that shows a giant clock: I can't remove it with just moving the mouse (as with any other desktop environment), the animation is slow, and it isn't asking me for a password!  I managed to disable it, just to discover that now I can't lock my screen on purpose, so I can't go away from the computer.  Just to clarify, I want to:   After some time the screen could go black, but if I move the mouse or press any key then I can use it directly (like a normal screensaver). If I press super-L then it is locked, and I must type the password to unlock (like a normal lock screen).   I found several "solutions", but none seems to work: Any group of index 2 is normal I'm trying to understand the proof that any group of index $2$ is normal.   Let $G$ be a group and $H$ a subgroup of index $2$.  I understand that if $x\in H$ then $xH=H=Hx$ since $H$ is a subgroup. However, I don't understand why if $x\in G\setminus H$ then $xH=G\setminus H.$  I know there are other proofs of this on this site but none of them specifically address this question. Freeze first column in SharePoint List View? I am working in SP2013 , in a particular list view  we want to freeze first column on horizontal scrolling.  Please help on this if any one having idea/code/any reference URLS.