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Added some solutions #10
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ignored built files in .gitignore
added myself as second author
Third exercise of second chapter
Thank you! I might not get around to this until the weekend, but in any case the contribution is very much appreciated. |
I'm finally returning to this project. Yay. Should have this merged soon. |
main.out | ||
main.pdf | ||
main.synctex.gz | ||
main.toc |
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FWIW I set my latex system to put built files in a build/
directory (hence the top line of this file). No problem adding the other lines too, for folks who build in-place.
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Thanks, this is great. There are a couple of little punctuation errors. If you can fix them up I'll merge this.
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Calculate $Q_s$ for the given recipe of construction of a random set of dots | ||
\levelstay{Solution} | ||
We need to find a description of a sequence of random events at $\tau_1$, $\tau_2$, ... in terms of the probability distribution $Q_s$ using the probability $w$. The $w$ probability is the simplest description of correlated random events : the new arrival is dependent on the timing from the previous arrival and both arrivals are governed by the same probability function $w$. We may as well represent this situation by having $s$ replicas of the system and reporting the first random events in each of these systems.Such first event would be governed by a probability $w$. We can write $Q_s$ as a probability of events that are independent of one another in each of these systems. |
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There are a few punctuation errors here, i.e. a space missing at the end of a sentence, etc.
chapter2/Mean_square_N_interval.tex
Outdated
& \Leftrightarrow \int_{t_a}^{t_b}\left[d\tau_1\int_{t_a}^{t_b}d\tau_2\int_{-\infty}^{\infty}Q_s(\tau_1,\tau_2,...,\tau_s)d\tau_3...d\tau_s\right] \\ | ||
\end{split} | ||
\end{equation} | ||
in the end we can rewrite $\langle N^2 \rangle$ |
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Capitalize beginning of new sentence?
& P(\tau_2)= \int_{0}^{\tau_2}w(\tau_2-\tau_1)d\tau_1\\ | ||
& P(\tau_3)= \int_{0}^{\tau_3}w(\tau_3-\tau_2)d\tau_2\\ | ||
& ... \\ | ||
& P(\tau_s)= \int_{0}^{\tau_s}w(\tau_s-\tau_{s-1})d\tau_{s-1}\\ |
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Just FYI, in TeX you can do, for example, \int_0^\infty
, i.e. you don't need braces in superscripts and subscripts if there's only one symbol.
Hi,
No problem, I'll fix this after work today. And thanks for the feedback.
…--
Thomas
--
Thomas
2017-03-06 9:39 GMT+01:00 Daniel Sank <notifications@github.com>:
***@***.**** requested changes on this pull request.
Thanks, this is great. There are a couple of little punctuation errors. If
you can fix them up I'll merge this.
------------------------------
In chapter2/Description_sequence_random_events.tex
<#10 (comment)>
:
> @@ -0,0 +1,24 @@
+\leveldown{Description of a sequence of random events - pg. 32}
+
+\leveldown{Problem}
+
+Calculate $Q_s$ for the given recipe of construction of a random set of dots
+\levelstay{Solution}
+We need to find a description of a sequence of random events at $\tau_1$, $\tau_2$, ... in terms of the probability distribution $Q_s$ using the probability $w$. The $w$ probability is the simplest description of correlated random events : the new arrival is dependent on the timing from the previous arrival and both arrivals are governed by the same probability function $w$. We may as well represent this situation by having $s$ replicas of the system and reporting the first random events in each of these systems.Such first event would be governed by a probability $w$. We can write $Q_s$ as a probability of events that are independent of one another in each of these systems.
There are a few punctuation errors here, i.e. a space missing at the end
of a sentence, etc.
------------------------------
In chapter2/Mean_square_N_interval.tex
<#10 (comment)>
:
> +\begin{equation}
+\begin{split}
+& \int_{-\infty}^{\infty}\chi^2(\tau_i)Q_s(\tau_1,\tau_2,...,\tau_i,...,\tau_s)d\tau_1d\tau_2...d\tau_s\\
+& \Leftrightarrow \int_{-\infty}^{\infty}\chi^2(\tau_i)Q_s(\tau_i,\tau_2,...,\tau_1,...,\tau_s)d\tau_1d\tau_2...d\tau_s \\
+& \Leftrightarrow \int_{-\infty}^{\infty}\chi^2(\tau_1)Q_s(\tau_1,\tau_2,...,\tau_i,...,\tau_s)d\tau_id\tau_2...d\tau_1...d\tau_s \\
+& \Leftrightarrow\int_{t_a}^{t_b}\left[d\tau_1 \int_{-\infty}^{\infty}Q_s(\tau_1,...,\tau_s)d\tau_2...d\tau_s \right]
+\end{split}
+\end{equation}
+in the same fashion we can transform the expression $(b)$ getting the following result
+\begin{equation}
+\begin{split}
+& \int_{-\infty}^{\infty}\chi(\tau_i)\chi(\tau_j)Q_s(\tau_1,\tau_2,...,\tau_s)d\tau_1d\tau_2...d\tau_s \\
+& \Leftrightarrow \int_{t_a}^{t_b}\left[d\tau_1\int_{t_a}^{t_b}d\tau_2\int_{-\infty}^{\infty}Q_s(\tau_1,\tau_2,...,\tau_s)d\tau_3...d\tau_s\right] \\
+\end{split}
+\end{equation}
+in the end we can rewrite $\langle N^2 \rangle$
Capitalize beginning of new sentence?
------------------------------
In chapter2/Description_sequence_random_events.tex
<#10 (comment)>
:
> +\leveldown{Problem}
+
+Calculate $Q_s$ for the given recipe of construction of a random set of dots
+\levelstay{Solution}
+We need to find a description of a sequence of random events at $\tau_1$, $\tau_2$, ... in terms of the probability distribution $Q_s$ using the probability $w$. The $w$ probability is the simplest description of correlated random events : the new arrival is dependent on the timing from the previous arrival and both arrivals are governed by the same probability function $w$. We may as well represent this situation by having $s$ replicas of the system and reporting the first random events in each of these systems.Such first event would be governed by a probability $w$. We can write $Q_s$ as a probability of events that are independent of one another in each of these systems.
+\begin{equation}
+Q_s(\tau_1, \tau_2,...,\tau_s)=P(\tau_1)P(\tau_2)...P(\tau_s)
+\end{equation}
+Thus we have
+\begin{equation}
+\begin{split}
+& P(\tau_1)= w(\tau_1) \\
+& P(\tau_2)= \int_{0}^{\tau_2}w(\tau_2-\tau_1)d\tau_1\\
+& P(\tau_3)= \int_{0}^{\tau_3}w(\tau_3-\tau_2)d\tau_2\\
+& ... \\
+& P(\tau_s)= \int_{0}^{\tau_s}w(\tau_s-\tau_{s-1})d\tau_{s-1}\\
Just FYI, in TeX you can do, for example, \int_0^\infty, i.e. you don't
need braces in superscripts and subscripts if there's only one symbol.
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<#10 (review)>,
or mute the thread
<https://github.com/notifications/unsubscribe-auth/AD1Tokr079lGvTq6WnyQVuBmyWWzlVKhks5ri8YogaJpZM4LkA2e>
.
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I made some changes as you asked. Is it okay now ? sorry for the time it took me to get to this, I had some unexpected last minutes things that came up. |
Woah, I'm sorry I forgot about this. I'll try to look at it this weekend. |
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