diff --git a/Lectures_my/MC_2016/Lecture10/images/boundary.png b/Lectures_my/MC_2016/Lecture10/images/boundary.png new file mode 100644 index 0000000..5959d91 --- /dev/null +++ b/Lectures_my/MC_2016/Lecture10/images/boundary.png Binary files differ diff --git a/Lectures_my/MC_2016/Lecture10/images/muller.png b/Lectures_my/MC_2016/Lecture10/images/muller.png new file mode 100644 index 0000000..4ab0057 --- /dev/null +++ b/Lectures_my/MC_2016/Lecture10/images/muller.png Binary files differ diff --git a/Lectures_my/MC_2016/Lecture10/mchrzasz.log b/Lectures_my/MC_2016/Lecture10/mchrzasz.log index 81f1303..76075de 100644 --- a/Lectures_my/MC_2016/Lecture10/mchrzasz.log +++ b/Lectures_my/MC_2016/Lecture10/mchrzasz.log @@ -1,4 +1,4 @@ -This is XeTeX, Version 3.1415926-2.5-0.9999.3 (TeX Live 2013/Debian) (format=xelatex 2015.4.1) 11 MAY 2016 19:45 +This is XeTeX, Version 3.1415926-2.5-0.9999.3 (TeX Live 2013/Debian) (format=xelatex 2015.4.1) 27 MAY 2016 09:47 entering extended mode restricted \write18 enabled. %&-line parsing enabled. @@ -3252,7 +3252,7 @@ Here is how much of TeX's memory you used: 50454 strings out of 493918 990095 string characters out of 6150564 - 1348134 words of memory out of 5000000 + 1349134 words of memory out of 5000000 52716 multiletter control sequences out of 15000+600000 37200 words of font info for 150 fonts, out of 8000000 for 9000 1144 hyphenation exceptions out of 8191 diff --git a/Lectures_my/MC_2016/Lecture10/mchrzasz.pdf b/Lectures_my/MC_2016/Lecture10/mchrzasz.pdf index 007e25d..d3808a7 100644 --- a/Lectures_my/MC_2016/Lecture10/mchrzasz.pdf +++ b/Lectures_my/MC_2016/Lecture10/mchrzasz.pdf Binary files differ diff --git a/Lectures_my/MC_2016/Lecture10/mchrzasz.synctex.gz b/Lectures_my/MC_2016/Lecture10/mchrzasz.synctex.gz index 2b66ff0..feecc3b 100644 --- a/Lectures_my/MC_2016/Lecture10/mchrzasz.synctex.gz +++ b/Lectures_my/MC_2016/Lecture10/mchrzasz.synctex.gz Binary files differ diff --git a/Lectures_my/MC_2016/Lecture10/mchrzasz.tex b/Lectures_my/MC_2016/Lecture10/mchrzasz.tex index 79c8808..3a21e5d 100644 --- a/Lectures_my/MC_2016/Lecture10/mchrzasz.tex +++ b/Lectures_my/MC_2016/Lecture10/mchrzasz.tex @@ -294,7 +294,7 @@ \label{eq1} \end{align} \begin{align} -\pi_{\nu}=\frac{1}{2k} \sum^{ \prime} \pi_{\nu}(x_1\prime,x_2\prime,...,x_k\prime) +\pi_{\nu}=\frac{1}{2k} \sum^{ \prime} \pi_{\nu-1}(x_1\prime,x_2\prime,...,x_k\prime) \label{eq2} \end{align} @@ -319,7 +319,7 @@ \end{align*} one gets: \begin{align*} -\kappa(x_1,x_2,...,x_k)=\frac{1}{2k}\sum_{\nu=1}^{\infty} \left[ \nu \sum^{\prime}\pi_{\nu -1 }(x_1,x_2,...,x_k) \right]\\ = \frac{1}{2k} \sum_{\nu =1 }^{\infty} \left[ (\nu-1)\sum^{\prime} \pi_{\nu-1}(x_1\prime,x_2\prime,...,x_k\prime) \right] + \frac{1}{2k} \sum_{\nu=1}^{\infty} \sum^{\prime} \pi_{\nu-1}x_1\prime,x_2\prime,...,x_k\prime) +\kappa(x_1,x_2,...,x_k)=\frac{1}{2k}\sum_{\nu=1}^{\infty} \left[ \nu \sum^{\prime}\pi_{\nu -1 }(x_1\prime,x_2\prime,...,x_k\prime) \right]\\ = \frac{1}{2k} \sum_{\nu =1 }^{\infty} \left[ (\nu-1)\sum^{\prime} \pi_{\nu-1}(x_1\prime,x_2\prime,...,x_k\prime) \right] + \frac{1}{2k} \sum_{\nu=1}^{\infty} \sum^{\prime} \pi_{\nu-1}(x_1\prime,x_2\prime,...,x_k\prime) \end{align*} \ARROW From which we get: \begin{align*} @@ -378,7 +378,7 @@ u(x,y) & =\frac{1}{4} \left[ u(x-1,y)+u(x+1,y)+u(x,y-1)+u(x,y+1) \right],~~(x,y) \in D \\ u(x,y) & =f(x,y),~~~(x,y) \in \Gamma(D) \end{align*} -\ARROW Now we can order the grid ($(x,y) \in D \cup D$), we can represente the above equations as a linear system: +\ARROW Now we can order the grid ($(x,y) \in D \cup \Gamma(D)$), we can represente the above equations as a linear system: \begin{align*} u_i=a_i+\sum_{j=1}^n h_{i j}u_j, ~~~~i=1,2,....,n \end{align*} @@ -416,9 +416,9 @@ &-u_1/4 & u_2 & -u_3/4 & & -u_5/4 & & & = (f_2)/4\\ & & -u_2/4 & ~~~~u_3 & & & -u_6/4 & & = (f_3+f_4)/4\\ &-u_1/4 & & & u_4 & -u_5/4 & & & = (f_8+f_9)/4\\ -&-u_1 /4 & & & -u_4/4 &~~~~ u_5 & -u_6/4 & -u_7/4 & = 0\\ +& & -u_2 /4& & -u_4/4 &~~~~ u_5 & -u_6/4 & -u_7/4 & = 0\\ & & & -u_3/4 & & -u_5/4 & u_6 & & = (f_5+f_6)/4\\ -& & & & & -u_5/4 & &~~~~~ u_7 & = (f_5+f_6)/4 +& & & & & -u_5/4 & &~~~~~ u_7 & = (f_6+f_7 + f_8)/4 \end{align*} \end{tiny} diff --git a/Lectures_my/MC_2016/Lecture11/mchrzasz.aux b/Lectures_my/MC_2016/Lecture11/mchrzasz.aux index c0c72c0..d208499 100644 --- a/Lectures_my/MC_2016/Lecture11/mchrzasz.aux +++ b/Lectures_my/MC_2016/Lecture11/mchrzasz.aux @@ -145,8 +145,14 @@ \@writefile{nav}{\headcommand {\beamer@framepages {19}{19}}} \pgfsyspdfmark {pgfid60}{0}{0} \pgfsyspdfmark {pgfid61}{0}{0} -\@writefile{nav}{\headcommand {\beamer@partpages {1}{19}}} -\@writefile{nav}{\headcommand {\beamer@subsectionpages {1}{19}}} -\@writefile{nav}{\headcommand {\beamer@sectionpages {1}{19}}} -\@writefile{nav}{\headcommand {\beamer@documentpages {19}}} -\@writefile{nav}{\headcommand {\def \inserttotalframenumber {18}}} +\HyPL@Entry{19<>} +\pgfsyspdfmark {pgfid62}{23867907}{17900937} +\@writefile{nav}{\headcommand {\slideentry {0}{0}{20}{20/20}{}{0}}} +\@writefile{nav}{\headcommand {\beamer@framepages {20}{20}}} +\pgfsyspdfmark {pgfid63}{0}{0} +\pgfsyspdfmark {pgfid64}{0}{0} +\@writefile{nav}{\headcommand {\beamer@partpages {1}{20}}} +\@writefile{nav}{\headcommand {\beamer@subsectionpages {1}{20}}} +\@writefile{nav}{\headcommand {\beamer@sectionpages {1}{20}}} +\@writefile{nav}{\headcommand {\beamer@documentpages {20}}} +\@writefile{nav}{\headcommand {\def \inserttotalframenumber {19}}} diff --git a/Lectures_my/MC_2016/Lecture11/mchrzasz.log b/Lectures_my/MC_2016/Lecture11/mchrzasz.log index e3daed7..7edea16 100644 --- a/Lectures_my/MC_2016/Lecture11/mchrzasz.log +++ b/Lectures_my/MC_2016/Lecture11/mchrzasz.log @@ -1,4 +1,4 @@ -This is XeTeX, Version 3.1415926-2.5-0.9999.3 (TeX Live 2013/Debian) (format=xelatex 2015.4.1) 25 MAY 2016 19:19 +This is XeTeX, Version 3.1415926-2.5-0.9999.3 (TeX Live 2013/Debian) (format=xelatex 2015.4.1) 26 MAY 2016 10:13 entering extended mode restricted \write18 enabled. %&-line parsing enabled. @@ -3050,11 +3050,8 @@ [14 ] -Overfull \vbox (6.34827pt too high) detected at line 671 - 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The problem is to find the shortest way. +\item For large $n$ the problem can't be solver by brutal force as the complexity of the problem is $(n-1)!$ +\item There exist simplified numerical solutions assuming factorizations. Unfortunately even those require anonymous computing power. +\item Can MC help? YES :) +\item The minimum distance $l$ has to depend on 2 factors: $P$ the area of the city the Salesman is travelling and the density of places he wants to visit: $\dfrac{n}{P}$ +\item Form this we can assume: +\end{itemize} +\begin{equation} +l \sim P^a (\dfrac{n}{P})^b=P^{a-b}n^b. \nonumber +\end{equation} + +\end{frame} + + \begin{frame}\frametitle{Traveling Salesman Problem} \begin{itemize} \item From dimension analysis: diff --git a/Lectures_my/MC_2016/Lecture7/mchrzasz.synctex.gz b/Lectures_my/MC_2016/Lecture7/mchrzasz.synctex.gz new file mode 100644 index 0000000..f526e2c --- /dev/null +++ b/Lectures_my/MC_2016/Lecture7/mchrzasz.synctex.gz Binary files differ diff --git a/Lectures_my/MC_2016/Lecture8/images/walk.png b/Lectures_my/MC_2016/Lecture8/images/walk.png new file mode 100644 index 0000000..bf43a3b --- /dev/null +++ b/Lectures_my/MC_2016/Lecture8/images/walk.png Binary files differ diff --git a/Lectures_my/MC_2016/Lecture8/mchrzasz.pdf b/Lectures_my/MC_2016/Lecture8/mchrzasz.pdf new file mode 100644 index 0000000..39938f8 --- /dev/null +++ b/Lectures_my/MC_2016/Lecture8/mchrzasz.pdf Binary files differ diff --git a/Lectures_my/MC_2016/Lecture8/mchrzasz.synctex.gz b/Lectures_my/MC_2016/Lecture8/mchrzasz.synctex.gz new file mode 100644 index 0000000..5a9c86f --- /dev/null +++ b/Lectures_my/MC_2016/Lecture8/mchrzasz.synctex.gz Binary files differ