diff --git a/Lectures_my/MC_2016/Lecture11/mchrzasz.log b/Lectures_my/MC_2016/Lecture11/mchrzasz.log index 7edea16..42fa3bd 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) 26 MAY 2016 10:13 +This is XeTeX, Version 3.1415926-2.5-0.9999.3 (TeX Live 2013/Debian) (format=xelatex 2015.4.1) 3 JUN 2016 11:29 entering extended mode restricted \write18 enabled. %&-line parsing enabled. @@ -2396,11 +2396,11 @@ ))) Package hyperref Warning: Token not allowed in a PDF string (Unicode): -(hyperref) removing `\fontspec' on input line 212. +(hyperref) removing `\fontspec' on input line 215. Package hyperref Warning: Token not allowed in a PDF string (Unicode): -(hyperref) removing `\fontspec' on input line 219. +(hyperref) removing `\fontspec' on input line 222. Package biblatex Info: Trying to load language 'english'... Package biblatex Info: ... file 'english.lbx' found. @@ -2420,40 +2420,40 @@ (./mchrzasz.aux) \openout1 = `mchrzasz.aux'. -LaTeX Font Info: Checking defaults for OML/cmm/m/it on input line 225. -LaTeX Font Info: ... okay on input line 225. -LaTeX Font Info: Checking defaults for T1/cmr/m/n on input line 225. -LaTeX Font Info: ... okay on input line 225. -LaTeX Font Info: Checking defaults for OT1/cmr/m/n on input line 225. -LaTeX Font Info: ... okay on input line 225. -LaTeX Font Info: Checking defaults for OMS/cmsy/m/n on input line 225. -LaTeX Font Info: ... okay on input line 225. -LaTeX Font Info: Checking defaults for OMX/cmex/m/n on input line 225. -LaTeX Font Info: ... okay on input line 225. -LaTeX Font Info: Checking defaults for U/cmr/m/n on input line 225. -LaTeX Font Info: ... okay on input line 225. -LaTeX Font Info: Checking defaults for PD1/pdf/m/n on input line 225. -LaTeX Font Info: ... okay on input line 225. -LaTeX Font Info: Checking defaults for PU/pdf/m/n on input line 225. -LaTeX Font Info: ... okay on input line 225. -LaTeX Font Info: Checking defaults for OT4/cmr/m/n on input line 225. -LaTeX Font Info: Try loading font information for OT4+cmr on input line 225. +LaTeX Font Info: Checking defaults for OML/cmm/m/it on input line 228. +LaTeX Font Info: ... okay on input line 228. +LaTeX Font Info: Checking defaults for T1/cmr/m/n on input line 228. +LaTeX Font Info: ... okay on input line 228. +LaTeX Font Info: Checking defaults for OT1/cmr/m/n on input line 228. +LaTeX Font Info: ... okay on input line 228. +LaTeX Font Info: Checking defaults for OMS/cmsy/m/n on input line 228. +LaTeX Font Info: ... okay on input line 228. +LaTeX Font Info: Checking defaults for OMX/cmex/m/n on input line 228. +LaTeX Font Info: ... okay on input line 228. +LaTeX Font Info: Checking defaults for U/cmr/m/n on input line 228. +LaTeX Font Info: ... okay on input line 228. +LaTeX Font Info: Checking defaults for PD1/pdf/m/n on input line 228. +LaTeX Font Info: ... okay on input line 228. +LaTeX Font Info: Checking defaults for PU/pdf/m/n on input line 228. +LaTeX Font Info: ... okay on input line 228. +LaTeX Font Info: Checking defaults for OT4/cmr/m/n on input line 228. +LaTeX Font Info: Try loading font information for OT4+cmr on input line 228. (/usr/share/texlive/texmf-dist/tex/latex/polski/ot4cmr.fd File: ot4cmr.fd 2008/02/24 v1.2.1 Font defs for fonts PL (MW) ) -LaTeX Font Info: ... okay on input line 225. -LaTeX Font Info: Checking defaults for LY1/ptm/m/n on input line 225. -LaTeX Font Info: ... okay on input line 225. -LaTeX Font Info: Checking defaults for EU1/lmr/m/n on input line 225. -LaTeX Font Info: ... okay on input line 225. -LaTeX Font Info: Checking defaults for T3/cmr/m/n on input line 225. -LaTeX Font Info: Try loading font information for T3+cmr on input line 225. +LaTeX Font Info: ... okay on input line 228. +LaTeX Font Info: Checking defaults for LY1/ptm/m/n on input line 228. +LaTeX Font Info: ... okay on input line 228. +LaTeX Font Info: Checking defaults for EU1/lmr/m/n on input line 228. +LaTeX Font Info: ... okay on input line 228. +LaTeX Font Info: Checking defaults for T3/cmr/m/n on input line 228. +LaTeX Font Info: Try loading font information for T3+cmr on input line 228. (/usr/share/texmf/tex/latex/tipa/t3cmr.fd File: t3cmr.fd 2001/12/31 TIPA font definitions ) -LaTeX Font Info: ... okay on input line 225. +LaTeX Font Info: ... okay on input line 228. *geometry* driver: auto-detecting *geometry* detected driver: xetex @@ -2491,7 +2491,7 @@ ABD: EveryShipout initializing macros \AtBeginShipoutBox=\box119 -Package hyperref Info: Link coloring OFF on input line 225. +Package hyperref Info: Link coloring OFF on input line 228. (/usr/share/texlive/texmf-dist/tex/latex/hyperref/nameref.sty Package: nameref 2012/10/27 v2.43 Cross-referencing by name of section @@ -2501,9 +2501,9 @@ ) \c@section@level=\count448 ) -LaTeX Info: Redefining \ref on input line 225. -LaTeX Info: Redefining \pageref on input line 225. -LaTeX Info: Redefining \nameref on input line 225. +LaTeX Info: Redefining \ref on input line 228. +LaTeX Info: Redefining \pageref on input line 228. +LaTeX Info: Redefining \nameref on input line 228. (./mchrzasz.out) (./mchrzasz.out) \@outlinefile=\write10 @@ -2534,7 +2534,7 @@ tionary/translator-theorem-dictionary-English.dict Dictionary: translator-theorem-dictionary, Language: English ) -LaTeX Info: Redefining \includegraphics on input line 225. +LaTeX Info: Redefining \includegraphics on input line 228. *** you should *not* be loading the inputenc package *** XeTeX expects the source to be in UTF8 encoding @@ -2631,8 +2631,8 @@ Package biblatex Info: Trying to load bibliographic data... Package biblatex Info: ... file 'mchrzasz.bbl' not found. No file mchrzasz.bbl. -Package biblatex Info: Reference section=0 on input line 225. -Package biblatex Info: Reference segment=0 on input line 225. +Package biblatex Info: Reference section=0 on input line 228. +Package biblatex Info: Reference segment=0 on input line 228. (./mchrzasz.nav) ................................................. . fontspec info: "no-scripts" @@ -2660,53 +2660,53 @@ . * 'bold italic' with NFSS spec.: . <->"Trebuchet MS/BI/ICU:mapping=tex-text;" ................................................. -LaTeX Font Info: Try loading font information for OML+plm on input line 225. +LaTeX Font Info: Try loading font information for OML+plm on input line 228. (/usr/share/texlive/texmf-dist/tex/latex/polski/omlplm.fd File: omlplm.fd 2008/02/24 v1.2.1 Font defs for fonts PL (MW) ) -LaTeX Font Info: Try loading font information for OMS+plsy on input line 225 +LaTeX Font Info: Try loading font information for OMS+plsy on input line 228 . (/usr/share/texlive/texmf-dist/tex/latex/polski/omsplsy.fd File: omsplsy.fd 2008/02/24 v1.2.1 Font defs for fonts PL (MW) ) -LaTeX Font Info: Try loading font information for OMX+plex on input line 225 +LaTeX Font Info: Try loading font information for OMX+plex on input line 228 . (/usr/share/texlive/texmf-dist/tex/latex/polski/omxplex.fd File: omxplex.fd 2008/02/24 v1.2.1 Font defs for fonts PL (MW) ) LaTeX Font Info: External font `plex10' loaded for size -(Font) <10> on input line 225. +(Font) <10> on input line 228. LaTeX Font Info: External font `plex10' loaded for size -(Font) <7> on input line 225. +(Font) <7> on input line 228. LaTeX Font Info: External font `plex10' loaded for size -(Font) <5> on input line 225. -LaTeX Font Info: Try loading font information for U+msa on input line 225. +(Font) <5> on input line 228. +LaTeX Font Info: Try loading font information for U+msa on input line 228. (/usr/share/texlive/texmf-dist/tex/latex/amsfonts/umsa.fd File: umsa.fd 2013/01/14 v3.01 AMS symbols A ) -LaTeX Font Info: Try loading font information for U+msb on input line 225. +LaTeX Font Info: Try loading font information for U+msb on input line 228. (/usr/share/texlive/texmf-dist/tex/latex/amsfonts/umsb.fd File: umsb.fd 2013/01/14 v3.01 AMS symbols B ) -LaTeX Font Info: Try loading font information for U+rsfs on input line 225. +LaTeX Font Info: Try loading font information for U+rsfs on input line 228. (/usr/share/texlive/texmf-dist/tex/latex/jknapltx/ursfs.fd File: ursfs.fd 1998/03/24 rsfs font definition file (jk) ) \c__siunitx_mathsf_int=\count451 LaTeX Font Info: External font `plex10' loaded for size -(Font) <10.95> on input line 225. +(Font) <10.95> on input line 228. LaTeX Font Info: External font `plex10' loaded for size -(Font) <8> on input line 225. +(Font) <8> on input line 228. LaTeX Font Info: External font `plex10' loaded for size -(Font) <6> on input line 225. +(Font) <6> on input line 228. \c__siunitx_mathtt_int=\count452 -LaTeX Font Info: Try loading font information for OT4+cmtt on input line 225 +LaTeX Font Info: Try loading font information for OT4+cmtt on input line 228 . (/usr/share/texlive/texmf-dist/tex/latex/polski/ot4cmtt.fd @@ -2784,19 +2784,9 @@ ] LaTeX Font Info: External font `plex10' loaded for size -(Font) <9> on input line 316. - -Overfull \hbox (40.00084pt too wide) in paragraph at lines 316--316 -[] - [] - - -Overfull \hbox (40.00084pt too wide) in paragraph at lines 316--316 -[]$[]$ - [] - +(Font) <9> on input line 319. File: images/BG_lower.png Graphic file (type QTm) - + Overfull \vbox (19.18185pt too high) has occurred while \output is active [] ................................................. @@ -2984,7 +2974,7 @@ [11 ] -Overfull \vbox (36.75867pt too high) detected at line 570 +Overfull \vbox (36.75867pt too high) detected at line 573 [] File: images/BG_lower.png Graphic file (type QTm) @@ -3071,7 +3061,7 @@ [15 ] -Overfull \vbox (6.34827pt too high) detected at line 687 +Overfull \vbox (6.34827pt too high) detected at line 690 [] File: images/BG_lower.png Graphic file (type QTm) @@ -3189,21 +3179,21 @@ \tf@snm=\write13 \openout13 = `mchrzasz.snm'. -Package atveryend Info: Empty hook `BeforeClearDocument' on input line 754. -Package atveryend Info: Empty hook `AfterLastShipout' on input line 754. +Package atveryend Info: Empty hook `BeforeClearDocument' on input line 757. +Package atveryend Info: Empty hook `AfterLastShipout' on input line 757. (./mchrzasz.aux) -Package atveryend Info: Empty hook `AtVeryEndDocument' on input line 754. -Package atveryend Info: Empty hook `AtEndAfterFileList' on input line 754. +Package atveryend Info: Empty hook `AtVeryEndDocument' on input line 757. +Package atveryend Info: Empty hook `AtEndAfterFileList' on input line 757. Package logreq Info: Writing requests to 'mchrzasz.run.xml'. \openout1 = `mchrzasz.run.xml'. -Package atveryend Info: Empty hook `AtVeryVeryEnd' on input line 754. +Package atveryend Info: Empty hook `AtVeryVeryEnd' on input line 757. ) Here is how much of TeX's memory you used: - 50402 strings out of 493918 - 988875 string characters out of 6150564 - 1339168 words of memory out of 5000000 - 52675 multiletter control sequences out of 15000+600000 + 50403 strings out of 493918 + 988881 string characters out of 6150564 + 1339184 words of memory out of 5000000 + 52676 multiletter control sequences out of 15000+600000 33273 words of font info for 135 fonts, out of 8000000 for 9000 1144 hyphenation exceptions out of 8191 55i,25n,77p,10405b,1477s stack positions out of 5000i,500n,10000p,200000b,80000s diff --git a/Lectures_my/MC_2016/Lecture11/mchrzasz.pdf b/Lectures_my/MC_2016/Lecture11/mchrzasz.pdf index e1edc96..088c1b4 100644 --- a/Lectures_my/MC_2016/Lecture11/mchrzasz.pdf +++ b/Lectures_my/MC_2016/Lecture11/mchrzasz.pdf Binary files differ diff --git a/Lectures_my/MC_2016/Lecture11/mchrzasz.synctex.gz b/Lectures_my/MC_2016/Lecture11/mchrzasz.synctex.gz deleted file mode 100644 index f34eb02..0000000 --- a/Lectures_my/MC_2016/Lecture11/mchrzasz.synctex.gz +++ /dev/null Binary files differ diff --git a/Lectures_my/MC_2016/Lecture11/mchrzasz.tex b/Lectures_my/MC_2016/Lecture11/mchrzasz.tex index a38bba9..ac6b963 100644 --- a/Lectures_my/MC_2016/Lecture11/mchrzasz.tex +++ b/Lectures_my/MC_2016/Lecture11/mchrzasz.tex @@ -66,6 +66,10 @@ \usepackage{subfigure} \usepackage{tikz} \usepackage{hyperref} +\newcommand*{\Scale}[2][4]{\scalebox{#1}{$#2$}}% +\newcommand*{\Resize}[2]{\resizebox{#1}{!}{$#2$}}% + + %\usepackage{hepparticles} \usepackage[italic]{hepparticles} @@ -144,7 +148,6 @@ \newcommand{\Alert}[1]{\textcolor{Alert}{#1}} % louder alert \newcommand{\ALERT}[1]{\textcolor{ALERT}{#1}} % loudest alert %% "\alert" is already a beamer pre-defined -\newcommand*{\Scale}[2][4]{\scalebox{#1}{$#2$}}% \def\Put(#1,#2)#3{\leavevmode\makebox(0,0){\put(#1,#2){#3}}} @@ -295,14 +298,14 @@ \phi_0(x)=0,~~~~~~~~~~~~~\phi_1(x)=f(x)+\int_a^b K(x,y) \phi_0(y) dy=f(x) \end{align*} \begin{align*} -\phi_2(x)=f(x) + \int_a^b K(x,y) \phi_1(y)dy = f(x) \int_a^b K(x,y) f(y)dy +\phi_2(x)=f(x) + \int_a^b K(x,y) \phi_1(y)dy = f(x) + \int_a^b K(x,y) f(y)dy \end{align*} \begin{align*} -\phi_3(x)= f(x) \int_a^b K(x,y) dy = f(x)+\int_a^b K(x,y) f(y) dy + \int_a^b \int_a^b K(x,y) K(y,z) f(z) dy dz +\Scale[0.75]{\phi_3(x)= f(x)+ \int_a^b K(x,y) dy = f(x)+\int_a^b K(x,y) f(y) dy + \int_a^b \int_a^b K(x,y) K(y,z) f(z) dy dz} \end{align*} \ARROW Now we put the following notations: \begin{align*} -K^{(1)}=K(x,y)~~~~~~~~~~~~~~~~K^{(2)}(x,y)= \int_a^b K(x,t)K(t,y) dt +K^{(1)}(x,y)=K(x,y)~~~~~~~~~~~~~~~~K^{(2)}(x,y)= \int_a^b K(x,t)K(t,y) dt \end{align*} \ARROW One gets: \begin{align*} @@ -442,14 +445,14 @@ \ARROW We define a new random variable: \begin{align*} c_r(x)=\begin{cases} -\frac{V(\gamma_{n-r} f(x_{n-r}}{\rho(x_{n-r}},~~& r \leq n,\\ +\frac{V(\gamma_{n-r})f(x_{n-r})}{\rho(x_{n-r})},~~& r \leq n,\\ 0,~~&r> n \end{cases} \end{align*} where $\rho_r(x)$ is defined as: \begin{align*} \rho_1(x) &= \int_{-\infty}^{a-x} \rho(y)dy + \int_{b-x}^{+\infty}\rho(y)dy,\\ -\rho_r(x) &= \int_a^b ... \int_a^b \rho(x_1-x) \rho(x_2-x)...\rho(x_{r-1}-x_{r-2})\rho_1(x_{r-1}) dx_1...dx_{r-1} +\rho_r(x) &= \int_a^b ... \int_a^b \rho(x_1-x) \rho(x_2-x_1)...\rho(x_{r-1}-x_{r-2})\rho_1(x_{r-1}) dx_1...dx_{r-1} \end{align*} is the probability that the particle that is at given time in the $x$ coordinate will survive $r$ moments.\\ \ARROWR One can prove that $E\left[c_r(x)\right]$ treated as a function of $x$ variable is the solution to the integral equation. @@ -544,9 +547,9 @@ \ARROW Let $Q=(q_{ij})$, $i,j=1,2,...,n$ is the probability matrix: \begin{align*} -q_{ij} \geq 0,~~~\sum_{j=1}^{n}=1 +q_{ij} \geq 0,~~~\sum_{j=1}^{n} q_{ij}=1 \end{align*} -\ARROW We construct a random walk on the set: $\lbrace 1,2,.... n \rbrace$ accordingly to the above rules: +\ARROW We construct a random walk on the set: $\lbrace 1,2,.... n \rbrace$ accordingly to the below rules: \begin{itemize} \item In the $t=0$ the particle is in a randomly chosen state $i_0$ accordingly to binned \pdf : $p_j$. \item If in the moment $t=n-1$ the particle is in $i_{n-1}$ state then in the next moment it goes to the state $i_n$ with the probability $q_{i_{n-1} j}$. @@ -592,7 +595,7 @@ where: \begin{align*} r_i=\begin{cases} -1-p_1,~~& \delta_i=0\\ +1-p_i,~~& \delta_i=0\\ p_i,~~~& \delta_i=1 \end{cases} \end{align*} @@ -673,7 +676,7 @@ \item Now we can multiply the area by alpha factor that keeps the density constant then: \end{itemize} \begin{equation} -l \sim \alpha^0.5 \alpha6{a-0.5} = \alpha^a \nonumber +l \sim \alpha^{0.5} \alpha^{a-0.5} = \alpha^a \nonumber \end{equation} \begin{itemize} \item In this case the distance between the clients will not change, but the number of clients will increase by $\alpha$ so: