From 7e62e483a111b35f0938c34fedb25e4cd031402b Mon Sep 17 00:00:00 2001 From: Yu Cong Date: Fri, 2 May 2025 23:05:12 +0800 Subject: [PATCH 1/8] fira sans --- beamerthemeSimple.sty | 2 +- main.pdf | Bin 646830 -> 619892 bytes 2 files changed, 1 insertion(+), 1 deletion(-) diff --git a/beamerthemeSimple.sty b/beamerthemeSimple.sty index 2825eb4..c16f44e 100644 --- a/beamerthemeSimple.sty +++ b/beamerthemeSimple.sty @@ -2,7 +2,7 @@ % % This file may be distributed and/or modified % under the LaTeX Project Public License -\usepackage{libertine} +\usepackage[sfdefault]{FiraSans} \RequirePackage[english]{babel} \RequirePackage{fancyhdr} % header footer \RequirePackage{xcolor} diff --git a/main.pdf b/main.pdf index aa5d1e421548effc59c227e4ceacdcc9bd605908..10ac3693a528a0bd51ffc5c9724cd11832ef970d 100644 GIT binary patch delta 232535 zcmV)#K##w!y(jeQC9qur0XCCC0V;pBQp--mKn%R+D}3CQ=*ITGk{be1Bm@$a+<-$> z(vm|{=!4hS<0z?GS}M43npNx>kHDWJp#^*bpa?igPveCZEa&P7TWAN5sPCz*t$}=b);Z9vubv3O% 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zrl0)ef$%?wBsYo*Wo~41baG{3Z3<;>WN%_>3UhQ}a&&ldWo8OCF*r3fISM5uMNdWw D7h59V From 14ab89e74866617838294210bed8572548965852 Mon Sep 17 00:00:00 2001 From: Yu Cong Date: Sat, 3 May 2025 23:16:17 +0800 Subject: [PATCH 3/8] firamath & use xelatex --- beamerthemeSimple.sty | 23 +++++++++++++---------- main.pdf | Bin 651211 -> 422233 bytes main.tex | 2 +- 3 files changed, 14 insertions(+), 11 deletions(-) diff --git a/beamerthemeSimple.sty b/beamerthemeSimple.sty index 5491f91..f8ad7f1 100644 --- a/beamerthemeSimple.sty +++ b/beamerthemeSimple.sty @@ -1,13 +1,16 @@ -% Copyright 2018 by Zhibo Wang -% -% This file may be distributed and/or modified -% under the LaTeX Project Public License -\usepackage[sfdefault]{FiraSans} +% !TEX program = xelatex +% !TEX TS-program = xelatex +% fonts +\RequirePackage[sfdefault]{FiraSans} +\RequirePackage[mathrm=sym]{unicode-math} +\setmathfont{Fira Math} + \RequirePackage[english]{babel} \RequirePackage{fancyhdr} % header footer -\RequirePackage{xcolor} +\RequirePackage[dvipsnames]{xcolor} \RequirePackage{bookmark} \RequirePackage{hyperref}[colorlinks=true,urlcolor=Blue,citecolor=Green,linkcolor=BrickRed,unicode] +\RequirePackage{natbib} \RequirePackage{graphicx} % Allows including images \RequirePackage{booktabs} % Allows the use of \toprule, \midrule and \bottomrule in tables % \RequirePackage{tikz} @@ -20,9 +23,9 @@ \RequirePackage{subcaption} \RequirePackage{amsmath} \RequirePackage{amsthm} -\RequirePackage[utf8]{inputenc} -\RequirePackage{CJKutf8} -\def\zh#1{\begin{CJK}{UTF8}{gbsn}#1\end{CJK}} +% \RequirePackage[utf8]{inputenc} +% \RequirePackage{CJKutf8} +% \def\zh#1{\begin{CJK}{UTF8}{gbsn}#1\end{CJK}} \RequirePackage{aliascnt} % a color box @@ -125,7 +128,7 @@ \setbeamercolor{alerted text}{fg=beamer@simple@color} \setbeamerfont{block title alerted}{series=\mdseries} \setbeamerfont{alerted text}{series=\bfseries\boldmath} -\hypersetup{colorlinks,linkcolor=,urlcolor=oliver} 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+++ b/main.tex @@ -1,6 +1,6 @@ \documentclass{beamer} -\title[template example]{Minimizing the Sum of Piecewise Linear Convex Functions} +\title[template example]{Title} \date{\today} \author{丛宇} % \AtBeginSection[]{ @@ -23,6 +23,7 @@ \section{Problems \& Definitions} \begin{frame}{$\min \sum f_i(a_i\cdot x-b_i)$} + $A\setminus B$ 测试中文: \begin{problem} Given $n$ piecewise linear convex functions $f_1,...,f_n:\R \to \R$ of total $m$ breakpoints, and $n$ linear functions $a_i\cdot x-b_i:\R^d\to \R$, find $\min_x \sum_i f_i(a_i\cdot x-b_i)$. \end{problem} @@ -78,7 +79,7 @@ However, observe that in our problem the piecewise linear convex function is not Let $n_i$ be the number of line segments in $f_i$. Note that $\sum_i n_i=m+n$. We can formulate the optimization problem as the following linear program, - \newpage + \framebreak \begin{align*} \min &\sum_{i=1}^n f_i\\ @@ -92,10 +93,8 @@ However, observe that in our problem the piecewise linear convex function is not \section{LP in Low Dimensions} \begin{frame}[allowframebreaks]{Megiddo's algorithm}% - \boxfill{ - \tiny - \url{https://people.inf.ethz.ch/gaertner/subdir/texts/own_work/chap50-fin.pdf} - } + \url{https://people.inf.ethz.ch/gaertner/subdir/texts/own_work/chap50-fin.pdf} + The dimension $d$ (in our problem, the dimension of $x$) is small while the number of constraints are huge. We need only $d$ linearly independent tight constraints to identify the optimal solution $x^*$. Thus most of the constraints are useless. @@ -106,7 +105,7 @@ However, observe that in our problem the piecewise linear convex function is not Through inquiries. Let $a\cdot x \leq b$ be the constraint. Define 3 hyperplanes, $a\cdot x = c$ where $c\in \set{b,b-\e,b+\e}$. Now solve three $d-1$ dimension linear programming. The largest of the three objective functions tells us where $x^*$ lies with respect to the hyperplane. - \newpage + \framebreak Finding the optimal solution $x^*$ is therefore equivalent to the following problem, \begin{problem}[Multidimensional Search Problem] Suppose that there exists a point $x^*$ which is not known to us, but there is a oracle that can tell the position of $x^*$ relative to any hyperplane in $\R^d$. Given $n$ hyperplanes, we want to know the position of $x^*$ relative to each of them. @@ -114,7 +113,7 @@ However, observe that in our problem the piecewise linear convex function is not \textbf{What about 1 dimension search?} A fastest way will be using the linear time median algorithm. We can find the median of $n$ numbers and call the oracle to compare the median with $x^*$. Thus with $O(n)$ time median finding and one oracle call, we find the relative position of $n/2$ elements relative to $x^*$. - \newpage + \framebreak If we can do similar things in $\R^d$, i.e., there is a method which makes $A(d)$ oracle calls and determines at least $B(d)$ fraction of relative positions, then we can apply this method $\log_{\frac{1}{1-B(d)}} n$ times to find all relative positions. @@ -124,7 +123,7 @@ However, observe that in our problem the piecewise linear convex function is not \[T(n,d)=n(3T(n-1,d-1)+O(nd))\] Note that in this setting $A(d)=1$ and $B(d)=1/n$. - \newpage + \framebreak Megiddo designed a clever method where $A(d)=2^{d-1}$ and $B(d)=2^{-(2^d-1)}$. \begin{lemma} @@ -133,7 +132,7 @@ However, observe that in our problem the piecewise linear convex function is not \end{figure} Given two lines through the origin with slopes of opposite sign, knowing which quadrant $x^*$ lies in allows us to locate it with respect to at least one of the lines. \end{lemma} - \newpage + \framebreak Let $l_H$ be the intersection of hyperplane $H$ and $x_1x_2$ plane. Compute a partition $S_1\sqcup S_2=\mathcal H$. $H\in S_1$ iff $l_H$ has positive slope. Otherwise $l_H\in S_2$. We further assume that $|S_1|=|S_2|=n/2$. @@ -148,12 +147,8 @@ However, observe that in our problem the piecewise linear convex function is not Now we have $n/2$ pairs $(H_1,H_2)$, where $H_i\in S_i$. Let $l_i$ be the intersection of $H_i$ and $x_1x_2$ plane. Let $H_{x_i}$ be the linear combination of $H_1$ and $H_2$ s.t. $x_i$ is eliminated. \end{minipage} - - { - % Now we have $n/2$ pairs $(H_1,H_2)$, where $H_i\in S_i$. Let $l_i$ be the intersection of $H_i$ and $x_1x_2$ plane. - % Let $H_{x_i}$ be the linear combination of $H_1$ and $H_2$ s.t. $x_i$ is eliminated. - By the previous lemma, calling oracle on $l_{x_1}$ and $l_{x_2}$ locate $x^*$ with respect to at least one of $H_1$ and $H_2$.} - \newpage + By the previous lemma, calling oracle on $l_{x_1}$ and $l_{x_2}$ locate $x^*$ with respect to at least one of $H_1$ and $H_2$. + \framebreak Input: $S_1,S_2$ and the pairs. \begin{enumerate} \item recursively locate $x^*$ respect to $B(d-1)n/2$ hyperplanes($H_{x_i}$) with $A(d-1)$ oracle calls in $S_1$. diff --git a/readme.md b/readme.md new file mode 100644 index 0000000..89ed742 --- /dev/null +++ b/readme.md @@ -0,0 +1,11 @@ +To use this theme: + +1. install fonts. [FiraGO](https://github.com/bBoxType/FiraGO), [firamath](https://github.com/firamath/firamath)(build from source) and [Source Han Sans SC](https://github.com/adobe-fonts/source-han-sans/releases). +2. use xelatex. `.latexmkrc` generated by chatgpt +```latexmk +$pdf_mode = 1; +$latex = 'xelatex %O %S'; +$pdflatex = 'xelatex %O %S'; +$dvi_mode = 0; +$postscript_mode = 0; +``` \ No newline at end of file From b3ae4ccec4a27702f6b655149e79c84ce38d34e9 Mon Sep 17 00:00:00 2001 From: Yu Cong Date: Mon, 5 May 2025 14:35:50 +0800 Subject: [PATCH 7/8] add more setCJKxxxfont to make xelatex happy --- beamerthemeSimple.sty | 2 ++ main.pdf | Bin 422768 -> 422770 bytes 2 files changed, 2 insertions(+) diff --git a/beamerthemeSimple.sty b/beamerthemeSimple.sty index 9612291..1e5818a 100644 --- a/beamerthemeSimple.sty +++ b/beamerthemeSimple.sty @@ -12,6 +12,8 @@ \setmathfont{Fira Math}[BoldFont=*-SemiBold] \RequirePackage{xeCJK} \setCJKmainfont{Source Han Sans SC} +\setCJKsansfont{Source Han Sans SC} +\setCJKmonofont{Source Han Sans SC} \RequirePackage[english]{babel} \RequirePackage{fancyhdr} % header footer diff --git a/main.pdf b/main.pdf index 0c98ad70a5ffd1d8cba9cc078854ee4247240bb1..4268c7bfe2bd697f7a8308a41b09e249d7a746cc 100644 GIT binary patch delta 7576 zcmai2RZtv&lEghga3>I0+$C6WcVAfC2@>3bEEa;h2X}W30fM``hQ$_##huHmx~i-9 zbss&|AM@4I(^EAU`=poqq;i{yilxm9Ojt&?3IN4CWQ9`?Y=V zpNH;u$o)?_jv=!ONXN;uoKT&v*_K29~778m^^1x zk;(G8j+?(py;(2)>(5s;SdINmsMi@)9hbblPMx|uw+|*Ai52KGTc{8r-Cf#JO~bhr z5IGMQbJ*+k>(kRzZO0<;Zw@ui+3eS+xP92E2SbeQdW4P1c?dr9MVG*OZDGerhZe`; 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support --- .latexmkrc | 5 +++++ beamerthemeSimple.sty | 7 +++++-- main.pdf | Bin 422233 -> 422691 bytes main.tex | 2 +- 4 files changed, 11 insertions(+), 3 deletions(-) create mode 100644 .latexmkrc diff --git a/.latexmkrc b/.latexmkrc new file mode 100644 index 0000000..87e785f --- /dev/null +++ b/.latexmkrc @@ -0,0 +1,5 @@ +$pdf_mode = 1; # 生成PDF +$latex = 'xelatex %O %S'; # 用 xelatex 替代 latex +$pdflatex = 'xelatex %O %S'; # 用 xelatex 替代 pdflatex +$dvi_mode = 0; # 禁用DVI输出 +$postscript_mode = 0; # 禁用PS输出 \ No newline at end of file diff --git a/beamerthemeSimple.sty b/beamerthemeSimple.sty index f8ad7f1..01be7ed 100644 --- a/beamerthemeSimple.sty +++ b/beamerthemeSimple.sty @@ -2,8 +2,11 @@ % !TEX TS-program = xelatex % fonts \RequirePackage[sfdefault]{FiraSans} -\RequirePackage[mathrm=sym]{unicode-math} -\setmathfont{Fira Math} +\RequirePackage{FiraMono} +\renewcommand{\rmfamily}{\sffamily} +\RequirePackage[fakebold]{firamath-otf} +\RequirePackage{xeCJK} +\setCJKmainfont{Source Han 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diff --git a/beamerthemeSimple.sty b/beamerthemeSimple.sty index 01be7ed..728ace4 100644 --- a/beamerthemeSimple.sty +++ b/beamerthemeSimple.sty @@ -4,7 +4,9 @@ \RequirePackage[sfdefault]{FiraSans} \RequirePackage{FiraMono} \renewcommand{\rmfamily}{\sffamily} -\RequirePackage[fakebold]{firamath-otf} +% \RequirePackage[fakebold]{firamath-otf} +\usepackage[mathrm=sym]{unicode-math} +\setmathfont{Fira Math} \RequirePackage{xeCJK} \setCJKmainfont{Source Han Sans SC} diff --git a/main.pdf b/main.pdf index 1229b3455c45890cbaf2ee6b331206df9611114d..179366c2973527f356cd2ec6969b8ccecf4fcd32 100644 GIT binary patch delta 32635 zcmZU)WmH^S(=CjeYKx^%^~ARn6LY2e>m!xUrl7E&%~JXBQ_^Lt8kHl?vrCt6d?K_Cwld=(&p_z8-`z z5ws<3taTBja3TSEn~aZ;KNfU0?bh+4D6I1|C1uvF&>OyfXNI9*B7t&-1~4#yY)?o*aRux5#1wdf82qCDXE;r&Np z-HVroPh^17B}m|2?s;_$$7wlI1P{>xGJqB4Cf3CRbrtv z!Fus3jnAj@kIMt7K=yJfQ1}WGy>15-3=EV7SP=(GlE9z{Uxxz0fdtA_Cy7P`4#vU_ z)UyDiNI-!=sms7zMNHTS@2%q|r>9MjK*LV(R!9bA{=0#)jz`g>8k7}?iU3LhU}gKS 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422768 bytes main.tex | 27 +++++++++++---------------- readme.md | 11 +++++++++++ 4 files changed, 32 insertions(+), 22 deletions(-) create mode 100644 readme.md diff --git a/beamerthemeSimple.sty b/beamerthemeSimple.sty index 728ace4..9612291 100644 --- a/beamerthemeSimple.sty +++ b/beamerthemeSimple.sty @@ -1,12 +1,15 @@ % !TEX program = xelatex % !TEX TS-program = xelatex % fonts -\RequirePackage[sfdefault]{FiraSans} +% \usefonttheme{professionalfonts} +% \RequirePackage[sfdefault]{FiraSans} \RequirePackage{FiraMono} \renewcommand{\rmfamily}{\sffamily} % \RequirePackage[fakebold]{firamath-otf} -\usepackage[mathrm=sym]{unicode-math} -\setmathfont{Fira Math} +\RequirePackage{unicode-math} +\unimathsetup{math-style=ISO, bold-style=ISO, mathrm=sym} +\setsansfont{FiraGO}[BoldFont=* SemiBold, Numbers=Monospaced] +\setmathfont{Fira Math}[BoldFont=*-SemiBold] \RequirePackage{xeCJK} \setCJKmainfont{Source Han Sans SC} @@ -138,7 +141,7 @@ \setbeamerfont{frametitle}{series=\bfseries\boldmath} \setbeamerfont{block title}{series=\bfseries\boldmath} \setbeamerfont{title}{series=\bfseries\boldmath} -\setbeamertemplate{frametitle}{\vskip2pt\hskip-6pt\underline{\insertframetitle}} % add line under frametitle +\setbeamertemplate{frametitle}{\vskip2pt\hskip-6pt\underbar{\insertframetitle}} % add line under frametitle % theorem env \setbeamertemplate{theorem begin}{% @@ -167,8 +170,9 @@ } % more theorem env -\newtheorem{observation}{Observation} -\newtheorem{question}{Question} +\newtheorem{conjecture}[theorem]{Conjecture} +\newtheorem{observation}[theorem]{Observation} +\newtheorem{question}[theorem]{Question} % ---------------------------------------------------------------------- diff --git a/main.pdf b/main.pdf index 179366c2973527f356cd2ec6969b8ccecf4fcd32..0c98ad70a5ffd1d8cba9cc078854ee4247240bb1 100644 GIT binary patch delta 58766 zcmZs?V|1j^w*B34I#$QFZQHhO+eyW?ZFX$4W7{@6w%#1v`<^rI|Jxq>sr{j9JoQ_9 z&NbKE3dZ#jMjQ)(k)4s37s|=m(Zs+8%6+X$eo}IPAEx^a#lzn;ae^<2Fo4!w>r{q& 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