EPH A blog about my work / Thu, 24 Aug 2017 17:36:35 -0400 Thu, 24 Aug 2017 17:36:35 -0400 Jekyll v2.5.3 The arrow of time in RIS Excerpt: <div style="display:none"><div style="text-align:center;"><img src="http://latex.codecogs.com/png.latex?\DeclareMathOperator{\tr}{Tr}\newcommand{\H}{\mathcal{H}}\newcommand{\B}{\mathcal{B}}\newcommand{\sys}{\mathcal{S}}\newcommand{\env}{\mathcal{E}}\newcommand{\invar}{^\text{inv}}\newcommand{\inv}{^{-1}}\newcommand{\init}{^\text{i}}\newcommand{\fin}{^\text{f}}\newcommand{\envstate}{\xi}\newcommand{\sysstate}{\rho}\newcommand{\hsys}{h_\sys}\newcommand{\henv}{h_\env}\DeclareMathOperator{\id}{Id}\newcommand{\L}{\mathcal{L}}\newcommand{\bP}{\mathbb{P}}" alt="\DeclareMathOperator{\tr}{Tr}\newcommand{\H}{\mathcal{H}}\newcommand{\B}{\mathcal{B}}\newcommand{\sys}{\mathcal{S}}\newcommand{\env}{\mathcal{E}}\newcommand{\invar}{^\text{inv}}\newcommand{\inv}{^{-1}}\newcommand{\init}{^\text{i}}\newcommand{\fin}{^\text{f}}\newcommand{\envstate}{\xi}\newcommand{\sysstate}{\rho}\newcommand{\hsys}{h_\sys}\newcommand{\henv}{h_\env}\DeclareMathOperator{\id}{Id}\newcommand{\L}{\mathcal{L}}\newcommand{\bP}{\mathbb{P}}" /></div></div> <p>I gave an informal talk today on the <a href="https://en.wikipedia.org/wiki/Arrow_of_time">arrow of time</a> in repeated interaction systems and I thought I’d write about it here.</p> Wed, 18 Jan 2017 21:09:03 +0000 /posts/2017/the-arrow-of-time-in-ris /posts/2017/the-arrow-of-time-in-ris The traveling salesman and 10 lines of Python Excerpt: <p>A few weeks ago I got an email about a high performance computing course I had signed up for; the professor wanted all of the participants to send him the ``most complicated’’ 10 line Python program they could, in order to gauge the level of the class<label for="sn1" class="margin-toggle sidenote-number"></label><input type="checkbox" id="sn1" class="margin-toggle" /><span class="sidenote">And to submit 10 blank lines if we didn’t know any Python! </span>.</p> Tue, 25 Oct 2016 00:00:00 -0400 /posts/2016/the-traveling-salesman-and-10-lines-of-python /posts/2016/the-traveling-salesman-and-10-lines-of-python Setting up SublimeText Excerpt: <p>I’m setting up a new laptop and figured it was a good chance to document setting up SublimeText for LaTeX, as quasi follow up to my <a href="/posts/2016/live-notetaking-with-latex">recent post</a> about live LaTeXing. However, installing LaTeX can be hard, and configuring the SublimeText package LaTeXTools to work with LaTeX has the potential to be hard (often just works, but if not, can be confusing), and I won’t write about those parts, because they are better documented elsewhere. So this is simply the easy part (configuring SublimeText) to try to remove a barrier from those who might be looking to switch.</p> Fri, 14 Oct 2016 00:00:00 -0400 /posts/2016/setting-up-sublimetext /posts/2016/setting-up-sublimetext Live notetaking with LaTeX Excerpt: <p>A friend suggested I write a guide about live notetaking in LaTeX, since it’s pretty useful and something I have a fair amount of experience with. I had been making attempts at live-LaTeXing course notes for a year or two before I was able to make it through a semester long class; the first course I fully LaTeX’d was Vojkan Jaksic’s excellent Analysis 3 (introduction to metric spaces and topology)<label for="sn1" class="margin-toggle sidenote-number"></label><input type="checkbox" id="sn1" class="margin-toggle" /><span class="sidenote">PDF available <a href="https://www.dropbox.com/s/p5wwwws1l44sm1z/Analysis_3_Fall_2013_notes.pdf">here</a>. Not my best work, but it did the job. </span>. Most recently, I wrote notes for Sergey Norin’s Combinatorics course which I submitted as a project for the class<label for="sn2" class="margin-toggle sidenote-number"></label><input type="checkbox" id="sn2" class="margin-toggle" /><span class="sidenote">PDF available <a href="https://www.dropbox.com/s/ysvmcw88hf5h4h9/CombinatoricsNotes.pdf?dl=0">here</a>. Probably my best work. </span>.</p> Sat, 24 Sep 2016 00:00:00 -0400 /posts/2016/live-notetaking-with-latex /posts/2016/live-notetaking-with-latex Landauer's Principle and the balance equation Excerpt: <div style="display:none"><div style="text-align:center;"><img src="http://latex.codecogs.com/png.latex?\DeclareMathOperator{\tr}{Tr}\newcommand{\H}{\mathcal{H}}\newcommand{\B}{\mathcal{B}}\newcommand{\sys}{\mathcal{S}}\newcommand{\env}{\mathcal{E}}\newcommand{\invar}{^\text{inv}}\newcommand{\inv}{^{-1}}\newcommand{\init}{^\text{i}}\newcommand{\fin}{^\text{f}}\newcommand{\envstate}{\xi}\newcommand{\sysstate}{\rho}\newcommand{\hsys}{h_\sys}\newcommand{\henv}{h_\env}\DeclareMathOperator{\id}{Id}" alt="\DeclareMathOperator{\tr}{Tr}\newcommand{\H}{\mathcal{H}}\newcommand{\B}{\mathcal{B}}\newcommand{\sys}{\mathcal{S}}\newcommand{\env}{\mathcal{E}}\newcommand{\invar}{^\text{inv}}\newcommand{\inv}{^{-1}}\newcommand{\init}{^\text{i}}\newcommand{\fin}{^\text{f}}\newcommand{\envstate}{\xi}\newcommand{\sysstate}{\rho}\newcommand{\hsys}{h_\sys}\newcommand{\henv}{h_\env}\DeclareMathOperator{\id}{Id}" /></div></div> <p>I’ve been working on my thesis over reading week, and I think I’ve finished my introduction to Landauer’s Principle. I ended up writing a pretty detailed derivation of the balance equation, and thus Landauer’s bound, so I thought it might be useful to post here.</p> <p><span class="newthought">Landauer's principle</span> states that there is a minimal energetic cost for a state transformation <img src="http://latex.codecogs.com/png.latex?\sysstate\init \to \sysstate\fin\inline"/> on a system <img src="http://latex.codecogs.com/png.latex?\sys\inline"/> via the action of a thermal reservoir <img src="http://latex.codecogs.com/png.latex?\env\inline"/> at temperature <img src="http://latex.codecogs.com/png.latex?(k_B\beta)\inv\inline"/>.</p> Mon, 29 Feb 2016 16:50:00 -0500 /posts/2016/Landauer's_Principle_and_the_balance_equation /posts/2016/Landauer's_Principle_and_the_balance_equation Landauer's Principle physics derivation post Cantor's Set and Cantor's Function Excerpt: <p>I’m giving tutorials for McGill’s honours analysis 2 course this semester, and I wrote some notes on Cantor’s Set and Cantor’s Function; I thought they might be helpful to others, so I’ll post them here<label for="sn-id-1" class="margin-toggle sidenote-number"></label><input type="checkbox" id="sn-id-1" class="margin-toggle" /><span class="sidenote">McGill has its own MyCourses system where I put the notes for students in the class, but I think it’s better to be in the habit of posting work in a publicly-accessible place. </span>.</p> <p>I’ve given up<label for="sn-id-2" class="margin-toggle sidenote-number"></label><input type="checkbox" id="sn-id-2" class="margin-toggle" /><span class="sidenote">for now </span> on actually converting my LaTeX to something web-native, so I’ll just put the pdf here.</p> Tue, 09 Feb 2016 15:40:00 -0500 /posts/2016/Cantor /posts/2016/Cantor analysis math post Completeness I Excerpt: <div style="display:none"><div class="mathblock"><script type="math/tex; mode=display"> \newcommand{\doccmd}[1]{\texttt{\textbackslash#1}} \newcommand{\docopt}[1]{\ensuremath{\langle}\textrm{\textit{#1}}\ensuremath{\rangle}} \newcommand{\docarg}[1]{\textrm{\textit{#1}}} \newcommand{\docenv}[1]{\textsf{#1}} \newcommand{\docpkg}[1]{\texttt{#1}} \newcommand{\doccls}[1]{\texttt{#1}} \newcommand{\docclsopt}[1]{\texttt{#1}} \DeclareMathOperator{\cl}{cl}\newcommand{\R}{\mathbb{R}}\newcommand{\N}{\mathbb{N}}\newcommand{\Q}{\mathbb{Q}}\newcommand{\Jaksic}{Jaksic}\newcommand{\imp}{\Rightarrow}\newcommand{\inv}{^{-1}}</script></div></div> <p>Last semester, I helped a friend review McGill's Analyis 3 course by trying to provide a better feel for completeness; this post will be a slightly edited version of that. Originally, I wanted to write about both completeness and compactness, and their connections, but I ended up only getting to completeness, and actually not everything I wanted to talk about. So I'll call this <em>Completeness I</em>, leaving open the possibility for more of these in the future. Hopefully the style is casual and expository without being misleading.</p> Fri, 01 Jan 2016 10:40:00 -0500 /posts/2016/Completeness_I /posts/2016/Completeness_I math analysis completeness post New blog Excerpt: <p>I’ve made a new blog!</p> <p>I started a “coffee blog” a month or so ago but only posted once (I think I’ll bring that post over here, too). I do like the idea though, and want to write about math and my research. So this should become a place for me to do that.</p> Sun, 13 Dec 2015 23:40:00 -0500 /posts/2015/New-blog /posts/2015/New-blog meta post