diff --git a/.sessions/Journal.vim b/.sessions/Journal.vim index 5dfcc98f..7a0c9a07 100644 --- a/.sessions/Journal.vim +++ b/.sessions/Journal.vim @@ -14,14 +14,14 @@ else set shortmess=aoO endif badd +1 ~/Documents/Dane\'s\ Vault/Journal/2025_07_30.md -badd +10 ~/Documents/Dane\'s\ Vault/Writing/Journal//JRNL-20250904-135850.md -badd +96 ~/Documents/Dane\'s\ Vault/Writing/Journal//JRNL-20251003-174601.md -badd +0 journal_config.txt +badd +10 JRNL-20250904-135850.md +badd +96 JRNL-20251003-174601.md +badd +14 journal_config.txt argglobal %argdel edit journal_config.txt argglobal -balt ~/Documents/Dane\'s\ Vault/Writing/Journal//JRNL-20251003-174601.md +balt JRNL-20251003-174601.md setlocal foldmethod=manual setlocal foldexpr=0 setlocal foldmarker={{{,}}} @@ -32,12 +32,12 @@ setlocal foldnestmax=20 setlocal foldenable silent! normal! zE let &fdl = &fdl -let s:l = 13 - ((12 * winheight(0) + 33) / 66) +let s:l = 14 - ((13 * winheight(0) + 32) / 64) if s:l < 1 | let s:l = 1 | endif keepjumps exe s:l normal! zt -keepjumps 13 -normal! 018| +keepjumps 14 +normal! 0 tabnext 1 if exists('s:wipebuf') && len(win_findbuf(s:wipebuf)) == 0 && getbufvar(s:wipebuf, '&buftype') isnot# 'terminal' silent exe 'bwipe ' . s:wipebuf diff --git a/Writing/CV/cv.aux b/Writing/CV/cv.aux new file mode 100644 index 00000000..35ad33a2 --- /dev/null +++ b/Writing/CV/cv.aux @@ -0,0 +1,27 @@ +\relax +\providecommand\hyper@newdestlabel[2]{} +\providecommand\HyField@AuxAddToFields[1]{} +\providecommand\HyField@AuxAddToCoFields[2]{} +\providecommand\BKM@entry[2]{} +\BKM@entry{id=1,dest={73656374696F6E2A2E31},srcline={34}}{5C3337365C3337375C303030455C303030645C303030755C303030635C303030615C303030745C303030695C3030306F5C3030306E} +\BKM@entry{id=2,dest={73656374696F6E2A2E32},srcline={53}}{5C3337365C3337375C303030415C303030775C303030615C303030725C303030645C303030735C3030305C3034305C3030305C3034365C3030305C3034305C303030485C3030306F5C3030306E5C3030306F5C303030725C30303073} 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\& Honors}{1}{section*.2}\protected@file@percent } +\@writefile{toc}{\contentsline {section}{Publications and Presentations}{1}{section*.3}\protected@file@percent } +\@writefile{toc}{\contentsline {subsection}{First Author}{1}{subsection*.4}\protected@file@percent } +\@writefile{toc}{\contentsline {subsection}{Major Contributor}{1}{subsection*.5}\protected@file@percent } +\BKM@entry{id=6,dest={73656374696F6E2A2E36},srcline={102}}{5C3337365C3337375C303030535C3030306B5C303030695C3030306C5C3030306C5C30303073} +\BKM@entry{id=7,dest={73656374696F6E2A2E37},srcline={113}}{5C3337365C3337375C303030505C303030725C3030306F5C303030665C303030655C303030735C303030735C303030695C3030306F5C3030306E5C303030615C3030306C5C3030305C3034305C303030455C303030785C303030705C303030655C303030725C303030695C303030655C3030306E5C303030635C30303065} 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\mbox{\hrefWithoutArrow{mailto:yourstruly@danesabo.com}{{\footnotesize\faEnvelope[regular]}\hspace*{0.13cm}yourstruly@danesabo.com}}% + \kern 0.25cm% + \AND% + \kern 0.25cm% + \mbox{\hrefWithoutArrow{https://danesabo.com/}{{\footnotesize\faLink}\hspace*{0.13cm}danesabo.com}}% + \kern 0.25cm% + \AND% + \kern 0.25cm% + \mbox{\hrefWithoutArrow{https://linkedin.com/in/dane-sabo-819b211b6/}{{\footnotesize\faLinkedinIn}\hspace*{0.13cm}Dane Sabo}}% + \kern 0.25cm% + \AND% + \kern 0.25cm% + \mbox{\hrefWithoutArrow{https://github.com/namelessfaceless}{{\footnotesize\faGithub}\hspace*{0.13cm}namelessfaceless}}% + \end{header} + + \vspace{0.3cm} + + \section{Education} + + \begin{threecolentry}{\textbf{Ph.D.}}{August 2023 - Present} + \textbf{NRC Fellow, University of Pittsburgh}, Mechanical Engineering + \begin{highlights} + \item GPA: 3.896/4.0 (\href{https://danesabo.com/transcript.pdf}{Unofficial Transcript}) + \item \textbf{Coursework:} High-Assurance Cyber-Physical Systems, Linear and Digital Control Systems, Nonlinear Dynamical Systems, Advanced Dynamics + \item \textbf{Nuclear Engineering Certificate Coursework:} Fundamentals of Nuclear Engineering, Integration of Nuclear Plant Systems, Nuclear Core Dynamics, Radiation Detection \& Measurement, Management Principles for Nuclear Power + \end{highlights} + \end{threecolentry} + + \begin{threecolentry}{\textbf{BS}}{August 2019 - August 2023} + \textbf{University of Pittsburgh}, Mechanical Engineering + \begin{highlights} + \item GPA: 3.433, Dean's Honor List throughout + \item \textbf{Coursework:} Linear Algebra for Machine Learning (Graduate), Mechatronics + \end{highlights} + \end{threecolentry} + + \section{Awards \& Honors} + + \begin{twocolentry}{2025} + \textbf{Best Student Paper Award}, Nuclear Plant Instrumentation and Control \& Human-Machine Interface Technology (NPIC\&HMIT 2025) + \begin{highlights} + \item Awarded for "Employing a Hardware-in-the-Loop Approach to Realize a Fully Homomorphic Encrypted Controller for a Small Modular Advanced High Temperature Reactor" + \end{highlights} + \end{twocolentry} + + \begin{twocolentry}{2025} + \textbf{Student Representative}, MEMS Department Chair Search Committee + \begin{highlights} + \item Selected as student representative on the search committee for the next Department Chair of Mechanical Engineering and Materials Science at the University of Pittsburgh + \end{highlights} + \end{twocolentry} + + \begin{twocolentry}{2023 – Present} + \textbf{NRC Graduate Fellowship}, U.S. Nuclear Regulatory Commission + \begin{highlights} + \item Competitive fellowship supporting graduate research in nuclear engineering and related fields + \end{highlights} + \end{twocolentry} + + \section{Publications and Presentations} + + \subsection{First Author} + + \begin{twocolentry}{2023} + \textbf{Analysis of Vortex Generating Fences on a Formula Student Multi-Element Rear Wing} + + Published in \textit{Ingenium – Undergraduate Research at the Swanson School of Engineering}, Pages 106–111 + \end{twocolentry} + + \subsection{Major Contributor} + + \begin{twocolentry}{2025} + \textbf{Employing a Hardware-in-the-Loop Approach to Realize a Fully Homomorphic Encrypted Controller for a Small Modular Advanced High Temperature Reactor} + + Nuclear Plant Instrumentation and Control \& Human-Machine Interface Technology (NPIC\&HMIT 2025), Conference Paper (Second Author) + + \textit{Best Student Paper Award} + \end{twocolentry} + + \begin{twocolentry}{2024} + \textbf{Demonstration of Advanced Encryption for an Instrumentation and Control System using ARCADE} + + National Organization of Test, Research and Training Reactors (TRTR 2024 Annual Meeting), Presentation + \end{twocolentry} + + \section{Skills} + + \begin{adjustwidth}{5em}{2em} + \begin{itemize} + \item[Programming:] C/C++ (embedded), LaTeX, MATLAB, Python (Pandas, NumPy, SciPy, SymPy, etc...), Rust + \item[Engineering:] ANSYS Simulation Suite, FDM printing, Fusion 360, soldering, Solidworks + \item[Business:] Customer discovery, Team management, Office Suite + \item[Other:] Adobe Illustrator, Adobe Photoshop, Blender + \end{itemize} + \end{adjustwidth} + + \section{Professional Experience} + + \begin{twocolentry}{Pittsburgh, PA\\ August 2023 – Present} + \textbf{Graduate Student Researcher}, Instrumentation and Controls Laboratory \\ + Advisor: Dr. Daniel G. Cole + \begin{highlights} + \item Developing formal verification methods for autonomous hybrid control systems with application to nuclear reactor startup sequences and safety-critical cyber-physical systems + \item Collaborating with Idaho National Laboratory and Sandia National Laboratory on hardware-in-the-loop control system validation and encrypted controller implementations for advanced reactor designs + \item Conducting research on virtualized networks to simulate control systems with genuine network traffic for nuanced analysis of system dynamics + \end{highlights} + \end{twocolentry} + + \vspace{0.2cm} + + \begin{twocolentry}{Remote // Pittsburgh, PA\\ December 2022 – June 2023} + \textbf{Independent Contractor (Mechanical Engineer)}, Human Motion Technologies LLC + \begin{highlights} + \item \textbf{Hip Exoskeleton EXO-004 (Dec 2022 – Jan 2023):} Provided expertise in composites and manufacturing for carbon fiber-reinforced polymer (CFRP) parts, adopting resin infusion as a standard practice. + \item \textbf{Prosthetics Foot Testing TES-001A02 (Mar 2023 – Jun 2023):} Developed a testing fixture for prosthetic feet, evaluating products for fatigue and ultimate strength failure per ISO-10328 standards, designed for up to 5700 N and two million cycles. + \end{highlights} + \end{twocolentry} + + \vspace{0.2cm} + + \begin{twocolentry}{Pittsburgh, PA\\ June 2022 – August 2022} + \textbf{Summer Undergraduate Research Intern}, University of Pittsburgh + \begin{highlights} + \item Analyzed the effects of corotating and counterrotating pairs of vortex-generating fences, focusing on separation prevention at various yaw angles and speeds. + \end{highlights} + \end{twocolentry} + + \vspace{0.2cm} + + \begin{twocolentry}{Spartanburg, SC\\ August 2021 – December 2021, January 2021 – April 2021} + \textbf{Mechanical Engineering Co-op}, BMW Manufacturing + \begin{highlights} + \item \textbf{Pruefcubing (Aug 2021 – Dec 2021):} Evaluated buildability and geometric validity of supplier parts for BMW XM performance SUV, supporting metrology processes. + \item \textbf{Quality Steering (Jan 2021 – Apr 2021, Aug 2021 – Dec 2021):} Monitored development series buildability on manufacturing lines and audited prototype vehicles (X3, X4, X5, X6, X7, XM). Developed data management tools to enhance workflows and database accessibility. + \end{highlights} + \end{twocolentry} + + \section{Teaching Experience} + + \begin{twocolentry}{Pittsburgh, PA\\ August 2022 – December 2022} + \textbf{Content Developer and Teaching Assistant}, MEMS 0071 "Intro to Fluid Mechanics" + \begin{highlights} + \item Developed curriculum incorporating fundamental CFD concepts, with a focus on postprocessing, simulation, and meshing for hydrostatic and hydrodynamic problems. + \item Conducted weekly office hours to assist students in understanding course material. + \end{highlights} + \end{twocolentry} + + \section{Projects} + + \begin{twocolentry}{2020 – 2022} + \textbf{Panther Racing, Formula Society of Automotive Engineers Team} + + \textbf{Technical Director} | 2021 – 2022 + \begin{highlights} + \item Led a team of 30+ engineers and associated majors. + \item Managed a six-figure budget for researching and producing an open-wheel-style racecar. + \item Rehabilitated team culture and mentored younger members to develop engineering and communication skills. + \item Delivered a final car that completed all events at FSAE Michigan without any failures or breakdowns. + \item Improved team performance from 37th/40 (45.4 points) in 2021 to 32nd/99 (462.6 points) in 2022, achieving a 10x points increase. + \end{highlights} + + \vspace{0.1cm} + + \textbf{Aerodynamics and Composites Subteam Lead} | 2021 – 2022 + \begin{highlights} + \item Engineered and designed the aerodynamic package for the 2022 car. + \item Demonstrated expertise in carbon fiber composites manufacturing, including vacuum-bagging, wet lay-up methods, and mold preparation. + \item Conducted workshops to train prospective team members in composites manufacturing techniques. + \end{highlights} + \end{twocolentry} + +\end{document} diff --git a/Writing/CV/dane_cv.cls b/Writing/CV/dane_cv.cls new file mode 100644 index 00000000..9514c54c --- /dev/null +++ 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b/Writing/ERLM/goals-and-outcomes/research_statement.tex new file mode 100644 index 00000000..e1d2fd19 --- /dev/null +++ b/Writing/ERLM/goals-and-outcomes/research_statement.tex @@ -0,0 +1,111 @@ +\section*{Formal Synthesis of Hybrid Controllers for Nuclear Power} +\subsection*{PI: Dane Sabo, NRC Fellow, University of Pittsburgh} +% GOAL PARAGRAPH +The goal of this research is to develop a methodology for creating autonomous +control systems with event-driven control laws that have guarantees of safe and +correct behavior. + +% INTRODUCTORY PARAGRAPH Hook +Nuclear power relies on extensively trained operators who follow detailed +written procedures to manage reactor control. Based on these procedures and +operators' interpretation of plant conditions, operators make critical decisions +about when to switch between control objectives. +% Gap +While human operators have maintained the nuclear industry's exceptional safety +record, reliance on human operators has created an economic challenge for +next-generation nuclear power plants. Small modular reactors face significantly +higher per-megawatt staffing costs than conventional plants, threatening their +economic viability. Autonomous control systems are needed that can safely manage +complex operational sequences with the same assurance as human-operated systems, +but without constant supervision. + +% APPROACH PARAGRAPH Solution +To address this need, we will combine formal methods from computer science with +control theory to build hybrid control systems that are correct by construction. +% Rationale +Hybrid systems use discrete logic to switch between continuous control modes, +similar to how operators change control strategies. Existing formal methods +generate provably correct switching logic but cannot handle continuous dynamics +during transitions, while traditional control theory verifies continuous +behavior but lacks tools for proving discrete switching correctness. +% Hypothesis and Technical Approach +We will bridge this gap through a three-stage methodology. First, we will +translate written operating procedures into temporal logic specifications using +NASA's Formal Requirements Elicitation Tool (FRET), which structures +requirements into scope, condition, component, timing, and response elements. +This structured approach enables realizability checking to identify conflicts +and ambiguities in procedures before implementation. Second, we will synthesize +discrete mode switching logic from these specifications using reactive synthesis +tools such as Strix, which generates deterministic automata that are provably +correct by construction. Third, we will develop and verify continuous +controllers for each discrete mode using standard control theory and +reachability analysis. We will classify continuous modes based on their +transition objectives, and then employ assume-guarantee contracts and barrier +certificates to prove that mode transitions occur safely and as defined by the +deterministic automata. This compositional approach enables local verification +of continuous modes without requiring global trajectory analysis across the +entire hybrid system. We will demonstrate this methodology by developing an +autonomous startup controller for a Small Modular Advanced High Temperature +Reactor (SmAHTR) and implementing it on an Emerson Ovation control system using +the ARCADE hardware-in-the-loop platform. +% Pay-off +This approach will demonstrate autonomous control can be used for complex +nuclear power operations while maintaining safety guarantees. + +\vspace{11pt} + +% OUTCOMES PARAGRAPHS +If this research is successful, we will be able to do the following: +\begin{enumerate} + % OUTCOME 1 Title + \item \textit{Synthesize written procedures into verified control logic.} + % Strategy + We will develop a methodology for converting written operating procedures + into formal specifications. These specifications will be synthesized into + discrete control logic using reactive synthesis tools. This process uses + structured intermediate representations to bridge natural language and + mathematical logic. + % Outcome + Control engineers will be able to generate mode-switching controllers from + regulatory procedures with little formal methods expertise, reducing + barriers to high-assurance control systems. + + % OUTCOME 2 Title + \item \textit{Verify continuous control behavior across mode transitions. } + % Strategy + We will develop methods using reachability analysis to ensure continuous control modes + satisfy discrete transition requirements. + % Outcome + Engineers will be able to design continuous controllers using standard + practices while ensuring system correctness and proving mode transitions + occur safely at the right times. + + % OUTCOME 3 Title + \item \textit{Demonstrate autonomous reactor startup control with safety + guarantees. } + % Strategy + We will implement this methodology on a small modular reactor simulation + using industry-standard control hardware. This trial will include multiple + coordinated control modes from cold shutdown through criticality to power + operation on a SmAHTR reactor simulation in a hardware-in-the-loop + experiment. + % Outcome + Control engineers will be able to implement high-assurance autonomous + controls on industrial platforms they already use, enabling users to + achieve autonomy without retraining costs or developing new equipment. + +\end{enumerate} +% +% % IMPACT PARAGRAPH Innovation +% The innovation is unifying discrete synthesis and continuous verification to +% enable end-to-end correctness guarantees for hybrid systems. +% % Outcome Impact +% If successful, control engineers will be able to create autonomous controllers from existing +% procedures with mathematical proof of correct behavior, making high-assurance +% autonomous control practical for safety-critical applications. +% % Impact/Pay-off +% This capability is essential for economic viability of next-generation nuclear +% power. Small modular reactors represent a promising solution to growing energy +% demands, but success depends on reducing per-megawatt operating costs through +% increased autonomy. This research will provide the tools to achieve that autonomy +% while maintaining the exceptional safety record required by the nuclear industry. diff --git a/Writing/ERLM/main.aux b/Writing/ERLM/main.aux deleted file mode 100644 index aa78092f..00000000 --- a/Writing/ERLM/main.aux +++ /dev/null @@ -1,18 +0,0 @@ -\relax -\bibstyle{unsrt} -\providecommand \oddpage@label [2]{} -\@writefile{toc}{\contentsline {section}{\numberline {1}Goals and Outcomes}{1}{}\protected@file@percent } -\@writefile{toc}{\contentsline {section}{\numberline {2}State of the Art and Limits of Current Practice}{2}{}\protected@file@percent } -\@writefile{toc}{\contentsline {section}{\numberline {3}Research Approach}{2}{}\protected@file@percent } -\@writefile{toc}{\contentsline {subsection}{\numberline {3.1}$(Procedures \wedge FRET) \rightarrow Temporal Specifications$}{3}{}\protected@file@percent } -\@writefile{toc}{\contentsline {subsection}{\numberline {3.2}$(TemporalLogic \wedge ReactiveSynthesis) \rightarrow 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6f85f82a..f2523c9a 100644 --- a/Writing/ERLM/main.tex +++ b/Writing/ERLM/main.tex @@ -10,5 +10,4 @@ \newpage \bibliography{references} - \end{document} diff --git a/Writing/Journal/JRNL-20251012-210736.md b/Writing/Journal/JRNL-20251012-210736.md new file mode 100644 index 00000000..abe2b809 --- /dev/null +++ b/Writing/Journal/JRNL-20251012-210736.md @@ -0,0 +1,137 @@ +--- +id: JRNL-20251012-210736 +title: Sunday, October 12, 2025 - 09:07 PM +type: journal +created: 2025-10-13T01:07:36Z +modified: 2025-10-13T01:07:36Z +tags: [journal] +--- + +# Sunday, October 12, 2025 - 09:07 PM + +Hi future me, it's been another minute. But, not as long as +last time though. Here's some things I want to write about +tonight: + +1. I'm getting closer to an internship opportunity at INL. +2. Matilda is now my girlfriend at the current moment. This + might be problematic. +3. I got dinner with Lucas and his sister at Noodlehead +4. I hosted a poker night. That was fun! + +So first things first. + +I talked to Dan last week about how an internship +opportunity might be a really good thing for me to pursue +next summer. He totally agrees. I'd love to potentially do a +stint at INL or somewhere similar. It could be really cool, +and being in Idaho for the summer could be a lot of fun too +(especially if I bring the bike :eyes). I wonder what the +weather is like up there! I wrote a one page research +statement for Greg Shannon, as he was interested in +receiving one. Dan helped me revise it, and we got to +'better than an 8/10'. Dan is so coy about praise sometimes, +but he knows it can go to my head. He's careful in that way. +Keeps me guessing. I'll presume he was impressed by it. + +Work is going a bit better. My motivation is pretty good, +and I'm making progress on my proposal. I still don't feel +completely locked in, but we're getting there. This is +really challenging, and even though it's my full time task, +I don't feel like I'm going as fast as I could. One proposal +in a fall semester? Hmph. I know its for my thesis, and by +the end of the semester if it's ready to go, I think that is +good enough. I'll check back in on this thought later. + +Okay, now to the dating front. + +I've hung out with Matilda a few more times, and asked her +to be my girlfriend. She makes me feel really good, but that +in itself makes me uncomfortable. It's not the 'feeling +happy' part of that that makes me uncomfortable, but when I +look far into the future, do I see one with her? The answer +is not really. And that fucking sucks. She is so, so nice, +but if I'm being honest, I don't think we're on the same +level or maybe compatible as partners. + +I don't know how to end things. Part of me feels like I'm +being premature, but part of me just feels so anxious and +frankly guilty that I haven't cut things off with her +already. I am really trying to understand why I feel this +way. I know she's an adult with her own stakes and emotions, +and I wonder why I just don't feel like I connect with her +the same way. But at the same time, when she smiles at me +and tells me she feels so special, my heart *sinks*. I don't +know what else to say but to affirm her. That's fucked up. + +Well we went apple picking, and that was a lot of fun. I was +invited to a bonfire afterwards, and I asked her if she'd +like to go. It was with a couple of my engineering friends, +notably Josh, Patrick, and Logan. Everyone got along, but +before we went, I asked how I should introduce her. I +smoothly said I could introduce her as 'my girlfriend, +Matilda'. Smooth, but fuck why did I do that. She was very +excited, and at the moment, I felt good about it too, but +now I just kind of dread this entire series of events. + +Sam mentioned to me that 'I am allowed to be happy'. And +he's right, it's very nice to have someone that does really +like me, is super nice to me, is generally supportive, and +*does* make me happy when I'm with her. But there's also +other happiness that I'm trying to pursue. I feel like I +need time to do my own hobbies. I like this newfound freedom +that I have after breaking up with Amber. I like going on +dates with different people. Fuck. I don't want to have the +*responsibility* that comes with being in a relationship +right now. I just don't think I'm ready for that. + +On a different note, I got dinner and caught up with Lucas. +He's in town because his sister, Lydia, is visiting Pitt. +She's a senior in high school considering Pitt for +engineering. She's funny, charming, and I suspect she was +slightly in to me. She teased me somewhat, and laughed at +all my jokes. I think I was able to answer all her +questions. But, maybe that's my own arrogance. What did +surprise me though is that she recognized my watch as being +a Mr. Jones Watch. That really took me aback, and honestly +set things somewhat into perspective. I need someone like +that in my life, and while Lydia is not necessarily that +person, I do not feel that *spark* with Matilda in the same +way. Lucas is doing well though, and we're going to try and +keep in better touch. + +Finally, I hosted a poker night. Eric, Sam, and Krzyzstof +came over. We had pizzas, and I won $7.65 on 10 dollar buy +ins. I'm pretty stoked about that. We're going to run +another one this next Friday :). It's a nice guys night +thing. + +So I think I have to breakup with Matilda. Maybe I'm being +premature, but honestly, I don't really think so. I don't +want to hurt her worse by pretending that I'm falling for +her in the way I suspect she might be falling for me. +Perhaps we have got to get coffee or something soon and we +can talk. I don't know exactly what I'll say, but probably +something along the lines of: + +1. I know our relationship just started, but I think we need + to end it. +2. I don't know exactly why, but I just don't feel + comfortable right now being in one, and I'm sorry I can't + be that guy for you. +3. That said, you are so, so nice and I wish I could get + there emotionally, but I'm just not. +4. I'm not him for you. But I have really enjoyed getting to + know you, and I wish you the best of luck going forward. + +It's going to suck, but I'd imagine we'd be non contact +after that. I don't know what I would want, but that's +probably what I'd go with. I hate that I'm so romantic +because fuck I worry this will crush her in a way. In the +future, no more flowers or pizzas from scratch? Is making +someone feel too special a bad thing? + +Of course not, that's silly I think. Those can still be +positive memories even if it doesn't work. Fuck this will be +an adjustment, and I've never done this before. I just don't +want to feel so tumultuous right now. diff --git a/Writing/Journal/compiled_journal.pdf b/Writing/Journal/compiled_journal.pdf index 7b994957..912114d2 100644 Binary files a/Writing/Journal/compiled_journal.pdf and b/Writing/Journal/compiled_journal.pdf differ