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# BSP - Random Variables
## Discrete Random Variables
Imagine two sets, A and B.
There is A+B, which the set of elements in A or B,
and $AB = A \union B$, which is the elements in A and B.
Suppose our set S is {1, 2, 3, 4, 5, 6} where A is the evens,
and B is less than 5. AB is {2, 4}, while A+B is {1, 2, 3,
4, 6}.
Sometimes -A is known as NOT A, or $\bar A$.
$\bar S = {}$.
## Probability and Random Variables
Set $\Omega$ is the set of all possible outcomes of an
experiment.
Events of some subset of outcomes are called
$\omega = {odd, even}$
A trial is a single performance of an experiment (single
sample).
An experiment is to observe an single outcome $\zeta_i$.
Experiment E means a set S of outcomes $\zeta$, certain
subsets of S can be considered events.
The space S is the certain event. Basically if it's in S, it
happened. The null space is events that are impossible. E.g.
can't get a 7 on a six-sided die.
If event $\zeta_i$ consists of a single outcome then it is
an elementary event.
Events A and B are mutually exclusive if they have no common
elements (AB = null space)
**Defining exactly what the events and outcomes are is super
important**. It's very easy to get paradoxical results if
careful choice of outcome and event is not chosen.
### Example
Assign each event a number $A \rightarrow P(A)$
Axioms:
1. $P(A) \geq 0$
2. $P(S) = 1$
3. if $AB = 0$ then $P(A+B) = P(A) + P(B)$
Corollaries:
1. $P(0) = 0$
2. $P(A) = 1 - P(\bar A) \leq 1$
*fundamentally the probability of an event is some number
between 1 and 0*
3. If $A$ and $B$ are not mutually exclusive, then
$P(A+B) = P(A) + P(B) - P(AB) \leq P(A) + P(B)$
4. If $B \subset A \rightarrow P(A) = P(B) + P(\bar A B)
\geq P(B)$
## Conditional Probability
Given an event $B: P(B)\geq 0$, we define conditional
probability as $P(A|B) = \frac{P(AB)}{P(B)}$.
Sometimes people write *joint probability* as $P(A,B)$ which
is exactly the same as $P(AB)$.
Given $n$ mutually exclusive events $A_i,...,A_n$ where $A_1
+ A_2 + ... + A_n = S$. For an arbitrary event $B$,
$P(B) = \sum_i P(A_i, B)$
$P(B) = \sum_i P(B | A_i) P(A_i)$
We know $B = BS = B(A_1+...+A_n)$. With some rearranging
knowing each of the A's are independent, $BA_i$ and $BA_j$
are independent for all $i\neq j$.
Thus, $P(B) = P(BA_1) + ... + P(BA_n)$ but we showed earlier
there's a different way to find $P(B)$.
if $B = S$, $P(S|A_i) = 1$, then $P(S) = 1 = \sum_i P(A_i)$
if $B = A_i$, $P(A_j|A_i) = 1$ when i = j, 0 otherwise
> [!important] Development of Bayes' Theorem
>
> Bayesian statistics are a way of thinking about a **degree
> of belief** in a probability, not an estimation of the
> probability from a number of experiments.
>
> We know:
>
> $P(AB) = P(A|B)P(B) = P(B|A)P(A)$
>
> Then Bayes Theorem becomes
> $$P(A|B) = \frac{P(B|A) P(A)}{P(B)}$$
>
> and then when events $A_i$ are mutually exclusive...
>
> $$P(A_i|B) = \frac{P(B|A_i) P(A_i)}{\sum_i P(B|A_i) P(A_i)}$$
>

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---
id: 2025-08-15
title: Daily — 2025-08-15
type: daily
created: 2025-08-15T21:38:18Z
modified: 2025-08-15T21:41:25Z
tags: [daily]
---
# Daily — 2025-08-15
## Quick capture
- Today I didn't really do anything! But I made a bit more
progress on my Zettelkasten. It actually exists now and I
made commands to use it.
- I also made git pushing commands.
## Tasks
- [ ]
## Notes

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---
id: 2025-08-18
title: Daily — 2025-08-18
type: daily
created: 2025-08-18T17:12:19Z
modified: 2025-08-19T13:43:54Z
tags: [daily]
---
# Daily — 2025-08-18
## Quick capture
- Installed VimTex and got latex working on my laptop with
neovim
- Zettled more about Strix and logic
- Meeting with Babay's group in the INFSCI building.
- Signed up for Strava. Considering doing a run club. Could
be coool!!!
## Tasks
-
## Notes
Notes from Babay meeting:
Emerson is going to upgrade the Ovation system in Cole's
group. We're looking for controllers and things to use.
Ideas from Babay's group:
- Protocols: MODBUS and DNP3, HART protocol. Highway
Addressable Remote something something. Similar to MODBUS
and DNP3 in principal.
- Instrument light panel.
- Testbed before Energy Innovation Center (EIC)? What tests can we do before going to
EIC?

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---
id: 2025-08-19
title: Daily — 2025-08-19
type: daily
created: 2025-08-19T14:31:15Z
modified: 2025-08-19T19:06:40Z
tags: [daily]
---
# Daily — 2025-08-19
## Quick capture
Goals for today:
- Write powerpoint for Strix
- Write heilmeir paragraphs for thesis idea
- Tour new gym
- Get details on dSPACE and speedgoat systems
## Tasks
- [ ]
## Notes
Here is a list of I/O we can use in the PLC Cabinet:
1. MODBUS compatibility (Babay / Cole)
- Over Ethernet is ideal, but other mediums would also
be nice to have.
2. DNP3 (Babay)
3. HART (Babay)
4. Analog Inputs / Outputs
- +/- 10 V for dSPACE (Maximum range)
- +/- 10 V for TQ Equipment (Ball and Beam)
- 0-1.8V for BeagleBone Black
- IO101 from Speedgoat can use all of above (and +/- 5
V, +/- 3.3V)
5. Digital Inputs / Outputs
- 10 V dSPACE and related
- 3.3 V for BeagleBone Black
- 5 V for Arduino
- IO101 can use all of above
6. OPC UA, don't need right now but could be useful for
historians and working with data later.
Obviously for digital signals we can use voltage regulators
if required but it would definitely be nice to have 3.3V
capability for the BeagleBone, and 5V for an Arduino.

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---
id: 2025-08-20
title: Daily — 2025-08-20
type: daily
created: 2025-08-20T13:54:13Z
modified: 2025-08-22T15:06:52Z
tags: [daily]
---
# Daily — 2025-08-20
## Quick capture
- Workin in the morning on Strix presentaiton
- Cole Group Meeting 10am - 11am
- Write down weekly plan 11am+
## Notes

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---
id: 2025-08-22
title: Daily — 2025-08-22
type: daily
created: 2025-08-22T15:41:02Z
modified: 2025-08-22T16:03:15Z
tags: [daily]
---
# Daily — 2025-08-22
## Quick capture
- Got to work kind of late. Feeling sicky af. Probably no
darts tonight with PSM.
- Working on moving all my notes into zettels
- Lunch w AS today
- Okay i'm starting to feel a little better (12:03PM)
## Tasks
- [ ]
## Notes

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---
id: 2025-08-25
title: Daily — 2025-08-25
type: daily
created: 2025-08-25T16:02:00Z
modified: 2025-08-26T13:56:53Z
tags: [daily]
---
# Daily — 2025-08-25
## Quick capture
- Got in a little later today, but the bike is here! Gotta
text Alisa about it.
- I have 2 classes today (grumble grumble grumble).
- ME 3100 ERLM is Monday and Wednesday at 1PM-2:15PM
- NUCE 2101 - Nuclear Core Dynamics is tonight
6PM-8:30PM, like usual
- I also enrolled in my health insurance.
## Tasks
- [ ]
## Notes

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---
id: 2025-08-26
title: Daily — 2025-08-26
type: daily
created: 2025-08-26T15:05:38Z
modified: 2025-08-26T15:06:58Z
tags: [daily]
---
# Daily — 2025-08-26
## Quick Capture
- I started this morning doing some email
- Now I'm hangin out in starbucks doing some work for the
quad chart n'at
- First, what the fuck is a quad chart??
## Notes

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---
id: 2025-08-27
title: Daily — 2025-08-27
type: daily
created: 2025-08-27T18:33:33Z
modified: 2025-08-28T17:57:53Z
tags: [daily]
---
# Daily — 2025-08-27
## Quick capture
COLE GROUP MEETING
Accomplishments:
- Quad chart
- writing more about LTL and building out some notes from
papers
- Found resources about temporal logic
- first nuce class has happened. Codes and standards were
cancelled
to do:
- Write goals and outcomes
- Write more about approach. This is squishtastic
- Actually finalize some outcomes. How do i navigate the
fact that within switching mechanisms there is dynamics
happening
- I didn't say anything about what a hybrid system is.
That's kind of the whole point of the thing.
## Notes

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---
id: 2025-08-29
title: Daily — 2025-08-29
type: daily
created: 2025-08-29T14:23:06Z
modified: 2025-08-29T15:44:16Z
tags: [daily]
---
# Daily — 2025-08-29
## Quick capture
Yesterday I wrapped up a couple small things I needed to get
done. First, I sold my bike to Alisa for 250! Pretty good
deal for me, I made 30 on the sale. Then, I went to Harbor
Freight and got some critical tools for working on the bike.
It turns out, it's actually really hard to put a dirt bike
on a stand. Heavy as all hell. But today, I'll get the sumo
wheels on the bike!
- [?] What tire pressure should I use for these new wheels?
For work stuff, I've got to answer more Heilmeier questions
and start writing a goals and outcomes section. The G&O
should likely be a LaTeX document.
The Emerson guys were here today too to fix up the ovation
system. They told us they took the top off, affixed the
power strip to the upper right side, and finally they told
use we can totally take all the doors off if we wanted. They
also said no 3.3V, they do all 24V stuff so they just don't
carry the modules that go that low in power.
## Tasks
- [ ]
## Notes

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# What should I do about my PhD?
---
The quick brown fox jumps over the lazy dog. The dog stays blissfully asleep. :)
This time, I'm actually going to begin writing a journal. I feel like I have a
lot of thoughts that I let swim around, without doing much about them. To quote
*the Happiness Lab* episode that I listened to today:
"Good intentions mean nothing if they don't translate into actions."
So I'll take Dan's advice, and use writing to do thinking. I also think that
writing this journal can improve my writing skills.
So what's going on today?
Well as I'm writing this, I'm on the 61D on my way into school listening to
*Spanish Pipedream* by John Prine. But what I really want to tell you about is
the decision I'm trying to make about whether or not to finish my PhD here at
Pitt with Dan. Last Friday, I had a meeting with Dan about an idea I was
interested in pursuing that at the core involved working with a real, tangible
system. That idea was politely dismissed, and I was 'nudged' back towards formal
methods for critical infrastructure. My immediate impression is that formal
methods for our lab is a crock of shit.
Dan means well and is genuinely looking out for my best interest, but that
doesn't translate into belief into his mission. Formal methods are an intense
mathematical pursuit in order to prove 'correctness' of something to something
else. Formal methods experts may disagree with that characterization, but
ultimately that second 'something' can be a lot of things, such as a model of a
plant, a written specification, or anything that can be logically defined. Dan
wants to use formal methods to prove things about physical systems. His idea is
aligned with what Manyu just finished up: can we use formal methods to prove that
certain systems adhere to requirements using formal methods? This is connected
in part to the HARDENS report, which tried to use formal methods tools at several
layers of abstraction to prove that a written requirement can be translated into
a proof for a determined plant design. There is certainly work to be done there.
But is that work that I want to do? My brain says I could do it, but my gut
screams out a vehement no. This is the core issue--I know I could do it, but
once I would finish, where does that leave me? The answer: a formal methods
expert. Formal methods experts are highly sought after, but it is an intensely
theoretical oriented field. When I think about what I want to do in my career
and what my values are, they are not only working through a computer (despite
my aptitude for such). I want to build real things, works you can touch, and
that interact with the world. A formal methods proof about a reactor that *might*
get built is not in that alignment.
So what the hell do I do? As I write this, it seems pretty clear the relationship
between myself and the Cole Lab's work is fractured. Going forward, I see three
main options:
1) Find another PhD advisor at Pitt. Bajaj is an obvious choice.
2) Master out and go find a job.
3) Go find another PhD opportunity somewhere else. Yichen did this.
Pros and cons of each situation:
1) Find another PhD advisor at Pitt
+ I would be able to keep my NRC Fellowship
+ I know people here already
+ I've already passed the qualifying exam
- Money is garbage
- I don't think anyone is actually doing work that I really want to do
- Have to stay in Pittsburgh
- NRC debt keeps growing
2) Master out and go find a job
+ I would immediately make much more money
+ Can move somewhere else (Boston?)
+ NRC commitment is only a year
+ Could find an interesting R&D job?
+ Could get a second publication out for Bajaj's project
+ Could pick up PhD again in a year or so. Work on projects to make
myself super competitive
- Dr. Sabo is on hold
- No thesis!
3) Master out and start a PhD at another school
+ Dr. Sabo is slightly delayed
+ Could go work in Boston
+ Could go work on something I feel passionate about
+ Better degree diversity
+ Teaching plan could still work out
- Slightly longer timeline
- Have to take another qualifying exam
- Still have the NRC commitment likely
- Would not make much money
I think the smartest thing is to master out, find a job for a year that will
satisfy the NRC requirement, and then if I want to, restart the PhD somewhere
else. This would put me finishing sometime in 2030 or so. That's certainly a lot.
If I went to find a PhD now, I would finish somewhere in 2029 or so, then have
the 1-year NRC commitment. Hmmm.
I checked my current progress in my degree, and learned that I satisfy the controls
track masters degree after this semester. I would need to negotiate two things:
either ME 2046 or ME 2150 would need to count as a DSC elective, and NUCE 2100
would have to be accepted as a ME elective (it is cross listed as ME 2100, so
shouldn't be impossible to argue for). The next thing I need to do for this would
to be to talk to Dan about it.
Thinking about stopping with the Master's feels good. I think I should seriously
pursue this, and maybe talk to Rachel and my family about it.
## Chat w/ Pat
Patrick and I got lunch today. He was generally pretty supportive and gave me
some sound advice that I can use. He asked me "have you read some literature
reviews?" And the answer to that is no, not really. He also advised to "just do
something", which perhaps will help me feel like I'm actually getting something
built. I think that is helpful. Going forward, I'm going to really try and do
two things:
1) Read at least 3 literature reviews by Friday
2) Get ARCADE and I2C working by next Monday
[Could be interesting](https://www.adafruit.com/product/2264?gQT=0)
I really don't know what I should do. This certainly is not a one day decision.
Honestly, I may like the idea of option 3 the best, but I do need to do some work.
I've got it in the works to:figure out how to get the MS along the way with Antoine,
so we'll see how that happens. I think the earliest things would happen would be at
the end of the summer.

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The quick brown fox jumps over the lazy dog. The dog stays blissfully asleep. :)
Since last time, I have found a bit more resolve on what I'm going to do about
this whole PhD thing. I have decided I am going to earnestly try to find a topic
that fits with the lab's formal methods bend--at least for the rest of the
spring and into the beginning of the summer. I am taking action to try and find
a topic, like trying to read more surveys and actually doing things. This past
week was not necessarily super successful in that regard, but on the margins was
an improvement. Oh, well.
There is a couple reasons I think this is the right move. First, I am already
here. Any other route that ends with my PhD will add extra time before I am
finished. Any job search right now is also probably not a great idea, since
Trump and his merry men are starting a trade war, and consequently likely a
recession. I am in a good position right now, and there is value in taking stock
of the opportunity that I have.
Robert also lended some helpful advice: certainly the topic of my PhD does not
pigeon hole me into a field for the rest of my career. I think this is true in
a restricted sense, but not in the general sense. For my sake, this means if I
do something formal methods adjacent, it does not mean I need to be stuck in
formal methods forever, but also I should be careful that the work I do also
lends itself to another field I find interesting. One such area is perhaps using
formal methods with artificial intelligence to leverage these tools to create
explainable AI based control.
I need to read more to really understand what that can be. Update to come.
Now for a slight change of pace, some more personal details.
The pursuit of an apartment for Amber and I continues to be a contentious topic.
Amber was quite upset coming back from her trip that I 'did not take care of
myself'--her accusation is that I did not eat balanced meals or in general act
with personal motivation to do things that are good for me. This also compounded
with my food habits with my night classes. I have eaten out a lot recently before
class instead of cooking food at home the night before or so. Amber attributes
this to lazyness. This argument culminated in her saying that she feels more
like a mom than a girlfriend. That makes me really upset.
Do I think she is right? Well, in terms of food, sure. She has a good point. I
could certainly eat better, and this past weekend I see what she is saying about
balanced meals. Fair point and this is something I must correct. Something that
does make me worried however is this idea that she is like my mom rather than
my girlfriend, and more broadly that she feels I make changes because she tells
me so rather than because I want to on my own. This is a frustrating catch-22 in
my opinion. If I do not learn what is upsetting her, I cannot change that
behavior. But, if she tells me and I do change that behavior, she takes credit
for it and gets upset anyways. Honestly, it makes me feel like damned in a way.
I'll try and change nonetheless, but it is incredibly demotivating to think
she will believe it is just because 'she told me so'.

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---
---
# 2025-07-30
## Morning Brief
Today's goal is to finish writing up some thesis ideas. I
need to have 6 of them for a meeting with Dan. I used
ChatGPT to help me brainstorm some ideas, but I need to go
over them and format them in a way that is more
approachable.
On the other hand, I've been working on leaving my phone
behind. I'm trying a new technique of just leaving it out of
my reach. I can feel the itch in my brain that yearns for
it... that's definitely an addiction I have to kick.
Anyways, here's the goals for today:
- [ ] Write down 6 ideas for a thesis: [[thesis-ideas]]
- [ ] Review literature notes, and organize my notes
- [ ] Finish [[automation-levels-for-nuclear-reactor-operations-a-revised-perspective]]

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---
---
# 2025-07-31
## Morning Brief
Yesterday I wrote 2 thesis ideas and started a third. Today,
we finish them! I'm struggling to write outcomes but we'll
get there over time. I can do this.
I started the morning with an hour of doomscrolling. I
really have to sort that out.
Tasks are the same from [[2025-07-30|yesterday]]. Maybe I
should make a centralized page for tasks.
- [ ] Make task page #admin
## Lunch Brief
## Note for tomorrow

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---
---
# 2025-08-01
## Morning Brief
Yesterday I finished two additional thesis ideas and got
some more reading done
- [ ] Fill out health insurance enrollment

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---
---
# 2025-08-04
## Morning Brief
I didn't do shit. But I emailed Dan that I'd be OOO
Wednesday and Thursday for the motorcycle course.
I'm finishing those fucking thesis ideas today. ON GOD.
[[thesis-ideas-2025-07-30]]
I'm' also supposed to have a date with Miranda today, but
she hasn't texted me back. Interesting. Jackie also
complimented my socks and show combo. That was nice. I
showed her and Natan [Angus](ourcowangus.com).

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---
---
# 2025-08-05
## Morning Brief
I didn't finish the thesis ideas from yesterday. Oopsie!
Today is different though. Curently, I'm working from
home^*, which really means I'm working in a coffee shop on
Washington road. I'm at the Orbis Cafe, where I purchased a
cinnamon roll and a cappucino. The caffeine has yet to hit,
but when it does, I'll be cooking I'm sure. This is a nice
spot and it's very relaxing to get things done while other
people are around. I like this a lot, and perhaps I should
do this more often while I'm at school too.
Anyways, Dan is OOO taking time off while he can before the
fall semester. Who can blame him?
Patrick and I discussed more PINN stuff yesterday. I should
make a simple PINN demonstration.

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---
---
# 2025-08-06
Today was the first day of the motorcycle safety course. It was
good! I felt like I was honestly the best rider there. That being
said, tomorrow is a new day and we'll see how it goes. Jackie
looked like she had fun too.
I had a great date yesterday. Miranda is very, very cool. She
loves facebook marketplace, mac.bid, camping, and said her
favorite book was *Dune*. My jaw just about fell open when I
heard that. We're potentially going to go look at a van on
Saturday.
I missed the Jumet Financial Open House. I slept right through
that mf after getting back from the course. Whoops. I feel bad
about it as Sam gave me a call right in the middle. No voicemail.
Yikes. I'll see how that works out.
Then, last thing today is getting some final writing done to say
that I did any work today. No group meeting this week it looks
like.

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---
---
# 2025-08-07
Today I have not gotten too much done, but I did get here
early today. Today, I'll sell the truck and work on Sam's
car. I saw Patrick today too, which was nice. Robert's stuff
is all gone.
My main focus for today is to finish the thesis ideas and
tune up the writing. That'll be enough.

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---
---
# 2025-08-11
Today I'm finishing the thesis ideas, for real this time.
I'm also going to get a model of a heat exchanger working.

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---
---
# 2025-08-12
Yesterday I finished my thesis ideas! Hooray! It feels
really good to actually have some writing finished. Today,
I'm making a model for a simple heat exchanger in python.
Then, I'm going to train a physics informed neural network
on it and start fucking with parameters.

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---
---
# 2025-08-13
Today is August 13th, 2025, otherwise known as judgment
day. Just kidding, but today I have my meeting with Dan
about my topic ideas. I feel anxious, but pretty good in
general. I saw Dan this morning and he seems to be in good
spirits. I can do this!
My eye doctor appointment was also today. The results? My
prescription is pretty much the same. I also do not have
glaucoma it looks like. Doc was surprised I wear glasses at
all, figuring the binocular detriment of glasses in my case.
Honestly, he's right, I should wear contacts more often.
I'll try to make a point to do that. Now that I have this
new prescription, I can get on ordering more contacts from
Costco. Dr. Clermont also recommend to try and stay around
twelve hours of usage a day to minimize hydration issues. He
said pushing 16 some times is okay. 12 hours would be 7-7
(duh), while 16 would be 7-11pm. We also discussed LASIK,
and he said honestly I'd be a great candidate. He gave me a
note with a number to call.
Today is also our group meeting. Apparently it's a
'standup' now.
## Personal
Personally I'm doing pretty okay. I'm trying to focus on
framing things in a more positive way. I think it is working
somewhat; there's moments where things click in a way I
don't feel as anxious about.
On the lady front, I finally hit app-burnout. I was reading
a text and the typos just made me angry. Like, c'mon, read
your message! This isn't rational, however, as any number of
things can create a typo and it really isn't a big deal.
There's no reason I should get so frustrated at something so
small like that.
Anyways, here's the roster and relevant updates:
**Miranda**:
Miranda is cool and I like her a good bit. She's funny,
seems somewhat interested in me, and is a great time to be
around. That being said, I need to be careful. I'm getting
somewhat infatuated with her but there isn't really a super
strong connection there yet. This is one that I need to
really step off the brakes with and see how things develop.
She is going on vacation with her family next Friday, and
then going solo camping after that. Then, I'm really going
to try and let her set something up.
**Katarina**:
Katarina is a recent match and is interesting as a prospect.
She seems pretty nice and is a bioengineering PhD student in
her 5th year. So almost done maybe? I'll get more details on
Thursday night!
**Abby:**
Abby is a nurse who I've had an interesting conversation
with about religion. She has 'catholic' in her profile but
is apparently not very religious actually. She has a dog
named Goose! We're meeting up on Sunday to take Goosey-boy
for a walk.

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---
---
# 2025-08-14
## Work
Yesterday Dan and I had our meeting about
[[thesis-ideas-2025-07-30 | topic ideas]]. The results were
as follows:
5. Integrating Shielding in Nuclear Power
3. Formally Verified NN CTRL of CRS
1. Temporal Logic Specifications for Autonomous Control
Synthesis.
1. Formally Verified Runtime Monitoring and Fallback
6. High Assurance Fault Detection with Digital Twins
4. Verified Adaptive Control.
The final topic result?
*Hybrid Controller Synthesis from Temporal Logic
Specifications*
The research will be basically a mix of the third and fourth
idea. More work to come on this one.
I also got roped into making a presentation about Strix for
next week's meeting. So I must learn about that!
## Reading
Yesterday I read more of *The Power of Habit* and I learned
about the **craving**. A craving is what actually makes the
habit loop work. It was explained to me that the brain
releases a spike in activity at first when it recognizes the
reward. Once the cue and routine are associated with the
reward, the brain over time will deliver the activity spike
as an anticipation of the reward *earlier and earlier*. The
result is that the brain gets the activity spike as soon as
it sees the cue, anticipates the reward, and is thus
motivated to do the routine. The craving is what makes
habits easy.
## Personal
Finally my personal info. I feel pretty good today. I didn't
get a lot done this morning but I'm steady cooking now that
I'm working in a Starbucks on campus. I've been
peoplewatching as people slowly move in for the fall
semester. It's fun to see all the different kinds of people
walking around and to see the connection between kids and
parents. The kids definitely look more nervous on average
than the parents. And I get it, the parents know what to
expect, but for the kids, this is the transition to the deep
end. They'll be fine.
On the lady front, here's today's update:
**Miranda:**
Honestly I'm getting a little bored. I think it might just
be a texting issue, or perhaps the infatuation wearing off.
That's okay though, she's really busy this week som maybe
that has something to do with it.
**Abby:**
No update!
**Katarina:**
Also no update, but I'm excited for our date tonight. We'll
see how it goes.
I made some updates to my hinge profile to make things sound
more serious and better indicate what I want / who I am.
Maybe this'll stand out more. Honestly, I tried to write the
profile like one I'd be looking for.

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---
---
# 2025-08-14
## Work
## Reading
## Personal

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# Internship Locations
This is a short list of internship spots I am considering.
The goal is to find an internship that starts next summer,
and maybe can eventually be parlay'd into a job.
## National Laboratories
**Idaho National Laboratory**
- Contacted Greg with research statement.
- He's talking about it with Wayne and Simon Pemblott.
**Sandia National Laboratory**
- Sent research statement to Lee. He liked it and offered
comments.
- There's a fellowship internship opportunity. I should
check that out
## Nuclear Companies
**Westinghouse**
- Is there any opportunities here? Maybe, maybe not. They
seem pretty humdrummy
**Oklo**
- Do they have opportunities? Must find a recruiter.
## Other Companies
**Anduril**
- Hehe cool robotics military tech
- find a recruiter. They've got lots of jobs open
**CIA**
- Do they have internships?
**Lockheed Martin**
- Any cool advanced military gigs?
**Applied Physics Lab**
- We know Chris D'Angelo there
**Loonwerks**
- Spoke to Daren Cofer at NASA FM conference. Any
opportunities there?

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# Meeting with Ginger and Benjamin about Summer Internship
Also not directly an interview, but rather a check-in and
conversation. Good conversation about the thrust they would
be interested in me working on. CIE-group. They want to do a
push about how we define resilliency, especially when it
comes to cyber control systems. Probabilism and defense in
depth is not enough, or perhaps not the right approach.
Ginger also brought up good points. We want to be able to
have evidence for autonomous control systems for things like
liability courts. If something goes wrong, we want to be
able to say why the control system made the right choice,
based on formal methods approaches to justify control
actions. Also talk about *graded* responses and saying
whether or not we can justify operation of a degraded
system.
16-wk on-site internship. Relocation help included. Spoke
highly of Dan and continued collaboration is an option.
Two main deliverables:
- a kind of state of the art on what 'resilience' is and how
it is determined
- a thrust or way forward of what new metrics for resilience
could look like. Sounds like an advanced proposal
- Conference paper?
Team: Ginger, Benjamin, a gentleman named John, other
individuals.
Benjamin has a reachability manifesto he wants to send us.
Dan as INL-vetted will probably get an email about it.
More to come in the next couple of weeks. Need to evaluate
against Emerson opportunity. This seems to have more
direction.

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# CISA ICS Training Notes
## Russ' Quiz
% data breaches involving phishing --- 15%
% of all breaches involving human error --- 68%
% financially motivated incidents that involve ransomware or
extrotion --- 92%
Year the PLC was invented? --- 1968

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# Notes from INL Internship Meeting
**Attendees:**
- Dane
- DGC
- Greg Shannon
- Wayne Austad

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# Meeting With Emerson about Internship
## Attendees
Dan
Myself
Rick
##
## Questions I have:
- What does the day to day work you'd have me working on
look like?
- Size of the team?
- On site in cranberry?
- Next steps? When should I hear from you?

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[Vim for MATLAB](https://github.com/daeyun/vim-matlab)

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---
id: 2025-34
title: Weekly — 2025-08-20
type: Weekly
created: 2025-08-20T13:54:13Z
modified: 2025-08-20T19:10:24Z
tags: [weekly]
---
# Weekly - 2025 CW 34 (Aug 18 - Aug 22)
## Accomplishments
1. Met with Babay's group and collected their needs for the
new ovation system stuff. The notes are in [[daily-2025-08-18]]
2. Learned about logic. Started with propositional logic,
then did predicate logic, now am working on temporal
logic.
3. Made a presentation about Strix, and learned about parity
games. Strix uses determnistic parity games to do
synthesis, and yields automata that are very small relative
to competition. They're old though--2017 was the first Strix
paper.
## This week's plan
1. Write heilmeir paragraphs for thesis topic
2. Make Quad chart for ERLM
3. Find and keep working on an LTL book

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---
id: 2025-35
title: Weekly — 2025-08-20
type: Weekly
created: 2025-08-20T13:54:13Z
modified: 2025-08-20T19:10:33Z
tags: [weekly]
---
# Weekly - 2025 CW 35 (Aug 25 - Aug 30)
## Last week's plan
1. Write heilmeir paragraphs for thesis topic
2. Make Quad chart for ERLM
3. Find and keep working on an LTL book

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---
id: 2025-36
title: Weekly — 2025-09-02
type: Weekly
created: 2025-08-20T13:54:13Z
modified: 2025-09-03T18:59:44Z
tags: [weekly]
---
# Weekly - 2025 CW 36 (Aug 25 - Aug 30)
## Accomplishments
- Wrote the goals and outcomes, went up to V4.
- Goal was flubbed but have new content
- started thinking about how continuous dynamics need to be
included.
- Tried to watch a video about hybrid system verification.
Made fun of 'trajectories' nomenclature instead of
executions and then shit really went off the rails fast.
Lots of pretty figures but I have to be honest I have no
idea what the fuck he was talking about.
- Had crises about intellectual mert
## To Do
- Rewrite GO
- SOTA. Start writing.
- look up cones for math

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---
id: 2025-46
title: Weekly — 2025-11-12
type: Weekly
created: 2025-11-11T13:55:31-05:00
modified: 2025-11-12T15:43:57-05:00
tags: [weekly]
---
# Weekly - 2025 CW 46 (Wed 2025-11-12)
## Accomplishments
### Internship
- ✓ Write cover letter for INL Application
- ✓ Apply for INL Internship
- ✓ Submit INL Application on Taleo
### class.NUCE2-101.Exam2
- ✓ Problem 1
- ✓ Problem 2
- ✓ Problem 3
- ✓ Problem 4
- ✓ Problem 5
- ✓ Problem 6
- ✓ Submit Exam 2
### ERLM
- ✓ Assertion-Evidence - do in lieu of class
### General
- ✓ Get Dan's approval for course
- ✓ Create updated plan of study document
## Pushed or Rescheduled
### ERLM
- Mock Peer Review Assignment (rescheduled)
- Make data management plan (rescheduled)
- Make biographical sketch (rescheduled)
- Make facilities section (rescheduled)
- Add more tasks for this week (rescheduled)
- Draft Presentations (rescheduled)
- Tune up state of the art for Proposal (rescheduled)
- Final Presentations (rescheduled)
## Cancelled or Deleted
No tasks were cancelled or deleted this week.
## To Do
### Immediate (Due within 24 hours)
None
### Due Saturday, November 16 (4 days)
- Submit enrollment form to Antoine
- Mock Peer Review Assignment (ERLM)
- Create ORCID account (ERLM)
- Make data management plan (ERLM)
- Make biographical sketch (ERLM)
- Make facilities section (ERLM)

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---
id: 2025-47
title: Weekly — 2025-11-19
type: Weekly
created: 2025-11-19T14:34:56-05:00
modified: 2025-11-19T14:34:56-05:00
tags: [weekly]
---
# Weekly - 2025 CW 47 (Wed 2025-11-19)
## Accomplishments
### ERLM
- ✓ Assertion-Evidence --- do in lieu of class
- ✓ Read Proposal 1
- ✓ Read Proposal 2
- ✓ Read Proposal 6
- ✓ Create ORCID account
- ✓ Make data management plan
- ✓ Make biographical sketch
- ✓ Make facilities section
- ✓ Mock Peer Review Assignment
- ✓ Add more tasks for this week
### General
- ✓ Get Dan's approval for course
- ✓ Create updated plan of study document
## Pushed or Rescheduled
No tasks were rescheduled during this period.
## Cancelled or Deleted
No tasks were cancelled or deleted during this period.
## To Do
### Due This Week (Nov 19-26)
**ERLM**
- Draft Presentations (due 2025-11-21) [urgency: 8.75]
### High Priority
**ERLM**
- Tune up state of the art for Proposal (due in 2 weeks) [urgency: 3.44]
- Final Presentations (due in 2 weeks) [urgency: 3.44]
**Zettelkasten (zk)**
- Write zettels about Andre Platzer and differential dynamic logic [urgency: 3.19]
- Write zettels about webofscience database [urgency: 3.19]
- Deterministic Parity Automata [urgency: 2.95]
- Mealy Machines [urgency: 2.95]
- AIGER Circuits [urgency: 2.95]
- Reactive Synthesis [urgency: 2.95]
- Write about opp. chall. and res. needs for remote micro ope. [urgency: 2.92]

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---
id: 2025-49
title: Weekly — 2025-12-03
type: Weekly
created: 2025-12-03T21:01:29-05:00
modified: 2025-12-03T21:01:29-05:00
tags: [weekly]
---
# Weekly - 2025 CW 49 (Wed 2025-12-03)
## Accomplishments
### ERLM
- ✓ Draft Presentations
### Chair-Search
- ✓ Make list of tasks for contact about student groups
## Pushed or Rescheduled
The following tasks had their due dates modified during the past week:
- Review and edit Goals and Outcomes section
- Review and edit State of the Art section
- Review and edit Research Approach section
- Review and edit Metrics of Success section
- Review and edit Risks and Contingencies section
- Review and edit Broader Impacts section
- Review and edit Budget section
- Review and edit Schedule section
- Verify RFP compliance for all sections
- Final proofread and polish entire proposal
- Review and edit Literature Review section
- Review and edit Methodology Details section
- Review and edit Expected Contributions section
- Review and edit Timeline and Milestones section
- Review and edit Team Qualifications section
- Review and edit References section
- Review and edit Appendices
## Cancelled or Deleted
No tasks were cancelled or deleted during this period.
## To Do
### Due This Week (Dec 4-10)
**ERLM Project - Editing Tasks (Due Tomorrow: Dec 4)**
All of the following editing tasks are due tomorrow and are high priority:
- Review and edit Goals and Outcomes section (Urgency: 22.1) ⚡ ACTIVE
- Review and edit State of the Art section (Urgency: 22.1) ⚡ ACTIVE
- Review and edit Research Approach section (Urgency: 18.1)
- Review and edit Metrics of Success section (Urgency: 18.1)
- Review and edit Risks and Contingencies section (Urgency: 18.1)
- Review and edit Broader Impacts section (Urgency: 18.1)
- Review and edit Budget section (Urgency: 18.1)
- Review and edit Schedule section (Urgency: 18.1)
- Verify RFP compliance for all sections (Urgency: 18.1)
- Final proofread and polish entire proposal (Urgency: 18.1)
- Review and edit Literature Review section (Urgency: 18.1)
- Review and edit Methodology Details section (Urgency: 18.1)
- Review and edit Expected Contributions section (Urgency: 18.1)
- Review and edit Timeline and Milestones section (Urgency: 18.1)
- Review and edit Team Qualifications section (Urgency: 18.1)
- Review and edit References section (Urgency: 18.1)
- Review and edit Appendices (Urgency: 18.1)
- Update abstract based on final content (Urgency: 18.1)
- Compile final PDF submission (Urgency: 18.1)
### High Priority
All high-priority tasks are already listed above in the "Due This Week" section.

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---
id: 2025-50
title: Weekly — 2025-12-17
type: Weekly
created: 2025-12-17T20:56:30Z
modified: 2025-12-17T20:56:30Z
tags: [weekly]
---
# Weekly - 2025 CW 50 (Wed 2025-12-17)
## Accomplishments
### Chair-Search
- ✓ Review Zbeeb, Khaled application
- ✓ Review Christopher, Gordon application
- ✓ Review Robles Hernandez, Francisco Carlos application
- ✓ Review Asmatulu, Ramazan application
- ✓ Review Gupta, Sanju application
- ✓ Review Yang, Xiaodong application
- ✓ Review Kim, Harrison application
- ✓ Review Makhlouf, Abdelsalam application
- ✓ Review Gouma, Pelagia application
- ✓ Review Akkus, Ozan application
- ✓ Review Narayan, Roger application
### Internship
- ✓ Tune up presentation for Emerson... digital twins
## Pushed or Rescheduled
No tasks were rescheduled during this period.
## Cancelled or Deleted
No tasks were cancelled or deleted during this period.
## To Do
### Due This Week
**Due within 24 hours:**
- **Union** — Talk to Jessica about getting a room for an event (Due: 1d, Urgency: 9.23)
### High Priority
**Zettelkasten (zk):**
- Write zettels about Andre Platzer and differential dynamic logic (Urgency: 3.34)
- Write zettels about webofscience database (Urgency: 3.34)
- Deterministic Parity Automata (Urgency: 3.1)
- Mealy Machines (Urgency: 3.1)
- AIGER Circuits (Urgency: 3.1)
- Reactive Synthesis (Urgency: 3.1)
- Write about opp. chall. and res. needs for remote micro ope. (Urgency: 3.07)
**Other Projects:**
- **ERLM** — Add research tasks to research approach section (Urgency: 2.36)
- **Thesis** — The Algorithmic Analysis of Hybrid Systems (1995) [reading] (Urgency: 2.3)

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---
id: 2026-02
title: Weekly — 2026-01-07
type: Weekly
created: 2026-01-07T18:49:47Z
modified: 2026-01-07T18:49:47Z
tags: [weekly]
---
# Weekly - 2026 CW 02 (Wed 2026-01-07)
## Accomplishments
### Union
- ✓ Talk to Jessica about getting a room for an event
### Thesis
- ✓ Find out what 10 CFR is. Specifically, 10 CFR 50.34 and 10 CFR 55.59. Emergency Operating Procedures?
### Internship
- INL internship meeting yesterday. Went very well.
## Pushed or Rescheduled
- (Union) Follow up with Jessica about room booking
- (Chair-Search) Read Clarks application and provide review scores
- (Chair-Search) Read remaining two applicants and provide scores
## Cancelled or Deleted
No tasks were cancelled or deleted in the past 7 days.
## To Do
### Due This Week
**Due in 10 hours:**
- (Chair-Search) Read additional applican and provide scords
**Due 2026-01-08:**
- (Thesis) The Algorithmic Analysis of Hybrid Systems (1995) [Urgency: 14.6]
- (Thesis) Hybrid Automata: An Algorithmic Approach to the Specification and Verification of Hybrid Systems (1993) [Urgency: 10.6]
- (Thesis) Hamilton-Jacobi Reachability: A Brief Overview and Recent Advances (2017) [Urgency: 10.6]
- (Chair-Search) Read Clarks application and provide review scores [Urgency: 9.15]
- (Chair-Search) Read remaining two applicants and provide scores [Urgency: 9.15]
- (ENGR1933) Complete RAMP training [Urgency: 9.15]
**Due 2026-01-13:**
- Fill out graduate student evaluation form [Urgency: 5.86]
### High Priority
- (Union) Follow up with Jessica about room booking [Urgency: 16.8]
- (Thesis) Do FRET tutorials [Urgency: 13.1]
- (zk) AIGER Circuits [Urgency: 3.22]
- (zk) Reactive Synthesis [Urgency: 3.22]
- (zk) Write about opp. chall. and res. needs for remote micro ope. [Urgency: 3.18]
- (ERLM) Add research tasks to research approach section [Urgency: 2.48]
- (Thesis) Hybrid Systems: Review and Recent Progress (2003) [Urgency: 2.41]
- Have meeting with Dan about performance review
- Internship items: Follow up with Emerson next week about paperwork

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---
id: 2026-03
title: Weekly — 2026-01-14
type: Weekly
created: 2026-01-14T18:46:24Z
modified: 2026-01-14T19:21:41Z
tags: [weekly]
---
# Weekly - 2026 CW 03 (Wed 2026-01-14)
## Accomplishments
- Finished FRET tutorial I was working on. I've still got
weird dependency things I need to figure out. Moving to a
mac has caused some interesting quirks but I'm working them
out.
- Read Hybrid Automata: An Algorithmic Approach to
Specification and Verification of Hybrid Systems
- Did 2 interviews for chair search and read additional
applicants stuff.
- Bob asked me for help for ENGR 1933. I completed my RAMP
training to get recertified.
- Completed the review form.
- Did maneuvering with Emerson to get them moving on an
offer. INL sent me a formal offer letter.
### Chair-Search
- ✓ Read additional applican and provide scords
- ✓ Read Clarks application and provide review scores
- ✓ Read remaining two applicants and provide scores
### Thesis
- ✓ Do FRET tutorials
## Pushed or Rescheduled
### Thesis
- The Algorithmic Analysis of Hybrid Systems (1995) — rescheduled
- Hybrid Automata: An Algorithmic Approach to the Specification and Verification of Hybrid Systems (1993) — rescheduled
- Hamilton-Jacobi Reachability: A Brief Overview and Recent Advances (2017) — rescheduled
### Other
- Investigate DICE conference — rescheduled
## Cancelled or Deleted
No tasks were cancelled or deleted this week.
## To Do
- Decide on an internship
- Additional interviews this week
- Review meeting is this week.
- Re-outline research approach. Identify the holes
- Plan out a prelim problem. Maybe a simple version of what
HARDENS did. Just initiating scram?
- Follow up with IT about what the hell is sending packets
from the ARCADE puter.
### Due This Week
No tasks are due in the next 7 days.
### High Priority
**Thesis (reading)**
- The Algorithmic Analysis of Hybrid Systems (1995) — Urgency: 17.8 (overdue by 5 days)
- Hybrid Automata: An Algorithmic Approach to the Specification and Verification of Hybrid Systems (1993) — Urgency: 13.8 (overdue by 5 days)
- Hamilton-Jacobi Reachability: A Brief Overview and Recent Advances (2017) — Urgency: 13.8 (overdue by 5 days)
- Hybrid Systems: Review and Recent Progress (2003) — Urgency: 2.45
- Multiple Lyapunov Functions and Other Analysis Tools for Switched and Hybrid Systems (1998) — Urgency: 2.45
**Other**
- Investigate DICE conference — Urgency: 15.8
**ERLM (editing/writing)**
- Add research tasks to research approach section — Urgency: 2.51
**Zettelkasten**
- AIGER Circuits — Urgency: 3.25
- Reactive Synthesis — Urgency: 3.25
- Write about opp. chall. and res. needs for remote micro ope. — Urgency: 3.22

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---
id: 2026-05
title: Weekly — 2026-01-28
type: Weekly
created: 2026-01-28T18:38:10Z
modified: 2026-01-28T18:45:48Z
tags: [weekly]
---
# Weekly - 2026 CW 05 (Wed 2026-01-28)
## Accomplishments
**Thesis**
- ✓ Edit research approach some
- ✓ The Algorithmic Analysis of Hybrid Systems (1995) (reading, overdue from 2026-01-09)
- ✓ Edit research approach
- Set up the ARCADE computer and got the undergrads an
account
- Couple of the last interviews for the chair search. Things
are looking really good and should wind down in intensity
for a bit
**General**
- ✓ Write email to INL about rejecting offer
- ✓ Make groupchat for Sam's bachelor party
## Pushed or Rescheduled
**Poker**
- Make development plan (overdue by 3 days)
- Make plan about table layout (overdue by 3 days)
**Thesis**
- Write: Define hybrid systems and requirements (tablesetting intro) (overdue by 13 hours)
- Write: Requirements mapping to system components (operational vs strategic) (overdue by 13 hours)
- Write: Requirements extraction and discrete abstraction (overdue by 13 hours)
- Write: Reactive synthesis implementation and tools (LTL, FRET) (overdue by 13 hours)
- Write: Continuous components intro and mode types overview (overdue by 13 hours)
- Write: Transitory modes (entry/exit, reachability verification) (overdue by 13 hours)
- Write: Stabilizing modes (barrier certificates) (overdue by 13 hours)
- Write: Expulsory modes (failure detection, ...) (overdue by 13 hours)
## Cancelled or Deleted
No tasks were cancelled or deleted in the past week.
## To Do
Finish writing about research approach. Redo risks and
contingencies section based on research approach. For
example, risk of continuous discrete abstraction being not
good, risk of how much system variation is needed? Can only
really do parametric uncertainty. Unless?
**Due This Week**
No tasks with explicit due dates in the next 7 days.
**High Priority**
These tasks are overdue and require immediate attention:
**Thesis (urgency 14.5)**
- Hybrid Automata: An Algorithmic Approach to the Specification and Verification of Hybrid Systems (1993) (reading, overdue by 2 weeks)
- Hamilton-Jacobi Reachability: A Brief Overview and Recent Advances (2017) (reading, overdue by 2 weeks)
**Poker (urgency 11.4)**
- Make development plan (overdue by 3 days)
- Make plan about table layout (overdue by 3 days)
**Thesis Writing (urgency 10.9)**
- Write: Define hybrid systems and requirements (tablesetting intro) (overdue by 13 hours)
- Write: Requirements mapping to system components (operational vs strategic) (overdue by 13 hours)
- Write: Requirements extraction and discrete abstraction (overdue by 13 hours)
- Write: Reactive synthesis implementation and tools (LTL, FRET) (overdue by 13 hours)
- Write: Continuous components intro and mode types overview (overdue by 13 hours)
- Write: Transitory modes (entry/exit, reachability verification) (overdue by 13 hours)

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---
id: HUB-20250818131731
title: Logics
type: hub
created: 2025-08-18T17:17:31Z
modified: 2025-08-18T19:44:30Z
tags: [hub]
aliases: []
---
# Logics
> Logic is a way of transforming ideas in a plain language
> into precise mathematical statements. There are a bunch of
> different types of logic, as linked below, but in all of
> them there's an emphasis on precision.
## Contents (map of notes)
- [[Propositional Logic]]
- [[Predicate Logic]]
- [[Temporal Logic]]
## Permanent seeds (key ideas)
- [[ ]]
## Related hubs
- [[]]
## Sources / Literature
-
## Open questions / Next actions
- [ ]

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---
id: HUB-20250822135454
title: Formal Methods
type: hub
created: 2025-08-22T17:54:54Z
modified: 2025-08-22T17:57:39Z
tags: [hub]
aliases: []
---
# Formal Methods
> The purpose of this hub is to make a high level hub of
> everything formal methods related (which is a lot!!!)
## Related hubs
- [[formal-methods-in-machine-learning]]
## Related Zettels
### Topics
[[Abstract Interpretation for Formal Methods]]
[[Satisfiability Modulo Theory]]
[[Mixed Integer Linear Programming]]
[[Complete vs. Incomplete Formal Methods]]
### Tools
[[Strix]]
## Sources / Literature
- [[a-review-of-formal-methods-applied-to-machine-learning]]
## Open questions / Next actions
- [ ]

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---
id: 20250815170942
title: Zettelkasten
type: permanent
created: 2025-08-15T21:09:42Z
modified: 2025-08-15T21:18:21Z
tags: []
---
# Zettelkasten
Zettelkasten is a note taking system that uses a series of
single idea notes to build connections between notes. There
are different kinds of zettelkasten notes:
1. [[permanent-notes]]
2. [[literature-notes]]
3. [[hub-notes]]
and
4. [[fleeting-notes]]

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---
id: 20250815171141
title: Permanent Notes
type: permanent
created: 2025-08-15T21:11:41Z
modified: 2025-08-15T21:11:56Z
tags: []
---
# Permanent Notes

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---
id: 20250815171436
title: Literature Notes
type: permanent
created: 2025-08-15T21:14:36Z
modified: 2025-08-15T21:20:37Z
tags: []
---
# Literature Notes
Literature notes are notes that reference research. They
should be like fleeting notes almost, where they only have
one real connection--the resource used to derive the notes.
From that point, the individual thoughts should be moved
into permanent notes that are focused on each idea rather
than the resource itself.
I've created two folders in my literature notes: Processed
and the root folder. This is pretty self explanatory, but
for thoroughness, once lit notes are processed into
zettels they move into the processed folder.

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---
id: 20250815171449
title: Hub Notes
type: permanent
created: 2025-08-15T21:14:49Z
modified: 2025-08-15T21:22:59Z
tags: []
---
# Hub Notes
Hub notes are a way to systemitize knowledge. They include
mostly links to other things that are derivatives or subsets
of the hub note topic. Here's an example:
A hub note might contain 'Functional Programming Languages'
and link to several language topics 'Haskell', 'F*', etc.
where each of those might also be a hub note.
Hub notes are supposed to be a map in a sense of all the
notes they contain.

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@ -0,0 +1,19 @@
---
id: 20250815171459
title: Fleeting Notes
type: permanent
created: 2025-08-15T21:14:59Z
modified: 2025-08-15T21:24:24Z
tags: []
---
# Fleeting Notes
Fleeting Notes are notes that are similar to unprocessed
notes in [[literature-notes]], but they are not connected to
a resource like a literature note is. They are notes that
won't often get revisited (if at all). Daily notes are
pretty much the quintessential example of a fleeting note,
but also random ideas are a thing for fleeting notes too. I
have a processed folder in my fleeting notes to do a similar
process as lit notes.

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@ -0,0 +1,38 @@
---
id: 20250818132007
title: Propositional Logic
type: permanent
created: 2025-08-18T17:20:07Z
modified: 2025-08-18T19:52:42Z
tags: []
---
# Propositional Logic
Propositional logic makes statements saying things like 'if
x, then y'. They are statements that are either **true or
false**, and have binary variables (P, Q, R, X, Y, etc...)
Here's some examples:
*If x, then y.*
$$x\rightarrow y$$
*If x and y, then z.*
$ (x \wedge y) \rightarrow z $
*Either the pump is on or the power is out.*
$ Pump \oplus \neg Power $
The pump is on and water is flowing if and only if the power
is on.
$( Pump \wedge Water) \leftrightarrow Power$
Propositional logic is expanded upon by
[[predicate-logic]].

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---
id: 20250818132018
title: Predicate Logic
type: permanent
created: 2025-08-18T17:20:18Z
modified: 2025-08-18T20:20:03Z
tags: []
---
# Predicate Logic
Predicate logic extends propositional logic by using
predicates and quantifiers.
- **Predicates** express properties or relations (e.g.,
$Pump(x)$ or $Connected(v,c)$).
- **Quantifiers** let us say something about *all* or *some*
in the domain.
- $\forall$ = for all
- $\exists$ = exists, at least one
- $\exists!$ = there exists exactly one
Predicates kind of look like functions: $Pump(x)$ means $x$ is
a pump.
**Relational Predicates** have two inputs:
$Connected(x,y)$ means pump $x$ is connected to valve $y$
## Examples
Predicate logic requires you to *introduce the
variable first*. This feels weird at first, but is
mathematically explicit. The predicate does not define the
input, it only defines the property!
Here's an example:
$\forall x (Pump(x) \rightarrow Working(x))$
Means that 'every pump works'. But, we define first a set x,
then specify it is a pump for all x, and that they all of x,
which are all pumps, work.
What if we have one pump that doesn't work?
$\exists x(Pump(x) \wedge \neg Working(x))$
## Nested Qualifiers
We can stack qualifiers and do some nifty things.
How do we say: There exists one controller that stabilizes
every plant?
$ \exists k \forall G (Plant(G) \rightarrow Stabilizes(k,G))$
This is obviously not possible. So how do we say the
opposite, that for any plant there exists at least one
stabilizing controller:
$ \forall G \exists k (Plant(G) \rightarrow (Controller(k)
\wedge Stabilizes(k,G)))$

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---
id: 20250818132022
title: Temporal Logic
type: permanent
created: 2025-08-18T17:20:22Z
modified: 2025-08-21T16:42:25Z
tags: []
---
# Temporal Logic
## What is Temporal Logic?
An extension of **predicate logic** that allows reasoning
about how statements evolve over **time**.
- Used heavily in **formal verification**, **model
checking**, and **control systems safety**.
- Reasoning is over **infinite traces** (sequences of
states).
---
## Core Temporal Operators
| Symbol | LaTeX | Name | Meaning |
|--------|-------|------|---------|
| X φ | `X \varphi` | Next | φ holds in the **next** state |
| F φ | `\Diamond \varphi` | Eventually | φ will hold at some time in the **future** |
| G φ | `\Box \varphi` | Globally (Always) | φ holds at **all future times** |
| φ U ψ | `\varphi \, U \, \psi` | Until | φ must hold until ψ holds |
---
## Example Specifications
1. **Safety:**
*“The reactor temperature never exceeds 600°C.”*
$G\,(temp < 600)$
2. **Liveness:**
*“The pump will eventually turn on.”*
$F(PumpOn)$
3. **Response:**
*“Whenever a request occurs, it will eventually be granted.”*
$G\,(request \rightarrow F\,grant)$
4. **Stability:**
*“If the valve opens, it stays open until pressure is safe.”*
$G\,(ValveOpen\rightarrow (ValveOpen\;U\;PressureSafe))$
## Why It Matters
- **Formal Methods:** Express constraints on **system behaviors over time**.
- **Model Checking:** Tools like SPIN, NuSMV, Spot verify LTL specs.
- **Engineering Applications:**
- Ensure control systems obey safety invariants.
- Specify liveness goals for controllers (e.g., “eventually stabilize temperature”).
- Used in **TLA+**, runtime monitoring, and shield synthesis.
## Related Notes
[[strix]] - a reactive synthesis tool using temporal logic
specs

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---
id: 20250818164800
title: Safety Properties
type: permanent
created: 2025-08-18T20:48:00Z
modified: 2025-08-18T20:54:35Z
tags: []
---
# Safety Properties
Safety properites say that nothing bad ever happens. They
often are specified as such using some formal requirement.
In [[Temporal Logic | LTL]], they can look like this:
*The traffic light will never been red and green at the same
time.*
$G \neg (green \wedge red)$
A sort of opposite of safety proprerties is [[liveness-properties]].

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@ -0,0 +1,22 @@
---
id: 20250818165010
title: Liveness Properties
type: permanent
created: 2025-08-18T20:50:10Z
modified: 2025-08-18T20:54:38Z
tags: []
---
# Liveness Properties
Liveness properties are kinda the dual of
[[safety-properties]], but instead they say that something
good will eventually happen.
Here's an example:
*If there's someone waiting, the light will eventually turn
green:*
$ G(request \rightarrow F\, green)$

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@ -0,0 +1,31 @@
---
id: 20250819103208
title: Strix
type: permanent
created: 2025-08-19T14:32:08Z
modified: 2025-08-21T16:42:39Z
tags: []
---
# Strix
Strix is a reactive synthesis tool that takes linear
temporal logic specifications and turns them into
implementations using Mealy machines or AIGER circuits.
Strix does this using deterministic parity automata (DPA).
With these, they can use much more efficient parity game
algorithms as opposed to using symbolic methods.
Strix was debuted after SYNTCOMP2017, to great success.
Their automata at the time were much smaller than
competitive models, and their solve times were on average
much faster. They also solved some benchmarks that other
tools previously had been unable to solve.
## Related Notes
[[Temporal Logic]]
[[SYNTCOMP]]
[[Deterministic Parity Automata]]
[[Mealy Machines]]
[[AIGER Circuits]]
[[Reactive Synthesis]]

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@ -0,0 +1,21 @@
---
id: 20250821123741
title: SYNTCOMP
type: permanent
created: 2025-08-21T16:37:41Z
modified: 2025-08-21T16:42:25Z
tags: []
---
# SYNTCOMP
SYNTCOMP, otherwise known as the Reactive Synthesis
Competition, is a yearly competition for reactive synthesis
tools to compete against one another to try and solve
synthesis benchmarks.
SYNTCOMP has been around since 2014. Usually, they run all
the code on their own machines to ensure fairness.
SYNTCOMP is a satelite event of CAV, the International
Conference on Computer-Aided Verification.

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@ -0,0 +1,10 @@
---
id: 20250822134355
title: Formal Methods in Machine Learning
type: permanent
created: 2025-08-22T17:43:55Z
modified: 2025-08-22T17:43:55Z
tags: []
---
# Formal Methods in Machine Learning

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@ -0,0 +1,15 @@
---
id: 20250822135802
title: Abstract Interpretation for Formal Methods
type: permanent
created: 2025-08-22T17:58:02Z
modified: 2025-08-25T16:01:46Z
tags: []
---
# Abstract Interpretation for Formal Methods
Abstract interpretation in a formal methods context takes
something about a system and makes an approximation of it in
order to make reasoning about it easier.

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@ -0,0 +1,58 @@
---
id: 20250826111220
title: Quad Charts
type: permanent
created: 2025-08-26T15:12:20Z
modified: 2025-08-26T15:20:50Z
tags: []
---
# Quad Charts
Quad charts are the briefest of research proposals, and are
a way of conveying a research idea in just one
slide.
The audience for a quad chart is usually non-technical. The
content should reflect this.
Quad charts consist of quadrants:
## Quadrant 1 (Upper Left): Goals and Objectives
This quadrant states the goal of the research in a single
sentence, and lists the outcomes underneath it. Often you
can start with "The goal of this research is to..."
Then, the outcomes follow: "If this research is
successful, we should be able to do the following:
1. ...
2. ...
3. ...
(4.?)
It is critical that no jargon is used here. It is very
tempting to do so.
## Quadrant 2 (Bottom Left): Research Approach
This quadrant answers the question: "What's new in your
approach?"
## Quadrant 3 (Top Right): Pretty Picture
This is a break for the reader, and likely the first thing
they'll actually look at on the chart. This figure should
illustrate a key idea about the work that you want the
reader to take away.
No personal information should be included.
## Quadrant 4 (Bottom Right): Impact and Contact Info
This quadrant answers the question of "Who cares? What
difference will it make if you're successful?"
This quadrant should also contain contact info of the
principal investigator, and if applicable, their advisor.

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@ -0,0 +1,40 @@
---
id: 20250826114550
title: Heilmeier Catechism
type: permanent
created: 2025-08-26T15:45:50Z
modified: 2025-08-26T16:02:59Z
tags: []
---
# Heilmeier Catechism
George Heilmeier was a program manager at the Defense
Advanced Research Projects Administration (DARPA) who was
flummoxed with research proposals for artificial
intelligence. In order to quickly sort through the
proposals, he developed an 8 question system to quickly cut
through the muck.
This is the Heilmeier Catechism:
1. What are you trying to do? Articulate your research with
absolutely no jargon.
2. How is it done today and what are the limits of current
practice?
3. What's new in your approach and why will you be
successful?
4. Who cares? If you're successful, what difference will it
make?
5. What are the risks?
6. How long will it take?
7. How much will it cost?
8. What are the midterm and final exams? How will you
measure success?

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@ -0,0 +1,57 @@
---
id: 20250829114522
title: Hybrid Systems
type: permanent
created: 2025-08-29T15:45:22Z
modified: 2025-09-11T21:46:53Z
tags: []
---
# Hybrid Systems
I'm borrowing a lot from
[[multiple-lyapunov-functions-and-other-analysis-tools-for-swtiched-and-hybrid-systems]].
Hybrid systems are those that combine continuous and
discrete dynamics together. This is usually some sort of
finite automata + differential equations.
Hybrid systems can be written like:
$$\dot{x}(t) = \xi(t), \quad t\geq 0$$
where $x(t)$ is the continuous component of the state.
$\xi(t)$ is a vector field that depends on $x(t)$ and the
hybrid dynamics.
Switching between modes (aka discontinuities in $\xi(\cdot)$)
can happen in one of two ways:
1. **Autonomous Switching** - Autonomous switches happen
depending on state values of $x(t)$.
2. **Controlled Switching** - $\xi(\cdot)$ changes abruptly
in response to a control command.
One may write a continuous time autonomous hybrid system
like this:
$$\dot{x}(t) = f(x(t), q(t))$$
$$q(t) = \nu(x(t), q(t^-))$$
where:
- $x(t) \in R^n$
- $q(t) \in Q \simeq {1,...,N}$
- $f(\cdot,q): R^n \rightarrow R^n,q \in Q$, with each
[[lipschitz-continuous]]. These are the *continuous
dynamics*.
- $\nu: R^n \times Q \rightarrow Q$ is the *finite dynamics*
A controlled system might be written as:
$$\dot{x}(t) = f(x(t), q(t), u(t))$$
$$q(t) = \nu(x(t), q(t^-), u(t))$$
where:
- $u(t) \in R^m$

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@ -0,0 +1,35 @@
---
id: 20250911165736
title: Switched Systems
type: permanent
created: 2025-09-11T20:57:36Z
modified: 2025-09-11T21:09:55Z
tags: []
---
# Switched Systems
Switched systems are those that mix continuous and discrete
dynamics. They are systems that are 'multimodal'. This means
that they can have different continuous dynamic modes.
I'm borrowing form
[[multiple-lyapunov-functions-and-other-analysis-tools-for-swtiched-and-hybrid-systems]],
but here's a short description of how they work.
A prototypical switched system is as follows:
$$\dot{x}(t)=f_i ( x(t)), \quad i \in Q \simeq {1,...,N}$$
with two conditions:
1. Each $f_i$ is globally [[Lipschitz Continuous]]
2. The i's are picked in a way that there are finite
switches in finite time.
There's also this thing called a *continuous switched
system*. A continuous switched system is one that does not
change continuous states when a switch occurs. That is to
say when switching from $i$ to $i'$:
$$f_i(x(t_i),t_i) = f_{i'}(x(t_{i'}),t_{i'})$$

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@ -0,0 +1,24 @@
---
id: 20250911170650
title: Lipschitz Continuous
type: permanent
created: 2025-09-11T21:06:50Z
modified: 2025-09-16T16:32:37Z
tags: []
---
# Lipschitz Continuous
Lipschitz continuous functions are a special case of
continuous functions. Lipschitz continuity means that a cone
can be created with slope less than some real number
$K$.
Fora a real valued function in one dimension, Lipschitz
continuity is defined as:
$$| f(x_1) - f(x_2)| \leq K|x_1 - x_2|$$
Lipschitz continuity can be expanded to vector fields. From
here, we can say that ODE trajectories do NOT intersect, and
that every trajectory is unique.

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---
id: 20251030141457
title: Nuclear Operating Procedures
type: permanent
created: 2025-10-30T18:14:57Z
modified: 2025-10-30T18:19:21Z
tags: []
---
# Nuclear Operating Procedures
Nuclear operating procedures are big books of procedures
that reactor operators use to perform control of reactors.
Operating procedures are built on a per-plant basis, but are
also designed with the general plant architecture in mind
[[nureg899]].
Operating procedures have different categories:
1. Regular operating procedures
2. [[Emergency Operating Procedures]]
3. Theres ones about severe accidents too.

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@ -0,0 +1,40 @@
---
id: 20251030141936
title: Emergency Operating Procedures
type: permanent
created: 2025-10-30T18:19:36Z
modified: 2025-10-30T19:30:12Z
tags: []
---
# Emergency Operating Procedures
Emergency operating procedures for nuclear power are special
procedures that are used when off-normal conditions are
present. They are for when 'shit hits the fan'.
EOPs have defining regulations. Most notably [[nureg899]].
NUREG899 is a writers guide to emergency operating
procedures.
EOPs should be 'function-oriented'. This means operators
should not need to know a root cause to start performing
control operations in an emergency. Critical functions in an
emergency are usually:
1. [[Containment Integrity]]
2. [[Reactivity Control]]
3. [[Heat Removal]]
4. [[Reactor Coolant Inventory Control]]
If each of these are maintained, the reactor can be 'safe',
and the risk of environmental release is minimized. [[nureg899]]
EOPs should minimize cross referencing because it increases
decision time and is disruptive changing between documents
[[nureg899]].
EOPs today are reveiwed with simulation exercises,
control-room walkthroughs, seminars, and numerical analysis
[[nureg899]].

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@ -0,0 +1,22 @@
---
id: 20251223161108
title: Andre Platzer
type: permanent
created: 2025-12-23T21:11:08Z
modified: 2025-12-23T21:53:21Z
tags: []
---
# Andre Platzer
Andre Platzer is a computer scientist who is a professor at
both Carnegie Mellon and the Karlsruhe Institute of
Technology. Platzer is a leading researcher in
[[differential dynamic logic]] and [[cyber-physical
systems]]. He has helped to create
software like [[KeYmaera X]].
He has also written a book, called "Logical Foundations of
Cyber-Physical Systems." Manyu worked with KeYmaera X some
and was inspired by his work.

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@ -0,0 +1,17 @@
---
id: 20251223162450
title: Web of Science
type: permanent
created: 2025-12-23T21:24:50Z
modified: 2025-12-23T21:29:48Z
tags: []
---
# Web of Science
Web of Science is a citation aggregator and database. Web of
Science has both forward and backward citation sources, and
other tools for doing source analysis. It is good to find
resources, but also to connect resources to one another.
This is useful in [[snowballing]].

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@ -0,0 +1,21 @@
---
id: 20251223162954
title: Snowballing
type: permanent
created: 2025-12-23T21:29:54Z
modified: 2025-12-23T21:31:23Z
tags: []
---
# Snowballing
Snowballing is a form of source discovery. Snowballing means
to start with a source, and travel forwards and backwards
in time with respect to citations. From this, one can find
closely related papers to an original source without too
much effort.
Snowballing has been found in the literature to be an
efficient source of collecting relevant sources given a
certain topic. One needs to find the first bit of snow (a
good first resource), to start the snowball.

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@ -0,0 +1,27 @@
---
id: 20251223163648
title: Deterministic Parity Automata
type: permanent
created: 2025-12-23T21:36:48Z
modified: 2025-12-23T21:40:09Z
tags: []
---
# Deterministic Parity Automata
Deterministic parity automata are a type of automata where
the environment and the system play against one another, and
describes the interactions therein. DPA are exhaustive, and
end up with a result determining which player 'wins'.
DPA's have a scoring mechanism that results in an even or
odd final score. An even final score indicates that the
'controller' wins the game. There is no input from the
environment that can't be controlled by the controller. All
traces end up in a favorable state, with no infinite loops.
An odd score means the opposite. There exists some limit
cycle where the controller can't reach a desired mode and
stay there.
DPA's are used in [[strix]]. They're how Strix does it's
generation from temporal logics to a final automaton.

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---
id: 20251223165340
title: Mealy Machines
type: permanent
created: 2025-12-23T21:53:40Z
modified: 2025-12-23T22:38:18Z
tags: []
---
# Mealy Machines
Mealy machines are a formalization of a system that has
states drawn as nodes and transitions drawn from state to
state.
From Wikipedia:
```
A mealy machine is a finite state machine whose
output values are determined by both its current state, and
the current inputs.
```
Mealy machines can also be defined as a six-tuple:
$$(S, S_0, \Sigma, \Lambda, T, G)$$
where
- S is the finite set of states
- S_0 is the start state
- $\Sigma$ is the input alphabet
- $\Lambda$ is the output alphabet
- $T : S \times \Sigma \rightarrow S$ is the state
transition function
- $G : S \times \Sigma \rightarrow \Lambda$ is the output
function
Mealy machines have the advantage that they generally can
produce smaller sized automata (aka less states). This is
because transitions themselves in a Mealy machine are states
in a Moore machine. The state of 'opening' in a Moore
machine is the transition itself in a Mealy machine. Outputs
aren't just based on state, so it isn't necesary to create a
state to produce an output like a Moore machine. An output
action can be created with the current state AND the input
together.
## Related
[[Finite State Machines]]

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@ -0,0 +1,49 @@
---
id: 20251223170627
title: Finite State Machines
type: permanent
created: 2025-12-23T22:06:27Z
modified: 2025-12-23T22:39:00Z
tags: []
---
# Finite State Machines
Finite State Machines are a computer science term for
machines that have a finite number of states, with clearly
defined transitions between them. Sometimes, FSM are
referred to simply as *state machines*.
FSM are an abstraction of a computational system. FSM are
heavily used in systems that have clearly defined discrete
states. Examples include traffic lights, elevators,
combination locks, or others.
FSM have **actions**. Actions are the unabstractified
version of whatever the execution is. For physical systems,
it might be something like turning a motor on.
FSM can be categorized into two main categories:
## Acceptors (or 'detectors' or 'recognizers') Acceptors are
a type of FSM that produce binary output, recognizing
whether or not a given input is accepted. Examples of
systems that are acceptors include things like ready-commit
systems, or a password checker. These systems have an input,
and reach a state that determines the input is acceptable,
or incorrect.
## Transducers
Transducers are a set of finite state machines that produce
an output based on input or state using *actions*. Actions
in this case represent a transition between state that
also has some external change. A finite state machine of an
elevator would have actions of the elevator changing between
floors, for example.
Transducers with respect to control have two different
types:
[[mealy-machines]] -- these have output depend on state and input
[[moore-machines]] -- these have output depend on state ONLY

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---
id: 20251223171835
title: Moore Machines
type: permanent
created: 2025-12-23T22:18:35Z
modified: 2025-12-23T22:52:38Z
tags: []
---
# Moore Machines
Moore machines are a type of finite state machine whose
output only depends on output state. Moore machines are
useful because they simplify the behavior of a system to the
simplest behaviours possible. They can be defined as a
six-tuple:
$$(S, S_0, \Sigma, \Lambda, T, G)$$
where
- S is the finite set of states
- S_0 is the start state
- $\Sigma$ is the input alphabet
- $\Lambda$ is the output alphabet
- $T : S \times \Sigma \rightarrow S$ is the state
transition function
- $G : S \rightarrow \Lambda$ is the output
function
Moore machines do not have exit actions. They can only
change their output based on a change of state. This means
for systems with physical characteristics, such as a door
opening or closing system, the intermediate states of
opening and closing have to exist in a Moore machine. It is
not possible to go from Open to Closed directly, because
Open can't generate the output Closed. Instead, Open + the
input 'open_door' or similar goes to the state 'closing',
which can then create an action of 'motor_on' or similar,
and then finally get to the final state Closed.

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---
id: 20260109155358
title: Hybrid Automata
type: permanent
created: 2026-01-09T20:53:58Z
modified: 2026-01-09T21:08:30Z
tags: []
---
# Hybrid Automata
Hybrid automata are a framework for the formal modeling of
computed systems. Hybrid automata are a generalization of
[[timed automata]], where all states are governed by
differential equations.
## Relevant Sources
[[hybrid-automata-an-algorithmic-approach-to-the-specification-and-verification-of-hybrid-systems]]

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@ -0,0 +1,16 @@
---
id: 20260109155410
title: Linear Hybrid Automata
type: permanent
created: 2026-01-09T20:54:10Z
modified: 2026-01-09T21:11:18Z
tags: []
---
# Linear Hybrid Automata
Linear hybrid automata are [[hybrid-automata]] systems where
'the rate of change with time is constant' for each
variable, and the 'terms involved in the invariants, guards,
and assignments are required to be linear'.
A special case of linear hybrid automata are [[timed-automata]].

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@ -0,0 +1,27 @@
---
id: 20260109155415
title: Timed Automata
type: permanent
created: 2026-01-09T20:54:15Z
modified: 2026-01-09T21:13:51Z
tags: []
---
# Timed Automata
Timed automata are linear hybrid automata with the
special condition that every continuously changing variable
is a *clock*. That means that every variable varies one to
one with time, just counting time.
Timed automata have invariants and guards that compare time
only with constants. There are no other continuous dynamics
here.
An example of a timed automata is something like an alarm.
Easy peasy, is time greater or less than a value. If it is,
trigger the alarm! One might also have a constant setting
whether or not an alarm is 'enabled'. But, there's no other
dynamics than time itself.
## Relevant Sources
[[hybrid-automata-an-algorithmic-approach-to-the-specification-and-verification-of-hybrid-systems]]

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---
id: 20260109155838
title: Reactive Programs
type: permanent
created: 2026-01-09T20:58:38Z
modified: 2026-01-09T21:08:01Z
tags: []
---
# Reactive Programs
Reactive programs, or reactive systems, are those that have
an output or state change controlled by the current state
and input. These programs react to environmental changes in
real time. Basically every relevant control system is a
'reactive' system, but in computer science, reactive
programs have a unique meaning. Reactive computer programs
are those that have computation depending on external
inputs, a.k.a. stuff from OUTSIDE of the computer's world.
## Relevant Sources
[[strix-explicit-reactive-synthesis-strikes-back]]
[[hybrid-automata-an-algorithmic-approach-to-the-specification-and-verification-of-hybrid-systems]]

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---
id: 20260114132351
title: Bayes' Theorem
type: permanent
created: 2026-01-14T18:23:51Z
modified: 2026-01-14T18:43:20Z
tags: []
---
# Bayes' Theorem
Suppose we know $P(x)$, *the prior*, and we get some data
$Y$, and we want to know the probability $P(X|Y)$, which in
English is *the probability of our model being correct given
the data we've collected*.
We can use Bayes' Theorem to find it!
$$ P(X|Y) = \frac{P(Y|X) P(X)}{P(Y)} $$
Where:
- $P(X|Y)$ is called the *posterior*
- $P(Y|X)$ is called the *likelihood*
- $P(X)$ is called the *prior*
- $P(Y)$ is called the *evidence*
We can usually find the evidence by the following formula:
$$ P(Y) = \sum P(Y|x_i) P(x_i) $$
We can apply Bayes' Theorem to states in time too.
$$ P(X_t|Y_t) = \frac{P(Y_t|X_t) P(X_t)}{P(Y_t)} $$
where:
- $X_{t+1} = f(x_t, w_t)$
- $Y_{t} = f(x_t) + v_t$
$w_t$ is process noise, while $v_t$ is measurement noise.
Bayes' Rule is great for simulation and data-based
approaches.
## Related Ideas
[[Expected Value]]
## Sources
Bayesian Signal Processing w/ Dan (1/12)

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---
id: 20260114133159
title: Expected Value
type: permanent
created: 2026-01-14T18:31:59Z
modified: 2026-01-14T18:41:57Z
tags: []
---
# Expected Value
Expected value is pretty much the mean of a function, but
more specifically, it's the weighted average of all possible
outcomes of a function:
$$ \hat X = E{X} $$
If we have an estimate of a posterior using [[Bayes'
Theorem]], we can get the following result:
$$ \hat X = \sum_i X^i \hat{Pr}(X^i|Y) $$

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---
id: 20260114153529
title: Random Number Generation
type: permanent
created: 2026-01-14T20:35:29Z
modified: 2026-01-14T20:46:35Z
tags: []
---
# Random Number Generation (RNG)
Random number generation is all about getting random
numbers, and is easily defined as picking a number from a
uniform distribution. Generally, there's two types:
## True RNG
True RNG is systems that are truly random. Random systems
are almost always derived from [[chaotic systems]], which
technically are deterministic, but as so final state
sensitive they're basically intractable and 'random' values
can be extracted. Sometimes lava lamps (turbulence) is used,
sometimes isotope decay is the thing.
## Pseudo RNG
Computers can't really do true RNG. They just can't handle
non-deterministic outcomes. In addition, true RNG is *slow*.
As such computers build PRNG.
>[!definition] Pseudo Random Number Generator
>
> $\text{Struct}(S, \mu, f, U, g)$
>
> Where:
> - $S$ is a finite set of states
> - $\mu$ is a distribution on S for the initial state (seed!)
> - $f:S \rightarrow S$, the state transition function
> - $U$ is the output space [0,1), or perhaps {0,...,m-1}
> - $g:S \rightarrow U$, the output function
>

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---
id: LIT-20250819112550
title: Strix Explicit Reactive Synthesis Strikes Back!
type: literature
created: 2025-08-19T15:25:50Z
modified: 2026-01-09T21:08:06Z
citekey: meyerStrixExplicitReactive2018
---
# Strix: Explicit Reactive Synthesis Strikes Back!
Authors:
1. [[Phillipp Meyer]]
2. [[Salomon Sickert]]
3. [[Michael Luttenberger]]
## First Pass
**Category:** Design paper. They made a new LTL synthesizer
**Context:**
Strix is a response to other reative LTL syntehsizer
competition entries.
**Correctness:**
Seems good to me! They have data to back up their stuff.
**Contributions:**
They contribute Strix, a tool that uses Determinstic Parity
Automata (DPA) to simplify synthesis. DPA helps Strix solve
problems faster by using parity game solvers as opposed to
symbolic or bounded methods currently used.
**Clarity:**
Easy to read!
## Second Pass
**What is the main thrust?**
The main thrust is their new tool, Strix.
**What is the supporting evidence?**
They make a testing suite that is supposed to be similar to
the SYNTCOMP2017 testing setup, and run their solver
through the same trials that the competition included. They
achieve pretty good results: much much faster solve times
while also keeping automata size small.
**What are the key findings?**
Strix is pretty good. The use of DBAs seems effective. Their
'quality', a measure of automata size vs specification size,
is also pretty good compared to other synthesizers.
## Third Pass
**Recreation Notes:**
**Hidden Findings:**
**Weak Points? Strong Points?**
## Spawned Zettels
[[Reactive Programs]]

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---
id: LIT-20250822120822
title: A Review of Formal Methods applied to Machine Learning
type: literature
created: 2025-08-22T16:08:22Z
modified: 2025-08-22T16:11:25Z
citekey:
---
# A Review of Formal Methods applied to Machine Learning
**Category:** This is a review paper.
**Context:** This paper tries to keep up with where formal
methods are for machine learning based systems. It is not
necessarily a controls paper, but a broader machine learning
paper in general.
**Correctness:** Really well written on the first pass. Easy
to understand and things seem well cited.
**Contributions:** Great citations showing links to
different papers and also provides nice spots for forward
research. Talks about how verification needs to be done
along the whole pipeline: from data prep to training to
implementation. There needs to be more work on proving
things about model behavior, but in general this review has
a positive outlook on the field.
**Clarity:** Very well written, easy to understand. Except,
what is abstractification of a network?
## Second Pass
This review gives an overview of formal
methods applied to machine learning. Formal methods has been
used for ML to test for robustness for various perturbations
on inputs. They start by talking about several types of
formal methods, including deductive verification, design by
refinement, proof assistants, model checking, and semantic
static analysis, and then finally, abstract interpretation
of semantic static analysis. The last one has been used the
most in FM of ML.
A large part of the paper focuses on formal methods for
neural network perturbation robustness. They split up the
methods into two types: complete and incomplete formal
methods. Complete formal methods are *sound* and *complete*.
This means they do not have false positives or false
negatives. These methods generally do not apply well to
large networks (beyond hundreds gets rough), but give the
highest level of assurance. Here, there are two more
subcategories: SMT based solvers and MILP-based solvers.
SMT solvers are Satisfiability Modulo Theory solvers. These
solvers a set of constraints and check to see whether or not
all of the constraints can be satisfied. Safety conditions
are encoded as the *nA Review of Formal Methods applied to Machine Learningegation* of the safety constraint. That
way, if a safety condition is violated, the SMT solver will
pick it up as a counter example.
MILP based solvers are Mixed Integer Linear Programming
solvers. MILPs use linear programming where certain
constraints are integers to reduce the solving space.
Instead of having an explicity satisffiability condition on
safety or not, MILPs instead can use a minimizing function
to generate counter examples. For example, a MILP saftey
condition might be formalized as: $$ \text{min}\space
\bf{x}_n$$ where a negative value of $\bf{x}_n$ is 'a valid
counter example'.
There are also 'incomplete formal methods'. These incomplete
methods are sound, meaning they will not produce false
negatives, but they may not be complete, meaning they may
produce false positives. They scale better, but the false
positives can be pretty annoying.
One of the main incomplete methods is abstract
interpretation. Things get very weird very fast--this is all
about zonotopes and using over approximation of sets to say
things about stability. There is weird stuff going on with
cell splitting and merging that seems like a to grasp. But,
apparently it works.
Next, they spend some time talking about other machine
learning methods and the formal methods that have been
applied to them. Of particular interest to me is the formal
method application to support vector machines and decision
trees. There are some useful methods for detecting
robustness to adversarial inputs, and knowing what the
nearest misclassification adversarial case is.
## Third Pass
**Recreation Notes:**
**Hidden Findings:**
**Weak Points? Strong Points?**

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---
id: LIT-20250819112550
title: How To Choose a Good Scientific Problem
type: literature
created: 2025-08-19T15:25:50Z
modified: 2025-09-02T01:41:17Z
citekey:
---
# How to Choose a Good Scientific Problem
## Authors
[[Uri Alon]]
## Notes
Uri is all about the 'nuturing lab', which means a lab's
goal is not just to advance knowledge, but to nurture future
scientists.
He describes problems on two axes: interest and difficulty.
Interest here means how much knowledge we gain from solving
the problem. He says grad students should choose easy
problems, with ideally low interest, then postdocs move to
high interest and easy (to save time), and finally new
professors move towards the hard problems with high impact,
as they have time to do so.
Uri also argues that taking time to find a good topic is
time well spent. It can save a lot of time down the line.
The inner and outer voices can lead to different ideas.
Outer voices are those of peers, the department, or speakers
at a conference-- but the inner voice is the more valuable
voice. That is your own voice. Uri descirbes the inner voice
is often something that needs nurtured, but can lead to
less laborious science, and more self expression.
Finally Uri talks about the schema that should be considered
during research. It is not useful to think students will go
from A->B taking the shortest path. There must be room to
wander, as that is where new problems can be best found.
This is what really lets students grow.

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---
id: LIT-20250911143337
title: Multiple Lyapunov Functions and Other Analysis Tools for Swtiched and Hybrid Systems
type: literature
created: 2025-09-11T18:33:37Z
modified: 2025-09-16T17:23:17Z
citekey:
---
# Multiple Lyapunov Functions and Other Analysis Tools for Swtiched and Hybrid Systems
## First Pass
**Category:**
Theoretical methods paper. This paper introduces a couple of
new ways to work with hybrid systems and also does
introduction of a lot of terms.
**Context:**
Branicky is doing a lot of work with hybrid systems. He
defines what a switched system is, what a hybrid system is,
what a continuous switched system is and also included
definitions of autonomy in there too
**Correctness:**
Been cited like 2000 times.
**Contributions:**
Multiple Lyapunov theory and Stability via Iterated Function
Systems.
**Clarity:**
Complex ideas written simply. Easy to read.
## Second Pass
**What is the main thrust?**
**What is the supporting evidence?**
**What are the key findings?**
## Third Pass
**Recreation Notes:**
**Hidden Findings:**
**Weak Points? Strong Points?**
## Zettels Created
[[Switched Systems]]
[[hybrid-systems]]
[[lipschitz-continuous]]

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---
id: LIT-20251023125758
title: NUREG899
type: literature
created: 2025-10-23T16:57:58Z
modified: 2025-10-30T18:20:30Z
citekey:
---
# NUREG899
Emergency operating procedures should be
*function-oriented*. That means that operators 'do not have
to immediately diagnose an event... to maintain the plant in
a safe configuration." Critical functions are cited as:
1. Containment integrity
2. Reactivity Control
3. Heat Removal
4. Reactor coolant inventory control
Functions are maintained by 'tasks'. Tasks are specific
actions that are taken to maintain or achieve a function.
This doc says EOPs are verified and validated by:
1. Excercising EOPs on simulators
2. Control room walk-throughs
3. Desk top reviews
4. Seminars
5. Computer modeling and analysis
OPs should minimize the use of cross referencing because it
increases decision times and increases the chance of human
error. It's 'disruptive'.
Operator Aids are things like flowcharts or graphs that can
help an operator learn things more quickly and clearly than
text alone can provide. They should be easily learned and
retained, while being precise and not cluttered.
Interpretability is paramount.
EOPs have segments:
1. Cover page
2. Table of contents if applicable
3. Scope
4. A set of entry conditions
5. Automatic actions that happen by automated systems
6. What the operator should do immediately
7. Things the operator should do afterwards based on
reference to written procedures
8. Relevant supporting material.
Control rooms should have a sufficient number of EOP
handbooks such that everyone can use one, they're easy to
get to, and also be located such that they don't interfere
with workstations or cover up controls. If there's multiple
control rooms that share a common area, each control room
should have it's own set of EOPs. They should not be sharing
copies, essentially.
Appendix B talks about logical statements. They're written
strangely like program control flow, underlined, and
capitalized:
IF RPS scram has not initiated,
THEN initiate SLC and isolate RWCU

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---
id: LIT-20260109152249
title: Hybrid automata: An algorithmic approach to the specification and verification of hybrid systems
type: literature
created: 2026-01-09T20:22:49Z
modified: 2026-01-09T21:14:05Z
citekey:
---
# Hybrid automata: An algorithmic approach to the specification and verification of hybrid systems
## First Pass
**Category:**
New methods paper
**Context:**
This paper was released in the early 1990's when formal
methods was gaining some steam for proving algorithms. This
paper talks about the challenges of hybrid systems, where
there are discrete changes on top of continuous dynamics.
**Correctness:**
It's an extremely well cited paper.
**Contributions:**
The [[Hybrid Automata]]
**Clarity:**
4/5. Dense. Mathematical.
## Second Pass
**What is the main thrust?**
**What is the supporting evidence?**
**What are the key findings?**
## Third Pass
**Recreation Notes:**
**Hidden Findings:**
**Weak Points? Strong Points?**
## Spawned Zettels
[[Hybrid Automata]]
[[Linear Hybrid Automata]]
[[Timed Automata]]
[[reactive-programs]]

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# First Pass
**Category:**
This is a review paper.
**Context:**
This paper tries to keep up with where formal methods are for machine
learning based systems. It is not necessarily a controls paper, but a broader
machine learning paper in general.
**Correctness:**
Really well written on the first pass. Easy to understand and things seem
well cited.
**Contributions:**
Great citations showing links to different papers and also provides nice spots
for forward research. Talks about how verification needs to be done along the
whole pipeline: from data prep to training to implementation. There needs to
be more work on proving things about model behavior, but in general this
review has a positive outlook on the field.
**Clarity:**
Very well written, easy to understand. Except, what is abstractification of a
network?
# Second Pass
This review gives an overview of formal methods applied to machine learning.
Formal methods has been used for ML to test for robustness for various
perturbations on inputs. They start by talking about several types of formal
methods, including deductive verification, design by refinement, proof
assistants, model checking, and semantic static analysis, and then finally,
abstract interpretation of semantic static analysis. The last one has been
used the most in FM of ML.
A large part of the paper focuses on formal methods for neural network
perturbation robustness. They split up the methods into two types: complete
and incomplete formal methods. Complete formal methods are *sound* and
*complete*. This means they do not have false positives or false negatives.
These methods generally do not apply well to large networks (beyond
hundreds gets rough), but give the highest level of assurance. Here, there
are two more subcategories: SMT based solvers and MILP-based solvers.
SMT solvers are Satisfiability Modulo Theory solvers. These solvers a set
of constraints and check to see whether or not all of the constraints can be
satisfied. Safety conditions are encoded as the *negation* of the safety constraint.
That way, if a safety condition is violated, the SMT solver will pick it up as a
counter example.
MILP based solvers are Mixed Integer Linear Programming solvers. MILPs use
linear programming where certain constraints are integers to reduce the
solving space. Instead of having an explicity satisffiability condition on safety
or not, MILPs instead can use a minimizing function to generate counter
examples. For example, a MILP saftey condition might be formalized as:
$$ \text{min}\space \bf{x}_n$$
where a negative value of $\bf{x}_n$ is 'a valid counter example'.
There are also 'incomplete formal methods'. These incomplete methods are
sound, meaning they will not produce false negatives, but they may not be
complete, meaning they may produce false positives. They scale better, but
the false positives can be pretty annoying.
One of the main incomplete methods is abstract interpretation. Things get very
weird very fast--this is all about zonotopes and using over approximation of sets
to say things about stability. There is weird stuff going on with cell splitting
and merging that seems like a to grasp. But, apparently it works.
Next, they spend some time talking about other machine learning methods and
the formal methods that have been applied to them. Of particular interest to me
is the formal method application to support vector machines and decision
trees. There are some useful methods for detecting robustness to adversarial
inputs, and knowing what the nearest misclassification adversarial case is.
# Third Pass
**Recreation Notes:**
**Hidden Findings:**
**Weak Points? Strong Points?**

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# First Pass
**Category:**
This paper is a literature review
**Context:**
Mukul says that there are a whole bunch of thrusts out there about neural
network based controllers, and that there needs to be a better way to
parse what research is what
**Correctness:**
Looks good to me I suppose.
**Contributions:**
Here's the most important figure in the whole thing:
![[Pasted image 20250721095146.png]]
**Clarity:**
Well written.
# Second Pass
**What is the main thrust?**
**What is the supporting evidence?**
**What are the key findings?**
# Third Pass
**Recreation Notes:**
**Hidden Findings:**
**Weak Points? Strong Points?**

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---
alias: tee-hee-hee
---
# An autonomous control framework for advanced reactors notes
## First Pass
**Category:**
This is a vision-like paper.
**Context:**
Dr. Wood is a professor of nuclear engineering at the University of Tennesse.
He started working at UT after working at ORNL for 20+ years where he was
a senior researcher. He works on common cause failures.
**Correctness:**
There are not many citations, and a lot of the paper seems like it is off-the-cuff.
This was an invited article though in the *Nuclear Engineering and Technology*
journal. He's also got quite the resume.
**Contributions:**
Dr. Wood gives a good overview of where we are (automated control), and
where we need to go (autonomous control). Comparisons are made to other
industries, and how they've addressed these challenges. Clarifications are made
with respect to how the nuclear industry is unique.
**Clarity:**
Well written and clear, but a bit wordy at times. Examples are used but
sometimes it just feels like a mouthful.
## Second Pass
**What is the main thrust?**
Wood talks a lot about what it means for a system to be autonomous. He
actually starts with a etymological argument- "*automatos* means self-acting,
whereas *autonomos* means independent." The point of an autonomous system
is that it must be able to make intelligent decisions that a human would
otherwise make. Knowing how to handle degraded or faulty sensors or
actuators, switching controller trains, and knowing when scramming is
necessary are all decisions that an autonomous system would make, that
a simple automated system could not. The key is in the decision making.
**What is the supporting evidence?**
Dr. Wood compares a lot to NASA control systems for the Mars rovers. These
systems use two tiers of controllers: a decision layer and a functionality layer.
The functionality layer does what you think--it manages the physical
functioning. The decision layer is different. It decides on controller modes and
works instead with operational level goals.
**What are the key findings?**
The biggest findings are that an autonomous control system for a nuclear
power plant is possible, but by far the biggest roadblock is a high assurance
decision making system.
## Third Pass
**Recreation Notes:**
**Hidden Findings:**
**Weak Points? Strong Points?**

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# First Pass
**Category:**
This is a paper following a workshop. It is kind of a big picture / idea
type paper.
**Context:**
This paper was written after a workshop took place to talk about recent NRC
regulations. They talk about how different industries categorize the level
of autonomy in systems, and create autonomous levels of reactor control.
**Correctness:**
Vivek Agarwal chaired ANS in Chicago this past year. He's the real deal
**Contributions:**
They contribute a first thought on how to go about creating milestones for
autonomous systems, and give us a language to use when describing what level
of autonomy a system is gunning for.
**Clarity:**
Clearly written. Very nice!
# Second Pass
**What is the main thrust?**
**What is the supporting evidence?**
**What are the key findings?**
# Third Pass
**Recreation Notes:**
**Hidden Findings:**
**Weak Points? Strong Points?**
<!The quick brown fox jumps over the lazy dog. The dog takes a nice nap. :)>

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# First Pass
**Category:**
Systematic Review
**Context:**
This paper is from the civil engineering school at the University of Leeds.
They are doing an overview of economics and finance research of small
modular reactors.
**Correctness:**
Can not say. Is a review!
**Contributions:**
They do a good break down of the research we have done ('what we know') and
what needs done ('what we do not know'). They point out a big discrepancy that we do not have a lot of research on operations and maintenance costs.
**Clarity:**
Nicely written. Easy to understand.
# Second Pass
**What is the main thrust?**
**What is the supporting evidence?**
**What are the key findings?**
# Third Pass
**Recreation Notes:**
**Hidden Findings:**
**Weak Points? Strong Points?**

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# First Pass
**Category:** This paper is an experimental paper.
**Context:** The context of this paper is using a couple different techniques
synthesize control programs using different formal methods tools.
**Correctness:** I trust Max's integrity. Some of the citations were funky and
the intro was fluffy though.
**Contributions:**
This paper shows that using LTL and other formal methods still struggles to
generate controllers for significantly challenging systems. The high bay
warehouse used to create this paper had to be simplified. Then, they introduce
an SMT solver based method to try to generate code.
**Clarity:**
The intro and conclusion do not provide very strong clarity on what they
actually did other than "high assurance is high difficulty", and that we're not
really there yet on HACPS.
# Second Pass
**What is the main thrust?**
**What is the supporting evidence?**
**What are the key findings?**
# Third Pass
**Recreation Notes:**
**Hidden Findings:**
**Weak Points? Strong Points?**

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# First Pass
**Category:**
This is a methods paper.
**Context:**
This paper proposes a way of using mixed integer linear programming (MILP)
to evaluate properties of neural networks.
**Correctness:**
Formal
**Contributions:**
They do nifty things with bounds tightening and presolving that makes their
solver very fast compared to the state of the art or Reluplex. They also talk
about stable and unstable neurons.
**Clarity:**
They have a really good explanation of what a MILP problem is and how one
might encode a neural network as one.
# Second Pass
**What is the main thrust?**
The main thrust is their new solving method of MILPs for neural networks.
With their method, neural networks can have their neurons analyzed to
prove whether or not the network is robust to input perturbations. This is
especially important for classifiers, who need to know if there are sneaky
nonlinearities that can be harmful to a built system (like a glitch). This
method of bounds tightening and MILP usage makes their solver much faster
and therein more capable to handle large networks.
**What is the supporting evidence?**
They have a whole bunch of experimental results.
**What are the key findings?**
MILPs and bound tightening is very good!
# Third Pass
**Recreation Notes:**
**Hidden Findings:**
**Weak Points? Strong Points?**

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# First Pass
**Category:**
This is a weird one. This paper is essentially just a 'state-of-the-FRET' paper
**Context:**
FRET comes from NASA and is a tool to line up requirements in a temporal
language.
**Correctness:**
Formal. But they don't really go into details.
**Contributions:**
Really I don't think they contribute much here than an explanation of what's
going on.
**Clarity:**
Easy to read.
# Second Pass
**What is the main thrust?**
**What is the supporting evidence?**
**What are the key findings?**
# Third Pass
**Recreation Notes:**
**Hidden Findings:**
**Weak Points? Strong Points?**

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# First Pass
**Category:**
Methods paper
**Context:**
Using NN w/ LiDAR to say safety reliability claims using FM
**Correctness:**
Assumptions seem good, other than anticipating LiDAR as a
continuous data stream.
**Contributions:**
1. Framewok for formally proving safety properties of autonomous robots using LiDAR and NNs
2. Something something imaging-adapted partitions. A 'notion'
**Clarity:**
Very well written and clear.
# Second Pass
**What is the main thrust?**
**What is the supporting evidence?**
**What are the key findings?**
# Third Pass
**Recreation Notes:**
**Hidden Findings:**
**Weak Points? Strong Points?**

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@ -0,0 +1,50 @@
---
creation date: 2024-08-08
modification date: Thursday 8th August 2024 09:57:16
tags:
- Research
- "#Survey"
---
# Preamble
### Notable Links
[[ARCADE Implementation at the University of Pittsburgh]]
[[1. A shortlist of ARCADE Experiments]]
## What are we doing?
Collecting and organizing papers about HiTL testing. Making notes about 'em. Stuff like that.
## Why are we doing it?
08-08-2024: I'm writing a paper for [[2. (SR-CIST) Workshop on Security and Resiliency of Critical Infrastructure and Space Technologies]] and really need to know about hardware in the loop testing.
## Who cares?
Me. Andrew, probably. Dan, a lot.
# Papers
## Summary Table
```dataview
table without id
link(file.path, title) as "Title", year as "Year", authors as "Authors", readstatus as "Read Status"
from outgoing([[]])
where readstatus or readstatus=False
sort readstatus desc, year desc
```
## Papers about ARCADE
[[maccaroneADVANCEDREACTORCYBER]]
[[chenFullscopeHighfidelitySimulatorbased2024]]
## Hardware In The Loop Papers
[[mihalicHardwareintheLoopSimulationsHistorical2022]]
[[bullockHardwareintheloopSimulation2004]]
[[puysHardwareInTheLoopLabsSCADA2021]]
[[choiRealTimeHardwareintheLoopHIL2021]]
## Cybersecurity of OT Papers
[[sunSoKAttacksIndustrial2021]]
[[mclaughlinControllerawareFalseData2014]]
[[chekoleEnforcingMemorySafety2018]]
[[kushnerRealStoryStuxnet2013]]
[[CyberAttackGerman2015]]
[[sguegliaFederalOfficialsInvestigating2023]]
## Formal Methods and PLCs
[[fernandezadiegoApplyingModelChecking2015]]
[[lopez-miguelPLCverifStatusFormal2022]]
[[kleinFormallyVerifiedSoftware2018]] -- Littlebird paper
## Kry10
[[Kry10TechnicalOverview]]

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