So I got checked out by my doctor, and it seems like the back pain that I experienced was just a very severe muscle spasm. I don’t show any signs of having a herniated disk, and I seems to have maintained full mobility and flexibility in my spine. I can even touch my toes again! Going forward, I’m going to need to be more cautious when doing stand-up, but other than that, I got off easy....

I managed to injure my lower back like an idiot this week. The day immediately after, I had difficulty walking and sitting without grimacing. Considering that I need to sit down for extended periods of time during the day, this was troubling. As a result, I fell down a spiral of Youtube videos and WebMD posts (not the best idea in hindsight…) to try and fix my problem. I managed to find some stretches (things like piriformis muscle stretch, child’s pose etc....

I spent most of January just relaxing. For me, “relaxing” involved writing a chess engine, trudging my way through an online FPGA course, and video games (what a strange definition). The chess engine went pretty well: I managed to get a working prototype in Typescript up and running. It’s butt-ugly and has a terrible UI, but it works. I made a half-hearted attempt to train a neural-net to act as the evaluation function during the tree search, but ran into issues with convergence....

Notes following this MIT course and is based on the xv6 toy operating system. Operating System Interfaces Processes and Memory Forking Exec Operating System Organization Abstracting Physical Resources CPU Modes Processes xv6 startup Security Page Tables Kernel Address space Xv6 Implementation Physical Memory Allocation Xv6 Physical Memory Implementation Process Address Space Sbrk (Xv6) Exec (Xv6) Real World Paging Traps and System Calls RISC-V traps User Space Traps Syscalls Kernel Space Traps Page Fault Exceptions Interrupts ad Device Drivers Console Input Console Output Timer Interrupts Locking Races Spinlocks Using Locks Deadlocks Spinlocks Scheduling Context Switching Scheduler Sleep and Wakeup Semaphores Lost Wake-Up Problem Pipes Process Locks Real World Scheduling File System Buffer Cache Layer Logging Layer Block Allocator Inode Layer Operating System Interfaces Operating systems serve a number of purposes Abstracts away lower level hardware, so that programs don’t have to care about what disk you are writing to Allows multiple programs to run “at the same time” Provide well defined interface for programs to interact with each other For the interface, we want a simple interface that is easy to implement, but allows high sophisticated operations to happen UNIX philosophy of composing many simple programs together helps keep this problem trackable Can divide operating system into kernel space and user space kernel space is the program which provides services to other programs....

Linear Regression You have a set of data $(x_{i},y_{i},\sigma_[i])$, where x is the independent variable, y is the dependent variable, and $\sigma$ is the uncertainty in the dependent variable You want to fit a line to the data ($\hat{y} = mx+b$) You also want the uncertainties of the parameters Why would you want to do this? To know the parameters of the model To extrapolate/interpolate values of the dataset that you don’t have How you do this depends on your viewpoint a frequentist approach would try to maximize the likelihood estimate (information theory) Suppose that you have a probability density for the data $y_{i}$ ranging from 1 to N Treat this density as a function of the parameters....

Logistics Book(s) Landau and Lifshitz Kardar Pathria Thermodynamics 0th Law Thermodynamic equilibrium means that each object in thermal contact with each other have the same temperature Ideal gases, as you cool them down, all converge to a single point, which defines absolute zero. For Kelvin,, the triple point of water defines the size of each step on the scale (273.16 K) 1st Law $dE = \delta W + \delta Q$ The change is energy can either come from work, or heat $dE = E_{f}-E_{i}$ Energy is a function of state (path independent) $\delta W$ and $\delta Q$ are path dependent Can expand out $\delta W$ into more parts: $dE = -p dV + \delta Q$, where the negative sign comes from the fact that the system does work on the outside environment You don’t need to be restricted to pressure and volume....

The Basics Hibert Space Review In an infinitely dimensional space, we have some abstract vector $\Psi$. We can choose coordinate axes such that all values can be taken by the position x, so that we can describe $\Psi$ as as set of components $\Psi(x)$ Could have also chosen p instead for our coordinate axes $(v,w) \geq 0$, where (a,b) denotes an inner product This is linear in the right argument, and anti-linear in the first argument (ie....

Happy New Year! The semester is over, and I passed all my classes, and that’s all that matters! First, I finished integrating my POVFan, and it works! (see below) It doesn’t look like a continuous image, since the frame rate of my camera is much higher than the angular frequency of the motor. But in person, you see a continuous image (the “framerate” of your eyes can’t keep up with the rotation speed of the blade)....

The bad news: It’s midterm season ATM, so life could be better. I got my first roach. Don’t know how I haven’t encountered one in the 5 years I’ve been in New York, but here we are. Dealt with it immediately though. The good news: With regards to the Lox Rust compiler, I managed to implement functions and closure (closures are such a pain…). I’m now starting down the barrel of writing a garbage collector for the VM, which would require a fundamental restructuring of the codebase....

IEEE Floating Point Standard Arrays Numerics Random Numbers LCM (Linear Congruent Method) Testing RNG Nonuniform Distributions Non-Analytic Nonuniform Distributions Interpolation Linear Interpolation Fitting Basis Coefficients Polynomial fits Fourier Basis Integration Trapezoid Rule Simpson’s Rule Rescaling Integrals Differentiation Scaling Linear Algebra LU SVD Eigensystems Uses Principal Component Analysis (PCA) Dimensional Reduction Root-Finding Minimization Quadratic Fit Golden Section Search Multi-Dimensional FFTs ODEs PDEs Initial Condition Problems Boundary Condition Problems MCMC (Markov Chain Monte Carlo) Markov Chain Metropolis Hastings Burn-in and Proposal Distribution IEEE Floating Point Standard $\pm 1+ 2^{e-127}\Sigma_{i=0}^{22} f_{i} 2^{-(i-23)}$ e is the exponent number $f_{i}$ represents the floating bits Some edge cases: e = 0, $f \neq 0$ are called subnormal numbers, where “1” above is replaced with 0 and $e-127$ is replaced by $e-126$ e=0 and f=0 is a signed zero e=255, f=0 is a signed $\inf$ e=255, $f\neq = 0$ is NaN Arrays TL;DR if you want to go fast, then use numpy arrays, since they are more contiguous in memory (and hence cache friendly) compared to python lists You also don’t have to worry about type checking since Python needs to check if operations There are also some built-in functions that numpy provides which are faster than Python built-ins Numerics TL;DR Keep numbers from being too small and too large and you’re good $E[\delta (f(a))^{2}] \approx E[[\frac{\partial f}{\partial a}]^{2} \delta a^{2}]$ Assuming similar errors for each operations, you find that the round-off error scales as $\sqrt{N}$ Making finer time steps yields a better approximation, but the round-off error degrades this....