I can't speak to oz's error messages, but for the vega-lite + python integration, I've found altair pretty usable. In particular, simple scatter plots with tooltips were easy to get up and running.
The definition of the Markov property is that the process is memoryless - the probability distribution of the next state only depends on the previous state. This makes them an easy tool to use for mathematical analysis, but limits the amount of things they can model completely.
One simple way to add memory is to make states more complex. For example, instead of recording the weather each day as a state, you could record the weather for two day tuples. This allows more complex dynamics, but the number of states quickly increases.
Hierarchical Markov Models are another way to achieve this. In a HMM, there is a probability matrix for different types of weather (winter vs summer) and a probability matrix that governs transitions between each of these types.
Are you referring to the Cueva paper? I also spent a considerable amount of time trying to replicate it without success. Do you know if the author has released any code yet?
His solution doesn't seem to solve the hard problem of "stuffing the ballot box." Any voter can verify their own vote is correct, but they can't verify that each vote is cast by a real citizen.
Could a lighter weight website serve more users for the same dollar of bandwidth as bloated website?
It seems to me there's a business strategy, where rather than pushing for more ads, a website pushes for lighter weight and promises its few advertisers a wider audience.
I guess I was trying to advocate for somewhat orthogonal ideas.
On the one hand, learning how to approximate functions with arbitrary precision definitely solidifies an understanding of what those functions are doing.
On the other hand high school math classes are often taught quite algorithmically. Therefore, rather than tests and problem sets, what if the student's chief deliverable was a small python package that performed the algorithms for that lesson? This has a really good advantage of teach basic life skills of turning a specification or intention into a physical product. It also does not significantly impair students that need a strong math background going forward. Finally, makes life a little easier for teachers because some of their grading work could be automated.
Now these two approaches could be applied independently, but I think they would work well together, particularly because the numerical approximation programs generalize a bit better than symbolic ones.
One small change I'd like is to teach a lot of math from a more numerical approach. Learning to approximate sines, cosines, limits, derivatives, and integrals in university made me feel much more confident in my understanding of the concepts. An advantage of this approach is it still gives STEM bound students a good intro to core math, but allows all students to learn a bit of programming. It also teaches how to implement something concrete from an abstract specification. I felt like a lot of high school math was very algorithmic, so why not just teach kids how to implement basic algorithms?
https://altair-viz.github.io/
https://altair-viz.github.io/gallery/scatter_tooltips.html?h...