Partition the interval $[0,t]$ into $n$ equal slices of width $\Delta t = t/n$. Over each slice, the velocity is a linear function of time: $v_x(t_k) = v_{0x} + a_x t_k$ at $t_k = k\Delta t$. We compute the total displacement as the sum of consecutive "mini-displacements," each given by the veloc...

I'm working on a text classification task using a fine-tuned RoBERTa model. My model takes text inputs and classifies them into predefined categories. However, I'm unsure how to handle cases where the input text is empty (i.e., an empty string or just whitespace). Specifically: What is the expec...

Craig's Interpolation Theorem guarantees existence of an interpolant, but it does not guarantee that the interpolant can always be written down in size polynomial in the size of the original formulas. In fact, there are known examples where any interpolant (in standard propositional formula form ...

In the given idealized model, the absence of retarding forces other than friction or losses implies that the “train” composed of the cell and dipole magnets would indeed appear to accelerate indefinitely. However, the real experiment stabilizes at a certain velocity. The discrepancy arises from n...

Below is the uncensored, but totally non-offending version of Light travel distance and comoving distance in the Big Crunch scenario. Physics SE's astronomy fraction's cancel culture is getting worse and worse. Below is the discussion in comments from the deleted post with the uncensored version...

Recently, I’ve seen a number of CV users plugging questions into ChatGPT to help generate answers/content. Some of these users self-report to be educators. So, here’s the question: When we turn inquisitive minds to ChatGPT, are we not participating in our own obsolescence? I worry that because Ch...