Where exciting things happen
I ve been spending some of my time recently developing a tool called FPSan in collaboration with Pawel Szczerbuk. It s implemented as a Triton compiler pass, but has none of the desirable properties expected of a compiler pass: in particular, it Continue reading
This is an atypical post, being chiefly about the history of a rather obscure computer that was built in 1960 out of repurposed PDP parts, but it needs to be written somewhere lest it be forgotten. It has been referred Continue reading
In the post on threelds, we investigated under what conditions the additive group of one field (the inner field ) could be isomorphic to the multiplicative group of another field (the outer field ). To summarise, this happens in the following cases: Continue reading
A phoenix is an oscillator in Conway s Life where every cell dies in every generation. The smallest example is Phoenix 1, which oscillates with period 2 and has a constant population of 12: All known finite phoenices have period 2, Continue reading
Soon after the previous post announcing the discovery of an aperiodic monotile by Smith, Myers, Kaplan, and Goodman-Strauss, the same authors published a second aperiodic monotile which has the property that all of the tiles are of the same orientation: Continue reading
David Smith, Joseph Myers, Craig Kaplan, and Chaim Goodman-Strauss have discovered an aperiodic monotile: a polygon that tiles the plane by rotations and reflections, but cannot tile the plane periodically. Any tiling induced by the monotile is scalemic: the majority Continue reading
A couple of years ago I described a prime p which possesses various properties that renders it useful for computing number-theoretic transforms over the field . Specifically, we have: where the first of these equalities uses the identity that: where rad(k) Continue reading
I gave a half-hour talk on Tuesday about the project to search for optimal Boolean chains for all equivalence classes of 5-input 1-output and 4-input 2-output functions. The talk was not recorded, but the slides and transcript are included here Continue reading
In the tensor rank paper we introduced a new family of axis-aligned n-dimensional polytopes, one for each positive integer n. The vertices are naturally identified with ordered partial partitions (OPPs) of {1, , n}, and the edges correspond to converting Continue reading
Robin Houston, Nathaniel Johnston, and I have established some new bounds on the tensor rank of the determinant over various fields. The paper is now available as an arXiv preprint and contains the following results: A new formula for the Continue reading