Related papers: Constructing spoke subfactors using the jellyfish …
We construct subfactors where one of the principal graphs is a spoke graph using an algorithm which computes two-strand jellyfish relations. One of the subfactors we construct is a 3^{Z/4} subfactor known to Izumi, which has not previously…
In this paper, we construct the "2221" subfactor planar algebra by finding it as a subalgebra of the graph planar algebra of its principal graph. In particular, we give a presentation of the "2221" subfactor planar algebra consisting of…
We find generating functions the number of strings (words) containing a specified number of occurrences of certain types of order-isomorphic classes of substrings called subword patterns. In particular, we find generating functions for the…
In this paper, we contribute to the Kuperberg program by giving a diagrammatic presentation of generators and relations for the affine $E_7$ unshaded subfactor planar algebra. Using this presentation, we prove that its jellyfish algorithm…
We show that if the principal graph of a subfactor planar algebra of modulus \delta>2 is stable for two depths, then it must end in A_{finite} tails. This result is analogous to Popa's theorem on principal graph stability. We use these…
We propose to model parallel streams of data, such as overlapped speech, using shuffles. Specifically, this paper shows how the shuffle product and partial order finite-state automata (FSAs) can be used for alignment and speaker-attributed…
We investigate a (potentially infinite) series of subfactors, called $3^n$ subfactors, including $A_4$, $A_7$, and the Haagerup subfactor as the first three members corresponding to $n=1,2,3$. Generalizing our previous work for odd $n$, we…
Segmentation, a new approach based on successive edge contraction is introduced for extract method refactoring. It targets identification of distinct functionalities implemented within a method. Segmentation builds upon data and control…
Practical algorithms for solving the Subgraph Homeomorphism Problem are known for only a few small pattern graphs: among these are the wheel graphs with four, five, six, and seven spokes. The length and difficulty of the proofs leading to…
Nanophrases have a filtered structure consisting of an infinite number of categories, and each category has a homotopy structure. Among these categories, the one that we are most familiar with is the category of links. Interestingly, the…
Despite several years of research in deepfake and spoofing detection for automatic speaker verification, little is known about the artefacts that classifiers use to distinguish between bona fide and spoofed utterances. An understanding of…
Structure factors obtained from diffraction experiments are one of the most important quantities for characterizing the electronic and structural properties of materials. Methods for calculating this quantity from plane-wave density…
If $G$ is a countable, discrete group generated by two finite subgroups $H$ and $K$ and $P$ is a II$_1$ factor with an outer G-action, one can construct the group-type subfactor $P^H \subset P \rtimes K$ introduced in \cite{BH}. This…
We introduce an algorithm for the efficient generation of cubic pregraphs which have a 2-factor in which each component is a quotient of $C_4$. This class of pregraphs is of particular interest, since it corresponds to the class of…
We have constructed a Carmichael number with 10,333,229,505 prime factors, and have also constructed Carmichael numbers with k prime factors for every k between 3 and 19,565,220. These computations are the product of implementations of two…
This paper addresses the problem of generating questions from a given context and an answer, specifically focusing on questions that require multi-hop reasoning across an extended context. Previous studies have suggested that key phrase…
Large language models (LLMs) are enabling reasoning over 2D and 3D structures, yet existing methods remain modality-specific and typically compress structural inputs through sequence-based tokenization or fixed-length query connectors. Such…
The powerful (and so far under-utilized) Goulden-Jackson Cluster method for finding the generating function for the number of words avoiding, as factors, the members of a prescribed set of `dirty words', is tutorialized and extended in…
Conformal field theory (CFT) in two dimensions provide a rich source of subfactors. The fact that there are so many subfactors coming from CFT have led people to conjecture that perhaps all finite depth subfactors are related to CFT. In…
Pseudorandomness has played a central role in modern cryptography, finding theoretical and practical applications to various fields of computer science. A function that generates pseudorandom strings from shorter but truly random seeds is…