Tootfinder

word_assoc: Edinburgh word associations
A network of word associations showing the count of such associations as collected from subjects, from the Edinburgh Associative Thesaurus (EAT). Each node represents a word, and a directed edge (i, j) denotes that word i was used as a stimulus to which word j was given as a response. Multiple edges are allowed.
This network has 23132 nodes and 312342 edges.
Tags: Informational, Language, Unweighted, Multigraph

This https://arxiv.org/abs/2404.16889 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Non-associative versions of Hilbert's basis theorem
We prove several new versions of Hilbert's basis theorem for non-associative Ore extensions and non-associative skew Laurent polynomial rings, non-associative skew power series rings, and non-associative skew Laurent series rings. For non-associative skew Laurent polynomial rings, we show that both a left and a right version of Hilbert's basis theorem hold. For non-associative Ore extensions, we show that a right version holds, but give a counterexample to a left version; a difference that does…

This https://arxiv.org/abs/2309.13198 has been replaced.
initial toot: https://mastoxiv.page/@a…

Associative memory by virtual oscillator network based on single spin-torque oscillator
A coupled oscillator network may be able to perform an energy-efficient associative memory operation. However, its realization has been difficult because inhomogeneities unavoidably arise among the oscillators during fabrication and lead to an unreliable operation. This issue could be resolved if the oscillator network were able to be formed from a single oscillator. Here, we performed numerical simulations and theoretical analyses on an associative memory operation that uses a virtual oscillat…

This https://arxiv.org/abs/2404.16889 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Non-associative versions of Hilbert's basis theorem
We prove several new versions of Hilbert's basis theorem for non-associative Ore extensions and non-associative skew Laurent polynomial rings, non-associative skew power series rings, and non-associative skew Laurent series rings. For non-associative skew Laurent polynomial rings, we show that both a left and a right version of Hilbert's basis theorem hold. For non-associative Ore extensions, we show that a right version holds, but give a counterexample to a left version; a difference that does…

Root Graded Groups
Torben Wiedemann
https://arxiv.org/abs/2404.02042 https://arxiv.org/pdf/2404.02042<…

Root Graded Groups
We define and study root graded groups, that is, groups graded by finite root systems. This notion generalises several existing concepts in the literature, including in particular Jacques Tits' notion of RGD-systems. The most prominent examples of root graded groups are Chevalley groups over commutative associative rings. Our main result is that every root graded group of rank at least 3 is coordinatised by some algebraic structure satisfying a variation of the Chevalley commutator formula. Thi…

On the locality of formal distributions over pre-Lie and Novikov algebras
L. A. Bokut, P. S. Kolesnikov
https://arxiv.org/abs/2404.17232 https://

On the locality of formal distributions over pre-Lie and Novikov algebras
The Dong Lemma in the theory of vertex algebras states that the locality property of formal distributions over a Lie algebra is preserved under the action of a vertex operator. A~similar statement is known for associative algebras. We study local formal distributions over pre-Lie (right-symmetric), pre-associative (dendriform), and Novikov algebras to show that the analogue of the Dong Lemma holds for Novikov algebras but does not hold for pre-Lie and pre-associative ones.

Strong minimal model theorem and Massey products
Martin Markl
https://arxiv.org/abs/2404.19607 https://arxiv.org/pdf/2404.19607

Strong minimal model theorem and Massey products
Kadeishvili's minimal model theorem establishes the existence of an $A_\infty$-structure, unique up to isomorphism, on the cohomology of a dg associative algebra, which captures its homotopy type. In this note we prove the existence of minimal models that are unique up to isotopy, a stronger result obviously known to T. Kadeishvili and certainly to others, yet seemingly overlooked by mankind. We will explore how this stronger result can help in the study of Massey products. First, we show that …

Using #PHP arrays as pseudo-objects is almost never the right answer. They're less self-documenting, slower, worse on memory, and more bug prone.
https://peakd.com/php/@crell/php-use-a

Non-associative versions of Hilbert's basis theorem
Per B\"ack, Johan Richter
https://arxiv.org/abs/2404.16889 https://arxiv…

Non-associative versions of Hilbert's basis theorem
We prove several new versions of Hilbert's basis theorem for non-associative Ore extensions and non-associative skew Laurent polynomial rings, non-associative skew power series rings, and non-associative skew Laurent series rings. For non-associative skew Laurent polynomial rings, we show that both a left and a right version of Hilbert's basis theorem hold. For non-associative Ore extensions, we show that a right version holds, but give a counterexample to a left version; a difference that does…

Strong minimal model theorem and Massey products
Martin Markl
https://arxiv.org/abs/2404.19607 https://arxiv.org/pdf/2404.19607

Strong minimal model theorem and Massey products
Kadeishvili's minimal model theorem establishes the existence of an $A_\infty$-structure, unique up to isomorphism, on the cohomology of a dg associative algebra, which captures its homotopy type. In this note we prove the existence of minimal models that are unique up to isotopy, a stronger result obviously known to T. Kadeishvili and certainly to others, yet seemingly overlooked by mankind. We will explore how this stronger result can help in the study of Massey products. First, we show that …