Tootfinder

This https://arxiv.org/abs/2311.03619 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csIT_…

Construction and Fast Decoding of Binary Linear Sum-Rank-Metric Codes
Sum-rank-metric codes have wide applications in the multishot network coding and the distributed storage. Linearized Reed-Solomon codes, sum-rank BCH codes and their Welch-Berlekamp type decoding algorithms were proposed and studied. They are sum-rank versions of Reed-Solomon codes and BCH codes in the Hamming metric. In this paper, we construct binary linear sum-rank-metric codes of the matrix size $2 \times 2$, from BCH, Goppa and additive quaternary Hamming metric codes. Larger sum-rank-metr…

@… One might hope crash metrics are associated with version numbers.
But I could easily see that not being the case for some given team.

Representation theory of the reflection equation algebra I: A quantization of Sylvester's law of inertia
Kenny De Commer, Stephen T. Moore
https://arxiv.org/abs/2404.03640

Representation theory of the reflection equation algebra I: A quantization of Sylvester's law of inertia
We prove a version of Sylvester's law of inertia for the Reflection Equation Algebra (=REA). We will only be concerned with the REA constructed from the $R$-matrix associated to the standard $q$-deformation of $GL(N,\mathbb{C})$. For $q$ positive, this particular REA comes equipped with a natural $*$-structure, by which it can be viewed as a $q$-deformation of the $*$-algebra of polynomial functions on the space of self-adjoint $N$-by-$N$-matrices. We will show that this REA satisfies a type $I…

This https://arxiv.org/abs/2402.15317 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Logarithmic concavity of bimatroids
A bimatroid is a matroid-like generalization of the collection of regular minors of a matrix. In this article, we use the theory of Lorentzian polynomials to study the logarithmic concavity of natural sequences associated to bimatroids. Bimatroids can be used to characterize morphisms of matroids and this observation (originally due to Kung) allows us to prove a weak version of logarithmic concavity of the number of bases of a morphism of matroids. This is weaker than the original result by Eur…

This https://arxiv.org/abs/2401.05235 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csSI_…

A Survey on Optimization Studies of Group Centrality Metrics
Centrality metrics have become a popular concept in network science and optimization. Over the years, centrality has been used to assign importance and identify influential elements in various settings, including transportation, infrastructure, biological, and social networks, among others. That said, most of the literature has focused on nodal versions of centrality. Recently, group counterparts of centrality have started attracting scientific and practitioner interest. The identification of s…

This https://arxiv.org/abs/2303.11972 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csCR_…

A Post Quantum Key Agreement Protocol Based on a Modified Matrix Power Function over a Rectangular Matrices Semiring
We present an improved post-quantum version of Sakalauskas matrix power function key agreement protocol, using rectangular matrices instead of the original square ones. Sakalauskas matrix power function is an efficient and secure way to generate a shared secret key, and using rectangular matrices provides additional flexibility and security. This method reduces the computational complexity by allowing smaller random integer matrices while maintaining a high level of security. We dont rely on ma…

This https://arxiv.org/abs/2401.05235 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csSI_…

A Survey on Optimization Studies of Group Centrality Metrics
Centrality metrics have become a popular concept in network science and optimization. Over the years, centrality has been used to assign importance and identify influential elements in various settings, including transportation, infrastructure, biological, and social networks, among others. That said, most of the literature has focused on nodal versions of centrality. Recently, group counterparts of centrality have started attracting scientific and practitioner interest. The identification of s…

This https://arxiv.org/abs/2403.12804 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

The Bayes Principle and Segal Axioms for $P(ϕ)_2$, with application to Periodic Covers
The goal of the present paper is to reconcile the so-called $P(ϕ)_2$ model from classical constructive quantum field theory (CQFT) with (metric version of) geometric and categorical axioms proposed by G. Segal (see refs in Kontsevich and Segal arXiv:2105.10161) in the 90's, in showing that the $P(ϕ)_2$ model satisfies these axioms, appropriately adjusted. The approach is based on previous works of Dimock arXiv:math-ph/0305017 and Pickrell arXiv:math-ph/0702077, while we give a new proof to a …

This https://arxiv.org/abs/2303.11972 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csCR_…

A Post Quantum Key Agreement Protocol Based on a Modified Matrix Power Function over a Rectangular Matrices Semiring
We present an improved post-quantum version of Sakalauskas matrix power function key agreement protocol, using rectangular matrices instead of the original square ones. Sakalauskas matrix power function is an efficient and secure way to generate a shared secret key, and using rectangular matrices provides additional flexibility and security. This method reduces the computational complexity by allowing smaller random integer matrices while maintaining a high level of security. We dont rely on ma…

Metric geometry of the privacy-utility tradeoff
March Boedihardjo, Thomas Strohmer, Roman Vershynin
https://arxiv.org/abs/2405.00329 https://

Metric geometry of the privacy-utility tradeoff
Synthetic data are an attractive concept to enable privacy in data sharing. A fundamental question is how similar the privacy-preserving synthetic data are compared to the true data. Using metric privacy, an effective generalization of differential privacy beyond the discrete setting, we raise the problem of characterizing the optimal privacy-accuracy tradeoff by the metric geometry of the underlying space. We provide a partial solution to this problem in terms of the "entropic scale", a quanti…