Tootfinder

Unconditional correctness of recent quantum algorithms for factoring and computing discrete logarithms
C\'edric Pilatte
https://arxiv.org/abs/2404.16450

Unconditional correctness of recent quantum algorithms for factoring and computing discrete logarithms
In 1994, Shor introduced his famous quantum algorithm to factor integers and compute discrete logarithms in polynomial time. In 2023, Regev proposed a multi-dimensional version of Shor's algorithm that requires far fewer quantum gates. His algorithm relies on a number-theoretic conjecture on the elements in $(\mathbb{Z}/N\mathbb{Z})^{\times}$ that can be written as short products of very small prime numbers. We prove a version of this conjecture using tools from analytic number theory such as z…

This https://arxiv.org/abs/2403.16636 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Detecting affine equivalences between rational or non-rational, meromorphic parametric curves in any dimension
We generalize previous results by the authors to provide an algorithm for computing the affine equivalences between two parametric curves, either rational or with non-algebraic, meromorphic components under certain conditions, in any dimension. The algorithm completely avoids polynomial system solving, and uses bivariate factoring, instead, as a fundamental tool.

This https://arxiv.org/abs/2310.00899 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_qu…

Space-Efficient and Noise-Robust Quantum Factoring
We provide two improvements to Regev's recent quantum factoring algorithm (arXiv:2308.06572), addressing its space efficiency and its noise-tolerance. Our first contribution is to improve the quantum space efficiency of Regev's algorithm while keeping the circuit size the same. Our main result constructs a quantum factoring circuit using $O(n \log n)$ qubits and $O(n^{3/2} \log n)$ gates. We achieve the best of Shor and Regev (upto a logarithmic factor in the space complexity): on the one han…

Truth Factors
Robert E. Kent
https://arxiv.org/abs/2404.14470 https://arxiv.org/pdf/2404.14470<…

Truth Factors
Truth refers to the satisfaction relation used to define the semantics of model-theoretic languages. The satisfaction relation for first order languages (truth classification), and the preservation of truth by first order interpretations (truth infomorphism), is a motivating example in the theory of Information Flow (IF) (Barwise and Seligman 1997). The abstract theory of satisfaction is the basis for the theory of institutions (Goguen and Burstall 1992). Factoring refers to categorical factori…

This https://arxiv.org/abs/2311.05545 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csCR_…

Extending Regev's factoring algorithm to compute discrete logarithms
Regev recently introduced a quantum factoring algorithm that may be perceived as a $d$-dimensional variation of Shor's factoring algorithm. In this work, we extend Regev's factoring algorithm to an algorithm for computing discrete logarithms in a natural way. Furthermore, we discuss natural extensions of Regev's factoring algorithm to order finding, and to factoring completely via order finding. For all of these algorithms, we discuss various practical implementation considerations, including i…

A Collision-Aware Cable Grasping Method in Cluttered Environment
Lei Zhang, Kaixin Bai, Qiang Li, Zhaopeng Chen, Jianwei Zhang
https://arxiv.org/abs/2402.14498

A Collision-Aware Cable Grasping Method in Cluttered Environment
We introduce a Cable Grasping-Convolutional Neural Network designed to facilitate robust cable grasping in cluttered environments. Utilizing physics simulations, we generate an extensive dataset that mimics the intricacies of cable grasping, factoring in potential collisions between cables and robotic grippers. We employ the Approximate Convex Decomposition technique to dissect the non-convex cable model, with grasp quality autonomously labeled based on simulated grasping attempts. The CG-CNN i…

A faster algorithm for the construction of optimal factoring automata
Thomas Erlebach, Kleitos Papadopoulos
https://arxiv.org/abs/2404.02354 https://

A faster algorithm for the construction of optimal factoring automata
The problem of constructing optimal factoring automata arises in the context of unification factoring for the efficient execution of logic programs. Given an ordered set of $n$ strings of length $m$, the problem is to construct a trie-like tree structure of minimum size in which the leaves in left-to-right order represent the input strings in the given order. Contrary to standard tries, the order in which the characters of a string are encountered can be different on different root-to-leaf path…

A Collision-Aware Cable Grasping Method in Cluttered Environment
Lei Zhang, Kaixin Bai, Qiang Li, Zhaopeng Chen, Jianwei Zhang
https://arxiv.org/abs/2402.14498

A Collision-Aware Cable Grasping Method in Cluttered Environment
We introduce a Cable Grasping-Convolutional Neural Network designed to facilitate robust cable grasping in cluttered environments. Utilizing physics simulations, we generate an extensive dataset that mimics the intricacies of cable grasping, factoring in potential collisions between cables and robotic grippers. We employ the Approximate Convex Decomposition technique to dissect the non-convex cable model, with grasp quality autonomously labeled based on simulated grasping attempts. The CG-CNN i…

This https://arxiv.org/abs/2306.13635 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Factoring determinants and applications to number theory
Products of shifted characteristic polynomials, and ratios of such products, averaged over the classical compact groups are of great interest to number theorists as they model similar averages of L-functions in families with the same symmetry type as the compact group. We use Toeplitz and Toeplitz plus Hankel operators and the identities of Borodin - Okounkov, Case - Geronimo, and Basor - Erhardt to prove that, in certain cases, these unitary averages factor as polynomials in the matrix size in…

This https://arxiv.org/abs/2404.05796 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

What is the Modular Fourier Transform?
The discrete Fourier transform can be viewed as an isomorphism of the group algebra of a cyclic group to its decomposition in terms of irreducible representations when the characteristic of the field does not divide the order of the group. We describe the DFT when $p|n$ by factoring $x^N - 1$ over finite fields. For the symmetric group, the Fourier transform is implemented using representations, Specht modules $S^λ$ for partitions $λ$, and Maschke's theorem. In the modular case, we const…

This https://arxiv.org/abs/2402.09686 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_grqc_…

Lorentz violation induces isospectrality breaking in Einstein-Bumblebee gravity theory
In this paper, we investigate the quasinormal modes (QNMs) of a Lorentz-violating spacetime, factoring in a cosmological constant, within the framework of Einstein-Bumblebee gravity. Our findings reveal that the interaction of spacetime with an anisotropic bumblebee field imparts distinct contributions to the axial and polar sectors of the vector perturbations. This subsequently breaks the isospectrality typically observed in vector modes. Numerical evidence strongly indicates isospectral break…

Linear Codes for Hyperdimensional Computing
Netanel Raviv
https://arxiv.org/abs/2403.03278 https://arxiv.org/pdf/2403.03278

Linear Codes for Hyperdimensional Computing
Hyperdimensional Computing (HDC) is an emerging computational paradigm for representing compositional information as high-dimensional vectors, and has a promising potential in applications ranging from machine learning to neuromorphic computing. One of the long-standing challenges in HDC is factoring a compositional representation to its constituent factors, also known as the recovery problem. In this paper we take a novel approach to solve the recovery problem, and propose the use of random li…

This https://arxiv.org/abs/2309.14403 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Should Sports Professionals Consider Their Adversary's Strategy? A Case Study of Match Play in Golf
This study explores strategic considerations in professional golf's Match Play format, challenging the conventional focus on individual performance. Leveraging PGA Tour data, we investigate the impact of factoring in an adversary's strategy. Our findings suggest that while slight strategy adjustments can be advantageous in specific scenarios, the overall benefit of considering an opponent's strategy remains modest. This confirms the common wisdom in golf, reinforcing the recommendation to adher…

What is the Modular Fourier Transform?
Jackson Walters
https://arxiv.org/abs/2404.05796 https://arxiv.org/pdf/2404.05796

What is the Modular Fourier Transform?
The discrete Fourier transform can be viewed as an isomorphism of the group algebra of a cyclic group to its decomposition in terms of irreducible representations when the characteristic of the field does not divide the order of the group. We describe the DFT when $p|n$ by factoring $x^N - 1$ over finite fields. For the symmetric group, the Fourier transform is implemented using representations, Specht modules $S^λ$ for partitions $λ$, and Maschke's theorem. In the modular case, we const…