Tootfinder

Algorithmic strategies for finding the best TSP 2-OPT move in average sub-quadratic time
Giuseppe Lancia, Paolo Vidoni
https://arxiv.org/abs/2403.19878 htt…

Algorithmic strategies for finding the best TSP 2-OPT move in average sub-quadratic time
We describe an exact algorithm for finding the best 2-OPT move which, experimentally, was observed to be much faster than the standard quadratic approach. To analyze its average-case complexity, we introduce a family of heuristic procedures and discuss their complexity when applied to a random tour in graphs whose edge costs are either uniform random numbers in [0, 1] or Euclidean distances between random points in the plane. We prove that, for any probability p: (i) there is a heuristic in the…

Uncertainty relation and the constrained quadratic programming
Lin Zhang, Dade Wu, Ming-Jing Zhao, Hua Nan
https://arxiv.org/abs/2404.18671 https://…

Uncertainty relation and the constrained quadratic programming
The uncertainty relation is a fundamental concept in quantum theory, plays a pivotal role in various quantum information processing tasks. In this study, we explore the additive uncertainty relation pertaining to two or more observables, in terms of their variance,by utilizing the generalized Gell-Mann representation in qudit systems. We find that the tight state-independent lower bound of the variance sum can be characterized as a quadratic programming problem with nonlinear constraints in opt…

This https://arxiv.org/abs/2402.04385 has been replaced.
link: https://scholar.google.com/scholar?q=a

Locating the roots of a quadratic equation in one variable through a Line-Circumference (LC) geometric construction in the plane of complex numbers
This paper describes a geometrical method for finding the roots $r_1$, $r_2$ of a quadratic equation in one complex variable of the form $x^2+c_1 x+c_2=0$, by means of a Line $L$ and a Circumference $C$ in the complex plane, constructed from known coefficients $c_1$, $c_2$. This Line-Circumference (LC) geometric structure contains the sought roots $r_1$, $r_2$ at the intersections of its component elements $L$ and $C$. Line $L$ is mapped onto Circumference $C$ by a Mobius transformation. The lo…

This https://arxiv.org/abs/2402.06133 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_sta…

Leveraging Quadratic Polynomials in Python for Advanced Data Analysis
Objectives: This study aims to provide a comprehensive overview of the role of quadratic polynomials in data modeling and analysis, particularly in representing the curvature of natural phenomena. Methods: We begin with a fundamental explanation of quadratic polynomials and describe their general forms and theoretical significance. We then explored the application of these polynomials in regression analysis, detailing the process of fitting quadratic models to the data using Python libraries Nu…

This https://arxiv.org/abs/2312.11329 has been replaced.
link: https://scholar.google.com/scholar?q=a

Convergence guarantees for adaptive model predictive control with kinky inference
We analyze the convergence properties of a robust adaptive model predictive control algorithm used to control an unknown nonlinear system. We show that by employing a standard quadratic stabilizing cost function, and by recursively updating the nominal model through kinky inference, the resulting controller ensures convergence of the true system to the origin, despite the presence of model uncertainty. We illustrate our theoretical findings through a numerical simulation.

This https://arxiv.org/abs/2403.02040 has been replaced.
link: https://scholar.google.com/scholar?q=a

On Generalised Albert Forms over Discretely Valued Fields
For a discrete valuation ring $R$ with quotient field $K$ and residue field $F$ both of characteristic not 2, we study low-dimensional quadratic forms with Witt class in the $n$-th power of the fundamental ideal of $F$ resp. $K$ and point out connections between forms over these fields. We analyse the minimal number of Pfister forms such that a given form is Witt equivalent to the sum of these and study forms congruent modulo a higher power of the fundamental ideal towards similarity.

Moduli spaces of quadratic differentials: Abel-Jacobi map and deformation
Yu Qiu
https://arxiv.org/abs/2403.10265 https://arxiv.org/p…

Moduli spaces of quadratic differentials: Abel-Jacobi map and deformation
We study the moduli space of quadratic differentials with prescribed singularities parameterized by a decorated marked surface with punctures (DMSp), where simple zeros, double poles and higher order poles respectively correspond to decorations, punctures and boundary components. We show that the fundamental group of this space equals the kernel of the Abel-Jacobi map from the mapping class group of DMSp to the first homology group of the marked surface (without decorations/punctures). Moreover…

Failures of integral Springer's Theorem
Nicolas Daans, V\'it\u{e}zslav Kala, Jakub Kr\'asensk\'y, Pavlo Yatsyna
https://arxiv.org/abs/2404.12844

Failures of integral Springer's Theorem
We discuss the phenomenon where an element in a number field is not integrally represented by a given positive definite quadratic form, but becomes integrally represented by this form over a totally real extension of odd degree. We prove that this phenomenon happens infinitely often, and, conversely, establish finiteness results about the situation when the quadratic form is fixed.

A Log-domain Interior Point Method for Convex Quadratic Games
Bingqi Liu, Dominic Liao-McPherson
https://arxiv.org/abs/2403.13290 https://

A Log-domain Interior Point Method for Convex Quadratic Games
In this paper, we propose an equilibrium-seeking algorithm for finding generalized Nash equilibria of non-cooperative monotone convex quadratic games. Specifically, we recast the Nash equilibrium-seeking problem as variational inequality problem that we solve using a log-domain interior point method and provide a general purpose solver based on this algorithm. This approach is suitable for non-potential, general sum games and does not require extensive structural assumptions. We demonstrate the…

Moduli spaces of quadratic differentials: Abel-Jacobi map and deformation
Yu Qiu
https://arxiv.org/abs/2403.10265 https://arxiv.org/p…

Moduli spaces of quadratic differentials: Abel-Jacobi map and deformation
We study the moduli space of quadratic differentials with prescribed singularities parameterized by a decorated marked surface with punctures (DMSp), where simple zeros, double poles and higher order poles respectively correspond to decorations, punctures and boundary components. We show that the fundamental group of this space equals the kernel of the Abel-Jacobi map from the mapping class group of DMSp to the first homology group of the marked surface (without decorations/punctures). Moreover…