Tootfinder

Automatic Generation of Explicit Quadratic Programming Solvers
Maximilian Schaller, Daniel Arnstr\"om, Alberto Bemporad, Stephen Boyd
https://arxiv.org/abs/2506.11513

Automatic Generation of Explicit Quadratic Programming Solvers
We consider a family of convex quadratic programs in which the coefficients of the linear objective term and the righthand side of the constraints are affine functions of a parameter. It is well known that the solution of such a parametrized quadratic program is a piecewise affine function of the parameter. The number of (polyhedral) regions in the solution map can grow exponentially in problem size, but when the number of regions is moderate, a so-called explicit solver is practical. Such a so…

Proofs of singularity-free solutions and scalarization in nonlinear Einstein-scalar-Gauss-Bonnet cosmology
Chihang He, Chao Liu, Jinhua Wang
https://arxiv.org/abs/2507.15304

Proofs of singularity-free solutions and scalarization in nonlinear Einstein-scalar-Gauss-Bonnet cosmology
We establish the global existence and precise estimates of a class of singularity-free cosmological solutions in nonlinear Einstein-scalar-Gauss-Bonnet (ESGB) gravity with quadratic coupling, in close agreement with previous numerical results. Our analysis also yields a rigorous mathematical proof of nonlinear spontaneous scalarization, triggered by a tachyonic instability induced by the Gauss-Bonnet term. The proof is based on a set of decoupled differential inequalities for the Hubble paramet…

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Carry the Tail in Consensus Protocols
Suyash Gupta, Dakai Kang, Dahlia Malkhi, Mohammad Sadoghi
https://arxiv.org/abs/2508.12173 https://arxiv.org/pdf/2508…

Carry the Tail in Consensus Protocols
We present Carry-the-Tail, the first deterministic atomic broadcast protocol in partial synchrony that, after GST, guarantees a constant fraction of commits by non-faulty leaders against tail-forking attacks, and maintains optimal, worst-case quadratic communication under a cascade of faulty leaders. The solution also guarantees linear amortized communication, i.e., the steady-state is linear. Prior atomic broadcast solutions achieve quadratic word communication complexity in the worst case. …

K3 surfaces over small number fields and Kummer constructions in families
Stefan Schr\"oer
https://arxiv.org/abs/2506.14732 https://

K3 surfaces over small number fields and Kummer constructions in families
We construct K3 surfaces over number fields that have good reduction everywhere. These do not exists over the rational numbers, by results of Abrashkin and Fontaine. Our surfaces exist for three quadratic number fields, and an infinite family of $S_3$-number fields. To this end we develop a theory of Kummer constructions in families, based on Romagny's notion of the effective models, here applied to sign involutions. This includes quotients of non-normal surfaces by infinitesimal group schemes …

Efficient DFT of Zadoff-Chu Sequences using lmFH Pattern
Fanping Du
https://arxiv.org/abs/2507.23200 https://arxiv.org/pdf/2507.23200

Efficient DFT of Zadoff-Chu Sequences using lmFH Pattern
Having established that Zadoff-Chu (ZC) sequences are inherently linear micro-frequency hopping (lmFH) symbols, this paper first presents an intuitive and visual exposition of the computation of the DFT and IDFT of ZC sequences using the lmFH pattern. This yields interesting results. Subsequently, an alternative form for computing the cumulative sum of ZC sequences using the Generalized Quadratic Gauss Sum is introduced. Furthermore, building on the micro-frequency hopping (mFH) concept, this p…

This https://arxiv.org/abs/2503.13965 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

First-Order Projected Algorithms With the Same Linear Convergence Rate Bounds as Their Unconstrained Counterparts
In this paper, we propose a systematic approach for constructing first-order projected algorithms for optimization problems with general set constraints, building upon their unconstrained counterparts. We show that these projected algorithms retain the same linear convergence rate bounds, when the latter are obtained for the unconstrained algorithms via quadratic Lyapunov functions arising from integral quadratic constraint (IQC) characterizations. The projected algorithms are constructed by ap…

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Spin-dependent transport through edge states in 2D semi-Dirac materials with Rashba spin-orbit coupling and band inversion
Marta Garc\'ia-Olmos, Yuriko Baba, Alexander L\'opez, Mario Amado, Rafael A. Molina
https://arxiv.org/abs/2505.24745

Spin-dependent transport through edge states in 2D semi-Dirac materials with Rashba spin-orbit coupling and band inversion
We investigate the bulk-boundary correspondence in two-dimensional type-I semi-Dirac materials with band inversion and Rashba spin-orbit coupling. Employing a dimensional reduction framework, we identify the Zak phase along the quadratically dispersing direction as a topological invariant that captures the presence of edge states. In the non-trivial topological regime, systems with finite width exhibit energy-dependent edge states that are topologically protected only at specific momenta. At kx…

Instance Space Analysis for the Quadratic Assignment Problem
Jeffrey Christiansen (ARC Training Centre in Optimisation Technologies, Integrated Methodologies and Applications), Kate Smith-Miles (ARC Training Centre in Optimisation Technologies, Integrated Methodologies and Applications)
https://arxiv.org/abs/2506.20172

Instance Space Analysis for the Quadratic Assignment Problem
For any optimisation problem where diverse algorithmic approaches are available, the task of predicting algorithm performance and selecting the algorithm most likely to perform well on a given instance holds great practical interest. However, if our test instances do not adequately represent the potential problem space, we may be misled about the strengths and weaknesses of an algorithm. In this paper we consider algorithm prediction and selection for the Quadratic Assignment Problem (QAP). We …