Tootfinder

Relaxations of KKT Conditions do not Strengthen Finite RLT and SDP-RLT Bounds for Nonconvex Quadratic Programs
E. Alper Yildirim
https://arxiv.org/abs/2506.09892

Relaxations of KKT Conditions do not Strengthen Finite RLT and SDP-RLT Bounds for Nonconvex Quadratic Programs
We consider linear and semidefinite programming relaxations of nonconvex quadratic programs given by the reformulation-linearization technique (RLT relaxation), and the Shor relaxation combined with the RLT relaxation (SDP-RLT relaxation). By incorporating the first-order optimality conditions, a quadratic program can be formulated as an optimization problem with complementarity constraints. We investigate the effect of incorporating optimality conditions on the strength of the RLT and SDP-RLT …

Machine Learning-based quadratic closures for non-intrusive Reduced Order Models
Gabriele Codega, Anna Ivagnes, Nicola Demo, Gianluigi Rozza
https://arxiv.org/abs/2506.09830

Machine Learning-based quadratic closures for non-intrusive Reduced Order Models
In the present work, we introduce a data-driven approach to enhance the accuracy of non-intrusive Reduced Order Models (ROMs). In particular, we focus on ROMs built using Proper Orthogonal Decomposition (POD) in an under-resolved and marginally-resolved regime, i.e. when the number of modes employed is not enough to capture the system dynamics. We propose a method to re-introduce the contribution of neglected modes through a quadratic correction term, given by the action of a quadratic operator…

Maximal curves with respect to quadratic extensions over finite fields
Yves Aubry (IMATH, I2M, UTLN), Fabien Herbaut (UCA INSPE, UniCA, IMATH), Julien Monaldi (IMATH)
https://arxiv.org/abs/2506.08603

Maximal curves with respect to quadratic extensions over finite fields
We propose a detailed study of a canonical bound which relates the numbers of rational points of a curve over a finite field with that over its quadratic extension. Alternative proofs which relate to the variance enable to complete the inequality in a symmetrical way and to obtain optimal refinements. We focus on the curves reaching the bound, which we call Diophantinemaximal curves. We provide different characterizations and stress natural links with the curves which attain the Ihara bound. As…

Visible Brillouin-quadratic microlaser in a high-Q thin-film lithium niobate microdisk
Xiaochao Luo, Chuntao Li, Xingzhao Huang, Jintian Lin, Renhong Gao, Yifei Yao, Yingnuo Qiu, Yixuan Yang, Lei Wang, Huakang Yu, Ya Cheng
https://arxiv.org/abs/2506.08615

Visible Brillouin-quadratic microlaser in a high-Q thin-film lithium niobate microdisk
Narrow-linewidth lasers at short/visible wavelengths are crucial for quantum and atomic applications, such as atomic clocks, quantum computing, atomic and molecular spectroscopy, and quantum sensing. However, such lasers are often only accessible in bulky tabletop systems and remain scarce in integrated photonic platform. Here, we report an on-chip visible Brillouin-quadratic microlaser in a 117-um-diameter thin-film lithium niobate (TFLN) microdisk via dispersion engineering. Enabled by the ul…

Plug-and-Play Linear Attention for Pre-trained Image and Video Restoration Models
Srinivasan Kidambi, Pravin Nair
https://arxiv.org/abs/2506.08520 https://…

Plug-and-Play Linear Attention for Pre-trained Image and Video Restoration Models
Multi-head self-attention (MHSA) has become a core component in modern computer vision models. However, its quadratic complexity with respect to input length poses a significant computational bottleneck in real-time and resource constrained environments. We propose PnP-Nystra, a Nyström based linear approximation of self-attention, developed as a plug-and-play (PnP) module that can be integrated into the pre-trained image and video restoration models without retraining. As a drop-in replacemen…

This https://arxiv.org/abs/2504.01139 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hept…

Power Spectra in Double-Field Inflation Using Renormalization-Group Techniques
A perturbative strategy for inflation described by two-inflaton fields is developed using a mathematical analogy with the renormalization-group. Two small quantities, $α$ and $λ$, corresponding to standard slow-roll parameters are defined and systematic expansions of all inflationary quantities in terms of powers of $α$ and $λ$ are found. No other slow-roll parameters are needed. To illustrate this perturbative method in the multi-field context, we adopt a simple two-inflaton model with qua…

This https://arxiv.org/abs/2502.03415 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Cycles on abelian 2n-folds of Weil type from secant sheaves on abelian n-folds
A. Weil identified a 2-dimensional space of rational classes of Hodge type (n,n) in the middle cohomology of every 2n-dimensional abelian variety with a suitable complex multiplication by an imaginary quadratic number field. These abelian varieties are said to be of Weil type and these Hodge classes are known as Weil classes. We prove that the Weil classes are algebraic for all abelian sixfold of Weil type of discriminant -1, for all imaginary quadratic number fields. The algebraicity of the We…

This https://arxiv.org/abs/2303.17475 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csLG_…

Learning distributed representations with efficient SoftMax normalization
Learning distributed representations, or embeddings, that encode the relational similarity patterns among objects is a relevant task in machine learning. A popular method to learn the embedding matrices $X, Y$ is optimizing a loss function of the term ${\rm SoftMax}(XY^T)$. The complexity required to calculate this term, however, runs quadratically with the problem size, making it a computationally heavy solution. In this article, we propose a linear-time heuristic approximation to compute the …

An Efficient Augmented Lagrangian Method for Dynamic Optimal Transport on Surfaces Based on Second-Order Cone Programming
Liang Chen, Youyicun Lin, Yuxuan Zhou
https://arxiv.org/abs/2506.08988

An Efficient Augmented Lagrangian Method for Dynamic Optimal Transport on Surfaces Based on Second-Order Cone Programming
This paper proposes an efficient numerical optimization approach for solving dynamic optimal transport (DOT) problems on general smooth surfaces, computing both the quadratic Wasserstein distance and the associated transportation path. Building on the convex DOT model of Benamou and Brenier, we first properly reformulate its dual problem, discretized on a triangular mesh for space together with a staggered grid for time, to a linear second-order cone programming. Then the resulting finite-dimen…

This https://arxiv.org/abs/2411.10121 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_sta…

Quadratic Form based Multiple Contrast Tests for Comparison of Group Means
Comparing the mean vectors across different groups is a cornerstone in the realm of multivariate statistics, with quadratic forms commonly serving as test statistics. However, when the overall hypothesis is rejected, identifying specific vector components or determining the groups among which differences exist requires additional investigations. Conversely, employing multiple contrast tests (MCT) allows conclusions about which components or groups contribute to these differences. However, they …