Tootfinder

Quadratic Embedding Constants of Cartesian Products and Joins of Graphs
Projesh Nath Choudhury, Raju Nandi
https://arxiv.org/abs/2508.10834 https://arxiv.o…

Quadratic Embedding Constants of Cartesian Products and Joins of Graphs
The quadratic embedding constant (QEC) of a finite, simple, connected graph originated from the classical work of Schoenberg [Ann. of Math., 1935] and [Trans. Amer. Math. Soc., 1938] on Euclidean distance geometry. In this article, we study the QEC of graphs in terms of two graph operations: the Cartesian product and the join of graphs. We derive a general formula for the QEC of the join of an arbitrary graph with a regular graph and with a complete multipartite graph. We then provide quadratic…

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…

Vanishing Metric Commutation Relation and Higher-derivative De Donder Gauge in Quadratic Gravity
Ichiro Oda
https://arxiv.org/abs/2507.10712 https://

Vanishing Metric Commutation Relation and Higher-derivative De Donder Gauge in Quadratic Gravity
We show that the equal-time commutation relations (ETCRs) among the time derivatives of the metric tensor identically vanish in the higher-derivative de Donder gauge as well as the conventional de Donder gauge (or harmonic gauge) for general coordinate invariance in the manifestly covariant canonical operator formalism of quadratic gravity. These ETCRs provide us with the vanishing four-dimensional commutation relation, which implies that the metric tensor behaves as if it were not a quantum op…

Natively Trainable Sparse Attention for Hierarchical Point Cloud Datasets
Nicolas Lapautre, Maria Marchenko, Carlos Miguel Pati\~no, Xin Zhou
https://arxiv.org/abs/2508.10758 ht…

Natively Trainable Sparse Attention for Hierarchical Point Cloud Datasets
Unlocking the potential of transformers on datasets of large physical systems depends on overcoming the quadratic scaling of the attention mechanism. This work explores combining the Erwin architecture with the Native Sparse Attention (NSA) mechanism to improve the efficiency and receptive field of transformer models for large-scale physical systems, addressing the challenge of quadratic attention complexity. We adapt the NSA mechanism for non-sequential data, implement the Erwin NSA model, and…

Composition laws of binary quadratic forms and isolations of quadratic forms
Jangwon Ju, Daejun Kim, Kyoungmin Kim, Mingyu Kim, Byeong-Kweon Oh
https://arxiv.org/abs/2508.07916 …

Composition laws of binary quadratic forms and isolations of quadratic forms
A positive definite and integral quadratic form $f$ is called irrecoverable if there is a quadratic form $F$ such that it represents all proper subforms of $f$, whereas it does not represent $f$ itself. In this case, $F$ is called an isolation of $f$. In this article, we prove that there does not exist a binary isolation of any unary quadratic form. We also prove that there does not exist a ternary isolation of any binary quadratic form. Furthermore, if the form class group of a primitive binar…

Rate of metastability of an iterative algorithm for quadratic optimization
Paulo Firmino
https://arxiv.org/abs/2506.11342 https://arx…

Rate of metastability of an iterative algorithm for quadratic optimization
In this paper, relying on methods from proof mining, we provide a quantitative analysis of a theorem due to Xu, stating that an iteration strongly converges to the solution of a well known quadratic optimization problem. Rates of metastability and some rates of asymptotic regularity were obtained. We get quadratic rates of asymptotic regularity for particular sequences.

FLARE: Agile Flights for Quadrotor Cable-Suspended Payload System via Reinforcement Learning
Dongcheng Cao, Jin Zhou, Xian Wang, Shuo Li
https://arxiv.org/abs/2508.09797 https:/…

FLARE: Agile Flights for Quadrotor Cable-Suspended Payload System via Reinforcement Learning
Agile flight for the quadrotor cable-suspended payload system is a formidable challenge due to its underactuated, highly nonlinear, and hybrid dynamics. Traditional optimization-based methods often struggle with high computational costs and the complexities of cable mode transitions, limiting their real-time applicability and maneuverability exploitation. In this letter, we present FLARE, a reinforcement learning (RL) framework that directly learns agile navigation policy from high-fidelity sim…

SuperADMM: Solving Quadratic Programs Faster with Dynamic Weighting ADMM
P. C. N. Verheijen, D. Goswami, M. Lazar
https://arxiv.org/abs/2506.11608 https://…

SuperADMM: Solving Quadratic Programs Faster with Dynamic Weighting ADMM
In this paper we develop an accelerated Alternating Direction Method of Multipliers (ADMM) algorithm for solving quadratic programs called superADMM. Unlike standard ADMM QP solvers, superADMM uses a novel dynamic weighting method that penalizes each constraint individually and performs weight updates at every ADMM iteration. We provide a numerical stability analysis, methods for parameter selection and infeasibility detection. The algorithm is implemented in c with efficient linear algebra pac…

Near optimal controls for partially observed stochastic linear quadratic problems
Jingrui Sun, Jiaqiang Wen, Jie Xiong, Wen Xu
https://arxiv.org/abs/2506.11778

Near optimal controls for partially observed stochastic linear quadratic problems
In this article, we consider a stochastic linear quadratic control problem with partial observation. A near optimal control in the weak formulation is characterized. The main features of this paper are the presence of the control in the diffusion term of the state equation, the circular dependence between the control process and the filtration generated by the observation, and the observation process contains an unbounded drift term. We address these difficulties by first restricting the contro…

Linear-quadratic stochastic nonzero-sum differential games between graphon teams
De-xuan Xu, Zhun Gou, Nan-jing Huang
https://arxiv.org/abs/2506.11468 http…

Linear-quadratic stochastic nonzero-sum differential games between graphon teams
We study a class of nonzero-sum stochastic differential games between two teams with agents in each team interacting through graphon aggregates. On the one hand, in each large population group, agents act together to optimize a common social cost function. On the other hand, these two groups compete with each other, forming a Nash game between two graphon teams. We note that the original problem can be equivalently formulated as an infinite-dimensional two-agent Nash game. Applying the dynamic …