Tootfinder

The Ramsey number of the 4-cycle versus a book graph
Chunyang Dou, Tianyu Li, Qizhong Lin, Xing Peng
https://arxiv.org/abs/2506.10477 https://

The Ramsey number of the 4-cycle versus a book graph
Given positive integers $n$ and $k$, the book graph $B_n^{(k)}$ consists of $n$ copies of $K_{k+1}$ sharing a common $K_k$. The book graph is a common generalization of a star and a clique, which can be seen by taking $k=1$ and $n=1$ respectively. In addition, the Ramsey number of a book graph is closely related to the diagonal Ramsey number. Thus the study of extremal problems related to the book graph is of substantial significance. In this paper, we aim to investigate the Ramsey number $r(C_…

NFL analyst suggests Cowboys trade All-Pro due $94 million to Falcons https://cowboyswire.usatoday.com/story/sports/nfl/cowboys/2025/06/05/nfl-analyst-suggest-cowboys-trade-daron-bland-to-falcons/…

On the sharp critical mass threshold for the 3D Patlak-Keller-Segel-Navier-Stokes system via Couette flow
Shikun Cui, Lili Wang, Wendong Wang, Juncheng Wei
https://arxiv.org/abs/2506.10578

On the sharp critical mass threshold for the 3D Patlak-Keller-Segel-Navier-Stokes system via Couette flow
As is well-known, the solution of the Patlak-Keller-Segel system in 3D may blow up in finite time regardless of any initial cell mass. In this paper, we are interested in the suppression of blow-up and the critical mass threshold for the 3D Patlak-Keller-Segel-Navier-Stokes system via the Couette flow $(Ay, 0, 0)$. It is proved that if the Couette flow is sufficiently strong ($A$ is large enough), then the solutions for the system are global in time in the periodic domain $(x,y,z)\in\mathbb{T}^…

Clustering of large deviations events in heavy-tailed moving average processes: the catastrophe principle in the short-memory case
Jiaqi Wang, Gennady Samorodnitsky
https://arxiv.org/abs/2506.10256

Clustering of large deviations events in heavy-tailed moving average processes: the catastrophe principle in the short-memory case
How do large deviation events in a stationary process cluster? The answer depends not only on the type of large deviations, but also on the length of memory in the process. Somewhat unexpectedly, it may also depend on the tails of the process. In this paper we work in the context of large deviations for partial sums in moving average processes with short memory and regularly varying tails. We show that the structure of the large deviation cluster in this case markedly differs from the correspon…

Toward Scalable Quantum Compilation for Modular Architecture: Qubit Mapping and Reuse via Deep Reinforcement Learning
Sokea Sang, Leanghok Hour, Youngsun Han
https://arxiv.org/abs/2506.09323

Toward Scalable Quantum Compilation for Modular Architecture: Qubit Mapping and Reuse via Deep Reinforcement Learning
Modular quantum architectures have emerged as a promising approach for scaling quantum computing systems by connecting multiple Quantum Processing Units (QPUs). However, this approach introduces significant challenges due to costly inter-core operations between chips and quantum state transfers, which contribute to noise and quantum decoherence. This paper presents QARMA, a novel Qubit mapping using Attention-based deep Reinforcement learning (DRL) for Modular quantum Architectures, along with …

Z3Guide: A Scalable, Student-Centered, and Extensible Educational Environment for Logic Modeling
Ruanqianqian Huang, Ayana Monroe, Peli de Halleux, Sorin Lerner, Nikolaj Bj{\o}rner
https://arxiv.org/abs/2506.08294

Z3Guide: A Scalable, Student-Centered, and Extensible Educational Environment for Logic Modeling
Constraint-satisfaction problems (CSPs) are ubiquitous, ranging from budgeting for grocery shopping to verifying software behavior. Logic modeling helps solve CSPs programmatically using SMT solvers. Despite its importance in many Computer Science disciplines, resources for teaching and learning logic modeling are scarce and scattered, and challenges remain in designing educational environments for logic modeling that are accessible and meet the needs of teachers and students. This paper explor…

Towards Data-Driven Model-Free Safety-Critical Control
Zhe Shen, Yitaek Kim, Christoffer Sloth
https://arxiv.org/abs/2506.06931 https://

Towards Data-Driven Model-Free Safety-Critical Control
This paper presents a framework for enabling safe velocity control of general robotic systems using data-driven model-free Control Barrier Functions (CBFs). Model-free CBFs rely on an exponentially stable velocity controller and a design parameter (e.g. alpha in CBFs); this design parameter depends on the exponential decay rate of the controller. However, in practice, the decay rate is often unavailable, making it non-trivial to use model-free CBFs, as it requires manual tuning for alpha. To ad…

Recurrence relations and the Christoffel-Darboux formula for elliptic orthogonal polynomials
Harini Desiraju, Sampad Lahiry
https://arxiv.org/abs/2506.09582

Recurrence relations and the Christoffel-Darboux formula for elliptic orthogonal polynomials
In recent years, there has been significant progress in the theory of orthogonal polynomials on algebraic curves, particularly on genus 1 surfaces. In this paper, we focus on elliptic orthogonal polynomials and establish several of their fundamental properties. In particular, we derive general five-term and seven-term recurrence relations, which lead to a Christoffel-Darboux formula and the construction of an associated point process on the A-cycle of the torus. Notably, the recurrence coeffici…

This https://arxiv.org/abs/2506.05047 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csLG_…

Reliably detecting model failures in deployment without labels
The distribution of data changes over time; models operating operating in dynamic environments need retraining. But knowing when to retrain, without access to labels, is an open challenge since some, but not all shifts degrade model performance. This paper formalizes and addresses the problem of post-deployment deterioration (PDD) monitoring. We propose D3M, a practical and efficient monitoring algorithm based on the disagreement of predictive models, achieving low false positive rates under no…

Global well-posedness for the 1D cubic nonlinear Shcr\"odinger equation in $L^p,\,p>2$
Ryosuke Hyakuna
https://arxiv.org/abs/2506.08554 https://

Global well-posedness for the 1D cubic nonlinear Shcrödinger equation in $L^p,\,p>2$
In this paper, we show that the one dimensional cubic nonlinear Schrödinger equation is globally well posed in $L^p$ for $2\le p <13/6$. In particular, we prove that the global solution enjoys the persistence property for a twisted variable at any time, which implies the result is a natural exetension of the classical global well-posedness in $L^2$ to $L^p$. The proof exploits the data-decomposition argument originally developed by Vargas-Vega in the functional framework introduced by Zhou.