Tootfinder

Legendre-Gauss-Lobatto Collocation Method for Optimal Control via Polynomial Approximations of Differential Equation Vector Fields
Gabriela Abadia-Doyle, William W. Hager, Anil V. Rao
https://arxiv.org/abs/2506.13938

Legendre-Gauss-Lobatto Collocation Method for Optimal Control via Polynomial Approximations of Differential Equation Vector Fields
A new method is described for solving optimal control problems using direct collocation at Legendre-Gauss-Lobatto points. The approach of this paper employs a polynomial approximation of the right-hand side vector field of the differential equations and leads to the following important outcomes. First, the first-order optimality conditions of the LGL integral form are derived, which lead to a full-rank transformed adjoint system and novel costate estimate. Next, a derivative-like form of the LG…

Special Cases of the Shafarevich Conjecture for Complete Intersections in Abelian Varieties
Frank Lu
https://arxiv.org/abs/2506.14935 https://

Special Cases of the Shafarevich Conjecture for Complete Intersections in Abelian Varieties
In this paper, we prove the Shafarevich conjecture for certain complete intersections of hypersurfaces in abelian varieties defined over a number field $K$ using the Lawrence-Venkatesh method. The main new inputs we need are computation of certain Euler characteristics of these complete intersections and a big monodromy statement for the variation of Hodge structure arising from the middle cohomology of a family of such complete intersections. Following \cite{ls25}, we prove the latter by relat…

Harnessing the "Reactive Falling Effect" for rehabilitation and performance boosting
Paul-Emmanuel Sornette, Didier Sornette
https://arxiv.org/abs/2506.13959

Harnessing the "Reactive Falling Effect" for rehabilitation and performance boosting
We present Logic Workout, a novel training method based on radical dynamic instability combining rolling, deformation and spring instability on small fitballs. By exploiting the "reactive falling effect", it re-engages innate balance mechanisms and forces real-time motor corrections, leading to better joint control, coordination, and movement precision. Preliminary results from a cohort of 18 participants show complete resolution of chronic pain, enhanced functional mobility, and surprising imp…

Navigating the growing field of research on AI for software testing -- the taxonomy for AI-augmented software testing and an ontology-driven literature survey
Ina K. Schieferdecker
https://arxiv.org/abs/2506.14640

Navigating the growing field of research on AI for software testing -- the taxonomy for AI-augmented software testing and an ontology-driven literature survey
In industry, software testing is the primary method to verify and validate the functionality, performance, security, usability, and so on, of software-based systems. Test automation has gained increasing attention in industry over the last decade, following decades of intense research into test automation and model-based testing. However, designing, developing, maintaining and evolving test automation is a considerable effort. Meanwhile, AI's breakthroughs in many engineering fields are opening…

Newton optimization for the Multiconfiguration Self Consistent Field method at the basis set limit: closed-shell two-electron systems
Evgueni Dinvay, Rasmus Vikhamar-Sandberg, Luca Frediani
https://arxiv.org/abs/2506.12906

Newton optimization for the Multiconfiguration Self Consistent Field method at the basis set limit: closed-shell two-electron systems
The multiconfiguration self-consistent-field (MCSCF) method is revisited with the specific focus on the two electron systems for simplicity. A wave function is represented as a linear combination of Slater determinants. Both orbitals and coefficients of this configuration interaction expansion are optimized following the variational principle making use of the Newton optimization technique. It reduces the MCSCF problem to solving a particular differential Newton system, which can be discretized…

VerIF: Verification Engineering for Reinforcement Learning in Instruction Following
Hao Peng, Yunjia Qi, Xiaozhi Wang, Bin Xu, Lei Hou, Juanzi Li
https://arxiv.org/abs/2506.09942 …

VerIF: Verification Engineering for Reinforcement Learning in Instruction Following
Reinforcement learning with verifiable rewards (RLVR) has become a key technique for enhancing large language models (LLMs), with verification engineering playing a central role. However, best practices for RL in instruction following remain underexplored. In this work, we explore the verification challenge in RL for instruction following and propose VerIF, a verification method that combines rule-based code verification with LLM-based verification from a large reasoning model (e.g., QwQ-32B). …

Scenarios in Computing Research: A Systematic Review of the Use of Scenario Methods for Exploring the Future of Computing Technologies in Society
Julia Barnett, Kimon Kieslich, Jasmine Sinchai, Nicholas Diakopoulos
https://arxiv.org/abs/2506.05605

Scenarios in Computing Research: A Systematic Review of the Use of Scenario Methods for Exploring the Future of Computing Technologies in Society
Scenario building is an established method to anticipate the future of emerging technologies. Its primary goal is to use narratives to map future trajectories of technology development and sociotechnical adoption. Following this process, risks and benefits can be identified early on, and strategies can be developed that strive for desirable futures. In recent years, computer science has adopted this method and applied it to various technologies, including Artificial Intelligence (AI). Because c…

On Chaos in QFT
Jacob Sonnenschein, Nadav Shrayer
https://arxiv.org/abs/2506.10784 https://arxiv.org/pdf/2506.10784

On Chaos in QFT
In this note we explore the chaotic behavior of non-integrable QFTs and compare them to integrable ones. We choose as prototypes the double sine-Gordon and the sine-Gordon models. We analyze their discrete spectrum determined by a truncation method. We examine the map of the corresponding energy eigenvalues to the eigenvalues of the random matrix theory (RMT) Gaussian orthogonal ensemble (GOE). This is done by computing the following properties: (a) The distribution of the adjacent spacings and…

Rule-Assisted Attribute Embedding
Sibo Zhao, Michael Bewong, Selasi Kwashie, Junwei Hu, Zaiwen Feng
https://arxiv.org/abs/2506.08314 https://

Rule-Assisted Attribute Embedding
Recommendation systems often overlook the rich attribute information embedded in property graphs, limiting their effectiveness. Existing graph convolutional network (GCN) models either ignore attributes or rely on simplistic triples, failing to capture deeper semantic structures. We propose RAE (Rule- Assisted Approach for Attribute Embedding), a novel method that improves recommendations by mining semantic rules from property graphs to guide attribute embedding. RAE per…

This https://arxiv.org/abs/2505.20597 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hept…

LSZ ghostbusters in the quadratic gravity stage
The present letter considers the quantization method developed in [1]-[9], which postulates that, in several situations, negative norm or ghost states can be avoided in order to give positive probabilities. These authors also postulate a candidate for a path integral for those theories, following pioneer works initiated by Dirac [10]} and Pauli \[11]. However, taking into account the non standard oscillator algebra inherent to this method, in order to be sure that unitarity is not violated, one…