Henrique Ennes

Raphaël Tinarrage, Henrique Ennes, Lucas Resck et al. · cambridge

Binding precedents (súmulas vinculantes) constitute a juridical instrument unique to the Brazilian legal system and whose objectives include the protection of the Federal Supreme Court against repetitive demands. Studies of the effectiveness of these instruments in decreasing the Court's exposure to similar cases, however, indicate that they tend to fail in such a direction, with some of the binding precedents seemingly creating new demands. We empirically assess the legal impact of five binding precedents, 11, 14, 17, 26, and 37, at the highest Court level through their effects on the legal subjects they address. This analysis is only possible through the comparison of the Court's ruling about the precedents' themes before they are created, which means that these decisions should be detected through techniques of Similar Case Retrieval, which we tackle from the angle of Case Classification. The contributions of this article are therefore twofold: on the mathematical side, we compare the use of different methods of Natural Language Processing -- TF-IDF, LSTM, Longformer, and regex -- for Case Classification, whereas on the legal side, we contrast the inefficiency of these binding precedents with a set of hypotheses that may justify their repeated usage. We observe that the TF-IDF models performed slightly better than LSTM and Longformer when compared through common metrics; however, the deep learning models were able to detect certain important legal events that TF-IDF missed. On the legal side, we argue that the reasons for binding precedents to fail in responding to repetitive demand are heterogeneous and case-dependent, making it impossible to single out a specific cause. We identify five main hypotheses, which are found in different combinations in each of the precedents studied.

Jui-Ting Lu, Henrique Ennes, Chih-Kang Huang et al.

Quantum brushes are computational arts software introduced by Ferreira et al (2025) that leverage quantum behavior to generate novel artistic effects. In this outreach paper, we introduce the mathematical framework and describe the implementation of two quantum brushes based on variational quantum algorithms, Steerable and Chemical. While Steerable uses quantum geometric control theory to merge two works of art, Chemical mimics variational eigensolvers for estimating molecular ground energies to evolve colors on an underlying canvas. The implementation of both brushes is available open-source at https://github.com/moth-quantum/QuantumBrush and is fully compatible with the original quantum brushes.

Henrique Ennes, Raphaël Tinarrage

We suggest a new algorithm to estimate representations of compact Lie groups from finite samples of their orbits. Different from other reported techniques, our method allows the retrieval of the precise representation type as a direct sum of irreducible representations. Moreover, the knowledge of the representation type permits the reconstruction of its orbit, which is useful for identifying the Lie group that generates the action, from a finite list of candidates. Our algorithm is general for any compact Lie group, but only instantiations for SO(2), T^d, SU(2), and SO(3) are considered. Theoretical guarantees of robustness in terms of Hausdorff and Wasserstein distances are derived. Our tools are drawn from geometric measure theory, computational geometry, and optimization on matrix manifolds. The algorithm is tested for synthetic data up to dimension 32, as well as real-life applications in image analysis, harmonic analysis, density estimation, equivariant neural networks, chemical conformational spaces, and classical mechanics systems, achieving very accurate results.