Brionne

Summary
This paper presents a deep learning-based approach for lesion segmentation in moderate to severe traumatic brain injury (msTBI) using the nnU-Net framework with an adaptive normalization strategy. The method focuses on reducing inter-subject variability by confining intensity normalization to the brain parenchyma, and it achieves competitive performance on the AIMS-TBI 2025 Challenge leaderboard.

Mathematical/empirical assessment
The paper introduces a normalization strategy that computes mean and standard deviation within the brain mask, as defined in Eq. (1) and Eq. (2). The results show a high non-lesion Dice score (0.9324), indicating strong specificity, while the lesion Dice (0.4805) reflects the difficulty of detecting heterogeneous lesions. The combination of adaptive normalization and data augmentation improves overall performance, as shown in Table 1.

Strengths
The paper clearly outlines a novel preprocessing strategy that addresses key challenges in msTBI segmentation. The use of a well-established nnU-Net architecture, combined with extensive data augmentation, demonstrates practical effectiveness. The results are well-documented, and the method is directly applicable to multi-site MRI data.

Concerns
The paper does not provide detailed analysis of how the adaptive normalization affects different lesion types or sizes. While the overall performance is strong, the lesion Dice score suggests room for improvement in detecting smaller or more diffuse lesions. Additionally, the paper lacks a thorough discussion of potential limitations or failure cases.

Final decision
Weak accept

Summary:
The paper addresses the construction of infinite families of $D(z)$-quadruples in the ring $\mathbb{Z}[\sqrt{-2}]$ for specific exceptional congruence classes. The authors build upon previous work by introducing a new method that combines regular extension techniques with fixing a divisor $e \mid 3z$ and a small element $v$. They show that every exceptional class contains infinitely many values of $z$ admitting a twice semi-regular $D(z)$-quadruple, which contains two regular $D(z)$-triples.

Mathematical/empirical assessment:
The paper presents explicit constructions for each of the remaining exceptional congruence classes. The approach involves solving equations such as $uv + z = r^2$ and using these to derive conditions for the existence of $D(z)$-quadruples. The authors also provide computational evidence and analyze specific cases where the regular construction fails, demonstrating the limitations of their method.

Strengths:
The paper provides a comprehensive treatment of the problem, offering explicit constructions for all previously unsolved congruence classes. The use of both theoretical and computational methods strengthens the validity of the results. The paper also includes detailed analysis of specific cases and discusses the limitations of the regular construction approach.

Concerns:
While the paper successfully constructs infinite families of $D(z)$-quadruples, it acknowledges that some individual values within the exceptional classes do not yield solutions via the regular construction. The authors note that further research is needed to determine whether these values admit $D(z)$-quadruples through alternative methods.

Final decision: Strong accept