Angle-encoded quantum kernels on tabular data collapse when the feature map is wider than the intrinsic dimension of the data. We propose the correlation fractal dimension D2 as an a priori qubit budget: encode D2 coordinates chosen by FD-ASE instead of the PCA-95% width or all E attributes. On nine data sets and a statevector simulator (n= 32), a one-layer ZZ fidelity kernel at q=D2 stays geometrically alive while the same kernel at the PCA-95% width has already collapsed. The budget is map-dependent: product-state and IQP maps overshoot it; a second ZZ layer undershoots it. Packed dense-angle and re-uploading encodings still live at the fractal q, but not when PCA-95% features are stacked onto those qubits. Shrinking the angle bandwidth moves the ZZ knee later; stretching it kills the kernel earlier. On IBM Quantum (ibm_fez, 256 shots, n=8) the one-layer ZZ kernel at the fractal width matches the exact kernel (MAE 0.021); past that width both hardware and simulator have collapsed. The ceiling is a property of the map-data pair at a stated bandwidth, not of the classical table alone.
Joao Batista Florindo, Amanda Pontes de Oliveira Ornelascs.CV
Biomedical image segmentation is a critical task in medical diagnosis and treatment planning, enabling precise delineation of anatomical structures and pathological regions. Despite significant advancements, challenges persist due to the inherent variability, noise, and complex morphology present in diverse medical imaging modalities. This paper introduces ConvNeXt-FD, a novel deep learning architecture for robust biomedical image segmentation, built upon a U-Net-like encoder-decoder framework leveraging the powerful ConvNeXt backbone. Our approach integrates a hybrid loss function combining the Dice coefficient with a boundary-aware regularization term inspired by a differentiable formulation of Fractal Dimension, designed to enhance the model's sensitivity to object boundaries and shape fidelity. We rigorously evaluate ConvNeXt-FD across six distinct biomedical datasets: BUSI (Breast Ultrasound Images), DDTI (Thyroid Ultrasound Images), FluoCells (Fluorescent Cell Images), IDRiD (Diabetic Retinopathy Images for Optic Disc Segmentation), ISIC2018 (Skin Lesion Images), and MoNuSeg (Nuclei Segmentation). Experimental results demonstrate that ConvNeXt-FD, particularly when initialized with ImageNet pre-trained weights, achieves competitive and often superior performance compared to existing state-of-the-art methods across various metrics, including Dice, Jaccard, Accuracy, Sensitivity, Specificity, and False Positive Rate. The integration of ConvNeXt as a strong encoder, coupled with the boundary-aware regularization, proves effective in capturing both high-level semantic features and fine-grained boundary details, leading to more accurate and reliable segmentations in challenging biomedical contexts.