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We propose a method to enhance the stability of a neural ordinary differential equation (neural ODE) by means of a control over the Lipschitz constant $C$ of its flow. Since it is known that $C$ depends on the logarithmic norm of the Jacobian matrix associated with the neural ODE, we tune this parameter at our convenience by suitably perturbing the Jacobian matrix with a perturbation as small as possible in Frobenius norm. We do so by introducing an optimization problem for which we propose a nested two-level algorithm. For a given perturbation size, the inner level computes the optimal perturbation with a fixed Frobenius norm, while the outer level tunes the perturbation amplitude. We embed the proposed algorithm in the training of the neural ODE to improve its stability. Numerical experiments on the MNIST and FashionMNIST datasets show that an image classifier including a neural ODE in its architecture trained according to our strategy is more stable than the same classifier trained in the classical way, and therefore, it is more robust and less vulnerable to adversarial attacks., Comment: 22 pages, 3 figures, 2 tables

Precision agriculture relies heavily on effective weed management to ensure robust crop yields. This study presents RoWeeder, an innovative framework for unsupervised weed mapping that combines crop-row detection with a noise-resilient deep learning model. By leveraging crop-row information to create a pseudo-ground truth, our method trains a lightweight deep learning model capable of distinguishing between crops and weeds, even in the presence of noisy data. Evaluated on the WeedMap dataset, RoWeeder achieves an F1 score of 75.3, outperforming several baselines. Comprehensive ablation studies further validated the model's performance. By integrating RoWeeder with drone technology, farmers can conduct real-time aerial surveys, enabling precise weed management across large fields. The code is available at: \url{https://github.com/pasqualedem/RoWeeder}., Comment: Computer Vision for Plant Phenotyping and Agriculture (CVPPA) workshop at ECCV 2024

We present Label Anything, an innovative neural network architecture designed for few-shot semantic segmentation (FSS) that demonstrates remarkable generalizability across multiple classes with minimal examples required per class. Diverging from traditional FSS methods that predominantly rely on masks for annotating support images, Label Anything introduces varied visual prompts -- points, bounding boxes, and masks -- thereby enhancing the framework's versatility and adaptability. Unique to our approach, Label Anything is engineered for end-to-end training across multi-class FSS scenarios, efficiently learning from diverse support set configurations without retraining. This approach enables a "universal" application to various FSS challenges, ranging from $1$-way $1$-shot to complex $N$-way $K$-shot configurations while remaining agnostic to the specific number of class examples. This innovative training strategy reduces computational requirements and substantially improves the model's adaptability and generalization across diverse segmentation tasks. Our comprehensive experimental validation, particularly achieving state-of-the-art results on the COCO-$20^i$ benchmark, underscores Label Anything's robust generalization and flexibility. The source code is publicly available at: https://github.com/pasqualedem/LabelAnything.

A photonic integrated circuit (PIC) for the coherent combination of 32 input optical signals into a single output fiber is reported. The PIC was fabricated using a low-loss thick silicon-on-insulator (SOI) process and packaged with 32 input and 1 output fibers. The basic building block is a 2x2 Mach-Zehnder interferometer (MZI) with an external (to the MZI branches) and an internal thermal phase shifter, and a bandwidth in excess of 80 kHz. The PIC monolithically integrates 31 MZIs and 31 germanium photodetectors, and is suitable in principle for turbulence mitigation in LEO-ground and horizontal free space optics links. Improvements to the device for the coherent combination of 64 inputs and for the reduction of insertion losses are also discussed

We propose a novel methodology to solve a key eigenvalue optimization problem which arises in the contractivity analysis of neural ODEs. When looking at contractivity properties of a one layer weight-tied neural ODE $\dot{u}(t)=\sigma(Au(t)+b)$ (with $u,b \in {\mathbb R}^n$, $A$ is a given $n \times n$ matrix, $\sigma : {\mathbb R} \to {\mathbb R}$ denotes an activation function and for a vector $z \in {\mathbb R}^n$, $\sigma(z) \in {\mathbb R}^n$ has to be interpreted entry-wise), we are led to study the logarithmic norm of a set of products of type $D A$, where $D$ is a diagonal matrix such that ${\mathrm{diag}}(D) \in \sigma'({\mathbb R}^n)$. Specifically, given a real number $c$ (usually $c=0$), the problem consists in finding the largest positive interval $\text{I}\subseteq \mathbb [0,\infty)$ such that the logarithmic norm $\mu(DA) \le c$ for all diagonal matrices $D$ with $D_{ii}\in \text{I}$. We propose a two-level nested methodology: an inner level where, for a given $\text{I}$, we compute an optimizer $D^\star(\text{I})$ by a gradient system approach, and an outer level where we tune $\text{I}$ so that the value $c$ is reached by $\mu(D^\star(\text{I})A)$. We extend the proposed two-level approach to the general multilayer, and possibly time-dependent, case $\dot{u}(t) = \sigma( A_k(t) \ldots \sigma ( A_{1}(t) u(t) + b_{1}(t) ) \ldots + b_{k}(t) )$ and we propose several numerical examples to illustrate its behaviour, including its stabilizing performance on a one-layer neural ODE applied to the classification of the MNIST handwritten digits dataset., Comment: 26 pages, 6 figures, 4 tables

Lesion segmentation is a crucial step of the radiomic workflow. Manual segmentation requires long execution time and is prone to variability, impairing the realisation of radiomic studies and their robustness. In this study, a deep-learning automatic segmentation method was applied on computed tomography images of non-small-cell lung cancer patients. The use of manual vs automatic segmentation in the performance of survival radiomic models was assessed, as well. METHODS A total of 899 NSCLC patients were included (2 proprietary: A and B, 1 public datasets: C). Automatic segmentation of lung lesions was performed by training a previously developed architecture, the nnU-Net, including 2D, 3D and cascade approaches. The quality of automatic segmentation was evaluated with DICE coefficient, considering manual contours as reference. The impact of automatic segmentation on the performance of a radiomic model for patient survival was explored by extracting radiomic hand-crafted and deep-learning features from manual and automatic contours of dataset A, and feeding different machine learning algorithms to classify survival above/below median. Models' accuracies were assessed and compared. RESULTS The best agreement between automatic and manual contours with DICE=0.78 +(0.12) was achieved by averaging predictions from 2D and 3D models, and applying a post-processing technique to extract the maximum connected component. No statistical differences were observed in the performances of survival models when using manual or automatic contours, hand-crafted, or deep features. The best classifier showed an accuracy between 0.65 and 0.78. CONCLUSION The promising role of nnU-Net for automatic segmentation of lung lesions was confirmed, dramatically reducing the time-consuming physicians' workload without impairing the accuracy of survival predictive models based on radiomics.

We present a novel framework inspired by the Immersed Boundary Method for predicting the fluid-structure interaction of complex structures immersed in flows with moderate to high Reynolds numbers. The main novelties of the proposed fluid-structure interaction framework are 1) the use of elastodynamics equations for the structure, 2) the use of a high-order Navier-Stokes solver for the flow, and 3) the variational transfer (L2-projection) for coupling the solid and fluid subproblems. The dynamic behavior of a deformable structure is simulated in a finite element framework by adopting a fully implicit scheme for its temporal integration. It allows for mechanical constitutive laws including nonhomogeneous and fiber-reinforced materials. The Navier-Stokes equations for the incompressible flow are discretized with high-order finite differences which allow for the direct numerical simulation of laminar, transitional and turbulent flows. The structure and the flow solvers are coupled by using an L2-projection method for the transfer of velocities and forces between the fluid grid and the solid mesh. This strategy allows for the numerical solution of coupled large scale problems based on nonconforming structured and unstructured grids. The framework is validated with the Turek-Hron benchmark and a newly proposed benchmark modelling the flow-induced oscillation of an inert plate. A three-dimensional simulation of an elastic beam in transitional flow is provided to show the solver's capability of coping with anisotropic elastic structures immersed in complex fluid flow., Comment: submitted Journal of Computational Physics (28th February 2018)