Luis Rodrigues

Harishwar Reddy Kasireddy, Patricio S. La Rosa, Akshita Gupta et al.

Histopathology foundation models (HFMs), pretrained on large-scale cancer datasets, have advanced computational pathology. However, their applicability to non-cancerous chronic kidney disease remains underexplored, despite coexistence of renal pathology with malignancies such as renal cell and urothelial carcinoma. We systematically evaluate 11 publicly available HFMs across 11 kidney-specific downstream tasks spanning multiple stains (PAS, H&E, PASM, and IHC), spatial scales (tile and slide-level), task types (classification, regression, and copy detection), and clinical objectives, including detection, diagnosis, and prognosis. Tile-level performance is assessed using repeated stratified group cross-validation, while slide-level tasks are evaluated using repeated nested stratified cross-validation. Statistical significance is examined using Friedman test followed by pairwise Wilcoxon signed-rank testing with Holm-Bonferroni correction and compact letter display visualization. To promote reproducibility, we release an open-source Python package, kidney-hfm-eval, available at https://pypi.org/project/kidney-hfm-eval/ , that reproduces the evaluation pipelines. Results show moderate to strong performance on tasks driven by coarse meso-scale renal morphology, including diagnostic classification and detection of prominent structural alterations. In contrast, performance consistently declines for tasks requiring fine-grained microstructural discrimination, complex biological phenotypes, or slide-level prognostic inference, largely independent of stain type. Overall, current HFMs appear to encode predominantly static meso-scale representations and may have limited capacity to capture subtle renal pathology or prognosis-related signals. Our results highlight the need for kidney-specific, multi-stain, and multimodal foundation models to support clinically reliable decision-making in nephrology.

Francis Filbet, Luis Rodrigues

We propose a class of Particle-In-Cell (PIC) methods for the Vlasov-Poisson system with a strong and inhomogeneous external magnetic field with fixed direction, where we focus on the motion of particles in the plane orthogonal to the magnetic field (so-called poloidal directions). In this regime, the time step can be subject to stability constraints related to the smallness of Larmor radius and plasma frequency. To avoid this limitation, our approach is based on first and higher-order semi-implicit numerical schemes already validated on dissipative systems [3] and for homogeneous magnetic fields [10]. Thus, when the magnitude of the external magnetic field becomes large, this method provides a consistent PIC discretization of the guiding-center system taking into account variations of the magnetic field. We carry out some theoretical proofs and perform several numerical experiments that establish a solid validation of the method and its underlying concepts.

Luis Rodrigues, Sidney Givigi

This paper addresses the analysis and design of quadratic neural networks, which have been recently introduced in the literature, and their applications to regression, classification, system identification and control of dynamical systems. These networks offer several advantages, the most important of which are the fact that the architecture is a by-product of the design and is not determined a-priori, their training can be done by solving a convex optimization problem so that the global optimum of the weights is achieved, and the input-output mapping can be expressed analytically by a quadratic form. It also appears from several examples that these networks work extremely well using only a small fraction of the training data. The results in the paper cast regression, classification, system identification, stability and control design as convex optimization problems, which can be solved efficiently with polynomial-time algorithms to a global optimum. Several examples will show the effectiveness of quadratic neural networks in applications.

Lucas Souza e Silva, Luis Rodrigues

This paper formulates an optimal control framework for computing cruise airspeeds in predecessor-follower platoons of all-electric aircraft that balance operational cost and airspace complexity. To quantify controller workload and coordination effort, a novel pairwise dynamic workload (PDW) function is developed. Within this framework, the optimal airspeed solution is derived for all-electric aircraft under longitudinal wind disturbances. Moreover, an analytical suboptimal solution for heterogeneous platoons with nonlinear aircraft dynamics is determined, for which a general sufficient condition for string stability is formally established. The methodology is validated through case studies of all-electric aircraft operating in air corridors that are suitable for low-altitude advanced/urban air mobility (AAM/UAM) applications. Results show that the suboptimal solution closely approximates the optimal, while ensuring safe separations, maintaining string stability, and reducing operational cost and airspace complexity. These findings support the development of sustainable and more autonomous air traffic procedures that will enable the implementation of emerging air transportation technologies, such as AAM/UAM, and their integration to the air traffic system environment.

Steven Li, Luis Rodrigues

Electrified propulsion is expected to play an important role in the sustainable development of Advanced Air Mobility (AAM). However, the limited energy density of batteries motivates the need to minimize energy consumption during flight. This paper studies the minimum total energy problem for an all-electric aircraft in steady cruise flight. The problem is formulated as an optimal control problem in which the cruise airspeed and final cruise time are optimization variables. The battery supply voltage is modeled as an affine function of the battery charge. Pontryagin's Minimum Principle is used to derive the necessary and sufficient conditions for optimality, from which closed-form expressions for the optimal cruise airspeed and optimal final cruise time are obtained. Additional analytical conditions are derived that determine when all-electric operation is feasible, one of which is that sufficient electric charge must be available. Numerical simulations based on the BETA Technologies CX300 all-electric aircraft and a representative AAM scenario illustrate how the aircraft weight, cruising altitude, electrical system efficiency, and initial battery charge influence the optimal airspeed and the feasibility of all-electric cruise.

Zachary Yetman Van Egmond, Luis Rodrigues

This paper provides a least squares formulation for the training of a 2-layer convolutional neural network using quadratic activation functions, a 2-norm loss function, and no regularization term. Using this method, an analytic expression for the globally optimal weights is obtained alongside a quadratic input-output equation for the network. These properties make the network a viable tool in system theory by enabling further analysis, such as the sensitivity of the output to perturbations in the input, which is crucial for safety-critical systems such as aircraft or autonomous vehicles. The least squares method is compared to previously proposed strategies for training quadratic networks and to a back-propagation-trained ReLU network. The proposed method is applied to a system identification problem and a GPS position estimation problem. The least squares network is shown to have a significantly reduced training time with minimal compromises on prediction accuracy alongside the advantages of having an analytic input-output equation. Although these results only apply to 2-layer networks, this paper motivates the exploration of deeper quadratic networks in the context of system theory.