We study the optimal control of multiple-input and multiple-output dynamical systems via the design of neural network-based controllers with stability and output tracking guarantees. While neural network-based nonlinear controllers have shown superior performance in various applications, their lack of provable guarantees has restricted their adoption in high-stake real-world applications.

--Early and accurate assessment of brain microstruc-ture using diffusion Magnetic Resonance Imaging (dMRI) is crucial for identifying neurodevelopmental disorders in neonates, but remains challenging due to low signal-to-noise ratio (SNR), motion artifacts, and ongoing myelination. In this study, we propose a rotationally equivariant Spherical Convolutional Neural Network (sCNN) framework tailored for neonatal dMRI. We predict the Fiber Orientation Distribution (FOD) from multi-shell dMRI signals acquired with a reduced set of gradient directions (30% of the full protocol), enabling faster and more cost-effective acquisitions. We train and evaluate the performance of our sCNN using real data from 43 neonatal dMRI datasets provided by the Developing Human Connectome Project (dHCP). Our results demonstrate that the sCNN achieves significantly lower mean squared error (MSE) and higher angular correlation coefficient (ACC) compared to a Multi-Layer Perceptron (MLP) baseline, indicating improved accuracy in FOD estimation. Furthermore, tractography results based on the sCNN-predicted FODs show improved anatomical plausibility, coverage, and coherence compared to those from the MLP . These findings highlight that sCNNs, with their inherent rotational equivariance, offer a promising approach for accurate and clinically efficient dMRI analysis, paving the way for improved diagnostic capabilities and characterization of early brain development. Medical diagnostics is undergoing a transformative shift, fueled by the rapid advancements in artificial intelligence (AI) and deep learning.

Forest transitions, characterized by dynamic shifts between forest, agricultural, and abandoned lands, are complex phenomena. This study developed a stochastic differential equation model to capture the intricate dynamics of these transitions. We established the existence of global positive solutions for the model and conducted numerical analyses to assess the impact of model parameters on deforestation incentives. To address the challenge of parameter estimation, we proposed a novel deep learning approach that estimates all model parameters from a single sample containing time-series observations of forest and agricultural land proportions. This innovative approach enables us to understand forest transition dynamics and deforestation trends at any future time.

We study the optimal control of multiple-input and multiple-output dynamical systems via the design of neural network-based controllers with stability and output tracking guarantees. While neural network-based nonlinear controllers have shown superior performance in various applications, their lack of provable guarantees has restricted their adoption in high-stake real-world applications. Using equilibrium-independent passivity, a property present in a wide range of physical systems, we propose neural Proportional-Integral (PI) controllers that have provable guarantees of stability and zero steady-state output tracking error. The key structure is the strict monotonicity on proportional and integral terms, which is parameterized as gradients of strictly convex neural networks (SCNN). We construct SCNN with tunable softplus- \beta activations, which yields universal approximation capability and is also useful in incorporating communication constraints.

This work highlights the significance of equivariant networks as efficient and high-performance approaches for tomography applications. Our study builds upon the limitations of conventional Convolutional Neural Networks (CNNs), which have shown promise in post-processing various medical imaging systems. However, the efficiency of conventional CNNs heavily relies on an undiminished and proper training set. To tackle this issue, in this study, we introduce an equivariant network, aiming to reduce CNN's dependency on specific training sets. We evaluate the efficacy of equivariant spherical CNNs (SCNNs) for 2- and 3- dimensional medical imaging problems. Our results demonstrate superior quality and computational efficiency of SCNNs in denoising and reconstructing benchmark problems. Furthermore, we propose a novel approach to employ SCNNs as a complement to conventional image reconstruction tools, enhancing the outcomes while reducing reliance on the training set. Across all cases, we observe a significant decrease in computational costs while maintaining the same or higher quality of image processing using SCNNs compared to CNNs. Additionally, we explore the potential of this network for broader tomography applications, particularly those requiring omnidirectional representation.

Suppose you have a thousand-page book, but each page has only a single line of text. You're supposed to extract the information contained in the book using a scanner, only this particular scanner systematically goes through each and every page, scanning one square inch at a time. It would take you a long time to get through the whole book with that scanner, and most of that time would be wasted scanning empty space. Original story reprinted with permission from Quanta Magazine, an editorially independent publication of the Simons Foundation whose mission is to enhance public understanding of science by covering research developments and trends in mathematics and the physical and life sciences. Such is the life of many an experimental physicist.

Multivariate time-series (MTS) forecasting is a paramount and fundamental problem in many real-world applications. The core issue in MTS forecasting is how to effectively model complex spatial-temporal patterns. In this paper, we develop a modular and interpretable forecasting framework, which seeks to individually model each component of the spatial-temporal patterns. We name this framework SCNN, short for Structured Component-based Neural Network. SCNN works with a pre-defined generative process of MTS, which arithmetically characterizes the latent structure of the spatial-temporal patterns. In line with its reverse process, SCNN decouples MTS data into structured and heterogeneous components and then respectively extrapolates the evolution of these components, the dynamics of which is more traceable and predictable than the original MTS. Extensive experiments are conducted to demonstrate that SCNN can achieve superior performance over state-of-the-art models on three real-world datasets. Additionally, we examine SCNN with different configurations and perform in-depth analyses of the properties of SCNN.

Diffusion-weighted magnetic resonance imaging is sensitive to the microstructural properties of brain tissue. However, estimating clinically and scientifically relevant microstructural properties from the measured signals remains a highly challenging inverse problem that deep learning may help solve. This study investigated if recently developed orientationally invariant spherical convolutional neural networks can improve microstructural parameter estimation. A spherical convolutional neural network was trained to predict the ground-truth parameter values from simulated noisy data and applied to imaging data acquired in a clinical setting to generate microstructural parameter maps. The spherical convolutional neural network was more accurate and less orientationally variant than the benchmark methods (multi-layer perceptrons and the spherical mean technique). Our results show that spherical convolutional neural networks can be a compelling alternative to predicting parameters from powder-averaged data (i.e., data averaged over the acquired diffusion encoding directions). While we focused on constrained two- and three-compartment models of neuronal tissue, the presented network and training pipeline are generalizable and can be used to estimate the parameters of other Gaussian compartment models.

Currently there exists rather promising new trend in machine leaning (ML) based on the relationship between neural networks (NN) and Gaussian processes (GP), including many related subtopics, e.g., signal propagation in NNs, theoretical derivation of learning curve for NNs, QFT methods in ML, etc. An important feature of convolutional neural networks (CNN) is their equivariance (consistency) with respect to the symmetry transformations of the input data. In this work we establish a relationship between the many-channel limit for CNNs equivariant with respect to two-dimensional Euclidean group with vector-valued neuron activations and the corresponding independently introduced equivariant Gaussian processes (GP).

We have presented a Spiking Convolutional Neural Network (SCNN) that incorporates retinal foveal-pit inspired Difference of Gaussian filters and rank-order encoding. The model is trained using a variant of the backpropagation algorithm adapted to work with spiking neurons, as implemented in the Nengo library. We have evaluated the performance of our model on two publicly available datasets - one for digit recognition task, and the other for vehicle recognition task. The network has achieved up to 90% accuracy, where loss is calculated using the cross-entropy function. This is an improvement over around 57% accuracy obtained with the alternate approach of performing the classification without any kind of neural filtering. Overall, our proof-of-concept study indicates that introducing biologically plausible filtering in existing SCNN architecture will work well with noisy input images such as those in our vehicle recognition task. Based on our results, we plan to enhance our SCNN by integrating lateral inhibition-based redundancy reduction prior to rank-ordering, which will further improve the classification accuracy by the network.