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Magnetic Resonance Imaging (MRI) is a powerful technique employed for non-invasive in vivo visualization of internal structures. Sparsity is often deployed to accelerate the signal acquisition or overcome the presence of motion artifacts, improving the quality of image reconstruction. Image reconstruction algorithms use TV-regularized LASSO (Total Variation-regularized LASSO) to retrieve the missing information of undersampled signals, by cleaning the data of noise and while optimizing sparsity. A tuning parameter moderates the balance between these two aspects; its choice affecting the quality of the reconstructions. Currently, there is a lack of general deterministic techniques to choose these parameters, which are oftentimes manually selected and thus hinder the reliability of the reconstructions. Here, we present ALMA (Algorithm for Lagrange Multipliers Approximation), an iterative mathematics-inspired technique that computes tuning parameters for generalized LASSO problems during MRI reconstruction. We analyze quantitatively the performance of these parameters for imaging reconstructions via TV-LASSO in an MRI context on phantoms. Although our study concentrates on TV-LASSO, the techniques developed here hold significant promise for a wide array of applications. ALMA is not only adaptable to more generalized LASSO problems but is also robust to accommodate other forms of regularization beyond total variation. Moreover, it extends effectively to handle non-Cartesian sampling trajectories, broadening its utility in complex data reconstruction scenarios. More generally, ALMA provides a powerful tool for numerically solving constrained optimization problems across various disciplines, offering a versatile and impactful solution for advanced computational challenges.

This research presents a comprehensive approach to predicting the duration of traffic incidents and classifying them as short-term or long-term across the Sydney Metropolitan Area. Leveraging a dataset that encompasses detailed records of traffic incidents, road network characteristics, and socio-economic indicators, we train and evaluate a variety of advanced machine learning models including Gradient Boosted Decision Trees (GBDT), Random Forest, LightGBM, and XGBoost. The models are assessed using Root Mean Square Error (RMSE) for regression tasks and F1 score for classification tasks. Our experimental results demonstrate that XGBoost and LightGBM outperform conventional models with XGBoost achieving the lowest RMSE of 33.7 for predicting incident duration and highest classification F1 score of 0.62 for a 30-minute duration threshold. For classification, the 30-minute threshold balances performance with 70.84\% short-term duration classification accuracy and 62.72\% long-term duration classification accuracy. Feature importance analysis, employing both tree split counts and SHAP values, identifies the number of affected lanes, traffic volume, and types of primary and secondary vehicles as the most influential features. The proposed methodology not only achieves high predictive accuracy but also provides stakeholders with vital insights into factors contributing to incident durations. These insights enable more informed decision-making for traffic management and response strategies. The code is available by the link: //github.com/Future-Mobility-Lab/SydneyIncidents

This paper presents a multivariate normal integral expression for the joint survival function of the cumulated components of any multinomial random vector. This result can be viewed as a multivariate analog of Equation (7) from Carter & Pollard (2004), who improved Tusn\'ady's inequality. Our findings are based on a crucial relationship between the joint survival function of the cumulated components of any multinomial random vector and the joint cumulative distribution function of a corresponding Dirichlet distribution. We offer two distinct proofs: the first expands the logarithm of the Dirichlet density, while the second employs Laplace's method applied to the Dirichlet integral.

We present and analyze a structure-preserving method for the approximation of solutions to nonlinear cross-diffusion systems, which combines a Local Discontinuous Galerkin spatial discretization with the backward Euler time stepping scheme. The proposed method makes use of the underlying entropy structure of the system, expressing the main unknown in terms of the entropy variable by means of a nonlinear transformation. Such a transformation allows for imposing the physical positivity or boundedness constraints on the approximate solution in a strong sense. Moreover, nonlinearities do not appear explicitly within differential operators or interface terms in the scheme, which significantly improves its efficiency and ease its implementation. We prove the existence of discrete solutions and their asymptotic convergence to continuous weak solutions. Numerical results for some one- and two-dimensional problems illustrate the accuracy and entropy stability of the proposed method.

Practical parameter identifiability in ODE-based epidemiological models is a known issue, yet one that merits further study. It is essentially ubiquitous due to noise and errors in real data. In this study, to avoid uncertainty stemming from data of unknown quality, simulated data with added noise are used to investigate practical identifiability in two distinct epidemiological models. Particular emphasis is placed on the role of initial conditions, which are assumed unknown, except those that are directly measured. Instead of just focusing on one method of estimation, we use and compare results from various broadly used methods, including maximum likelihood and Markov Chain Monte Carlo (MCMC) estimation. Among other findings, our analysis revealed that the MCMC estimator is overall more robust than the point estimators considered. Its estimates and predictions are improved when the initial conditions of certain compartments are fixed so that the model becomes globally identifiable. For the point estimators, whether fixing or fitting the that are not directly measured improves parameter estimates is model-dependent. Specifically, in the standard SEIR model, fixing the initial condition for the susceptible population S(0) improved parameter estimates, while this was not true when fixing the initial condition of the asymptomatic population in a more involved model. Our study corroborates the change in quality of parameter estimates upon usage of pre-peak or post-peak time-series under consideration. Finally, our examples suggest that in the presence of significantly noisy data, the value of structural identifiability is moot.

The choice of the shape parameter highly effects the behaviour of radial basis function (RBF) approximations, as it needs to be selected to balance between ill-condition of the interpolation matrix and high accuracy. In this paper, we demonstrate how to use neural networks to determine the shape parameters in RBFs. In particular, we construct a multilayer perceptron trained using an unsupervised learning strategy, and use it to predict shape parameters for inverse multiquadric and Gaussian kernels. We test the neural network approach in RBF interpolation tasks and in a RBF-finite difference method in one and two-space dimensions, demonstrating promising results.

Machine learning (ML) plays an important role in quantum chemistry, providing fast-to-evaluate predictive models for various properties of molecules. However, most existing ML models for molecular electronic properties use density functional theory (DFT) databases as ground truth in training, and their prediction accuracy cannot surpass that of DFT. In this work, we developed a unified ML method for electronic structures of organic molecules using the gold-standard CCSD(T) calculations as training data. Tested on hydrocarbon molecules, our model outperforms DFT with the widely-used hybrid and double hybrid functionals in computational costs and prediction accuracy of various quantum chemical properties. As case studies, we apply the model to aromatic compounds and semiconducting polymers on both ground state and excited state properties, demonstrating its accuracy and generalization capability to complex systems that are hard to calculate using CCSD(T)-level methods.

We consider the problem of analyzing multivariate time series collected on multiple subjects, with the goal of identifying groups of subjects exhibiting similar trends in their recorded measurements over time as well as time-varying groups of associated measurements. To this end, we propose a Bayesian model for temporal biclustering featuring nested partitions, where a time-invariant partition of subjects induces a time-varying partition of measurements. Our approach allows for data-driven determination of the number of subject and measurement clusters as well as estimation of the number and location of changepoints in measurement partitions. To efficiently perform model fitting and posterior estimation with Markov Chain Monte Carlo, we derive a blocked update of measurements' cluster-assignment sequences. We illustrate the performance of our model in two applications to functional magnetic resonance imaging data and to an electroencephalogram dataset. The results indicate that the proposed model can combine information from potentially many subjects to discover a set of interpretable, dynamic patterns. Experiments on simulated data compare the estimation performance of the proposed model against ground-truth values and other statistical methods, showing that it performs well at identifying ground-truth subject and measurement clusters even when no subject or time dependence is present.

We consider the problem of function approximation by two-layer neural nets with random weights that are "nearly Gaussian" in the sense of Kullback-Leibler divergence. Our setting is the mean-field limit, where the finite population of neurons in the hidden layer is replaced by a continuous ensemble. We show that the problem can be phrased as global minimization of a free energy functional on the space of (finite-length) paths over probability measures on the weights. This functional trades off the $L^2$ approximation risk of the terminal measure against the KL divergence of the path with respect to an isotropic Brownian motion prior. We characterize the unique global minimizer and examine the dynamics in the space of probability measures over weights that can achieve it. In particular, we show that the optimal path-space measure corresponds to the F\"ollmer drift, the solution to a McKean-Vlasov optimal control problem closely related to the classic Schr\"odinger bridge problem. While the F\"ollmer drift cannot in general be obtained in closed form, thus limiting its potential algorithmic utility, we illustrate the viability of the mean-field Langevin diffusion as a finite-time approximation under various conditions on entropic regularization. Specifically, we show that it closely tracks the F\"ollmer drift when the regularization is such that the minimizing density is log-concave.

Nowadays, the Convolutional Neural Networks (CNNs) have achieved impressive performance on many computer vision related tasks, such as object detection, image recognition, image retrieval, etc. These achievements benefit from the CNNs outstanding capability to learn the input features with deep layers of neuron structures and iterative training process. However, these learned features are hard to identify and interpret from a human vision perspective, causing a lack of understanding of the CNNs internal working mechanism. To improve the CNN interpretability, the CNN visualization is well utilized as a qualitative analysis method, which translates the internal features into visually perceptible patterns. And many CNN visualization works have been proposed in the literature to interpret the CNN in perspectives of network structure, operation, and semantic concept. In this paper, we expect to provide a comprehensive survey of several representative CNN visualization methods, including Activation Maximization, Network Inversion, Deconvolutional Neural Networks (DeconvNet), and Network Dissection based visualization. These methods are presented in terms of motivations, algorithms, and experiment results. Based on these visualization methods, we also discuss their practical applications to demonstrate the significance of the CNN interpretability in areas of network design, optimization, security enhancement, etc.