Vector autoregression (VAR) models are widely used for forecasting and macroeconomic analysis, yet they remain limited by their reliance on a linear parameterization. Recent research has introduced nonparametric alternatives, such as Bayesian additive regression trees (BART), which provide flexibility without strong parametric assumptions. However, existing BART-based frameworks do not account for time dependency or allow for sparse estimation in the construction of regression tree priors, leading to noisy and inefficient high-dimensional representations. This paper introduces a sparsity-inducing Dirichlet hyperprior on the regression tree's splitting probabilities, allowing for automatic variable selection and high-dimensional VARs. Additionally, we propose a structured shrinkage prior that decreases the probability of splitting on higher-order lags, aligning with the Minnesota prior's principles. Empirical results demonstrate that our approach improves predictive accuracy over the baseline BART prior and Bayesian VAR (BVAR), particularly in capturing time-dependent relationships and enhancing density forecasts. These findings highlight the potential of developing domain-specific
Many factors influence the yielding result of a driver-pedestrian interaction, including traffic volume, vehicle speed, roadway characteristics, etc. While individual aspects of these interactions have been explored, comprehensive, naturalistic studies, particularly those considering the built environment's influence on driver-yielding behavior, are lacking. To address this gap, our study introduces an extensive open-source dataset, compiled from video data at 18 unsignalized intersections across Minnesota. Documenting more than 3000 interactions, this dataset provides a detailed view of driver-pedestrian interactions and over 50 distinct contextual variables. The data, which covers individual driver-pedestrian interactions and contextual factors, is made publicly available at https://github.com/tianyi17/pedestrian_yielding_data_MN. Using logistic regression, we developed a classification model that predicts driver yielding based on the identified variables. Our analysis indicates that vehicle speed, the presence of parking lots, proximity to parks or schools, and the width of major road crossings significantly influence driver yielding at unsignalized intersections. Through our fi
Previous studies have found correlations between the implementation of transit signal priority (TSP) and the reduction in number of crashes. To further understand how TSP affects traffic safety, a more in-depth evaluation was carried out using detailed bus automatic vehicle location (AVL) data. The data was from Minneapolis-Saint Paul Metro Transit Bus Route 5, where TSP was implemented at 30 signalized intersections in early 2019. A surrogate safety measure, bus speed volatility (BSV), was used to estimate the safety effects of TSP, with a higher BSV indicating more safety risks. A regression analysis was carried out on 23,123 event-level observations, with event defined as a bus traversal of a TSP-equipped intersection. Results indicate that with a TSP request, BSV was significantly lower than without a TSP request, confirming the effectiveness of TSP in smoothing bus trips through intersections, thus reducing risks of bus collisions and passenger fall-overs.
In many applications, the dataset under investigation exhibits heterogeneous regimes that are more appropriately modeled using piece-wise linear models for each of the data segments separated by change-points. Although there have been much work on change point linear regression for the low dimensional case, high-dimensional change point regression is severely underdeveloped. Motivated by the analysis of Minnesota House Price Index data, we propose a fully Bayesian framework for fitting changing linear regression models in high-dimensional settings. Using segment-specific shrinkage and diffusion priors, we deliver full posterior inference for the change points and simultaneously obtain posterior probabilities of variable selection in each segment via an efficient Gibbs sampler. Additionally, our method can detect an unknown number of change points and accommodate different variable selection constraints like grouping or partial selection. We substantiate the accuracy of our method using simulation experiments for a wide range of scenarios. We apply our approach for a macro-economic analysis of Minnesota house price index data. The results strongly favor the change point model over a
In October 1924, the Physical Review, a relatively minor journal at the time, published a remarkable two-part paper by John H. Van Vleck, working in virtual isolation at the University of Minnesota. Van Vleck combined advanced techniques of classical mechanics with Bohr's correspondence principle and Einstein's quantum theory of radiation to find quantum analogues of classical expressions for the emission, absorption, and dispersion of radiation. For modern readers Van Vleck's paper is much easier to follow than the famous paper by Kramers and Heisenberg on dispersion theory, which covers similar terrain and is widely credited to have led directly to Heisenberg's "Umdeutung" paper. This makes Van Vleck's paper extremely valuable for the reconstruction of the genesis of matrix mechanics. It also makes it tempting to ask why Van Vleck did not take the next step and develop matrix mechanics himself.
Colon and rectum cancer share many risk factors, and are often tabulated together as ``colorectal cancer'' in published summaries. However, recent work indicating that exercise, diet, and family history may have differential impacts on the two cancers encourages analyzing them separately, so that corresponding public health interventions can be more efficiently targeted. We analyze colon and rectum cancer data from the Minnesota Cancer Surveillance System from 1998--2002 over the 16-county Twin Cities (Minneapolis--St. Paul) metro and exurban area. The data consist of two marked point patterns, meaning that any statistical model must account for randomness in the observed locations, and expected positive association between the two cancer patterns. Our model extends marked spatial point pattern analysis in the context of a log Gaussian Cox process to accommodate spatially referenced covariates (local poverty rate and location within the metro area), individual-level risk factors (patient age and cancer stage), and related interactions. We obtain smoothed maps of marginal log-relative intensity surfaces for colon and rectum cancer, and uncover significant age and stage differences b
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This is essentially the content of a talk at the workshop on Character Sheaves on Loop Groups at the University of Minnesota (June 8,2026). It describes the early days of the theory and also some recent developments.
The agricultural sector is undergoing a transformation with the integration of advanced technologies, particularly in data-driven decision-making. This work proposes a federated learning framework for smart farming, aiming to develop a scalable, efficient, and secure solution for crop disease detection tailored to the environmental and operational conditions of Minnesota farms. By maintaining sensitive farm data locally and enabling collaborative model updates, our proposed framework seeks to achieve high accuracy in crop disease classification without compromising data privacy. We outline a methodology involving data collection from Minnesota farms, application of local deep learning algorithms, transfer learning, and a central aggregation server for model refinement, aiming to achieve improved accuracy in disease detection, good generalization across agricultural scenarios, lower costs in communication and training time, and earlier identification and intervention against diseases in future implementations. We outline a methodology and anticipated outcomes, setting the stage for empirical validation in subsequent studies. This work comes in a context where more and more demand fo
An epidemic Susceptible-Vaccinated-Infected-Removed-Susceptible (SVIRS) model is presented on a weighted-undirected network with graph Laplacian diffusion. Disease-free equilibrium always exists while the existence and uniqueness of endemic equilibrium have been shown. When the basic reproduction number is below unity, the disease-free equilibrium is asymptotically globally stable. The endemic equilibrium is asymptotically globally stable if the basic reproduction number is above unity. Numerical analysis is illustrated with a road graph of the state of Minnesota. The effect of all important model parameters has been discussed.
Urban flooding triggered by intense rainfall is becoming increasingly frequent and widespread. While flood prediction and monitoring in high spatio-temporal resolution are desired, practical constraints in time, budget, and technology hinder its full implementation. How to monitor urban drainage networks and predict flow conditions under constrained resources is a major challenge. To address this, we introduced a data-driven sparse sensing (DSS) approach, demonstrated via a digital-twin of the Woodland catchment in Duluth, Minnesota. Specifically, we coupled EPA-SWMM with singular value decomposition and QR factorization-based sensor selection to optimize monitoring locations for system-level flow reconstruction. An ensemble of SWMM simulations, driven by diverse scenarios, provided the necessary hydraulic data to extract the reduced basis and identify informative sensor locations. Cross-event validation showed that three strategically placed sensors among 77 candidate nodes achieved a mean system-level Nash-Sutcliffe efficiency (NSE) of 0.949 across observed storm events. The QR-selected sensor sets were benchmarked against reference sensor configurations obtained from exhaustive
The recently introduced approach, combining the parameter-free Armiento-Kümmel generalized gradient approximation exchange functional with the nonseparable gradient approximation Minnesota correlation functional, was used to calculate the electronic structure of the Cs$_3$Bi$_2$Br$_{9-x}$I$_x$ series within density functional theory including the spin-orbit coupling. The changes in the band gap size and its dependence on the $x$ value was investigated. The band gap was found to be of indirect nature and it decreases with increasing I content as long as the system is in the $P\overline{3}m1$ phase. A clear non-linear dependence of the band gap size on $x$ was established which is in qualitative and quantitative agreement with reported experimental data. The quasi-rigid band behavior of the states in the valence and conduction bands of the $P\overline{3}m1$ phase is discussed since no significant changes in the shape of the total density of unoccupied states were observed upon the isovalent substitution.
We consider Bayesian tensor vector autoregressions (TVARs) in which the VAR coefficients are arranged as a three-dimensional array or tensor, and this coefficient tensor is parameterized using a low-rank CP decomposition. We develop a family of TVARs using a general stochastic volatility specification, which includes a wide variety of commonly-used multivariate stochastic volatility and COVID-19 outlier-augmented models. In a forecasting exercise involving 40 US quarterly variables, we show that these TVARs outperform the standard Bayesian VAR with the Minnesota prior. The results also suggest that the parsimonious common stochastic volatility model tends to forecast better than the more flexible Cholesky stochastic volatility model.
The first Edition of this book was released in 2000, just before the symposium ``Thirty Years of Supersymmetry'' was held at the William I. Fine Theoretical Physics Institute (FTPI) of the University of Minnesota. Founders and trailblazers of supersymmetry descended on FTPI, as well as a large crowd of younger theorists deeply involved in research in this area. Since then 23 years have elapsed and significant changes happened in supersymmetry (SUSY). Its history definitely needs an update. Such an update is presented below. The Second Edition of the revised collection will be released in 2024.
Conditional matrix variate student $t$ distribution was introduced by Battulga (2024a). In this paper, we propose a new version of the conditional matrix variate student $t$ distribution. The paper provides EM algorithms, which estimate parameters of the conditional matrix variate student $t$ distributions, including general cases and special cases with Minnesota prior.
The employment of the parameter-free Armiento-Kümmel generalized gradient approximation (AK13-GGA) exchange functional was examined as means of the band gap prediction for hybrid metal halide perovskites (HaPs) or systems with strong spin-orbit coupling in the full-relativistic density-functional-theory (DFT) calculations. The new combination of AK13 with the nonseparable gradient approximation Minnesota correlation functional (GAM) was established as an approach allowing for the efficient band gap estimation with accuracy similar to the GW approximation method but at the computational costs of conventional DFT. This was further supported by results of the AK13/GAM calculations performed for various HaPs. The described approach creates an opportunity for the effective assessment of the electronic structure of large, complex, doped or defective HaPs and modelling of new materials.
When COVID-19 first started spreading and quarantine was implemented, the Society for Industrial and Applied Mathematics (SIAM) Student Chapter at the University of Minnesota-Twin Cities began a collaboration with Ecolab to use our skills as data scientists and mathematicians to extract useful insights from relevant data relating to the pandemic. This collaboration consisted of multiple groups working on different projects. In this write-up we focus on using clustering techniques to help us find groups of similar counties in the US and use that to help us understand the pandemic. Our team for this project consisted of University of Minnesota students Cora Brown, Sarah Milstein, Tianyi Sun, and Cooper Zhao, with help from Ecolab Data Scientist Jimmy Broomfield and University of Minnesota student Skye Ke. In the sections below we describe all of the work done for this project. In Section 2, we list the data we gathered, as well as the feature engineering we performed. In Section 3, we describe the metrics we used for evaluating our models. In Section 4, we explain the methods we used for interpreting the results of our various clustering approaches. In Section 5, we describe the diff
The purpose of this research is to identify correlates of bike station activity for Nice Ride Minnesota, a bike share system in Minneapolis - St. Paul Metropolitan Area in Minnesota. We obtained the number of trips to and from each of the 116 bike share stations operating in 2011 from Nice Ride Minnesota. Data for independent variables included in models come from a variety of sources; including the 2010 US Census, the Metropolitan Council, a regional planning agency, and the cities of Minneapolis and St. Paul. We use log-linear and negative binomial regression models to evaluate the marginal effects of these factors on average daily station trips. Our models have high goodness of fit, and each of 13 independent variables is significant at the 10% level or higher. The number of trips at Nice Ride stations is associated with neighborhood socio demographics (i.e., age and race), proximity to the central business district, proximity to water, accessibility to trails, distance to other bike share stations, and measures of economic activity. Analysts can use these results to optimize bike share operations, locate new stations, and evaluate the potential of new bike share programs.
These are lecture notes compiled for a short lecture series at the 2023 Condensed Matter Summer School at the University of Minnesota. They are designed to be conversational and fun, and not to take the place of review articles that do a serious job of stating things precisely and citing literature thoroughly. The goal of the notes is to introduce some central ideas underlying the study of entanglement dynamics in random unitary circuits and the measurement-induced entanglement phase transition. A particular focus is the concept of the "minimal cut" and its associated stat mech mappings.