arXiv subjects

Shahrzad Jamshidi

Publications and source records attributed to Shahrzad Jamshidi.

6 recordsLinked to original sources

arXiv2026

College closures from 2020 to 2025: An exploratory analysis and its implications for the enrollment cliff

The COVID-19 pandemic produced a modest wave of college closures and mergers that may offer an early, if imperfect, preview of the demographic "enrollment cliff" anticipated in the coming decade. This paper examines the institutions that closed or merged between 2020 and the end of 2025. We assemble a dataset of 65 such institutions, pairing institutional characteristics with state- and regional-level demographic, economic, and financial indicators, and supplement it with a corpus of news coverage of the closures. Using a combination of Bayesian models, dimensionality reduction, clustering, and topic modeling, we describe where these closures occurred, what the closed institutions had in common, and how they were discussed publicly. Consistent with prior demographic projections, closures were more frequent in the Northeast and Midwest, though the absolute numbers remain small. The closed institutions were heterogeneous rather than uniform: financial structure, regional demographics, and institutional mission each contributed to distinguishing them, and religious affiliation recurred prominently in media coverage. We frame these results as exploratory and descriptive given the small sample, and we discuss what they may, and may not, imply for institutions navigating the enrollment cliff.

stat.AP↗

arXiv2026

Algebraic Expressivity Certificates for Shallow Polynomial Neural Networks

We study exact representability by bias-free shallow polynomial neural networks using algebraic geometry. Over $\mathbb{C}$, a width-$r$ network with activation $z\mapsto z^d$ computes a sum of $r$ $d$-th powers of linear forms, whose Zariski closure is a Veronese secant variety. Ideal elimination therefore yields polynomial certificates of nonrepresentability. We implement this construction as a generic architecture-to-certificate pipeline. For quadratics, we recover the exact symmetric determinantal description and explain its dimension through orthogonal symmetry. In higher degree, the implementation recovers classical catalecticant and secant equations and maps the practical reach of direct elimination across a finite architecture sweep. We also derive the exact population loss floor for a rank-two quadratic network on the sphere, illustrating how an algebraic obstruction induces irreducible approximation error.

math.AC↗

arXiv2025

Predicting the cardinality and maximum degree of a reduced Gröbner basis

We construct neural network regression models to predict key metrics of complexity for Gröbner bases of binomial ideals. This work illustrates why predictions with neural networks from Gröbner computations are not a straightforward process. Using two probabilistic models for random binomial ideals, we generate and make available a large data set that is able to capture sufficient variability in Gröbner complexity. We use this data to train neural networks and predict the cardinality of a reduced Gröbner basis and the maximum total degree of its elements. While the cardinality prediction problem is unlike classical problems tackled by machine learning, our simulations show that neural networks, providing performance statistics such as $r^2 = 0.401$, outperform naive guess or multiple regression models with $r^2 = 0.180$.

math.AC↗

arXiv2025

A Brain Age Residual Biomarker (BARB): Leveraging MRI-Based Models to Detect Latent Health Conditions in U.S. Veterans

Age prediction using brain imaging, such as MRIs, has achieved promising results, with several studies identifying the model's residual as a potential biomarker for chronic disease states. In this study, we developed a brain age predictive model using a dataset of 1,220 U.S. veterans (18--80 years) and convolutional neural networks (CNNs) trained on two-dimensional slices of axial T2-weighted fast spin-echo and T2-weighted fluid attenuated inversion recovery MRI images. The model, incorporating a degree-3 polynomial ensemble, achieved an $R^{2}$ of 0.816 on the testing set. Images were acquired at the level of the anterior commissure and the frontal horns of the lateral ventricles. Residual analysis was performed to assess its potential as a biomarker for five ICD-coded conditions: hypertension (HTN), diabetes mellitus (DM), mild traumatic brain injury (mTBI), illicit substance abuse/dependence (SAD), and alcohol abuse/dependence (AAD). Residuals grouped by the number of ICD-coded conditions demonstrated different trends that were statistically significant ($p = 0.002$), suggesting a relationship between disease states and predicted brain age. This association was particularly pronounced in patients over 49 years, where negative residuals (indicating advanced brain aging) correlated with the presence of multiple ICD codes. These findings support the potential of residuals as biomarkers for detecting latent health conditions.

cs.LG↗

arXiv2025

Letters, Colors, and Words: Constructing the Ideal Building Blocks Set

Define a building blocks set to be a collection of n cubes (each with six sides) where each side is assigned one letter and one color from a palette of m colors. We propose a novel problem of assigning letters and colors to each face so as to maximize the number of words one can spell from a chosen dataset that are either mono words, all letters have the same color, or rainbow words, all letters have unique colors. We explore this problem considering a chosen set of English words, up to six letters long, from a typical vocabulary of a US American 14 year old and explore the problem when n=6 and m=6, with the added restriction that each color appears exactly once on the cube. The problem is intractable, as the size of the solution space makes a brute force approach computationally infeasible. Therefore we aim to solve this problem using random search, simulated annealing, two distinct tree search approaches (greedy and best-first), and a genetic algorithm. To address this, we explore a range of optimization techniques: random search, simulated annealing, two distinct tree search methods (greedy and best-first), and a genetic algorithm. Additionally, we attempted to implement a reinforcement learning approach; however, the model failed to converge to viable solutions within the problem's constraints. Among these methods, the genetic algorithm delivered the best performance, achieving a total of 2846 mono and rainbow words.

cs.AI↗

arXiv2023

The Spark Randomizer: a learned randomized framework for computing Gröbner bases

We define a violator operator which captures the definition of a minimal Gröbner basis of an ideal. This construction places the problem of computing a Gröbner basis within the framework of violator spaces, introduced in 2008 by G{ä}rtner, Matou{š}ek, R{ü}st, and {Š}kovro{ň} in a different context. The key aspect which we use is their successful utilization of a Clarkson-style fast sampling algorithm from geometric optimization. Using the output of a machine learning algorithm, we combine the prediction of the size of a minimal Gröbner basis of an ideal with the Clarkson-style biased random sampling method to compute a Gröbner basis in expected runtime linear in the size of the violator space.

math.AC↗