arXiv subjects

Mohammad-Reza Siadat

Publications and source records attributed to Mohammad-Reza Siadat.

3 recordsLinked to original sources

arXiv2026

The Tropical Moduli Space of Degree-3 Rational Maps

We study tropical rational functions on the tropical projective line with three zeros and three poles in the torus, counted with multiplicity, modulo target automorphisms. The principal divisor identifies their moduli space with unordered pairs of disjoint effective divisors of degree three. We classify its \(53\) cells and prove that it is six-dimensional with ten contractible connected components. Source--target automorphism groups are trivial or of order two, and reflection loci are defined by linear gap equations. Allowing common support and points at infinity gives a divisor-pair compactification. Over an algebraically closed non-Archimedean field with value group \(\mathbb{R}\), root--pole tropicalization is surjective from valuation-separated cubic rational functions modulo the target torus normalizer. Explicit counterexamples show that the valuation of the conjugacy invariant \(J^2/I^3\) does not descend to this tropical moduli space. Generic functions admit minimal six-unit shallow ReLU representations with three positive and three negative unit output weights.

math.AG↗

arXiv2026

Predicting Alzheimer's disease progression using rs-fMRI and a history-aware graph neural network

Alzheimer's disease (AD) is a neurodegenerative disorder that affects more than seven million people in the United States alone. AD currently has no cure, but there are ways to potentially slow its progression if caught early enough. In this study, we propose a graph neural network (GNN)-based model for predicting whether a subject will transition to a more severe stage of cognitive impairment at their next clinical visit. We consider three stages of cognitive impairment in order of severity: cognitively normal (CN), mild cognitive impairment (MCI), and AD. We use functional connectivity graphs derived from resting-state functional magnetic resonance imaging (rs-fMRI) scans of 303 subjects, each with a different number of visits. Our GNN-based model incorporates a recurrent neural network (RNN) block, enabling it to process data from the subject's entire visit history. It can also work with irregular time gaps between visits by incorporating visit distance information into our input features. Our model demonstrates robust predictive performance, even with missing visits in the subjects' visit histories. It achieves an accuracy of 82.9%, with an especially impressive accuracy of 68.8% on CN to MCI conversions - a task that poses a substantial challenge in the field. Our results highlight the effectiveness of rs-fMRI in predicting the onset of MCI or AD and, in conjunction with other modalities, could offer a viable method for enabling timely interventions to slow the progression of cognitive impairment.

cs.CV↗

arXiv2025

Transformer Model for Alzheimer's Disease Progression Prediction Using Longitudinal Visit Sequences

Alzheimer's disease (AD) is a neurodegenerative disorder with no known cure that affects tens of millions of people worldwide. Early detection of AD is critical for timely intervention to halt or slow the progression of the disease. In this study, we propose a Transformer model for predicting the stage of AD progression at a subject's next clinical visit using features from a sequence of visits extracted from the subject's visit history. We also rigorously compare our model to recurrent neural networks (RNNs) such as long short-term memory (LSTM), gated recurrent unit (GRU), and minimalRNN and assess their performances based on factors such as the length of prior visits and data imbalance. We test the importance of different feature categories and visit history, as well as compare the model to a newer Transformer-based model optimized for time series. Our model demonstrates strong predictive performance despite missing visits and missing features in available visits, particularly in identifying converter subjects -- individuals transitioning to more severe disease stages -- an area that has posed significant challenges in longitudinal prediction. The results highlight the model's potential in enhancing early diagnosis and patient outcomes.

cs.LG↗