arXiv subjects

Vasileios Maroulas

Publications and source records attributed to Vasileios Maroulas.

At least 19 recordsLinked to original sources

arXiv2026

Topological Fingerprints of Commensurate Order in Twisted Moiré Lattices

Moiré patterns in twisted bilayer materials exhibit long-range periodic order that is highly sensitive to twist angle. Identifying commensurate angles from real-space atomic structures remains challenging, as spectral and geometric methods emphasize global periodicity and are sensitive to disorder and finite-size effects. Here, we introduce a data-driven topological framework that quantifies moiré periodicity by treating atomic configurations as point-cloud data and extracting multiscale signatures using persistent homology. At the core of our approach is a small-neighborhood separation filter that removes redundant local motifs in persistence diagrams while preserving key structural features, enabling sharp minima in Wasserstein distances between twisted and untwisted reference configurations that accurately recover commensurate angles. We benchmark this framework against geometric and spectral similarity measures and show that the resulting topological descriptors remain stable under positional disorder ranging from weak to strong perturbations in the bond length. We further transfer these descriptors using a constrained Gaussian process surrogate to sparsely sampled configurations of a twisted MoTe$_2$ dichalcogenide bilayer. These results establish topological descriptors with neighborhood separation as a robust framework for identifying commensurate order in moiré systems and tracking commensurate structural similarity under disorder, sparsity, and finite-size effects.

cond-mat.dis-nn↗

arXiv2026

Spectral-Stimulus Information for Self-Supervised Stimulus Encoding

Mammalian spatial navigation relies on specialized neurons, such as place and grid cells, which encode position based on self-motion and environmental cues. While extensive research has explored the computational role of grid cells, the principles underlying efficient place cell coding remain less understood. Existing spatial information rate measures primarily assess single-neuron encoding, limiting insights into population-level representations, while, the role of correlation in neural coding remains a subject of considerable debate. To address this, we introduce novel, correlation-aware information-theoretic measures that quantify the encoding efficiency of multiple neurons, including the joint stimulus information rate for neuron pairs and the spectral-stimulus information for arbitrary sized populations. The spectral-stimulus information, defined as the leading eigenvalue of the stimulus information matrix, is maximized when neurons exhibit localized, non-overlapping firing fields, mirroring place cell and head direction cell activity. We apply these measures to neural data recorded in mice and monkeys, elucidating differences in encoding efficiency across neuronal pairs and populations. Then, we demonstrate that these measures can be used to train recurrent neural networks (RNNs) via self-supervised learning, leading to the emergence of place cells and head direction cells. Our findings highlight how neural populations collectively encode stimuli, offering a more comprehensive framework for understanding stimulus encoding and optimizing artificial navigation systems in novel environments.

q-bio.NC↗

arXiv2026

From Classical to Topological Neural Networks Under Uncertainty

This chapter explores neural networks, topological data analysis, and topological deep learning techniques, alongside statistical Bayesian methods, for processing images, time series, and graphs to maximize the potential of artificial intelligence in the military domain. Throughout the chapter, we highlight practical applications spanning image, video, audio, and time-series recognition, fraud detection, and link prediction for graphical data, illustrating how topology-aware and uncertainty-aware models can enhance robustness, interpretability, and generalization.

cs.LG↗

arXiv2026

Accurate Helium-Benzene Potential: from CCSD(T) to Gaussian Process Regression

The accurate modeling of non-covalent interactions between helium and graphitic materials is important for understanding quantum phenomena in reduced dimensions, with the helium-benzene complex serving as the fundamental prototype. However, creating a quantitatively reliable potential energy surface (PES) for this weakly bound system remains a significant computational challenge. In this work, we present a comprehensive, multi-level investigation of the He-Bz interaction, establishing benchmark energies using high-level coupled-cluster singles-and-doubles with perturbative triples (CCSD(T)) methods extrapolated to the complete basis set limit and assessing higher-order (CCSDT(Q)) contributions. We use symmetry-adapted perturbation theory (SAPT) to benchmark it against CCSD(T) and to decompose the interaction into its physical components-confirming it is dominated by a balance between dispersion and exchange-repulsion. A continuous, three-dimensional PES is constructed from discrete ab initio points using multifidelity Gaussian process regression that combines density functional theory results with sparse coupled-cluster energies. The result is a highly accurate PES with sub-cm-1 accuracy that obeys physical laws. This new PES is applied to path integral Monte Carlo (PIMC) simulations to study the solvation of 4He atoms on benzene at low temperatures. Our PIMC results reveal qualitatively different solvation behavior, particularly in the filling of adsorption layers, when compared to simulations using commonly employed empirical Lennard-Jones potentials. This work provides a benchmark PES essential for accurate many-body simulations of helium on larger polycyclic aromatic hydrocarbons towards graphene.

physics.chem-ph↗

arXiv2025

Bayesian Topological Convolutional Neural Nets

Convolutional neural networks (CNNs) have been established as the main workhorse in image data processing; nonetheless, they require large amounts of data to train, often produce overconfident predictions, and frequently lack the ability to quantify the uncertainty of their predictions. To address these concerns, we propose a new Bayesian topological CNN that promotes a novel interplay between topology-aware learning and Bayesian sampling. Specifically, it utilizes information from important manifolds to accelerate training while reducing calibration error by placing prior distributions on network parameters and properly learning appropriate posteriors. One important contribution of our work is the inclusion of a consistency condition in the learning cost, which can effectively modify the prior distributions to improve the performance of our novel network architecture. We evaluate the model on benchmark image classification datasets and demonstrate its superiority over conventional CNNs, Bayesian neural networks (BNNs), and topological CNNs. In particular, we supply evidence that our method provides an advantage in situations where training data is limited or corrupted. Furthermore, we show that the new model allows for better uncertainty quantification than standard BNNs since it can more readily identify examples of out-of-distribution data on which it has not been trained. Our results highlight the potential of our novel hybrid approach for more efficient and robust image classification.

cs.CV↗

arXiv2025

Bayesian Sheaf Neural Networks

Equipping graph neural networks with a convolution operation defined in terms of a cellular sheaf offers advantages for learning expressive representations of heterophilic graph data. The most flexible approach to constructing the sheaf is to learn it as part of the network as a function of the node features. However, this leaves the network potentially overly sensitive to the learned sheaf. As a counter-measure, we propose a variational approach to learning cellular sheaves within sheaf neural networks, yielding an architecture we refer to as a Bayesian sheaf neural network. As part of this work, we define a novel family of reparameterizable probability distributions on the rotation group $SO(n)$ using the Cayley transform. We evaluate the Bayesian sheaf neural network on several graph datasets, and show that our Bayesian sheaf models achieve leading performance compared to baseline models and are less sensitive to the choice of hyperparameters under limited training data settings.

cs.LG↗

arXiv2025

Functional Ultrasound Imaging Combined with Machine Learning for Whole-Brain Analysis of Drug-Induced Hemodynamic Changes

Functional ultrasound imaging (fUSI) is a cutting-edge technology that measures changes in cerebral blood volume (CBV) by detecting backscattered echoes from red blood cells moving within its field of view (FOV). It offers high spatiotemporal resolution and sensitivity, allowing for detailed visualization of cerebral blood flow dynamics. While fUSI has been utilized in preclinical drug development studies to explore the mechanisms of action of various drugs targeting the central nervous system, many of these studies rely on predetermined regions of interest (ROIs). This focus may overlook relevant brain activity outside these specific areas, which could influence the results. To address this limitation, we compared three machine learning approaches-convolutional neural network (CNN), support vector machine (SVM), and vision transformer (ViT)-combined with fUSI to analyze the pharmacodynamics of Dizocilpine (MK-801), a potent non-competitive NMDA receptor antagonist commonly used in preclinical models for memory and learning impairments. While all three machine learning techniques could distinguish between drug and control conditions, CNN proved particularly effective due to their ability to capture hierarchical spatial features while maintaining anatomical specificity. Class activation mapping revealed brain regions, including the prefrontal cortex and hippocampus, that are significantly affected by drug administration, consistent with the literature reporting a high density of NMDA receptors in these areas. Overall, the combination of fUSI and CNN creates a novel analytical framework for examining pharmacological mechanisms, allowing for data-driven identification and regional mapping of drug effects while preserving anatomical context and physiological relevance.

q-bio.NC↗

arXiv2025

Investigating the importance of county-level characteristics in opioid-related mortality across the United States

The opioid crisis remains a critical public health challenge in the United States. Despite national efforts which reduced opioid prescribing rates by nearly 45\% between 2011 and 2021, opioid-related overdose deaths more than tripled during the same period. This alarming trend reflects a major shift in the crisis, with illegal opioids now driving the majority of overdose deaths instead of prescription opioids. Although much attention has been given to supply-side factors fueling this transition, the underlying structural conditions that perpetuate and exacerbate opioid misuse remain less understood. Moreover, the COVID-19 pandemic intensified the opioid crisis through widespread social isolation and record-high unemployment; consequently, understanding the underlying drivers of this epidemic has become even more crucial in recent years. To address this need, our study examines the correlation between opioid-related mortality and thirteen county-level characteristics related to population traits, economic stability, and infrastructure. Leveraging a nationwide county-level dataset spanning consecutive years from 2010 to 2022, this study integrates empirical insights from exploratory data analysis with feature importance metrics derived from machine learning models. Our findings highlight critical regional characteristics strongly correlated with opioid-related mortality, emphasizing their potential roles in worsening the epidemic when their levels are high and mitigating it when their levels are low.

cs.CY↗

arXiv2025

Topological Data Analysis and Topological Deep Learning Beyond Persistent Homology -- A Review

Topological data analysis (TDA) is a rapidly evolving field in applied mathematics and data science that leverages tools from topology to uncover robust, shape-driven insights in complex datasets. The main workhorse is persistent homology, a technique rooted in algebraic topology. Paired with topological deep learning (TDL) or topological machine learning, persistent homology has achieved tremendous success in a wide variety of applications in science, engineering, medicine, and industry. However, persistent homology has many limitations due to its high-level abstraction, insensitivity to non-topological changes, and reliance on point cloud data. This paper presents a comprehensive review of TDA and TDL beyond persistent homology. It analyzes how persistent topological Laplacians and Dirac operators provide spectral representations to capture both topological invariants and homotopic evolution. Other formulations are presented in terms of sheaf theory, Mayer topology, and interaction topology. For data on differentiable manifolds, techniques rooted in differential topology, such as persistent de Rham cohomology, persistent Hodge Laplacian, and Hodge decomposition, are reviewed. For one-dimensional (1D) curves embedded in 3-space, approaches from geometric topology are discussed, including multiscale Gauss-link integrals, persistent Jones polynomials, and persistent Khovanov homology. This paper further discusses the appropriate selection of topological tools for different input data, such as point clouds, sequential data, data on manifolds, curves embedded in 3-space, and data with additional non-geometric information. A review is also given of various topological representations, software packages, and machine learning vectorizations. Finally, this review ends with concluding remarks.

math.HO↗

arXiv2025

Identifying Spatiotemporal Patterns in Opioid Vulnerability: Investigating the Links Between Disability, Prescription Opioids and Opioid-Related Mortality

The opioid crisis remains one of the most daunting and complex public health problems in the United States. This study investigates the national epidemic by analyzing vulnerability profiles of three key factors: opioid-related mortality rates, opioid prescription dispensing rates, and disability rank ordered rates. This study utilizes county level data, spanning the years 2014 through 2020, on the rates of opioid-related mortality, opioid prescription dispensing, and disability. To successfully estimate and predict trends in these opioid-related factors, we augment the Kalman Filter with a novel spatial component. To define opioid vulnerability profiles, we create heat maps of our filter's predicted rates across the nation's counties and identify the hotspots. In this context, hotspots are defined on a year-by-year basis as counties with rates in the top 5 percent nationally. Our spatial Kalman filter demonstrates strong predictive performance. From 2014 to 2018, these predictions highlight consistent spatiotemporal patterns across all three factors, with Appalachia distinguished as the nation's most vulnerable region. Starting in 2019 however, the dispensing rate profiles undergo a dramatic and chaotic shift. The initial primary drivers of opioid abuse in the Appalachian region were likely prescription opioids; however, it now appears that abuse is sustained by illegal drugs. Additionally, we find that the disabled subpopulation may be more at risk of opioid-related mortality than the general population. Public health initiatives must extend beyond controlling prescription practices to address the transition to and impact of illicit drug use.

stat.AP↗

arXiv2024

Geometric sparsification in recurrent neural networks

A common technique for ameliorating the computational costs of running large neural models is sparsification, or the pruning of neural connections during training. Sparse models are capable of maintaining the high accuracy of state of the art models, while functioning at the cost of more parsimonious models. The structures which underlie sparse architectures are, however, poorly understood and not consistent between differently trained models and sparsification schemes. In this paper, we propose a new technique for sparsification of recurrent neural nets (RNNs), called moduli regularization, in combination with magnitude pruning. Moduli regularization leverages the dynamical system induced by the recurrent structure to induce a geometric relationship between neurons in the hidden state of the RNN. By making our regularizing term explicitly geometric, we provide the first, to our knowledge, a priori description of the desired sparse architecture of our neural net, as well as explicit end-to-end learning of RNN geometry. We verify the effectiveness of our scheme under diverse conditions, testing in navigation, natural language processing, and addition RNNs. Navigation is a structurally geometric task, for which there are known moduli spaces, and we show that regularization can be used to reach 90% sparsity while maintaining model performance only when coefficients are chosen in accordance with a suitable moduli space. Natural language processing and addition, however, have no known moduli space in which computations are performed. Nevertheless, we show that moduli regularization induces more stable recurrent neural nets, and achieves high fidelity models above 90% sparsity.

cs.LG↗

arXiv2024

Quantum Distance Approximation for Persistence Diagrams

Topological Data Analysis methods can be useful for classification and clustering tasks in many different fields as they can provide two dimensional persistence diagrams that summarize important information about the shape of potentially complex and high dimensional data sets. The space of persistence diagrams can be endowed with various metrics such as the Wasserstein distance which admit a statistical structure and allow to use these summaries for machine learning algorithms. However, computing the distance between two persistence diagrams involves finding an optimal way to match the points of the two diagrams and may not always be an easy task for classical computers. In this work we explore the potential of quantum computers to estimate the distance between persistence diagrams, in particular we propose variational quantum algorithms for the Wasserstein distance as well as the $d^{c}_{p}$ distance. Our implementation is a weighted version of the Quantum Approximate Optimization Algorithm that relies on control clauses to encode the constraints of the optimization problem.

quant-ph↗

arXiv2024

Position: Topological Deep Learning is the New Frontier for Relational Learning

Topological deep learning (TDL) is a rapidly evolving field that uses topological features to understand and design deep learning models. This paper posits that TDL is the new frontier for relational learning. TDL may complement graph representation learning and geometric deep learning by incorporating topological concepts, and can thus provide a natural choice for various machine learning settings. To this end, this paper discusses open problems in TDL, ranging from practical benefits to theoretical foundations. For each problem, it outlines potential solutions and future research opportunities. At the same time, this paper serves as an invitation to the scientific community to actively participate in TDL research to unlock the potential of this emerging field.

cs.LG↗

arXiv2024

On the Relation between Graph Ricci Curvature and Community Structure

The connection between curvature and topology is a very well-studied theme in the subject of differential geometry. By suitably defining curvature on networks, the study of this theme has been extended into the domain of network analysis as well. In particular, this has led to curvature-based community detection algorithms. In this paper, we reveal the relation between community structure of a network and the curvature of its edges. In particular, we give apriori bounds on the curvature of intercommunity edges of a graph.

cs.SI↗

arXiv2023

A Topological Deep Learning Framework for Neural Spike Decoding

The brain's spatial orientation system uses different neuron ensembles to aid in environment-based navigation. Two of the ways brains encode spatial information is through head direction cells and grid cells. Brains use head direction cells to determine orientation whereas grid cells consist of layers of decked neurons that overlay to provide environment-based navigation. These neurons fire in ensembles where several neurons fire at once to activate a single head direction or grid. We want to capture this firing structure and use it to decode head direction grid cell data. Understanding, representing, and decoding these neural structures requires models that encompass higher order connectivity, more than the 1-dimensional connectivity that traditional graph-based models provide. To that end, in this work, we develop a topological deep learning framework for neural spike train decoding. Our framework combines unsupervised simplicial complex discovery with the power of deep learning via a new architecture we develop herein called a simplicial convolutional recurrent neural network. Simplicial complexes, topological spaces that use not only vertices and edges but also higher-dimensional objects, naturally generalize graphs and capture more than just pairwise relationships. Additionally, this approach does not require prior knowledge of the neural activity beyond spike counts, which removes the need for similarity measurements. The effectiveness and versatility of the simplicial convolutional neural network is demonstrated on head direction and trajectory prediction via head direction and grid cell datasets.

cs.NE↗

arXiv2022

Quantum Persistent Homology for Time Series

Persistent homology, a powerful mathematical tool for data analysis, summarizes the shape of data through tracking topological features across changes in different scales. Classical algorithms for persistent homology are often constrained by running times and memory requirements that grow exponentially on the number of data points. To surpass this problem, two quantum algorithms of persistent homology have been developed based on two different approaches. However, both of these quantum algorithms consider a data set in the form of a point cloud, which can be restrictive considering that many data sets come in the form of time series. In this paper, we alleviate this issue by establishing a quantum Takens's delay embedding algorithm, which turns a time series into a point cloud by considering a pertinent embedding into a higher dimensional space. Having this quantum transformation of time series to point clouds, then one may use a quantum persistent homology algorithm to extract the topological features from the point cloud associated with the original times series.

quant-ph↗

arXiv2022

A Random Persistence Diagram Generator

Topological data analysis (TDA) studies the shape patterns of data. Persistent homology is a widely used method in TDA that summarizes homological features of data at multiple scales and stores them in persistence diagrams (PDs). In this paper, we propose a random persistence diagram generator (RPDG) method that generates a sequence of random PDs from the ones produced by the data. RPDG is underpinned by a model based on pairwise interacting point processes, and a reversible jump Markov chain Monte Carlo (RJ-MCMC) algorithm. A first example, which is based on a synthetic dataset, demonstrates the efficacy of RPDG and provides a comparison with another method for sampling PDs. A second example demonstrates the utility of RPDG to solve a materials science problem given a real dataset of small sample size.

stat.ML↗

arXiv2022

Quantum Persistent Homology

Persistent homology is a powerful mathematical tool that summarizes useful information about the shape of data allowing one to detect persistent topological features while one adjusts the resolution. However, the computation of such topological features is often a rather formidable task necessitating the subsampling the underlying data. To remedy this, we develop an efficient quantum computation of persistent Betti numbers, which track topological features of data across different scales. Our approach employs a persistent Dirac operator whose square yields the persistent combinatorial Laplacian, and in turn the underlying persistent Betti numbers which capture the persistent features of data. We also test our algorithm on point cloud data.

quant-ph↗