arXiv subjects

D. Vijay Anand

Publications and source records attributed to D. Vijay Anand.

5 recordsLinked to original sources

arXiv2026

Causality as a Minimum Energy Principle

Classical causal models, such as Granger causality and structural equation modeling, are largely restricted to acyclic interactions and struggle to represent cyclic and higher-order dynamics in complex networks. We introduce a causal framework grounded in a variational principle, interpreting causality as directional energy flow from high- to low-energy states along network connections. Using Hodge theory, network flows are decomposed into dissipative components and a persistent harmonic component that captures stable cyclic interactions. Applied to resting-state fMRI connectivity, our variational framework reveals robust cyclic causal patterns that are not detected by conventional causal models, highlighting the value of variational principles for causality.

q-bio.NC↗

arXiv2026

Multi-Modal AI for Remote Patient Monitoring in Cancer Care

For patients undergoing systemic cancer therapy, the time between clinic visits is full of uncertainties and risks of unmonitored side effects. To bridge this gap in care, we developed and prospectively trialed a multi-modal AI framework for remote patient monitoring (RPM). This system integrates multi-modal data from the HALO-X platform, such as demographics, wearable sensors, daily surveys, and clinical events. Our observational trial is one of the largest of its kind and has collected over 2.1 million data points (6,080 patient-days) of monitoring from 84 patients. We developed and adapted a multi-modal AI model to handle the asynchronous and incomplete nature of real-world RPM data, forecasting a continuous risk of future adverse events. The model achieved an accuracy of 83.9% (AUROC=0.70). Notably, the model identified previous treatments, wellness check-ins, and daily maximum heart rate as key predictive features. A case study demonstrated the model's ability to provide early warnings by outputting escalating risk profiles prior to the event. This work establishes the feasibility of multi-modal AI RPM for cancer care and offers a path toward more proactive patient support.(Accepted at Europe NeurIPS 2025 Multimodal Representation Learning for Healthcare Workshop. Best Paper Poster Award.)

cs.LG↗

arXiv2025

Hodge-Decomposition of Functional Brain Networks

We propose to analyze dynamically changing brain networks by decomposing them into three orthogonal components through the Hodge decomposition. We propose to quantify the magnitude and relative strength of each component. We performed extensive simulation studies with known ground truth. The Hodge decomposition is then applied to the dynamically changing human brain networks obtained from a resting-state functional magnetic resonance imaging study. Our results indicate that the components of the Hodge decomposition contain biologically interpretable topological features that provide statistically significant findings not easily captured by traditional methods.

q-bio.NC↗

arXiv2023

Hodge-Laplacian of Brain Networks

The closed loops or cycles in a brain network embeds higher order signal transmission paths, which provide fundamental insights into the functioning of the brain. In this work, we propose an efficient algorithm for systematic identification and modeling of cycles using persistent homology and the Hodge Laplacian. Various statistical inference procedures on cycles are developed. We validate the our methods on simulations and apply to brain networks obtained through the resting state functional magnetic resonance imaging. The computer codes for the Hodge Laplacian are given in https://github.com/laplcebeltrami/hodge.

q-bio.NC↗

arXiv2022

Topological Data Analysis of Human Brain Networks Through Order Statistics

Understanding the common topological characteristics of the human brain network across a population is central to understanding brain functions. The abstraction of human connectome as a graph has been pivotal in gaining insights on the topological properties of the brain network. The development of group-level statistical inference procedures in brain graphs while accounting for the heterogeneity and randomness still remains a difficult task. In this study, we develop a robust statistical framework based on persistent homology using the order statistics for analyzing brain networks. The use of order statistics greatly simplifies the computation of the persistent barcodes. We validate the proposed methods using comprehensive simulation studies and subsequently apply to the resting-state functional magnetic resonance images. We found a statistically significant topological difference between the male and female brain networks.

q-bio.QM↗