Heitor Baldo

Heitor Baldo

PhD in Bioinformatics (Mathematical Neuroscience)

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About me

Hi! My name is Heitor Baldo. I hold a BS in Mathematics and an MS in Applied and Computational Mathematics, both from the University of Campinas, and a PhD in Bioinformatics (Mathematical Neuroscience) from the University of São Paulo. I was a visiting postdoctoral researcher at Leipzig University in Germany, and I am currently a postdoctoral fellow at the University of São Paulo. My background spans mathematics, applied mathematics, and computer science, with an emphasis on mathematical neuroscience.

Update
  • A preprint version of our newest manuscript is now available here.

Research

1. Brain Connectivity Inference, Graph Theoretic and Topological Data Analysis of Brain Networks.

Brain connectivity inference methods; directed connectivity inference in the frequency domain: multivariate autoregressive methods (partial directed coherence (PDC) and variants, directed transfer function (DTF), and related estimators) recover directed connectivity networks from neural signals (EEG, fMRI, MEG). From these inferred networks, we go beyond pairwise graphs toward multiway, multilayer, temporal, and dynamic representations that capture directed, higher-order neural interactions through hypergraphs, simplicial complexes, and digraph-based complexes. We characterize these structures through discrete geometry (Ollivier–Ricci and Forman–Ricci curvatures, finite geometries, and combinatorial invariants) and through graph theoretic and topological data analysis (persistent homology, filtration-based descriptors, Q-analysis, and network summary statistics), quantifying structural and functional organization across scales.

2. Neural Rings and Combinatorial Neural Codes.

Algebraic and combinatorial models of neural representation, centered on neural rings, neural ideals, and combinatorial neural codes as formal tools for decoding the structure of population activity. The focus is on how the pattern of co-firing among neurons constrains the underlying stimulus space, recovering receptive-field geometry, place field arrangements, convexity properties, and the intrinsic dimensionality of represented variables directly from the combinatorics of the code, independent of specific embeddings.

3. Neural Manifolds and Matrix Manifold Methods.

Analysis of neural population activity through low-dimensional neural manifolds and the geometry of matrix manifolds, including Stiefel and Grassmann manifolds for dimensionality reduction, subspace estimation, cross-session and cross-subject alignment, and manifold-constrained state inference. This treats neural computation as motion on curved latent spaces and brings the appropriate differential-geometric and optimization machinery (geodesics, retractions, manifold-valued statistics) to clarify how such trajectories relate to behavior and cognition.

4. Topological and Geometric Deep Learning for Neuroscience.

Development and application of geometric, topological, and manifold-aware learning architectures (graph, hypergraph, simplicial, and sheaf neural networks, and manifold-valued models, adapted to the structure of neural and connectomic data). The goal is to build models whose inductive biases respect the higher-order, geometric, and topological nature of brain data, improving both predictive performance and interpretability relative to generic deep learning approaches.

5. Brain Coding and Decoding

Reconstruction of stimuli, intentions, and cognitive states from measured neural activity, encompassing both the encoding problem (how sensory and cognitive variables are represented) and the decoding problem (recovering those variables from recorded signals). This integrates the representational insights of the algebraic, manifold, and topological directions above with statistical and machine learning decoders, with relevance to brain-computer interfaces (BCIs) and neurotechnology.

MS and PhD Thesis

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