Starr Talley

Greetings. I am Starr Talley, a computational neuroscientist and applied mathematician dedicated to bridging dynamical systems theory with neural network architectures for modeling spatiotemporal continuums. With a Ph.D. in Neuro-Mathematical Physics (Caltech, 2024) and leadership experience at the Allen Institute for Spatiotemporal Dynamics, my work pioneers neuro-differential equation frameworks that unify discrete neural activities with continuum-scale physical laws.

My mission: "To decode the universe's spatiotemporal fabric through mathematics that speaks the language of both neurons and spacetime."

Theoretical Framework and Methodology

1. Neuro-Differential Equation Architecture

I developed a hierarchical neural ODE-PDE hybrid model integrating:

• Temporal dynamics: Adaptive recurrent neural networks (RNNs) with Lie group symmetries 1

• Spatial propagation: Graph-convolutional operators encoding conservation laws 5

• Continuum coupling: Entropy-regularized attention mechanisms for multiscale interactions

This framework achieves 83% accuracy in predicting turbulent flow transitions, outperforming conventional CFD-PINN hybrids by 22% 1.

2. Key Innovations

• Causal Spacetime Embedding: A geometrodynamic latent space preserving light-cone causality constraints

• Topological Memory Cells: Persistent homology-guided LSTM modules capturing non-Markovian dependencies

• Uncertainty-Aware Solver: Monte Carlo dropout adapted for stochastic PDEs, reducing prediction variance by 37%

Applications and Impact

1. Neural Astrophysics

Modeled black hole accretion disk instabilities using:

• Kerr metric-informed neural operators

• Multi-observational constraints from radio/X-ray timing data 3
  Result: Predicted QPO frequency shifts (3σ confidence) matching Event Horizon Telescope observations.

2. Urban Mobility Optimization

Designed Meta-Spacetime Traffic Simulator for NYC Metropolitan Area:

• Fused taxi GPS (discrete events) with continuum traffic flow PDEs

• Dynamic rebalancing reduced congestion hotspots by 41% during peak hours 1

3. Neurodegenerative Disease Research

Revealed Alzheimer's progression patterns through:

• Whole-brain fMRI-EEG fused continuum modeling

• Tau protein diffusion-reaction equation neural analogs
  Breakthrough: Identified preclinical propagation corridors 6-8 years before symptom onset.

Future Directions

1. Quantum-Neural Continuum Synthesis
   Merging tensor network methods 6 with neural PDEs to model spacetime at Planck scales.

2. Historical Spatiotemporal Inference
   Applying continuum models to reconstruct ancient trade routes from fragmentary records 7.

3. Ethical AI for Spatiotemporal Systems
   Developing causality-preserving regularization for geopolitical conflict prediction.

Philosophy and Collaboration

My work embodies three principles:

1. Physical Consistency: All neural components must satisfy Noether's theorem symmetries

2. Computational Parsimony: 1 PFLOOP efficiency target for exascale spacetime simulations

3. Transdisciplinary Resonance: Bridging Whitehead's process philosophy with deep learning

I welcome collaborations to explore neural continuum mathematics in:

• Cosmic structure formation 2

• Multilingual knowledge graph temporalization 7

• Biohybrid spacetime processing systems