Introduction | Parallel Processing Overview | Setup | Benchmarking Parallel vs Sequential | Tangent Computations | Frechet Mean Computation | Parquet I/O Benchmarks | Scaling Analysis | Worker Count Scaling | Dataset Size Impact | Optimization Guidelines | When to Use Parallel Processing | Optimal Worker Count | Memory Optimization | Progress Reporting Overhead | Benchmarking Best Practices | 1. Use microbenchmark for Accurate Measurements | 2. Control for Caching Effects | 3. Report System Information | Common Performance Patterns | Pattern 1: Compute-Bound Operations | Pattern 2: Iteration-Heavy Operations | Pattern 3: I/O-Bound Operations | Platform-Specific Notes | Windows | Mac/Linux | HPC Clusters | Summary

Introduction | Benefits of Parquet Storage | Installation | Basic Workflow | 1. Writing Connectomes to Parquet | 2. Validating Parquet Directory | 3. Creating a CSample with Parquet Backend | 4. Computing with Parquet-backed CSample | 5. Lazy Loading Behavior | Working with CSuperSample | Backwards Compatibility | Performance Tips | Cache Size Tuning | Batch Operations | Parallel Processing with Parquet | Enabling Parallel Processing | Parallel I/O and Computation | Batch Loading with Parallel I/O | Performance Comparison | Progress Reporting | Best Practices | Auto-Detection | Parallel Strategies | Metadata Access | Advanced: Custom File Patterns | Troubleshooting | Large Datasets | Memory Monitoring | Summary

Introduction | Code Organization: The Two-File Pattern | Example: Setting Up a Symbol Library | Creating Powerful Helper Functions | Pattern 1: Building Complex Expressions | Pattern 2: Multi-line Equation Builders | Complex Example: Statistical Proof | Conclusion

Example | Implementation Details | Discussion

Introduction | Key Features | Installation | Basic Usage | Loading the Package and Setting Up | Working with Metrics | Creating and Manipulating Samples | Creating Random Samples | Computing Different Representations | Statistical Analysis | Computing the Fréchet Mean | Computing Sample Statistics | Advanced Examples | Discriminating Between Two Samples | Working with Real Data | Key Classes | CSample Class | Metric Objects | Performance Considerations | References