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Develop very good app time in second, min, hours option and stepsize option using code "import numpy as np import pandas as pd import matplotlib.pyplot as plt from scipy.constants import N_A # Avogadro's number # ============================================= # PARAMETERS (24-hour simulation) # ============================================= initial_cells = 1e4 # Initial T-cell count (10,000 cells) growth_rate = 0.15 # Growth rate (0.15 per hour) blood_volume = 5 # Blood volume (5 liters) noise_level = 0.05 # 5% multiplicative noise total_seconds = 86400 # 24 hours in seconds step_size = 1 # 1-second resolution # ============================================= # TIME GRID (1-second steps) # ============================================= time_seconds = np.arange(0, total_seconds + 1, step_size) time_hours = time_seconds / 3600 # Convert to hours # ============================================= # GROWTH MODEL CALCULATIONS # ============================================= # Convert growth rate to per-second growth_rate_per_second = growth_rate / 3600 # Exponential growth model ideal_counts = initial_cells * np.exp(growth_rate_per_second * time_seconds) # Add log-normal noise (preserves positivity) np.random.seed(42) # For reproducibility noise = np.random.lognormal(mean=0, sigma=noise_level, size=len(time_seconds)) noisy_counts = ideal_counts * noise # Convert to molar concentration molar_conversion = 1 / (N_A * blood_volume) molar_ideal = ideal_counts * molar_conversion molar_noisy = noisy_counts * molar_conversion # ============================================= # CREATE DATAFRAME (86,401 rows) # ============================================= data = { 'time_seconds': time_seconds, 'time_hours': np.round(time_hours, 6), 'ideal_cell_count': np.round(ideal_counts, 2), 'noisy_cell_count': np.round(noisy_counts, 2), 'molar_ideal': molar_ideal, 'molar_noisy': molar_noisy } df = pd.DataFrame(data) print(f"Generated {len(df)} data points (1-second resolution)") print(df.head()) print(df.tail()) # ============================================= # VISUALIZATION (Sampled for clarity) # ============================================= sample_interval = 300 # Show every 5 minutes fig, (ax1, ax2) = plt.subplots(2, 1, figsize=(12, 8)) # Linear-scale plot (sampled) ax1.plot(time_seconds[::sample_interval], molar_ideal[::sample_interval], 'b--', label='Ideal Growth') ax1.plot(time_seconds[::sample_interval], molar_noisy[::sample_interval], 'r-', alpha=0.7, label='Noisy Measurements') ax1.set_xlabel('Time (seconds)') ax1.set_ylabel('Concentration (M)') ax1.set_title('T-cell Growth (Linear Scale)') ax1.legend() ax1.grid(True) # Log-scale plot (sampled) ax2.semilogy(time_seconds[::sample_interval], molar_ideal[::sample_interval], 'b--', label='Ideal Growth') ax2.semilogy(time_seconds[::sample_interval], molar_noisy[::sample_interval], 'r-', alpha=0.7, label='Noisy Measurements') ax2.set_xlabel('Time (seconds)') ax2.set_ylabel('Concentration (M)') ax2.set_title('T-cell Growth (Log Scale)') ax2.legend() ax2.grid(True, which="both", ls="--") plt.tight_layout() plt.show() # ============================================= # DATA EXPORT # ============================================= df.to_csv('tcell_growth_1sec_resolution_24h.csv', index=False) print("Data saved to 'tcell_growth_1sec_resolution_24h.csv'")" - Initial Deployment
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