Aging#

Energy#

From the point of view of form, the archetype of all the arts is the art of the musician.-Oscar Wilde 4

                1. Sensory
                          \
             2. Memory -> 4. Frailty -> 5. Omics -> 6. Independence
                          /
                          3. Agility
https://miro.medium.com/v2/resize:fit:1400/format:webp/1*VrPAkfuA_IZHzZkx644iHw.png

When does aging begin?. From the ii-V7-i theme of a character arc, What variations might we perceive here? What departure-struggle-return? For our protagonist it is (ii) metabolism \(f(t)\), age \(S(t)\), energy \(h(t)\), encoded as (V7) frailty \((X'X)^T \cdot X'Y\), decoded as (i) determinism \(\beta\) vs. freewill \(SV_t'\). As a part of cosmic dirt, we departed from lifeless forms & manifested that with life & the energy of youth ii. But there’s a steady loss of energy from conception to death & the entirety of life is a losing battle against our return to cosmic dust V7. It is predetermined that we all complete the arc from dust-to-dust i. Lookout for the sentinal evidence from our sensory acuity (vision, olfaction, audition, gustation, chemistry, balance), cognitive state (memory, learning, updating) and motor agility (calories/day, m/s, dynamometer, bone-density, reflex-speed, falls, gymnastic-feats, vertigo). These encode all the insults that time & comorbidity bring upon the body, into a latent-space of the physical frailty phenotype, which may be decoded using -omics, and ultimately GRIP with predictive accuracy for loss of independence in activities of daily living.#

\(\mu\) Base-case#

  • \(f(t)\) Senses: Note that A4-A6 is normal range for human speech

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import numpy as np
import matplotlib.pyplot as plt

# Parameters
sample_rate = 44100  # Hz
duration = 20.0       # seconds
A4_freq = 440.0      # Hz

# Time array
t = np.linspace(0, duration, int(sample_rate * duration), endpoint=False)

# Fundamental frequency (A4)
signal = np.sin(2 * np.pi * A4_freq * t)

# Adding overtones (harmonics)
harmonics = [2, 3, 4, 5, 6, 7, 8, 9]  # First few harmonics
amplitudes = [0.5, 0.25, 0.15, 0.1, 0.05, 0.03, 0.01, 0.005]  # Amplitudes for each harmonic

for i, harmonic in enumerate(harmonics):
    signal += amplitudes[i] * np.sin(2 * np.pi * A4_freq * harmonic * t)

# Perform FFT (Fast Fourier Transform)
N = len(signal)
yf = np.fft.fft(signal)
xf = np.fft.fftfreq(N, 1 / sample_rate)

# Plot the frequency spectrum
plt.figure(figsize=(12, 6))
plt.plot(xf[:N//2], 2.0/N * np.abs(yf[:N//2]), color='navy', lw=1.5)

# Aesthetics improvements
plt.title('Simulated Frequency Spectrum of A440 on a Grand Piano', fontsize=16, weight='bold')
plt.xlabel('Frequency (Hz)', fontsize=14)
plt.ylabel('Amplitude', fontsize=14)
plt.xlim(0, 4186)  # Limit to the highest frequency on a piano (C8)
plt.ylim(0, None)

# Shading the region for normal speaking range (approximately 85 Hz to 255 Hz)
plt.axvspan(500, 2000, color='lightpink', alpha=0.5)

# Annotate the shaded region
plt.annotate('Normal Speaking Range (500 Hz - 2000 Hz)',
             xy=(2000, 0.7), xycoords='data',
             xytext=(2500, 0.5), textcoords='data',
             arrowprops=dict(facecolor='black', arrowstyle="->"),
             fontsize=12, color='black')

# Remove top and right spines
plt.gca().spines['top'].set_visible(False)
plt.gca().spines['right'].set_visible(False)

# Customize ticks
plt.xticks(fontsize=12)
plt.yticks(fontsize=12)

# Light grid
plt.grid(color='grey', linestyle=':', linewidth=0.5)

# Show the plot
plt.tight_layout()
plt.show()
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../_images/c0265f9458eb5f77bc370fdf863d0c424999cc21732d60a3d126fd5da7d63078.png
  • \(S(t)\) Memory: What quick tests are out there?

  • \(h(t)\) Emotions: Let’s focus on how they translate to motion!

\(\sigma\) Varcov-matrix#

  • \((X'X)^T \cdot X'Y\): Frailty: Energy, Omics, Activity, Muscle, Strength, Pace,

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import matplotlib.pyplot as plt
import numpy as np

# Clock settings; f(t) random disturbances making "paradise lost"
clock_face_radius = 1.0
number_of_ticks = 7
tick_labels = [
    "Root-iADL (i)",
    "Hunter-gather (ii7♭5)", "Peasant (III)", "Farmer (iv)", "Manufacturer (V7♭9♯9♭13)",
    "Energy (VI)", "Transport (VII)"
]

# Calculate the angles for each tick (in radians)
angles = np.linspace(0, 2 * np.pi, number_of_ticks, endpoint=False)
# Inverting the order to make it counterclockwise
angles = angles[::-1]

# Create figure and axis
fig, ax = plt.subplots(figsize=(8, 8))
ax.set_xlim(-1.2, 1.2)
ax.set_ylim(-1.2, 1.2)
ax.set_aspect('equal')

# Draw the clock face
clock_face = plt.Circle((0, 0), clock_face_radius, color='lightgrey', fill=True)
ax.add_patch(clock_face)

# Draw the ticks and labels
for angle, label in zip(angles, tick_labels):
    x = clock_face_radius * np.cos(angle)
    y = clock_face_radius * np.sin(angle)
    
    # Draw the tick
    ax.plot([0, x], [0, y], color='black')
    
    # Positioning the labels slightly outside the clock face
    label_x = 1.1 * clock_face_radius * np.cos(angle)
    label_y = 1.1 * clock_face_radius * np.sin(angle)
    
    # Adjusting label alignment based on its position
    ha = 'center'
    va = 'center'
    if np.cos(angle) > 0:
        ha = 'left'
    elif np.cos(angle) < 0:
        ha = 'right'
    if np.sin(angle) > 0:
        va = 'bottom'
    elif np.sin(angle) < 0:
        va = 'top'
    
    ax.text(label_x, label_y, label, horizontalalignment=ha, verticalalignment=va, fontsize=10)

# Remove axes
ax.axis('off')

# Show the plot
plt.show()
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../_images/27e040d08e633f630e1f9c273497a6101713684d3a59bc65c4f9ab4012e1af26.png

\(\%\) Precision#

  • \(\beta\) Omics: No isolated one should be of great significance

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import matplotlib.pyplot as plt
import numpy as np

# Clock settings; f(t) random disturbances making "paradise lost"
clock_face_radius = 1.0
number_of_ticks = 9
tick_labels = [
    "Sun-Genomics", "Chlorophyll-Transcriptomics", "Flora-Proteomics", "Animals-Metabolomics",
    "Wood-Epigenomics", "Coal-Lipidomics", "Hydrocarbons-Glycomics", "Renewable-Metagenomics", "Nuclear-Phenomics"
]

# Calculate the angles for each tick (in radians)
angles = np.linspace(0, 2 * np.pi, number_of_ticks, endpoint=False)
# Inverting the order to make it counterclockwise
angles = angles[::-1]

# Create figure and axis
fig, ax = plt.subplots(figsize=(8, 8))
ax.set_xlim(-1.2, 1.2)
ax.set_ylim(-1.2, 1.2)
ax.set_aspect('equal')

# Draw the clock face
clock_face = plt.Circle((0, 0), clock_face_radius, color='lightgrey', fill=True)
ax.add_patch(clock_face)

# Draw the ticks and labels
for angle, label in zip(angles, tick_labels):
    x = clock_face_radius * np.cos(angle)
    y = clock_face_radius * np.sin(angle)
    
    # Draw the tick
    ax.plot([0, x], [0, y], color='black')
    
    # Positioning the labels slightly outside the clock face
    label_x = 1.1 * clock_face_radius * np.cos(angle)
    label_y = 1.1 * clock_face_radius * np.sin(angle)
    
    # Adjusting label alignment based on its position
    ha = 'center'
    va = 'center'
    if np.cos(angle) > 0:
        ha = 'left'
    elif np.cos(angle) < 0:
        ha = 'right'
    if np.sin(angle) > 0:
        va = 'bottom'
    elif np.sin(angle) < 0:
        va = 'top'
    
    ax.text(label_x, label_y, label, horizontalalignment=ha, verticalalignment=va, fontsize=10)

# Remove axes
ax.axis('off')

# Show the plot
plt.show()
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../_images/70de0a53a875dc3a54a3423648462f09ab630e23443cd31eaedf80639499556c.png
  • \(SV_t'\) Independence: modal-interchange-nondiminishing. The modes here include the -omics & so much more

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import numpy as np
import matplotlib.pyplot as plt

# Define the total utility function U(Q)
def total_utility(Q):
    return 100 * np.log(Q + 1)  # Logarithmic utility function for illustration

# Define the marginal utility function MU(Q)
def marginal_utility(Q):
    return 100 / (Q + 1)  # Derivative of the total utility function

# Generate data
Q = np.linspace(1, 100, 500)  # Quantity range from 1 to 100
U = total_utility(Q)
MU = marginal_utility(Q)

# Plotting
plt.figure(figsize=(14, 7))

# Plot Total Utility
plt.subplot(1, 2, 1)
plt.plot(Q, U, label=r'Total Utility $U(Q) = 100 \log(Q + 1)$', color='blue')
plt.title('Total Utility')
plt.xlabel('Quantity (Q)')
plt.ylabel('Total Utility (U)')
plt.legend()
plt.grid(True)

# Plot Marginal Utility
plt.subplot(1, 2, 2)
plt.plot(Q, MU, label=r'Marginal Utility $MU(Q) = \frac{dU(Q)}{dQ} = \frac{100}{Q + 1}$', color='red')
plt.title('Marginal Utility')
plt.xlabel('Quantity (Q)')
plt.ylabel('Marginal Utility (MU)')
plt.legend()
plt.grid(True)

# Adding some calculus notation and Greek symbols
plt.figtext(0.5, 0.02, r"$MU(Q) = \frac{dU(Q)}{dQ} = \lim_{\Delta Q \to 0} \frac{U(Q + \Delta Q) - U(Q)}{\Delta Q}$", ha="center", fontsize=12)

plt.tight_layout()
plt.show()
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../_images/afa91f0bcf337e9d0a0901707fe1aa1c7a332b551fb5b7af920037b2996fc9ee.png
                1. Exposure
                           \
               2. Role ->  4. Categorical.Imperative -> 5. Determinism -> 6. Freewill
                           /
                           3. Impulse

hearing

../_images/activity_counts.png

Activity Counts. While association isn’t causation, there is a strong one between hearing acuity & physical activity. Investiage “arousal” across all senses external & internal to see impact on DNA-HAT-E.Box-mRNA-Wide-Associations#

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import matplotlib.pyplot as plt
import numpy as np

# Stages of life (x-axis)
stages_of_life = [
    'Conceptus', 'Morula', 'Bilaminar Disk', 'Embryo', 'Fetus', 
    'Birth', 'Childhood', 'Adolescence', 'Adulthood', '100 Years'
]

# Approximate rate of cell-division or growth (y-axis)
growth_rate = [
    100, 90, 85, 75, 60, 30, 20, 10, 5, 2
]

# Recreate the plot with the specified style

plt.figure(figsize=(12, 6))
plt.plot(stages_of_life, growth_rate, marker='o', linestyle='-', color='blue')

# Remove upper and right borders
ax = plt.gca()
ax.spines['top'].set_visible(False)
ax.spines['right'].set_visible(False)

# Add labels and title
plt.xlabel('Stage of Life')
plt.ylabel('Rate of Cell-Division/Growth')
plt.title('Rate of Cell-Division/Growth from Conceptus to 100 Years')

# Annotate the stages
for i, txt in enumerate(growth_rate):
    plt.annotate(txt, (stages_of_life[i], growth_rate[i]), textcoords="offset points", xytext=(0,10), ha='center')

# Add a very light dotted grid
plt.grid(True, which='both', linestyle=':', linewidth=0.5)

plt.show()
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