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Cells and Cancer in Python

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import matplotlib.pyplot as plt import numpy as np # Plot 1: Order Parameter vs Time (S vs t) t = np.linspace(0, 10, 500) S = 1 / (1 + np.exp(-2 * (t - 5)))  # sigmoid rise plt.figure() plt.plot(t, S) plt.title(" Order Parameter S vs Time ") plt.xlabel("Time (t)") plt.ylabel("Order Parameter (S)") plt.grid(True) plt.show() # Plot 2: Energy Collapse E = np.maximum(0, 1 - 0.1 * t**1.5) plt.figure() plt.plot(t, E, color='red') plt.title(" Cellular Energy (E) Collapse Over Time ") plt.xlabel("Time (t)") plt.ylabel("Energy (E)") plt.grid(True) plt.show() # Plot 3: Standing Wave Stability x = np.linspace(0, 2*np.pi, 500) standing_wave = np.sin(x) * np.cos(5 * x) plt.figure() plt.plot(x, standing_wave) plt.title(" Standing Wave Pattern Around DNA ") plt.xlabel("Distance") plt.ylabel("Amplitude") plt.grid(True) plt.show() # Plot 4: DNA Repair Rate vs Redox State redox = np.linspace(0, 1, 100) repa...
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Modeling the Bond Market as a First Order Lag

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Dynamics of U.S. Treasury Yields as a First-Order Lag System under Macroeconomic Shocks Introduction U.S. Treasury bonds across the maturity spectrum (from short-term bills to long-term bonds) exhibit distinct dynamic responses to macroeconomic events. When a clearly timestamped event occurs – such as a tariff announcement, a fiscal policy change, a central bank interest rate decision, or a major geopolitical action – bond yields typically move as the market processes the new information ( Yield curve - Wikipedia ). Rather than changing instantaneously to a new equilibrium, yields often adjust with a lag : an initial jump or dip is followed by a gradual approach toward a new level or a reversion back to the prior trend. This behavior suggests that the bond market might be viewed through the lens of control theory , treating yields as the output of a system responding over time to an input shock. In particular, an intriguing question is whether Treasury yields can be modeled as firs...
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John

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John Historical Accounts Early non-biblical sources about John the Apostle are limited. The Jewish historian Josephus, who mentions other New Testament figures (like John the Baptist), makes no mention of John, son of Zebedee ( 1 ). Likewise, there are no direct Roman records naming John; references to Christian persecution under Roman emperors (e.g. by Tacitus or Suetonius) do not cite John individually. Knowledge of John instead comes from early Christian writers. The 2nd-century bishop Irenaeus of Lyons (a student of Polycarp, who in turn was a disciple of John) testified that John lived in Ephesus until the reign of Emperor Trajan (98–117 AD) ( 2 ) ( 3 ). Irenaeus also recorded the tradition that John “ did himself write a Gospel during his residence at Ephesus ” after the other Gospels were written ( 4 ). Another early source, Polycrates of Ephesus (c. 190 AD), wrote that “John, who rested upon the bosom of the Lord... fell asleep at Ephesus ” ( 5 ), confirming the belief ...
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