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Partial Fractions01:28

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A partial fraction is a component of a rational expression represented as the sum of simpler fractions. When a rational function is expressed as a ratio of two polynomials, it can often be decomposed into a sum of fractions whose denominators are simpler polynomials, typically linear or irreducible quadratic factors. This process is called partial fraction decomposition, and it is used to simplify complex expressions for integration, solving equations, or analysis.Partial fraction decomposition...
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Fermi Level Dynamics01:12

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The vacuum level denotes the energy threshold required for an electron to escape from a material surface. It is usually positioned above the conduction band of a semiconductor and acts as a benchmark for comparing electron energies within various materials.
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Rational functions are expressions written as the ratio of two polynomials, and their integrals are evaluated by simplifying the integrand into manageable parts. These functions are classified as proper or improper based on the degrees of the numerator and denominator.A rational function is proper when the degree of the numerator is less than the degree of the denominator. In this case, partial fraction decomposition is used to rewrite the function as a sum of simpler rational terms. The...
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James Clerk Maxwell (1831–1879) was one of the significant contributors to physics in the nineteenth century. He is probably best known for having combined existing knowledge of the laws of electricity and the laws of magnetism with his insights to form a complete overarching electromagnetic theory, represented by Maxwell's equations. The four basic laws of electricity and magnetism were discovered experimentally through the work of physicists such as Oersted, Coulomb, Gauss, and...
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A separable differential equation is a type of first-order differential equation where the derivative dy/dx can be expressed as a product of two functions: one that depends only on x and another that depends only on y. This allows for the rearrangement of the equation so that all terms involving y are on one side, and all terms involving x are on the other. This process, known as the separation of variables, simplifies the process of solving the equation by enabling the integration of both...
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Generation and Coherent Control of Pulsed Quantum Frequency Combs
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A dynamical framework for complex fractional killing.

Richard Ballweg1, Andrew L Paek2, Tongli Zhang3

  • 1Department of Molecular and Cellular Physiology, College of Medicine, University of Cincinnati, Cincinnati, OH, USA.

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|August 16, 2017
PubMed
Summary
This summary is machine-generated.

Chemotherapy causes fractional killing in cancer cells through a p53-mediated feedback loop. Understanding this dynamic process can help develop new strategies to overcome drug resistance.

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Area of Science:

  • Cancer Biology
  • Systems Biology
  • Molecular Oncology

Background:

  • Chemotherapy exhibits fractional killing, where some tumor cells survive treatment, contributing to drug resistance.
  • An incoherent feedforward loop involving p53 activation and apoptosis inhibitors drives this differential cell survival.
  • The timing of p53 activation critically determines cell fate, leading to apoptosis or survival.

Purpose of the Study:

  • To elucidate the complex dynamics of chemotherapy-induced fractional killing.
  • To develop a computational model integrating apoptosis control and signaling pathways.
  • To identify predictable frameworks for altering cancer cell fate and overcoming drug resistance.

Main Methods:

  • Construction of a computational model of apoptosis signaling pathways.
  • Model training to replicate observed fractional killing phenomena.
  • Analysis of the model using nonlinear dynamical tools.

Main Results:

  • A simple dynamical framework for fractional killing was established.
  • The framework predicts three mechanisms for altering cell fate: modifying bifurcation geometry, cell trajectories, or both.
  • These mechanisms align with existing and suggest novel strategies against fractional killing.

Conclusions:

  • Fractional killing is a complex dynamical process governed by the timing of p53 activation.
  • The proposed dynamical framework offers insights into cancer drug resistance.
  • This research facilitates the design of improved therapeutic strategies to combat cancer survival and resistance.