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Related Concept Videos

Constraints and Statical Determinacy01:26

Constraints and Statical Determinacy

In structural engineering, the equilibrium of a system is not only determined by its equations of equilibrium but also with the help of constraints. Constraints refer to restrictions on the motion of a system. The proper combinations of constraints can minimize the total number of constraints needed to maintain a system in mechanical equilibrium. When this happens, the system is said to be statically determinate. For such systems, the unknown reaction supports can be estimated using equilibrium...
Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
Lagrange Multipliers: Two Constraints01:28

Lagrange Multipliers: Two Constraints

The method of Lagrange multipliers with two constraints is used to optimize a function subject to two independent constraints. In many applications, the objective function represents a quantity to be maximized or minimized, such as cost, area, distance, or energy. The two constraints represent requirements that the solution must satisfy, such as fixed volume, limited resources, or prescribed dimensions.For a function of three variables, each constraint forms a surface in three-dimensional space.
Combinatorial Gene Control02:33

Combinatorial Gene Control

Combinatorial gene control is the synergistic action of several transcriptional factors to regulate the expression of a single gene. The absence of one or more of these factors may lead to a significant difference in the level of gene expression or repression.
The expression of more than 30,000 genes is controlled by approximately 2000-3000 transcription factors. This is possible because a single transcription factor can recognize more than one regulatory sequence. The specificity in gene...
Lagrange Multipliers: One Constraint01:29

Lagrange Multipliers: One Constraint

In constrained optimization, the objective is to maximize or minimize a quantity while satisfying a fixed condition. A standard example is a rectangular pen built against a barn wall using 100 meters of fencing. Because the wall provides one side of the enclosure, only the other three sides require fencing. The problem is to find the dimensions that produce the greatest possible area.Let L represent the length parallel to the wall and W the width perpendicular to it. The area of the pen is A =...
Statically Indeterminate Problem Solving01:16

Statically Indeterminate Problem Solving

Statically indeterminate problems are those where statics alone can not determine the internal forces or reactions. Consider a structure comprising two cylindrical rods made of steel and brass. These rods are joined at point B and restrained by rigid supports at points A and C. Now, the reactions at points A and C and the deflection at point B are to be determined. This rod structure is classified as statically indeterminate as the structure has more supports than are necessary for maintaining...

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Related Experiment Videos

Optimal control policy for probabilistic Boolean networks with hard constraints.

W-K Ching1, S-Q Zhang, Y Jiao

  • 1The University of Hong Kong, Advanced Modeling and Applied Computing Laboratory, Department of Mathematics, Hong Kong, People's Republic of China.

IET Systems Biology
|March 19, 2009
PubMed
Summary

This study introduces a new method for controlling gene regulatory networks, incorporating treatment limits to prevent excessive side effects in diseases like cancer. The approach optimizes gene interventions within practical constraints for better patient outcomes.

Related Experiment Videos

Area of Science:

  • Systems Biology
  • Computational Biology
  • Biophysics

Background:

  • Genetic regulatory networks govern cellular functions and disease states.
  • Controlling gene expression is crucial for treating diseases like cancer.
  • Boolean networks (BNs) and probabilistic Boolean networks (PBNs) model these complex systems.

Purpose of the Study:

  • To develop an optimal finite-horizon control method for PBNs that includes hard constraints on the number of interventions.
  • To address the limitations of previous control strategies that did not consider treatment capacity or potential side effects.
  • To propose an approximation method for reducing computational cost in solving the constrained optimal control problem.

Main Methods:

  • Formulation of a state-independent optimal finite-horizon control problem for PBNs with upper bounds on control applications.
  • Objective function focused on the distance between desirable and terminal states.
  • Development of an approximation algorithm to enhance computational efficiency.

Main Results:

  • A novel formulation for constrained optimal control in PBNs was successfully developed.
  • An approximation method was introduced, demonstrating efficiency in reducing computational load.
  • Experimental results validated the effectiveness of the proposed formulations and methods.

Conclusions:

  • The proposed constrained optimal control framework offers a more realistic approach to gene regulatory network intervention.
  • The method accounts for practical limitations in treatment application, crucial for clinical relevance.
  • The study provides efficient computational tools for designing targeted gene therapies.