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Related Concept Videos

Linear time-invariant Systems01:23

Linear time-invariant Systems

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A system is linear if it displays the characteristics of homogeneity and additivity, together termed the superposition property. This principle is fundamental in all linear systems. Linear time-invariant (LTI) systems include systems with linear elements and constant parameters.
The input-output behavior of an LTI system can be fully defined by its response to an impulsive excitation at its input. Once this impulse response is known, the system's reaction to any other input can be...
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Stability01:28

Stability

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The time response of a linear time-invariant (LTI) system can be divided into transient and steady-state responses. The transient response represents the system's initial reaction to a change in input and diminishes to zero over time. In contrast, the steady-state response is the behavior that persists after the transient effects have faded.
The stability of an LTI system is determined by the roots of its characteristic equation, known as poles. A system is stable if it produces a bounded...
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Construction of Root Locus01:15

Construction of Root Locus

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The construction of a root locus involves several key steps to analyze and visualize the behavior of a system's poles with varying gain. The number of branches in the root locus equals the number of closed-loop poles and is symmetrical about the real axis.
For positive gain values, the root locus exists on the real axis to the left of an odd number of finite open-loop poles or zeros. The root locus starts at the open-loop poles and traces the paths of the closed-loop poles as the gain...
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Root Loci for Positive-Feedback Systems01:23

Root Loci for Positive-Feedback Systems

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The Hartley oscillator is a positive feedback system that sustains oscillations by feeding the output back to the input in phase, thereby reinforcing the signal. Positive feedback systems can be viewed as negative feedback systems with inverted feedback signals. In these systems, the root locus encompasses all points on the s-plane where the angle of the system transfer function equals 360 degrees.
The construction rules for the root locus in positive feedback systems are similar to those in...
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Simplified Synchronous Machine Model01:30

Simplified Synchronous Machine Model

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The Synchronous Machine Model is a fundamental tool in analyzing and ensuring the transient stability of power systems. This model simplifies the representation of a synchronous machine under balanced three-phase positive-sequence conditions, assuming constant excitation and ignoring losses and saturation. The model is pivotal for understanding the behavior of synchronous generators connected to a power grid, particularly during transient events.
In this model, each generator is connected to a...
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Classification of Systems-I01:26

Classification of Systems-I

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Linearity is a system property characterized by a direct input-output relationship, combining homogeneity and additivity.
Homogeneity dictates that if an input x(t) is multiplied by a constant c, the output y(t) is multiplied by the same constant. Mathematically, this is expressed as:
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Related Experiment Video

Updated: Apr 4, 2026

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline
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ILP/SMT-Based Method for Design of Boolean Networks Based on Singleton Attractors.

Koichi Kobayashi, Kunihiko Hiraishi

    IEEE/ACM Transactions on Computational Biology and Bioinformatics
    |September 11, 2015
    PubMed
    Summary
    This summary is machine-generated.

    This study introduces a new method for designing gene regulatory networks with specific fixed points using Boolean networks. The approach utilizes matrix representations to solve Integer Linear Programming and Satisfiability Modulo Theories problems for network design.

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    Area of Science:

    • Systems Biology
    • Synthetic Biology
    • Computational Biology

    Background:

    • Gene regulatory networks (GRNs) govern cellular functions and states.
    • Attractors in GRNs, particularly fixed points, represent stable cell types or states.
    • Designing GRNs with specific attractors is crucial for systems and synthetic biology applications.

    Purpose of the Study:

    • To develop a method for constructing Boolean networks (BNs) with desired singleton attractors (fixed points).
    • To ensure the designed BNs lack undesired fixed points.
    • To provide a foundational approach for the rational design of gene regulatory networks.

    Main Methods:

    • A matrix-based representation for Boolean networks (BNs) was developed.
    • The problem of finding suitable Boolean functions was reformulated as an Integer Linear Programming (ILP) problem.
    • The problem was also reformulated as a Satisfiability Modulo Theories (SMT) problem.

    Main Results:

    • The proposed matrix-based approach enables the identification of Boolean functions for desired network attractors.
    • The ILP and SMT formulations provide computational frameworks for solving the network design problem.
    • A numerical example using the WNT5A network demonstrated the method's effectiveness.

    Conclusions:

    • The developed matrix-based method offers a systematic approach to designing gene regulatory networks with specific fixed points.
    • This work provides a fundamental tool for synthetic biology and systems biology, enabling the engineering of cellular functions.
    • The WNT5A network example highlights the practical applicability in biological contexts like melanoma research.