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Related Concept Videos

Phasor Arithmetics01:13

Phasor Arithmetics

Phasors and their corresponding sinusoids are interrelated, offering unique insights into the behavior of alternating current (AC) circuits. One way to understand this relationship is through the operations of differentiation and integration in both the time and phasor domains.
When the derivative of a sinusoid is taken in the time domain, it transforms into its corresponding phasor multiplied by j-omega (jω) in the phasor domain, where j is the imaginary unit, and ω is the angular frequency.
Phasors01:12

Phasors

Phasors are a powerful mathematical tool used to analyze alternating current (AC) circuits. They provide a complex number representation of sinusoids, with the magnitude of the phasor equating to the amplitude of the sinusoid and the angle of the phasor representing the phase measured from the positive x-axis.
One of the significant benefits of using phasors is that they simplify the analysis of AC circuits by eliminating the time dependence of the current and voltage. This transformation...
Phasor Relationships for Circuit Elements01:16

Phasor Relationships for Circuit Elements

Phasor representation is a powerful tool used to transform the voltage-current relationship for resistors, inductors, and capacitors from the time domain to the frequency domain. This transformation simplifies the analysis of alternating current (AC) circuits.
In the time domain, Ohm's law provides a fundamental relation between the current flowing through a resistor and the voltage across it:
Kirchoff's Laws using Phasors01:12

Kirchoff's Laws using Phasors

Analyzing AC circuits in electrical systems is a fundamental aspect of electrical engineering. In these circuits, AC power is supplied from a distribution panel and wired to various household appliances in parallel. To perform a comprehensive analysis, electrical engineers use Kirchhoff's voltage and current laws, which are equally applicable in AC circuits as in DC circuits.
Kirchhoff's voltage law (KVL) states that the sum of phasor voltages around a closed loop in an AC circuit equals zero.
Harmonic Mean01:09

Harmonic Mean

The arithmetic mean is usually skewed towards the larger values in the data set. Therefore, to avoid this inherent bias towards smaller values, the harmonic mean is used.
Take the example of the speed of a car, which is the measure of the rate of distance traveled. If the vehicle traverses the same distance back-and-forth, its average speed equals the total distance traveled divided by the total time taken. However, if the car moves with varying speeds, then the arithmetic mean is more skewed...
Neural Circuits01:25

Neural Circuits

Neural circuits and neuronal pools are two of the main structures found in the nervous system. Neural circuits are networks of neurons that work together to carry out a specific task or process. They consist of interconnected neurons and glial cells, which provide structural and metabolic support.
Neuronal pools are collections of nerve cells with similar functions and interact through chemical and electrical signals. These pools include both interneurons (the central neural circuit nodes that...

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Related Experiment Videos

Harmonic memory in phasor neural networks.

F Hoppensteadt1

  • 1Courant Institute of Mathematical Sciences, New York University, New York, US. fh21@nyu.edu.

Biological Cybernetics
|June 22, 2026
PubMed
Summary
This summary is machine-generated.

Stable collective phase patterns emerge in coupled inertial phasor units. A feedback structure reveals a geometric theory of harmonic memory, where resonant harmonics select memory loops for recall.

Related Experiment Videos

Area of Science:

  • Physics
  • Complex Systems
  • Nonlinear Dynamics

Background:

  • Coupled oscillators can exhibit stable collective behaviors.
  • Phasor units and their interactions are key to understanding complex system dynamics.
  • Feedback mechanisms are crucial for emergent properties in physical systems.

Purpose of the Study:

  • To investigate stable collective phase patterns in an array of inertial phasor units.
  • To explore the role of a closed array-interface-substrate feedback structure.
  • To develop a geometric theory of harmonic memory within this system.

Main Methods:

  • Modeling an array of inertial phasor units with device-level angular coordinates.
  • Analyzing the interface's production of harmonics indexed by integer mode vectors.
  • Investigating substrate feedback in gradient form generated by a harmonic potential.

Main Results:

  • Identified stable phase-locked periodic solutions (memory loops) selected by resonant harmonics.
  • Demonstrated that memory recall is achieved by tuning drive parameters to a harmonic channel.
  • Observed relaxation toward recurrent activity in the array during memory recall.

Conclusions:

  • The array-interface-substrate feedback structure supports a geometric theory of harmonic memory.
  • Resonance plays a critical role in selecting and recalling stored patterns.
  • Attentional control variables can tune the system towards specific memory channels.