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Related Concept Videos

Switching of BJT01:22

Switching of BJT

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Switching behavior in Bipolar Junction Transistors (BJTs) is a fundamental aspect utilized in various electronic circuits, particularly for digital logic applications like switches and amplifiers. In a typical switching circuit, a BJT alternates between cut-off and saturation modes, corresponding to the "off" and "on" states, respectively, thus behaving like an ideal switch.
Cut-off Mode ("Off" State): In this state, both the emitter-base and collector-base junctions are...
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Sampling Continuous Time Signal01:11

Sampling Continuous Time Signal

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In signal processing, a continuous-time signal can be sampled using an impulse-train sampling technique, followed by the zero-order hold method. Impulse-train sampling involves the use of a periodic impulse train, which consists of a series of delta functions spaced at regular intervals determined by the sampling period. When a continuous-time signal is multiplied by this impulse train, it generates impulses with amplitudes corresponding to the signal's values at the sampling points.
In the...
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Upsampling01:22

Upsampling

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Managing signal sampling rates is essential in digital signal processing to maintain signal integrity. A decimated signal, characterized by a reduced frequency range due to its lower sampling rate, can be upsampled by inserting zeros between each sample. This upsampling process expands the original spectrum and introduces repeated spectral replicas at intervals dictated by the new Nyquist frequency. To refine this zero-inserted sequence, it is passed through a lowpass filter with a cutoff...
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Clipper Circuit01:18

Clipper Circuit

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A clipper circuit is a fundamental wave-shaping device that harnesses the unique properties of diodes to alter and control waveform characteristics. This technology is widely used in electronic devices, especially in television and radar communication systems, where it enhances waveform modulation in both transmitters and receivers.
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Downsampling01:20

Downsampling

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When considering a sampled sequence with zero values between sampling instants, one can replace it by taking every N-th value of the sequence. At these integer multiples of N, the original and sampled sequences coincide. This process, known as decimation, involves extracting every N-th sample from a sequence, thereby creating a more efficient sequence.
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Transient and Steady-state Response01:24

Transient and Steady-state Response

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In control systems, test signals are essential for evaluating performance under various conditions. The ramp function is effective for systems undergoing gradual changes, while the step function is suitable for assessing systems facing sudden disturbances. For systems subjected to shock inputs, the impulse function is the most appropriate test signal.
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Related Experiment Video

Updated: Jun 30, 2025

Automated, Quantitative Cognitive/Behavioral Screening of Mice: For Genetics, Pharmacology, Animal Cognition and Undergraduate Instruction
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Truncated stochastically switching processes.

Paul C Bressloff1

  • 1Department of Mathematics, Imperial College London, London SW7 2AZ, United Kingdom.

Physical Review. E
|March 16, 2024
PubMed
Summary

This study explores how limiting switching events in hybrid stochastic systems, like those in neural dynamics or particle search, impacts their behavior. Restricting switches modifies system dynamics and search efficiency, offering insights into energy-costly processes.

Area of Science:

  • * Stochastic processes
  • * Statistical physics
  • * Mathematical biology

Background:

  • * Hybrid stochastic systems couple continuous dynamics with discrete state switching.
  • * Examples include neuron potentials, gene networks, and active particle motion.
  • * Stochastic resetting involves particles returning to a fixed point at random times.

Purpose of the Study:

  • * Investigate the impact of a maximum number of switching events within a time interval.
  • * Motivated by energy costs associated with each switch.
  • * Analyze modifications to hybrid stochastic differential equations (hSDEs) and diffusive search processes.

Main Methods:

  • * Analyzing hybrid stochastic differential equations (hSDEs).
  • * Truncating Volterra series expansions for particle propagators and survival probabilities.

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  • * Calculating splitting probabilities and conditional mean first passage times (MFPTs).

    • Main Results:

    • * For hSDEs, limiting switches is equivalent to truncating Volterra series, altering propagator moments.
    • * For diffusive search, limiting resets affects absorption probabilities and search efficiency.
    • * Truncation of Volterra series yields specific calculations for splitting probabilities and conditional MFPTs.

    Conclusions:

    • * Fixing the maximum number of switching events significantly alters the behavior of stochastic systems.
    • * This constraint introduces a form of renormalization in hybrid stochastic differential equations.
    • * The findings have implications for understanding energy-constrained search and dynamic processes.