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Related Concept Videos

Long-Term Memory01:18

Long-Term Memory

Long-term memory is a relatively permanent type of memory, capable of storing vast amounts of information over extended periods. Its storage capacity is generally considered unlimited.
Long-term memory can be categorized into two primary types: explicit and implicit memory. Explicit memory, also known as declarative memory, involves the conscious recollection of information that we deliberately try to remember, recall, and articulate. This type of memory encompasses specific facts, events, and...
System of Memory01:23

System of Memory

Memory is categorized into three major systems: sensory memory, short-term memory (STM), and long-term memory (LTM). These systems differ in their capacity and the duration for which they can hold information. Sensory memory captures raw sensory input from the environment, holding it for just a few seconds or less. For example, on hearing a brief, loud sound, like a car horn honking, the sound seems to linger in the mind for a moment even after it stops. This is an instance of sensory memory...
Understanding Memory01:19

Understanding Memory

Memory is the retention of information or experiences over time, facilitated through three main processes: encoding, storage, and retrieval. Encoding is the process of inputting information into the memory system. For instance, when listening to a lecture, watching a play, reading a book, or having a conversation, the brain is actively encoding information. This initial stage involves transforming sensory input into a form that can be processed and stored by the brain. Various factors, such as...
Model Approaches for Pharmacokinetic Data: Distributed Parameter Models01:06

Model Approaches for Pharmacokinetic Data: Distributed Parameter Models

Pharmacokinetic models are mathematical constructs that represent and predict the time course of drug concentrations in the body, providing meaningful pharmacokinetic parameters. These models are categorized into compartment, physiological, and distributed parameter models.
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Storage01:23

Storage

A schema is a mental framework that helps individuals organize and interpret information. Schemata, formed from previous experiences, influence how we process new information: how we encode it, the inferences we make, and how we retrieve it. For instance, a schema for what a typical classroom looks like might include desks, a teacher's desk, a whiteboard, and students in such an environment. This expectation helps us quickly understand and navigate new classrooms without needing to analyze each...
Interference and Decay01:16

Interference and Decay

Forgetting is a complex cognitive phenomenon influenced by several factors, among which interference and decay are particularly prominent. These processes explain why individuals often struggle to retrieve specific information from memory, leading to lapses in recall that can be observed in everyday situations.
Interference occurs when competing memories hinder the retrieval of particular information. It can be classified into two types: proactive and retroactive interference. Proactive...

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Related Experiment Videos

Modeling long-range memory with stationary Markovian processes.

Salvatore Miccichè1

  • 1Dipartimento di Fisica e Tecnologie Relative, Università degli Studi di Palermo, Viale delle Scienze, Ed. 18, I-90128 Palermo, Italy.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|April 28, 2009
PubMed
Summary

This study demonstrates how coordinate transformations of power-law processes create new stationary Markovian processes. These processes exhibit Gaussian or exponential tails but retain long-range correlations with power-law decay in their autocorrelation functions.

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Area of Science:

  • Statistical physics
  • Stochastic processes
  • Complex systems

Background:

  • Long-range correlated processes are crucial for modeling complex systems.
  • Stationary Markovian processes typically exhibit short-range dependence.
  • Understanding the interplay between process tails and autocorrelation is key.

Purpose of the Study:

  • To construct long-range correlated stationary Markovian processes with Gaussian or exponential tails.
  • To investigate the relationship between autocorrelation decay and probability density function (pdf) tails.
  • To clarify the association between long-range dependence and extreme events.

Main Methods:

  • Coordinate transformation of a known power-law correlated process.
  • Analytical derivations of autocorrelation function decay.
  • Numerical simulations to verify theoretical findings.
  • Investigation of generic continuous and monotonically increasing transformations.

Main Results:

  • Generated stationary Markovian processes with Gaussian/exponential tails and power-law decaying autocorrelation with logarithmic corrections.
  • Established an analytical link between autocorrelation decay and pdf tails for generic transformations.
  • Demonstrated that long-range dependence does not necessitate extreme events.

Conclusions:

  • Stationary Markovian processes can exhibit long-range correlations without necessarily producing extreme events.
  • Coordinate transformations offer a simple method to model long-memory effects in continuous-time stationary Markovian processes.
  • Findings are relevant for modeling complex systems with memory.