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Related Concept Videos

Downsampling01:20

Downsampling

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.
The Fourier transform of the decimated sequence reveals a combination of scaled and shifted versions of the original spectrum. This...
Sampling Methods: Overview01:06

Sampling Methods: Overview

A sample refers to a smaller subset representative of a larger population. In analytical chemistry, studying or analyzing an entire population is often impractical or impossible. Therefore, samples are used to draw inferences and generalize the whole population. The sampling method selects individuals or items from a population to create a sample. Standard sampling methods include random, judgemental, systematic, stratified, and cluster sampling. 
In analytical chemistry, the choice of sampling...
Upsampling01:22

Upsampling

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...
Extraction: Partition and Distribution Coefficients01:14

Extraction: Partition and Distribution Coefficients

The distribution law or Nernst's distribution law is the law that governs the distribution of a solute between two immiscible solvents. This law, also known as the partition law, states that if a solute is added to the mixture of two immiscible solvents at a constant temperature, the solute is distributed between the two solvents in such a way that the ratio of solute concentrations in the solvents remains constant at equilibrium.
For extracting a solute from an aqueous phase into an organic...
Sampling Methods: Sample Types01:18

Sampling Methods: Sample Types

Sampling materials are classified into three main types: solid, liquid, and gas.
Solid samples include a variety of substances, such as sediments from water bodies, soil, metals, and biological tissues. Two standard methods for extracting sediments from water bodies are grab sampling and piston coring. Grab sampling involves using a device to collect a discrete sediment sample from the bottom of a water body with minimal disturbance. Grab samples do not always represent the entire area due to...
One-Compartment Open Model: Wagner-Nelson and Loo Riegelman Method for ka Estimation01:24

One-Compartment Open Model: Wagner-Nelson and Loo Riegelman Method for ka Estimation

This lesson introduces two critical methods in pharmacokinetics, the Wagner-Nelson and Loo-Riegelman methods, used for estimating the absorption rate constant (ka) for drugs administered via non-intravenous routes. The Wagner-Nelson method relates ka to the plasma concentration derived from the slope of a semilog percent unabsorbed time plot. However, it is limited to drugs with one-compartment kinetics and can be impacted by factors like gastrointestinal motility or enzymatic degradation.
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Low-sampling-rate Kramers-Moyal coefficients.

C Anteneodo1, S M Duarte Queirós

  • 1Department of Physics, PUC-Rio and National Institute of Science and Technology for Complex Systems, Rua Marquês de São Vicente 225, Gávea, CEP 22453-900 Rio de Janeiro, RJ, Brazil.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|January 15, 2011
PubMed
Summary
This summary is machine-generated.

The sampling interval significantly impacts Kramers-Moyal coefficient estimation. Understanding this relationship is crucial for accurate data-driven analysis and extracting meaningful information from stochastic processes.

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Area of Science:

  • * Stochastic processes and statistical physics.
  • * Data analysis and information theory.

Background:

  • * Kramers-Moyal coefficients are essential for characterizing the dynamics of stochastic processes.
  • * Accurate estimation of these coefficients is vital for data-driven analysis.

Purpose of the Study:

  • * To investigate the influence of sampling interval on Kramers-Moyal coefficient estimation.
  • * To provide finite-time expressions for standard processes and reference limits.

Main Methods:

  • * Derivation of finite-time expressions for Kramers-Moyal coefficients.
  • * Analysis of limiting cases: independence and no-fluctuation limits.

Main Results:

  • * The sampling interval demonstrably affects the accuracy of Kramers-Moyal coefficient estimation.
  • * Finite-time expressions were derived for several standard stochastic processes.
  • * Extreme limits provide valuable benchmarks for coefficient estimation.

Conclusions:

  • * The choice of sampling interval is a critical parameter in Kramers-Moyal analysis.
  • * The derived expressions and analyzed limits facilitate more reliable information extraction from data.
  • * This work aids in the proper application of data-driven methods for understanding complex systems.