•Journal•ISSN: 1941-6016
Scholarpedia
Scholarpedia Corporation
About: Scholarpedia is an academic journal published by Scholarpedia Corporation. The journal publishes majorly in the area(s): Saddle-node bifurcation & Pitchfork bifurcation. It has an ISSN identifier of 1941-6016. It is also open access. Over the lifetime, 515 publications have been published receiving 26182 citations. The journal is also known as: Scholarpedia: The Peer-Reviewed Open-Access Encyclopedia.
Topics: Saddle-node bifurcation, Pitchfork bifurcation, Bogdanov–Takens bifurcation, Quantum gravity, Quantum chaos
Papers published on a yearly basis
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1,862 citations
TL;DR: The study of waves can be traced back to antiquity where philosophers, such as Pythagoras, studied the relation of pitch and length of string in musical instruments and the subject of classical acoustics was laid down and presented as a coherent whole by John William Strutt in his treatise Theory of Sound.
Abstract: The study of waves can be traced back to antiquity where philosophers, such as Pythagoras (c.560-480 BC), studied the relation of pitch and length of string in musical instruments. However, it was not until the work of Giovani Benedetti (1530-90), Isaac Beeckman (1588-1637) and Galileo (1564-1642) that the relationship between pitch and frequency was discovered. This started the science of acoustics, a term coined by Joseph Sauveur (1653-1716) who showed that strings can vibrate simultaneously at a fundamental frequency and at integral multiples that he called harmonics. Isaac Newton (1642-1727) was the first to calculate the speed of sound in his Principia. However, he assumed isothermal conditions so his value was too low compared with measured values. This discrepancy was resolved by Laplace (1749-1827) when he included adiabatic heating and cooling effects. The first analytical solution for a vibrating string was given by Brook Taylor (1685-1731). After this, advances were made by Daniel Bernoulli (1700-82), Leonard Euler (1707-83) and Jean d’Alembert (1717-83) who found the first solution to the linear wave equation, see section (3.2). Whilst others had shown that a wave can be represented as a sum of simple harmonic oscillations, it was Joseph Fourier (1768-1830) who conjectured that arbitrary functions can be represented by the superposition of an infinite sum of sines and cosines now known as the Fourier series. However, whilst his conjecture was controversial and not widely accepted at the time, Dirichlet subsequently provided a proof, in 1828, that all functions satisfying Dirichlet’s conditions (i.e. non-pathological piecewise continuous) could be represented by a convergent Fourier series. Finally, the subject of classical acoustics was laid down and presented as a coherent whole by John William Strutt (Lord Rayleigh, 1832-1901) in his treatise Theory of Sound. The science of modern acoustics has now moved into such diverse areas as sonar, auditoria, electronic amplifiers, etc.
1,428 citations
TL;DR: The basic principles of MR Signal Generation, Signal, Noise, and Preprocessing of fMRI Data, and Ethical Issues in fMRI Research are outlined.
Abstract: 1. An Introduction to fMRI 2. MRI Scanners 3. Basic Principles of MR Signal Generation 4. Basic Principles of MR Image Formation 5. MR Contrast Mechanisms and Acquisition Techniques 6. From Neuronal to Hemodynamic Activity 7. Properties of the fMRI BOLD Response 8. Signal, Noise, and Preprocessing of fMRI Data 9. Experimental Design 10. Statistical Analysis I: Hypothesis Testing 11. Statistical Analysis II: Data-Driven Approaches 12. Applications of fMRI 13. Converging Operations 14. Ethical Issues in fMRI Research
1,308 citations