False nearest neighbor algorithm

Last updated

Within abstract algebra, the false nearest neighbor algorithm is an algorithm for estimating the embedding dimension. The concept was proposed by Kennel et al. (1992). [1] The main idea is to examine how the number of neighbors of a point along a signal trajectory change with increasing embedding dimension. In too low an embedding dimension, many of the neighbors will be false, but in an appropriate embedding dimension or higher, the neighbors are real. With increasing dimension, the false neighbors will no longer be neighbors. Therefore, by examining how the number of neighbors change as a function of dimension, an appropriate embedding can be determined. [2] [3]

See also

Related Research Articles

<span class="mw-page-title-main">Roton</span> Collective excitation in superfluid helium-4 (a quasiparticle)

In theoretical physics, a roton is an elementary excitation, or quasiparticle, seen in superfluid helium-4 and Bose–Einstein condensates with long-range dipolar interactions or spin-orbit coupling. The dispersion relation of elementary excitations in this superfluid shows a linear increase from the origin, but exhibits first a maximum and then a minimum in energy as the momentum increases. Excitations with momenta in the linear region are called phonons; those with momenta close to the minimum are called rotons. Excitations with momenta near the maximum are called maxons.

Numerical relativity is one of the branches of general relativity that uses numerical methods and algorithms to solve and analyze problems. To this end, supercomputers are often employed to study black holes, gravitational waves, neutron stars and many other phenomena governed by Einstein's theory of general relativity. A currently active field of research in numerical relativity is the simulation of relativistic binaries and their associated gravitational waves.

In quantum mechanics, separable states are quantum states belonging to a composite space that can be factored into individual states belonging to separate subspaces. A state is said to be entangled if it is not separable. In general, determining if a state is separable is not straightforward and the problem is classed as NP-hard.

In metric theories of gravitation, particularly general relativity, a static spherically symmetric perfect fluid solution is a spacetime equipped with suitable tensor fields which models a static round ball of a fluid with isotropic pressure.

<span class="mw-page-title-main">Bak–Sneppen model</span>

The Bak–Sneppen model is a simple model of co-evolution between interacting species. It was developed to show how self-organized criticality may explain key features of the fossil record, such as the distribution of sizes of extinction events and the phenomenon of punctuated equilibrium. It is named after Per Bak and Kim Sneppen.

A two-dimensional electron gas (2DEG) is a scientific model in solid-state physics. It is an electron gas that is free to move in two dimensions, but tightly confined in the third. This tight confinement leads to quantized energy levels for motion in the third direction, which can then be ignored for most problems. Thus the electrons appear to be a 2D sheet embedded in a 3D world. The analogous construct of holes is called a two-dimensional hole gas (2DHG), and such systems have many useful and interesting properties.

CLEO was a general purpose particle detector at the Cornell Electron Storage Ring (CESR), and the name of the collaboration of physicists who operated the detector. The name CLEO is not an acronym; it is short for Cleopatra and was chosen to go with CESR. CESR was a particle accelerator designed to collide electrons and positrons at a center-of-mass energy of approximately 10 GeV. The energy of the accelerator was chosen before the first three bottom quark Upsilon resonances were discovered between 9.4 GeV and 10.4 GeV in 1977. The fourth Υ resonance, the Υ(4S), was slightly above the threshold for, and therefore ideal for the study of, B meson production.

In statistical physics, the axialnext-nearest neighbor Ising model, usually known as the ANNNI model, is a variant of the Ising model in which competing ferromagnetic and antiferromagnetic exchange interactions couple spins at nearest and next-nearest neighbor sites along one of the crystallographic axes of the lattice. The model is a prototype for complicated spatially modulated magnetic superstructures in crystals.

The percolation threshold is a mathematical concept in percolation theory that describes the formation of long-range connectivity in random systems. Below the threshold a giant connected component does not exist; while above it, there exists a giant component of the order of system size. In engineering and coffee making, percolation represents the flow of fluids through porous media, but in the mathematics and physics worlds it generally refers to simplified lattice models of random systems or networks (graphs), and the nature of the connectivity in them. The percolation threshold is the critical value of the occupation probability p, or more generally a critical surface for a group of parameters p1, p2, ..., such that infinite connectivity (percolation) first occurs.

Mitsutaka Fujita was a Japanese physicist. He proposed the edge state that is unique to graphene zigzag edges. Also, he theoretically pointed out the importance and peculiarity of nanoscale and edge shape effects in nanographene. The theoretical concept of graphene nanoribbons was introduced by him and his research group to study the nanoscale effect of graphene. He was an associate professor at Tsukuba University, and died of a subarachnoid hemorrhage on March 18, 1998. His posthumous name is Rikakuin-Shinju-Houkou-Koji (理覚院深珠放光居士) in Japanese.

The Wolff algorithm, named after Ulli Wolff, is an algorithm for Monte Carlo simulation of the Ising model and Potts model in which the unit to be flipped is not a single spin but a cluster of them. This cluster is defined as the set of connected spins sharing the same spin states, based on the Fortuin-Kasteleyn representation.

In the context of the physical and mathematical theory of percolation, a percolation transition is characterized by a set of universal critical exponents, which describe the fractal properties of the percolating medium at large scales and sufficiently close to the transition. The exponents are universal in the sense that they only depend on the type of percolation model and on the space dimension. They are expected to not depend on microscopic details such as the lattice structure, or whether site or bond percolation is considered. This article deals with the critical exponents of random percolation.

<span class="mw-page-title-main">Epidemic models on lattices</span>

Classic epidemic models of disease transmission are described in Compartmental models in epidemiology. Here we discuss the behavior when such models are simulated on a lattice. Lattice models, which were first explored in the context of cellular automata, act as good first approximations of more complex spatial configurations, although they do not reflect the heterogeneity of space. Lattice-based epidemic models can also be implemented as fixed agent-based models.

<span class="mw-page-title-main">Modern searches for Lorentz violation</span> Overview about the modern searches for Lorentz violation

Modern searches for Lorentz violation are scientific studies that look for deviations from Lorentz invariance or symmetry, a set of fundamental frameworks that underpin modern science and fundamental physics in particular. These studies try to determine whether violations or exceptions might exist for well-known physical laws such as special relativity and CPT symmetry, as predicted by some variations of quantum gravity, string theory, and some alternatives to general relativity.

<span class="mw-page-title-main">Interatomic potential</span> Functions for calculating potential energy

Interatomic potentials are mathematical functions to calculate the potential energy of a system of atoms with given positions in space. Interatomic potentials are widely used as the physical basis of molecular mechanics and molecular dynamics simulations in computational chemistry, computational physics and computational materials science to explain and predict materials properties. Examples of quantitative properties and qualitative phenomena that are explored with interatomic potentials include lattice parameters, surface energies, interfacial energies, adsorption, cohesion, thermal expansion, and elastic and plastic material behavior, as well as chemical reactions.

<span class="mw-page-title-main">Random sequential adsorption</span>

Random sequential adsorption (RSA) refers to a process where particles are randomly introduced in a system, and if they do not overlap any previously adsorbed particle, they adsorb and remain fixed for the rest of the process. RSA can be carried out in computer simulation, in a mathematical analysis, or in experiments. It was first studied by one-dimensional models: the attachment of pendant groups in a polymer chain by Paul Flory, and the car-parking problem by Alfréd Rényi. Other early works include those of Benjamin Widom. In two and higher dimensions many systems have been studied by computer simulation, including in 2d, disks, randomly oriented squares and rectangles, aligned squares and rectangles, various other shapes, etc.

Continuous-variable (CV) quantum information is the area of quantum information science that makes use of physical observables, like the strength of an electromagnetic field, whose numerical values belong to continuous intervals. One primary application is quantum computing. In a sense, continuous-variable quantum computation is "analog", while quantum computation using qubits is "digital." In more technical terms, the former makes use of Hilbert spaces that are infinite-dimensional, while the Hilbert spaces for systems comprising collections of qubits are finite-dimensional. One motivation for studying continuous-variable quantum computation is to understand what resources are necessary to make quantum computers more powerful than classical ones.

<span class="mw-page-title-main">David Tománek</span>

David Tománek (born July 1954) is a U.S.-Swiss physicist of Czech origin and researcher in nanoscience and nanotechnology. He is Emeritus Professor of Physics at Michigan State University. He is known for predicting the structure and calculating properties of surfaces, atomic clusters including the C60 buckminsterfullerene, nanotubes, nanowires and nanohelices, graphene, and two-dimensional materials including phosphorene.

The KBD algorithm is a cluster update algorithm designed for the fully frustrated Ising model in two dimensions, or more generally any two dimensional spin glass with frustrated plaquettes arranged in a checkered pattern. It is discovered in 1990 by Daniel Kandel, Radel Ben-Av, and Eytan Domany, and generalized by P. D. Coddington and L. Han in 1994. It is the inspiration for cluster algorithms used in quantum monte carlo simulations.

Quantum turbulence involves the chaotic dynamics of many interacting quantum vortices. In bulk superfluid, quantum turbulent states form a complex tangle of highly excited vortex lines. By introducing tight confinement along one direction the Kelvin wave excitations can be strongly suppressed, favouring vortex alignment with the axis of tight confinement. Vortex dynamics enters a regime of effective 2D motion, equivalent to point vortices moving on a plane. In general, 2D quantum turbulence (2DQT) can exhibit complex phenomenology involving coupled vortices and sound in compressible superfluids. The quantum vortex dynamics can exhibit signatures of turbulence including a Kolmogorov −5/3 power law, a quantum manifestation of the inertial transport of energy to large scales observed in classical fluids, known as an inverse energy cascade.

References

  1. Kennel, Matthew B.; Brown, Reggie; Abarbanel, Henry D. I. (1 March 1992). "Determining embedding dimension for phase-space reconstruction using a geometrical construction". Physical Review A. 45 (6): 3403–3411. Bibcode:1992PhRvA..45.3403K. doi:10.1103/PhysRevA.45.3403. PMID   9907388.
  2. Rhodes, C.; Morari, M. (1997). "The false nearest neighbors algorithm: An overview". Computers & Chemical Engineering. 21: S1149–S1154. doi:10.1016/S0098-1354(97)87657-0.
  3. Hegger, R.; Kantz, H. (1999). "Improved false nearest neighbor method to detect determinism in time series data". Physical Review E. 60 (4): 4970–3. Bibcode:1999PhRvE..60.4970H. doi:10.1103/PhysRevE.60.4970. PMID   11970367.