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coupling reaction. In 1981, Kagan and collaborators described the first non-linear effects in asymmetric catalysis and gave rational explanations for these phenomena
Non-linear_effects
Statistical model containing both fixed effects and random effects
will discuss mainly linear mixed-effects models rather than generalized linear mixed models or nonlinear mixed-effects models. Linear mixed models (LMMs)
Mixed_model
Non linear piezoelectric effects in polar semiconductors are the manifestation that the strain induced piezoelectric polarization depends not just on the
Non linear piezoelectric effects in polar semiconductors
Non_linear_piezoelectric_effects_in_polar_semiconductors
Non-destructive audio, video, or image editing
Non-linear editing (NLE) is a form of offline editing for audio, video, and image editing. In offline editing, the original content is not modified in
Non-linear_editing
Approximation method in statistics
Non-linear least squares is the form of least squares analysis used to fit a set of m observations with a model that is non-linear in n unknown parameters
Non-linear_least_squares
Undesired resistance, inductance, or capacitance within electrical components
functions. The parasitic effects in the dielectric of capacitors and parasitic magnetic effects in inductors also include non-linear effects that vary with frequency
Parasitic_impedance
Statistical model
fixed effects. They also inherit from generalized linear models the idea of extending linear mixed models to non-normal data. Generalized linear mixed
Generalized linear mixed model
Generalized_linear_mixed_model
American chemist
development of Reaction Progress Kinetic Analysis (RPKA), analysis of non-linear effects of catalyst enantiopurity, biological homochirality, and amino acid
Donna_Blackmond
Statistical technique to aid interpretation of data
extract maximum information from the data series. If there are other non-linear effects that have a correlation to the independent variable (such as cyclic
Linear_trend_estimation
Change of voltage or current per unit of time
undesirable effects as ringing or radiated interference. In amplifiers, limitations in slew rate capability can give rise to non-linear effects. For a sinusoidal
Slew_rate
System where changes of output are not proportional to changes of input
In mathematics and science, a nonlinear system (or a non-linear system) is a system in which the change of the output is not proportional to the change
Nonlinear_system
Science of determining past climates from trees
some confounding effects, for example picking sites undisturbed by modern man.[citation needed] In general, climatologists assume a linear dependence of
Dendroclimatology
Digital motion graphics and compositing software
other things, After Effects can be used for keying, tracking, compositing, and animation. It also functions as a very basic non-linear editor, audio editor
Adobe_After_Effects
outside of the normal communications window, four-wave mixing and other non-linear effects are minimized. Other types of NZDSF include RS-NZDSF[clarification
Non-zero dispersion-shifted fiber
Non-zero_dispersion-shifted_fiber
Concept used in the field of medical psychology
testing interaction effects between correlated continuous variables, it is recommended to investigate the potential non-linear effects of negative affectivity
Type_D_personality
Branch of physics
phonons. Nonlinear effects fall into two qualitatively different categories, parametric and non-parametric effects. A parametric non-linearity is an interaction
Nonlinear_optics
Electron-many photon scattering
Non-linear inverse Compton scattering (NICS), also known as non-linear Compton scattering and multiphoton Compton scattering, is the scattering of multiple
Non-linear inverse Compton scattering
Non-linear_inverse_Compton_scattering
Statistical method for genetic variance component estimation
Gene-Environment interactions; quantifying the contribution of non-additive/non-linear effects of SNPs; and bivariate analyses of multiple phenotypes to quantify
Genome-wide complex trait analysis
Genome-wide_complex_trait_analysis
Method for estimating the unknown parameters in a linear regression model
ordinary least squares (OLS) is a type of linear least squares method for choosing the unknown parameters in a linear regression model by the principle of
Ordinary_least_squares
energy and momentum transfer are strongly influenced by inertial or non-linear effects that are unique to the simulation. Transition also occurs by different
Transition_modeling
Potential natural disaster
2001, but used hydrodynamic modelling that accounts for dispersion, non-linear effects and the deformation of the landslide material itself to simulate waves
Cumbre_Vieja_tsunami_hazard
French chemist (born 1930)
behavior of such catalysts. This was a major discovery, making non-linear effects a field of chemistry in its own right: not only are they a tool for
Henri_B._Kagan
Magnetic field plasma confinement device
it tends to be more susceptible to non-linear effects and turbulence. This makes it a useful system for studying non-ideal (resistive) magnetohydrodynamics
Reversed_field_pinch
Type of statistical model
known as hierarchical linear models, linear mixed-effect models, mixed models, nested data models, random coefficient, random-effects models, random parameter
Multilevel_model
transfer, viscoelasticity, and thermorheology. Biot's interest in the non-linear effects of initial stress and the inelastic behavior of solids led to his
Maurice_Anthony_Biot
Statistical modeling method
In statistics, linear regression is a model that estimates the relationship between a scalar response (dependent variable) and one or more explanatory
Linear_regression
Minor character from Monty Python's The Meaning of Life
Malm and Wim Carton interpret the scene as an illustration of the non-linear effects of climate change in their 2025 book The Long Heat. Hind, John (20
Mr_Creosote
Type of optical fiber
cylindrical optical fiber amplifiers generally increases the level of non-linear effects such as stimulated Brillouin scattering. The result of forming a tapered
Tapered_double-clad_fiber
Chemical compound
low intensity signal (λ2), non-linear effects at both λ1 and λ2 arise. So, it is possible to trigger the non-linear effects on the low-intensity signal
Tantalum_diselenide
Transmitting information over optical fiber
diminishes the system performance due to linear and non-linear transmitter effects. These effects can be categorized as linear distortions due to DAC bandwidth
Fiber-optic_communication
Model for approximating non-linear effects, similar to a Taylor series
a model for non-linear behavior similar to the Taylor series. It differs from the Taylor series in its ability to capture "memory" effects. The Taylor
Volterra_series
Theorem related to ordinary least squares
estimator across samples) within the class of linear unbiased estimators, if the errors in the linear regression model are uncorrelated, have equal variances
Gauss–Markov_theorem
Electronic devices that generate electronic signals
simultaneously, and are used to check for intermodulation distortion and other non-linear effects), and tone bursts (used to measure response to transients). Pitch
Signal_generator
Unstable behavior of two contacting fluids of different densities
sinusoidal shape. However, after the end of this first stage, when non-linear effects begin to appear, one observes the beginnings of the formation of the
Rayleigh–Taylor_instability
Gameplay involving unordered sequences
challenges may be played in a different order. Conversely, a video game with linear gameplay will confront a player with a fixed sequence of challenges: every
Nonlinear_gameplay
American aircraft prototype
aircraft motions and reactions, were altered to better account for non-linear effects of control surface rate/position saturation and PIO triggering mechanisms
Lockheed_YF-22
Branch of thermodynamics
situations where there are appreciable non-linear effects even at the local scale. Some concepts of particular importance for non-equilibrium thermodynamics include
Non-equilibrium thermodynamics
Non-equilibrium_thermodynamics
Special case of regression analysis
methods in their nlmefit system. SPSS at the moment does not support non-linear mixed effects methods. WinBUGS is an implementation of the Metropolis-Hastings
Non-linear mixed-effects modeling software
Non-linear_mixed-effects_modeling_software
Statistical model
fixed effects model is a statistical model in which the model parameters are fixed or non-random quantities. This is in contrast to random effects models
Fixed_effects_model
Spectral density of light emitted by a black body
mechanics. Heisenberg's explanation of the Planck oscillators, as non-linear effects apparent as Fourier modes of transient processes of emission or absorption
Planck's_law
Measure of the electric polarizability of a dielectric material
characteristic absorption frequencies. The above effects often combine to cause non-linear effects within capacitors. For example, dielectric absorption
Permittivity
Integral equation
where the absorbed and emitted light have different wavelengths, Non-linear effects, where very intense light can increase the energy level of an electron
Rendering_equation
Topics referred to by the same term
catalysis Linear-nonlinear-Poisson cascade model (LNP model), a description of neural spike response Non-linear effects (NLE), deviations from linear behavior
Nonlinearity_(disambiguation)
Regression models accounting for possible errors in independent variables
samples. For simple linear regression the effect is an underestimate of the coefficient, known as the attenuation bias. In non-linear models the direction
Errors-in-variables_model
Measurement of a signal at discrete time intervals
hold effects can be analyzed as a form of low-pass filtering. The non-linearities of either ADC or DAC are analyzed by replacing the ideal linear function
Sampling_(signal_processing)
Moving average and polynomial regression method for smoothing data
before LOESS). LOESS and LOWESS thus build on "classical" methods, such as linear and nonlinear least squares regression. They address situations in which
Local_regression
Practice of recording information
set off with bullets showing where a new thought begins. Approaches to non-linear note-taking include clustering, concept mapping, Cornell Notes, idea mapping
Note-taking
Method for solving certain optimization problems
IRLS is used to find the maximum likelihood estimates of a generalized linear model, and in robust regression to find an M-estimator, as a way of mitigating
Iteratively reweighted least squares
Iteratively_reweighted_least_squares
Statistical model
used for small area estimation. Bühlmann model Hierarchical linear modeling Fixed effects MINQUE Covariance estimation Conditional variance Panel analysis
Random_effects_model
Regularization technique for ill-posed problems
constrained linear inversion method, L2 regularization, and the method of linear regularization. It is related to the Levenberg–Marquardt algorithm for non-linear
Ridge_regression
Class of statistical models
generalized linear model (GLM) is a flexible generalization of ordinary linear regression. The GLM generalizes linear regression by allowing the linear model
Generalized_linear_model
Least squares approximation of linear functions to data
Linear least squares (LLS) is the least squares approximation of linear functions to data. It is a set of formulations for solving statistical problems
Linear_least_squares
Screening method
model output; the measure σ {\displaystyle \sigma } , describing non-linear effects and interactions. These two measures are obtained through a design
Elementary_effects_method
Quasiparticle of mechanical vibrations
James, D. F. V. (2003). "Phonon–phonon interactions due to non-linear effects in a linear ion trap" (PDF). Applied Physics B. 76 (3): 199–208. arXiv:quant-ph/0211079
Phonon
Special glass type used for optical systems
the design of optical systems, and transmission, glass strength and non-linear effects. The refractive index indicates the refractive power of a glass, i
Optical_glass
Regression for more than two discrete outcomes
techniques, is to construct a linear predictor function that constructs a score from a set of weights that are linearly combined with the explanatory
Multinomial logistic regression
Multinomial_logistic_regression
Main model used in radioprotection to minimize radiation exposures
The linear no-threshold model (LNT) is a dose-response model used in radiation protection to estimate stochastic health effects such as radiation-induced
Linear_no-threshold_model
Basic concept in accelerator physics
lattices using high order magnets, such as sextupoles or octupoles, non-linear effects appear leading to tune shift with amplitude. Kerst, D. W.; Serber
Betatron_oscillations
extraction, for instance in Permian basin in Texas Climate TRACE Non-linear effects Non-methane volatile organic compound Guevara, Marc; Enciso, Santiago;
List of locations and entities by greenhouse gas emissions
List_of_locations_and_entities_by_greenhouse_gas_emissions
Statistical estimation technique
method used to estimate the unknown parameters in a linear regression model. It is used when there is a non-zero amount of correlation between the residuals
Generalized_least_squares
Regression analysis
least squares and non-linear least squares. The assumption underlying this procedure is that the model can be approximated by a linear function, namely
Nonlinear_regression
Method for model fitting in statistics
squares (WLS), also known as weighted linear regression, is a generalization of ordinary least squares and linear regression in which knowledge of the
Weighted_least_squares
Type of fluid
(1963). "Non -Newtonian effects in some elastic-viscous liquids whose behavior at small rates of shear is characterized by a general linear equations
Non-Newtonian_fluid
Apparent contradiction in physical descriptions of the universe
violation of Newton's law of cooling but in reality it is due to non-linear effects that influence the freezing process. The assumption that only the
Physical_paradox
Constrained least squares problem
03.026. Lawson, Charles L.; Hanson, Richard J. (1995). "23. Linear Least Squares with Linear Inequality Constraints". Solving Least Squares Problems. SIAM
Non-negative_least_squares
Approximation method in statistics
linear or ordinary least squares and nonlinear least squares, depending on whether or not the model functions are linear in all unknowns. The linear least-squares
Least_squares
Nonlinear form of the Schrödinger equation
quasi-monochromatic waves in weakly nonlinear media that have dispersion. Unlike the linear Schrödinger equation, the NLSE never describes the time evolution of a quantum
Nonlinear Schrödinger equation
Nonlinear_Schrödinger_equation
Method of measuring spectral phase of ultrashort laser pulses
referred to as cross-correlation FROG or XFROG. In addition, other non-linear effects besides second harmonic generation may be used, such as third harmonic
Frequency-resolved optical gating
Frequency-resolved_optical_gating
Nonlinear optical effect of light-matter interaction
management, because dispersion can partly mitigate the SPM effect Other non-linear effects: Cross-phase modulation – XPM Four-wave mixing – FWM Modulational
Self-phase_modulation
Standard on surge immunity
impulse without undershoot. An ideal circuit model cannot predict these non-linear effects, and should not be treated as a complete circuit model of practical
IEC_61000-4-5
Process of constructing a curve that has the best fit to a series of data points
the curve. Geometric fits are not popular because they usually require non-linear and/or iterative calculations, although they have the advantage of a more
Curve_fitting
properties of fused quartz and the force balancing which eliminates most non-linear effects these sensors can be accurate to around 1PPM of full scale. Due to
Pressure_measurement
Statistical modeling technique
variable,. Quantile regression is an extension of linear regression used when the conditions of linear regression are not met. It was introduced by Roger
Quantile_regression
Astronomical neutrinos produced during core-collapse supernova explosion
as neutrino–neutrino interactions. Neutrino self-interactions are non-linear effects that result in collective flavor conversions. They are significant
Supernova_neutrinos
Statistical optimality criterion
parameters that need to be determined. For instance, the simplest form would be linear: f(x) = bx + c, where b and c are parameters whose values are not known
Least_absolute_deviations
Concept in regression analysis mathematics
two main reasons. The first comes up when the number of variables in the linear system exceeds the number of observations. In such settings, the ordinary
Regularized_least_squares
Statistical technique
regression and also of orthogonal regression, and can be applied to both linear and non-linear models. The total least squares approximation of the data is generically
Total_least_squares
Measure of performance in digital converters
differential non-linearity. Differential non-linearity may be expressed in fractional bits or as a percentage of full scale. A differential non-linearity greater
Differential_nonlinearity
American atmospheric physicist
climate predictions were valid. Lindzen has stated that due to the non-linear effects of carbon dioxide in the atmosphere, CO2 levels are now around 30%
Richard_Lindzen
Reaction in organic chemistry
as proposed by Agami is disputed by Barbas based on the lack of a non-linear effects and supported by later studies of List based on reaction kinetics
Proline-catalyzed aldol reactions
Proline-catalyzed_aldol_reactions
Cancer caused by ionizing radiation exposure
hormetic effect, and thus have a negative impact on health. Other non-linear effects have been observed, particularly for internal doses. For example,
Radiation-induced_cancer
French geophysicist
'source, path and site effects' is widely used. It introduced the joint use of seismic data and radar interferometry in a non-linear inversion of the slip
Michel_Campillo
Collection of statistical models
randomization and blinding were soon added. An eloquent non-mathematical explanation of the additive effects model was available in 1885. Ronald Fisher introduced
Analysis_of_variance
Statistical method
maximum variance between the response and independent variables, it finds a linear regression model by projecting the predicted variables and the observable
Partial least squares regression
Partial_least_squares_regression
Statistical regression where the dependent variable can take only two values
logistic regression using similar techniques. When viewed in the generalized linear model framework, the probit model employs a probit link function. It is
Probit_model
Type of mathematical model
can show complex and synergetic nonlinear effects. Contrary to traditional modelling methods, such as linear regression and basic statistical methods,
Nonlinear_modelling
Series of waves generated by distant weather systems
investigating the non-linear effects that are most pronounced near the peaks of the highest waves. He showed that, through these non-linearities, two wave trains
Swell_(wave)
Image processing technique
colour space where γ is not equal to 1 then the operation will lead to non-linear effects which can potentially be seen as aliasing artifacts (or "jaggies")
Digital_compositing
Statistics concept
as a statistical estimation problem it is linear, in the sense that the regression function E(y | x) is linear in the unknown parameters that are estimated
Polynomial_regression
Observation that the intrinsic rate of human performance is exponential
on the propensity of humans to envision and achieve scale, and its non-linear effects. Engelbart labeled Collective IQ as the measure of how well people
Engelbart's_law
Feature of surface gravity waves
and they can be mirrored in both the crest and the trough. Due to Non-linear effects, waves can transform from sinusoidal to a skewed and asymmetric shape
Wave_nonlinearity
Paradox in wave propagation
implies that a finite-amplitude wave cannot keep a fixed shape and non-linear effects must be introduced. Higher-pressure regions travel faster than lower
Earnshaw_paradox
disturbances grow to have a significant amplitude, non-linear effects begin to dominate breakup behavior. The non-linear behavior of the thread governs its final
Fluid_thread_breakup
Open source software for computational fluid dynamics
following phenomena: Propagation of long waves, taking into account non-linear effects Bed friction Influence of Coriolis force Influence of meteorological
TELEMAC
Device to couple energy between circuits
non-linear due to saturation effects. However, all impedances of the equivalent circuit shown are by definition linear and such non-linearity effects
Transformer
Astrophysical theory
Relativistic numerical studies confirmed the effects of the instability, probed the non-linear effects primarily responsible for setting the final amplitude
Papaloizou–Pringle instability
Papaloizou–Pringle_instability
region of the state space has been caused by the desire to explain the non-linear effects revealed during the getting out of controllability of ships. Subsequently
Bifurcation_memory
Statistics concept
Instead, the data sets include outliers, high-leverage points, or non-linearities. One problem with the R2 as a measure of model validity is that it
Regression_validation
including memory effects (fast processes, polymers, superfluids), non-local effects (micro- and nano-materials), non-linear effects (high powers, shock
Extended irreversible thermodynamics
Extended_irreversible_thermodynamics
Physical phenomenon
amplitude of the oscillations, while for linear systems this is independent of amplitude. The mixing of modes in non-linear systems is termed resonant interaction
Nonlinear_resonance
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