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Free convolution is the free probability analog of the classical notion of convolution of probability measures. Due to the non-commutative nature of free
Free_convolution
Theorem in mathematics
In mathematics, the convolution theorem states that under suitable conditions the Fourier transform of a convolution of two functions (or signals) is the
Convolution_theorem
Integral expressing the amount of overlap of one function as it is shifted over another
In mathematics (in particular, functional analysis), convolution is a mathematical operation on two functions f {\displaystyle f} and g {\displaystyle
Convolution
Type of feedforward neural network
A convolutional neural network (CNN) is a type of feedforward neural network that learns features via filter (or kernel) optimization. This type of deep
Convolutional_neural_network
Mathematical theory on random variables
Circular law Free convolution Speicher, Roland (1994), "Multiplicative functions on the lattice of non-crossing partitions and free convolution", Mathematische
Free_probability
Type of error-correcting code using convolution
represents the 'convolution' of the encoder over the data, which gives rise to the term 'convolutional coding'. The sliding nature of the convolutional codes facilitates
Convolutional_code
Discrete probability distribution
\lambda } arises in free probability theory as the limit of repeated free convolution ( ( 1 − λ N ) δ 0 + λ N δ α ) ⊞ N {\displaystyle \left(\left(1-{\frac
Poisson_distribution
replaced by free independence. Examples of this include: the free central limit theorem; notions of free convolution; existence of free stochastic calculus
Free_independence
Set of quantities in probability theory
"Multiplicative functions on the lattice of non-crossing partitions and free convolution". Mathematische Annalen. 298 (4): 611–628. doi:10.1007/BF01459754.
Cumulant
Convolutional neural network structure
LeNet is a series of convolutional neural network architectures created by a research group at AT&T Bell Laboratories between of the period of 1988 to
LeNet
Music genre
exploring timbre. Free jazz was a reaction to the convolution of bop. Conductor and jazz writer Loren Schoenberg wrote that free jazz "gave up on functional
Free_jazz
Neurological factors responsible for intelligence
[dubious – discuss] The folding of the brain's surface, known as cortical convolution, has become more pronounced throughout human evolution. It has been suggested
Neuroscience_and_intelligence
In image processing, the free boundary condition is the convention used when applying a convolution kernel to a digital image in which pixel locations
Free_boundary_condition
Influential 2012 deep convolutional neural network
AlexNet is a convolutional neural network architecture developed for image classification tasks, notably achieving prominence through its performance
AlexNet
Mathematical transform
of graph structured learning algorithms, such as the widely employed convolutional networks. Given an undirected weighted graph G = ( V , E ) {\displaystyle
Graph_Fourier_transform
Reconstruction of a filtered signal
In mathematics, deconvolution is the inverse of convolution. Both operations are used in signal processing and image processing. For example, it may be
Deconvolution
1984 novel by Gene Wolfe
so I'll finish'. A nice idea which got buried under a blanket of over-convolution." At the SF Site, Jean-Louis Trudel called it "deeply engaging", with
Free_Live_Free
Class of organic compounds
inert, their concentration in the ocean interior reflects simply the convolution of their atmospheric time evolution and ocean circulation and mixing
Chlorofluorocarbon
Class of reinforcement learning algorithm
In reinforcement learning (RL), a model-free algorithm is an algorithm which does not estimate the transition probability distribution (and the reward
Model-free (reinforcement learning)
Model-free_(reinforcement_learning)
Topics referred to by the same term
the diagonal of a matrix Kernel density estimation, the width of the convolution kernel used in statistics Graph bandwidth, in graph theory Coherence
Bandwidth
Deep learning framework
Caffe (Convolutional Architecture for Fast Feature Embedding) is a deep learning framework, originally developed at University of California, Berkeley
Caffe_(software)
Topics referred to by the same term
increased mobility Convolute laminations in geology Distal convoluted tubule Convolution (disambiguation) This disambiguation page lists articles associated with
Convolute
Topics referred to by the same term
operating systems Kernel (image processing), a matrix used for image convolution Compute kernel, in GPGPU programming Kernel method, in machine learning
Kernel
Vector field related to displacement current and flux density
material. In this case, P is a convolution of the impulse response susceptibility χ and the electric field E. Such a convolution takes on a simpler form in
Electric_displacement_field
known for its simplicity and use of 3x3 convolution filters Inception — CNN architecture using parallel convolutional layers of different sizes LAION OpenAssistant
Lists of open-source artificial intelligence software
Lists_of_open-source_artificial_intelligence_software
Intelligence of machines
dependencies and are less sensitive to the vanishing gradient problem. Convolutional neural networks (CNNs) use layers of kernels to more efficiently process
Artificial_intelligence
Formal power series
transformations Knuth's article titled "Convolution Polynomials" defines a generalized class of convolution polynomial sequences by their special generating
Generating_function
Image-generating machine learning model
models. The "zero convolution" is a 1×1 convolution with both weight and bias initialized to zero. Before training, all zero convolutions produce zero output
Stable_Diffusion
Type of imaging sensor
arbitrary convolution kernel around the event coordinate in an array of integrate-and-fire pixels. Extension to multi-kernel event-driven convolutions allows
Event_camera
Study of the properties of codes and their fitness
the output of the system convolutional encoder, which is the convolution of the input bit, against the states of the convolution encoder, registers. Fundamentally
Coding_theory
Rational mathematical function indexed by integer partitions
prove that the algebra of the gaussian unitary ensemble converges to the free probability algebra. Higher order expansions exist, of the form d − n − |
Weingarten_function
Digital audio workstation
effects. Among Logic's reverb plugins is Space Designer, which uses convolution reverb to simulate the acoustics of audio played in different environments
Logic_Pro
Multimedia framework
Filtering Blurring (boxblur, gblur, avgblur, sab, smartblur) Convolution filters Convolution (convolution) Edge detection (edgedetect) Sobel Filter (sobel) Prewitt
FFmpeg
Study of classical optics using Fourier transforms
δ(t − t′), applied at time t'. This is where the convolution equation above comes from. The convolution equation is useful because it is often much easier
Fourier_optics
Changing the resolution of a digital image
Iterative Curvature-Based Interpolation (ICBI), and Directional Cubic Convolution Interpolation (DCCI). A 2013 analysis found that DCCI had the best scores
Image_scaling
Visual examples of techniques for image scaling
; Dong, W. (24 August 2012). "Image Zooming Using Directional Cubic Convolution Interpolation (Paper and Code)". IET Image Processing. 6 (6): 627–634
Comparison gallery of image scaling algorithms
Comparison_gallery_of_image_scaling_algorithms
Scheme for controlling errors in data over noisy communication channels
increasing constraint length of the convolutional code, but at the expense of exponentially increasing complexity. A convolutional code that is terminated is also
Error_correction_code
Branch of machine learning
connected networks, deep belief networks, recurrent neural networks, convolutional neural networks, generative adversarial networks, transformers, and
Deep_learning
Online database of integer sequences
1s in binary expansion of nth prime. Nov 20, 2003 A091345 Exponential convolution of A069321(n) with itself, where we set A069321(0) = 0. Jan 1, 2004 A100000
On-Line Encyclopedia of Integer Sequences
On-Line_Encyclopedia_of_Integer_Sequences
Mathematical transform that expresses a function of time as a function of frequency
Borel measures, with multiplication given by convolution of measures. With the convention above, convolution corresponds to operator multiplication with
Fourier_transform
Aesthetic quality of blur in the out-of-focus parts of an image
point source taken with a real camera. Unlike conventional convolution, this convolution has a kernel that depends on the distance of each image point
Bokeh
Computational model used in machine learning
units (GPUs), and large datasets. Architectural innovations such as convolutional neural networks (CNNs) significantly improved performance in computer
Neural network (machine learning)
Neural_network_(machine_learning)
Covariance and correlation
and neurophysiology. The cross-correlation is similar in nature to the convolution of two functions. In an autocorrelation, which is the cross-correlation
Cross-correlation
Collaborative map database
derived from OSM's road network. Computer vision researchers have trained convolutional neural networks on OSM's land use areas to perform feature detection
OpenStreetMap
Mathematical form
\mathrm {d} \tau } is well defined and is called the convolution. Under the Fourier transform, convolution becomes point-wise function multiplication. The
Product_(mathematics)
Subset of artificial intelligence
ISBN 978-0-13-461099-3. Honglak Lee, Roger Grosse, Rajesh Ranganath, Andrew Y. Ng. "Convolutional Deep Belief Networks for Scalable Unsupervised Learning of Hierarchical
Machine_learning
Feature observed in spectroscopy
each effect is independent of the other, the observed line profile is a convolution of the line profiles of each mechanism. Thus, a combination of Doppler
Spectral_line_shape
Generating high-resolution video frames from given low-resolution ones
frame sequence, k {\displaystyle k} — blur kernel, ∗ {\displaystyle *} — convolution operation, ↓ s {\displaystyle \downarrow {_{s}}} — downscaling operation
Video_super-resolution
Measure of the shape of a function
_{i=0}^{n}{n \choose i}E\left[(x-a)^{i}\right](a-b)^{n-i}.} The raw moment of a convolution h ( t ) = ( f ∗ g ) ( t ) = ∫ − ∞ ∞ f ( τ ) g ( t − τ ) d τ {\textstyle
Moment_(mathematics)
Type of code in quantum computing
lower complexity. Quantum convolutional coding theory offers a different paradigm for coding quantum information. The convolutional structure is useful for
Quantum_convolutional_code
Algorithm for modelling sequential data
n-steps-behind, by a matrix multiplication. By taking a linear sum, any convolution can also be implemented as linear transformations: ∑ j c j f ( t + Δ
Transformer_(deep_learning)
Physical implementation of an artificial neural network with optical components
classification in free-space optics, introduced by Cahng et al., employs a 4F system that is based on the convolution theorem to perform convolution operations
Optical_neural_network
Response if an optical system to a point source of light
everywhere in the imaging space, the image of a complex object is then the convolution of that object and the PSF. The PSF can be derived from diffraction integrals
Point_spread_function
Near-field diffraction
{k}{2z}}(x^{2}+y^{2})},} then the integral can be expressed in terms of a convolution: E ( x , y , z ) = E ( x , y , 0 ) ∗ h ( x , y , z ) ; {\displaystyle
Fresnel_diffraction
Slave of Thomas Jefferson (c. 1773–1835)
Jefferson-Hemings Myth: An American Travesty, an essay collection of considerable convolution and belligerence. Stockman, Farah (June 16, 2018). "Monticello Is Done
Sally_Hemings
Function equal to the product of its values on coprime factors
function, so called because it is the multiplicative identity for Dirichlet convolution. Sometimes written as u ( n ) {\displaystyle u(n)} ; not to be confused
Multiplicative_function
Arithmetic function related to the divisors of an integer
(s-a-b)}{\zeta (2s-a-b)}},} which is a special case of the Rankin–Selberg convolution. A Lambert series involving the divisor function is: ∑ n = 1 ∞ q n σ
Divisor_function
Discrete Fourier transform algorithm
size n as a cyclic convolution of (composite) size n – 1, which can then be computed by a pair of ordinary FFTs via the convolution theorem (although Winograd
Fast_Fourier_transform
Method of hydrodynamics simulation
SPH convolution shall be practiced close to a boundary, i.e. closer than s · h, then the integral support is truncated. Indeed, when the convolution is
Smoothed-particle hydrodynamics
Smoothed-particle_hydrodynamics
French computer scientist (born 1960)
his work on optical character recognition and computer vision using convolutional neural networks (CNNs). He is also one of the main creators of the DjVu
Yann_LeCun
expansion joint is a metallic assembly that consists of a series of toroidal convolutions which are circular tubes wrapped around pipe ends or weld ends and have
Toroidal_expansion_joint
Vector field describing the density of electric dipole moments in a dielectric material
the field is an arbitrary function of time t, the polarization is a convolution of the Fourier transform of χ(ω) with the E(t). This reflects the fact
Polarization_density
Multiplicative function in number theory
Dirichlet convolution as: 1 ∗ μ = ε {\displaystyle 1*\mu =\varepsilon } where ε {\displaystyle \varepsilon } is the identity under the convolution. One way
Möbius_function
Distance function defined between probability distributions
y ) {\displaystyle f(x)=\inf _{y}d(x,y)-g(y)} , making it an infimal convolution of − g {\displaystyle -g} with a cone. This implies f ( x ) − f ( y )
Wasserstein_metric
Interdisciplinary research area
function as CNN. The convolution filter is the most basic technique for making use of spatial information. One or more quantum convolutional filters make up
Quantum_machine_learning
AI that generates content
(GPT) series developed by OpenAI, replacing traditional recurrent and convolutional models. The self-attention mechanism enables the model to determine
Generative_AI
Topics referred to by the same term
reduction rules in term rewriting systems Overlap add, an efficient convolution method using FFT Overlap coefficient, a similarity measure between sets
Overlap
High-performance forward error correction codes
processing. The first class of turbo code was the parallel concatenated convolutional code (PCCC). Since the introduction of the original parallel turbo codes
Turbo_code
Mathematical function having a characteristic S-shaped curve or sigmoid curve
functions.. These include algebraic transformations, integration and convolution methods, constructions from bell-shaped functions, solutions of ordinary
Sigmoid_function
Computer scientist (born 1986)
With Alex Krizhevsky and Geoffrey Hinton, he co-created AlexNet, a convolutional neural network. One of the most highly cited computer scientists in
Ilya_Sutskever
1879 = a prime with square index 1880 = the 10th element of the self convolution of Lucas numbers 1881 = tricapped prism number 1882 = number of linearly
1000_(number)
2019 text-generating language model
transformer model, which uses attention instead of older recurrence- and convolution-based architectures. Attention mechanisms allow the model to selectively
GPT-2
Technique for the generative modeling of a continuous probability distribution
good image-to-class translator, we get a class-to-image translator "for free". In the equation for backward diffusion, the score ∇ ln p ( x ) {\displaystyle
Diffusion_model
Technique for setting initial values of trainable parameters in a neural network
how both of these are initialized. Similarly, trainable parameters in convolutional neural networks (CNNs) are called kernels and biases, and this article
Weight_initialization
Type of machine learning model
Yanming (2021). "Review of Image Classification Algorithms Based on Convolutional Neural Networks". Remote Sensing. 13 (22): 4712. Bibcode:2021RemS..
Large_language_model
Neural network coding model
The convolutional sparse coding paradigm is an extension of the global sparse coding model, in which a redundant dictionary is modeled as a concatenation
Convolutional_sparse_coding
contains artifacts. Then, a convolutional neural network (CNN) is trained to remove the artifacts, in order to produce an artifact-free representation of the
Deep learning in photoacoustic imaging
Deep_learning_in_photoacoustic_imaging
Explainable AI technique
classification, in convolutional neural networks (CNNs). These methods generate heatmaps by weighting the feature maps from a convolutional layer according
Class_activation_mapping
Method of solution to differential equations
solution of the inhomogeneous problem L y = f {\displaystyle Ly=f} is the convolution, y = ( G ∗ f ) . {\displaystyle y=(G\ast f).} By the superposition principle
Green's_function
Java-based image processing program
logical and arithmetical operations between images, contrast manipulation, convolution, Fourier analysis, sharpening, smoothing, edge detection, and median
ImageJ
AI research laboratory
pixels as data input. Their initial approach used deep Q-learning with a convolutional neural network. They tested the system on video games, notably early
Google_DeepMind
Construction in algebra
coassociative) bialgebra over a field K . {\displaystyle K.} One can consider the convolution algebra Hom K ( H , H ) {\displaystyle \operatorname {Hom} _{K}(H,H)}
Hopf_algebra
Image scaling algorithm
and other types of photos. waifu2x was inspired by Super-Resolution Convolutional Neural Network (SRCNN). It uses Nvidia's CUDA for computing, although
Waifu2x
Partial differential equation describing the evolution of temperature in a region
condition u(x, 0) = g(x) for −∞ < x < ∞ and 0 < t < ∞ by applying a convolution: u ( x , t ) = ∫ Φ ( x − y , t ) g ( y ) d y . {\displaystyle u(x,t)=\int
Heat_equation
Topics referred to by the same term
number of tasks Pooling layer, a form of non-linear down-sampling in convolutional neural networks Pool (John Zorn album), 1980 Pool (Porches album), 2016
Pool
Math YouTube channel
language and Grant Sanderson's animations to explain various topics: convolutions, image processing, COVID-19 data visualization, epidemic modelling, ray
3Blue1Brown
Signal representation used in automatic speech recognition
Hence, y ( n ) = x ( n ) ∗ h ( n ) {\displaystyle y(n)=x(n)*h(n)} (convolution) As speech is not stationary signal, it is divided into overlapped frames
Mel-frequency_cepstrum
Method of data analysis
covariance-free approach avoids the np2 operations of explicitly calculating and storing the covariance matrix XTX, instead utilizing one of matrix-free methods
Principal_component_analysis
Semiconductor light source
Stern, Maike Lorena; Schellenberger, Martin (March 31, 2020). "Fully convolutional networks for chip-wise defect detection employing photoluminescence
Light-emitting_diode
Short "burst" or "envelope" of restricted wave action that travels as a unit
summed over all the possible starting points. In other words, it is a convolution of the kernel K with the arbitrary initial condition ψ0, ψ t = K ∗ ψ
Wave_packet
Deep learning method
typically a deconvolutional neural network, and the discriminator is a convolutional neural network. GANs are implicit generative models, which means that
Generative adversarial network
Generative_adversarial_network
Elementary particle with negative charge
basis of modern electronics. Electrons can exist as free particles. As particle beams in a vacuum, free electrons can be accelerated, focused, and used for
Electron
British science fiction author (1941–2010)
1980, Stellar #5, an adapted version appears in Catastrophes, Chaos & Convolutions). "Neander-Tale" (December 1980, The Magazine of Fantasy & Science Fiction
James_P._Hogan_(writer)
Multilingual neural machine translation service
Irish.[citation needed] The service uses a proprietary algorithm with convolutional neural networks (CNNs) that have been trained with the Linguee database
DeepL_Translator
Free and open-source chess engine
Stockfish is a free and open-source chess engine, available for various desktop and mobile platforms. It can be used in chess software through the Universal
Stockfish_(chess)
Form of sound synthesis
Frequency modulation synthesis (or FM synthesis) is a form of sound synthesis whereby the frequency of a waveform is changed by modulating its frequency
Frequency modulation synthesis
Frequency_modulation_synthesis
Technique in neural networks for learning joint representations of text and images
the CNN (the "stem"), they used three stacked 3x3 convolutions instead of a single 7x7 convolution, as suggested by. There is an average pooling of stride
Contrastive Language–Image Pre-training
Contrastive_Language–Image_Pre-training
Electrically insulating substance able to be polarised by an applied electric field
_{e}\left(t-t'\right)\mathbf {E} (t')\,dt'.} That is, the polarisation is a convolution of the electric field at previous times with time-dependent susceptibility
Dielectric
Software library for natural language processing
learning library Thinc. Using Thinc as its backend, spaCy features convolutional neural network models for part-of-speech tagging, dependency parsing
SpaCy
Topics referred to by the same term
Ligation-independent cloning, a form of molecular cloning Line integral convolution, a technique to visualize fluid motion Linear integrated circuit Listed
LIC
FREE CONVOLUTION
FREE CONVOLUTION
Girl/Female
Irish American
Hill. Also abbreviation of Brina and Breanna.
Boy/Male
German, Swedish
Lord
Boy/Male
British, English
Peace
Surname or Lastname
English
English : nickname from Middle English freil, frel(i)e ‘frail’, ‘weak’.Possibly an Americanized spelling of German Friel 2.
Surname or Lastname
English
English : from Old French and Middle English frere ‘friar’ (Latin frater, literally ‘brother’). This was a status name for a member a religious order, especially a mendicant order, and may also have been a nickname for a pious person or for someone employed at a monastery.Americanized spelling of French Frère (see Frere).North German and Dutch : cognate of Friedrich.
Boy/Male
English Norse Scandinavian
Lord.
Surname or Lastname
English
English : variant of Freer 1.French (Frère) : from frère ‘brother’, used as a byname for the younger of two brothers.
Boy/Male
Australian, British, English
In Liberty
Female
English
English form of Irish BrÃgh, BREE means "force, strength."
Male
English
Short form of English Frederick, FRED means "peaceful ruler."
Boy/Male
British, English
Seed
Surname or Lastname
English (chiefly East Anglia)
English (chiefly East Anglia) : nickname or status name from Old English frēo ‘free(-born)’, i.e. not a serf.North German : topographic or habitational name from a place named Frede or Frede(n).North German : nickname from a variant of Middle Low German wrēd ‘crooked’.
Boy/Male
English American Teutonic German
Sage, wise. From the Old English Aelfraed, meaning elf counsel. Also from Ealdfrith or Alfrid,...
Male
Icelandic
Icelandic form of Old Norse Freyr, FREY means "lord, master."
Male
Swedish
Danish and Swedish form of Old Norse Freyr, FREJ means "lord, master."
Boy/Male
British, English
Generous
Female
English
Anglicized form of Danish Freya, FREA means "lady, mistress."
Boy/Male
Anglo, British, English
Foreign
Surname or Lastname
English (mainly southeastern)
English (mainly southeastern) : topographic name for someone who lived near a conspicuous tree, Middle English tre(w).
Surname or Lastname
English
English : variant spelling of Fry.North German : variant of Frey.Joseph Frye (1711/12–94) was a military officer from Andover, MA, where the family had long been of local prominence. In 1762, he was granted a township in ME, later named Fryeburg after him, and moved his family there. His great-great-grandson William Pierce Frye was born in Lewiston, ME, and served in Congress, first as a member of the House of Representatives and then the Senate from 1871 until his death in 1911.
FREE CONVOLUTION
FREE CONVOLUTION
Boy/Male
American, Australian, British, Celtic, Chinese, Christian, English, Gaelic, German, Greek, Irish, Latin, Scottish
Wisdom; Chief; Wise; Counsel; Reason; Intelligence; Surname; Freeman; Head; Hound; Strength; Fifth
Girl/Female
British, Christian, English
Feminine of Earl; Noblewoman; Leader
Boy/Male
Bengali, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Oriya, Telugu
Advise; King
Girl/Female
French
Victorious.
Surname or Lastname
English
English : habitational name from any of various places named Cranmore, for example in Somerset (see Cranmer) and the Isle of Wight, which is named with Old English cran ‘crane’ + mÅr ‘moor’, ‘marshy ground’.
Male
Greek
(ΒαλτάσαÏ) Greek form of Aramaic Belsha'tstsar, BALTASAR means "Ba'al protect the king." In the bible, this is the name of a king of Babylon at the time of its fall; he to whom Daniel interpreted the writing on the wall.
Girl/Female
Muslim
White cloud, A musical instrument
Boy/Male
Australian, Danish, Dutch, German, Latin
Crowned with Laurel; From Laurentium; Laurentium was a City South of Rome Known for Its Numerous Laurel Trees
Boy/Male
English American Spanish
Earnest.
Female
Hungarian
Hungarian form of Latin Flora, FLÓRA means "flower."
FREE CONVOLUTION
FREE CONVOLUTION
FREE CONVOLUTION
FREE CONVOLUTION
FREE CONVOLUTION
a.
To make free; to set at liberty; to rid of that which confines, limits, embarrasses, oppresses, etc.; to release; to disengage; to clear; -- followed by from, and sometimes by off; as, to free a captive or a slave; to be freed of these inconveniences.
adv.
Without charge; as, children admitted free.
superl.
Ready; eager; acting without spurring or whipping; spirited; as, a free horse.
superl.
Exempt; clear; released; liberated; not encumbered or troubled with; as, free from pain; free from a burden; -- followed by from, or, rarely, by of.
v. t.
To make free.
superl.
Not gained by importunity or purchase; gratuitous; spontaneous; as, free admission; a free gift.
superl.
Privileged or individual; the opposite of common; as, a free fishery; a free warren.
superl.
Not close or parsimonious; liberal; open-handed; lavish; as, free with his money.
n.
One who frees, or sets free.
superl.
Certain or honorable; the opposite of base; as, free service; free socage.
a.
Free from the power of love.
n.
One who believes in or practices free-love.
a.
Open; frank; unreserved; liberal; generous; as, free-hearted mirth.
superl.
Not united or combined with anything else; separated; dissevered; unattached; at liberty to escape; as, free carbonic acid gas; free cells.
imp. & p. p.
of Free
a.
Not perplexed; having a mind free from care.
v. t.
To place upon a tree; to fit with a tree; to stretch upon a tree; as, to tree a boot. See Tree, n., 3.
a.
Free from charge or expense; hence, unpunished; scot-free.
superl.
Not arbitrary or despotic; assuring liberty; defending individual rights against encroachment by any person or class; instituted by a free people; -- said of a government, institutions, etc.