Physical world and mathematics

Cross-entropy benchmarking

Cross-entropy benchmarking (XEB) is a quantum computing protocol introduced by Sergio Boixo and Google colleagues in 2018 that estimates the fidelity of noisy quantum processors.

Cross-flow filtration (CFF), also called tangential flow filtration (TFF), is a membrane separation method in which feed flows tangentially across the membrane surface, limiting fouling in bioprocessing and water treatment.

Cross-lagged panel analysis

Cross-lagged panel analysis is a longitudinal statistical method that models reciprocal relationships between variables measured repeatedly in the same units, widely used since the 1970s but contested for potentially spurious causal estimates.

Cross-lagged panel model

The cross-lagged panel model, or CLPM, is a longitudinal structural equation model that estimates reciprocal influences between two or more variables measured repeatedly over time.

Cross-lagged panel network

A cross-lagged panel network (CLPN) is a longitudinal statistical method combining cross-lagged panel regression with network analysis, estimating time-lagged relationships among variables such as psychological symptoms.

Cross-link

A cross-link is a junction in a macromolecule from which at least four polymer chains emanate, tying individual chains into a network that swells in solvent without dissolving.

Cross-linked polyethylene

Cross-linked polyethylene, abbreviated XLPE or PEX, is a thermosetting polyethylene with a three-dimensional covalent network, widely used as wire and cable insulation and as plumbing pipe for hot and cold water.

Cross-metathesis of natural oils

Cross-metathesis of natural oils is a catalytic reaction that cleaves unsaturated fatty acid chains in plant oils into shorter fatty acids and olefins, using ruthenium catalysts.

Cross-polarization (NMR)

Cross-polarization is a solid-state NMR technique that transfers spin polarization from abundant nuclei such as hydrogen-1 to dilute, low-sensitivity nuclei like carbon-13, enhancing their weak signals.

Cross-polarization magic angle spinning

Cross-polarization magic angle spinning (CP-MAS) is a solid-state NMR experiment that yields sensitive, high-resolution spectra of solids by transferring polarization from abundant protons to rare nuclei while the sample spins at the magic angle.

Cross-ratio

The cross-ratio, also called the double ratio or anharmonic ratio, is a number attached to four collinear points that stays unchanged under any projective transformation, playing the role length plays in Euclidean geometry.

Cross-resonance effect

The cross-resonance effect is a microwave-driven interaction between two fixed-frequency superconducting qubits, generating the entangling ZX gate that IBM used as its native two-qubit gate until 2023.

Cross-resonance gate

The cross-resonance gate is an all-microwave two-qubit entangling gate for superconducting qubits that drives the control qubit at the target's transition frequency, yielding a ZX interaction.

Cross-section measurement and unfolding in particle physics

Cross-section measurement in particle physics converts counted events into rates, and unfolding is the statistical correction removing detector resolution, efficiency, and acceptance distortions so results refer to particle-level quantities.

Cross-sectional regression

Cross-sectional regression estimates relationships between variables measured across different units, such as firms, households, or stocks, at a single point in time, unlike time-series regression.

Cross-validation (statistics)

Cross-validation, also known as out-of-sample testing, is a statistical technique that estimates a model's predictive performance by repeatedly splitting data into training and test sets.

Crossed molecular beam

A crossed molecular beam experiment crosses two dilute gas beams in a vacuum so single collisions can be observed, a technique honored with the 1986 Nobel Prize in Chemistry.

Crossed polarizers

Crossed polarizers are a pair of polarizing filters oriented at 90 degrees, blocking unaltered light and revealing birefringence, following Malus's law; they underpin polarizing microscopes and photoelastic stress analysis.

Crossed product of von Neumann algebras

The crossed product of von Neumann algebras, or Verschränktes Produkt, is a von Neumann algebra M ⋊ G built from M and a group action, analogous to the semidirect product.

Crossing angle (accelerator physics)

In accelerator physics, a crossing angle is a small angle between two particle beams where they meet at a collider, separating the beams and reducing luminosity.

Crossing number (graph theory)

The crossing number of a graph is the fewest edge crossings possible in any plane drawing of it, and it is 0 exactly when the graph is planar.

Crossing symmetry

Crossing symmetry is a property of scattering amplitudes in quantum field theory: amplitudes for different processes, like a particle collision and a related particle-antiparticle collision, are boundary values of one analytic function.

Crossover analysis

Crossover analysis is the statistical analysis of trials in which each subject receives a sequence of treatments in successive periods, so each subject serves as their own control.

Crossover study

A crossover study is a randomized clinical trial design in which every participant receives all compared treatments in randomized order, suited to chronic, stable conditions with short-lived treatment effects.

Crossref

Crossref is a not-for-profit membership organization, founded in 2000, that registers DOIs and maintains the world's largest scholarly metadata registry, holding over 177 million records from 26,000 members.

Crotonaldehyde

Crotonaldehyde (2-butenal) is a reactive α,β-unsaturated aldehyde, a flammable and highly toxic liquid made from acetaldehyde and used mainly to manufacture the food preservative sorbic acid.

Crowd collapses and crushes

Crowd collapses and crushes, also called crowd disasters, are mass-casualty events in which dense crowds transmit forces that immobilize people, causing suffocation, as at Hillsborough in 1989.

Crown ether

A crown ether is a macrocyclic polyether whose cyclic ring binds metal cations inside its cavity, discovered accidentally by Charles J. Pedersen at DuPont in 1967.

CrSBr

CrSBr, or chromium sulfide bromide, is an air-stable, layered van der Waals magnetic semiconductor in which ferromagnetic layers stack antiferromagnetically below its 132 K Néel temperature.