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Topics referred to by the same term
pairwise in Wiktionary, the free dictionary. Pairwise generally means "occurring in pairs" or "two at a time." Pairwise may also refer to: Pairwise disjoint
Pairwise
Topics referred to by the same term
Pairwise comparison may refer to: Pairwise comparison (psychology) Round-robin voting This disambiguation page lists articles associated with the title
Pairwise_comparison
Set of random variables of which any two are independent
independent random variables is pairwise independent, but some pairwise independent collections are not mutually independent. Pairwise independent random variables
Pairwise_independence
Topics referred to by the same term
Pairwise testing may refer to: All-pairs testing Pairwise comparison Paired difference test This disambiguation page lists articles associated with the
Pairwise_testing
A Pairwise Algorithm is an algorithmic technique with its origins in Dynamic programming. Pairwise algorithms have several uses including comparing a protein
Pairwise_Algorithm
Voting systems using paired comparisons
votes rank each candidate over the other. Pairwise counts are often displayed in a beats, tournament, pairwise comparison, or outranking matrix such as
Round-robin_voting
Two numbers without shared prime factors
the set is said to be pairwise coprime (or pairwise relatively prime, mutually coprime or mutually relatively prime). Pairwise coprimality is a stronger
Coprime_integers
Algorithmic technique
In numerical analysis, pairwise summation, also called cascade summation, is a summation algorithm, i.e. a technique to sum a sequence of finite-precision
Pairwise_summation
Process of comparing two entities to determine preference
Pairwise comparison generally is any process of comparing entities in pairs to judge which of each entity is preferred, or has a greater amount of some
Pairwise comparison (psychology)
Pairwise_comparison_(psychology)
Chance of wrongly rejecting the null hypothesis
In statistics, when performing multiple comparisons, a false positive ratio (also known as fall-out or false alarm rate ) is the probability of falsely
False_positive_rate
Pairwise-comparison electoral system
Condorcet method. Condorcet methods use pairwise counting. For each possible pair of candidates, one pairwise count indicates how many voters prefer one
Condorcet_method
Use of machine learning to rank items
of three approaches: pointwise (where individual documents are ranked), pairwise (where pairs of documents are ranked into a relative order), and listwise
Learning_to_rank
Potentially All Pairwise RanKings of all possible Alternatives (PAPRIKA) is a method for multi-criteria decision making (MCDM) or conjoint analysis, as
Potentially all pairwise rankings of all possible alternatives
Potentially_all_pairwise_rankings_of_all_possible_alternatives
Statistical methodology
Generalized pairwise comparisons (GPC) is a non-parametric statistical methodology for comparing treatments or interventions in clinical trials using one
Generalized pairwise comparisons
Generalized_pairwise_comparisons
Sets with no element in common
is pairwise disjoint. A Helly family is a system of sets within which the only subfamilies with empty intersections are the ones that are pairwise disjoint
Disjoint_sets
Single-winner ranked-choice voting system
The minimax Condorcet method selects the candidate for whom the greatest pairwise score for another candidate against them is the least such score among
Minimax_Condorcet_method
alternatives with respect to a set of decision criteria. The BWM is based on pairwise comparisons of the decision criteria. That is, after identifying the decision
Best_worst_method
When the occurrence of one event does not affect the likelihood of another
notions of independence need to be distinguished. The events are called pairwise independent if any two events in the collection are independent of each
Independence (probability theory)
Independence_(probability_theory)
pairwise compact, pairwise Hausdorff, and pairwise zero-dimensional. Pairwise Stone spaces are a bitopological version of Stone spaces. Pairwise Stone spaces
Pairwise_Stone_space
The pairwise sorting network is a sorting network discovered and published by Ian Parberry in 1992 in Parallel Processing Letters. The pairwise sorting
Pairwise_sorting_network
IEEE standard version
or 802.1X authentication, a shared secret key is generated, called the Pairwise Master Key (PMK). In PSK authentication, the PMK is actually the PSK, which
IEEE_802.11i-2004
Statistical model for pairwise comparisons
The Bradley–Terry model is a probability model for the outcome of pairwise comparisons between items, teams, or objects. Given a pair of items i and j
Bradley–Terry_model
Worked example of using the Analytic Hierarchy Process to choose a car
fifteen comparisons for each of the eight covering criteria. When the pairwise comparisons are as numerous as those in our example, specialized AHP software
Analytic hierarchy process – car example
Analytic_hierarchy_process_–_car_example
Post-hoc statistical test for pairwise comparisons
inflating the family-wise error rate. Pairwise comparisons: if the omnibus F-test from step 1 is significant, pairwise t-tests are conducted for all pairs
Fisher's least significant difference
Fisher's_least_significant_difference
alignment software is a compilation of software tools and web portals used in pairwise sequence alignment and multiple sequence alignment. See structural alignment
List of sequence alignment software
List_of_sequence_alignment_software
Producing colors by combining the primary or secondary colors in different amounts
color mixing in the RGB model. The primaries red, green, and blue combine pairwise to produce the additive secondaries cyan, magenta, and yellow. Combining
Color_mixing
Two or more species influencing each other's evolution
pressures drive an evolutionary arms race between the species involved. Pairwise or specific coevolution, between exactly two species, is not the only possibility;
Coevolution
About simultaneous modular congruences
the product of these integers, under the condition that the divisors are pairwise coprime (no two divisors share a common factor other than 1). The theorem
Chinese_remainder_theorem
Process in bioinformatics that identifies equivalent sites within molecular sequences
testing. Pairwise sequence alignment methods are used to find the best-matching piecewise (local or global) alignments of two query sequences. Pairwise alignments
Sequence_alignment
Pairwise error probability is the error probability that for a transmitted signal ( X {\displaystyle X} ) its corresponding but distorted version ( X ^
Pairwise_error_probability
Graph class
In graph theory, a graph G {\displaystyle G} is a pairwise compatibility graph (PCG) if there exists a weighted tree T {\displaystyle T} and two non-negative
Pairwise_compatibility_graph
Interactions between groups of atoms that do not arise from chemical bonds
Waals forces are often among the weakest chemical forces. For example, the pairwise attractive van der Waals interaction energy between H (hydrogen) atoms
Van_der_Waals_force
Single-winner electoral system
voters rank 5 candidates. The pairwise preferences have to be computed first. For example, when comparing A and B pairwise, there are 5+5+3+7=20 voters
Schulze_method
Statistical method in data analysis
criterion, which specifies the dissimilarity of sets as a function of the pairwise distances of observations in the sets. The choice of metric as well as
Hierarchical_clustering
Three linked but pairwise separated rings
enneagram; like the Borromean rings these three triangles are linked and not pairwise linked, but this crossing pattern describes a different link than the Borromean
Borromean_rings
Election result affecting losing candidate
table of pairwise counts eliminates the step-by-step redistribution of votes, which is usually the cause for spoilers in other methods. This pairwise comparison
Spoiler_effect
Proportionality constant in some physical laws
The diffusivity is generally prescribed for a given pair of species and pairwise for a multi-species system. The higher the diffusivity (of one substance
Mass_diffusivity
Information used for message authentication and integrity checking
XORed together to output the MAC. Universal hashing and in particular pairwise independent hash functions provide a secure message authentication code
Message_authentication_code
Stochastic process in probability theory
point whose successive displacements are random, in which displacements in pairwise disjoint time intervals are independent, and displacements in different
Lévy_process
Machine learning technique
converting them into pairwise comparisons for prediction purposes. In the online scenario, when human feedback is collected through pairwise comparisons under
Reinforcement learning from human feedback
Reinforcement_learning_from_human_feedback
"Highly entangled" quantum state of 3 or more qubits
In physics, in the area of quantum information theory, a Greenberger–Horne–Zeilinger (GHZ) state is an entangled quantum state that involves at least three
Greenberger–Horne–Zeilinger state
Greenberger–Horne–Zeilinger_state
builds on the development of methods for comparing treatment outcomes using pairwise comparisons. Finkelstein and Schoenfeld (1999) proposed a method for combining
Net_treatment_benefit
Paul Hansen at the University of Otago, the PAPRIKA method is based on pairwise comparisons, as illustrated in the accompanying image. An AI assistant
1000minds
concept in this case is Pairwise Stability, which accounts for the mutual approval of both players. A network is considered pairwise stable if: (i) for all
Strategic_network_formation
Criterion of fair item allocation
{MMS} _{v_{i}}^{1{\text{-out-of-}}n}(C)} . An allocation is a vector of n pairwise-disjoint subsets of C {\displaystyle C} -- one subset per agent. An allocation
Maximin_share
Type of software that helps make decisions
(ELECTRE) Multi-attribute global inference of quality (MAGIQ) Potentially All Pairwise RanKings of all possible Alternatives (PAPRIKA) Preference Ranking Organization
Decision-making_software
Software testing method
In computer science, all-pairs testing or pairwise testing is a combinatorial method of software testing that, for each pair of input parameters to a system
All-pairs_testing
Property of electoral systems
equals are present), all three Minimax methods (winning votes, margins and pairwise opposite) elect the same winners: [X] indicates voters who preferred the
Condorcet_loser_criterion
2026–27 season. In 2025, the NCAA announced that they would stop using the PairWise rankings for determining at-large bids to the NCAA tournament in favor
2026–27 NCAA Division I men's ice hockey season
2026–27_NCAA_Division_I_men's_ice_hockey_season
Area of discrete mathematics
is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of vertices
Graph_theory
the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of vertices
Glossary_of_computer_science
Set of vectors used to define coordinates
breaks, and the number of such pairwise almost orthogonal vectors (length of the chain) is recorded. For each n, 20 pairwise almost orthogonal chains were
Basis_(linear_algebra)
Single-winner electoral system
The Kemeny method is an electoral system that uses ranked ballots and pairwise comparison counts to identify the most popular choices in an election. It
Kemeny_method
Moreover, (X,τ+,τ−) is a pairwise Stone space. The pairwise Stone space (X,τ+,τ−) is called the bitopological dual of L. Each pairwise Stone space is bi-homeomorphic
Duality theory for distributive lattices
Duality_theory_for_distributive_lattices
Assessment tool
individual weighting of these subscales by letting the subjects compare them pairwise based on their perceived importance. This requires the user to choose which
NASA-TLX
Term in computer science
multiple objects, a naive approach would require detecting collisions for all pairwise combinations of objects. As the number of objects increases, the number
Collision_detection
Sequence of numbers with distinct sums
n>1} , a n {\displaystyle a_{n}} is the smallest integer such that every pairwise sum a i + a j {\displaystyle a_{i}+a_{j}} is distinct, for all i {\displaystyle
Mian–Chowla_sequence
for treating van der Waals forces between bodies which does not assume pairwise additivity of the individual intermolecular forces; that is to say, the
Lifshitz theory of van der Waals force
Lifshitz_theory_of_van_der_Waals_force
Property of points all lying on a single line
Look up collinearity or collinear in Wiktionary, the free dictionary. In geometry, collinearity of a set of points is the property of their lying on a
Collinearity
Multiple comparison method in statistics
estimates of all possible contrasts among the factor level means, not just the pairwise differences considered by the Tukey–Kramer method. It works on similar
Scheffé's_method
Property of electoral systems
clones competes. The preferences would be: The Kemeny method arranges the pairwise comparison counts in the following tally table: The ranking scores of all
Independence of clones criterion
Independence_of_clones_criterion
Partition of a simple polygon into triangles
polygon) P into a set of triangles, i.e., finding a set of triangles with pairwise non-intersecting interiors whose union is P. Triangulations may be viewed
Polygon_triangulation
would be tabulated as follows: Result: Both A and B have two pairwise wins and one pairwise tie, so A and B are tied for the Copeland winner. Depending
Later-no-help_criterion
Principle that voting for a candidate should help them
the participation criterion. All deterministic voting rules that satisfy pairwise majority-rule can fail in situations involving four-way cyclic ties, though
Participation_criterion
Concept in natural language processing
Other measures calculate the similarity between ontological instances: Pairwise: measure functional similarity between two instances by combining the semantic
Semantic_similarity
Natural number
telephone number, specifically, the number of ways of connecting 5 points with pairwise connections. There are 26 sporadic groups. The 26-dimensional Lorentzian
26_(number)
Database of handwritten digits
Classifier Data augmentation Preprocessing Error rate (%) Linear classifier Pairwise linear classifier Affine transformation Deskewing 7.6 K-Nearest Neighbors
MNIST_database
Property of electoral systems
are expressed on the ballots. The results would be tabulated as follows: Pairwise election results X A B C D Y A [X] 2 [Y] 2 [X] 2 [Y] 2 [X] 1 [Y] 3 B [X]
Later-no-harm_criterion
OV in complexity theory
d} increases, the performance of all of these algorithms excluding the pairwise dot product algorithm deteriorates. This is due to the bit-parallel and
Orthogonal_vectors_problem
Theorem in arithmetic combinatorics
{\displaystyle A+A} and A ⋅ A {\displaystyle A\cdot A} (the sets of pairwise sums and pairwise products, respectively) form a significantly larger set. More
Erdős–Szemerédi_theorem
Proof strategy for showing a collection of statements are equivalent
equivalence of several statements can be proven without having to prove all pairwise equivalences directly. In English it is also sometimes called a cycle of
Ringschluss
2024. Retrieved December 4, 2024. "PairWise Rankings explanation". Retrieved August 16, 2023. "Men's Division I PairWise Rankings". Retrieved August 16,
2024–25 NCAA Division I men's ice hockey season
2024–25_NCAA_Division_I_men's_ice_hockey_season
Statistical hypothesis test
comparisons"/ "planned comparisons"- a particular set of comparisons "pairwise comparisons"-all possible comparisons i.e. Fisher's least significant difference
F-test
On sets of points with integer distances
The integer multiples of the angle of a 3–4–5 right triangle. All pairwise distances among the even multiples (every other point from this set) are rational
Erdős–Anning_theorem
Theory of stochastic processes
where Zk are pairwise uncorrelated random variables and the functions ek are continuous real-valued functions on [a, b] that are pairwise orthogonal in
Kosambi–Karhunen–Loève theorem
Kosambi–Karhunen–Loève_theorem
Problem in computer science
Then, the set packing problem asks if some k subsets in the list are pairwise disjoint (in other words, no two of them share an element). More formally
Set_packing
Statistical test for multiple comparisons
other treatment; that is, it applies simultaneously to the set of all pairwise comparisons μ i − μ j , {\displaystyle \mu _{i}-\mu _{j}\ ,} and identifies
Tukey's_range_test
Structure in combinatorial mathematics
pair of elements is found in the same number of blocks and the design is pairwise balanced. For t = 1, each element occurs in the same number of blocks (the
Block_design
difference) – are primarily used as measures of effect size in the generalised pairwise comparisons (GPC) framework, a generalisation of the theory underpinning
Win_statistics
Concept in genealogy and genetics
detects pairwise IBD segments in sequencing data GERMLINE: discovers in linear-time IBD segments in pairs of individuals DASH: builds upon pairwise IBD segments
Identity_by_descent
Square matrix containing the distances between elements in a set
square matrix (two-dimensional array) containing the distances, taken pairwise, between the elements of a set. Depending upon the application involved
Distance_matrix
Family closed under complements and countable disjoint unions
countable unions of pairwise disjoint sets: if A 1 , A 2 , A 3 , … {\displaystyle A_{1},A_{2},A_{3},\ldots } is a sequence of pairwise disjoint sets in D
Dynkin_system
Sports season
2019. "USA Hockey Men's Poll". USCHO.com. Retrieved November 26, 2019. "Men's Division I PairWise Rankings". USCHO.com. Retrieved November 26, 2019.
2023–24 NCAA Division I independent men's ice hockey season
2023–24_NCAA_Division_I_independent_men's_ice_hockey_season
Named range of Unicode code points
"supplemental_arrows_a", "SupplementalArrowsA" and "SUPPLEMENTALARROWSA". Blocks are pairwise disjoint; that is, they do not overlap. The starting code point and the
Unicode_block
Algorithm in numerical analysis
mean square errors of pairwise summation actually grow as O ( log n ) {\displaystyle O\left({\sqrt {\log n}}\right)} . Pairwise summation is used by
Kahan_summation_algorithm
Logic problem, AND of pairwise ORs
for solving constraint satisfaction problems with binary variables and pairwise constraints. They apply this technique to a problem of classroom scheduling
2-satisfiability
Sports season
"Player Stats". Big Ten Hockey. Retrieved July 28, 2022. "Men's Division I PairWise Rankings". USCHO.com. Retrieved November 26, 2019. "Bracket Announced for
2024–25 Big Ten Conference ice hockey season
2024–25_Big_Ten_Conference_ice_hockey_season
Fiber bundle of the 3-sphere over the 2-sphere, with 1-spheres as fibers
Pairwise linked keyrings mimic part of the Hopf fibration.
Hopf_fibration
Process of replacing missing data with substituted values
missing data include: hot deck and cold deck imputation; listwise and pairwise deletion; mean imputation; non-negative matrix factorization; regression
Imputation_(statistics)
Mathematical concept in algebra
vice versa). A set of matrices A1,…,Ak is said to commute if they commute pairwise, meaning that every pair of matrices in the set commutes. Commuting matrices
Commuting_matrices
17th-century conjecture proved by Andrew Wiles in 1994
{\displaystyle x^{4}-y^{4}=z^{2}} has no primitive solutions in integers (no pairwise coprime solutions). In turn, this proves Fermat's Last Theorem for the
Fermat's_Last_Theorem
Concept in probability theory
matrix was estimated from ν {\displaystyle \nu } observations with sum of pairwise deviation products Ψ {\displaystyle {\boldsymbol {\Psi }}} t ν ′ − p +
Conjugate_prior
Statistical method that summarizes and/or integrates data from multiple sources
Meta-analysis is a method of synthesis of quantitative data from multiple independent studies addressing a common research question. An important part
Meta-analysis
Measure of inequality of a statistical distribution
ratio of the standard deviation to the mean, effectively squaring the pairwise differences. This makes the CV highly sensitive to extreme outliers, such
Gini_coefficient
Sports season
will be via at-large bids. Those 10 teams are determined based upon the PairWise rankings. The rankings take into account all games played but are heavily
2022–23 Big Ten Conference ice hockey season
2022–23_Big_Ten_Conference_ice_hockey_season
Geometric model of the physical space
directions do not lie in the same plane. Furthermore, if these directions are pairwise perpendicular, the three values are often labeled by the terms width/breadth
Three-dimensional_space
Basic circuit in quantum computing
also with n qubits initialized to | 0 ⟩ {\displaystyle |0\rangle } and pairwise CNOT its qubits with the qubits in register A, such that for each p the
Quantum_logic_gate
Sum of pairwise divisible unit fractions
Sum of pairwise divisible unit fractions
Engel_expansion
Structured technique for organizing and analyzing complex decisions
it through a series of pairwise comparisons that derive numerical scales of measurement for the nodes. The criteria are pairwise compared against the goal
Analytic_hierarchy_process
Species of cat native to Africa and Asia
subspecies as valid taxa: Results of an analysis of molecular variance and pairwise fixation index of 182 African leopard museum specimens showed that some
Leopard
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