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Family of graphs whose shallow minors are sparse graphs
classes of bounded expansions are that all shallow minors have chromatic number bounded by a function of t, or that the given family has a bounded value of
Bounded_expansion
Computer science field
properties. This method is known as bounded model checking. The success of Boolean satisfiability solvers in bounded model checking led to the widespread
Model_checking
Increase in distance between parts of the universe
The expansion of the universe is the increase in distance between gravitationally unbound parts of the observable universe with time. It is an intrinsic
Expansion_of_the_universe
Making of satisfactory, not optimal, decisions
approach to increase their utility. In addition to bounded rationality, bounded willpower and bounded selfishness are two other key concepts in behavioral
Bounded_rationality
Graph coloring related to treedepth
{\displaystyle q} -centered coloring is bounded as a function of q {\displaystyle q} in the graphs of bounded expansion. A centered coloring is a graph coloring
Centered_coloring
Graph layout on multiple half-planes
bounded book thickness have bounded expansion. However, even the graphs of bounded degree, a much stronger requirement than having bounded expansion,
Book_embedding
Invariant in graph theory
graph and m denotes the number of edges. Graphs of bounded queue number also have bounded expansion, meaning that their shallow minors are sparse graphs
Queue_number
Graph with almost the max amount of edges
l)-sparse is equivalent to the graphs in the family having bounded degeneracy or having bounded arboricity. More precisely, it follows from a result of Nash-Williams
Dense_graph
Graph minor formed from subgraphs of small diameter
type of graph family, described similarly, are the graph families of bounded expansion. These are graph families for which there exists a function f such
Shallow_minor
International outdoor education network
September 2023. "Outward Bound 2015 Program Guide". Issuu. Retrieved 5 February 2016. Outward Bound International. "International Expansion". Archived from the
Outward_Bound
French mathematician
for the papers Grad and classes with bounded expansion I. Decompositions, Grad and classes with bounded expansion II. Algorithmic aspects, First order
Patrice_Ossona_de_Mendez
Czech mathematician (born 1946)
for the papers Grad and classes with bounded expansion I. Decompositions, Grad and classes with bounded expansion II. Algorithmic aspects, First order
Jaroslav_Nešetřil
for their papers Grad and classes with bounded expansion I. Decompositions, Grad and classes with bounded expansion II. Algorithmic aspects, First order
Nerode_Prize
Maximum number of colors in a greedy graph coloring
particular, for graphs of bounded degeneracy (such as planar graphs) or graphs for which the chromatic number and degeneracy are bounded within constant factors
Grundy_number
Graph with at most one crossing per edge
graphs have bounded book thickness, but some 1-planar graphs including K2,2,2,2 have book thickness at least four. 1-planar graphs have bounded local treewidth
1-planar_graph
has bounded twin-width. The family has bounded expansion, meaning that all its shallow minors are sparse. Such a family is said to have bounded sparse
Twin-width
Exponential representation for differential equations
In mathematics and physics, the Magnus expansion, named after Wilhelm Magnus (1907–1990), provides an exponential representation of the product integral
Magnus_expansion
Mathematical approximation of a function
In mathematical analysis, the Taylor series or Taylor expansion of a function is an infinite sum of terms that are expressed in terms of the function's
Taylor_series
Growth of the North American ice hockey league
The National Hockey League (NHL) has undergone several rounds of expansion and other organizational changes during its history to reach its current 32
Potential National Hockey League expansion
Potential_National_Hockey_League_expansion
time, these grants were ceded to the federal government. The first great expansion of the country came with the Louisiana Purchase of 1803, which doubled
Territorial evolution of the United States
Territorial_evolution_of_the_United_States
High-temperature expansion in statistical mechanics
mechanics, the cluster expansion (also called the high temperature expansion or hopping expansion) is a power series expansion of the partition function
Cluster_expansion
Leaf expansion is a process by which plants make efficient use of the space around them by causing their leaves to enlarge, or wither. This process enables
Leaf_expansion
Problem in theoretical computer science
choice of H). When G is a planar graph (or more generally a graph of bounded expansion) and H is fixed, the running time of subgraph isomorphism can be reduced
Subgraph_isomorphism_problem
Phenomenon in fluid dynamics
A Prandtl-Meyer expansion fan is a two-dimensional simple wave that occurs when a supersonic flow turns around a sharp convex corner. The fan consists
Prandtl–Meyer_expansion_fan
2015 video game
Matt (May 14, 2021). "Prison Architect's Alcatraz-inspired Island Bound expansion out in June". Eurogamer. Archived from the original on March 11, 2022
Prison_Architect
Japanese nation state from 1868 to 1947
expansion and non-intervention in China—he tried to resolve the crisis through diplomatic negotiation. The army ignored the Cabinet's "non-expansion"
Empire_of_Japan
Indentation in the thigh bone
shallow due to the expansion of the two trochanters. In lepidosaurs, the intertrochanteric fossa is shallow but broad. It is bounded medially by the internal/lesser
Trochanteric_fossa
2026 video game
Diablo IV: Lord of Hatred is a major expansion pack for the action role-playing dungeon crawling game Diablo IV, developed and published by Blizzard Entertainment
Diablo_IV:_Lord_of_Hatred
2004 video game
2004, and a port for MacOS by Aspyr was released on June 17, 2005. Eight expansion packs and nine "stuff packs" were subsequently released between 2005 and
The_Sims_2
DNA mutation involving an increase in number of trinucleotide repeats
A trinucleotide repeat expansion, also known as a triplet repeat expansion, is the DNA mutation responsible for causing any type of disorder categorized
Trinucleotide repeat expansion
Trinucleotide_repeat_expansion
Mathematical concept
The regions in the complex plane with different asymptotic behaviour are bounded by possibly one or two types of curves known as Stokes curves and Anti-Stokes
Stokes_phenomenon
U.S. national park in St. Louis, Missouri
Territorial Expansion Memorial Commission) to join if the City of St. Louis could raise money. The area to be included in the park was bounded by the Eads
Gateway_Arch_National_Park
Video game series
In 1996, Mother 3 (EarthBound 64 in North America), was announced. It was slated for release on the 64DD, a disk drive expansion peripheral for the Nintendo
Mother_(video_game_series)
Measure of algorithmic complexity
choice of description language; but the effect of changing languages is bounded (a result called the invariance theorem, see below). There are two definitions
Kolmogorov_complexity
1994 video game
to EarthBound for the Nintendo 64: Mother 3 (EarthBound 64 in North America). It was scheduled for release on the 64DD, a Nintendo 64 expansion peripheral
EarthBound
Series of functions in mathematics
In mathematics, an asymptotic expansion, asymptotic series or Poincaré expansion (after Henri Poincaré) is a formal series of functions which has the property
Asymptotic_expansion
Observation in physical cosmology
Friedmann equations showed the universe might be expanding, and presented the expansion speed if that were the case. Before Hubble, astronomer Carl Wilhelm Wirtz
Hubble's_law
Concerned with the notion of stability in model theory
These include graph classes with bounded expansion, which in turn include planar graphs and any graph class of bounded degree. Geometric stability theory
Stable_theory
Country in South Asia
world's seventh-largest country by area and the largest by population. Bounded by the Indian Ocean on the south, the Arabian Sea on the southwest, and
India
2004 video game
November 23, 2004. Since launch, World of Warcraft has had eleven major expansion packs: The Burning Crusade (2007), Wrath of the Lich King (2008), Cataclysm
World_of_Warcraft
Sparse graph with strong connectivity
expander family if h ( G i ) {\displaystyle h(G_{i})} is bounded away from zero. The expansion parameters defined above are related to each other. In particular
Expander_graph
Historical region of Western United States, c. 1607–1912
history, folklore, and culture associated with the forward wave of American expansion in mainland North America that began with European colonial settlements
American_frontier
Exponentially decreasing bounds on tail distributions of random variables
extremes of a bounded random variable, where the infima are attained for infinite t {\displaystyle t} . For unbounded random variables the bound is nowhere
Chernoff_bound
Organization based in Omaha, Nebraska
reorganizes - North Omaha campus for boys is cutting ties with Outward Bound - Expansion afoot at North Omaha's NorthStar campus". Omaha World Herald. Omaha
NorthStar_Foundation
Adoption of the euro by more countries
(2015), Croatia (2023), and Bulgaria (2026). Five remaining states are bound by the EU treaties to introduce the euro once they fulfil certain economic
Enlargement_of_the_eurozone
Optimization replacing a function call with that function's source code
Inline expansion is similar to macro expansion, but occurs during compiling, without changing the source code (the text), while macro expansion occurs
Inline_expansion
International airport in Essex, England
influential for airport architecture. From 1997 to 2007, Stansted had rapid expansion of passenger numbers on the back of the boom in low-cost air travel, peaking
London_Stansted_Airport
Path planner similar to potential field method with breadth first search modification
The wavefront expansion algorithm is a specialized potential field path planner with breadth-first search to avoid local minima. It uses a growing circle
Wavefront_expansion_algorithm
Result about when a matrix can be diagonalized
absence of eigenvectors. The next generalization we consider is that of bounded self-adjoint operators on a Hilbert space. Such operators may have no eigenvectors:
Spectral_theorem
Mathematical-logic system
abstraction through eta-expansion, as ( λ v . x x v ) {\displaystyle (\lambda v.xxv)} , thus preventing its premature expansion: Z = λ f . ( λ x . f (
Lambda_calculus
a graph whose edge expansion, vertex expansion, or spectral expansion is bounded away from zero. expansion 1. The edge expansion, isoperimetric number
Glossary_of_graph_theory
Sphere that contains a set of objects
a bounding sphere. A coreset is a small subset, that a 1 + ε {\displaystyle 1+\varepsilon } expansion of the solution on the subset is a bounding sphere
Bounding_sphere
Multiple comparisons correction
This section needs expansion. You can help by adding missing information. (September 2013)
Šidák_correction
Logical formulation of graph properties
linear time on graphs of bounded treewidth, and every fixed MSO1 property can be tested in linear time on graphs of bounded clique-width. The version
Logic_of_graphs
Phenomenon of non-ideal fluids changing temperature
Joule–Thomson expansion. The expansion is inherently irreversible. During this expansion, enthalpy remains unchanged (see proof below). Unlike a free expansion, work
Joule–Thomson_effect
Function in number theory given by Srinivasa Ramanujan
Srinivasa Ramanujan mentioned the sums in a 1918 paper. In addition to the expansions discussed in this article, Ramanujan's sums are used in the proof of Vinogradov's
Ramanujan's_sum
Algorithm used for pathfinding and graph traversal
leading to the development of memory-bounded heuristic searches, such as Iterative deepening A*, memory-bounded A*, and SMA*. A* is often used for the
A*_search_algorithm
Speakers of Austronesian languages
originated from a prehistoric seaborne migration, known as the Austronesian expansion, from Taiwan, circa 3000 to 1500 BCE. Austronesians reached the Batanes
Austronesian_peoples
Historic district in Wyoming, United States
(Lincolnway) Street and Central Avenue. The 1988 expansion encompassed 11 buildings to the north of the 1980 expansion. One of these buildings was previously listed
Downtown Cheyenne Historic District
Downtown_Cheyenne_Historic_District
North American professional baseball league
1960s. The AL and NL added eight clubs in the 1960s, which started the expansion era: two in 1961, two in 1962, and four in 1969. Player discontent with
Major_League_Baseball
Algebraic expansion of powers of a binomial
elementary algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial. According to the theorem, the
Binomial_theorem
History and future of the universe
Earth by the expansion of space at such a velocity that the observable universe will be limited to the solar system's gravitationally bound local galaxy
Chronology_of_the_universe
Country in South America
Portuguese-speaking country in the Americas, where it is the official language. Bounded by the Atlantic Ocean on the east, Brazil has a coastline of 7,491 kilometers
Brazil
have proposed numerous extensions to the subway system. The first major expansion of the subway system was the Dual Contracts, a set of agreements between
Proposed expansion of the New York City Subway
Proposed_expansion_of_the_New_York_City_Subway
Process in physical chemistry
Negative thermal expansion (NTE) is an unusual physicochemical process in which some materials contract upon heating, rather than expand as most other
Negative_thermal_expansion
Number representing a continuous quantity
numbers with an upper bound admits a least upper bound. This means the following: A set of real numbers S {\displaystyle S} is bounded above if there is a
Real_number
Country in South Asia
city and financial centre. Pakistan is the 33rd-largest country by area. Bounded by the Arabian Sea on the south, the Gulf of Oman on the southwest, and
Pakistan
Sailor-written newspaper
published maps showing American expansion by “rearrang[ing] global relationships through the agency of print.” The Bounding Billow also wrote letters to
The_Bounding_Billow
Spread of a species to new areas
woody plant encroachment, or by long-distance dispersal. The term range expansion is also used. Dispersion in biology is the dissemination, or scattering
Colonisation_(biology)
Model for approximating non-linear effects, similar to a Taylor series
to be compact. It is usually taken to be an equicontinuous, uniformly bounded set of functions, which is compact by the Arzelà–Ascoli theorem. In many
Volterra_series
Lutz's resource-bounded measure is a generalisation of Lebesgue measure to complexity classes. It was originally developed by Jack Lutz. Just as Lebesgue
Resource-bounded_measure
19th-century expansionist belief in the U.S.
slavery in these new states and territories. It is also associated with the expansion of European settlers onto the territories of Indigenous Americans and
Manifest_destiny
Northwest, Kokkina/Erenköy, which is bounded by the U.N. buffer zone and the Mediterranean Sea. East Timor: Oecusse is bounded by Indonesia and the Savu Sea
List_of_enclaves_and_exclaves
Suspension bridge connecting Detroit, Michigan, with Windsor, Ontario
While many of the stop lights commonly cited have been removed by the expansion of Highway 401 (Herb Gray Parkway) which will connect to the Gordie Howe
Ambassador_Bridge
Singaporean branch of Outward Bound
campus after Pulau Ubin and East Coast, and is intended to support the expansion of the Ministry of Education's MOE-OBS Challenge programme to all Secondary
Outward_Bound_Singapore
Decomposition of periodic functions
continuous T-periodic function need not converge pointwise. The uniform boundedness principle yields a simple non-constructive proof of this fact. In 1922
Fourier_series
Continuous probability distribution
virtually unlimited shape flexibility; a choice among unbounded, semi-bounded, and bounded distributions; ease of fitting to data with linear least squares;
Metalog_distribution
Professional Canadian football league
Blue Bombers. Although expansion teams have joined the league throughout its history, especially during the league's brief expansion into the United States
Canadian_Football_League
Finite sum of distinct unit fractions
These include problems of bounding the length or maximum denominator in Egyptian fraction representations, finding expansions of certain special forms
Egyptian_fraction
Archipelagic country in Southeast Asia
million, it is the world's twelfth-most-populous country. The Philippines is bounded by the South China Sea to the west, the Philippine Sea to the east, and
Philippines
1121–1269 Berber empire in North Africa and Iberia
pp. xiv+248. ISBN 978-0906559321. Taagepera, Rein (September 1997). "Expansion and Contraction Patterns of Large Polities: Context for Russia". International
Almohad_Caliphate
Continent
term has been in use since the mid-19th century. Europe is taken to be bounded by large bodies of water to the north, west and south; Europe's limits
Europe
Sequence of rational numbers
is bounded, because it never exceeds 0.4444444... = 4/9. The limit of this sequence is not a computable real number, since its decimal expansion contains
Specker_sequence
Analytic function on the upper half-plane with a certain behavior under the modular group
absolute value of F(Λ) remains bounded above as long as the absolute value of the smallest non-zero element in Λ is bounded away from 0. The key idea in
Modular_form
Theory of stochastic processes
functions, analogous to a Fourier series representation of a function on a bounded interval. The transformation is also known as Hotelling transform and eigenvector
Kosambi–Karhunen–Loève theorem
Kosambi–Karhunen–Loève_theorem
Borough in New York City and county in New York State
Situated on one of the world's largest natural harbors, the borough is bounded by the Hudson, East, and Harlem rivers and includes several small adjacent
Manhattan
American actor (born 1951)
Fugitive (1993), Baby's Day Out (1994), the Wachowskis' directorial debut Bound (1996), and Percy Jackson & the Olympians: The Lightning Thief (2010). In
Joe_Pantoliano
Property of a thermodynamic system
constant temperature T H {\textstyle T_{\mathsf {H}}} during isothermal expansion stage and the heat Q C {\textstyle Q_{\mathsf {C}}} is transferred from
Entropy
Cosmological model
increase exponentially. But this expansion is similar for every moment of time (hence the exponential law—the expansion of a local volume is the same number
Big_Rip
owned slaves at some time in their lives. The cotton industry's rapid expansion in the Deep South after the invention of the cotton gin greatly increased
Slavery_in_the_United_States
In mathematics, invariant of square matrices
{\displaystyle m<n} this is zero. By calculating the volume of the tetrahedron bounded by four points, they can be used to identify skew lines. The volume of
Determinant
Handheld game console
Nintendo's first hardware launch in support of its "Gaming Population Expansion" strategy, highlighting that its touch-based interface would allow for
Nintendo_DS
Complexity Index in India of 21.1. Various refineries are undergoing capacity expansions, and the Pachpadra Refinery got commissioned in 2026. Jamnagar (Reliance)
List of oil refineries in India
List_of_oil_refineries_in_India
Pair of polynomial sequences
possible leading coefficient whose absolute value on the interval [−1, 1] is bounded by 1. They are also the "extremal" polynomials for many other properties
Chebyshev_polynomials
Canadian professional soccer club based in Vancouver
Halbouni. The Whitecaps won their first Western Conference title, defeating expansion club San Diego FC in the conference finals to advance to their first MLS
Vancouver_Whitecaps_FC
Mountain range in Germany
mountain range in the state of Baden-Württemberg in southwest Germany, bounded by the Rhine Valley to the west and south and close to the borders with
Black_Forest
Online database of integer sequences
binary expansions (here 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, ... (A004601)), or continued fraction expansions (here
On-Line Encyclopedia of Integer Sequences
On-Line_Encyclopedia_of_Integer_Sequences
Series of border barriers
support safe and legal migration with the use of technology. The barrier expansion was opposed by a unanimous vote by the Laredo, Texas, City Council. Laredo
Mexico–United States border wall
Mexico–United_States_border_wall
Russian state from 1721 to 1917
system. Catherine the Great (r. 1762–1796) presided over further Russian expansion by conquest, colonization, and diplomacy, while continuing Peter's policy
Russian_Empire
Major League Baseball franchise in Arlington, Texas
Division. The team was founded as the Washington Senators in 1961, an expansion team awarded to Washington, D.C., after the previous Senators incarnation
Texas_Rangers_(baseball)
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