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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
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
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
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 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
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
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
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
for their papers Grad and classes with bounded expansion I. Decompositions, Grad and classes with bounded expansion II. Algorithmic aspects, First order
Nerode_Prize
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
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
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
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
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
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
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
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
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
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
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
Multiple comparisons correction
This section needs expansion. You can help by adding missing information. (September 2013)
Šidák_correction
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
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
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
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
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
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
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
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
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)
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
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
Power series with negative powers
may be used to express complex functions in cases where a Taylor series expansion cannot be applied. The Laurent series was named after and first published
Laurent_series
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
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
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
Generalization of the binomial theorem to other polynomials
multinomial coefficients can be written as closed-form expressions with bounded integer compositions: ( n k ) m − 1 = ∑ k 0 + k 1 + ⋯ + k m − 1 = n k 1
Multinomial_theorem
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
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
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
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
Method for finding sums of unit fractions
earliest and most notably by J. J. Sylvester (1880) A closely related expansion method that produces closer approximations at each step by allowing some
Greedy algorithm for Egyptian fractions
Greedy_algorithm_for_Egyptian_fractions
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
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
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
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
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
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
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
Canceled video game
EarthBound 64, known in Japan as Mother 3: Fall of the Pig King, is a canceled role-playing video game that was under development by Nintendo and HAL
EarthBound_64
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
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
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
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
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
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
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
Techniques to protect against brute-force attack
requirements – these can be effective in frustrating attacks by memory-bound adversaries. Key stretching algorithms depend on an algorithm which receives
Key_stretching
Computational hardness assumption
The small set expansion hypothesis or small set expansion conjecture in computational complexity theory is an unproven computational hardness assumption
Small set expansion hypothesis
Small_set_expansion_hypothesis
several terms in the Taylor series expansion of ƒ around a. Such a series expansion of ƒ, called the Mittag-Leffler expansion, is convergent in a larger set
Mittag-Leffler_star
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
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
How 435 seats are distributed to 50 states
districts in other states with the same population. Another proposed expansion rule, the cube root rule, calls for the membership of the legislature
United States congressional apportionment
United_States_congressional_apportionment
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
Stadium in Madrid, Spain
is located in the Chamartín district of Madrid. It occupies the block bounded by the Paseo de la Castellana and the streets of Concha Espina, Padre Damián
Bernabéu_(stadium)
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
Theorem in complex analysis
In complex analysis, Liouville's theorem states that every bounded entire function must be constant. That is, every holomorphic function f {\displaystyle
Liouville's theorem (complex analysis)
Liouville's_theorem_(complex_analysis)
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
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
American actor, filmmaker, and singer-songwriter (born 1955)
Ground, Bound by Honor, and Tombstone. He went on to write, direct, and star in the 1996 independent film Sling Blade. The film, an expansion of the short
Billy_Bob_Thornton
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
Describes approximate behavior of a function
{\textstyle D.} Common choices for the domain are intervals of real numbers, bounded or unbounded, the set of positive integers, the set of complex numbers
Big_O_notation
President of Russia (2000–2008; since 2012)
organizations receiving funding from abroad as "foreign agents". The law is an expansion of "foreign agent" legislation adopted in 2012. As of June 2020, per the
Vladimir_Putin
British joint-stock company (1600–1858)
two roses Gules seeded Or barbed Vert. Crest: A sphere without a frame, bounded with the Zodiac in bend Or, between two pennants flottant Argent, each
East_India_Company
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
Chicago "L" rapid transit line
Brown Line Capacity Expansion Project. ctabrownline.com Chicago Transit Authority (March 8, 2006). "Brown Line Capacity Expansion Project March 8, 2006"
Brown_Line_(CTA)
Park in Atlanta, GA
Public Realm (PDF). "Atlanta Beltline Announces Design Firm For Enota Park Expansion | What Now Atlanta". What Now Atlanta. 2018-03-23. Retrieved 2018-08-01
Enota_Park
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
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
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
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
British literary award
whereas former judge A. L. Kennedy welcomed the change. Following this expansion, the first winner not from the Commonwealth, Ireland, or Zimbabwe was
Booker_Prize
Entertainment facility in Arizona, United States
construction of the arena was part of the university's $200 million campus expansion and growth. It regularly hosts Christian and secular concerts, outside
Global_Credit_Union_Arena
Policy of interest rates or money supply
the field of behavioral economics that takes into account the concept of bounded rationality, people often deviate from the way that these neoclassical
Monetary_policy
All of space observable from the Earth at the present
reach the Solar System and Earth since the beginning of the cosmological expansion. The radius of this region is about 14.26 gigaparsecs (46.5 billion light-years
Observable_universe
1996 video game
Yu-no: A Girl Who Chants Love at the Bound of This World is a 1996 visual novel adventure game developed and published by ELF Corporation. It was originally
Yu-no
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
Bound on probability of a random variable being far from its mean
inequality (also called the Bienaymé–Chebyshev inequality) provides an upper bound on the probability of deviation of a random variable (with finite variance)
Chebyshev's_inequality
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
British mathematician (born 1987)
Maynard gave a different proof of Yitang Zhang's theorem that there are bounded gaps between primes, and resolved a longstanding conjecture by showing
James_Maynard_(mathematician)
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)
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
1861–1865 conflict in the United States
came to a head when Abraham Lincoln, a Republican who opposed slavery's expansion, won the 1860 presidential election. Seven slave states in the South responded
American_Civil_War
German fascist ideology
unite all Germans living in historically German territory, gain lands for expansion under the doctrine of Lebensraum, and exclude those deemed either Community
Nazism
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