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In the mathematical theory of dynamical systems, an exponential dichotomy is a property of an equilibrium point that extends the idea of hyperbolicity
Exponential_dichotomy
Exponent bias Exponential (disambiguation) Exponential backoff Exponential decay Exponential dichotomy Exponential discounting Exponential diophantine equation
List_of_exponential_topics
Stochastic control System dynamics, system analysis Takens' theorem Exponential dichotomy Liénard's theorem Krylov–Bogolyubov theorem Krylov-Bogoliubov averaging
List of dynamical systems and differential equations topics
List_of_dynamical_systems_and_differential_equations_topics
Problem of determining if a Boolean formula could be made true
into an equivalent conjunctive normal form, which may, however, be exponentially longer. For example, transforming the formula (x1∧y1) ∨ (x2∧y2) ∨ .
Boolean satisfiability problem
Boolean_satisfiability_problem
Brace Explicit symmetry breaking Exploration geophysics Explorer 1 Exponential dichotomy Exposure assessment Extended X-ray absorption fine structure Extended
Index_of_physics_articles_(E)
Conversion of continuous functions into discrete counterparts
can approximate a continuous variable as a binary variable (creating a dichotomy for modeling purposes, as in binary classification). Discretization is
Discretization
Complexity class of problems
question whether any "natural" problem has the same property: Schaefer's dichotomy theorem provides conditions under which classes of constrained Boolean
NP-intermediate
Number measuring the chance an event occurs
and stated that the frequency of an error could be expressed as an exponential function of the numerical magnitude of the error – disregarding sign
Probability
Theory or model concerning the origin of the universe
In this model the universe goes through a very short phase of intense exponential expansion. The expansion is so immense and fast that all pre-existing
Cosmogony
Statement in computational learning theory
is ambiguous with respect to a random ϕ {\textstyle \phi } -separable dichotomy of X {\textstyle X} is C ( N , d − 1 ) C ( N , d ) {\displaystyle {\frac
Cover's_theorem
Mathematical term in group theory
were many results establishing growth dichotomy (that is, that the growth is always either polynomial or exponential) for various classes of finitely generated
Grigorchuk_group
Italian philosopher and activist (born 1949)
Chaosmosis, a text by Félix Guattari, to establish a dichotomy of rhythm and chaos. This dichotomy is then compared with (regular and irregular) breathing
Franco_Berardi
Problem of counting solutions to logic formulas
number of solutions is #P-complete. This result follows from a general dichotomy characterizing which SAT-like problems are #P-complete. This is the counting
♯SAT
Period of rapid progress in AI
number of topics and display general knowledge. Investment in AI grew exponentially after 2020, with venture capital funding for generative AI companies
AI_boom
property. Logarithms and exponentials with the same base cancel each other. This is true because logarithms and exponentials are inverse operations –
List of logarithmic identities
List_of_logarithmic_identities
German psychologist (1850–1909)
a previously learned list wasn't useful to understanding memory. This dichotomy between descriptive and experimental study of memory would resonate later
Hermann_Ebbinghaus
question was settled in the positive for Boolean domains by Schaefer's dichotomy theorem and for any finite domain by Andrei Bulanov and Dmitriy Zhuk,
Complexity of constraint satisfaction
Complexity_of_constraint_satisfaction
Legal concept regulating rights of a creative work
the advent of copyright, 6th century to 18th century. Blue shows printed books. Log-lin plot; a straight line therefore shows an exponential increase.
Copyright
Political ideology promoting free-market capitalism
suggested these accusations arose from arguments that presented a false dichotomy between free-market economics and socialism, ignoring mixed economies
Neoliberalism
Structure-preserving correspondence between node-link graphs
equivalent to the Feder–Vardi conjecture (aka CSP conjecture, dichotomy conjecture) on CSP dichotomy, which states that for every constraint language Γ, CSP(Γ)
Graph_homomorphism
Eukaryotes other than animals, plants or fungi
under light microscopy. Protists were incorporated into the traditional dichotomy that defined all life as either plant or animal: non-motile algae were
Protist
Sharp rise in the price of natural uranium
The uranium bubble of 2007 was a period of nearly exponential growth in the price of natural uranium, starting in 2005 and peaking at roughly $300/kg
Uranium_bubble_of_2007
Appendix on analytic geometry by Descartes
of the alphabet, a, b, c, etc. denote constants. He introduces modern exponential notation for powers (except for squares, where he kept the older tradition
La_Géométrie
Mathematical function
approximation of ordinary elliptical galaxies. Setting n = 1 gives the exponential profile: I(R)∝e−bR which is a good approximation of spiral galaxy disks
Sérsic_profile
Online platform used to build relations
engage with technology in general. For a number of years, Prensky's (2001) dichotomy between Digital Natives and Digital Immigrants has been considered a relatively
Social_networking_service
Randomly determined process
its most extreme form (Hopper 1987, 1988), USF rejects the Saussurean dichotomies such as langue vs. parôle. For early interpretivist approaches to focus
Stochastic
Worldwide economic crisis
destruction, the number of patent applications was flat, compared to exponential increases in patent application in prior years. American families did
2008_financial_crisis
embodiment and knowing". This avoids the dichotomy between the immanent and transcendental. Other dichotomies according to which theories or descriptions
Theories_about_religion
Statistical model for a binary dependent variable
Inc. ISBN 978-0-8247-8587-1. Gouriéroux, Christian (2000). "The Simple Dichotomy". Econometrics of Qualitative Dependent Variables. New York: Cambridge
Logistic_regression
Two propositions or events that cannot both be true
multinomial probit or multinomial logit technique is used. Contrariety Dichotomy Disjoint sets Double bind Event structure Oxymoron Synchronicity MECE
Mutual_exclusivity
Psychologist
Ainslie, G. (2009). "Pleasure and aversion: Challenging the conventional dichotomy". Inquiry. 52 (4): 357–377. doi:10.1080/00201740903087342. Ainslie, G
George_Ainslie_(psychologist)
Term for 2010s–present technological era
Revolution. This is due to the following characteristics: Velocity – exponential speed at which incumbent industries are affected and displaced Scope
Fourth_Industrial_Revolution
Method of logical reasoning
inductive arguments in support of the uniformity of nature, this supposed dichotomy between merely two modes of inference, deduction and induction, has been
Inductive_reasoning
Computer science award
ISSN 0004-5411. S2CID 8964233. Dyer, Martin; Richerby, David (2013). "An Effective Dichotomy for the Counting Constraint Satisfaction Problem". SIAM Journal on Computing
Gödel_Prize
French philosopher and mathematician (1596–1650)
sum Evil demon Trademark argument Causal adequacy principle Mind–body dichotomy Cartesian circle Cartesian diver Balloonist theory Wax argument Res cogitans
René_Descartes
OAPEC petroleum embargo
capital controls in oil-importing economies. It marked the beginning of an exponential growth of Western capital markets. In the United States in 1974, seven
1973_oil_crisis
Rational-number approximation of a real number
known as the Duffin–Schaeffer conjecture on the analogue of Khinchin's dichotomy for general, not necessarily decreasing, sequences ψ . Beresnevich & Velani
Diophantine_approximation
Elliptical galaxy located in the constellation Draco
He, Yan-Qin; Hao, Cai-Na; Xia, Xiao-Yang (2014-01-30). "Revisiting the dichotomy of early-type galaxies". Research in Astronomy and Astrophysics. 14 (2):
J120011.1+680924.8
French-French Algerian economic development program
the same means that France is offering to give them. The speech noted a dichotomy of choice between either war or brotherhood. De Gaulle made it clear that
Constantine_Plan
Industrial shift to information technology
The amount of digital data stored appears to be growing approximately exponentially, reminiscent of Moore's law. As such, Kryder's law prescribes that the
Information_Age
1997 anime film
film also references the psychoanalysis of Sigmund Freud, including the dichotomy between Eros and Thanatos. According to critics, the characters remain
The_End_of_Evangelion
Soft substance meant to be chewed without swallowing
differentiated by the consumers' intent to form bubbles or the sugar/sugarless dichotomy. Chewing gum typically comes in three formats: tablets, coated pellets
Chewing_gum
expectations of future inflation). At worst, inflation tends to grow exponentially and leads to hyperinflation.[citation needed] Built-in inflation is
Inertial_inflation
Methods in artificial intelligence research
non-enumerative search be practical when the underlying problem is exponentially hard? The approach advocated by Simon and Newell is to employ heuristics:
Symbolic artificial intelligence
Symbolic_artificial_intelligence
Extension of rule over foreign nations
ResearchGate. Retrieved 15 June 2026. A multitude of combinations and dichotomies of both heterarchical and hierarchical polities are possible among nomads
Imperialism
Physical quantity
ISBN 978-0-08-049458-6. Mankovich, C.; Fortney, J. J. (December 2019). "Evidence for a Dichotomy in the Interior Structures of Jupiter and Saturn from Helium Phase Separation"
Energy
Sixth story arc of JoJo's Bizarre Adventure
evolution into Made in Heaven, which gives him superhuman speed and exponentially accelerates time (except for living beings). The group makes a desperate
Stone_Ocean
Accumulation of particles into planetesimals
velocity of the gas is deflected by one radian; the stopping time is the exponential timescale for the deceleration of an object due to gas drag, and the
Pebble_accretion
In logic, a statement which is always true
increases as 2k, where k is the number of variables in the formula. This exponential growth in the computation length renders the truth table method useless
Tautology_(logic)
Data whose unit can take on only two possible states
details. Number of states of a collection of discrete variables depends exponentially on the number of variables, and only as a power law on number of states
Binary_data
Interpretation of quantum mechanics
Roger (August 1991). "Roger Penrose Looks Beyond the Classic-Quantum Dichotomy". Sciencewatch. Archived from the original on 2007-10-23. Retrieved 2007-10-21
Many-worlds_interpretation
Neuron communication by electric impulses
ISSN 0031-9333. PMID 33118864. Golding NL, Kath WL, Spruston N (December 2001). "Dichotomy of action-potential backpropagation in CA1 pyramidal neuron dendrites"
Action_potential
Scenario for the dynamical evolution of the Solar System
Baldwin, Emily (25 January 2010). "Comet impacts explain Ganymede-Callisto dichotomy". Astronomy Now. Retrieved 23 December 2016 – via astronomynow.com. Nimmo
Nice_model
Field of research
jointly shape tool-use behaviour, making simple cultural/non-cultural dichotomies potentially misleading. Overall, primate archaeology helps researchers
Primate_archaeology
Convex polytope of parenthesizations
face normal vectors have coordinates that are 0, +1, or −1. There are exponentially many combinatorially distinct ways of doing this. Because K5 is a polyhedron
Associahedron
Security analysis methodology
Prechter, Robert R Jr; Parker, Wayne D (2007). "The Financial/Economic Dichotomy in Social Behavioral Dynamics: The Socionomic Perspective". Journal of
Technical_analysis
Branch of mathematics
instance, an infinite geometric sum is implicit in Zeno's paradox of the dichotomy. (Strictly speaking, the point of the paradox is to deny that the infinite
Mathematical_analysis
Extremely small quantity in calculus
traced as far back as the Greek philosopher Zeno of Elea, whose Zeno's dichotomy paradox was the first mathematical concept to consider the relationship
Infinitesimal
Entertainer dressed and acting with exaggerated femininity
show to his gender/sexualities class to challenge his students' ideas of dichotomy. Over time, he began inviting students to attend with him. He gathered
Drag_queen
concepts. Moreover, as mathematician Hung-Hsi Wu explained, the apparent dichotomy between basic skills and understanding of mathematical concepts is a delusion
Mathematics education in the United States
Mathematics_education_in_the_United_States
Grouping of evolved cool luminous stars
thousands of times the observed luminosity of the star, but decreases exponentially over just a few years. The shell flash causes the star to expand and
Asymptotic_giant_branch
System of stars and interstellar matter
Elliptical Galaxies in Coma, and an Explanation for the Alleged Structural Dichotomy between Dwarf and Bright Elliptical Galaxies". The Astronomical Journal
Galaxy
Geological system and early time period of Mars
lies about 5 km lower in elevation than the southern highlands. This dichotomy has existed since the Pre-Noachian. Water draining from the southern highlands
Noachian
Elliptical galaxy smaller than normal ones
approximated using de Vaucouleur's model, while dEs were approximated with an exponentially declining surface brightness profile. However, both types fit well by
Dwarf_elliptical_galaxy
Theory describing changing population patterns
about 30 to 50 years. Population growth is sustained and begins to be exponential. The Age of Degenerative and Man-Made Diseases: Mortality continues to
Epidemiological_transition
Hypothesis in biology
The latter option is an important consideration as there may be a false dichotomy between the hypotheses of Genes-First and Metabolism-First where both
Genes-first_hypothesis
Aspect of the topic
growth had been stagnant for some time. This meant that they did not have exponential growth, as the United States did, leaving them with less room to fall
Great Depression in the United Kingdom
Great_Depression_in_the_United_Kingdom
(pseudo-)Riemannian manifold whose geodesics are reversible
symmetric spaces can be classified. As shown by Katsumi Nomizu, there is a dichotomy: an irreducible symmetric space G / H is either flat (i.e., an affine
Symmetric_space
Designing solid structures with tailored properties
molecules generally drives the thermodynamic outcome. Understanding this dichotomy between the kinetics and thermodynamics constitutes the focus of research
Crystal_engineering
Significant surplus of crude oil
in Norwegian waters in the central North Sea. Discoveries increased exponentially in the 1970s and 1980s, and new fields were developed throughout the
1980s_oil_glut
Point in time when the maximum rate of petroleum extraction is reached
literally correct. The study observed that in most cases the asymmetric exponential model provided a better fit (as in the case of Seneca cliff model), and
Peak_oil
Model checking Trakhtenbrot's theorem Computable model theory Tarski's exponential function problem Undecidable problem Institutional model theory Institution
List of mathematical logic topics
List_of_mathematical_logic_topics
governments and intergovernmental bodies to ban land mines. This high/low dichotomy is one clear example of the difference between the two types of action
Networked_advocacy
Turkish-American theoretical physicist (1926–1994)
Magnetic-Moment - the Precession of Spin 1994 the Exponential Map for the Conformal-Group O(2, 4) 1994 the Exponential Map for the Unitary-Group Su(2,2) In Journal
Asım_Orhan_Barut
Experiment in which information about the test is masked to reduce bias
the common view of studies as blinded or unblinded exemplifies a false dichotomy. The success of blinding is assessed by asking study participants about
Blinded_experiment
Study of genetic variants in different individuals
Wray NR (May 2012). "Evidence-based psychiatric genetics, AKA the false dichotomy between common and rare variant hypotheses". Molecular Psychiatry. 17
Genome-wide_association_study
Theoretical framework for analysing performance guarantees in computer networks
-w. Cho and Y. Jiang: Fundamentals of the Backoff Process in 802.11: Dichotomy of the Aggregation, IEEE Trans. Information Theory 61(4): 1687-1701, 2015
Network_calculus
Relationships among bond yields of different maturities
Nelson-Siegel family, the Svensson family, the exponential polynomial family or the Cairns restricted-exponential family of curves). Van Deventer, Imai and
Yield_curve
science) Savitch's theorem (computational complexity theory) Schaefer's dichotomy theorem (computational complexity theory) Sipser–Lautemann theorem (probabilistic
List_of_theorems
Algebraic encoding of graph connectivity
remain #P-hard, even for bipartite planar graphs. In his paper on the dichotomy for planar graphs, Vertigan claims (in his conclusion) that the same result
Tutte_polynomial
The two early state court cases, Bliss and Buzzard, set the fundamental dichotomy in interpreting the Second Amendment, i.e., whether it secured an individual
Gun politics in the United States
Gun_politics_in_the_United_States
American linguist (1915–2001)
size. He argued that the number of possible classifications increases exponentially with the number of languages compared (1957:44). For comparison, the
Joseph_Greenberg
largely agrarian economy on the eve of global industrialisation, which exponentially multiplied world GDP." With "the major drop in India's per capita GDP
Economy of India under the British Raj
Economy_of_India_under_the_British_Raj
Branch of mathematical logic
of reals is the union of a perfect set and a countable set). Silver's dichotomy (every coanalytic equivalence relation has either countably many equivalence
Reverse_mathematics
Hormone that inhibits hunger
cancellous bone, but increases cortical bone. This "cortical-cancellous dichotomy" may represent a mechanism for enlarging bone size, and thus bone resistance
Leptin
Hypothetical non-therapeutic use of gene therapy by athletes
double the DNA sequences exponentially. In gene doping detection, If the sequence started to amplify producing an exponential graph, then the test is positive
Gene_doping
Elliptical galaxy in the constellation Hercules
He, Yan-Qin; Hao, Cai-Na; Xia, Xiao-Yang (2014-01-30). "Revisiting the dichotomy of early-type galaxies". Research in Astronomy and Astrophysics. 14 (2):
J171328.4+274336.6
Political party in Portugal
thesis). Universidade Nova de Lisboa. p. 5. This liberal/conservative dichotomy isn't applicable in the Portuguese context, where across the left-right
Portuguese_Communist_Party
How humans move within a network
Luca Pappalardo; et al. (8 September 2015). "Returners and Explorers dichotomy in Human Mobility". Nature Communications. 6: 8166. Bibcode:2015NatCo
Individual_mobility
Ideology merging socialism with green politics
words, "go beyond the market and the state" by rejecting the supposed dichotomy between private enterprise and state-owned production, while also rejecting
Eco-socialism
Kingdom in the North Sea. Hydraulic fracturing operations have grown exponentially since the mid-1990s, when technologic advances and increases in the
History of the petroleum industry in the United States
History_of_the_petroleum_industry_in_the_United_States
Study of the development of economic thought
ceremonial values, which became known as the Ceremonial/Instrumental Dichotomy. Joseph Alois Schumpeter (1883–1950) was an Austrian School economist
History_of_economic_thought
Evolution-related timelines
and Karenleigh A. Overmann, to move past the "internal" and "external" dichotomy by treating stone tools as objects with agency in both providing insight
Evolution of human intelligence
Evolution_of_human_intelligence
American archaeologist
abacus" to refer to temporary material forms with inherent place value (exponential structure), including collaborative finger-counting and counting by sorting
Karenleigh_A._Overmann
17th–19th century labor system in the British American colonies
national era, but as their numbers dwindled and the industry expanded exponentially, they made up a decreasingly small proportion of the labor force. Text
Indentured servitude in British America
Indentured_servitude_in_British_America
Ongoing American comic book series
Hickman's thoughts about the X-Men into more explicit focus. It's a story of dichotomies, where democracies and empires, dreams and realities sit side-by-side
X-Men_(comic_book)
Thai Buddhist temple
Bhasicharoen. The center became an official temple in 1977. The temple grew exponentially during the 1980s, when the temple's programs became widely known among
Wat_Phra_Dhammakaya
Infinite graph containing all countable graphs
Cherlin, Gregory (2011), "Forbidden substructures and combinatorial dichotomies: WQO and universality", Discrete Mathematics, 311 (15): 1543–1584, doi:10
Rado_graph
this dichotomy. Physical education would take more emphasis after World War I broke out, as it helped create fit soldiers. Baseball grew exponentially, reaching
Sports_in_Puerto_Rico
while coexists if d ≥ 3 {\displaystyle \scriptstyle d\geq 3} . This dichotomy is closely related to the fact that simple random walk on Z d {\displaystyle
Voter_model
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