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In mathematics, an acyclic space is a nonempty topological space X in which cycles are always boundaries, in the sense of homology theory. This implies
Acyclic_space
Topics referred to by the same term
acyclic in Wiktionary, the free dictionary. Acyclic may refer to: In chemistry, a compound which is an open-chain compound, e.g. alkanes and acyclic aliphatic
Acyclic
Directed graph with no directed cycles
mathematics, particularly graph theory, and computer science, a directed acyclic graph (DAG) is a directed graph with no directed cycles. That is, it consists
Directed_acyclic_graph
Generalization of graph theory
diagrams. Both β-acyclicity and γ-acyclicity can be tested in polynomial time. Those four notions of acyclicity are comparable: γ-acyclicity which implies
Hypergraph
satisfying only this weaker condition to be called "weakly exact." Acyclic space Essential manifold Whitehead conjecture Gompf, Robert E. (1998). "Symplectically
Aspherical_space
Tree node with two other nodes as descendants
called least common ancestor) of two nodes v and w in a tree or directed acyclic graph (DAG) T is the lowest (i.e. deepest) node that has both v and w as
Lowest_common_ancestor
Computational complexity class
acyclic constraint satisfaction problems LOGCFL is the set of decision problems solvable by nondeterministic auxiliary pushdown automata in log space
LOGCFL
Trail in which only the first and last vertices are equal
graph without cycles is called an acyclic graph. A directed graph without directed cycles is called a directed acyclic graph. A connected graph without
Cycle_(graph_theory)
Mathematical object in sheaf cohomology
applied to sheaves: flabby (flasque in French), fine, soft (mou in French), acyclic. In the history of the subject they were introduced before the 1957 "Tohoku
Injective_sheaf
Generalizes showing that two homology theories are isomorphic
In algebraic topology, a discipline within mathematics, the acyclic models theorem can be used to show that two homology theories are isomorphic. The
Acyclic_model
Data organization and storage formats
decision diagram And-inverter graph Directed graph Directed acyclic graph Propositional directed acyclic graph Multigraph Hypergraph Lightmap Winged edge Quad-edge
List_of_data_structures
Edges that hit all cycles in a graph
graph breaks all of the cycles, producing an acyclic subgraph of the given graph, often called a directed acyclic graph. A feedback arc set with the fewest
Feedback_arc_set
Exact sequence used to describe the structure of an object
is acyclic with respect to this functor. A flat resolution is acyclic for the tensor product by every M. Similarly, resolutions that are acyclic for
Resolution_(algebra)
Branch of mathematics
{Ker} \,d_{n}/\operatorname {Im} \,d_{n+1}.} A chain complex is called acyclic or an exact sequence if all its homology groups are zero. Chain complexes
Homological_algebra
Topological space
fibration, and are characterized by their fundamental groups. The total spaces are all acyclic. {b; (o1, 0); (3, b1), (3, b2), (3, b3)} (b integral, bi is 1
Seifert_fiber_space
Mathematical game
mathematical game played by placing "pebbles" or "markers" on a directed acyclic graph according to certain rules: A given step of the game consists of
Pebble_game
Topological manifold whose homology coincides with that of a sphere
Poincaré sphere. If there are at least 3 a′s, not 2, 3, 5, then this is an acyclic homology 3-sphere with infinite fundamental group that has a Thurston geometry
Homology_sphere
Red-orange pigment of the terpenoids class
e Types of terpenes and terpenoids (# of isoprene units) Basic forms: Acyclic (linear, cis and trans forms) Monocyclic (single ring) Bicyclic (2 rings)
Β-Carotene
Links the homology groups of a product space with those of the individual spaces
the acyclic model theorem. The theorem can be formulated as follows. Suppose X {\displaystyle X} and Y {\displaystyle Y} are topological spaces. Then
Eilenberg–Zilber_theorem
Graph with oriented edges
digraph. A directed graph is acyclic if it has no directed cycles. The usual name for such a digraph is directed acyclic graph (DAG). Multitrees are DAGs
Directed_graph
Topological space
{\displaystyle \operatorname {Ran} (X)} is acyclic if X is connected. A theorem of Beilinson and Drinfeld states that the Ran space of a connected manifold is weakly
Ran_space
Type of graph in mathematics
directed tree, oriented tree or singly connected network) is a directed acyclic graph whose underlying undirected graph is a tree. In other words, a polytree
Polytree
Mathematical category with weak equivalences, fibrations and cofibrations
equivalence is called an acyclic (or trivial) fibration and a cofibration that is also a weak equivalence is called an acyclic (or trivial) cofibration
Model_category
Type of direct current electrical generator
the orientation of the field. It is also known as a unipolar generator, acyclic generator, disk dynamo, or Faraday disc. The voltage is typically low,
Homopolar_generator
Any algorithm which solves the search problem
local graph search algorithms designed to work efficiently on directed acyclic graphs with a single root or starting node (trees). Tree search algorithms
Search_algorithm
Search tree data structure
each word), a minimal deterministic acyclic finite state automaton (DAFSA) or radix tree would use less storage space than a trie. This is because DAFSAs
Trie
complete coloring. acyclic 1. A graph is acyclic if it has no cycles. An undirected acyclic graph is the same thing as a forest. An acyclic directed graph
Glossary_of_graph_theory
Logic puzzle forming a picture in a grid
Hendrik Jan; Kosters, Walter; van Rijn, Jan N.; Vis, Jonathan K. (2014). "Acyclic Constraint Logic and Games". ICGA Journal. 37 (1): 3–16. arXiv:1604.05487
Nonogram
Theorem in geometric topology
equivalent to saying that the prime decomposition of the manifold has no acyclic components and turns out to be equivalent to the condition that all geometric
Poincaré_conjecture
Tool in algebraic topology
or a CW complex. A sheaf E of abelian groups on a topological space X is called acyclic if Hj(X,E) = 0 for all j > 0. By the long exact sequence of sheaf
Sheaf_cohomology
Graph representing faces of another graph
strongly connected graph) are dual to acyclic orientations (assignments of directions that produce a directed acyclic graph). In the same way, dijoins (sets
Dual_graph
cohomology using an acyclic resolution of the sheaf in question. Let F {\displaystyle {\mathcal {F}}} be a sheaf on a topological space X {\displaystyle
De_Rham–Weil_theorem
equivalence is called a trivial (or acyclic) fibration. A cofibration that is also a weak equivalence is called a trivial (or acyclic) cofibration. Hovey (1999)
Weak equivalence (homotopy theory)
Weak_equivalence_(homotopy_theory)
Visual depiction of a partially ordered set
sources, the phrase "Hasse diagram" has a different meaning: the directed acyclic graph obtained from the covering relation of a partially ordered set, independently
Hasse_diagram
Topological invariant in mathematics
is a finite resolution of F {\displaystyle \ {\mathcal {F}}\ } by acyclic sheaves. Another generalization of the concept of Euler characteristic
Euler_characteristic
Natural number
partially ordered sets ("posets") with n labeled elements (or labeled acyclic transitive digraphs))". The On-Line Encyclopedia of Integer Sequences.
219_(number)
Polish-American mathematician (1913–1998)
Lane, Saunders (1945). "Relations between homology and homotopy groups of spaces". Annals of Mathematics. 46 (3): 480–509. doi:10.2307/1969165. JSTOR 1969165
Samuel_Eilenberg
Set of methods for supervised statistical learning
class with the most votes determines the instance classification. Directed acyclic graph SVM (DAGSVM) Error-correcting output codes Crammer and Singer proposed
Support_vector_machine
Algorithm for visible surface determination in 3D graphics
valid ordering can be described as a topological ordering of a directed acyclic graph representing occlusions between objects. Conceptually Painter's Algorithm
Painter's_algorithm
Probabilistic model
f_{AB},f_{AC},f_{AD}} . If the network structure of the model is a directed acyclic graph, the model represents a factorization of the joint probability of
Graphical_model
American computer technology company
other scene geometry representations) and stream out to memory a directed acyclic graph of 3D volumes surrounding the geometry, known as a bounding volume
Caustic_Graphics
Diagram used in strategy computer games
these trees are technically directed and acyclic, they can more accurately be described as a directed acyclic graph of technologies. The diagram is tree-shaped
Technology_tree
Data structure for Boolean functions
and propositional directed acyclic graphs (PDAG). A Boolean function can be represented as a rooted, directed, acyclic graph, which consists of several
Binary_decision_diagram
Graph orientation with one source and sink
each edge (an orientation) that causes the graph to become a directed acyclic graph with a single source s and a single sink t, and an st-numbering of
Bipolar_orientation
Chemical compound
This ring form is in equilibrium with isocyanogen tetraazide, an isomeric acyclic structure that has long been known to cyclize quickly to the tetrazole
1-Diazidocarbamoyl-5-azidotetrazole
1-Diazidocarbamoyl-5-azidotetrazole
Concept category theory (mathematics)
\ell },C_{0}^{\perp \ell r}} are the classes of fibrations, acyclic cofibrations, acyclic fibrations, and cofibrations. Let sSet be the category of simplicial
Lifting_property
Parallel computing algorithm
computation, which means that a computation can be viewed as a directed acyclic graph with a single source (start of computation) and a single sink (end
Work_stealing
Probabilistic graphical representation of causal relationships
represents a set of variables and their conditional dependencies via a directed acyclic graph (DAG). While it is one of several forms of causal notation, causal
Bayesian_network
problem into another constraint satisfaction problem that is binary and acyclic. Decomposition methods work by grouping variables into sets, and solving
Decomposition method (constraint satisfaction)
Decomposition_method_(constraint_satisfaction)
Cohomology with real coefficients computed using differential forms
for i > 0 {\textstyle i>0} since all fine sheaves on paracompact spaces are acyclic. So the long exact cohomology sequences themselves ultimately separate
De_Rham_cohomology
Spectral sequence
and F {\displaystyle F} takes injective objects to G {\displaystyle G} -acyclic objects, then for each object A {\displaystyle A} of A {\displaystyle {\mathcal
Grothendieck spectral sequence
Grothendieck_spectral_sequence
Shading language for WebGPU
break/continue. Recursion is disallowed; entry-point call graphs must be acyclic. Shaders define stage entry points with @vertex, @fragment, or @compute
WebGPU_Shading_Language
Algorithm for finding shortest paths
However, specialized cases (such as bounded/integer weights, directed acyclic graphs etc.) can be improved further. If preprocessing is allowed, algorithms
Dijkstra's_algorithm
Minimizing problem in computer programming
Sumazin, Pavel (2005). "Lowest common ancestors in trees and directed acyclic graphs" (PDF). Journal of Algorithms. 57 (2): 75–94. doi:10.1016/j.jalgor
Range_minimum_query
Study of discrete mathematical structures
structures, as are proofs, which form finite trees or, more generally, directed acyclic graph structures (with each inference step combining one or more premise
Discrete_mathematics
Glossary of terms used in branch of mathematics
0–9 A B C D E F G H I J K L M N O P Q R S T U V W X Y Z Acyclic. A binary relation is acyclic if it contains no "cycles": equivalently, its transitive
Glossary_of_order_theory
Naturally produced monosaccharide
therefore an aldohexose. The glucose molecule can exist in an open-chain (acyclic) as well as ring (cyclic) form. Glucose is naturally occurring and is found
Glucose
Concept in natural language processing
ordered in a partially ordered set and represented as nodes of a directed acyclic graph (e.g., a taxonomy), would be the shortest-path linking the two concept
Semantic_similarity
Cryptocurrency
Nano (Abbreviation: XNO) is a cryptocurrency characterized by a directed acyclic graph data structure and distributed ledger, making it possible for Nano
Nano_(cryptocurrency)
Machine learning-powered structure design
the one-shot model) is defined. A supernetwork is a very large Directed Acyclic Graph (DAG) whose subgraphs are different candidate neural networks. Thus
Neural_architecture_search
Chemical reaction
equilibrium in both cyclic and acyclic systems may be predicted from the structures of the two equilibrating epoxides. In acyclic systems, these rules have
Payne_rearrangement
Finite-state machine
final states: { HALT } {\displaystyle \{{\text{HALT}}\}} . Deterministic acyclic finite state automaton DFA minimization Monadic second-order logic Powerset
Deterministic finite automaton
Deterministic_finite_automaton
Mathematical set with an ordering
acyclic graph ordered by reachability. The set of subspaces of a vector space ordered by inclusion. For a partially ordered set P, the sequence space
Partially_ordered_set
Polymer harvested from certain trees
lengths and angles: this caused the Challenger disaster, when the American Space Shuttle's flattened o-rings failed to relax to fill a widening gap. The
Natural_rubber
Subset of artificial intelligence
inherently multi-dimensional. A Bayesian network, belief network, or directed acyclic graphical model is a probabilistic graphical model that represents a set
Machine_learning
Tool in homological algebra
so that we can talk about cohomology, then the cone of a map f being acyclic means that the map is a quasi-isomorphism; if we pass to the derived category
Mapping cone (homological algebra)
Mapping_cone_(homological_algebra)
Data structure
Computer programming portal Prefix tree (also known as a Trie) Deterministic acyclic finite state automaton (DAFSA) Ternary search tries Hash trie Deterministic
Radix_tree
Relates abstract sheaf cohomology with Čech cohomology
space X {\displaystyle X} and U {\displaystyle {\mathcal {U}}} an open cover of X . {\displaystyle X.} If F {\displaystyle {\mathcal {F}}} is acyclic
Leray's_theorem
Chemical compound giving a proton or accepting an electron pair
because the electrons shared in the B—F bond are located in the region of space between the two atomic nuclei and are therefore more distant from the fluoride
Acid
Chemical group derived from alkanes (one hydrogen removed)
is intentionally unspecific to include many possible substitutions. An acyclic alkyl has the general formula of −CnH2n+1. A cycloalkyl group is derived
Alkyl_group
Software engineering
control in a code repository. Code history has the structure of a directed acyclic graph which can be topologically sorted. This makes it possible to use
Bisection (software engineering)
Bisection_(software_engineering)
Chemical compound
M. de Silva and J. M. Goodman (2005). "What Is the Smallest Saturated Acyclic Alkane that Cannot Be Made?". J. Chem. Inf. Model. 45 (1): 81–87. CiteSeerX 10
Heptadecane
Type of saturated hydrocarbon compound
paraffin (a historical trivial name that also has other meanings), is an acyclic saturated hydrocarbon. In other words, an alkane consists of hydrogen and
Alkane
Open problem on 3x+1 and x/2 functions
occurs for exactly one 2-adic integer, so that almost all trajectories are acyclic in Z 2 {\displaystyle \mathbb {Z} _{2}} . An equivalent formulation of
Collatz_conjecture
Abstract data type
have a bounded capacity. If the stack is full and does not contain enough space to accept another element, the stack is in a state of stack overflow. Stacks
Stack_(abstract_data_type)
Algorithm to search the nodes of a graph
D. Reverse postordering produces a topological sorting of any directed acyclic graph. This ordering is also useful in control-flow analysis as it often
Depth-first_search
2008 science fiction novel by Neal Stephenson
the many-worlds interpretation of quantum mechanics based on a directed acyclic graph, which accounts for the various "worldtracks" and "narratives" explored
Anathem
Deterministic finite automaton accepting set of all suffixes of particular string
suffix automaton of a string S {\displaystyle S} is the smallest directed acyclic graph with a dedicated initial vertex and a set of "final" vertices, such
Suffix_automaton
It is often in contrast to move-generation algorithms using a directed acyclic word graph (DAWG) such as the one used by Maven. It is generally twice
GADDAG
Software development tool
representation could be something like an abstract syntax tree or a directed acyclic graph. Semantic analysis takes the representation made from syntax analysis
Multi-pass_compiler
Open topological cover
follows from the fact that higher derived functors can be computed using acyclic resolutions. The two-dimensional surface of a sphere S 2 {\displaystyle
Good_cover
Concept in mathematical group theory
PSL(2, 5)). Every acyclic group is superperfect, but the converse is not true: the binary icosahedral group is superperfect, but not acyclic. A. Jon Berrick
Superperfect_group
an emerging space industry driven by the private sector. Kuwait's first satellite Kuwait's Orbital Space in collaboration with the Space Challenges Program
Economy_of_Kuwait
Bias in causal inference
Several notation systems and formal frameworks, such as causal directed acyclic graphs (DAGs), have been developed to represent and detect confounding
Confounding
Graph algorithm
vertex whose in-degree or out-degree is 0, or every vertex of a directed acyclic graph. The basic idea of the algorithm is this: a depth-first search (DFS)
Tarjan's strongly connected components algorithm
Tarjan's_strongly_connected_components_algorithm
Cubic graph Cycle graph De Bruijn graph Dense graph Dipole graph Directed acyclic graph Directed graph Distance regular graph Distance-transitive graph Edge-transitive
List_of_graph_theory_topics
Simple sugars such as glucose and fructose
Fischer projection is a systematic way of drawing the skeletal formula of an acyclic monosaccharide so that the handedness of each chiral carbon is well specified
Monosaccharide
the form of a directed acyclic graph. Ancestral graphs can encode conditional independence relations that arise in directed acyclic graph (DAG) models with
Ancestral_graph
Topics referred to by the same term
vertex color a graph using n colors Chromatic numbering Chromatic index Acyclic chromatic number Strong chromatic number Fractional chromatic number Vertex
Chromatic_(disambiguation)
Sequence of characters, data type
this, since characters a program treated specially (such as period and space and comma) were in the same place in all the encodings a program would encounter
String_(computer_science)
Whether one vertex can be reached from another in a graph
would contain a cycle, contradicting that it is acyclic. If G {\displaystyle G} is directed but not acyclic (i.e. it contains at least one cycle), then its
Reachability
Non-destructive audio, video, or image editing
effectively an edit decision list (EDL), for video and audio, or a directed acyclic graph for still images, is used to keep track of edits. Each time the edited
Non-linear_editing
On the homology of continuous maps between compact metric spaces
metric spaces, and let f : X → Y {\displaystyle f:X\to Y} be surjective and continuous. Suppose that the fibers of f {\displaystyle f} are acyclic, so that
Vietoris–Begle mapping theorem
Vietoris–Begle_mapping_theorem
Reflexive and transitive binary relation
longer has cycles; it is a partial order, and corresponds to a directed acyclic graph. A preorder that is symmetric is an equivalence relation; it can
Preorder
Fewest graph edges whose removal breaks all cycles
to make the graph acyclic; Feedback arc set - the minimum number of arcs to delete from a directed graph, in order to make it acyclic. Peter Robert Kotiuga
Cyclomatic_number
Knowledge base that represents semantic relations between concepts in a network
research field. Examples of the use of semantic networks in logic, directed acyclic graphs as a mnemonic tool, dates back centuries. The earliest documented
Semantic_network
Tree which includes all vertices of a graph
tree. A few graph theory authors define a spanning forest to be a maximal acyclic subgraph of the given graph, or equivalently a subgraph consisting of a
Spanning_tree
Purely functional package manager for the GNU system
system governed via the Shepherd daemon can represent its user space as a directed acyclic graph, with the "system-service," which is responsible for early
GNU_Guix
Square matrix used to represent a graph or network
there exists n such that An is the zero matrix), then it is a directed acyclic graph. The adjacency matrix may be used as a data structure for the representation
Adjacency_matrix
Algorithm for speeding up cellular automaton simulations
sharing of nodes in the quadtree (which is not so much a tree as a directed acyclic graph), we only want to use one node to represent all squares with the
Hashlife
ACYCLIC SPACE
ACYCLIC SPACE
Boy/Male
Biblical
Breadth, space, extent.
Boy/Male
Tamil
Limitless space Avatar incarnation
Boy/Male
Hindu
Space
Boy/Male
Indian
Open space, Battle field
Boy/Male
Hindu
Limitless space Avatar incarnation
Surname or Lastname
English or Scottish
English or Scottish : unexplained.
Boy/Male
Tamil
Antrix | அஂதà¯à®°à¯€à®•à¯à®·
Space
Antrix | அஂதà¯à®°à¯€à®•à¯à®·
Girl/Female
Maori
Open spaces.
Boy/Male
Muslim
Open space, Battle field
Girl/Female
Tamil
Antariksha | அஂதரிகà¯à®·
Space, Sky
Antariksha | அஂதரிகà¯à®·
Girl/Female
Indian, Telugu
Goddess of Space
Girl/Female
Biblical
Spaces, places.
Boy/Male
Arabic, Muslim, Pashtun
Battle Field; Open Space
Surname or Lastname
English
English : habitational name from either of two places in Cheshire. It is possible that the name originally denoted a building where village assemblies were held, named in Old English as ‘meeting-house’, from (ge)mÅt ‘meeting’ + ærn ‘house’, ‘hall’. Other possibilities are that the name derives from Old English (ge)mÅt-rÅ«m ‘meeting space’, or (ge)mÅt-treum ‘assembly trees’.
Surname or Lastname
English
English : occupational name for a wattler, Middle English watelere, i.e. someone who made the panels of interwoven twigs that were used to fill the spaces between the structural timbers of a timber frame building. See also Dauber.
Girl/Female
Indian, Telugu
Space
Girl/Female
Indian, Japanese, Tamil
Space; Star
Boy/Male
Hindu
Space
Girl/Female
Gujarati, Hindu, Indian
Star in Space
Boy/Male
Hindu
Space
ACYCLIC SPACE
ACYCLIC SPACE
Girl/Female
English American
Generous.
Girl/Female
Muslim
Wish, Desire
Boy/Male
Anglo, British, English, Finnish, Swedish
Valley; Usually with a Stream; From the Glen
Girl/Female
Bengali, Hindu, Indian
Shine; Ray; Light; Radiance; Beauty; Radiant; Smiling; Glow; Bright; Brilliant; Talented
Boy/Male
Hindu, Indian, Sanskrit
One who Subdues a Conquerer
Boy/Male
Indian
Well known, The group of people use to play traditional music at Shivaji ‘s period, Shayar or Shahir
Boy/Male
Tamil
Lord Vishnu, Leading to victory
Boy/Male
English Irish American
Broad hillside.
Boy/Male
Arabic, Gujarati, Hindu, Indian, Kannada, Muslim, Sindhi
Outstanding; Honourable; Gracious; Reward; Favour; Virtuous
Girl/Female
Indian
A narrator of Hadith
ACYCLIC SPACE
ACYCLIC SPACE
ACYCLIC SPACE
ACYCLIC SPACE
ACYCLIC SPACE
a.
Pertaining to, or designating, an acid C11H20O2, homologous with acrylic acid, and obtained as a white crystalline substance by the distillation of castor oil.
n.
A forest officer appointed to walk over a certain space for inspection; a forester.
a.
Of, pertaining to, or designating, an acid of the acrylic series, obtained by the distillation of terpenylic acid, as an only substance having a peculiar cheesy odor.
a.
Alt. of Encyclical
a.
Relating to bicycles.
a.
Pertaining to, derived from, or contained in, oil; as, oleic acid, an acid of the acrylic acid series found combined with glyceryl in the form of olein in certain animal and vegetable fats and oils, such as sperm oil, olive oil, etc. At low temperatures the acid is crystalline, but melts to an oily liquid above 14/ C.
a.
Alt. of Cyclical
a.
Of, pertaining to, or designating, a complex ketonic acid, C5H6O3, obtained as a white crystalline substance; -- so called because once supposed to contain a peculiar radical of four carbon atoms. Called also acetyl-acrylic acid.
imp. & p. p.
of Space
a.
Pertaining to, or designating, an isomeric variety of lastic acid that breaks down into acrylic acid and water.
a.
Adhering to a fixed circle of legends; cyclic; hence, mean; inferior. See Cyclic poets, under Cyclic.
a.
Of or containing acryl, the hypothetical radical of which acrolein is the hydride; as, acrylic acid.
a.
Without space.
n.
Alt. of Encyclical
a.
Pertaining to, or designating, an acid of the acrylic acid series, metameric with crotonic acid, and obtained as a colorless liquid; -- so called from having four carbon atoms in the molecule. Called also isocrotonic acid.
n.
A mean or inferior poet, perhaps from his habit of wandering around as a stroller; an itinerant poet. Also, a name given to the cyclic poets. See under Cyclic, a.
n.
A quantity or portion of extension; distance from one thing to another; an interval between any two or more objects; as, the space between two stars or two hills; the sound was heard for the space of a mile.
n.
To arrange or adjust the spaces in or between; as, to space words, lines, or letters.
a.
Pertaining to, or derived from, amyl; as, amylic ether.
n.
Dimensions; compass; space occupied, as measured by cubic units, that is, cubic inches, feet, yards, etc.; mass; bulk; as, the volume of an elephant's body; a volume of gas.