Searches , social queries for TOPOLOGICAL INDISTINGUISHABILITY
Search references for TOPOLOGICAL INDISTINGUISHABILITY. Phrases containing TOPOLOGICAL INDISTINGUISHABILITY
See searches and references containing TOPOLOGICAL INDISTINGUISHABILITY!
Search references for TOPOLOGICAL INDISTINGUISHABILITY. Phrases containing TOPOLOGICAL INDISTINGUISHABILITY
See searches and references containing TOPOLOGICAL INDISTINGUISHABILITY!TOPOLOGICAL INDISTINGUISHABILITY
Topological relational characteristic
In topology, two points of a topological space X are topologically indistinguishable if they have exactly the same neighborhoods. That is, if x and y
Topological indistinguishability
Topological_indistinguishability
Topics referred to by the same term
Computational indistinguishability Ciphertext indistinguishability Indistinguishability obfuscation Topological indistinguishability Indistinguishable processes
Indistinguishability
Mathematical concept
mathematics, a finite topological space is a topological space for which the underlying point set is finite. That is, it is a topological space which has only
Finite_topological_space
Type of topological space
is a topological space where distinct points have disjoint neighbourhoods. Of the many separation axioms that can be imposed on a topological space,
Hausdorff_space
Topological space in which all singleton sets are closed
constant nets) are unique (for T1 spaces) or unique up to topological indistinguishability (for R0 spaces). As it turns out, uniform spaces, and more
T1_space
Subset with finite complement
since the points of each doublet are topologically indistinguishable. It is, however, R0 since topologically distinguishable points are separated. The
Cofiniteness
Topological space that is connected
Connectedness is one of the principal topological properties that distinguish topological spaces. A subset of a topological space X {\displaystyle X} is a connected
Connected_space
Concept in topology
underlying topological space of any scheme. Given any topological space one can construct a T0 space by identifying topologically indistinguishable points
Kolmogorov_space
specialization preorder is just that of topological indistinguishability. That is, x and y are topologically indistinguishable if and only if x ≤ y and y ≤ x.
Specialization_preorder
discrete topology. List of topologies – List of concrete topologies and topological spaces Steen, Lynn Arthur; Seebach, J. Arthur Jr. (1995) [1978], Counterexamples
Partition_topology
In mathematics, specifically in the field of topology, a topological space is said to be a door space if every subset is open or closed (or both). The
Door_space
Type of topological space
Hilbert, is a topological space that provides an instructive example of some ideas in topology. Furthermore, many interesting topological spaces can be
Hilbert_cube
List of concrete topologies and topological spaces
properties that a topology or topological space might possess; for that, see List of general topology topics and Topological property. Discrete topology
List_of_topologies
Value to which an infinite sequence tends
mathematical analysis ultimately rests. Limits can be defined in any metric or topological space, but are usually first encountered in the real numbers. The Greek
Limit_of_a_sequence
Point not touching any other point
In mathematics, a closed point of a topological space is a point whose singleton is closed. In many areas of geometry and topology, all spaces under consideration
Closed_point
Phenomenon in many-body quantum systems
perturbations. Topological degeneracy can be used to protect qubits which allows topological quantum computation. It is believed that topological degeneracy
Topological_degeneracy
Type of two-dimensional quasiparticle
identifying 3+1‑dimensional topological orders. The multi-loop/string-braiding statistics of 3+1‑dimensional topological orders can be captured by the
Anyon
Concept in functional analysis
M ⊕ N {\displaystyle M\oplus N} in the category of topological vector spaces. Formally, topological direct sums strengthen the algebraic direct sum by
Complemented_subspace
Set of points on a line segment with certain topological properties
that is nowhere dense. More generally, in topology, a Cantor space is a topological space homeomorphic to the Cantor ternary set (equipped with its subspace
Cantor_set
Theorem in quantum mechanics
connection suggested that simple explanations remain elusive. An intuitive topological argument for why the spin-statistics theorem ought to be true is due
Spin–statistics_theorem
Local and global geometry of the universe
models alone, due to the existence of locally indistinguishable spaces with varying global topological characteristics. For example; a multiply connected
Shape_of_the_universe
Transformations induced by a mathematical group
{\displaystyle X/G} . Now assume G {\displaystyle G} is a topological group and X {\displaystyle X} a topological space on which it acts by homeomorphisms. The action
Group_action
Type of symmetry
Wiley. pp. 80–83. ISBN 978-0-470-01821-7. Fu, Liang; Kane, C. (2007). "Topological insulators with inversion symmetry". Physical Review B. 76 (4) 045302
Centrosymmetry
Method of quantum computing
implement topological quantum error correction. Topological cluster state computation is closely related to Kitaev's toric code, as the 3D topological cluster
One-way_quantum_computer
of these conditions. Locally compact topological spaces Locally connected and Locally path-connected topological spaces Locally Hausdorff, Locally regular
Local_property
Branch of mathematics that studies the properties of groups
between infinite abstract groups and topological groups: whenever a group Γ can be realized as a lattice in a topological group G, the geometry and analysis
Group_theory
Hypothetical particle with one magnetic pole
group at long distances, there are magnetic monopoles. The argument is topological: The holonomy of a gauge field maps loops to elements of the gauge group
Magnetic_monopole
Interference effect of two photons
high-fidelity quantum interference between topologically protected states on a photonic chip. Topological photonics have intrinsically high-coherence
Hong–Ou–Mandel_effect
Four-point non-Hausdorff topological space
The pseudocircle is the finite topological space X consisting of four distinct points {a,b,c,d} with the following non-Hausdorff topology: { { a , b
Pseudocircle
2019 text-generating language model
from a larger text, and generate text output on a level sometimes indistinguishable from that of humans; however, it could become repetitive or nonsensical
GPT-2
Branch of physics
study of topological properties of the fractional Hall effect remains an active field of research. Decades later, the aforementioned topological band theory
Condensed_matter_physics
Israeli electrical engineer and condensed matter physicist (born 1947)
FQHE (I)". YouTube. Topological Matter School. November 8, 2019. "TMS19 Moty Heiblum: Transport in FQHE (II)". YouTube. Topological Matter School. November
Mordehai_Heiblum
Lithographic technique that uses X-rays instead of light
photoresist, or simply "resist," on the substrate to reach extremely small topological size of a feature. A series of chemical treatments then engraves the
X-ray_lithography
Symmetry breaking through the vacuum state
described by spontaneous symmetry breaking. Notable exceptions include topological phases of matter like the fractional quantum Hall effect. Typically,
Spontaneous_symmetry_breaking
Function spaces generalizing finite-dimensional p norm spaces
The space L 0 {\displaystyle L^{0}} is always a topological abelian group but is only a topological vector space if μ ( S ) < ∞ . {\displaystyle \mu
Lp_space
Label to identify a network interface of a computer or other network node
the source. Anycast addresses are syntactically identical to and indistinguishable from unicast addresses. Their only difference is administrative. Scopes
IPv6_address
Idea that small causes can have large effects
together separate over time at an exponential rate. The definition is not topological, but essentially metrical. Lorenz defined sensitive dependence as follows:
Butterfly_effect
Hypothetical elementary particle that mediates gravity
be shown that any massless spin-2 field would give rise to a force indistinguishable from gravitation, because a massless spin-2 field would couple to
Graviton
Fiber bundle of the 3-sphere over the 2-sphere, with 1-spheres as fibers
the boundary of a ball, some geometric structure is lost although the topological structure is retained (see Topology and geometry). The loops are homeomorphic
Hopf_fibration
Class of artificial neural networks
Miolane, N.; Guzmán-Sáenz, A.; Ramamurthy, K. N.; Schaub, M. T. (2022). "Topological deep learning: Going beyond graph data". arXiv:2206.00606 [cs.LG]. Veličković
Graph_neural_network
Construction in algebraic geometry
633K, doi:10.1007/s002200050033 Sunada, Toshikazu (2012), "Lecture on topological crystallography", Japan. J. Math., 7: 1–39, doi:10.1007/s11537-012-1144-4
Abel–Jacobi_map
Pathogenic type of misfolded protein
molecular mass of 35–36 kDa and a mainly alpha-helical structure. Several topological forms exist; one cell surface form that is anchored via glycolipid, and
Prion
Transforming a function in such a way that it only takes a single argument
homotopy theory, one is commonly interested in continuous functions between topological spaces. One writes Hom ( X , Y ) {\displaystyle {\text{Hom}}(X,Y)} (the
Currying
Description of gravity using discrete values
fruit of an effort to formulate a background-independent quantum theory. Topological quantum field theory provided an example of background-independent quantum
Quantum_gravity
Cosmological model in which the observable universe is the interior of a black hole
1088/1126-6708/2001/06/024. Coleman, S. (1988). "Black holes as red herrings: Topological fluctuations and the loss of quantum coherence". Nuclear Physics B. 307
Black_hole_cosmology
Polyhedron with regular congruent polygons as faces
Euler characteristic of 2. This simply reflects that the surface is a topological 2-sphere, and so is also true, for example, of any polyhedron which is
Regular_polyhedron
Structure that repeats in time; a novel type or phase of non-equilibrium matter
Lindner, Netanel H.; Refael, Gil; Galitski, Victor (2011). "Floquet topological insulator in semiconductor quantum wells". Nature Physics. 7 (6): 490–495
Time_crystal
Theory of subatomic structure
geometric transformation, similar in spirit to flop transitions or other topological changes in the geometry of string theory. This interpretation requires
String_theory
Space of all possible states that a system can take
limit cycle is present for the chosen parameter value. The concept of topological equivalence is important in classifying the behaviour of systems by specifying
Phase_space
Hexagonal lattice made of carbon atoms
of opposite-sign mass is a hallmark of a topological phase and displays much the same physics as topological insulators. If the mass in graphene can be
Graphene
Chemical element with atomic number 83 (Bi)
stabilizes only below −60 °C (−76 °F). Sodium bismuthide has interest as a topological Dirac insulator. The reported abundance of bismuth in the Earth's crust
Bismuth
Statement that players know and also know that other players know (ad infinitum)
the same part of partition of an agent, it means that s1 and s2 are indistinguishable to that agent. In general, in state s, agent i knows that one of the
Common_knowledge_(logic)
Wave in general relativity
solitons lies primarily in their role as enforcers of the kinematic and topological laws of quantum gravity. When the topology of spacetime is allowed to
Gravitational_soliton
Physical phenomenon
Bennett, Brassard, Crépeau, Jozsa, Peres and Wootters, reflects the indistinguishability of quantum mechanical particles. For every qubit teleported, Alice
Quantum_teleportation
low-dimensional representations of high-dimensional data while preserving the topological structure of the data. They are trained using competitive learning. SOMs
History of artificial neural networks
History_of_artificial_neural_networks
State of matter
generation of so-called dark solitons in one-dimensional BECs. These topological objects feature a phase gradient across their nodal plane, which stabilizes
Bose–Einstein_condensate
Technique for the generative modeling of a continuous probability distribution
out to the rest of the image space, until the cloud becomes all but indistinguishable from a Gaussian distribution N ( 0 , I ) {\displaystyle {\mathcal
Diffusion_model
Simple polynomial map exhibiting chaotic behavior
oscillations at the onset of chaos) fully developed chaotic oscillations topological mixing (i.e. the tendency of oscillations to cover the full available
Logistic_map
How one process influences another
Causality has the properties of antecedence and contiguity. These are topological, and are ingredients for space-time geometry. As developed by Alfred
Causality
Concept in category theory
{C}}} be any category based on sets, e.g. groups—sets of elements—or topological spaces—sets of 'points'. As usual, write Ob ( C ) {\displaystyle \operatorname
Forgetful_functor
Combinatorial game theory theorem
for your Mathematical Plays and On Numbers and Games. Genus theory Indistinguishability quotient Sprague, R. P. (1936). "Über mathematische Kampfspiele"
Sprague–Grundy_theorem
Neural network that learns efficient data encoding in an unsupervised manner
}(x))=x} . This ideal autoencoder can then be used to generate messages indistinguishable from real messages, by feeding its decoder arbitrary code z {\displaystyle
Autoencoder
Probabilistic graphical representation of causal relationships
calculated from conditional probabilities using the chain rule (given a topological ordering of X) as follows: P ( X 1 = x 1 , … , X n = x n ) = ∏ v =
Bayesian_network
Mathematical structures that allow quantum mechanics to be explained
uncertainty principles that govern small scales. Hence the requirement of indistinguishability of quantum particles is presented by the symmetrization postulate
Mathematical formulation of quantum mechanics
Mathematical_formulation_of_quantum_mechanics
Loss of quantum coherence
Kitaev, Alexei; Landahl, Andrew; Preskill, John (1 September 2002). "Topological quantum memory". Journal of Mathematical Physics. 43 (9): 4452–4505.
Quantum_decoherence
Formulation of quantum mechanics
integral is taken to be fundamental, and reality is viewed as a single indistinguishable "class" of paths that all share the same events.[failed verification]
Path-integral_formulation
Method of data analysis
much more likely to substantially overlay each other, making them indistinguishable. Similarly, in regression analysis, the larger the number of explanatory
Principal_component_analysis
Concept in mathematical set theory
{\displaystyle {\boldsymbol {Top}}} (see category of topological spaces), the category with objects that are topological spaces and morphisms that are continuous
Near_sets
Polyhedron formed by joining mirroring pyramids base-to-base
octahedron is more symmetric still, as its base vertices and apices are indistinguishable and can be exchanged by reflections or rotations; the regular octahedron
Bipyramid
Wide-ranging representation of a game in game theory
further partitioned in information sets, which make certain choices indistinguishable for the player when making a move, in the sense that: there is a one-to-one
Extensive-form_game
Theory of gravitation as curved spacetime
At the energies reached in current experiments, these strings are indistinguishable from point-like particles, but, crucially, different modes of oscillation
General_relativity
Detector experiment at CERN
bottom quarks, which decay into a relatively long-lived B-meson through topological cuts.[citation needed] The short-lived heavy particles cover a very small
ALICE_experiment
Mathematical transform that expresses a function of time as a function of frequency
duality map defined above. Given an abelian locally compact Hausdorff topological group G, as before we consider the space L1(G), defined using a Haar
Fourier_transform
Chinese-American physicist (1926–2024)
Beginning in 1975, Lee and collaborators established the field of non-topological solitons, which led to his work on soliton stars and black holes throughout
Tsung-Dao_Lee
of opposite-sign mass is a hallmark of a topological phase and display much the same physics as topological insulators. If the mass in graphene can be
Electronic properties of graphene
Electronic_properties_of_graphene
regular self-intersecting faces, are now known to be inequivalent to the topological sphere as a simple connected surface (this is in contrast with the traditional
List of polyhedral stellations
List_of_polyhedral_stellations
Mathematics of smooth surfaces
century was the golden age for the theory of surfaces, from both the topological and the differential-geometric point of view, with most leading geometers
Differential geometry of surfaces
Differential_geometry_of_surfaces
Differential equations involving stochastic processes
very interesting because it never exhibits spontaneous breakdown of topological supersymmetry, i.e., (overdamped) Langevin SDEs are never chaotic. Brownian
Stochastic differential equation
Stochastic_differential_equation
Collection of random variables
probabilistic sense), its index set must be a separable space (in a topological or analytic sense), in addition to other conditions. The definition of
Stochastic_process
Computer networking protocol suite
acquired by Motorola in 2007) that also used the RS-422 port and was indistinguishable from LocalTalk as far as Apple's LocalTalk port drivers were concerned
AppleTalk
List of statements that appear to contradict themselves
A variation of the Monty Hall problem. Two-envelope paradox: Two indistinguishable envelopes each contains a positive sum of money. One envelope contains
List_of_paradoxes
Form of computer-aided engineering
are a useful representation for deforming surfaces that undergo many topological changes, such as fluids. The process of transforming representations
3D_modeling
Phase in art history
and celestial mechanics, and the methods used were the basis of its topological works. The singular points of the integral curves Saddle Focus Center
Proto-Cubism
Contraction of an astronomical object due to the influence of its gravity
star), and preon stars, if they exist, would, for the most part, be indistinguishable from a neutron star: in most cases, the exotic matter would be hidden
Gravitational_collapse
Quantum field theory of electromagnetism
product of the probability amplitudes of the sub-processes. The indistinguishability criterion in (a) is very important: it means that there is no observable
Quantum_electrodynamics
Number, approximately 1.3247
(sequence A013998 in the OEIS) Siegel, Anne; Thuswaldner, Jörg M. (2009). "Topological properties of Rauzy fractals". Mémoires de la Société Mathématique de
Plastic_ratio
Concept in literary theory
"then", "past" and "present" and "future" and "eternal"? Not only are the topological differences between the words relevant here, but the differentials between
Différance
Mathematical description of quantum state
(6th ed.). W. H. Freeman. ISBN 978-0-7167-8964-2. Trèves, François (2006). Topological Vector Spaces, Distributions and Kernels. Mineola, NY: Courier Corporation
Wave_function
Theory of gravity on antimatter
theories are extensions of general relativity, and are experimentally indistinguishable. The general idea remains that gravity is the deflection of a continuous
Gravitational interaction of antimatter
Gravitational_interaction_of_antimatter
bowline 1. A type of knot producing a strong loop of a fixed size, topologically similar to a sheet bend. 2. A rope attached to the side of a sail to
Glossary of nautical terms (A–L)
Glossary_of_nautical_terms_(A–L)
Restricted model of non-universal quantum computation
mechanism. The main advantages of PDC sources are the high photon indistinguishability, collection efficiency and relatively simple experimental setups
Boson_sampling
structures were abstracted using axioms and given names like metric spaces, topological spaces etc. As mathematicians do, the concept of an abstract structure
20th_century_in_science
Cryptography based on quantum mechanical phenomena
Nishimura, Harumichi; Yamakami, Tomoyuki (2011). "Computational Indistinguishability Between Quantum States and its Cryptographic Application". Journal
Quantum_cryptography
Theory of gravity
shares many of the same values as General Relativity, and is therefore indistinguishable using these tests. In particular light deflection is unchanged, so
F(R)_gravity
Structures of cyclohexane
negative), but it turns out that there is also a continuum of solutions, a topological circle where angle strain is zero, including the twist boat and the boat
Cyclohexane_conformation
Bound lattice in which every element has a complement
observed that the propositional calculus in quantum logic is "formally indistinguishable from the calculus of linear subspaces [of a Hilbert space] with respect
Complemented_lattice
Paradigm of quantum computer
{\displaystyle M} modes which are occupied by N {\displaystyle N} indistinguishable single photons (this is a ( M + N − 1 M ) {\displaystyle {\tbinom
Linear optical quantum computing
Linear_optical_quantum_computing
Introductory article
to the fact that all particles of a given type are experimentally indistinguishable from one another. Imagine that Alice and Betty are identical twins
Introduction_to_gauge_theory
Formulation to quantize gauge field theories in physics
about the relationship between topological invariants and the BRST operator may be found in: E. Witten, "Topological quantum field theory", Commun. Math
BRST_quantization
State of a physical system in phase space
vibrational band structure has two sub-lattice bands that can have nontrivial topological physics. The vibrations of any two atoms are coupled via a pairing interaction
Phase_space_crystal
travel, tourism, insurance
TOPOLOGICAL INDISTINGUISHABILITY
TOPOLOGICAL INDISTINGUISHABILITY
TOPOLOGICAL INDISTINGUISHABILITY
TOPOLOGICAL INDISTINGUISHABILITY
TOPOLOGICAL INDISTINGUISHABILITY
TOPOLOGICAL INDISTINGUISHABILITY
TOPOLOGICAL INDISTINGUISHABILITY
TOPOLOGICAL INDISTINGUISHABILITY
TOPOLOGICAL INDISTINGUISHABILITY
travel, tourism, insurance