Search results for "Diagram"

showing 10 items of 795 documents

On a generalization of Goguen's category Set(L)

2007

The paper considers a category which generalizes Goguen's category Set(L) of L-fuzzy sets with a fixed basis L. We show the necessary and sufficient conditions for the generalized category to be a quasitopos and consider additional inner structure supplied by the latter property.

Discrete mathematicsClosed categoryArtificial IntelligenceLogicDiagram (category theory)Complete categoryMathematics::Category TheoryCategoryConcrete categoryCategory of setsEnriched categoryMathematicsTopological categoryFuzzy Sets and Systems
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Reordering Method and Hierarchies for Quantum and Classical Ordered Binary Decision Diagrams

2017

We consider Quantum OBDD model. It is restricted version of read-once Quantum Branching Programs, with respect to “width” complexity. It is known that maximal complexity gap between deterministic and quantum model is exponential. But there are few examples of such functions. We present method (called “reordering”), which allows to build Boolean function g from Boolean Function f, such that if for f we have gap between quantum and deterministic OBDD complexity for natural order of variables, then we have almost the same gap for function g, but for any order. Using it we construct the total function REQ which deterministic OBDD complexity is \(2^{\varOmega (n/log n)}\) and present quantum OBD…

Discrete mathematicsComputational complexity theoryImplicit functionBinary decision diagram010102 general mathematics0102 computer and information sciencesFunction (mathematics)Computer Science::Artificial IntelligenceComputer Science::Computational Complexity01 natural sciencesCombinatorics010201 computation theory & mathematicsComputer Science::Logic in Computer ScienceComplexity class0101 mathematicsBoolean functionQuantum complexity theoryQuantum computerMathematics
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Some remarks on the category SET(L), part III

2004

This paper considers the category SET(L) of L-subsets of sets with a fixed basis L and is a continuation of our previous investigation of this category. Here we study its general properties (e.g., we derive that the category is a topological construct) as well as some of its special objects and morphisms.

Discrete mathematicsDiagram (category theory)General MathematicsConcrete categoryCategory of groupsL-set; category of L-subsets of sets; topological construct; topos; special morphism; special objectCombinatoricsClosed categoryMathematics::Category TheoryCategory of topological spacesCategory of setsEnriched category2-categoryMathematicsGlasnik matematički
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Very Narrow Quantum OBDDs and Width Hierarchies for Classical OBDDs

2014

In the paper we investigate a model for computing of Boolean functions – Ordered Binary Decision Diagrams (OBDDs), which is a restricted version of Branching Programs. We present several results on the comparative complexity for several variants of OBDD models. We present some results on the comparative complexity of classical and quantum OBDDs. We consider a partial function depending on a parameter k such that for any k > 0 this function is computed by an exact quantum OBDD of width 2, but any classical OBDD (deterministic or stable bounded-error probabilistic) needs width 2 k + 1. We consider quantum and classical nondeterminism. We show that quantum nondeterminism can be more efficient …

Discrete mathematicsImplicit functionBinary decision diagram010102 general mathematics02 engineering and technologyFunction (mathematics)Computer Science::Artificial IntelligenceComputer Science::Computational Complexity01 natural sciencesCombinatoricsNondeterministic algorithmComputer Science::Logic in Computer SciencePartial function0202 electrical engineering electronic engineering information engineering020201 artificial intelligence & image processing0101 mathematicsBoolean functionQuantumQuantum computerMathematics
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Asymptotics for the Amitsur's Capelli - Type Polynomials and Verbally Prime PI-Algebras

2006

We consider associativePI-algebras over a field of characteristic zero. The main goal of the paper is to prove that the codimensions of a verbally prime algebra [11] are asymptotically equal to the codimensions of theT-ideal generated by some Amitsur's Capelli-type polynomialsEM,L* [1]. We recall that two sequencesan,bnare asymptotically equal, and we writean≃bn,if and only if limn→∞(an/bn)=1.In this paper we prove that\(c_n \left( {M_k \left( G \right)} \right) \simeq c_n \left( {E_{k^2 ,k^2 }^ * } \right) and c_n \left( {M_{k,l} \left( G \right)} \right) \simeq c_n \left( {E_{k^2 + l^2 ,2kl}^ * } \right) \)% MathType!End!2!1!, whereG is the Grassmann algebra. These results extend to all v…

Discrete mathematicsJacobson RadicalGeneral MathematicsPolynomial IdentityZero (complex analysis)Associative AlgebraField (mathematics)Type (model theory)Prime (order theory)Young TableauYoung DiagramPiAlgebra over a fieldExterior algebraMathematics
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On simple families of functions and their Legendrian mappings

2004

We study germs of $n$-parameter families of functions, that is, function-germs of the type $f : (\mathbb{R}^n \times \mathbb{R}, 0) \to (\mathbb{R}, 0)$ defined on the total space of the trivial bundle $ \mathbb{R}^n \times \mathbb{R} \to \mathbb{R}^n $. There is a natural notion of $V$-equivalence for such function-germs. We introduce the Young diagram of $n$-parameter families satisfying a non-degeneracy condition. We classify all such simple $n$-parameter families and give their versal deformations. This result has direct applications to contact and projective geometry.

Discrete mathematicsMathematics::Algebraic GeometryDiagram (category theory)Simple (abstract algebra)General MathematicsType (model theory)Space (mathematics)MathematicsProjective geometryProceedings of the London Mathematical Society
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Quantum Finite State Transducers

2001

We introduce quantum finite state transducers (qfst), and study the class of relations which they compute. It turns out that they share many features with probabilistic finite state transducers, especially regarding undecidability of emptiness (at least for low probability of success). However, like their 'little brothers', the quantum finite automata, the power of qfst is incomparable to that of their probabilistic counterpart. This we show by discussing a number of characteristic examples.

Discrete mathematicsPure mathematicsFinite-state machineDeterministic finite automatonComputer scienceComputer Science::Logic in Computer ScienceProbabilistic logicQuantum finite automataNondeterministic finite automatonState diagramQuantumComputer Science::Formal Languages and Automata TheoryQuantum computer
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Tilted phases of fatty acid monolayers

1995

X‐ray diffraction data from water‐supported monolayers of fatty acids with chain lengths from 19 to 22 is presented. The structures of the tilted mesophases L2’, L2, and Ov are characterized in detail. The contributions to the unit cell distortion from the tilt and the ordering of the backbone planes of the molecules are separated. It is shown that at the swiveling transition L2’–L2, not only the tilt azimuth but also the packing of the backbone planes change discontinuously. We demonstrate that the tilting transition LS–L2 is accompanied by the ordering of the backbone planes and may be discontinuous. Evidence is presented for a herringbone ordering transition within the L2 region. The dis…

Distortion (mathematics)DiffractionQuantitative Biology::BiomoleculesCrystallographyTilt (optics)ChemistryX-ray crystallographyMonolayerGeneral Physics and AstronomyMoleculePhysical and Theoretical ChemistrySymmetry (geometry)Phase diagramThe Journal of Chemical Physics
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Concrete syntax-based find for graphical DSLs

2020

There are services available in the most software tools we have got used to like, copy, paste, cut, find, and replace. However, the state of the art is not so good with tools of graphical languages. Even many commercial modelling tools have limited support of the find feature. We propose to add find as a service of graphical DSL tool development frameworks. This way find is available in any DSL built using the DSL tool development framework. The concrete syntax-based find has been implemented as a service of the DSL tool development framework ajoo. Two graph-based languages: UML Activity diagrams and Deterministic Finite Automata (DFA) transition diagrams are used to demonstrate usage of th…

Domain-specific languageService (systems architecture)Computer sciencebusiness.industryProgramming language020207 software engineering02 engineering and technologyActivity diagramcomputer.software_genreDigital subscriber lineSoftwareDeterministic finite automatonUnified Modeling Language0202 electrical engineering electronic engineering information engineeringState (computer science)businesscomputercomputer.programming_languageProceedings of the 23rd ACM/IEEE International Conference on Model Driven Engineering Languages and Systems: Companion Proceedings
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Up and Down States During Slow Oscillations in Slow-Wave Sleep and Different Levels of Anesthesia

2021

Slow oscillations are a pattern of synchronized network activity generated by the cerebral cortex. They consist of Up and Down states, which are periods of activity interspersed with periods of silence, respectively. However, even when this is a unique dynamic regime of transitions between Up and Down states, this pattern is not constant: there is a range of oscillatory frequencies (0.1–4 Hz), and the duration of Up vs. Down states during the cycles is variable. This opens many questions. Is there a constant relationship between the duration of Up and Down states? How much do they vary across conditions and oscillatory frequencies? Are there different sub regimes within the slow oscillation…

Down statesCognitive NeuroscienceNeuroscience (miscellaneous)anesthesiaDeep anesthesiaBifurcation diagramlcsh:RC321-571Cellular and Molecular NeuroscienceDevelopmental NeuroscienceUp statessleeplcsh:Neurosciences. Biological psychiatry. NeuropsychiatrySlow-wave sleepPhysicsCortical modelslow oscillationsBrief Research Reportslow-wave sleepNetwork activityDuration (music)LIGHT ANESTHESIAAnesthesiacerebral cortexConstant (mathematics)cortical modelNeuroscience
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