scholarly journals Idiom recognition framework using topological embedding

2013 ◽  
Vol 10 (3) ◽  
pp. 1-34
Author(s):  
Motohiro Kawahito ◽  
Hideaki Komatsu ◽  
Takao Moriyama ◽  
Hiroshi Inoue ◽  
Toshio Nakatani
Keyword(s):  
Topological Embedding

A closer look at the stable completion

2017 ◽  
Author(s):  
Ehud Hrushovski ◽  
François Loeser
Keyword(s):  
Inverse Limit ◽  
Unit Vector ◽  
Vector Spaces ◽  
Dimensional Vector ◽  
Compact Sets ◽  
Linear Topology ◽  
Topological Embedding ◽  
Definable Set ◽  
Finite Dimensional ◽  
The One

This chapter introduces the concept of stable completion and provides a concrete representation of unit vector Mathematical Double-Struck Capital A superscript n in terms of spaces of semi-lattices, with particular emphasis on the frontier between the definable and the topological categories. It begins by constructing a topological embedding of unit vector Mathematical Double-Struck Capital A superscript n into the inverse limit of a system of spaces of semi-lattices L(Hsubscript d) endowed with the linear topology, where Hsubscript d are finite-dimensional vector spaces. The description is extended to the projective setting. The linear topology is then related to the one induced by the finite level morphism L(Hsubscript d). The chapter also considers the condition that if a definable set in L(Hsubscript d) is an intersection of relatively compact sets, then it is itself relatively compact.

scholarly journals The Brouwer invariance theorems in reverse mathematics

2020 ◽  
Vol 8 ◽  
Author(s):  
Takayuki Kihara
Keyword(s):  
Reverse Mathematics ◽  
Base System ◽  
Open Problems ◽  
Explicit Algorithm ◽  
Topological Embedding ◽  
Weak König’S Lemma ◽  
König’S Lemma

Abstract In [12], John Stillwell wrote, ‘finding the exact strength of the Brouwer invariance theorems seems to me one of the most interesting open problems in reverse mathematics.’ In this article, we solve Stillwell’s problem by showing that (some forms of) the Brouwer invariance theorems are equivalent to the weak König’s lemma over the base system ${\sf RCA}_0$ . In particular, there exists an explicit algorithm which, whenever the weak König’s lemma is false, constructs a topological embedding of $\mathbb {R}^4$ into $\mathbb {R}^3$ .

scholarly journals FINDING SMALLEST SUPERTREES UNDER MINOR CONTAINMENT

2000 ◽  
Vol 11 (03) ◽  
pp. 445-465 ◽  
Author(s):  
NAOMI NISHIMURA ◽  
PRABHAKAR RAGDE ◽  
DIMITRIOS M THILIKOS
Keyword(s):  
Structured Data ◽  
Input Tree ◽  
Subgraph Isomorphism ◽  
Common Elements ◽  
Bounded Degree ◽  
Topological Embedding ◽  
General Mapping ◽  
Np Complete ◽  
A Minor

The diversity of application areas relying on tree-structured data results in wide interest in algorithms which determine differences or similarities among trees. One way of measuring the similarity between trees is to find the smallest common superstructure or supertree, where common elements are typically defined in terms of a mapping or embedding. In the simplest case, a supertree will contain exact copies of each input tree, so that for each input tree, each vertex of a tree can be mapped to a vertex in the supertree such that each edge maps to the corresponding edge. More general mappings allow for the extraction of more subtle common elements captured by looser definitions of similarity. We consider supertrees under the general mapping of minor containment. Minor containment generalizes both subgraph isomorphism and topological embedding; as a consequence of this generality, however, it is NP-complete to determine whether or not G is a minor of H, even for genreal trees. By focusing on trees of bounded degree, we obtain an O(n3) algorithm which determines the smallest tree T such that both of the input trees are minors of T, even when the trees are assumed to be unrooted and unordered.

scholarly journals A homotopy equivalence that is not homotopic to a topological embedding

1998 ◽  
Vol 90 (1-3) ◽  
pp. 211-222 ◽  
Author(s):  
Vo Thanh Liem ◽  
Yukio Matsumoto ◽  
Gerard Venema
Keyword(s):  
Homotopy Equivalence ◽  
Topological Embedding

A Novel Method for Topological Embedding of Time-Series Data

2018 ◽  
Author(s):  
Sean M. Kennedy ◽  
John D. Roth ◽  
James W. Scrofani
Keyword(s):  
Time Series ◽  
Time Series Data ◽  
Series Data ◽  
Topological Embedding ◽  
Novel Method

Linearization of a Contractive Homeomorphism

1968 ◽  
Vol 20 ◽  
pp. 1387-1390
Author(s):  
Ludvik Janos
Keyword(s):  
Linear Operator ◽  
Topological Space ◽  
Vector Space ◽  
Topological Vector Space ◽  
Continuous Linear Operator ◽  
Continuous Linear ◽  
Topological Embedding

Let X be a topological space and ϕ: X ⟶ X a continuous self-mapping of X. We say that ϕ is linearized in L by Φ if there exists a topological embedding μ: X ⟶ L of the space X into the linear topological vector space L such that for all x ϵ X, μ (ϕ (x)) = Φ (μ (x)), where ϕ is a continuous linear operator on L.

A topological embedding of the lexicon for semantic distance computation

2010 ◽  
Vol 16 (3) ◽  
pp. 245-275
Author(s):  
N. DAVIS ◽  
C. GIRAUD-CARRIER ◽  
D. JENSEN
Keyword(s):  
Metric Space ◽  
Complete Metric Space ◽  
Order Relation ◽  
Semantic Distance ◽  
Distance Measures ◽  
Topological Transformation ◽  
Topological Embedding ◽  
Word Level ◽  
Natural Connection ◽  
Document Level

AbstractWe show how a quantitative context may be established for what is essentially qualitative in nature by topologically embedding a lexicon (here, WordNet) in a complete metric space. This novel transformation establishes a natural connection between the order relation in the lexicon (e.g., hyponymy) and the notion of distance in the metric space, giving rise to effective word-level and document-level lexical semantic distance measures. We provide a formal account of the topological transformation and demonstrate the value of our metrics on several experiments involving information retrieval and document clustering tasks.

scholarly journals Embeddings of quaternion space in S4

1998 ◽  
Vol 65 (3) ◽  
pp. 313-325 ◽  
Author(s):  
Atsuko Katanaga ◽  
Osamu Saeki
Keyword(s):  
Projective Plane ◽  
Fundamental Group ◽  
Euler Number ◽  
Projective Planes ◽  
Connected Components ◽  
Connected Component ◽  
Real Projective Plane ◽  
Quaternion Group ◽  
Topological Embedding ◽  
Quaternion Space

AbstractConsider a (real) projective plane which is topologically locally flatly embedded in S4. It is known that it always admits a 2-disk bundle neighborhood, whose boundary is homeomorphic to the quaternion space Q, the total space of the nonorientable S1-bundle over RP2 with Euler number ± 2, with fundamental group isomorphic to the quaternion group of order eight. Conversely let f: Q → S4 be an arbitrary locally flat topological embedding. Then we show that the closure of each connected component of S4 − f(Q) is always homeomorphic to the exterior of a topologically locally flatly embedded projective plane in S4. We also show that, for a large class of embedded projective planes in S4, a pair of exteriors of such embedded projective planes is always realized as the closures of the connected components of S4 − f(Q) for some locally flat topological embedding f: Q → S4.

On a topological embedding of a weak self-similar, zero-dimensional set

2004 ◽  
Vol 22 (1) ◽  
pp. 171-174 ◽  
Author(s):  
Akihiko Kitada
Keyword(s):  
Topological Embedding ◽  
Self Similar

scholarly journals The geometry of Niggli reduction:SAUC– search of alternative unit cells

2014 ◽  
Vol 47 (1) ◽  
pp. 360-364 ◽  
Author(s):  
Keith J. McGill ◽  
Mojgan Asadi ◽  
Maria T. Karakasheva ◽  
Lawrence C. Andrews ◽  
Herbert J. Bernstein
Keyword(s):  
Search Algorithms ◽  
Linear Measure ◽  
New Approach ◽  
Topological Embedding ◽  
Comparison Of Results ◽  
Complete Search ◽  
Unit Cells

A database of lattices using theG6representation of the Niggli-reduced cell as the search key provides a more robust and complete search than older techniques. Searching is implemented by finding the distance from the probe cell to other cells using a topological embedding of the Niggli reduction inG6, so that all cells representing similar lattices will be found. The embedding provides the first fully linear measure of distances between unit cells. Comparison of results with those from older cell-based search algorithms suggests significant value in the new approach.

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