Acoustic-to-Articulatory Inversion of a Three-dimensional Theoretical Vocal Tract Model Using Deep Learning-based Model
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Author list: Lapthawan T., Prom-On S.
Publisher: Springer
Publication year: 2019
Journal: Czechoslovak Mathematical Journal (0011-4642)
Volume number: 69
Issue number: 1
ISSN: 0011-4642
eISSN: 1572-9141
Languages: English-Great Britain (EN-GB)
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Abstract
For a digraph D, the niche hypergraph NH(D) of D is the hypergraph having the same set of vertices as D and the set of hyperedges E(NH(D))={e⊆V(D):|e|⩾2 and there exists a vertex v such that e=ND−(v) or e=ND+(v)}. A digraph is said to be acyclic if it has no directed cycle as a subdigraph. For a given hypergraph H, the niche number n^(H) is the smallest integer such that H together with n^(H) isolated vertices is the niche hypergraph of an acyclic digraph. C.Garske, M. Sonntag and H.M.Teichert (2016) conjectured that for a linear hypercycle Cm,m⩾2, if min { | e| : e∈ E(C m ) } ⩾ 3 , then n^ (C m ) = 0. In this paper, we prove that this conjecture is true. © 2018, Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic.
Keywords
05C65, digraph, linear hypercycle, niche hypergraph
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