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Subword topology

V.Rajkumar Dare, Rani Siromoney
1986 Theoretical Computer Science  
We introduce a topology on a language Lc X °°, called subword topology, which reflects certain interesting properties of subwords in a language.  ...  Well-known topological concepts such as compactness, closure of a language and closed sets reflect certain characteristic properties of subwords.  ...  A topology called SW topology is defined on a language L c V ~, where the sets Sx = {u ~ L: x is a subword of u} are taken as a subbase.  ... 
doi:10.1016/0304-3975(86)90143-x fatcat:cgsl6biaxbf3nnpq2ufm53xlfe

Infinitary Noetherian Constructions II. Transfinite Words and the Regular Subword Topology [article]

Jean Goubault-Larrecq, Simon Halfon, Aliaume Lopez
2022 arXiv   pre-print
We show that the spaces of transfinite words, namely ordinal-indexed words, over a Noetherian space, is also Noetherian, under a natural topology which we call the regular subword topology.  ...  Definition 2 (Regular subword topology).  ...  We define the regular subword topology on X <α in Section 3, based on socalled transfinite products.  ... 
arXiv:2202.05047v2 fatcat:j5fuqiuyvrd7vhodqwjxdzqd3q


Youssouf Chherawala, Robert Wisnovsky, Mohamed Cheriet
2011 Proceedings of the 2011 Workshop on Historical Document Imaging and Processing - HIP '11  
This paper proposes a novel lexicon-reduction method for Arabic subwords based on their shapes' topology and geometry.  ...  First the subword shape's topological and geometrical information is extracted from its skeleton and encoded into a graph.  ...  The saliency of Arabic subwords comes from their topology and geometry. The shape skeleton highlights these features of the subword shape.  ... 
doi:10.1145/2037342.2037345 dblp:conf/icdar/ChherawalaWC11 fatcat:xcmukoeb6jcunjcr7xo4xrxqre

Topological Entropy of DNA Sequences [article]

David Koslicki
2011 arXiv   pre-print
We define a new approximation to topological entropy free from the aforementioned difficulties.  ...  Topological entropy has been one of the most difficult to implement of all the entropy-theoretic notions. This is primarily due to finite sample effects and high-dimensionality problems.  ...  As can be seen from definition 3, our notion of topological entropy does not require the use of the actual subword frequencies.  ... 
arXiv:1101.4636v1 fatcat:6los44zn4bcjvdlocvmy2qps2a

Positive braid knots of maximal topological 4-genus

2016 Mathematical proceedings of the Cambridge Philosophical Society (Print)  
As an application, we determine all positive braid knots with maximal topological 4-genus and compute the topological 4-genus for all positive braid knots with up to 12 crossings.  ...  AbstractWe show that a positive braid knot has maximal topological 4-genus exactly if it has maximal signature invariant.  ...  Proposition 3 in [3] now implies non-maximality of the topological 4-genus.  ... 
doi:10.1017/s0305004116000670 fatcat:x3o6afybbrhdlecsrbjt76g7wy

A Generalized Topological Entropy for Analyzing the Complexity of DNA Sequences

Shuilin Jin, Renjie Tan, Qinghua Jiang, Li Xu, Jiajie Peng, Yong Wang, Yadong Wang, Zhongxue Chen
2014 PLoS ONE  
The relationship between the topological entropy and the generalized topological entropy is compared, which shows the topological entropy is a special case of the generalized entropy.  ...  In order to overcome these problems, a generalized topological entropy is introduced.  ...  However, by comparing the topological entropies of DNA sequences, we find the complexities of subwords, which are shorter than n, are also important.  ... 
doi:10.1371/journal.pone.0088519 pmid:24533097 pmcid:PMC3922877 fatcat:3n75oycpmzgktbl4jwof5se2ei

Subword Recognition in Historical Arabic Documents using C-GRUs

Hanadi Hassen, Somaya Al-Madeed, Ahmed Bouridane
2021 TEM Journal  
A comparison with existing techniques evaluated on the same datasets validates the effectiveness of our proposed model in characterizing Arabic subwords.  ...  These included the topological DAG (T-DAG) which preserves the information of the subword shape topology, the length DAG (L-DAG) which adds information about skeletal curve lengths by applying weights  ...  The subword DAG is then encoded into a topological signature vector (TSV) which is a low dimensional feature vector.  ... 
doi:10.18421/tem104-19 fatcat:v4z4eyksevb4pedqqiozfyatky

Subword complexes in Coxeter groups [article]

Allen Knutson, Ezra Miller
2003 arXiv   pre-print
Two formulae for double Grothendieck polynomials, one of which is due to Fomin and Kirillov, are recovered in the context of simplicial topology for subword complexes.  ...  Some open questions related to subword complexes are presented.  ...  Given their topological simplicity, the invariants of subword complexes necessarily derive from more refined combinatorial data, namely the links of all faces.  ... 
arXiv:math/0309259v1 fatcat:zkijscvdnzdpflyitigrvax27q

Circular codes, loop counting, and zeta-functions

Gerhard Keller
1991 Journal of combinatorial theory. Series A  
We apply this to the loop counting method for determining the topological entropy of a subshift of finite type, to the zeta-function of the Dyck-shift over 2N symbols, and to the zeta-function of a subshift  ...  product topology arising from the discrete topology on C. The shift-transformation 0: C + L' defined by a((~~)~~~) = (oi+ l)ieZ is a homeomorphism of L'" (cf. [3] ).  ...  ) copies of B but with no further occurrence of B as a subword.  ... 
doi:10.1016/0097-3165(91)90023-a fatcat:ah65kiqwhve3njcch3j6obk33y

Subword complexes in Coxeter groups

Allen Knutson, Ezra Miller
2004 Advances in Mathematics  
Two formulae for double Grothendieck polynomials, one of recovered in the context of simplicial topology for subword complexes. Some open questions related to subword complexes are presented. r  ...  An ordered list of elements in S and an element in P determine a subword complex, as introduced in Knutson and Miller (Ann. of Math. (2) (2003) , to appear).  ...  The general answer, when Q and p are arbitrary, lies in properties of the subword complex DðQ; pÞ; whose facets correspond (by definition) to reduced subwords of Q having product p: Both the topology and  ... 
doi:10.1016/s0001-8708(03)00142-7 fatcat:7rb47eau65fc7gej7z3gxuzuem

Certain Distance-Based Topological Indices of Parikh Word Representable Graphs

Nobin Thomas, Lisa Mathew, Sastha Sriram, Atulya K. Nagar, K. G. Subramanian, Ismail Naci Cangul
2021 Journal of Mathematics  
Also, several topological indices have been defined in terms of graph parameters and studied for different classes of graphs.  ...  In this study, we derive expressions for computing certain topological indices of PWRGs of binary core words, thereby enriching the study of PWRGs.  ...  In this study, certain distance-based topological indices of PWRGs of binary core words are investigated.  ... 
doi:10.1155/2021/5567663 fatcat:526gj7ahp5e7hksu4nre4xlid4

Infinitary Noetherian Constructions I. Infinite Words [article]

Jean Goubault-Larrecq
2021 arXiv   pre-print
We define and study Noetherian topologies for spaces of infinite sets, and infinite words.  ...  The asymptotic subword topology is finer than both the prefix and the suffix topologies, by Lemma 5.5 and Lemma 5.6.  ...  We equip each subspace of X ≤ω with the subspace topology. In particular, we will call asymptotic subword topology on X ω the subspace topology.  ... 
arXiv:1910.10054v3 fatcat:vznvlcl5uvb45eefedqq5t45ym

Infinitary Noetherian constructions I. Infinite words

Jean Goubault-Larrecq
2022 Colloquium Mathematicum  
We define and study Noetherian topologies for spaces of infinite sets and for spaces of infinite words.  ...  The asymptotic subword topology is finer than both the prefix and the suffix topologies, by Lemmas 5.  ...  We equip each subspace of X ≤ω with the subspace topology. In particular, we will call the subspace topology on X ω the asymptotic subword topology.  ... 
doi:10.4064/cm8077-4-2021 fatcat:a2pmkj352zfnxjj5qsox2fw5uq

On the genus defect of positive braid knots [article]

Livio Liechti
2018 arXiv   pre-print
We show that the difference between the Seifert genus and the topological 4-genus of a prime positive braid knot is bounded from below by an affine function of the minimal number of strands among positive  ...  Introduction The discrepancy between the smooth and the topological category in dimension four distinctly manifests itself in the behaviour of the smooth and the topological 4-genus of positive braid knots  ...  Since subwords induce surface minors, genus defect g − g top 4 > c of the closure is inherited from subwords in P n .  ... 
arXiv:1805.05749v1 fatcat:ywcjf6mwofe6rfmrjm7e4var6e

Thue-Morse sequence and p-adic topology for the free monoid

J. Berstel, M. Crochemore, J.E. Pin
1989 Discrete Mathematics  
Given two words u and v, the binomial coefficient (t) is the number of ways v appears as a subword (or subsequence) of u.  ...  It follows that, for each prime number p, there exists a sequence of left factors oft of increasing length, the limit of which is the empty word in the p-adic topology of the free monoid.  ...  It is the coarsest topology such that every monoid morph,sm from A* into a discrete p-group is continuous. A*, equipped with this topology, is a topological monoid.  ... 
doi:10.1016/0012-365x(89)90302-6 fatcat:pv4nfnyjajaiboem65bqrihntm
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