Statistical simulation and the distribution of distances between identical elements in a random sequence

Zörnig, Peter

doi:10.1016/j.csda.2010.01.005

Cited by 9 publications

(10 citation statements)

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“…is connected with research on the distribution of the distance between elements in a sequence, with edge length being a particular case [21,22]. If no constraint is imposed, the probability that an edge has a certain length decays linearly with the distance between the vertices [21,22]. When D is constrained (not necessarily reaching D min ), an exponential-like distribution is obtained [22].…”

Section: Introductionmentioning

confidence: 99%

“…As a problem of constraints on the ensemble of possible permutations of a sequence (defined by the vertices of a tree), the m.l.a. is connected with research on the distribution of the distance between elements in a sequence, with edge length being a particular case [21,22]. If no constraint is imposed, the probability that an edge has a certain length decays linearly with the distance between the vertices [21,22].…”

Section: Introductionmentioning

confidence: 99%

“…Suppose that D is the average value of D in uniformly random trees where vertex labels are taken as vertex positions. Then the growth of D as a function of n should be close to D random , the expectation of D in uniformly random linear arrangements of the n vertices of an arbitrary tree, which is [21,22] …”

Section: Introductionmentioning

confidence: 99%

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The scaling of the minimum sum of edge lengths in uniformly random trees

Esteban¹,

Ferrer-i-Cancho²,

Gómez-Rodríguez³

2016

J. Stat. Mech.

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Abstract. The minimum linear arrangement problem on a network consists of finding the minimum sum of edge lengths that can be achieved when the vertices are arranged linearly. Although there are algorithms to solve this problem on trees in polynomial time, they have remained theoretical and have not been implemented in practical contexts to our knowledge. Here we use one of those algorithms to investigate the growth of this sum as a function of the size of the tree in uniformly random trees. We show that this sum is bounded above by its value in a star tree. We also show that the mean edge length grows logarithmically in optimal linear arrangements, in stark contrast to the linear growth that is expected on optimal arrangements of star trees or on random linear arrangements.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The scaling of the minimum sum of edge lengths in uniformly random trees

Esteban¹,

Ferrer-i-Cancho²,

Gómez-Rodríguez³

2016

J. Stat. Mech.

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“…Some of the entities or their properties may be quantified and measured, other ones may be symbolic. But even in the latter case they constitute a sequence which has some further properties to be studied, e. g. all characteristics of a time series, transition properties, distances between equal or non-equal elements (Zörnig 1984(Zörnig , 1987(Zörnig , 2010(Zörnig , 2013a, motifs of different kind (cf. Köhler 2008a, b;Naumann 2008, 2010), Frumkina's sequential behavior (Frumkina 1962;Altmann and Köhler 2015), Skinner's behavior (Skinner 1939(Skinner , 1941(Skinner , 1957, Belza-chains (Chen and Altmann 2015), runs, and many others.…”

Section: Introductionmentioning

confidence: 99%

On Consensus Strings in Text Analysis

Zörnig¹,

Altmann²

2016

Glottotheory

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The present paper is a pilot study introducing a concept of computational biology -the closest string problem (CSP) -into linguistics. In quantitative studies, texts can be represented as sequences, and for any given set of sequences one can solve a CSP. The solution is called a consensus string (CS), which is a sequence that is "as close as possible to all the given strings". In this article we solve some CSP's resulting from the study of a Hungarian poem and illustrate possible interpretations.

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“…"Distance minimization" has therefore a higher predictive power and greater utility in a general theory of communication. Second, distance provides a "formal background" or a "specific background" (following Bunge's terminology [10]) from physics or mathematics such as the theory of geographical or spatial networks (where the syntactic dependency structures of sentences are particular cases in one dimension) [12,13] or the theory for the distance between like elements in sequences (where the couple of words involved in a syntactic dependency are particular cases of like elements) [14]. Therefore we agree with [1] on the convenience of the term distance.…”

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confidence: 99%

Towards a theory of word order

Ferrer-i-Cancho

2017

Physics of Life Reviews

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Liu et al's reflections on the term dependency length minimization [1] may look anecdotal but they are not. By the turn of the 20th century, we put forward a "Euclidean distance minimization" hypothesis for the distance between syntactically linked words and various word order phenomena [2,3] 1 . Later on, pressure from language researchers forced us to replace it with terms such as "online memory minimization" [5] because our initial formulation was obscure to them. Recently, researchers from all over the world have been granted to use the term "dependency length minimization" by the popes thanks to whom [6] came into light. Although "length" is a particular case of distance in this context and thus downsizes our original formulation, it is still abstract enough to allow for progress in theoretical research [7] and frees us from the heavy burden of contingency, i.e. the real implementation of the principle (at present believed to result from decay and interference as reviewed by Liu et al) or the current view of the architecture of memory [8,9]. Our position is grounded on the high predictive power of that principle per se [5].However, the lower generality of the term "dependency length" can be anEmail address: rferrericancho@cs.upc.edu (R. Ferrer-i-Cancho) 1 These were pieces of our PhD thesis [4] that were submitted for publication before its defense. Preprint submitted to ElsevierJune 16, 2017 obstacle to the construction of a fully-fledged scientific field [10]. First, distance minimization allows one to unify pressure to reduce dependency lengths (still distances) with constraints on word order variation and change arising from a principle of swap distance minimization [11]. "Distance minimization" has therefore a higher predictive power and greater utility in a general theory of communication. Second, distance provides a "formal background" or a "specific background" (following Bunge's terminology [10]) from physics or mathematics such as the theory of geographical or spatial networks (where the syntactic dependency structures of sentences are particular cases in one dimension) [12,13] or the theory for the distance between like elements in sequences (where the couple of words involved in a syntactic dependency are particular cases of like elements) [14]. Therefore we agree with [1] on the convenience of the term distance.A less flashy contribution of [6] has been promoting the need of controlling for sentence length (as a predictor of dependency length in their mixed-effects regression model) in research on dependency length minimization, an important methodological issue [15] that was addressed early [2] but neglected in subsequent research (e.g., [16,17,18]).Liu et al focus their review on the fundamental principle of dependency length minimization but understanding how it interacts with other principles is vital. In 2009, we put forward another fundamental word order principle, i.e. predictability maximization, and presented a theoretical framework culminating in a conflict between dependency lengt...

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Statistical simulation and the distribution of distances between identical elements in a random sequence

Cited by 9 publications

References 9 publications

The scaling of the minimum sum of edge lengths in uniformly random trees

The scaling of the minimum sum of edge lengths in uniformly random trees

On Consensus Strings in Text Analysis

Towards a theory of word order

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