The law of the iterated logarithm for random interval homeomorphisms

Czudek, Klaudiusz; Szarek, Tomasz Z.; Wojewódka–Ściążko, Hanna

doi:10.1007/s11856-021-2235-9

Cited by 4 publications

(3 citation statements)

References 3 publications

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“…When the recommendation index of a case description and each relevant law article is obtained, the probability distribution of the recommendation index can be obtained by combining them in order, and, at the same time, the ranking of the top five relevant articles with the largest recommendation index is constructed in order. Among them, P is the recommendation article of this case, and its index is the corresponding output of the reselection mechanism [14].…”

Section: Reselection Mechanismmentioning

confidence: 99%

Evidence Prediction Method Based on Sentence Selection for Legal Documents

Bai

2022

Advances in Multimedia

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In order to solve the problem that it is difficult to find evidence from a large number of legal document statements and the irrelevant statements in a large number of document sample data will cause a great interference to the prediction results and further improve the accuracy of evidence prediction, this paper puts forward an intelligent evidence criterion prediction method for legal documents based on the comprehensive consideration of legal problems, the nature of statements, and the characteristics of answers. The binary cross-entropy of different statements is used to obtain the interaction information between different statements. Through experiments, it is found that the score of Joint F1 proposed in this paper is 70.07%, which is more accurate than the mainstream model and also verifies the effectiveness of the scheme.

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Section: Reselection Mechanismmentioning

confidence: 99%

Evidence Prediction Method Based on Sentence Selection for Legal Documents

Bai

2022

Advances in Multimedia

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“…In recent years, a growing interest in low-dimensional random dynamics has led to an intensive study of random one-dimensional systems given by (semi)groups of interval and circle homeomorphisms, both from the stochastic and geometric points of view (see e.g. [1, 7, 8, 10–12, 16–18, 23, 24]). This can be seen as an extension of the research on the well-known case of groups of smooth circle diffeomorphisms (see e.g.…”

Section: Introductionmentioning

confidence: 99%

On the dimension of stationary measures for random piecewise affine interval homeomorphisms

Barański

Śpiewak

2023

Ergod. Th. Dynam. Sys.

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We study stationary measures for iterated function systems (considered as random dynamical systems) consisting of two piecewise affine interval homeomorphisms, called Alsedà–Misiurewicz (AM) systems. We prove that for an open set of parameters, the unique non-atomic stationary measure for an AM system has Hausdorff dimension strictly smaller than $1$ . In particular, we obtain singularity of these measures, answering partially a question of Alsedà and Misiurewicz [Random interval homeomorphisms. Publ. Mat.58(suppl.) (2014), 15–36].

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“…In recent years, a growing interest in low-dimensional random dynamics has led to an intensive study of random one-dimensional systems given by (semi)groups of interval and circle homeomorphisms, both from stochastic and geometric point of view (see e.g. [1,7,8,10,11,12,16,17,18,23,24]). This can be seen as an extension of the research on the well-known case of groups of smooth circle diffeomorphisms (see e.g.…”

Section: Introductionmentioning

confidence: 99%

Singular Stationary Measures for Random Piecewise Affine Interval Homeomorphisms

Barański

Śpiewak

2019

J Dyn Diff Equat

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We show that the stationary measure for some random systems of two piecewise affine homeomorphisms of the interval is singular, verifying partially a conjecture by Alsedà and Misiurewicz and contributing to a question of Navas on the absolute continuity of stationary measures, considered in the setup of semigroups of piecewise affine circle homeomorphisms. We focus on the case of resonant boundary derivatives.

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The law of the iterated logarithm for random interval homeomorphisms

Cited by 4 publications

References 3 publications

Evidence Prediction Method Based on Sentence Selection for Legal Documents

Evidence Prediction Method Based on Sentence Selection for Legal Documents

On the dimension of stationary measures for random piecewise affine interval homeomorphisms

Singular Stationary Measures for Random Piecewise Affine Interval Homeomorphisms

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