The EM Algorithm applied to determining new limit points of Mahler measures

Souad El Otmani; Georges Rhin; ean-Marc Sac-Epee

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The EM Algorithm applied to determining new limit points of Mahler measures

机译：EM算法用于确定Mahler测度的新极限点

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摘要

In this work, we propose new candidates expected to be limit points of Mahler measures of polynomials. The tool we use for determining these candidates is the Expectation-Maximization algorithm, whose goal is to optimize the likelihood for the given data points, i.e. the known Mahler measures up to degree 44, to be generated by a specific mixture of Gaussians. We will give the mean (which is a candidate to be a new limit point) and the relative amplitude of each component of the more likely gaussian mixture.

机译：在这项工作中，我们提出了新的候选对象，它们有望成为多项式马勒测度的极限点。我们用于确定这些候选者的工具是Expectation-Maximization算法，其目标是优化给定数据点的可能性，即由特定高斯混合生成的已知Mahler测度直至44度。我们将给出平均值（可能是新的极限点）和更可能的高斯混合的每个分量的相对幅度。

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来源
《Control and Cybernetics》 |2010年第4期|p.1185-1192|共8页
作者
Souad El Otmani; Georges Rhin; ean-Marc Sac-Epee;
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作者单位

Universite Paul Verlaine-Metz, LMAM, CNRS UMR 7122,He du Saulcy, METZ, F-57045, Prance;

Universite Paul Verlaine-Metz, LMAM, CNRS UMR 7122,He du Saulcy, METZ, F-57045, Prance;

Universite Paul Verlaine-Metz, LMAM, CNRS UMR 7122,He du Saulcy, METZ, F-57045, Prance;

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正文语种 eng
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关键词
Mahler Measure; EM algorithm;

机译：马勒测度EM算法;
入库时间 2022-08-18 00:45:44

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1. Finding New Limit Points of Mahler's Measure by Genetic Algorithms [J] . El Otmani S., Rhin G., Sac-Epee J. -M. Experimental mathematics . 2019,第2期

机译：通过遗传算法查找Mahler措施的新限度
2. FINDING NEW SMALL DEGREE POLYNOMIALS WITH SMALL MAHLER MEASURE BY GENETIC ALGORITHMS [J] . El Otmani S., Maul A., Rhin G., The Rocky Mountain journal of mathematics . 2017,第8期

机译：通过遗传算法找到新的小型Mahler测量的新小型多项式
3. Small limit points of Mahler's measure [J] . Boyd DW, Mossinghoff MJ Experimental mathematics . 2005,第4期

机译：马勒测度的小极限点
4. Mahler measure of the Horie unit and Weber's Class Number Problem in the Cyclotomic Zr-extension of Q [C] . Takayuki Morisawa Diophantine analysis and related fields . 2010

机译：Mahler测量Horie Unit和Weber的Carkotomic Zr-extension的Q型级数问题
5. Polynomials with Small Elliptic Mahler Measure Via Genetic Algorithms [D] . Clark, John Michael. 2020

机译：通过遗传算法具有小型椭圆马哈勒的多项式
6. An approach for determining and measuring network hierarchy applied to comparing the phosphorylome and the regulome [O] . Chao Cheng, Erik Andrews, Koon-Kiu Yan, 2015

机译：确定和测量网络层次结构的方法用于比较磷酸酶和正则基因组
7. Decision-making is the process of analyzing information about a problem situation and comparing it to a specific conclusion in order to solve a specific problematic (Yıkılmaz, 2001; Miller and Byrnes, 2001). Decision-making styles are a mechanism that is influenced by the internal and external conditions that determine the direction of the decisions of the individual, the content of the decision-making process, and the outcome of the decision-making process (Payne, Bettman and Johson, 1993; Bavol’ár and Orosová, 2015). ACT is a contemporary member of the Cognitive Behavioral Therapy family. ACT (Acceptance and commitment therapy) has both similar and different directions with Behavioral Therapies and Cognitive Therapies (Herbet and Forman, 2011; Hayes, 2004). KKT responds to classical behavioral treatments using both existential and cognitive approaches in the analysis of behavior. KKT is a science wing that tries to solve human problems with a wider perspective aimed at solving problematic human behaviors (Plumb, Stewart, Dahl and Lundgren, 2009). It is seen that there is very little research about the new approach of ACT approach when the aiming country of our country is screened and it is thought that our country will contribute to the field of psychological counseling with the work done. In the scope of the research, experimental and control groups and preliminary test, post-test and follow-up measurements of 2x3 experimental design were used. The study's study group consists of a total of 24 (12 experimental and 12 control groups) university students studying in different departments and levels, continuing their education in the academic year of 2015-2016 in Ağrı province and İbrahim Chechen University in 2015-2016 academic year. The average age of participants in the experiment and control group is 20. There were 12 participants in the experimental group, 7 female and 5 male, and 12 participants, 7 female and 5 male in the control group. Personal Information Form and Decision Making Style Scale prepared by the researcher were used in the research. In order to decide on the tests to be used in the course of analyzing the data, the scores of the participant's Decision Styles Scale pre-test, which are placed primarily in the experimental and control groups, it was analyzed whether the basic expectations of parametric tests were answered. As a result of the analysis made, the scores, skewness and kurtosis coefficients obtained from the Decision Making Styles Scale were given to the experimental and control groups. It was determined that the distribution was normal in the result of Shapiro-Wilk test, in which the skewness and kurtosis coefficients of each sub-scale were ranked between -1 and +1. Participants in the experimental and control groups; homogeneity test results for decision-style pre-test measurements indicate that the data are homogeneous. According to the results of the Mauchly Globalness Test, it has been determined that working supports the hypothesis. It was determined that there was no significant difference between the pre-test scores obtained from dependent decision-making style of experiment and control groups, but the test group showed lower mean scores at the significant level within the scores of post-test and follow-up tests. Therefore, it can be said that the ACT-oriented psychoeducation program applied to the experimental group reduces the dependent decision-making style scores from the decision style sub-dimensions and the psychoeducation program has a lasting effect. It was determined that there was no significant difference between pre-test, post-test and follow-up scores obtained from the Spontaneous-Instant Decision Style of experiment and control groups. Thus, it can be said that this situation does not cause a significant difference in the Spontaneous-Decision-Making Style scores from the decision style sub-dimensions of the ACT-oriented psychoeducation program applied to the experimental group. The ACT -oriented psychoeducation program had a decline in the intuitive decision-making styles of the individuals, but this decrease did not create significant differences. Thus, it can be said that this situation does not make a meaningful difference in the intuitive decision style scores from the decision style sub-dimensions of the KKT oriented psychoeducation program applied to the experimental group. The pre-test scores obtained from the rational decision-making style of the experimental and control groups showed that there was a difference between the post-test and the follow-up scores, but this difference was not significant. As a result of the analysis, it was determined that the test group had higher levels of rational decision style than the pre - test scores in the post test and follow - up scores, whereas the post test and follow - up test scores in the control group rational decision style showed a decrease compared to the pre - test scores. the pre - test scores. Decision-making Styles Scale Avoidant Decision Making As a result of the analysis of the mean scores of the subscale scores of pre-test, post-test and follow-up measures, the group effect was found to be insignificant. It was determined that the experimental and control groups differed significantly from the pre-test scores obtained from the avoidant decision-making style but did not show any significant change within the scores of the post-test and follow-up tests. [O] . mustafa ercengiz, ali haydar şar 2018

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8. New Limit Theorems for Regular Diffusion Processes with Finite Speed Measure. Probability Networks and Algorithms (PNA). [R] . van Zanten, J. H. 2000

机译：具有有限速度测度的正则扩散过程的新极限定理。概率网络和算法（pNa）。

The EM Algorithm applied to determining new limit points of Mahler measures

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