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Journal articles on the topic 'Uncertain sequences'

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Author: Grafiati

Published: 9 March 2023

Last updated: 10 March 2023

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1

Das, B., P. Debnath, and B. C. Tripathy. "On statistically convergent complex uncertain sequences." Carpathian Mathematical Publications 14, no. 1 (June 17, 2022): 135–46. http://dx.doi.org/10.15330/cmp.14.1.135-146.

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In this paper, we extend the study of statistical convergence of complex uncertain sequences in a given uncertainty space. We produce the relation between convergence and statistical convergence in an uncertain environment. We also initiate statistically Cauchy complex uncertain sequence to prove that a complex uncertain sequence is statistically convergent if and only if it is statistically Cauchy. We further characterize a statistically convergent complex uncertain sequence via boundedness and density operator.

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2

Datta, Debasish, and Binod Chandra Tripathy. "Convergence of Complex Uncertain Double Sequences." New Mathematics and Natural Computation 16, no. 03 (November 2020): 447–59. http://dx.doi.org/10.1142/s1793005720500271.

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Complex uncertain variables are measurable functions from an uncertainty space to the set of complex numbers and are used to model complex uncertain quantities. This paper introduces the convergence concepts of convergence almost surely (a.s.), convergence in measure, convergence in mean, convergence in distribution and convergence uniformly almost surely complex uncertain double sequences. In addition, relationships among the introduced classes of sequences have been introduced.

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3

Tripathy, Binod Chandra, and Pankaj Kumar Nath. "Statistical Convergence of Complex Uncertain Sequences." New Mathematics and Natural Computation 13, no. 03 (September 28, 2017): 359–74. http://dx.doi.org/10.1142/s1793005717500090.

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Complex uncertain variables are measurable functions from an uncertainty space to the set of complex numbers and are used to model complex uncertain quantities. This paper introduces the statistical convergence concepts of complex uncertain sequences: statistical convergence almost surely (a.s.), statistical convergence in measure, statistical convergence in mean, statistical convergence in distribution and statistical convergence uniformly almost surely (u.a.s.) In addition, decomposition theorems and relationships among them are discussed.

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4

Raj, Kuldip, Sonali Sharma, and Mohammad Mursaleen. "Almost λ-Statistical Convergence of Complex Uncertain Sequences." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 30, no. 05 (October 2022): 795–811. http://dx.doi.org/10.1142/s0218488522500234.

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In the present article, we introduced almost [Formula: see text]-statistical convergence of complex uncertain sequences in all five aspects of uncertainty viz., almost surely, mean, measure, distribution and uniformly almost surely. Further, with the aid of interesting examples and diagram we investigated some interrelationships among these uncertain complex sequences.

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5

Chen, Xiumei, Yufu Ning, and Xiao Wang. "Convergence of complex uncertain sequences." Journal of Intelligent & Fuzzy Systems 30, no. 6 (April 30, 2016): 3357–66. http://dx.doi.org/10.3233/ifs-152083.

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6

You, Cuilian, and Lijuan Yan. "Convergence Properties for Uncertain Sequence." Mathematical Problems in Engineering 2017 (2017): 1–6. http://dx.doi.org/10.1155/2017/6307439.

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Uncertainty theory is a branch of axiomatic mathematics for modeling belief degrees. Since convergence for uncertain sequences plays a very important role in uncertainty theory and applications, we investigated some properties of convergence in measure in this paper. In addition, some theorems and properties of convergence in p-distance were studied.

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7

Das, Birojit, Binod Chandra Tripathy, and Piyali Debnath. "Some results on statistically convergent triple sequences in an uncertainty space." Annals of the University of Craiova, Mathematics and Computer Science Series 49, no. 1 (June 24, 2022): 120–34. http://dx.doi.org/10.52846/ami.v49i1.1520.

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The concept of statistical convergence plays a very prominent role in the study of sequence spaces. In this treatise, we extend the research on different types of statistical convergence viz., statistical convergence in mean, in measure, in distribution, in almost surely and with respect to uniformly almost surely of complex uncertain triple sequences in a given uncertainty space. We emphasize to focus on characterizing statistical convergence of complex uncertain triple sequence in some extent. Moreover, we initiate the notion of complex uncertain Cauchy triple sequence and establish the interconnection of it with a statistically convergent triple sequence.

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8

Wu, Jianrong, and Yang Xia. "Convergence Theorems for Uncertain Variable Sequences." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 22, no. 04 (August 2014): 627–39. http://dx.doi.org/10.1142/s0218488514500329.

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For uncertain variable sequences, conditions of convergences such as Cauchy convergence in measure, convergence almost surely and convergence uniformly almost surely are given. Consequently, the relationships among convergences of uncertain variable sequences are shown. These results have not been proposed in literature so far.

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9

You, Cuilian. "On the convergence of uncertain sequences." Mathematical and Computer Modelling 49, no. 3-4 (February 2009): 482–87. http://dx.doi.org/10.1016/j.mcm.2008.07.007.

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10

Saha, Sangeeta, Binod Chandra Tripathy, and Santanu Roy. "Matrix map between complex uncertain sequences." Annals of the University of Craiova - Mathematics and Computer Science Series 48, no. 1 (June 30, 2021): 10–17. http://dx.doi.org/10.52846/ami.v48i1.1254.

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In this article we deﬁne matrix maps between complex uncertain sequences. We introduce the notion of bounded sequences of complex uncertain sequence for almost sure, mean, measure and distribution. We introduce the limitation method for different notion of boundedness of sequence of complex uncertain variables and establish relation between the different notions. The necessary condition for a matrix map to be a limitation method is established.

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11

Baliarsingh, P. "On Statistical Deferred A-Convergence of Uncertain Sequences." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 29, no. 04 (August 2021): 499–515. http://dx.doi.org/10.1142/s0218488521500215.

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In this paper, as a part of uncertain theory, we discuss various concepts of convergence and statistical convergence of complex uncertain sequences. Using uncertain variables, the convergence of uncertain sequences of complex numbers such as the idea of convergence in measure, convergence in mean, convergence in distribution and convergence uniformly almost surely via deferred Cesàro mean and a regular matrix A are introduced. Also, some relations among these convergence are established. Certain results on deferred statistical convergence of order α, (0 < α ≤ 1) for complex uncertain sequences are studied in detail.

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12

Saha, Sangeeta, Binod Chandra Tripathy, and Santanu Roy. "On Riesz mean of complex uncertain sequences." Journal of Mathematical Analysis and Applications 499, no. 2 (July 2021): 125017. http://dx.doi.org/10.1016/j.jmaa.2021.125017.

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13

Dowari, Pranab Jyoti, and Binod Chandra Tripathy. "Lacunary difference sequences of complex uncertain variables." Methods of Functional Analysis and Topology 26, no. 4 (December 28, 2020): 327–40. http://dx.doi.org/10.31392/mfat-npu26_4.2020.04.

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14

Das, Birojit, Binod Tripathy, Piyali Debnath, and Baby Bhattacharya. "Almost convergence of complex uncertain double sequences." Filomat 35, no. 1 (2021): 61–78. http://dx.doi.org/10.2298/fil2101061d.

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Convergence of real sequences, as well as complex sequences are studied by B. Liu and X. Chen respectively in uncertain environment. In this treatise, we extend the study of almost convergence by introducing double sequences of complex uncertain variable. Almost convergence with respect to almost surely, mean, measure, distribution and uniformly almost surely are presented and interrelationships among them are studied and depicted in the form of a diagram. We also define almost Cauchy sequence in the same format and establish some results. Conventionally we have, every convergent sequence is a Cauchy sequence and the converse case is not true in general. But taking complex uncertain variable in a double sequence, we find that a complex uncertain double sequence is a almost Cauchy sequence if and only if it is almost convergent. Some suitable examples and counter examples are properly placed to make the paper self sufficient.

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15

Wang, Xiaosheng, Dan Chen, Hamed Ahmadzade, and Rong Gao. "Some limit theorems on uncertain random sequences." Journal of Intelligent & Fuzzy Systems 34, no. 1 (January 12, 2018): 507–15. http://dx.doi.org/10.3233/jifs-17599.

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16

Wu, Jianrong, and Yang Xia. "Relations among convergence concepts of uncertain sequences." Information Sciences 198 (September 2012): 177–85. http://dx.doi.org/10.1016/j.ins.2012.02.048.

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17

Saha, Sangeeta, Binod Chandra Tripathy, and Santanu Roy. "On Almost Convergent of Complex Uncertain Sequences." New Mathematics and Natural Computation 16, no. 03 (November 2020): 573–80. http://dx.doi.org/10.1142/s1793005720500349.

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In this paper, we define almost convergence concepts of complex uncertain sequences: almost sure convergent, almost convergent in measure, almost convergent in mean and almost convergent in distribution and relationship among them are discussed. We also define Cesàro summable for complex uncertain sequence space. In addition, we derive relationships between convergent, Cesàro summable and almost convergent.

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18

Rahman, Md Mahmudur, Chowdhury Farhan Ahmed, and Carson Kai-Sang Leung. "Mining weighted frequent sequences in uncertain databases." Information Sciences 479 (April 2019): 76–100. http://dx.doi.org/10.1016/j.ins.2018.11.026.

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19

Ahmadzade, H., Y. Sheng, and M. Esfahani. "On the convergence of uncertain random sequences." Fuzzy Optimization and Decision Making 16, no. 2 (June 4, 2016): 205–20. http://dx.doi.org/10.1007/s10700-016-9242-z.

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20

Alzbutas, Robertas. "Probabilistic Dynamics for Integrated Analysis of Accident Sequences considering Uncertain Events." Science and Technology of Nuclear Installations 2015 (2015): 1–18. http://dx.doi.org/10.1155/2015/892502.

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The analytical/deterministic modelling and simulation/probabilistic methods are used separately as a rule in order to analyse the physical processes and random or uncertain events. However, in the currently used probabilistic safety assessment this is an issue. The lack of treatment of dynamic interactions between the physical processes on one hand and random events on the other hand causes the limited assessment. In general, there are a lot of mathematical modelling theories, which can be used separately or integrated in order to extend possibilities of modelling and analysis. The Theory of Probabilistic Dynamics (TPD) and its augmented version based on the concept of stimulus and delay are introduced for the dynamic reliability modelling and the simulation of accidents in hybrid (continuous-discrete) systems considering uncertain events. An approach of non-Markovian simulation and uncertainty analysis is discussed in order to adapt the Stimulus-Driven TPD for practical applications. The developed approach and related methods are used as a basis for a test case simulation in view of various methods applications for severe accident scenario simulation and uncertainty analysis. For this and for wider analysis of accident sequences the initial test case specification is then extended and discussed. Finally, it is concluded that enhancing the modelling of stimulated dynamics with uncertainty and sensitivity analysis allows the detailed simulation of complex system characteristics and representation of their uncertainty. The developed approach of accident modelling and analysis can be efficiently used to estimate the reliability of hybrid systems and at the same time to analyze and possibly decrease the uncertainty of this estimate.

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21

Allen, Julie M., J. Gordon Burleigh, Jessica E. Light, and David L. Reed. "Effects of 16S rDNA sampling on estimates of the number of endosymbiont lineages in sucking lice." PeerJ 4 (July 19, 2016): e2187. http://dx.doi.org/10.7717/peerj.2187.

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Phylogenetic trees can reveal the origins of endosymbiotic lineages of bacteria and detect patterns of co-evolution with their hosts. Although taxon sampling can greatly affect phylogenetic and co-evolutionary inference, most hypotheses of endosymbiont relationships are based on few available bacterial sequences. Here we examined how different sampling strategies ofGammaproteobacteriasequences affect estimates of the number of endosymbiont lineages in parasitic sucking lice (Insecta: Phthirapatera: Anoplura). We estimated the number of louse endosymbiont lineages using both newly obtained and previously sequenced 16S rDNA bacterial sequences and more than 42,000 16S rDNA sequences from otherGammaproteobacteria. We also performed parametric and nonparametric bootstrapping experiments to examine the effects of phylogenetic error and uncertainty on these estimates. Sampling of 16S rDNA sequences affects the estimates of endosymbiont diversity in sucking lice until we reach a threshold of genetic diversity, the size of which depends on the sampling strategy. Sampling by maximizing the diversity of 16S rDNA sequences is more efficient than randomly sampling available 16S rDNA sequences. Although simulation results validate estimates of multiple endosymbiont lineages in sucking lice, the bootstrap results suggest that the precise number of endosymbiont origins is still uncertain.

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22

Tripathy, Binod, and Pranab Dowari. "Nörlund and Riesz mean of sequence of complex uncertain variables." Filomat 32, no. 8 (2018): 2875–81. http://dx.doi.org/10.2298/fil1808875t.

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In this article we have investigated some properties of the N?rlund and Riesz mean of sequences of complex uncertain variables. Also, we prove results on oscillating sequences of complex uncertain variables.

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23

Nath, J., B. C. Tripathy, and B. Bhattacharya. "On strongly almost convergence of doubles equences via complex uncertain variable." Issues of Analysis 29, no. 1 (February 2022): 102–21. http://dx.doi.org/10.15393/j3.art.2022.10450.

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24

Ahmadzade, Hamed, Rong Gao, and Habib Naderi. "On the convergence of complex uncertain random sequences." Journal of Intelligent & Fuzzy Systems 35, no. 2 (August 26, 2018): 2459–67. http://dx.doi.org/10.3233/jifs-18080.

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25

Das, Birojit, Binod Tripathy, Piyali Debnath, and Baby Bhattacharya. "Study of matrix transformation of uniformly almost surely convergent complex uncertain sequences." Filomat 34, no. 14 (2020): 4907–22. http://dx.doi.org/10.2298/fil2014907d.

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In this paper, we introduce the concept of convergence of complex uncertain series. We initiate matrix transformation of complex uncertain sequence and extend the study via linearity and boundedness. In this context, we prove Silverman-Toeplitz theorem and Kojima-Schur theorem considering complex uncertain sequences. Finally, we establish some results on co-regular matrices .

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26

Das, B., P. Debnath, and B. C. Tripathy. "Characterization of matrix transformation of complex uncertain sequences via expected value operator." Carpathian Mathematical Publications 14, no. 2 (December 2, 2022): 419–28. http://dx.doi.org/10.15330/cmp.14.2.419-428.

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The aim of this paper is to study the concept of matrix transformation between complex uncertain sequences in mean. The characterization of the matrix transformation has been made by applying the concept of convergence of complex uncertain series. Moreover, in this context, some well-known theorems of real sequence spaces have been established by considering complex uncertain sequence via expected value operator.

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27

Debnath, Shyamal, and Bijoy Das. "Statistical Convergence of Order α for Complex Uncertain Sequences." Journal of Uncertain Systems 14, no. 02 (June 2021): 2150012. http://dx.doi.org/10.1142/s1752890921500124.

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In this paper, we introduce convergence concepts namely, statistical convergence of order [Formula: see text], statistical convergence of order [Formula: see text] almost surely, statistical convergence of order [Formula: see text] in measure, statistical convergence of order [Formula: see text] in mean, statistical convergence of order [Formula: see text] in distribution in complex uncertain theory. We also investigate some relationships among them.

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28

Liu, Huiting, Lili Wang, Zhizhong Liu, Peng Zhao, and Xindong Wu. "Efficient pattern matching with periodical wildcards in uncertain sequences." Intelligent Data Analysis 22, no. 4 (June 27, 2018): 829–42. http://dx.doi.org/10.3233/ida-173435.

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29

Dowari, Pranab Jyoti, and Binod Chandra Tripathy. "Lacunary statistical convergence of complex uncertain variables." Boletim da Sociedade Paranaense de Matemática 41 (December 21, 2022): 1–10. http://dx.doi.org/10.5269/bspm.52688.

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In this paper, we introduce the notion of lacunary statistical convergence for the sequences of complex uncertain variables for almost sure, mean, measure and distribution. We investigate some of the basic properties of the notion. We have established relation between these notions.

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30

Tessier, Laurence, Olivier Côté, and Dorothee Bienzle. "Sequence variant analysis of RNA sequences in severe equine asthma." PeerJ 6 (October 11, 2018): e5759. http://dx.doi.org/10.7717/peerj.5759.

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Background Severe equine asthma is a chronic inflammatory disease of the lung in horses similar to low-Th2 late-onset asthma in humans. This study aimed to determine the utility of RNA-Seq to call gene sequence variants, and to identify sequence variants of potential relevance to the pathogenesis of asthma. Methods RNA-Seq data were generated from endobronchial biopsies collected from six asthmatic and seven non-asthmatic horses before and after challenge (26 samples total). Sequences were aligned to the equine genome with Spliced Transcripts Alignment to Reference software. Read preparation for sequence variant calling was performed with Picard tools and Genome Analysis Toolkit (GATK). Sequence variants were called and filtered using GATK and Ensembl Variant Effect Predictor (VEP) tools, and two RNA-Seq predicted sequence variants were investigated with both PCR and Sanger sequencing. Supplementary analysis of novel sequence variant selection with VEP was based on a score of <0.01 predicted with Sorting Intolerant from Tolerant software, missense nature, location within the protein coding sequence and presence in all asthmatic individuals. For select variants, effect on protein function was assessed with Polymorphism Phenotyping 2 and screening for non-acceptable polymorphism 2 software. Sequences were aligned and 3D protein structures predicted with Geneious software. Difference in allele frequency between the groups was assessed using a Pearson’s Chi-squared test with Yates’ continuity correction, and difference in genotype frequency was calculated using the Fisher’s exact test for count data. Results RNA-Seq variant calling and filtering correctly identified substitution variants in PACRG and RTTN. Sanger sequencing confirmed that the PACRG substitution was appropriately identified in all 26 samples while the RTTN substitution was identified correctly in 24 of 26 samples. These variants of uncertain significance had substitutions that were predicted to result in loss of function and to be non-neutral. Amino acid substitutions projected no change of hydrophobicity and isoelectric point in PACRG, and a change in both for RTTN. For PACRG, no difference in allele frequency between the two groups was detected but a higher proportion of asthmatic horses had the altered RTTN allele compared to non-asthmatic animals. Discussion RNA-Seq was sensitive and specific for calling gene sequence variants in this disease model. Even moderate coverage (<10–20 counts per million) yielded correct identification in 92% of samples, suggesting RNA-Seq may be suitable to detect sequence variants in low coverage samples. The impact of amino acid alterations in PACRG and RTTN proteins, and possible association of the sequence variants with asthma, is of uncertain significance, but their role in ciliary function may be of future interest.

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31

Dowari, Pranab Jyoti, and Binod Chandra Tripathy. "Lacunary sequences of complex uncertain variables defined by Orlicz functions." Proyecciones (Antofagasta) 40, no. 2 (April 2021): 355–70. http://dx.doi.org/10.22199/issn.0717-6279-2021-02-0021.

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Using the concept of Orlicz function and uncertainty theory, some new class of lacunary convergent sequences defined by Orlicz functions have been introduced with the lacunary convergence concepts in this paper. Some topological properties of the defined sequence spaces along with the inclusion relations have been investigated.

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32

AlBaidani, Mashael M. "Notion of New Structure of Uncertain Sequences Using Δ -Spaces." Journal of Mathematics 2022 (September 20, 2022): 1–6. http://dx.doi.org/10.1155/2022/2615772.

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The object of this paper is to introduce a new approach of Δ -operator on the theory of uncertainty using sequence spaces. Also, some structural properties will be studied. Moreover, inclusion relations concerning the newly constructed spaces of this paper will be taken care of.

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33

Semenikhin, K. V. "Minimax linear filtering of random sequences with uncertain covariance function." Automation and Remote Control 77, no. 2 (February 2016): 226–41. http://dx.doi.org/10.1134/s0005117916020028.

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34

Nath, Pankaj Kumar, and Binod Chandra Tripathy. "Statistical convergence of complex uncertain sequences defined by Orlicz function." Proyecciones (Antofagasta) 39, no. 2 (April 2020): 301–15. http://dx.doi.org/10.22199/issn.0717-6279-2020-02-0019.

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35

Datta, Debasish, and Binod Chandra Tripathy. "Double Sequences of Complex Uncertain Variables Defined by Orlicz Function." New Mathematics and Natural Computation 16, no. 03 (November 2020): 541–50. http://dx.doi.org/10.1142/s1793005720500325.

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In this paper, we introduce double sequences of complex uncertain variables defined by Orlicz function. We study some of their properties like solidness, symmetricity, completeness, etc. and prove some inclusion results.

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36

Demirci, Işıl Açık, and Mehmet Gürdal. "On lacunary generalized statistical convergent complex uncertain triple sequence." Journal of Intelligent & Fuzzy Systems 41, no. 1 (August 11, 2021): 1021–29. http://dx.doi.org/10.3233/jifs-202964.

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In this work, we study the lacunary I -statistical convergence concept of complex uncertain triple sequence. Four types of lacunary I -statistically convergent complex uncertain triple sequences are presented, namely lacunary I -statistical convergence in measure, in mean, in distribution and with respect to almost surely, and some basic properties are proved.

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37

Granados, Carlos. "A Generalized of Sλ-I-Convergence of Complex Uncertain Double Sequences." Ingeniería y Ciencia 17, no. 34 (December 1, 2021): 53–75. http://dx.doi.org/10.17230/ingciencia.17.34.3.

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In this paper, we introduce the λI2 -statistically convergence sequence concepts which are namely λI2 -statistically convergence almost surely (Sλ(I2) a.s.), λI2 -statistically convergence in measure, λI2 -statistically convergence in mean, λI2 -statistically convergence in distribution and λI2 -statistically convergence uniformly almost surely (Sλ(I2) u.a.s.). Additionally, decomposition theorems and relationships among them are presented, further, when reciprocal of one theorem is not satisfied, an counterexample is shown to support the result.

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38

Liu, Xiao, and Huimin Ma. "A Two-Sided Matching Decision Model Based on Uncertain Preference Sequences." Mathematical Problems in Engineering 2015 (2015): 1–10. http://dx.doi.org/10.1155/2015/241379.

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Two-sided matching is a hot issue in the field of operation research and decision analysis. This paper reviews the typical two-sided matching models and their limitations in some specific contexts, and then puts forward a new decision model based on uncertain preference sequences. In this model, we first design a data processing method to get preference ordinal value in uncertain preference sequence, then compute the preference distance of each matching pair based on these certain preference ordinal values, set the optimal objectives as maximizing matching number and minimizing total sum of preference distances of all the matching pairs under the lowest threshold constraint of matching effect, and then solve it with branch-and-bound algorithm. Meanwhile, we take two numeral cases as examples and analyze the different matching solutions with one-norm distance, two-norm distance, and positive-infinity-norm distance, respectively. We also compare our decision model with two other approaches, and summarize their characteristics on two-sided matching.

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Casciotti, Karen L., and Bess B. Ward. "Dissimilatory Nitrite Reductase Genes from Autotrophic Ammonia-Oxidizing Bacteria." Applied and Environmental Microbiology 67, no. 5 (May 1, 2001): 2213–21. http://dx.doi.org/10.1128/aem.67.5.2213-2221.2001.

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ABSTRACT The presence of a copper-containing dissimilatory nitrite reductase gene (nirK) was discovered in several isolates of β-subdivision ammonia-oxidizing bacteria using PCR and DNA sequencing. PCR primers Cunir3 and Cunir4 were designed based on published nirK sequences from denitrifying bacteria and used to amplify a 540-bp fragment of the nirK gene fromNitrosomonas marina and five additional isolates of ammonia-oxidizing bacteria. Amplification products of the expected size were cloned and sequenced. Alignment of the nucleic acid and deduced amino acid (AA) sequences shows significant similarity (62 to 75% DNA, 58 to 76% AA) between nitrite reductases present in these nitrifiers and the copper-containing nitrite reductase found in classic heterotrophic denitrifiers. While the presence of a nitrite reductase in Nitrosomonas europaea is known from early biochemical work, preliminary sequence data from its genome indicate a rather low similarity to the denitrifier nirKs. Phylogenetic analysis of the partial nitrifier nirK sequences indicates that the topology of the nirK tree corresponds to the 16S rRNA andamoA trees. While the role of nitrite reduction in the metabolism of nitrifying bacteria is still uncertain, these data show that the nirK gene is present in closely related nitrifying isolates from many oceanographic regions and suggest thatnirK sequences retrieved from the environment may include sequences from ammonia-oxidizing bacteria.

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40

Arceo, Alejandro, Héctor F. Flores, Lino G. Garza, Luis E. Garza, and Gerardo Romero. "On Robust Stability for Hurwitz Polynomials via Recurrence Relations and Linear Combinations of Orthogonal Polynomials." Complexity 2022 (March 2, 2022): 1–13. http://dx.doi.org/10.1155/2022/9404316.

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In this contribution, we use the connection between stable polynomials and orthogonal polynomials on the real line to construct sequences of Hurwitz polynomials that are robustly stable in terms of several uncertain parameters. These sequences are constructed by using properties of orthogonal polynomials, such as the well-known three-term recurrence relation, as well as by considering linear combinations of two orthogonal polynomials with consecutive degree. Some examples are presented.

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41

Saini, Kavita, and Kuldip Raj. "Applications of Statistical Convergence in Complex Uncertain Sequences via Deferred Riesz Mean." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 29, no. 03 (May 27, 2021): 337–51. http://dx.doi.org/10.1142/s021848852150015x.

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In this paper, we intend to make a new approach to introduce the concept of tn-statistical convergence of complex uncertain sequences like tn-statistical convergence almost surely (a.s.), tn-statistical convergence in measure, tn-statistical convergence in mean, tn-statistical convergence in distribution and tn-statistical convergence in uniformly almost surely (u.a.s). Various inclusion relations are established between newly formed sequence spaces.

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42

Zárate, Selene, Sergei L. Kosakovsky Pond, Paul Shapshak, and Simon D. W. Frost. "Comparative Study of Methods for Detecting Sequence Compartmentalization in Human Immunodeficiency Virus Type 1." Journal of Virology 81, no. 12 (April 11, 2007): 6643–51. http://dx.doi.org/10.1128/jvi.02268-06.

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ABSTRACT Human immunodeficiency virus (HIV) infects different organs and tissues. During these infection events, subpopulations of HIV type 1 (HIV-1) develop and, if viral trafficking is restricted between subpopulations, the viruses can follow independent evolutionary histories, i.e., become compartmentalized. This phenomenon is usually detected via comparative sequence analysis and has been reported for viruses isolated from the central nervous system (CNS) and the genital tract. Several approaches have been proposed to study the compartmentalization of HIV sequences, but to date, no rigorous comparison of the most commonly employed methods has been made. In this study, we systematically compared inferences made by six different methods for detecting compartmentalization based on three data sets: (i) a sample of 45 patients with sequences gathered from the CNS, (ii) sequences from the female genital tract of 18 patients, and (iii) a set of simulated sequences. We found that different methods often reached contradictory conclusions. Methods based on the topology of a phylogenetic tree derived from clonal sequences were generally more sensitive in detecting compartmentalization than those that relied solely upon pairwise genetic distances between sequences. However, as the branching structure in a phylogenetic tree is often uncertain, especially for short, low-diversity, or recombinant sequences, tree-based approaches may need to be modified to take phylogenetic uncertainty into account. Given the frequently discordant predictions of different methods and the strengths and weaknesses of each particular methodology, we recommend that a suite of several approaches be used for reliable inference of compartmentalized population structure.

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Tang, Yi-Wei, Joe T. J. Huong, Robert M. Lloyd, Paul Spearman, and David W. Haas. "Comparison of Human Immunodeficiency Virus Type 1 RNA Sequence Heterogeneity in Cerebrospinal Fluid and Plasma." Journal of Clinical Microbiology 38, no. 12 (2000): 4637–39. http://dx.doi.org/10.1128/jcm.38.12.4637-4639.2000.

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The source of human immunodeficiency virus type 1 (HIV-1) RNA in cerebrospinal fluid (CSF) during HIV-1 infection is uncertain. The sequence heterogeneity of HIV-1 RNA in simultaneous CSF and plasma samples was characterized for five patients at the baseline and during the first week of antiretroviral therapy by two commercial genotyping methodologies. In individual subjects, the sequences in CSF samples differed significantly from those in plasma. In contrast, the viral sequences in CSF at the baseline did not differ from the sequences in CSF during treatment. Similarly, viral sequences in plasma did not vary over this interval. This study provides evidence that HIV-1 RNA in CSF and plasma arise from distinct compartments.

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Vences, Miguel, Dominik Stützer, Noromalala Rasoamampionona Raminosoa, and Thomas Ziegler. "Towards a DNA barcode library for Madagascar’s threatened ichthyofauna." PLOS ONE 17, no. 8 (August 11, 2022): e0271400. http://dx.doi.org/10.1371/journal.pone.0271400.

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In order to improve the molecular resources available for conservation management of Madagascar’s threatened ichthyofauna, we elaborated a curated database of 2860 mitochondrial sequences of the mitochondrial COI, 16S and ND2 genes of Malagasy fishes, of which 1141 sequences of freshwater fishes were newly sequenced for this data set. The data set is mostly composed of COI (2015 sequences) while 16S and ND2 sequences from partly the same samples were used to match the COI sequences to reliably identified reference sequences of these genes. We observed COI uncorrected pairwise genetic distances of 5.2‒31.0% (mean 20.6%) among species belonging to different genera, and 0.0‒22.4% (mean 6.4%) for species belonging to the same genus. Deeply divergent mitochondrial lineages of uncertain attribution were found among Malagasy freshwater eleotrids and gobiids, confirming these groups are in need of taxonomic revision. DNA barcodes assigned to introduced cichlids (tilapias) included Coptodon rendallii, C. zillii, Oreochromis aureus (apparently a new country record), O. cf. mossambicus, O. niloticus, and one undetermined species of Oreochromis, with sequences of up to three species found per location. In aplocheiloid killifishes of the genus Pachypanchax, most species from northern Madagascar had only low mitochondrial divergences, three of these species (P. omalonotus, P. patriciae, and P. varatraza) were not reciprocally monophyletic, and one genetically deviant lineage was discovered in a northern locality, suggesting a need for partial taxonomic revision of this genus. While the lack of voucher specimens for most of the samples sequenced herein precludes final conclusions, our first step towards a DNA barcoding reference library of Madagascar’s fishes already demonstrates the value of such a data set for improved taxonomic inventory and conservation management. We strongly suggest further exploration of Madagascar’s aquatic environments, which should include detailed photographic documentation and tissue sampling of large numbers of specimens, and collection of preserved voucher specimens as well as of living fish for the buildup of ex situ assurance populations of threatened species complying with the One Plan Approach proposed by the IUCN SSC Conservation Breeding Specialist Group (CBSG).

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Tin, Truong Chi, Tran Ngoc Anh, Duong Van Hai, and Le Hoai Bac. "HUPSMT: AN EFFICIENT ALGORITHM FOR MINING HIGH UTILITY-PROBABILITY SEQUENCES IN UNCERTAIN DATABASES WITH MULTIPLE MINIMUM UTILITY THRESHOLDS." Journal of Computer Science and Cybernetics 35, no. 1 (March 18, 2019): 1–20. http://dx.doi.org/10.15625/1813-9663/35/1/13234.

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The problem of high utility sequence mining (HUSM) in quantitative se-quence databases (QSDBs) is more general than that of frequent sequence mining in se-quence databases. An important limitation of HUSM is that a user-predened minimum tility threshold is used commonly to decide if a sequence is high utility. However, this is not convincing in many real-life applications as sequences may have diferent importance. Another limitation of HUSM is that data in QSDBs are assumed to be precise. But in the real world, collected data such as by sensor maybe uncertain. Thus, this paper proposes a framework for mining high utility-probability sequences (HUPSs) in uncertain QSDBs (UQS-DBs) with multiple minimum utility thresholds using a minimum utility. Two new width and depth pruning strategies are also introduced to early eliminate low utility or low probability sequences as well as their extensions, and to reduce sets of candidate items for extensions during the mining process. Based on these strategies, a novel ecient algorithm named HUPSMT is designed for discovering HUPSs. Finally, an experimental study conducted in both real-life and synthetic UQSDBs shows the performance of HUPSMT in terms of time and memory consumption.

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HLAVÁČEK, IVAN. "RELIABLE SOLUTION OF A TORSION PROBLEM IN HENCKY PLASTICITY WITH UNCERTAIN YIELD FUNCTION." Mathematical Models and Methods in Applied Sciences 11, no. 05 (July 2001): 855–65. http://dx.doi.org/10.1142/s0218202501001148.

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The worst scenario method is applied to the torsion problem of a homogeneous orthotropic elasto-plastic bar with uncertain yield function. According to the Haar–Kármán principle, the problem leads to a minimization of the complementary energy over a convex set of admissible stresses. The latter set is determined by a yield function with uncertain coefficients. We formulate two maximization problems with respect to the set of admissible coefficients, prove the solvability of the corresponding continuous and approximate problems, and discuss the convergence of some sequences of finite-element approximations.

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Das, Birojit, Binod Chandra Tripathy, and Piyali Debnath. "Results on Matrix Transformation of Complex Uncertain Sequences via Convergence in Almost Surely." Methods of Functional Analysis and Topology 27, no. 4 (2021): 320–27. http://dx.doi.org/10.31392/mfat-npu26_4.2021.04.

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Iwaszczuk, D., L. Hoegner, M. Schmitt, and U. Stilla. "HIERARCHICAL MATCHING OF UNCERTAIN BUILDING MODELS WITH OBLIQUE VIEW AIRBORNE IR IMAGE SEQUENCES." ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences XXXIX-B6 (July 26, 2012): 117–22. http://dx.doi.org/10.5194/isprsarchives-xxxix-b6-117-2012.

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Jiang, Peng, Yi-Chung Hu, Wenbao Wang, Hang Jiang, and Geng Wu. "Interval Grey Prediction Models with Forecast Combination for Energy Demand Forecasting." Mathematics 8, no. 6 (June 11, 2020): 960. http://dx.doi.org/10.3390/math8060960.

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Time series data for decision problems such as energy demand forecasting are often derived from uncertain assessments, and do not meet any statistical assumptions. The interval grey number becomes an appropriate representation for an uncertain and imprecise observation. In order to obtain nonlinear interval grey numbers with better forecasting accuracy, this study proposes a combined model by fusing interval grey numbers estimated by neural networks (NNs) and the grey prediction models. The proposed model first uses interval regression analysis using NNs to estimate interval grey numbers for a real valued sequence; and then a grey residual modification model is constructed using the upper and lower wrapping sequences obtained by NNs. It turns out that two different kinds of interval grey numbers can be estimated by nonlinear interval regression analysis. Forecasting accuracy on real data sequences was then examined by the best non-fuzzy performance values of the combined model. The proposed combined model performed well compared with the other interval grey prediction models considered.

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Ma, Meiyi, John Stankovic, Ezio Bartocci, and Lu Feng. "Predictive Monitoring with Logic-Calibrated Uncertainty for Cyber-Physical Systems." ACM Transactions on Embedded Computing Systems 20, no. 5s (October 31, 2021): 1–25. http://dx.doi.org/10.1145/3477032.

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Predictive monitoring—making predictions about future states and monitoring if the predicted states satisfy requirements—offers a promising paradigm in supporting the decision making of Cyber-Physical Systems (CPS). Existing works of predictive monitoring mostly focus on monitoring individual predictions rather than sequential predictions. We develop a novel approach for monitoring sequential predictions generated from Bayesian Recurrent Neural Networks (RNNs) that can capture the inherent uncertainty in CPS, drawing on insights from our study of real-world CPS datasets. We propose a new logic named Signal Temporal Logic with Uncertainty (STL-U) to monitor a flowpipe containing an infinite set of uncertain sequences predicted by Bayesian RNNs. We define STL-U strong and weak satisfaction semantics based on whether all or some sequences contained in a flowpipe satisfy the requirement. We also develop methods to compute the range of confidence levels under which a flowpipe is guaranteed to strongly (weakly) satisfy an STL-U formula. Furthermore, we develop novel criteria that leverage STL-U monitoring results to calibrate the uncertainty estimation in Bayesian RNNs. Finally, we evaluate the proposed approach via experiments with real-world CPS datasets and a simulated smart city case study, which show very encouraging results of STL-U based predictive monitoring approach outperforming baselines.

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