Increment definitions for scale-dependent analysis of stochastic data Article Swipe
Matthias Waechter
,
Alexei Kouzmitchev
,
Joachim Peinke
·
YOU?
·
· 2004
· Open Access
·
· DOI: https://doi.org/10.1103/physreve.70.055103
YOU?
·
· 2004
· Open Access
·
· DOI: https://doi.org/10.1103/physreve.70.055103
It is common for scale-dependent analysis of stochastic data to use the increment Delta(t,r) =xi(t+r)-xi(t) of a data set xi(t) as a stochastic measure, where r denotes the scale. For joint statistics of Delta(t,r) and Delta(t, r') the question of how to nest the increments on different scales r, r' is investigated. Here we show that in some cases spurious correlations between scales can be introduced by the common left-justified definition. The consequences for a Markov process are discussed. These spurious correlations can be avoided by an appropriate nesting of increments. We demonstrate this effect for different data sets and show how it can be detected and quantified. The problem allows to propose a unique method to distinguish between experimental data generated by a noiselike or a Langevin-like random-walk process, respectively.
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- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.1103/physreve.70.055103
- OA Status
- green
- Cited By
- 13
- References
- 12
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W2009159891
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- OpenAlex ID
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https://openalex.org/W2009159891Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.1103/physreve.70.055103Digital Object Identifier
- Title
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Increment definitions for scale-dependent analysis of stochastic dataWork title
- Type
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articleOpenAlex work type
- Language
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enPrimary language
- Publication year
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2004Year of publication
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2004-11-16Full publication date if available
- Authors
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Matthias Waechter, Alexei Kouzmitchev, Joachim PeinkeList of authors in order
- Landing page
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https://doi.org/10.1103/physreve.70.055103Publisher landing page
- Open access
-
YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
-
https://arxiv.org/pdf/physics/0404021Direct OA link when available
- Concepts
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Spurious relationship, Scale (ratio), Mathematics, Statistical physics, Data set, Measure (data warehouse), Stochastic process, Set (abstract data type), Markov chain, Statistics, Combinatorics, Computer science, Physics, Data mining, Quantum mechanics, Programming languageTop concepts (fields/topics) attached by OpenAlex
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13Total citation count in OpenAlex
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2019: 2, 2018: 1, 2015: 1Per-year citation counts (last 5 years)
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12Number of works referenced by this work
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10Other works algorithmically related by OpenAlex
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| abstract_inverted_index.or | 125 |
| abstract_inverted_index.r' | 49 |
| abstract_inverted_index.r, | 48 |
| abstract_inverted_index.to | 9, 41, 111, 116 |
| abstract_inverted_index.we | 53 |
| abstract_inverted_index.For | 29 |
| abstract_inverted_index.The | 71, 108 |
| abstract_inverted_index.and | 34, 99, 106 |
| abstract_inverted_index.are | 77 |
| abstract_inverted_index.can | 63, 82, 103 |
| abstract_inverted_index.for | 3, 73, 95 |
| abstract_inverted_index.how | 40, 101 |
| abstract_inverted_index.r') | 36 |
| abstract_inverted_index.set | 18 |
| abstract_inverted_index.the | 11, 27, 37, 43, 67 |
| abstract_inverted_index.use | 10 |
| abstract_inverted_index.Here | 52 |
| abstract_inverted_index.data | 8, 17, 97, 120 |
| abstract_inverted_index.nest | 42 |
| abstract_inverted_index.sets | 98 |
| abstract_inverted_index.show | 54, 100 |
| abstract_inverted_index.some | 57 |
| abstract_inverted_index.that | 55 |
| abstract_inverted_index.this | 93 |
| abstract_inverted_index.These | 79 |
| abstract_inverted_index.cases | 58 |
| abstract_inverted_index.joint | 30 |
| abstract_inverted_index.where | 24 |
| abstract_inverted_index.xi(t) | 19 |
| abstract_inverted_index.Markov | 75 |
| abstract_inverted_index.allows | 110 |
| abstract_inverted_index.common | 2, 68 |
| abstract_inverted_index.effect | 94 |
| abstract_inverted_index.method | 115 |
| abstract_inverted_index.scale. | 28 |
| abstract_inverted_index.scales | 47, 62 |
| abstract_inverted_index.unique | 114 |
| abstract_inverted_index.avoided | 84 |
| abstract_inverted_index.between | 61, 118 |
| abstract_inverted_index.denotes | 26 |
| abstract_inverted_index.nesting | 88 |
| abstract_inverted_index.problem | 109 |
| abstract_inverted_index.process | 76 |
| abstract_inverted_index.propose | 112 |
| abstract_inverted_index.Delta(t, | 35 |
| abstract_inverted_index.analysis | 5 |
| abstract_inverted_index.detected | 105 |
| abstract_inverted_index.measure, | 23 |
| abstract_inverted_index.process, | 129 |
| abstract_inverted_index.question | 38 |
| abstract_inverted_index.spurious | 59, 80 |
| abstract_inverted_index.different | 46, 96 |
| abstract_inverted_index.generated | 121 |
| abstract_inverted_index.increment | 12 |
| abstract_inverted_index.noiselike | 124 |
| abstract_inverted_index.Delta(t,r) | 13, 33 |
| abstract_inverted_index.discussed. | 78 |
| abstract_inverted_index.increments | 44 |
| abstract_inverted_index.introduced | 65 |
| abstract_inverted_index.statistics | 31 |
| abstract_inverted_index.stochastic | 7, 22 |
| abstract_inverted_index.appropriate | 87 |
| abstract_inverted_index.definition. | 70 |
| abstract_inverted_index.demonstrate | 92 |
| abstract_inverted_index.distinguish | 117 |
| abstract_inverted_index.increments. | 90 |
| abstract_inverted_index.quantified. | 107 |
| abstract_inverted_index.random-walk | 128 |
| abstract_inverted_index.consequences | 72 |
| abstract_inverted_index.correlations | 60, 81 |
| abstract_inverted_index.experimental | 119 |
| abstract_inverted_index.Langevin-like | 127 |
| abstract_inverted_index.investigated. | 51 |
| abstract_inverted_index.respectively. | 130 |
| abstract_inverted_index.=xi(t+r)-xi(t) | 14 |
| abstract_inverted_index.left-justified | 69 |
| abstract_inverted_index.scale-dependent | 4 |
| cited_by_percentile_year.max | 96 |
| cited_by_percentile_year.min | 89 |
| countries_distinct_count | 1 |
| institutions_distinct_count | 3 |
| citation_normalized_percentile.value | 0.76192408 |
| citation_normalized_percentile.is_in_top_1_percent | False |
| citation_normalized_percentile.is_in_top_10_percent | False |