Applications to probability theory: definitions of a random sequence

1993 ◽  
pp. 166-178
Author(s):  
Vladimir Uspensky ◽  
Alexei Semenov
Keyword(s):  
Probability Theory ◽  
Random Sequence

ON INEQUALITIES AND CRITICAL VALUES OF FUZZY RANDOM VARIABLES

2005 ◽  
Vol 13 (02) ◽  
pp. 163-175 ◽  
Author(s):  
LIXING YANG ◽  
BAODING LIU
Keyword(s):  
Probability Theory ◽  
Intelligent Systems ◽  
Random Sequence ◽  
Random Variables ◽  
Critical Values ◽  
Fuzzy Random Variables ◽  
Chance Measure ◽  
Mathematical Properties ◽  
Expected Value Operator ◽  
Fuzzy Random

It is well-known that Hölder, Minkowski, Markov, Chebyshev and Jensen's inequalities are important and useful results in probability theory. This paper proposes to extend the usefulness of the above inequalities to the context of uncertainty analysis in intelligent systems. In order to further discuss the mathematical properties of fuzzy random variables, the analogous inequalities for fuzzy random variables are first proved based on the chance measure and expected value operator. After that, monotonicity and continuity of critical values of fuzzy random variables are also investigated. Finally, a convergence theorem of critical values for fuzzy random sequence is obtained.

The d-Enantiomer Form of Indobufen Totally Accounts for the Anti-Cyclooxygenase and Antiplatelet Activity Ex Vivo and for the Increase in Bleeding Time by Indobufen in Man

1992 ◽  
Vol 67 (02) ◽  
pp. 258-263 ◽  
Author(s):  
Raffaele De Caterina ◽  
Rosa Sicari ◽  
An Yan ◽  
Walter Bernini ◽  
Daniela Giannessi ◽  
...  
Keyword(s):  
Arachidonic Acid ◽  
Platelet Aggregation ◽  
Plasma Levels ◽  
Bleeding Time ◽  
Ex Vivo ◽  
Random Sequence ◽  
Antiplatelet Agent ◽  
Antiplatelet Drug ◽  
Double Blind

SummaryIndobufen is an antiplatelet drug able to inhibit thromboxane production and cyclooxygenase-dependent platelet aggregation by a reversible inhibition of cyclooxygenase. Indobufen exists in two enantiomeric forms, of which only d-indobufen is active in vitro in inhibiting cyclooxygenase. In order to verify that also inhibition of platelet function is totally accounted for by d-indobufen, ten patients with proven coronary artery disease (8 male, 2 female, age, mean ± S.D., 58.7 ± 7.5 years) were given, in random sequence, both 100 mg d-indobufen and 200 mg dl-indobufen as single administrations in a double-blind crossover design study with a washout period between treatments of 72 h. In all patients thromboxane (TX) B2 generation after spontaneous clotting (at 0, 1, 2, 4, 6, 8, 12, 24 h), drug plasma levels (at the same times), platelet aggregation in response to ADP, adrenaline, arachidonic acid, collagen, PAF, and bleeding time (at 0, 2, 12 h) were evaluated after each treatment. Both treatments determined peak inhibition of TXB2 production at 2 h from administration, with no statistical difference between the two treatments (97 ±3% for both treatments). At 12 h inhibition was 87 ± 6% for d-indobufen and 88 ± 6% for dl-indobufen (p = NS). Inhibition of TXB2 production correlated significantly with plasma levels of the drugs. Maximum inhibitory effect on aggregation was seen in response to collagen 1.5 pg/ml (63 ± 44% for d-indobufen and 81 ± 22% for dl-indobufen) and arachidonic acid 0.5-2 mM (78 ± 34% for d-indobufen and 88 ± 24% for dl-indobufen) at 2 h after each administration. An effect of both treatments on platelet aggregation after 12 h was present only for adrenaline 2 μM (55 ± 41% for d-indobufen and 37 ± 54% for dl-indobufen), collagen 1.5 pg/ml (69 ± 30% for d-indobufen and 51 ± 61% for dl-indobufen), arachidonic acid 0.5-2 mM (56 ± 48% for d-indobufen and 35 ± 49% for dl-indobufen). The extent of inhibition of TX production and the extent of residual platelet aggregation were never significantly different between treatments. Bleeding time prolongation was similar in the two treatment groups without showing a pronounced and long lasting effect (from 7.0 ± 2.0 min to 10.0 ± 3.0 min at 2 h and 8.0 ± 2.0 min at 12 h for d-indobufen; from 6.0 ±1.0 min to 8.5 ± 2.0 min at 2 h and 8.0 ± 1.0 min at 12 h for dl-indobufen). These results demonstrate that the biological activity of dl-indobufen as an antiplatelet agent in vivo is totally accounted for by d-indobufen.

Validation of a monetary Taylor Aggression Paradigm: Associations with trait aggression and role of provocation sequence

2020 ◽  
Author(s):  
J Konzok ◽  
L Kreuzpointner ◽  
GI Henze ◽  
L Wagels ◽  
C Kärgel ◽  
...  
Keyword(s):  
Random Sequence ◽  
Reactive Aggression ◽  
Reaction Time Task ◽  
Competitive Reaction ◽  
Experimental Conditions ◽  
Fixed Sequence ◽  
Taylor Aggression Paradigm ◽  
Trait Aggression ◽  
Significant Difference ◽  
In Series

© 2020 Elsevier Inc. The Taylor Aggression Paradigm (TAP) is widely used to measure reactive aggression in laboratory settings. While modified versions (mTAPs) with various stimulus characteristics (shocks, noise, pressure, heat) have already been established, a modified version with monetary stimuli has only been introduced very recently. In this experiment, 209 young healthy participants (104 males, 105 females) completed a mock Competitive Reaction Time Task (CRTT) with a fictional opponent with preprogrammed 40 win and 60 lose trials. In lose trials, participants were provoked by subtracting a low (0–20 euro cents), medium (30–60 cents) or high (70–90 cents) amount of money from their fictitious account. Provocation stimuli were either presented randomly or in a fixed sequence (experimental conditions). In contrast to a random sequence, the fixed sequence was generated by repeating trials from the same provocation category in series of three. Linear mixed models (LMMs) considering aggression trajectories revealed significant effects of provocation (low, medium, high) and trait aggression (K-FAF) on reactive aggression. Men showed significantly higher reactive aggression levels than women. In regard to provocation sequence, we found no significant difference in reactive aggression between the random vs. fixed stimulus sequences. The findings provide new evidence supporting the view that the monetary mTAP is able to induce as well as capture reactive aggression in the laboratory. Additionally, we found no advantage of a fixed sequence as the level of reactive aggression in a given trial appeared to be mainly predicted by the preceding provocation trial.

Modeling a random sequence of extremes of loads for fatigue tests under irregular loading

2020 ◽  
pp. 13-19
Author(s):  
N.A. Mahutov ◽  
I.V. Gadolina ◽  
S.G. Lebedinskiy ◽  
E.S. Oganyan ◽  
A.A. Bautin
Keyword(s):  
Random Sequence ◽  
Fatigue Tests ◽  
Linear Hypothesis ◽  
Resource Estimation ◽  
Transition Matrices ◽  
Random Loading ◽  
Markov Transition ◽  
Random Nature ◽  
Irregular Loading ◽  
Markov Transition Matrices

Methods and approaches to tests under random loading are considered, their role is characterized. To ensure the random nature of loading, a modeling method based on Markov transition matrices and real processes recorded in operation is proposed. Keywords: random loading process, Markov repetition matrices, resource estimation, corrected linear hypothesis, parameter of completeness of the loading spectrum. [email protected]

Probability Theory for Fuzzy Quantum Spaces with Statistical Applications

2017 ◽  
Author(s):  
Renáta Bartková ◽  
Beloslav Riečan ◽  
Anna Tirpáková
Keyword(s):  
Probability Theory ◽  
Fuzzy Sets ◽  
Ergodic Theorem ◽  
Intuitionistic Fuzzy Sets ◽  
Mathematics Students ◽  
Intuitionistic Fuzzy ◽  
Individual Ergodic Theorem ◽  
Recurrence Theorem ◽  
The Individual ◽  
Atanassov Intuitionistic Fuzzy Sets

The reference considers probability theory in two main domains: fuzzy set theory, and quantum models. Readers will learn about the Kolmogorov probability theory and its implications in these two areas. Other topics covered include intuitionistic fuzzy sets (IF-set) limit theorems, individual ergodic theorem and relevant statistical applications (examples from correlation theory and factor analysis in Atanassov intuitionistic fuzzy sets systems, the individual ergodic theorem and the Poincaré recurrence theorem). This book is a useful resource for mathematics students and researchers seeking information about fuzzy sets in quantum spaces.

Arguments from Providence and from Miracles

2018 ◽  
Author(s):  
Timothy McGrew
Keyword(s):  
Probability Theory ◽  
20Th Century ◽  
Probabilistic Analysis ◽  
Interdisciplinary Collaboration ◽  
Formal Analysis ◽  
Empirical Science ◽  
The Subject

The mid-20th century consensus regarding Hume’s critique of reported miracles has broken down dramatically in recent years thanks to the application of probabilistic analysis to the issue and the rediscovery of its history. Progress from this point forward is likely to be made along one or more of three fronts. There is wide room for interdisciplinary collaboration, work that will bring together scholars with expertise in religion, psychology, philosophy, and empirical science. There is a great deal of work still to be done in formal analysis, making use of the tools of modern probability theory to model questions about testimony and inference. And the recovery and study of earlier works on the subject—works that should never have been forgotten—can significantly enrich our understanding of the underlying issues.

The Non-Causal Character of Renormalization Group Explanations

2018 ◽  
Author(s):  
Margaret Morrison
Keyword(s):  
Probability Theory ◽  
Renormalization Group ◽  
Dynamical Systems ◽  
Recent Literature ◽  
Mathematical Explanation ◽  
Causal Status ◽  
Physical Information ◽  
The Relationship ◽  
Structural Aspects

After reviewing some of the recent literature on non-causal and mathematical explanation, this chapter develops an argument as to why renormalization group (RG) methods should be seen as providing non-causal, yet physical, information about certain kinds of systems/phenomena. The argument centres on the structural character of RG explanations and the relationship between RG and probability theory. These features are crucial for the claim that the non-causal status of RG explanations involves something different from simply ignoring or “averaging over” microphysical details—the kind of explanations common to statistical mechanics. The chapter concludes with a discussion of the role of RG in treating dynamical systems and how that role exemplifies the structural aspects of RG explanations which in turn exemplifies the non-causal features.

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