Deviations from Michaelis–Menten kinetics. Computation of the probabilities of obtaining complex curves from simple kinetic schemes

1. It is possible to calculate the intrinsic probability associated with any curve shape that is allowed for rational functions of given degree when the coefficients are independent or dependent random variables with known probability distributions. 2. Computations of such probabilities are described when the coefficients of the rational function are generated according to several probability distribution functions and in particular when rate constants are varied randomly for several simple model mechanisms. 3. It is concluded that each molecular mechanism is associated with a specific set of curve-shape probabilities, and this could be of value in discriminating between model mechanisms. 4. It is shown how a computer program can be used to estimate the probability of new complexities such as extra inflexions and turning points as the degree of rate equations increases. 5. The probability of 3 : 3 rate equations giving 2 : 2 curve shapes is discussed for unrestricted coefficients and also for the substrate-modifier mechanisms. 6. The probability associated with the numerical values of coefficients in rate equations is also calculated for this mechanism, and a possible method for determining the approximate magnitude of product-release steps is given. 7. The computer programs used in the computations have been deposited as Supplement SUP 50113 (21 pages) with the British Library Lending Division, Boston Spa, Wetherby, West Yorkshire LS23 7BQ, U.K., from whom copies can be obtained on the terms indicated in Biochem, J. (1978) 169, 5.

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Parameterization of multifractal cascade models based on their breakdown coefficients

10.5194/egusphere-egu2020-593 ◽

2020 ◽

Author(s):

César Aguilar Flores ◽

Alin Andrei Carsteanu

Keyword(s):

Time Series ◽

Probability Distribution ◽

Rainfall Intensity ◽

Probability Distributions ◽

Asymptotic Properties ◽

Distribution Functions ◽

Marginal Probability ◽

Probability Distribution Functions ◽

Marginal Probability Distribution ◽

Cascade Models

<p>Breakdown coefficients of multifractal cascades have been shown, in various contexts, to be ergodic in their (marginal) probability distribution functions, however the necessary connection between the cascading process (or a tracer thereof, such as rainfall) and the breakdown coefficients of the measure generated by the cascade, was missing. This work presents a method of parameterization of certain types of multiplicative cascades, using the breakdown coefficients of the measures they generate. The method is based on asymptotic properties of the probability distributions of the breakdown coefficients in &#8220;dressed&#8221; cascades, as compared with the respective distributions of the cascading weights. An application to rainfall intensity time series is presented.</p>

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FORMULA OF INVERSION FOR RATIONAL CHARACTERISTIC FUNCTIONS OF PROBABILITY DISTRIBUTIONS

VESTNIK OF ASTRAKHAN STATE TECHNICAL UNIVERSITY ◽

10.24143/1812-9498-2018-2-7-22 ◽

2018 ◽

pp. 7-22

Author(s):

Georgiy Aleksandrovich Popov

Keyword(s):

Distribution Function ◽

Probability Distributions ◽

Rational Functions ◽

Distribution Functions ◽

Characteristic Functions ◽

Arbitrary Distribution ◽

Abscissa Axis ◽

Entire Axis ◽

Inversion Formulas ◽

Gamma Distributions

The paper deals with the problem of clarifying the well-known inversion formulas for distribution functions, usually describing the increment of these functions. The validity of the corresponding inversion formulas for the distribution function π and their densities has been proved for the particular case of distributions with rational characteristic functions. The obtained formulas for distribution functions, which include additionally constant terms equal to 0.5, were not previously known. Functions of positively distributed random variables and quantities distributed over the entire axis have been considered separately. To test the hypothesis of fairness of the obtained treatment formula, including a previously unknown term equal to 0.5, in the general case there have been given examples of calculating distribution functions, whose characteristic functions are not considered as rational functions: for constant and uniform laws. The verification confirmed the objectiveness of the formulated hypothesis about the obtained validity of the inversion form for arbitrary distribution functions. It has also been shown that any distribution function and any density can be represented as a limit of a mixture of gamma distributions (distribution functions and densities), having shifts along the abscissa axis and, possibly, with altered signs of the arguments. The obtained result proves that the set of gamma distributions with shifted arguments is uniformly dense in the set of all distributions.

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PROBABILITY DISTRIBUTION FUNCTIONS APPLIED IN THE WATER REQUIREMENT ESTIMATES IN IRRIGATION PROJECTS

Revista Caatinga ◽

10.1590/1983-21252019v32n119rc ◽

2019 ◽

Vol 32 (1) ◽

pp. 189-199

Author(s):

Rafael Dreux Miranda Fernandes ◽

Jefferson vieira José ◽

Wagner Wolff ◽

Jéfferson de oliveira Costa ◽

Marcos Vinícius Folegatti

Keyword(s):

Probability Distribution ◽

Probability Distributions ◽

Distribution Functions ◽

Spatial And Temporal Variability ◽

Irrigation Systems ◽

Probability Distribution Functions ◽

Irrigation Projects ◽

Irrigated Area ◽

Production Knowledge ◽

Sustainable Irrigation

ABSTRACT Spain contains a third the entire irrigated area of Europe, accounting for 15% of the cultivated area of the country and almost 60% of the national agricultural production. Knowledge of the spatial and temporal variability of reference evapotranspiration (ETo) and the probabilistic theory of extreme events is crucial for the elaboration of sustainable irrigation projects. The objective of this work was to define the frequency distribution that best describes ETo for the design of irrigation systems in the region of Andalusia. We used ETo data for the period 2001 to 2015 from 56 meteorological stations. The values were accumulated over three consecutive days. For all accumulated periods, nine probability distributions were adjusted. The probability distribution that best described ETo for the design of irrigation systems in the region was the Gumbel II distribution. The maximum daily ETo to be considered in irrigation projects in this region is, on average, 10 mm. The accumulated ETo for periods of 5, 10, and 30 days that should be considered are, on average, 42 mm, 78, mm and 224 mm, respectively.

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Probability distribution functions for short-term daily nitrous oxide fluxes in a prairie pothole agricultural landscape in western Canada

Canadian Journal of Soil Science ◽

10.4141/cjss10070 ◽

2011 ◽

Vol 91 (2) ◽

pp. 303-307 ◽

Cited By ~ 2

Author(s):

Alan Moulin ◽

Mario Tenuta ◽

David Lobb ◽

Adedeji Dunmola ◽

Priyantha Yapa

Keyword(s):

Nitrous Oxide ◽

Probability Distribution ◽

Agricultural Landscape ◽

Probability Distributions ◽

Distribution Functions ◽

Western Canada ◽

Prairie Pothole ◽

Short Term ◽

Probability Distribution Functions ◽

Temporal And Spatial Variability

Moulin, A., Tenuta, M., Lobb, D., Dunmola, A. and Yapa, P. 2011. Probability distribution functions for short-term daily nitrous oxide fluxes in a prairie pothole agricultural landscape in western Canada. Can. J. Soil Sci. 91: 303–307. Probability distributions of N2O fluxes are often non-normal due to large temporal and spatial variability of environmental factors. The most common approaches to statistical analyses of these fluxes in the scientific literature are to transform data with a log function, or conduct non-parametric tests. Analysis of N2O flux data for 128 sites within a 16-ha field, taken on 20 dates in 2005 and 2006 near Brandon, Manitoba, show that the Johnson Su and generalized log probability distributions provided the best fit for the majority of sample dates. The results of this research indicate that statistical analysis of N2O fluxes with the Johnson Su probability function should be considered as an alternative to the lognormal function.

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Extended two-dimensional belief function based on divergence measurement

Journal of Intelligent & Fuzzy Systems ◽

10.3233/jifs-201727 ◽

2020 ◽

pp. 1-8

Author(s):

Jianping Fan ◽

Jing Wang ◽

Meiqin Wu

Keyword(s):

Belief Function ◽

Distribution Functions ◽

Divergence Measure ◽

Uncertain Information ◽

Belief Functions ◽

Two Dimensional ◽

Probability Distribution Functions ◽

Basic Probability ◽

The Difference ◽

Supporting Degree

The two-dimensional belief function (TDBF = (mA, mB)) uses a pair of ordered basic probability distribution functions to describe and process uncertain information. Among them, mB includes support degree, non-support degree and reliability unmeasured degree of mA. So it is more abundant and reasonable than the traditional discount coefficient and expresses the evaluation value of experts. However, only considering that the expert’s assessment is single and one-sided, we also need to consider the influence between the belief function itself. The difference in belief function can measure the difference between two belief functions, based on which the supporting degree, non-supporting degree and unmeasured degree of reliability of the evidence are calculated. Based on the divergence measure of belief function, this paper proposes an extended two-dimensional belief function, which can solve some evidence conflict problems and is more objective and better solve a class of problems that TDBF cannot handle. Finally, numerical examples illustrate its effectiveness and rationality.

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Verb valency in interlanguage: An extension to valency theory and new perspective on L2 learning

Poznan Studies in Contemporary Linguistics ◽

10.1515/psicl-2020-0010 ◽

2020 ◽

Vol 56 (2) ◽

pp. 339-363

Author(s):

Qianying Zhao ◽

Jingyang Jiang

Keyword(s):

Probability Distributions ◽

Specific Property ◽

Distribution Functions ◽

Target Language ◽

Native Languages ◽

Language Competence ◽

English Writing ◽

Chinese Learners ◽

L2 Learning ◽

New Perspective

AbstractValency theory has been applied to investigate various languages, such as German, Chinese and English. However, most studies in this field were based on the linguistic materials produced by native speakers. The current research aimed to examine the valency structures in the interlanguage. Based on the English writing produced by L2 Chinese learners, we adopted the quantitative approach, trying to find out whether the distributional features of verb valency in the interlanguage also had regular probability distributions as those in the native languages, and whether there was a relationship between these valency distributional characteristics and L2 learners’ language competence. It was found that (1) verb valency in the interlanguage followed distributional regularities which had been identified in the native languages; (2) the valency features showed differences in the diversity of valency patterns, the use of valences and the complexity of forms of complements between the interlanguage and the target language; (3) the distribution functions and parameters related to verb valency could manifest the development of students’ language competence. The current research has extended valency theory to the study of interlanguage and the valency perspective has profound methodological and pedagogical implications for L2 learning. Its item-specific property and the integration of grammatical and lexical factors are conducive to analyzing the way various words combine with each other.

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Development and Evaluation of a Fluctuating Plume Model for Odor Impact Assessment

Applied Sciences ◽

10.3390/app11083310 ◽

2021 ◽

Vol 11 (8) ◽

pp. 3310

Author(s):

Marzio Invernizzi ◽

Federica Capra ◽

Roberto Sozzi ◽

Laura Capelli ◽

Selena Sironi

Keyword(s):

Experimental Data ◽

Distribution Functions ◽

Plume Model ◽

Probability Distribution Functions ◽

Weibull Pdf ◽

Fluctuating Plume ◽

Concentration Statistics ◽

Modified Weibull ◽

Instantaneous Concentration ◽

Mean Concentration

For environmental odor nuisance, it is extremely important to identify the instantaneous concentration statistics. In this work, a Fluctuating Plume Model for different statistical moments is proposed. It provides data in terms of mean concentrations, variance, and intensity of concentration. The 90th percentile peak-to-mean factor, R90, was tested here by comparing it with the experimental results (Uttenweiler field experiment), considering different Probability Distribution Functions (PDFs): Gamma and the Modified Weibull. Seventy-two percent of the simulated mean concentration values fell within a factor 2 compared to the experimental ones: the model was judged acceptable. Both the modelled results for standard deviation, σC, and concentration intensity, Ic, overestimate the experimental data. This evidence can be due to the non-ideality of the measurement system. The propagation of those errors to the estimation of R90 is complex, but the ranges covered are quite repeatable: the obtained values are 1–3 for the Gamma, 1.5–4 for Modified Weibull PDF, and experimental ones from 1.4 to 3.6.

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