Continuous majorisation and randomness

1984 ◽  
Vol 21 (4) ◽  
pp. 924-929 ◽  
Author(s):  
Raymond J. Hickey
Keyword(s):  
Continuous Case ◽  
Continuous Distributions ◽  
Parameter Values

Majorisation is used to compare continuous distributions in terms of randomness. General results on randomness in the continuous case are given and these are used to investigate the connection between randomness and parameter values in some well-known families of distributions including the normal and gamma.

Continuous majorisation and randomness

1984 ◽  
Vol 21 (04) ◽  
pp. 924-929 ◽  
Author(s):  
Raymond J. Hickey
Keyword(s):  
Continuous Case ◽  
Continuous Distributions ◽  
Parameter Values

Majorisation is used to compare continuous distributions in terms of randomness. General results on randomness in the continuous case are given and these are used to investigate the connection between randomness and parameter values in some well-known families of distributions including the normal and gamma.

scholarly journals A Note on Ordering Probability Distributions by Skewness

Symmetry ◽  
2018 ◽  
Vol 10 (7) ◽  
pp. 286
Author(s):  
V. García ◽  
M. Martel-Escobar ◽  
F. Vázquez-Polo
Keyword(s):  
Data Analysis ◽  
Probability Distributions ◽  
Continuous Distributions ◽  
Parameter Values

This paper describes a complementary tool for fitting probabilistic distributions in data analysis. First, we examine the well known bivariate index of skewness and the aggregate skewness function, and then introduce orderings of the skewness of probability distributions. Using an example, we highlight the advantages of this approach and then present results for these orderings in common uniparametric families of continuous distributions, showing that the orderings are well suited to the intuitive conception of skewness and, moreover, that the skewness can be controlled via the parameter values.

scholarly journals Continualization of Probabilistic Programs With Correction

2020 ◽  
pp. 366-393 ◽  
Author(s):  
Jacob Laurel ◽  
Sasa Misailovic
Keyword(s):  
Parameter Estimation ◽  
Real World ◽  
Stochastic Models ◽  
Original Model ◽  
Continuous Approximation ◽  
Continuous Distributions ◽  
True Parameter ◽  
Inference Algorithms ◽  
Parameter Values ◽  
Probabilistic Programs

AbstractProbabilistic Programming offers a concise way to represent stochastic models and perform automated statistical inference. However, many real-world models have discrete or hybrid discrete-continuous distributions, for which existing tools may suffer non-trivial limitations. Inference and parameter estimation can be exceedingly slow for these models because many inference algorithms compute results faster (or exclusively) when the distributions being inferred are continuous. To address this discrepancy, this paper presents Leios. Leios is the first approach for systematically approximating arbitrary probabilistic programs that have discrete, or hybrid discrete-continuous random variables. The approximate programs have all their variables fully continualized. We show that once we have the fully continuous approximate program, we can perform inference and parameter estimation faster by exploiting the existing support that many languages offer for continuous distributions. Furthermore, we show that the estimates obtained when performing inference and parameter estimation on the continuous approximation are still comparably close to both the true parameter values and the estimates obtained when performing inference on the original model.

Analysis of Myocardial Time-Activity Curves of 123l-Heptadecanoic Acid II. The Acquisition Time

1987 ◽  
Vol 26 (06) ◽  
pp. 248-252 ◽  
Author(s):  
M. J. van Eenige ◽  
F. C. Visser ◽  
A. J. P. Karreman ◽  
C. M. B. Duwel ◽  
G. Westera ◽  
...  
Keyword(s):  
Standard Deviation ◽  
Acquisition Time ◽  
Half Time ◽  
Constant Ratio ◽  
Time Activity ◽  
Time Activity Curve ◽  
Time Value ◽  
Activity Curve ◽  
Low Amplitude ◽  
Parameter Values

Optimal fitting of a myocardial time-activity curve is accomplished with a monoexponential plus a constant, resulting in three parameters: amplitude and half-time of the monoexponential and the constant. The aim of this study was to estimate the precision of the calculated parameters. The variability of the parameter values as a function of the acquisition time was studied in 11 patients with cardiac complaints. Of the three parameters the half-time value varied most strongly with the acquisition time. An acquisition time of 80 min was needed to keep the standard deviation of the half-time value within ±10%. To estimate the standard deviation of the half-time value as a function of the parameter values, of the noise content of the time-activity curve and of the acquisition time, a model experiment was used. In most cases the SD decreased by 50% if the acquisition time was increased from 60 to 90 min. A low amplitude/constant ratio and a high half-time value result in a high SD of the half-time value. Tables are presented to estimate the SD in a particular case.

Stable and Supported Semantics in Continuous Vector Spaces

2020 ◽  
Author(s):  
Yaniv Aspis ◽  
Krysia Broda ◽  
Alessandra Russo ◽  
Jorge Lobo
Keyword(s):  
Logic Program ◽  
Matrix Multiplication ◽  
Vector Spaces ◽  
Continuous Space ◽  
Continuous Vector ◽  
Novel Approach ◽  
Gradient Based ◽  
Normal Logic ◽  
Parameter Values ◽  
Normal Logic Program

We introduce a novel approach for the computation of stable and supported models of normal logic programs in continuous vector spaces by a gradient-based search method. Specifically, the application of the immediate consequence operator of a program reduct can be computed in a vector space. To do this, Herbrand interpretations of a propositional program are embedded as 0-1 vectors in $\mathbb{R}^N$ and program reducts are represented as matrices in $\mathbb{R}^{N \times N}$. Using these representations we prove that the underlying semantics of a normal logic program is captured through matrix multiplication and a differentiable operation. As supported and stable models of a normal logic program can now be seen as fixed points in a continuous space, non-monotonic deduction can be performed using an optimisation process such as Newton's method. We report the results of several experiments using synthetically generated programs that demonstrate the feasibility of the approach and highlight how different parameter values can affect the behaviour of the system.

Heterotrophic Kinetic Parameter Estimation for Enhanced Biological Phosphorus Removal Processes Operated in Conventional and Membrane-Assisted Modes

2006 ◽  
Vol 41 (1) ◽  
pp. 72-83 ◽  
Author(s):  
Zhe Zhang ◽  
Eric R. Hall
Keyword(s):  
Parameter Estimation ◽  
Phosphorus Removal ◽  
Growth Yield ◽  
Pilot Scale ◽  
Enhanced Biological Phosphorus Removal ◽  
Biological Phosphorus Removal ◽  
Nitrogen And Phosphorus ◽  
Parameter Values ◽  
The Impact ◽  
Biological Phosphorus

Abstract Parameter estimation and wastewater characterization are crucial for modelling of the membrane enhanced biological phosphorus removal (MEBPR) process. Prior to determining the values of a subset of kinetic and stoichiometric parameters used in ASM No. 2 (ASM2), the carbon, nitrogen and phosphorus fractions of influent wastewater at the University of British Columbia (UBC) pilot plant were characterized. It was found that the UBC wastewater contained fractions of volatile acids (SA), readily fermentable biodegradable COD (SF) and slowly biodegradable COD (XS) that fell within the ASM2 default value ranges. The contents of soluble inert COD (SI) and particulate inert COD (XI) were somewhat higher than ASM2 default values. Mixed liquor samples from pilot-scale MEBPR and conventional enhanced biological phosphorus removal (CEBPR) processes operated under parallel conditions, were then analyzed experimentally to assess the impact of operation in a membrane-assisted mode on the growth yield (YH), decay coefficient (bH) and maximum specific growth rate of heterotrophic biomass (µH). The resulting values for YH, bH and µH were slightly lower for the MEBPR train than for the CEBPR train, but the differences were not statistically significant. It is suggested that MEBPR simulation using ASM2 could be accomplished satisfactorily using parameter values determined for a conventional biological phosphorus removal process, if MEBPR parameter values are not available.

Modelling of Nitrification at the Mogden Treatment Works

1989 ◽  
Vol 21 (4-5) ◽  
pp. 305-314
Author(s):  
J. P. Lumbers ◽  
S. C. Cook ◽  
G. A. Thomas
Keyword(s):  
Sensitivity Analysis ◽  
Monte Carlo Simulation ◽  
River Basin Management ◽  
Independent Data ◽  
Activated Sludge Process ◽  
Basin Management ◽  
Alternative Control ◽  
Control Actions ◽  
Parameter Values ◽  
Generalised Sensitivity Analysis

An application of a dynamic model of the activated sludge process is described within the context of real-time river basin management. The model has been calibrated and validated on independent data and then applied to investigate losses of nitrification at the Mogden Works. Monte Carlo simulation and generalised sensitivity analysis were found to be effective ways of identifying appropriate parameter values and their importance. The prediction of unmeasured states such as the autotroph population enabled the effects of alternative control actions to be better understood and the most suitable measures found.

Oscillatory Dynamics of P53 Network With Time Delays

2018 ◽  
Vol 21 (6) ◽  
pp. 411-419 ◽  
Author(s):  
Conghua Wang ◽  
Fang Yan ◽  
Yuan Zhang ◽  
Haihong Liu ◽  
Linghai Zhang
Keyword(s):  
Hopf Bifurcation ◽  
Cell Fate ◽  
Time Delays ◽  
Sustained Oscillation ◽  
Multiple Time ◽  
Cell Fate Decisions ◽  
Oscillatory Dynamics ◽  
Main Components ◽  
Parameter Values ◽  
P53 Network

Aims and Objective: A large number of experimental evidences report that the oscillatory dynamics of p53 would regulate the cell fate decisions. Moreover, multiple time delays are ubiquitous in gene expression which have been demonstrated to lead to important consequences on dynamics of genetic networks. Although delay-driven sustained oscillation in p53-based networks is commonplace, the precise roles of such delays during the processes are not completely known. Method: Herein, an integrated model with five basic components and two time delays for the network is developed. Using such time delays as the bifurcation parameter, the existence of Hopf bifurcation is given by analyzing the relevant characteristic equations. Moreover, the effects of such time delays are studied and the expression levels of the main components of the system are compared when taking different parameters and time delays. Result and Conclusion: The above theoretical results indicated that the transcriptional and translational delays can induce oscillation by undergoing a super-critical Hopf bifurcation. More interestingly, the length of these delays can control the amplitude and period of the oscillation. Furthermore, a certain range of model parameter values is essential for oscillation. Finally, we illustrated the main results in detail through numerical simulations.

Recent Patents on Nanoporous Filtration Membranes with Complex Pores

2020 ◽  
Vol 14 (2) ◽  
pp. 229-233
Author(s):  
Yongbin Zhang
Keyword(s):  
Geometrical Parameter ◽  
Filtration Membranes ◽  
Analytical Results ◽  
Parameter Values ◽  
Mechanical Strengths ◽  
Better Than

Background:: The challenges to nanoporous filtration membranes are small fluxes and low membrane mechanical strengths. Objective:: To introduce newly invented nanoporous filtration membranes with complex pores, improved fluxes and mechanical strengths as registered in patents. Methods:: The analytical results are presented for the addressed membranes. Results:: The geometrical parameter values of the addressed membranes can be optimized for the highest fluxes. Conclusion:: The overall performances of nanoporous filtration membranes with complex cylindrical or/and conical pores can be significantly better than that of the conventional nanoporous filtration membranes with single cylindrical or conical pores.

Sampling Theory

2019 ◽  
Author(s):  
David Hankin ◽  
Michael S. Mohr ◽  
Kenneth B. Newman
Keyword(s):  
Natural Resource ◽  
Adaptive Sampling ◽  
Sampling Theory ◽  
Special Importance ◽  
Unequal Probability ◽  
Multi Stage ◽  
R Programming ◽  
Multi Phase ◽  
Systematic Cluster ◽  
Parameter Values

We present a rigorous but understandable introduction to the field of sampling theory for ecologists and natural resource scientists. Sampling theory concerns itself with development of procedures for random selection of a subset of units, a sample, from a larger finite population, and with how to best use sample data to make scientifically and statistically sound inferences about the population as a whole. The inferences fall into two broad categories: (a) estimation of simple descriptive population parameters, such as means, totals, or proportions, for variables of interest, and (b) estimation of uncertainty associated with estimated parameter values. Although the targets of estimation are few and simple, estimates of means, totals, or proportions see important and often controversial uses in management of natural resources and in fundamental ecological research, but few ecologists or natural resource scientists have formal training in sampling theory. We emphasize the classical design-based approach to sampling in which variable values associated with units are regarded as fixed and uncertainty of estimation arises via various randomization strategies that may be used to select samples. In addition to covering standard topics such as simple random, systematic, cluster, unequal probability (stressing the generality of Horvitz–Thompson estimation), multi-stage, and multi-phase sampling, we also consider adaptive sampling, spatially balanced sampling, and sampling through time, three areas of special importance for ecologists and natural resource scientists. The text is directed to undergraduate seniors, graduate students, and practicing professionals. Problems emphasize application of the theory and R programming in ecological and natural resource settings.

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