scholarly journals Efficient Simulation for the Maximum of Infinite Horizon Discrete-Time Gaussian Processes

2011 ◽  
Vol 48 (02) ◽  
pp. 467-489
Author(s):  
Jose Blanchet ◽  
Chenxin Li
Keyword(s):  
Relative Error ◽  
Numerical Experiments ◽  
Infinite Horizon ◽  
Sampling Procedure ◽  
Remarkable Feature ◽  
Efficient Simulation ◽  
Bounded Number ◽  
Great Generality ◽  
High Level ◽  
Positive Integers

We consider the problem of estimating the probability that the maximum of a Gaussian process with negative mean and indexed by positive integers reaches a high level, sayb. In great generality such a probability converges to 0 exponentially fast in a power ofb. Under mild assumptions on the marginal distributions of the process and no assumption on the correlation structure, we develop an importance sampling procedure, called the target bridge sampler (TBS), which takes a polynomial (inb) number of function evaluations to achieve a small relative error. The procedure also yields samples of the underlying process conditioned on hittingbin finite time. In addition, we apply our method to the problem of estimating the tail of the maximum of a superposition of a large number,n, of independent Gaussian sources. In this situation TBS achieves a prescribed relative error with a bounded number of function evaluations asn↗ ∞. A remarkable feature of TBS is that it isnotbased on exponential changes of measure. Our numerical experiments validate the performance indicated by our theoretical findings.

scholarly journals Efficient Simulation for the Maximum of Infinite Horizon Discrete-Time Gaussian Processes

2011 ◽  
Vol 48 (2) ◽  
pp. 467-489 ◽  
Author(s):  
Jose Blanchet ◽  
Chenxin Li
Keyword(s):  
Relative Error ◽  
Numerical Experiments ◽  
Infinite Horizon ◽  
Sampling Procedure ◽  
Remarkable Feature ◽  
Efficient Simulation ◽  
Bounded Number ◽  
Great Generality ◽  
High Level ◽  
Positive Integers

We consider the problem of estimating the probability that the maximum of a Gaussian process with negative mean and indexed by positive integers reaches a high level, sayb. In great generality such a probability converges to 0 exponentially fast in a power ofb. Under mild assumptions on the marginal distributions of the process and no assumption on the correlation structure, we develop an importance sampling procedure, called the target bridge sampler (TBS), which takes a polynomial (inb) number of function evaluations to achieve a small relative error. The procedure also yields samples of the underlying process conditioned on hittingbin finite time. In addition, we apply our method to the problem of estimating the tail of the maximum of a superposition of a large number,n, of independent Gaussian sources. In this situation TBS achieves a prescribed relative error with a bounded number of function evaluations asn↗ ∞. A remarkable feature of TBS is that it isnotbased on exponential changes of measure. Our numerical experiments validate the performance indicated by our theoretical findings.

scholarly journals Adoption of Rice Post-Harvest Technologies Among Smallholder Farmers in Osun State, Nigeria

2020 ◽  
Vol 69 (1-2) ◽  
pp. 20-26
Author(s):  
Banji Olalere Adisa ◽  
Michael Famakinwa ◽  
Kolawole Adelekan Adeloye
Keyword(s):  
Smallholder Farmers ◽  
Structured Interview ◽  
Sampling Procedure ◽  
Moderate Level ◽  
Chi Square ◽  
Post Harvest ◽  
Rice Milling ◽  
Multistage Sampling ◽  
The Right ◽  
High Level

SummaryThe study assessed adoption of rice post-harvest technologies among smallholder farmers in Osun State, Nigeria. Data were collected from 120 respondents through a structured interview schedule using a multistage sampling procedure. Percentages, means, Chi-square and correlation were used to analyse the data and draw inferences. The results show that about 52.5% of the respondents had favourable perception, while 47.5% had unfavourable perception towards adoption of the rice post-harvest technologies. Rice milling (mean=4.54) and harvesting matured panicles at the right time (mean=4.47) ranked highest among the adopted post-harvest technologies, while majority (65%) of the respondents adopted the rice post-harvest technologies at moderate level and 35% had high level of adoption. Inadequate capital (mean=1.75) and poor extension contacts (mean=1.67) were the major constraints associated with the adoption. Also, there was significant association between sex (χ2= 38.174), marital status (χ2=32.85) and adoption of the rice post-harvest technologies, while age (r=-0.531), household size (r=0.414) and the quantity of rice produced (r=0.345) had significant relationship with adoption of the post-harvest rice technologies. There was moderate level of adoption among the farmers. Financial institutions, governments and non-governmental organisations should provide functional credit facilities and government should employ more extension agents to promote adoption of high-quality enhancing post-harvest technologies for sustainable rice production in Nigeria.

PC-Based Computer Modeling of Combustion Processes

1999 ◽  
Author(s):  
Greg W. Gmurczyk ◽  
Ashwani K. Gupta
Keyword(s):  
Numerical Simulations ◽  
Computer Modeling ◽  
Numerical Experiments ◽  
Laboratory Experiments ◽  
Combustion Process ◽  
Numerical Algorithms ◽  
Computer Hardware ◽  
Simplifying Assumptions ◽  
High Level ◽  
Analytical Approaches

Abstract Constant and significant progress in both computer hardware and numerical algorithms, in recent years, have made it possible to investigate complex phenomena in engineering systems using computer modeling and simulations. Advanced numerical simulations can be treated as an extension of traditional analytical-theoretical analyses. In such cases, some of the simplifying assumptions can usually be dropped and the nonlinear interactions between various processes can be captured. One of the most complex engineering processes encountered in industry is a combustion process utilized either for power/thrust generation or incineration. However, even nowadays, because of the high level of complexity of the general problem of a combustion process in practical systems, it is not currently possible to simulate directly all the length and time scales of interest. Simplifying assumptions still need to be made, but they can be less drastic than in analytical approaches. Therefore, another view of numerical simulations is as a tool to simulate idealized systems and conduct numerical experiments. Such numerical experiments can be complementary to laboratory experiments and can also provide more detailed, nonintrusive diagnostics. Therefore, simulations, along with theory and laboratory experiments, can provide a more complete picture and better understanding of a combustion process. As an example of computer modeling of industrial combustion systems, an enclosed spray flame was considered. Such a flame can frequently be encountered in power generation units, turbine engines, and incinerators. Both the physical and mathematical models were formulated based on data from earlier laboratory studies and results obtained for open air spray flames. The purpose of this study was to use those data as model input to predict the characteristics of a confined flame and provide a means of optimizing the system design with a PC computer.

A Novel Neural Model with Lateral Interaction for Learning Tasks

2020 ◽  
pp. 1-24
Author(s):  
Dequan Jin ◽  
Ziyan Qin ◽  
Murong Yang ◽  
Penghe Chen
Keyword(s):  
Numerical Experiments ◽  
State Of The Art ◽  
Neural Model ◽  
Parameter Tuning ◽  
Small Sample ◽  
Lateral Interaction ◽  
Learning Tasks ◽  
Proposed Model ◽  
High Level ◽  
Elementary Field

We propose a novel neural model with lateral interaction for learning tasks. The model consists of two functional fields: an elementary field to extract features and a high-level field to store and recognize patterns. Each field is composed of some neurons with lateral interaction, and the neurons in different fields are connected by the rules of synaptic plasticity. The model is established on the current research of cognition and neuroscience, making it more transparent and biologically explainable. Our proposed model is applied to data classification and clustering. The corresponding algorithms share similar processes without requiring any parameter tuning and optimization processes. Numerical experiments validate that the proposed model is feasible in different learning tasks and superior to some state-of-the-art methods, especially in small sample learning, one-shot learning, and clustering.

scholarly journals Optimized Polynomial Virtual Fields Method for Constitutive Parameters Identification of Orthotropic Bimaterials

2020 ◽  
Vol 2020 ◽  
pp. 1-27
Author(s):  
Xueyi Ma ◽  
Yu Wang ◽  
Jian Zhao
Keyword(s):  
Relative Error ◽  
Numerical Experiments ◽  
A Priori ◽  
Heterogeneous Materials ◽  
Image Correlation ◽  
Constitutive Parameter ◽  
Virtual Fields Method ◽  
Bending Load ◽  
Virtual Field ◽  
Constitutive Parameters

Heterogeneous materials are widely applied in many fields. Owing to the spatial variation of its constitutive parameters, the mechanical characterization of heterogeneous materials is very important. The virtual fields method has been used to identify the constitutive parameters of materials. However, there is a limitation: constitutive parameters of one material have to be a priori; then, constitutive parameters of the other one can be identified. Aiming at this limitation, this article presents a method to identify the constitutive parameters of heterogeneous orthotropic bimaterials under the condition that constitutive parameters of both materials are all unknown from a single test. A constitutive parameter identification method of orthotropic bimaterials based on optimized virtual field and digital image correlation is proposed. The feasibility of this method is verified by simulating the deformation fields of a two-layer material under three-point bending load. The results of numerical experiments with FEM simulations show that the weighted relative error of the constitutive parameter is less than 1%. The results suggest that the variation coefficient-to-noise ratio can perform a priori evaluation of a confidence interval on the identified stiffness components. The results of numerical experiments with DIC simulations show that the weighted relative error is 1.44%, which is due to the noise in the strain data calculated by DIC method.

SUBSIDIARY HOMOCLINIC ORBITS TO A SADDLE-FOCUS FOR REVERSIBLE SYSTEMS

1994 ◽  
Vol 04 (06) ◽  
pp. 1447-1482 ◽  
Author(s):  
A.R. CHAMPNEYS
Keyword(s):  
Homoclinic Orbit ◽  
Water Waves ◽  
Numerical Experiments ◽  
Homoclinic Orbits ◽  
Reversible Systems ◽  
Reversible System ◽  
Type Analysis ◽  
Reversible Transformation ◽  
Positive Integers ◽  
Good Agreement

A dynamical system is said to be reversible if there is an involution of phase space that reverses the direction of the flow. Examples are classical Hamiltonian systems with quadratic kinetic energy. For reversible systems, homoclinic orbits that are invariant under the reversible transformation typically persist as parameters are varied. This paper concerns reversible systems for which a primary homoclinic orbit to a saddle-focus is assumed to exist. The problem under investigation is a characterisation of the subsidiary homoclinic orbits which then exist in a neighbourhood of the primary one. Such orbits have applications as solitary water waves and as buckling solutions of nonlinear struts. A Shil’nikov-type analysis is performed for four-dimensional linearly reversible systems. It is shown that each subsidiary homoclinic orbit can be labelled by a symmetric string of positive integers. All possible strings of length one, two or three correspond to the existence of a homoclinic orbit, whereas only certain of those of length four or greater do. This situation contrasts with known results if the reversible system is also Hamiltonian. The analysis is supported by performing careful numerical experiments on the equation [Formula: see text] where P and α are parameters; a good agreement with the theory is found.

scholarly journals NUMERICAL EXPERIMENTS WITH AN ALGORITHM FOR PROCESSING EXPERIMENTAL DATA TO DETERMINE THE PARAMETERS OF A RHEOLOGICAL MODEL OF A LIQUID WITH THE EFFECT OF «SOLIDIFICATION»

2021 ◽  
pp. 206-211
Author(s):  
В.Н. Колодежнов ◽  
А.В. Колтаков ◽  
С.С. Капранчиков ◽  
А.С. Веретенников
Keyword(s):  
Experimental Data ◽  
Polyethylene Glycol ◽  
Calcium Carbonate ◽  
Relative Error ◽  
Rheological Model ◽  
Numerical Experiments ◽  
Maximum Error ◽  
Viscoplastic Fluid ◽  
Maximum Relative Error ◽  
Hardening Effect

Предложена методика обработки экспериментальных данных и алгоритм для ее реализации по определению параметров реологической модели вязкопластической жидкости, которая демонстрирует проявление эффекта «отвердевания». С целью проверки работоспособности алгоритма проведены численные эксперименты с наборами генерируемых случайным образом “псевдоэкспериментальных” данных с заранее заданной величиной максимальной относительной погрешности. Проведен анализ влияния максимальной относительной погрешности исходных “псевдоэкспериментальных” данных на величину относительной погрешности определяемых в ходе численных экспериментов параметров реологической модели. По итогам проведенных экспериментов показано, что относительная погрешность определения параметров реологической модели соизмерима с максимальной погрешностью генерируемых “псевдоэкспериментальных” данных. Рассмотрен пример обработки экспериментальных данных для суспензии частиц карбоната кальция на основе полиэтиленгликоля. A technique for processing experimental data and an algorithm for its implementation to determine the parameters of a rheological model of a viscoplastic fluid, which demonstrates the manifestation of the "hardening" effect, are proposed. In order to test the algorithm's operability, numerical experiments were carried out with sets of randomly generated "pseudo-experimental" data with a predetermined maximum relative error. The analysis of the influence of the maximum relative error of the initial “pseudo-experimental” data on the value of the relative error of the parameters of the rheological model determined during numerical experiments was carried out. Based on the results of the conducted experiments, it is shown that the relative error in determining the parameters of the rheological model is commensurate with the maximum error of the generated “pseudo-experimental” data. An example of processing experimental data for a suspension of calcium carbonate particles based on polyethylene glycol is considered.

scholarly journals Assessment of Income Inequality, Structure and Conduct of Cocoa Marketers in Osun State, Nigeria

2020 ◽  
pp. 1-12
Author(s):  
A. I. Olutumise ◽  
L. O. Oparinde ◽  
O. O. Simon-Oke
Keyword(s):  
Income Inequality ◽  
Gini Coefficient ◽  
Concentration Ratio ◽  
Sampling Procedure ◽  
Labour Cost ◽  
Least Square ◽  
Primary Data ◽  
Herfindahl Index ◽  
Access To Credit ◽  
High Level

The level of income inequality and structure-conduct of cocoa marketers were evaluated in Osun State, Nigeria. Primary data were collected with the aid of a well-structured questionnaire, while a multistage sampling procedure was used to select 120 respondents for the study. Descriptive statistics, concentration ratio, Gini coefficient, index of dissimilarity, Herfindahl index; Ordinary Least Square (OLS) as well as Quantile Regression (QR) were used as analytical tools. The result showed the value of Gini coefficient as 0.76, which established a relatively high level of income inequality among cocoa marketers in the study area. The concentration ratio of one, two and four largest marketers in the cocoa marketing business also accounted for 19.2%, 31.9% and 45.8% respectively, of the total volume of cocoa beans sold in the study area, while the value (0.069) of the Herfindahl index further confirmed the presence of low concentration in the market share of cocoa marketers in the study area. The OLS result revealed that household size, education, access to credit, depreciation cost on fixed inputs and labour cost constituted the main factors affecting the income of the marketers, while depreciation cost on fixed inputs and labour cost were consistently significant in OLS and across the conditional quantiles (q25, q50 and q75). Therefore, it is expected that appropriate practical approach in addressing high level of income inequality as identified by the study should be taken by all stakeholders in the industry, with a view to making low-interest credit facilities and incentives available to the marketers in order to increase their scale of operations, and consequently bridge the inequality gap.

scholarly journals Comparative Analysis of the Level of Engagement in Palm Oil Processing Among Rural Households in Southeast Nigeria

2021 ◽  
Vol 25 (3) ◽  
pp. 26-35
Author(s):  
Samson Ejike Onu ◽  
Kenneth C. Ekwe ◽  
Gideon Chinedu Onuekwusi
Keyword(s):  
Oil Palm ◽  
Rural Households ◽  
Modern Method ◽  
Sampling Procedure ◽  
Gear Up ◽  
Anova Model ◽  
Multi Stage ◽  
Significant Difference ◽  
Basic Infrastructure ◽  
High Level

The study provided empirical evidence of rural household’s engagement in processing of oil palm produce in South east Nigeria. The study specifically identified the methods of processing oil palm produce, ascertained the level of household’s engagement in oil palm processing, identified the constraints to oil palm processing in the study area. Multi-stage random sampling procedure in selecting 540 respondents. Data for the study were collected with the use of structured questionnaire and analyzed with the use of both descriptive (frequency, percentage and mean) and inferential statistics (ANOVA model). The results showed that 58.1% of the respondents used semi-modern/mechanized in processing of oil palm produce. There was high level of engagement in the processing of oil palm produce (pooled grand mean = 3.67). The result revealed that lack of modern processing equipment (86.5%), instability of government policy (80.0%) and high cost of labour (76.7%) were the major constraints to engagement in oil palm processing. There was a statistically significant difference in the level of engagement of rural households in processing of oil palm produce across the states in South East Nigeria at 5% level of probability. The study concluded that most of the processors used a combination of both traditional and modern method in the processing of their oil palm produce and were highly engaged in the processing of oil palm produce as a profitable livelihood activity. The study therefore recommended that State and Federal Government should gear up efforts in providing basic infrastructure such as electricity and good, motorable roads in the study area so that the efficiency of processing of oil palm products can be guaranteed.

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