Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 3470

Search results for: interpolation of random variable

3470 Estimation of Probabilistic Fatigue Crack Propagation Models of AZ31 Magnesium Alloys under Various Load Ratio Conditions by Using the Interpolation of a Random Variable

Authors: Seon Soon Choi

Abstract:

The essential purpose is to present the good fatigue crack propagation model describing a stochastic fatigue crack growth behavior in a rolled magnesium alloy, AZ31, under various load ratio conditions. Fatigue crack propagation experiments were carried out in laboratory air under four conditions of load ratio, R, using AZ31 to investigate the crack growth behavior. The stochastic fatigue crack growth behavior was analyzed using an interpolation of random variable, Z, introduced to an empirical fatigue crack propagation model. The empirical fatigue models used in this study are Paris-Erdogan model, Walker model, Forman model, and modified Forman model. It was found that the random variable is useful in describing the stochastic fatigue crack growth behaviors under various load ratio conditions. The good probabilistic model describing a stochastic fatigue crack growth behavior under various load ratio conditions was also proposed.

Keywords: magnesium alloys, fatigue crack propagation model, load ratio, interpolation of random variable

Procedia PDF Downloads 331
3469 Overview of Adaptive Spline interpolation

Authors: Rongli Gai, Zhiyuan Chang

Abstract:

At this stage, in view of various situations in the interpolation process, most researchers use self-adaptation to adjust the interpolation process, which is also one of the current and future research hotspots in the field of CNC machining. In the interpolation process, according to the overview of the spline curve interpolation algorithm, the adaptive analysis is carried out from the factors affecting the interpolation process. The adaptive operation is reflected in various aspects, such as speed, parameters, errors, nodes, feed rates, random Period, sensitive point, step size, curvature, adaptive segmentation, adaptive optimization, etc. This paper will analyze and summarize the research of adaptive imputation in the direction of the above factors affecting imputation.

Keywords: adaptive algorithm, CNC machining, interpolation constraints, spline curve interpolation

Procedia PDF Downloads 60
3468 Node Insertion in Coalescence Hidden-Variable Fractal Interpolation Surface

Authors: Srijanani Anurag Prasad

Abstract:

The Coalescence Hidden-variable Fractal Interpolation Surface (CHFIS) was built by combining interpolation data from the Iterated Function System (IFS). The interpolation data in a CHFIS comprises a row and/or column of uncertain values when a single point is entered. Alternatively, a row and/or column of additional points are placed in the given interpolation data to demonstrate the node added CHFIS. There are three techniques for inserting new points that correspond to the row and/or column of nodes inserted, and each method is further classified into four types based on the values of the inserted nodes. As a result, numerous forms of node insertion can be found in a CHFIS.

Keywords: fractal, interpolation, iterated function system, coalescence, node insertion, knot insertion

Procedia PDF Downloads 32
3467 The Implementation of Secton Method for Finding the Root of Interpolation Function

Authors: Nur Rokhman

Abstract:

A mathematical function gives relationship between the variables composing the function. Interpolation can be viewed as a process of finding mathematical function which goes through some specified points. There are many interpolation methods, namely: Lagrange method, Newton method, Spline method etc. For some specific condition, such as, big amount of interpolation points, the interpolation function can not be written explicitly. This such function consist of computational steps. The solution of equations involving the interpolation function is a problem of solution of non linear equation. Newton method will not work on the interpolation function, for the derivative of the interpolation function cannot be written explicitly. This paper shows the use of Secton method to determine the numerical solution of the function involving the interpolation function. The experiment shows the fact that Secton method works better than Newton method in finding the root of Lagrange interpolation function.

Keywords: Secton method, interpolation, non linear function, numerical solution

Procedia PDF Downloads 283
3466 On Hankel Matrices Approach to Interpolation Problem in Infinite and Finite Fields

Authors: Ivan Baravy

Abstract:

Interpolation problem, as it was initially posed in terms of polynomials, is well researched. However, further mathematical developments extended it significantly. Trigonometric interpolation is widely used in Fourier analysis, while its generalized representation as exponential interpolation is applicable to such problem of mathematical physics as modelling of Ziegler-Biersack-Littmark repulsive interatomic potentials. Formulated for finite fields, this problem arises in decoding Reed--Solomon codes. This paper shows the relation between different interpretations of the problem through the class of matrices of special structure - Hankel matrices.

Keywords: Berlekamp-Massey algorithm, exponential interpolation, finite fields, Hankel matrices, Hankel polynomials

Procedia PDF Downloads 420
3465 Evaluation of Spatial Distribution Prediction for Site-Scale Soil Contaminants Based on Partition Interpolation

Authors: Pengwei Qiao, Sucai Yang, Wenxia Wei

Abstract:

Soil pollution has become an important issue in China. Accurate spatial distribution prediction of pollutants with interpolation methods is the basis for soil remediation in the site. However, a relatively strong variability of pollutants would decrease the prediction accuracy. Theoretically, partition interpolation can result in accurate prediction results. In order to verify the applicability of partition interpolation for a site, benzo (b) fluoranthene (BbF) in four soil layers was adopted as the research object in this paper. IDW (inverse distance weighting)-, RBF (radial basis function)-and OK (ordinary kriging)-based partition interpolation accuracies were evaluated, and their influential factors were analyzed; then, the uncertainty and applicability of partition interpolation were determined. Three conclusions were drawn. (1) The prediction error of partitioned interpolation decreased by 70% compared to unpartitioned interpolation. (2) Partition interpolation reduced the impact of high CV (coefficient of variation) and high concentration value on the prediction accuracy. (3) The prediction accuracy of IDW-based partition interpolation was higher than that of RBF- and OK-based partition interpolation, and it was suitable for the identification of highly polluted areas at a contaminated site. These results provide a useful method to obtain relatively accurate spatial distribution information of pollutants and to identify highly polluted areas, which is important for soil pollution remediation in the site.

Keywords: accuracy, applicability, partition interpolation, site, soil pollution, uncertainty

Procedia PDF Downloads 59
3464 Pattern Recognition Search: An Advancement Over Interpolation Search

Authors: Shahpar Yilmaz, Yasir Nadeem, Syed A. Mehdi

Abstract:

Searching for a record in a dataset is always a frequent task for any data structure-related application. Hence, a fast and efficient algorithm for the approach has its importance in yielding the quickest results and enhancing the overall productivity of the company. Interpolation search is one such technique used to search through a sorted set of elements. This paper proposes a new algorithm, an advancement over interpolation search for the application of search over a sorted array. Pattern Recognition Search or PR Search (PRS), like interpolation search, is a pattern-based divide and conquer algorithm whose objective is to reduce the sample size in order to quicken the process and it does so by treating the array as a perfect arithmetic progression series and thereby deducing the key element’s position. We look to highlight some of the key drawbacks of interpolation search, which are accounted for in the Pattern Recognition Search.

Keywords: array, complexity, index, sorting, space, time

Procedia PDF Downloads 76
3463 Effect of Correlation of Random Variables on Structural Reliability Index

Authors: Agnieszka Dudzik

Abstract:

The problem of correlation between random variables in the structural reliability analysis has been extensively discussed in literature on the subject. The cases taken under consideration were usually related to correlation between random variables from one side of ultimate limit state: correlation between particular loads applied on structure or correlation between resistance of particular members of a structure as a system. It has been proved that positive correlation between these random variables reduces the reliability of structure and increases the probability of failure. In the paper, the problem of correlation between random variables from both side of the limit state equation will be taken under consideration. The simplest case where these random variables are of the normal distributions will be concerned. The case when a degree of that correlation is described by the covariance or the coefficient of correlation will be used. Special attention will be paid on questions: how much that correlation changes the reliability level and can it be ignored. In reliability analysis will be used well-known methods for assessment of the failure probability: based on the Hasofer-Lind reliability index and Monte Carlo method adapted to the problem of correlation. The main purpose of this work will be a presentation how correlation of random variables influence on reliability index of steel bar structures. Structural design parameters will be defined as deterministic values and random variables. The latter will be correlated. The criterion of structural failure will be expressed by limit functions related to the ultimate and serviceability limit state. In the description of random variables will be used only for the normal distribution. Sensitivity of reliability index to the random variables will be defined. If the reliability index sensitivity due to the random variable X will be low when compared with other variables, it can be stated that the impact of this variable on failure probability is small. Therefore, in successive computations, it can be treated as a deterministic parameter. Sensitivity analysis leads to simplify the description of the mathematical model, determine the new limit functions and values of the Hasofer-Lind reliability index. In the examples, the NUMPRESS software will be used in the reliability analysis.

Keywords: correlation of random variables, reliability index, sensitivity of reliability index, steel structure

Procedia PDF Downloads 160
3462 Sub-Pixel Mapping Based on New Mixed Interpolation

Authors: Zeyu Zhou, Xiaojun Bi

Abstract:

Due to the limited environmental parameters and the limited resolution of the sensor, the universal existence of the mixed pixels in the process of remote sensing images restricts the spatial resolution of the remote sensing images. Sub-pixel mapping technology can effectively improve the spatial resolution. As the bilinear interpolation algorithm inevitably produces the edge blur effect, which leads to the inaccurate sub-pixel mapping results. In order to avoid the edge blur effect that affects the sub-pixel mapping results in the interpolation process, this paper presents a new edge-directed interpolation algorithm which uses the covariance adaptive interpolation algorithm on the edge of the low-resolution image and uses bilinear interpolation algorithm in the low-resolution image smooth area. By using the edge-directed interpolation algorithm, the super-resolution of the image with low resolution is obtained, and we get the percentage of each sub-pixel under a certain type of high-resolution image. Then we rely on the probability value as a soft attribute estimate and carry out sub-pixel scale under the ‘hard classification’. Finally, we get the result of sub-pixel mapping. Through the experiment, we compare the algorithm and the bilinear algorithm given in this paper to the results of the sub-pixel mapping method. It is found that the sub-pixel mapping method based on the edge-directed interpolation algorithm has better edge effect and higher mapping accuracy. The results of the paper meet our original intention of the question. At the same time, the method does not require iterative computation and training of samples, making it easier to implement.

Keywords: remote sensing images, sub-pixel mapping, bilinear interpolation, edge-directed interpolation

Procedia PDF Downloads 156
3461 Blind Data Hiding Technique Using Interpolation of Subsampled Images

Authors: Singara Singh Kasana, Pankaj Garg

Abstract:

In this paper, a blind data hiding technique based on interpolation of sub sampled versions of a cover image is proposed. Sub sampled image is taken as a reference image and an interpolated image is generated from this reference image. Then difference between original cover image and interpolated image is used to embed secret data. Comparisons with the existing interpolation based techniques show that proposed technique provides higher embedding capacity and better visual quality marked images. Moreover, the performance of the proposed technique is more stable for different images.

Keywords: interpolation, image subsampling, PSNR, SIM

Procedia PDF Downloads 425
3460 Estimation of Population Mean under Random Non-Response in Two-Phase Successive Sampling

Authors: M. Khalid, G. N. Singh

Abstract:

In this paper, we have considered the problem of estimation for population mean, on current (second) occasion in the presence of random non response in two-occasion successive sampling under two phase set-up. Modified exponential type estimators have been proposed, and their properties are studied under the assumptions that numbers of sampling units follow a distribution due to random non response situations. The performances of the proposed estimators are compared with linear combinations of two estimators, (a) sample mean estimator for fresh sample and (b) ratio estimator for matched sample under the complete response situations. Results are demonstrated through empirical studies which present the effectiveness of the proposed estimators. Suitable recommendations have been made to the survey practitioners.

Keywords: successive sampling, random non-response, auxiliary variable, bias, mean square error

Procedia PDF Downloads 337
3459 New Concept for Real Time Selective Harmonics Elimination Based on Lagrange Interpolation Polynomials

Authors: B. Makhlouf, O. Bouchhida, M. Nibouche, K. Laidi

Abstract:

A variety of methods for selective harmonics elimination pulse width modulation have been developed, the most frequently used for real-time implementation based on look-up tables method. To address real-time requirements based in modified carrier signal is proposed in the presented work, with a general formulation to real-time harmonics control/elimination in switched inverters. Firstly, the proposed method has been demonstrated for a single value of the modulation index. However, in reality, this parameter is variable as a consequence of the voltage (amplitude) variability. In this context, a simple interpolation method for calculating the modified sine carrier signal is proposed. The method allows a continuous adjustment in both amplitude and frequency of the fundamental. To assess the performance of the proposed method, software simulations and hardware experiments have been carried out in the case of a single-phase inverter. Obtained results are very satisfactory.

Keywords: harmonic elimination, Particle Swarm Optimisation (PSO), polynomial interpolation, pulse width modulation, real-time harmonics control, voltage inverter

Procedia PDF Downloads 429
3458 Assessing Effects of an Intervention on Bottle-Weaning and Reducing Daily Milk Intake from Bottles in Toddlers Using Two-Part Random Effects Models

Authors: Yungtai Lo

Abstract:

Two-part random effects models have been used to fit semi-continuous longitudinal data where the response variable has a point mass at 0 and a continuous right-skewed distribution for positive values. We review methods proposed in the literature for analyzing data with excess zeros. A two-part logit-log-normal random effects model, a two-part logit-truncated normal random effects model, a two-part logit-gamma random effects model, and a two-part logit-skew normal random effects model were used to examine effects of a bottle-weaning intervention on reducing bottle use and daily milk intake from bottles in toddlers aged 11 to 13 months in a randomized controlled trial. We show in all four two-part models that the intervention promoted bottle-weaning and reduced daily milk intake from bottles in toddlers drinking from a bottle. We also show that there are no differences in model fit using either the logit link function or the probit link function for modeling the probability of bottle-weaning in all four models. Furthermore, prediction accuracy of the logit or probit link function is not sensitive to the distribution assumption on daily milk intake from bottles in toddlers not off bottles.

Keywords: two-part model, semi-continuous variable, truncated normal, gamma regression, skew normal, Pearson residual, receiver operating characteristic curve

Procedia PDF Downloads 273
3457 Estimation of Population Mean under Random Non-Response in Two-Occasion Successive Sampling

Authors: M. Khalid, G. N. Singh

Abstract:

In this paper, we have considered the problems of estimation for the population mean on current (second) occasion in two-occasion successive sampling under random non-response situations. Some modified exponential type estimators have been proposed and their properties are studied under the assumptions that the number of sampling unit follows a discrete distribution due to random non-response situations. The performances of the proposed estimators are compared with linear combinations of two estimators, (a) sample mean estimator for fresh sample and (b) ratio estimator for matched sample under the complete response situations. Results are demonstrated through empirical studies which present the effectiveness of the proposed estimators. Suitable recommendations have been made to the survey practitioners.

Keywords: modified exponential estimator, successive sampling, random non-response, auxiliary variable, bias, mean square error

Procedia PDF Downloads 271
3456 Geo-Additive Modeling of Family Size in Nigeria

Authors: Oluwayemisi O. Alaba, John O. Olaomi

Abstract:

The 2013 Nigerian Demographic Health Survey (NDHS) data was used to investigate the determinants of family size in Nigeria using the geo-additive model. The fixed effect of categorical covariates were modelled using the diffuse prior, P-spline with second-order random walk for the nonlinear effect of continuous variable, spatial effects followed Markov random field priors while the exchangeable normal priors were used for the random effects of the community and household. The Negative Binomial distribution was used to handle overdispersion of the dependent variable. Inference was fully Bayesian approach. Results showed a declining effect of secondary and higher education of mother, Yoruba tribe, Christianity, family planning, mother giving birth by caesarean section and having a partner who has secondary education on family size. Big family size is positively associated with age at first birth, number of daughters in a household, being gainfully employed, married and living with partner, community and household effects.

Keywords: Bayesian analysis, family size, geo-additive model, negative binomial

Procedia PDF Downloads 465
3455 Comparison of Data Reduction Algorithms for Image-Based Point Cloud Derived Digital Terrain Models

Authors: M. Uysal, M. Yilmaz, I. Tiryakioğlu

Abstract:

Digital Terrain Model (DTM) is a digital numerical representation of the Earth's surface. DTMs have been applied to a diverse field of tasks, such as urban planning, military, glacier mapping, disaster management. In the expression of the Earth' surface as a mathematical model, an infinite number of point measurements are needed. Because of the impossibility of this case, the points at regular intervals are measured to characterize the Earth's surface and DTM of the Earth is generated. Hitherto, the classical measurement techniques and photogrammetry method have widespread use in the construction of DTM. At present, RADAR, LiDAR, and stereo satellite images are also used for the construction of DTM. In recent years, especially because of its superiorities, Airborne Light Detection and Ranging (LiDAR) has an increased use in DTM applications. A 3D point cloud is created with LiDAR technology by obtaining numerous point data. However recently, by the development in image mapping methods, the use of unmanned aerial vehicles (UAV) for photogrammetric data acquisition has increased DTM generation from image-based point cloud. The accuracy of the DTM depends on various factors such as data collection method, the distribution of elevation points, the point density, properties of the surface and interpolation methods. In this study, the random data reduction method is compared for DTMs generated from image based point cloud data. The original image based point cloud data set (100%) is reduced to a series of subsets by using random algorithm, representing the 75, 50, 25 and 5% of the original image based point cloud data set. Over the ANS campus of Afyon Kocatepe University as the test area, DTM constructed from the original image based point cloud data set is compared with DTMs interpolated from reduced data sets by Kriging interpolation method. The results show that the random data reduction method can be used to reduce the image based point cloud datasets to 50% density level while still maintaining the quality of DTM.

Keywords: DTM, Unmanned Aerial Vehicle (UAV), uniform, random, kriging

Procedia PDF Downloads 82
3454 Increasing the Apparent Time Resolution of Tc-99m Diethylenetriamine Pentaacetic Acid Galactosyl Human Serum Albumin Dynamic SPECT by Use of an 180-Degree Interpolation Method

Authors: Yasuyuki Takahashi, Maya Yamashita, Kyoko Saito

Abstract:

In general, dynamic SPECT data acquisition needs a few minutes for one rotation. Thus, the time-activity curve (TAC) derived from the dynamic SPECT is relatively coarse. In order to effectively shorten the interval, between data points, we adopted a 180-degree interpolation method. This method is already used for reconstruction of the X-ray CT data. In this study, we applied this 180-degree interpolation method to SPECT and investigated its effectiveness.To briefly describe the 180-degree interpolation method: the 180-degree data in the second half of one rotation are combined with the 180-degree data in the first half of the next rotation to generate a 360-degree data set appropriate for the time halfway between the first and second rotations. In both a phantom and a patient study, the data points from the interpolated images fell in good agreement with the data points tracking the accumulation of 99mTc activity over time for appropriate region of interest. We conclude that data derived from interpolated images improves the apparent time resolution of dynamic SPECT.

Keywords: dynamic SPECT, time resolution, 180-degree interpolation method, 99mTc-GSA.

Procedia PDF Downloads 415
3453 Spatial Interpolation Technique for the Optimisation of Geometric Programming Problems

Authors: Debjani Chakraborty, Abhijit Chatterjee, Aishwaryaprajna

Abstract:

Posynomials, a special type of polynomials, having singularities, pose difficulties while solving geometric programming problems. In this paper, a methodology has been proposed and used to obtain extreme values for geometric programming problems by nth degree polynomial interpolation technique. Here the main idea to optimise the posynomial is to fit a best polynomial which has continuous gradient values throughout the range of the function. The approximating polynomial is smoothened to remove the discontinuities present in the feasible region and the objective function. This spatial interpolation method is capable to optimise univariate and multivariate geometric programming problems. An example is solved to explain the robustness of the methodology by considering a bivariate nonlinear geometric programming problem. This method is also applicable for signomial programming problem.

Keywords: geometric programming problem, multivariate optimisation technique, posynomial, spatial interpolation

Procedia PDF Downloads 241
3452 Stochastic Simulation of Random Numbers Using Linear Congruential Method

Authors: Melvin Ballera, Aldrich Olivar, Mary Soriano

Abstract:

Digital computers nowadays must be able to have a utility that is capable of generating random numbers. Usually, computer-generated random numbers are not random given predefined values such as starting point and end points, making the sequence almost predictable. There are many applications of random numbers such business simulation, manufacturing, services domain, entertainment sector and other equally areas making worthwhile to design a unique method and to allow unpredictable random numbers. Applying stochastic simulation using linear congruential algorithm, it shows that as it increases the numbers of the seed and range the number randomly produced or selected by the computer becomes unique. If this implemented in an environment where random numbers are very much needed, the reliability of the random number is guaranteed.

Keywords: stochastic simulation, random numbers, linear congruential algorithm, pseudorandomness

Procedia PDF Downloads 237
3451 A Gradient Orientation Based Efficient Linear Interpolation Method

Authors: S. Khan, A. Khan, Abdul R. Soomrani, Raja F. Zafar, A. Waqas, G. Akbar

Abstract:

This paper proposes a low-complexity image interpolation method. Image interpolation is used to convert a low dimension video/image to high dimension video/image. The objective of a good interpolation method is to upscale an image in such a way that it provides better edge preservation at the cost of very low complexity so that real-time processing of video frames can be made possible. However, low complexity methods tend to provide real-time interpolation at the cost of blurring, jagging and other artifacts due to errors in slope calculation. Non-linear methods, on the other hand, provide better edge preservation, but at the cost of high complexity and hence they can be considered very far from having real-time interpolation. The proposed method is a linear method that uses gradient orientation for slope calculation, unlike conventional linear methods that uses the contrast of nearby pixels. Prewitt edge detection is applied to separate uniform regions and edges. Simple line averaging is applied to unknown uniform regions, whereas unknown edge pixels are interpolated after calculation of slopes using gradient orientations of neighboring known edge pixels. As a post-processing step, bilateral filter is applied to interpolated edge regions in order to enhance the interpolated edges.

Keywords: edge detection, gradient orientation, image upscaling, linear interpolation, slope tracing

Procedia PDF Downloads 187
3450 Eliminating Cutter-Path Deviation For Five-Axis Nc Machining

Authors: Alan C. Lin, Tsong Der Lin

Abstract:

This study proposes a deviation control method to add interpolation points to numerical control (NC) codes of five-axis machining in order to achieve the required machining accuracy. Specific research issues include: (1) converting machining data between the CL (cutter location) domain and the NC domain, (2) calculating the deviation between the deviated path and the linear path, (3) finding interpolation points, and (4) determining tool orientations for the interpolation points. System implementation with practical examples will also be included to highlight the applicability of the proposed methodology.

Keywords: CAD/CAM, cutter path, five-axis machining, numerical control

Procedia PDF Downloads 359
3449 Fatigue Life Prediction under Variable Loading Based a Non-Linear Energy Model

Authors: Aid Abdelkrim

Abstract:

A method of fatigue damage accumulation based upon application of energy parameters of the fatigue process is proposed in the paper. Using this model is simple, it has no parameter to be determined, it requires only the knowledge of the curve W–N (W: strain energy density N: number of cycles at failure) determined from the experimental Wöhler curve. To examine the performance of nonlinear models proposed in the estimation of fatigue damage and fatigue life of components under random loading, a batch of specimens made of 6082 T 6 aluminium alloy has been studied and some of the results are reported in the present paper. The paper describes an algorithm and suggests a fatigue cumulative damage model, especially when random loading is considered. This work contains the results of uni-axial random load fatigue tests with different mean and amplitude values performed on 6082T6 aluminium alloy specimens. The proposed model has been formulated to take into account the damage evolution at different load levels and it allows the effect of the loading sequence to be included by means of a recurrence formula derived for multilevel loading, considering complex load sequences. It is concluded that a ‘damaged stress interaction damage rule’ proposed here allows a better fatigue damage prediction than the widely used Palmgren–Miner rule, and a formula derived in random fatigue could be used to predict the fatigue damage and fatigue lifetime very easily. The results obtained by the model are compared with the experimental results and those calculated by the most fatigue damage model used in fatigue (Miner’s model). The comparison shows that the proposed model, presents a good estimation of the experimental results. Moreover, the error is minimized in comparison to the Miner’s model.

Keywords: damage accumulation, energy model, damage indicator, variable loading, random loading

Procedia PDF Downloads 326
3448 Existence Result of Third Order Functional Random Integro-Differential Inclusion

Authors: D. S. Palimkar

Abstract:

The FRIGDI (functional random integrodifferential inclusion) seems to be new and includes several known random differential inclusions already studied in the literature as special cases have been discussed in the literature for various aspects of the solutions. In this paper, we prove the existence result for FIGDI under the non-convex case of multi-valued function involved in it.Using random fixed point theorem of B. C. Dhage and caratheodory condition. This result is new to the theory of differential inclusion.

Keywords: caratheodory condition, random differential inclusion, random solution, integro-differential inclusion

Procedia PDF Downloads 348
3447 Existence Theory for First Order Functional Random Differential Equations

Authors: Rajkumar N. Ingle

Abstract:

In this paper, the existence of a solution of nonlinear functional random differential equations of the first order is proved under caratheodory condition. The study of the functional random differential equation has got importance in the random analysis of the dynamical systems of universal phenomena. Objectives: Nonlinear functional random differential equation is useful to the scientists, engineers, and mathematicians, who are engaged in N.F.R.D.E. analyzing a universal random phenomenon, govern by nonlinear random initial value problems of D.E. Applications of this in the theory of diffusion or heat conduction. Methodology: Using the concepts of probability theory, functional analysis, generally the existence theorems for the nonlinear F.R.D.E. are prove by using some tools such as fixed point theorem. The significance of the study: Our contribution will be the generalization of some well-known results in the theory of Nonlinear F.R.D.E.s. Further, it seems that our study will be useful to scientist, engineers, economists and mathematicians in their endeavors to analyses the nonlinear random problems of the universe in a better way.

Keywords: Random Fixed Point Theorem, functional random differential equation, N.F.R.D.E., universal random phenomenon

Procedia PDF Downloads 399
3446 A Generalized Family of Estimators for Estimation of Unknown Population Variance in Simple Random Sampling

Authors: Saba Riaz, Syed A. Hussain

Abstract:

This paper is addressing the estimation method of the unknown population variance of the variable of interest. A new generalized class of estimators of the finite population variance has been suggested using the auxiliary information. To improve the precision of the proposed class, known population variance of the auxiliary variable has been used. Mathematical expressions for the biases and the asymptotic variances of the suggested class are derived under large sample approximation. Theoretical and numerical comparisons are made to investigate the performances of the proposed class of estimators. The empirical study reveals that the suggested class of estimators performs better than the usual estimator, classical ratio estimator, classical product estimator and classical linear regression estimator. It has also been found that the suggested class of estimators is also more efficient than some recently published estimators.

Keywords: study variable, auxiliary variable, finite population variance, bias, asymptotic variance, percent relative efficiency

Procedia PDF Downloads 148
3445 Applications of Probabilistic Interpolation via Orthogonal Matrices

Authors: Dariusz Jacek Jakóbczak

Abstract:

Mathematics and computer science are interested in methods of 2D curve interpolation and extrapolation using the set of key points (knots). A proposed method of Hurwitz- Radon Matrices (MHR) is such a method. This novel method is based on the family of Hurwitz-Radon (HR) matrices which possess columns composed of orthogonal vectors. Two-dimensional curve is interpolated via different functions as probability distribution functions: polynomial, sinus, cosine, tangent, cotangent, logarithm, exponent, arcsin, arccos, arctan, arcctg or power function, also inverse functions. It is shown how to build the orthogonal matrix operator and how to use it in a process of curve reconstruction.

Keywords: 2D data interpolation, hurwitz-radon matrices, MHR method, probabilistic modeling, curve extrapolation

Procedia PDF Downloads 456
3444 A Very Efficient Pseudo-Random Number Generator Based On Chaotic Maps and S-Box Tables

Authors: M. Hamdi, R. Rhouma, S. Belghith

Abstract:

Generating random numbers are mainly used to create secret keys or random sequences. It can be carried out by various techniques. In this paper we present a very simple and efficient pseudo-random number generator (PRNG) based on chaotic maps and S-Box tables. This technique adopted two main operations one to generate chaotic values using two logistic maps and the second to transform them into binary words using random S-Box tables. The simulation analysis indicates that our PRNG possessing excellent statistical and cryptographic properties.

Keywords: Random Numbers, Chaotic map, S-box, cryptography, statistical tests

Procedia PDF Downloads 282
3443 Feature Location Restoration for Under-Sampled Photoplethysmogram Using Spline Interpolation

Authors: Hangsik Shin

Abstract:

The purpose of this research is to restore the feature location of under-sampled photoplethysmogram using spline interpolation and to investigate feasibility for feature shape restoration. We obtained 10 kHz-sampled photoplethysmogram and decimated it to generate under-sampled dataset. Decimated dataset has 5 kHz, 2.5 k Hz, 1 kHz, 500 Hz, 250 Hz, 25 Hz and 10 Hz sampling frequency. To investigate the restoration performance, we interpolated under-sampled signals with 10 kHz, then compared feature locations with feature locations of 10 kHz sampled photoplethysmogram. Features were upper and lower peak of photplethysmography waveform. Result showed that time differences were dramatically decreased by interpolation. Location error was lesser than 1 ms in both feature types. In 10 Hz sampled cases, location error was also deceased a lot, however, they were still over 10 ms.

Keywords: peak detection, photoplethysmography, sampling, signal reconstruction

Procedia PDF Downloads 260
3442 Estimation of a Finite Population Mean under Random Non Response Using Improved Nadaraya and Watson Kernel Weights

Authors: Nelson Bii, Christopher Ouma, John Odhiambo

Abstract:

Non-response is a potential source of errors in sample surveys. It introduces bias and large variance in the estimation of finite population parameters. Regression models have been recognized as one of the techniques of reducing bias and variance due to random non-response using auxiliary data. In this study, it is assumed that random non-response occurs in the survey variable in the second stage of cluster sampling, assuming full auxiliary information is available throughout. Auxiliary information is used at the estimation stage via a regression model to address the problem of random non-response. In particular, the auxiliary information is used via an improved Nadaraya-Watson kernel regression technique to compensate for random non-response. The asymptotic bias and mean squared error of the estimator proposed are derived. Besides, a simulation study conducted indicates that the proposed estimator has smaller values of the bias and smaller mean squared error values compared to existing estimators of finite population mean. The proposed estimator is also shown to have tighter confidence interval lengths at a 95% coverage rate. The results obtained in this study are useful, for instance, in choosing efficient estimators of the finite population mean in demographic sample surveys.

Keywords: mean squared error, random non-response, two-stage cluster sampling, confidence interval lengths

Procedia PDF Downloads 52
3441 Heuristic to Generate Random X-Monotone Polygons

Authors: Kamaljit Pati, Manas Kumar Mohanty, Sanjib Sadhu

Abstract:

A heuristic has been designed to generate a random simple monotone polygon from a given set of ‘n’ points lying on a 2-Dimensional plane. Our heuristic generates a random monotone polygon in O(n) time after O(nℓogn) preprocessing time which is improved over the previous work where a random monotone polygon is produced in the same O(n) time but the preprocessing time is O(k) for n < k < n2. However, our heuristic does not generate all possible random polygons with uniform probability. The space complexity of our proposed heuristic is O(n).

Keywords: sorting, monotone polygon, visibility, chain

Procedia PDF Downloads 362