scholarly journals Estimating Differential Entropy using Recursive Copula Splitting

Entropy ◽  
2020 ◽  
Vol 22 (2) ◽  
pp. 236 ◽  
Author(s):  
Gil Ariel ◽  
Yoram Louzoun
Keyword(s):  
Compact Support ◽  
Mixed Type ◽  
Random Variables ◽  
Differential Entropy ◽  
High Dimensions ◽  
Marginal Distributions ◽  
Numerical Examples ◽  
One Dimensional ◽  
Different Dimensions

A method for estimating the Shannon differential entropy of multidimensional random variables using independent samples is described. The method is based on decomposing the distribution into a product of marginal distributions and joint dependency, also known as the copula. The entropy of marginals is estimated using one-dimensional methods. The entropy of the copula, which always has a compact support, is estimated recursively by splitting the data along statistically dependent dimensions. The method can be applied both for distributions with compact and non-compact supports, which is imperative when the support is not known or of a mixed type (in different dimensions). At high dimensions (larger than 20), numerical examples demonstrate that our method is not only more accurate, but also significantly more efficient than existing approaches.

Dependent Random Variables with Independent Subsets - II

1990 ◽  
Vol 33 (1) ◽  
pp. 24-28 ◽  
Author(s):  
Y. H. Wang
Keyword(s):  
Joint Distribution ◽  
Random Variables ◽  
Marginal Distributions ◽  
Dependent Random Variables ◽  
One Dimensional ◽  
The One

AbstractIn this paper, we consolidate into one two separate problems - dependent random variables with independent subsets and construction of a joint distribution with given marginals. Let N = {1,2,3,...} and X = {Xn; n ∊ N} be a sequence of random variables with nondegenerate one-dimensional marginal distributions {Fn; n ∊ N}. An example is constructed to show that there exists a sequence of random variables Y = {Yn; n ∊ N} such that the components of a subset of Y are independent if and only if its size is ≦ k, where k ≧ 2 is a prefixed integer. Furthermore, the one-dimensional marginal distributions of Y are those of X.

Conservative solute transport with periodic velocity and sinusoidal source concentration in semi-infinite porous media: An analytical solution

2014 ◽  
Vol 6 (1) ◽  
pp. 1024-1031
Author(s):  
R R Yadav ◽  
Gulrana Gulrana ◽  
Dilip Kumar Jaiswal
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Laplace Transformation ◽  
Seepage Velocity ◽  
Transformation Technique ◽  
Numerical Examples ◽  
One Dimensional ◽  
Porous Domain ◽  
Conservative Solute Transport ◽  
Source Concentration

The present paper has been focused mainly towards understanding of the various parameters affecting the transport of conservative solutes in horizontally semi-infinite porous media. A model is presented for simulating one-dimensional transport of solute considering the porous medium to be homogeneous, isotropic and adsorbing nature under the influence of periodic seepage velocity. Initially the porous domain is not solute free. The solute is initially introduced from a sinusoidal point source. The transport equation is solved analytically by using Laplace Transformation Technique. Alternate as an illustration; solutions for the present problem are illustrated by numerical examples and graphs.

scholarly journals On the Numerical Simulation of HPDEs Using θ-Weighted Scheme and the Galerkin Method

Mathematics ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 78
Author(s):  
Haifa Bin Jebreen ◽  
Fairouz Tchier
Keyword(s):  
Differential Equation ◽  
Galerkin Method ◽  
Linear Ordinary Differential Equation ◽  
Time Interval ◽  
Hyperbolic Partial Differential Equation ◽  
Time Step ◽  
Numerical Examples ◽  
One Dimensional ◽  
The Stability ◽  
The Galerkin Method

Herein, an efficient algorithm is proposed to solve a one-dimensional hyperbolic partial differential equation. To reach an approximate solution, we employ the θ-weighted scheme to discretize the time interval into a finite number of time steps. In each step, we have a linear ordinary differential equation. Applying the Galerkin method based on interpolating scaling functions, we can solve this ODE. Therefore, in each time step, the solution can be found as a continuous function. Stability, consistency, and convergence of the proposed method are investigated. Several numerical examples are devoted to show the accuracy and efficiency of the method and guarantee the validity of the stability, consistency, and convergence analysis.

Optimization of synthetic jet actuation by analytical modeling

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Max Huber ◽  
Andreas Zienert ◽  
Perez Weigel ◽  
Martin Schüller ◽  
Hans-Reinhard Berger ◽  
...  
Keyword(s):  
High Performance ◽  
Synthetic Jet ◽  
Parameter Study ◽  
Content Type ◽  
One Dimensional ◽  
Wide Range ◽  
Jet Actuators ◽  
Different Dimensions ◽  
Oscillation Correction ◽  
Good Agreement

Purpose The purpose of this paper is to analyze and optimize synthetic jet actuators (SJAs) by means of a literature-known one-dimensional analytical model. Design/methodology/approach The model was fit to a wide range of experimental data from in-house built SJAs with different dimensions. A comprehensive parameter study was performed to identify coupling between parameters of the model and to find optimal dimensions of SJAs. Findings The coupling of two important parameters, the diaphragm resonance frequency and the cavity volume, can be described by a power law. Optimal orifice length and diameter can be calculated from cavity height in good agreement with literature. A transient oscillation correction is required to get correct simulation outcomes. Originality/value Based on these findings, SJA devices can be optimized for maximum jet velocity and, therefore, high performance.

scholarly journals Explicit Numerical Solution of High - Dimensional Advection - Diffusion

2013 ◽  
Vol 2 (3) ◽  
pp. 17-22
Author(s):  
Elham Bayatmanesh
Keyword(s):  
High Dimensional ◽  
Numerical Techniques ◽  
Science And Engineering ◽  
Numerical Examples ◽  
One Dimensional ◽  
Advection Diffusion Equation ◽  
Advection Diffusion ◽  
Constant Coefficients ◽  
The Subject ◽  
The One

The Several numerical techniques have been developed and compared for solving the one-dimensional and three-dimentional advection-diffusion equation with constant coefficients. the subject has played very important roles to fluid dynamics as well as many other field of science and engineering. In this article, we will be presenting the of n-dimentional and we neglect the numerical examples.

scholarly journals Speed up linear scan in high-dimensions by sorting one-dimensional projections

2011 ◽  
Vol 3 (4) ◽  
pp. 41-48
Author(s):  
Jiangtao Cui ◽  
Bin Xiao ◽  
Gengdai Liu ◽  
Lian Jiang
Keyword(s):  
High Dimensions ◽  
One Dimensional ◽  
Speed Up

Numerical solution of two-dimensional first kind Fredholm integral equations by using linear Legendre wavelet

2016 ◽  
Vol 14 (01) ◽  
pp. 1650004 ◽  
Author(s):  
M. Tahami ◽  
A. Askari Hemmat ◽  
S. A. Yousefi
Keyword(s):  
Integral Equation ◽  
Tensor Product ◽  
Numerical Solution ◽  
Fredholm Integral Equation ◽  
Fredholm Integral Equations ◽  
Wavelet Basis ◽  
Two Dimensional ◽  
Legendre Wavelets ◽  
Numerical Examples ◽  
One Dimensional

In one-dimensional problems, the Legendre wavelets are good candidates for approximation. In this paper, we present a numerical method for solving two-dimensional first kind Fredholm integral equation. The method is based upon two-dimensional linear Legendre wavelet basis approximation. By applying tensor product of one-dimensional linear Legendre wavelet we construct a two-dimensional wavelet. Finally, we give some numerical examples.

A one dimensional random space-filling problem

1968 ◽  
Vol 5 (02) ◽  
pp. 427-435 ◽  
Author(s):  
John P. Mullooly
Keyword(s):  
Asymptotic Behavior ◽  
Finite Number ◽  
Real Line ◽  
Random Variables ◽  
Random Interval ◽  
Space Filling ◽  
One Dimensional ◽  
The Real ◽  
Fixed Constant ◽  
Filling Problem

Consider an interval of the real line (0, x), x > 0; and place in it a random subinterval S(x) defined by the random variables Xx and Yx , the position of the center of S(x) and the length of S(x). The set (0, x)– S(x) consists of two intervals of length δ and η. Let a > 0 be a fixed constant. If δ ≦ a, then a random interval S(δ) defined by Xδ, Yδ is placed in the interval of length δ. If δ < a, the placement of the second interval is not made. The same is done for the interval of length η. Continue to place non-intersecting random subintervals in (0, x), and require that the lengths of all the random subintervals be ≦ a. The process terminates after a finite number of steps when all the segments of (0, x) uncovered by random subintervals are of length < a. At this stage, we say that (0, x) is saturated. Define N(a, x) as the number of random subintervals that have been placed when the process terminates. We are interested in the asymptotic behavior of the moments of N(a, x), for large x.

FEEDBACK SYNCHRONIZATION USING POLE-PLACEMENT CONTROL

2000 ◽  
Vol 10 (11) ◽  
pp. 2611-2617 ◽  
Author(s):  
ROBERTO TONELLI ◽  
YING-CHENG LAI ◽  
CELSO GREBOGI
Keyword(s):  
Chaotic Systems ◽  
Pole Placement ◽  
Active Area ◽  
High Dimensions ◽  
Mutual Synchronization ◽  
Numerical Examples ◽  
Placement Method ◽  
Pole Placement Control

Synchronization in chaotic systems has become an active area of research since the pioneering work of Pecora and Carroll. Most existing works, however, rely on a passive approach: A coupling between chaotic systems is necessary for their mutual synchronization. We describe here a feedback approach for synchronizing chaotic systems that is applicable in high dimensions. We show how two chaotic systems can be synchronized by applying small feedback perturbations to one of them. We detail our strategy to design the control based on the pole-placement method, and give numerical examples.

Assessment of inner reliability in the Gauss-Helmert model

2020 ◽  
Vol 14 (1) ◽  
pp. 13-28 ◽  
Author(s):  
Andreas Ettlinger ◽  
Hans Neuner
Keyword(s):  
Markov Model ◽  
Statistical Tests ◽  
Correlation Coefficients ◽  
Design Matrix ◽  
Numerical Examples ◽  
One Dimensional ◽  
Detection And Identification ◽  
Observation Matrix ◽  
Detectable Bias ◽  
Zero Vector

AbstractIn this contribution, the minimum detectable bias (MDB) as well as the statistical tests to identify disturbed observations are introduced for the Gauss-Helmert model. Especially, if the observations are uncorrelated, these quantities will have the same structure as in the Gauss-Markov model, where the redundancy numbers play a key role. All the derivations are based on one-dimensional and additive observation errors respectively offsets which are modeled as additional parameters to be estimated. The formulas to compute these additional parameters with the corresponding variances are also derived in this contribution. The numerical examples of plane fitting and yaw computation show, that the MDB is also in the GHM an appropriate measure to analyze the ability of an implemented least-squares algorithm to detect if outliers are present. Two sources negatively influencing detectability are identified: columns close to the zero vector in the observation matrix B and sub-optimal configuration in the design matrix A. Even if these issues can be excluded, it can be difficult to identify the correct observation as being erroneous. Therefore, the correlation coefficients between two test values are derived and analyzed. Together with the MDB these correlation coefficients are an useful tool to assess the inner reliability – and therefore the detection and identification of outliers – in the Gauss-Helmert model.

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