scholarly journals A Method for the Statistical Evaluation of Crosstalk Effect Between Three Parallel Conductors

1999 ◽  
Vol 22 (2) ◽  
pp. 111-119
Author(s):  
P. T. Trakadas ◽  
C. N. Capsalis
Keyword(s):  
Closed Form ◽  
Uniform Distribution ◽  
Transmission Lines ◽  
Statistical Evaluation ◽  
Unit Length ◽  
Surrounding Medium ◽  
Probabilistic Approach ◽  
Random Variable ◽  
Mutual Inductance ◽  
Theoretical Results

There are several cases at which, in order to evaluate the crosstalk effect among transmission lines carrying useful signals, there is a need for probabilistic approach. This paper considers the problem of crosstalk estimation between transmission lines consisting of three conductors in a homogeneous surrounding medium, where the distance between the conductors is a random variable described by uniform distribution. The transmission lines are considered as electrically short. A closed-form equation is developed for the statistical distribution of the per-unit-length mutual inductance(lm)and an analytical one is described for the evaluation of the per-unit-length capacitance(cm). Theoretical results are compared with simulated ones for validation purposes.

scholarly journals Smoothing approximations for piecewise smooth functions: A probabilistic approach

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Elmehdi Amhraoui ◽  
Tawfik Masrour
Keyword(s):  
Probability Distribution ◽  
Probabilistic Approach ◽  
Random Variable ◽  
Boltzmann Distribution ◽  
Piecewise Smooth ◽  
Smooth Functions ◽  
New Approach ◽  
One Dimensional ◽  
Piecewise Smooth Functions ◽  
Theoretical Results

<p style='text-indent:20px;'>In this article, we present a new approach to construct smoothing approximations for piecewise smooth functions. This approach proposes to formulate any piecewise smooth function as the expectation of a random variable. Based on this formulation, we show that smoothing all elements of a defined space of piecewise smooth functions is equivalent to smooth a single probability distribution. Furthermore, we propose to use the Boltzmann distribution as a smoothing approximation for this probability distribution. Moreover, we present the theoretical results, error estimates, and some numerical examples for this new smoothing method in both one-dimensional and multiple-dimensional cases.</p>

Generation of Correlated Logistic-Normal Random Variates for Medical Decision Trees

1998 ◽  
Vol 37 (03) ◽  
pp. 235-238 ◽  
Author(s):  
M. El-Taha ◽  
D. E. Clark
Keyword(s):  
Monte Carlo ◽  
Decision Trees ◽  
Computer Algebra ◽  
Taylor Series ◽  
Computer Algebra System ◽  
Random Variable ◽  
Monte Carlo Analysis ◽  
Normal Random Variable ◽  
Medical Decision ◽  
Theoretical Results

AbstractA Logistic-Normal random variable (Y) is obtained from a Normal random variable (X) by the relation Y = (ex)/(1 + ex). In Monte-Carlo analysis of decision trees, Logistic-Normal random variates may be used to model the branching probabilities. In some cases, the probabilities to be modeled may not be independent, and a method for generating correlated Logistic-Normal random variates would be useful. A technique for generating correlated Normal random variates has been previously described. Using Taylor Series approximations and the algebraic definitions of variance and covariance, we describe methods for estimating the means, variances, and covariances of Normal random variates which, after translation using the above formula, will result in Logistic-Normal random variates having approximately the desired means, variances, and covariances. Multiple simulations of the method using the Mathematica computer algebra system show satisfactory agreement with the theoretical results.

scholarly journals A New Mixed Functional-probabilistic Approach for Finite Element Accuracy

2020 ◽  
Vol 20 (4) ◽  
pp. 799-813
Author(s):  
Joël Chaskalovic ◽  
Franck Assous
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Asymptotic Relation ◽  
Probabilistic Approach ◽  
Random Variable ◽  
High Order ◽  
Relative Accuracy ◽  
The Difference ◽  
New Perspective

AbstractThe aim of this paper is to provide a new perspective on finite element accuracy. Starting from a geometrical reading of the Bramble–Hilbert lemma, we recall the two probabilistic laws we got in previous works that estimate the relative accuracy, considered as a random variable, between two finite elements {P_{k}} and {P_{m}} ({k<m}). Then we analyze the asymptotic relation between these two probabilistic laws when the difference {m-k} goes to infinity. New insights which qualify the relative accuracy in the case of high order finite elements are also obtained.

scholarly journals Random additions in urns of integers

2021 ◽  
Vol 58 (2) ◽  
pp. 335-346
Author(s):  
Mackenzie Simper
Keyword(s):  
Finite Group ◽  
Random Process ◽  
Uniform Distribution ◽  
Discrete Time ◽  
Random Variable ◽  
Urn Model ◽  
Infinite Type ◽  
The Mean ◽  
A Finite Group ◽  
Proof Of Convergence

AbstractConsider an urn containing balls labeled with integer values. Define a discrete-time random process by drawing two balls, one at a time and with replacement, and noting the labels. Add a new ball labeled with the sum of the two drawn labels. This model was introduced by Siegmund and Yakir (2005) Ann. Prob.33, 2036 for labels taking values in a finite group, in which case the distribution defined by the urn converges to the uniform distribution on the group. For the urn of integers, the main result of this paper is an exponential limit law. The mean of the exponential is a random variable with distribution depending on the starting configuration. This is a novel urn model which combines multi-drawing and an infinite type of balls. The proof of convergence uses the contraction method for recursive distributional equations.

Distribution of Consensus in a Broadcasting-based Consensus-forming Algorithm

2021 ◽  
Vol 48 (3) ◽  
pp. 91-96
Author(s):  
Shigeo Shioda
Keyword(s):  
Distribution Function ◽  
Probability Density Function ◽  
Closed Form ◽  
Probability Density ◽  
Infinite Number ◽  
Stable Distribution ◽  
Random Variable ◽  
Cauchy Distribution ◽  
Closed Form Expression ◽  
Form Expression

The consensus achieved in the consensus-forming algorithm is not generally a constant but rather a random variable, even if the initial opinions are the same. In the present paper, we investigate the statistical properties of the consensus in a broadcasting-based consensus-forming algorithm. We focus on two extreme cases: consensus forming by two agents and consensus forming by an infinite number of agents. In the two-agent case, we derive several properties of the distribution function of the consensus. In the infinite-numberof- agents case, we show that if the initial opinions follow a stable distribution, then the consensus also follows a stable distribution. In addition, we derive a closed-form expression of the probability density function of the consensus when the initial opinions follow a Gaussian distribution, a Cauchy distribution, or a L´evy distribution.

Grain Boundary Atomic Structures in SrTiO3 and BaTiO3

2007 ◽  
Vol 558-559 ◽  
pp. 851-856 ◽  
Author(s):  
Takahisa Yamamoto ◽  
Teruyasu Mizoguchi ◽  
S.Y. Choi ◽  
Yukio Sato ◽  
Naoya Shibata ◽  
...  
Keyword(s):  
Grain Boundary ◽  
Grain Boundaries ◽  
Annealing Temperature ◽  
Unit Length ◽  
Rate Dependency ◽  
Atomic Structures ◽  
Current Voltage ◽  
Single Grain ◽  
Current Voltage Characteristics ◽  
Theoretical Results

SrTiO3 bicrystals with various types of grain boundaries were prepared by joining two single crystals at high temperature. By using the bicrystals, we examined their current-voltage characteristics across single grain boundaries from a viewpoint of point defect segregation in the vicinity of the grain boundaries. Current-voltage property in SrTiO3 bicrystals was confirmed to show a cooling rate dependency from annealing temperature, indicating that cation vacancies accumulate due to grain boundary oxidation. The theoretical results obtained by ab-initio calculation clearly showed that the formation energy of Sr vacancies is the lowest comparing with Ti and O vacancies in oxidized atomosphere. The formation of a double Schottky barrier (DSB) in n-type SrTiO3 is considered to be closely related to the accumulation of the charged Sr vacancies. Meanwhile, by using three types of low angle boundaries, the excess charges related to one grain boundary dislocation par unit length was estimated. In this study, we summarized our results obtained in our group.

scholarly journals TRANSIENT RESPONSE OF A DISTRIBUTED RLC INTERCONNECT BASED ON DIRECT POLE EXTRACTION

2009 ◽  
Vol 18 (07) ◽  
pp. 1263-1285 ◽  
Author(s):  
GUOQING CHEN ◽  
EBY G. FRIEDMAN
Keyword(s):  
Closed Form ◽  
Transient Response ◽  
Transmission Lines ◽  
Average Error ◽  
Proposed Model ◽  
Newton Raphson ◽  
On Chip ◽  
Interconnect Systems ◽  
Interconnect System ◽  
Raphson Method

With higher operating frequencies, transmission lines are required to model global on-chip interconnects. In this paper, an accurate and efficient solution for the transient response at the far end of a transmission line based on a direct pole extraction of the system is proposed. Closed form expressions of the poles are developed for two special interconnect systems: an RC interconnect and an RLC interconnect with zero driver resistance. By performing a system conversion, the poles of an interconnect system with general circuit parameters are solved. The Newton–Raphson method is used to further improve the accuracy of the poles. Based on these poles, closed form expressions for the step and ramp response are determined. Higher accuracy can be obtained with additional pairs of poles. The computational complexity of the model is proportional to the number of pole pairs. With two pairs of poles, the average error of the 50% delay is 1% as compared with Spectre simulations. With ten pairs of poles, the average error of the 10%-to-90% rise time and the overshoots is 2% and 1.9%, respectively. Frequency dependent effects are also successfully included in the proposed method and excellent match is observed between the proposed model and Spectre simulations.

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