scholarly journals A Novel Gamma Distributed Random Variable (RV) Generation Method for Clutter Simulation with Non-Integral Shape Parameters

Sensors ◽  
2020 ◽  
Vol 20 (4) ◽  
pp. 955
Author(s):  
Shichao Chen ◽  
Feng Luo ◽  
Chong Hu
Keyword(s):  
Computational Complexity ◽  
Beta Distribution ◽  
Shape Parameter ◽  
Random Variable ◽  
Shape Parameters ◽  
Analysis And Design ◽  
Non Linear ◽  
Improved Methods ◽  
Very High ◽  
Research Endeavour

Sea clutter simulation is a well-known research endeavour in radar detector analysis and design, and many approaches to it have been proposed in recent years, among which zero memory non-linear (ZMNL) and spherically invariant random process (SIRP) are the most two widely used methods for compound Gaussian distribution. However, the shape parameter of the compound Gaussian clutter model cannot be a non-integer nor non-semi-integer in the ZMNL method, and the computational complexity of the SIRP method is very high because of the complex non-linear operation. Although some improved methods have been proposed to solve the problem, the fitting degree of these methods is not high because of the introduction of Beta distribution. To overcome these disadvantages, a novel Gamma distributed random variable (RV) generation method for clutter simulation is proposed in this paper. In our method, Gamma RV with non-integral or non-semi-integral shape parameters is generated directly by multiplying an integral-shape-parameter Gamma RV with a Beta RV whose parameters are larger than 0.5, thus avoiding the deviation of simulation of Beta RV. A large number of simulation experimental results show that the proposed method not only can be used in the clutter simulation with a non-integer or non-semi-integer shape parameter value, but also has higher fitting degree than the existing methods.

scholarly journals Stress-Strength Weibull Analysis with Different Shape Parameter β and Probabilistic Safety Factor

DYNA ◽  
2020 ◽  
Vol 87 (215) ◽  
pp. 28-33 ◽  
Author(s):  
Manuel Baro ◽  
Manuel Roman Piña Monarrez ◽  
Baldomero Villa
Keyword(s):  
Weibull Distribution ◽  
Safety Factor ◽  
Shape Parameter ◽  
Random Variable ◽  
Strength Analysis ◽  
Weibull Analysis ◽  
Shape Parameters ◽  
The Relationship ◽  
Close Solution ◽  
Probabilistic Safety

Since products are subjected to a random variable stress-strength, their reliability must be determined using the stress-strength analysis. Unfortunately, when both, stress and strength, follow a Weibull distribution with different shape parameters, the reliability stress-strength has not a close solution. Therefore, in this paper, the formulation to perform the analysis stress-strength Weibull with different shape parameters is derived. Furthermore, the formulation to determine the safety factor that corresponds to the designed reliability is also given. And because the relationship between the derived safety factor and the designed reliability is unique, then because reliability is random, the derived safety factor is random.

scholarly journals 2, 12, 117, 1959, 45171, 1170086, …: a Hilbert series for the QCD chiral Lagrangian

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Lukáš Gráf ◽  
Brian Henning ◽  
Xiaochuan Lu ◽  
Tom Melia ◽  
Hitoshi Murayama
Keyword(s):  
Hilbert Series ◽  
Charge Conjugation ◽  
External Fields ◽  
Dynkin Diagrams ◽  
Non Linear ◽  
Very High ◽  
Chiral Lagrangian

Abstract We apply Hilbert series techniques to the enumeration of operators in the mesonic QCD chiral Lagrangian. Existing Hilbert series technologies for non-linear realizations are extended to incorporate the external fields. The action of charge conjugation is addressed by folding the $$ \mathfrak{su}(n) $$ su n Dynkin diagrams, which we detail in an appendix that can be read separately as it has potential broader applications. New results include the enumeration of anomalous operators appearing in the chiral Lagrangian at order p8, as well as enumeration of CP-even, CP-odd, C-odd, and P-odd terms beginning from order p6. The method is extendable to very high orders, and we present results up to order p16.(The title sequence is the number of independent C-even and P-even operators in the mesonic QCD chiral Lagrangian with three light flavors of quarks, at chiral dimensions p2, p4, p6, …)

scholarly journals Local Convexity-PreservingC2Rational Cubic Spline for Convex Data

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Muhammad Abbas ◽  
Ahmad Abd Majid ◽  
Jamaludin Md. Ali
Keyword(s):  
Shape Parameter ◽  
Cubic Spline ◽  
Convex Curve ◽  
Shape Feature ◽  
Local Convexity ◽  
Shape Parameters ◽  
Numerical Examples ◽  
2D Data ◽  
Industrial Demand ◽  
Made In

We present the smooth and visually pleasant display of 2D data when it is convex, which is contribution towards the improvements over existing methods. This improvement can be used to get the more accurate results. An attempt has been made in order to develop the local convexity-preserving interpolant for convex data usingC2rational cubic spline. It involves three families of shape parameters in its representation. Data dependent sufficient constraints are imposed on single shape parameter to conserve the inherited shape feature of data. Remaining two of these shape parameters are used for the modification of convex curve to get a visually pleasing curve according to industrial demand. The scheme is tested through several numerical examples, showing that the scheme is local, computationally economical, and visually pleasing.

Non linear analysis and design of externally prestressed beams

2004 ◽  
Vol 88 (5) ◽  
pp. 167-172
Author(s):  
Aldo Cauvin ◽  
Massimo Giudici
Keyword(s):  
Linear Analysis ◽  
Analysis And Design ◽  
Non Linear ◽  
Prestressed Beams

Discrete differential operators for periodic and two-periodic time functions

2019 ◽  
Vol 38 (1) ◽  
pp. 325-347 ◽  
Author(s):  
Tadeusz Sobczyk ◽  
Michał Radzik ◽  
Natalia Radwan-Pragłowska
Keyword(s):  
Differential Operators ◽  
High Accuracy ◽  
Large Set ◽  
Periodic Functions ◽  
Content Type ◽  
Second Derivatives ◽  
Non Linear ◽  
Discrete Operators ◽  
Linear Differential ◽  
Very High

Purpose To identify the properties of novel discrete differential operators of the first- and the second-order for periodic and two-periodic time functions. Design/methodology/approach The development of relations between the values of first and second derivatives of periodic and two-periodic functions, as well as the values of the functions themselves for a set of time instants. Numerical tests of discrete operators for selected periodic and two-periodic functions. Findings Novel discrete differential operators for periodic and two-periodic time functions determining their first and the second derivatives at very high accuracy basing on relatively low number of points per highest harmonic. Research limitations/implications Reduce the complexity of creation difference equations for ordinary non-linear differential equations used to find periodic or two-periodic solutions, when they exist. Practical implications Application to steady-state analysis of non-linear dynamic systems for solutions predicted as periodic or two-periodic in time. Originality/value Identify novel discrete differential operators for periodic and two-periodic time functions engaging a large set of time instants that determine the first and second derivatives with very high accuracy.

scholarly journals Non-ohmic tissue conduction in cardiac electrophysiology: upscaling the non-linear voltage-dependent conductance of gap junctions

2019 ◽  
Author(s):  
Daniel E. Hurtado ◽  
Javiera Jilberto ◽  
Grigory Panasenko
Keyword(s):  
Computational Complexity ◽  
Gap Junctions ◽  
Cardiac Tissue ◽  
Tissue Level ◽  
Cardiac Conduction ◽  
Non Linear ◽  
Voltage Dependent ◽  
Junctional Coupling ◽  
Organ Level ◽  
Electrical Propagation

AbstractGap junctions are key mediators of the intercellular communication in cardiac tissue, and their function is vital to sustain normal cardiac electrical activity. Conduction through gap junctions strongly depends on the hemichannel arrangement and transjunctional voltage, rendering the intercellular conductance highly non-Ohmic. Despite this marked non-linear behavior, current tissue-level models of cardiac conduction are rooted on the assumption that gap-junctions conductance is constant (Ohmic), which results in inaccurate predictions of electrical propagation, particularly in the low junctional-coupling regime observed under pathological conditions. In this work, we present a novel non-Ohmic multiscale (NOM) model of cardiac conduction that is suitable for tissue-level simulations. Using non-linear homogenization theory, we develop a conductivity model that seamlessly upscales the voltage-dependent conductance of gap junctions, without the need of explicitly modeling gap junctions. The NOM model allows for the simulation of electrical propagation in tissue-level cardiac domains that accurately resemble that of cell-based microscopic models for a wide range of junctional coupling scenarios, recovering key conduction features at a fraction of the computational complexity. A unique feature of the NOM model is the possibility of upscaling the response of non-symmetric gap-junction conductance distributions, which result in conduction velocities that strongly depend on the direction of propagation, thus allowing to model the normal and retrograde conduction observed in certain regions of the heart. We envision that the NOM model will enable organ-level simulations that are informed by sub- and inter-cellular mechanisms, delivering an accurate and predictive in-silico tool for understanding the heart function.Author summaryThe heart relies on the propagation of electrical impulses that are mediated gap junctions, whose conduction properties vary depending on the transjunctional voltage. Despite this non-linear feature, current mathematical models assume that cardiac tissue behaves like an Ohmic (linear) material, thus delivering inaccurate results when simulated in a computer. Here we present a novel mathematical multiscale model that explicitly includes the non-Ohmic response of gap junctions in its predictions. Our results show that the proposed model recovers important conduction features modulated by gap junctions at a fraction of the computational complexity. This contribution represents an important step towards constructing computer models of a whole heart that can predict organ-level behavior in reasonable computing times.

scholarly journals On the progression of COVID19 in Portugal: A comparative analysis of active cases using non-linear regression

2020 ◽  
Author(s):  
Ana Milhinhos ◽  
Pedro M. Costa
Keyword(s):  
Linear Regression ◽  
Current Data ◽  
Mitigation Measures ◽  
Infected People ◽  
Successful Case ◽  
Non Linear ◽  
Containment Measures ◽  
In The Beginning ◽  
European Union Member States ◽  
Very High

Portugal has been portrayed as a relatively successful case in the control of the COVID-19's March 2020 outbreak in Europe due to the timely confinement measures taken. As other European Union member states, Portugal is now preparing the phased loosening of the confinement measures, starting in the beginning of May. Even so, the current data, albeit showing at least a reduction in infection rates, renders difficult to forecast scenarios in the imminent future. Using South Korea data as scaffold, which is becoming a paradigmatic case of recovery following a high number of infected people, we fitted Portuguese data to biphasic models using non-linear regression and compared the two countries. The results, which suggest good fit, show that recovery in Portugal can be much slower than anticipated, with a very high percentage of active cases (over 50%) remaining still active even months after the projected end of mitigation measures. This, together with the unknown number of asymptomatic carriers, may increase the risk of a much slower recovery if not of new outbreaks. Europe and elsewhere must consider this contingency when planning the relief of containment measures.

A Simple Method for Estimating the Parameters of the Beta Distribution Applied to Modeling Uncertainty in Gas Turbine Inlet Temperature

2002 ◽  
Author(s):  
Frederic A. Holland
Keyword(s):  
Standard Deviation ◽  
Conventional Method ◽  
Beta Distribution ◽  
Conventional Approach ◽  
Algebraic Solution ◽  
Inlet Temperature ◽  
Shape Parameters ◽  
Simple Method ◽  
New Approach ◽  
A Value

The beta distribution is a particularly convenient model for random variables when only the minimum, maximum and most likely values are available. It is also very useful for estimating the mean and standard deviation given this information. In this paper a simple method is proposed to estimate the beta parameters from these three values. The proposed method has advantages over the conventional approach. In the conventional approach, the four parameters of the beta distribution are determined from only three values by assuming a standard deviation that is one-sixth the range. In contrast, the new method assumes a value for one of the beta shape parameters based on an analogy with the normal distribution. This new approach allows for a very simple algebraic solution of the beta shape parameters in contrast to the simultaneous solution required by the conventional method. The results of the proposed method are very similar to the conventional method. However, the proposed method generally gives a slightly higher (more conservative) estimate of the standard deviation when the distribution is skewed. In addition, the new approach allows the standard deviation to vary as the shape or skew of the distribution varies. Both methods were applied to modeling the probability distribution of temperature.

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