Continuous Description of Discrete Biological Data

2019 ◽  
Vol 9 (1) ◽  
pp. 36-49
Author(s):  
Serge V. Chernyshenko
Keyword(s):  
Computer Simulation ◽  
Differential Equations ◽  
Biological Data ◽  
Stochastic Flow ◽  
Differential Model ◽  
Qualitative And Quantitative ◽  
Continuous Models ◽  
Continuous Analogue ◽  
Continuous Description ◽  
Discrete Nature

The applicability of differential equations to description of integer values dynamics in bio-informatics is investigated. It is shown that a differential model may be interpreted as a continuous analogue of a stochastic flow. The method of construction of a quasi-Poisson flow on the base of multi-dimension differential equations is proposed. Mathematical correctness of the algorithm is proven. The system has been studied by a computer simulation and a discrete nature of processes has been taken into account. The proposed schema has been applied to the classical Volterra's models, which are widely used for description of biological systems. It has been demonstrated that although behaviour of discrete and continuous models is similar, some essential qualitative and quantitative differences in their dynamics take place.

Computer Simulation of a Press Feed Mechanism and Experimental Confirmation

1994 ◽  
Vol 116 (1) ◽  
pp. 248-256 ◽  
Author(s):  
C. Chassapis ◽  
G. G. Lowen
Keyword(s):  
Computer Simulation ◽  
Data Acquisition System ◽  
Quantitative Agreement ◽  
Drive Shaft ◽  
Strain Gages ◽  
Motion Equations ◽  
Qualitative And Quantitative ◽  
Bending Strain ◽  
Out Of Plane ◽  
Set Up

An experimentally verified simulation of the elastic-dynamic behavior of a lever-type feed mechanism is presented. Based on a combination of experimental and analytical findings, simplified motion equations could be introduced. In the experimental set-up, the motion of the mechanism is monitored by three angular encoders, which are attached to the drive shaft, the rocker-link shaft, and the feed roller shaft, respectively. Their output, which is stored in a specially designed data acquisition system, allows the correlation of the instantaneous rotations of the feed roller and the rocker shafts to that of the drive shaft. Strain gages provide in and out-of-plane bending-strain histories of the bent coupler. Experiment and theory, for different loading conditions, are correlated by way of the coupler strain, the clutch windup angle and the total feed length. Good qualitative and quantitative agreement between computed and experimental results was found.

scholarly journals Qualitative and Quantitative Techniques for Differential Equations Arising in Mathematical Physics

2017 ◽  
Vol 2017 ◽  
pp. 1-2
Author(s):  
Rehana Naz ◽  
Mariano Torrisi ◽  
Igor Leite Freire ◽  
Imran Naeem
Keyword(s):  
Differential Equations ◽  
Mathematical Physics ◽  
Qualitative And Quantitative

scholarly journals A Continuous Analogue of Lattice Path Enumeration

10.37236/8788 ◽  
2019 ◽  
Vol 26 (3) ◽  
Author(s):  
Quang-Nhat Le ◽  
Sinai Robins ◽  
Christophe Vignat ◽  
Tanay Wakhare
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Lattice Paths ◽  
Lattice Path ◽  
Continuous Version ◽  
Continuous Analog ◽  
Continuous Analogue ◽  
Lattice Path Enumeration ◽  
Multinomial Coefficients ◽  
General Method

Following the work of Cano and Díaz, we consider a continuous analog of lattice path enumeration. This process allows us to define a continuous version of many discrete objects that count certain types of lattice paths. As an example of this process, we define continuous versions of binomial and multinomial coefficients, and describe some identities and partial differential equations that they satisfy. Finally, as an important byproduct of these continuous analogs, we illustrate a general method to recover discrete combinatorial quantities from their continuous analogs, via an application of the Khovanski-Puklikov discretizing Todd operators.  

scholarly journals On the continuous analogue of the Seidel method

2018 ◽  
Vol 20 (4) ◽  
pp. 364-377
Author(s):  
I. V. Boikov ◽  
A. I. Boikova
Keyword(s):  
Differential Equations ◽  
Systems Of Nonlinear Equations ◽  
Algebraic Equations ◽  
Seidel Method ◽  
Linear Algebraic Equations ◽  
Nonlinear Algebraic Equations ◽  
Continuous Analogue ◽  
Solution Methods ◽  
Linear And Nonlinear ◽  
Equations With Delay

Continuous Seidel method for solving systems of linear and nonlinear algebraic equations is constructed in the article, and the convergence of this method is investigated. According to the method discussed, solving a system of algebraic equations is reduced to solving systems of ordinary differential equations with delay. This allows to use rich arsenal of numerical ODE solution methods while solving systems of algebraic equations. The main advantage of the continuous analogue of the Seidel method compared to the classical one is that it does not require all the elements of the diagonal matrix to be non-zero while solving linear algebraic equations’ systems. The continuous analogue has the similar advantage when solving systems of nonlinear equations.

scholarly journals Love and Rayleigh Correction Terms and Padé Approximants

2007 ◽  
Vol 2007 ◽  
pp. 1-8 ◽  
Author(s):  
I. Andrianov ◽  
J. Awrejcewicz
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Type Theory ◽  
Padé Approximation ◽  
Beam Equation ◽  
Plate Equation ◽  
Partial Differential ◽  
Continuous Models ◽  
Spatial Coordinates ◽  
Correction Terms

Simplified theories governing behavior of beams and plates keeping the fundamental characteristics of the being modeled objects are proposed and discussed. By simplification, we mean decrease of order of partial differential equations (PDEs) with respect to spatial coordinates. Our approach is used for both discrete and continuous models. An advantage of Padé approximation is addressed. First part of this report deals with approximation of a beam equation by string-like one, and plate equation by membrane-like one. Second part is devoted to the construction of Love-type theory for rods vibrations and Rayleigh-type theory for beams vibrations.

Exact solutions for the bending of Timoshenko beams using Eringen’s two-phase nonlocal model

2018 ◽  
Vol 24 (3) ◽  
pp. 559-572 ◽  
Author(s):  
Yuanbin Wang ◽  
Kai Huang ◽  
Xiaowu Zhu ◽  
Zhimei Lou
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Exact Solutions ◽  
Nonlocal Parameter ◽  
Beam Theory ◽  
Nonlocal Model ◽  
Bernoulli Beam ◽  
Two Phase ◽  
Differential Model ◽  
Euler Bernoulli Beam

Eringen’s nonlocal differential model has been widely used in the literature to predict the size effect in nanostructures. However, this model often gives rise to paradoxes, such as the cantilever beam under end-point loading. Recent studies of the nonlocal integral models based on Euler–Bernoulli beam theory overcome the aforementioned inconsistency. In this paper, we carry out an analytical study of the bending problem based on Eringen’s two-phase nonlocal model and Timoshenko beam theory, which accounts for a better representation of the bending behavior of short, stubby nanobeams where the nonlocal effect and transverse shear deformation are significant. The governing equations are established by the principal of virtual work, which turns out to be a system of integro-differential equations. With the help of a reduction method, the complicated system is reduced to a system of differential equations with mixed boundary conditions. After some detailed calculations, exact analytical solutions are obtained explicitly for four types of boundary conditions. Asymptotic analysis of the exact solutions reveals clearly that the nonlocal parameter has the effect of increasing the deflections. In addition, as compared with nonlocal Euler–Bernoulli beam, the shear effect is evident, and an additional scale effect is captured, indicating the importance of applying higher-order beam theories in the analysis of nanostructures.

scholarly journals Simultaneous parameter estimation and variable selection via the logit-normal continuous analogue of the spike-and-slab prior

2019 ◽  
Vol 16 (150) ◽  
pp. 20180572 ◽  
Author(s):  
W. Thomson ◽  
S. Jabbari ◽  
A. E. Taylor ◽  
W. Arlt ◽  
D. J. Smith
Keyword(s):  
Parameter Estimation ◽  
Statistical Models ◽  
Prior Distribution ◽  
Biological Data ◽  
Variable Model ◽  
Machine Learning Methods ◽  
Spike And Slab Prior ◽  
Unseen Data ◽  
Continuous Analogue ◽  
Bayesian Prior

We introduce a Bayesian prior distribution, the logit-normal continuous analogue of the spike-and-slab, which enables flexible parameter estimation and variable/model selection in a variety of settings. We demonstrate its use and efficacy in three case studies—a simulation study and two studies on real biological data from the fields of metabolomics and genomics. The prior allows the use of classical statistical models, which are easily interpretable and well known to applied scientists, but performs comparably to common machine learning methods in terms of generalizability to previously unseen data.

scholarly journals Effective Approaches to Control the Epidemic Based on the Improved SIR Model

2016 ◽  
Vol 6 (2) ◽  
pp. 154
Author(s):  
Shuai Shao ◽  
Hao Li ◽  
Yuanbiao Zhang ◽  
Kailong Li
Keyword(s):  
Differential Equation ◽  
Computer Simulation ◽  
Quantitative Method ◽  
Sir Model ◽  
Equation Model ◽  
Control Measures ◽  
Uncertain Parameters ◽  
Differential Equation Model ◽  
Qualitative And Quantitative ◽  
Epidemic Area

<p class="zhengwen">In this paper, we have established a SECADI model on the basis of the traditional epidemic model and under the consideration of factors such as the spread of the disease, the quantity of the medicine in need, the medicine production speedetc. We have improved the crowd classification standard and the spread styledifferential equation model in classical SIR model. We distinguished the crowd into six categories, including the susceptible, the exposed, the curable, the advanced, the dead and the immune, and we established integrated transformation relationships between them after taking control measures through qualitative and quantitative method, and then derive the adequate epidemic differential equation model before taking controls. We applied the method of computer simulation to solve the model, worked out uncertain parameters with the method of parameter identification, and we verified the validity and accuracy of the SECADI model. Meanwhile, we calculated with the actual data of Ebola in the epidemic area in WesternAfrica, simulated the evolution of the epidemic, analyze and offered effective approaches to control the epidemic situation. We further discussed development directions of this model in the end.</p>

Comparison results for functional differential equations with impulses

2013 ◽  
Vol 63 (1) ◽  
Author(s):  
Xiao Li
Keyword(s):  
Differential Equations ◽  
Quantitative Study ◽  
Functional Differential Equations ◽  
Comparison Principles ◽  
Qualitative And Quantitative ◽  
First Order ◽  
Comparison Results ◽  
Functional Differential ◽  
Qualitative And Quantitative Study

AbstractComparison principles play an important role in the qualitative and quantitative study of differential equations. In this paper, we investigate a first order functional differential equations with impulses and establish new comparison results.

INDUSTRIAL POLLUTION AND ASTHMA: A MATHEMATICAL MODEL

2000 ◽  
Vol 08 (04) ◽  
pp. 347-371 ◽  
Author(s):  
MINI GHOSH
Keyword(s):  
Mathematical Model ◽  
Computer Simulation ◽  
Differential Equations ◽  
Mathematical Models ◽  
Stability Theory ◽  
Industrial Pollution ◽  
Air Pollutant ◽  
Logistic Growth ◽  
Nonlinear Mathematical Models

In this paper, some nonlinear mathematical models are proposed and analyzed to study the spread of asthma due to inhaled pollutants from Industry. The following two types of demographics are considered here; (i) population with constant immigration, (ii) population with logistic growth. In each type of demography, the following three cases have been considered regarding the release of pollutant into the environment; (i) when emission of the pollutant into the environment is constant, (ii) when emission of the pollutant is population dependent, and (iii) when emission of the pollutant is periodic. Using stability theory of differential equations and computer simulation, it is shown that due to an increase in the air pollutant, the asthmatic (diseased) population increases in the region under consideration.

Sign in / Sign up

Export Citation Format

Share Document