scholarly journals Consequences of Stability-Induced Epistasis for Substitution Rates

2020 ◽  
Vol 37 (11) ◽  
pp. 3131-3148 ◽  
Author(s):  
Noor Youssef ◽  
Edward Susko ◽  
Joseph P Bielawski
Keyword(s):  
Evolutionary Dynamics ◽  
Direct Method ◽  
Average Effect ◽  
Substitution Rates ◽  
Codon Substitution ◽  
Individual Site ◽  
Si Model ◽  
Selection Intensities ◽  
The Stability ◽  
Reasonable Inference

Abstract Do interactions between residues in a protein (i.e., epistasis) significantly alter evolutionary dynamics? If so, what consequences might they have on inference from traditional codon substitution models which assume site-independence for the sake of computational tractability? To investigate the effects of epistasis on substitution rates, we employed a mechanistic mutation-selection model in conjunction with a fitness framework derived from protein stability. We refer to this as the stability-informed site-dependent (S-SD) model and developed a new stability-informed site-independent (S-SI) model that captures the average effect of stability constraints on individual sites of a protein. Comparison of S-SI and S-SD offers a novel and direct method for investigating the consequences of stability-induced epistasis on protein evolution. We developed S-SI and S-SD models for three natural proteins and showed that they generate sequences consistent with real alignments. Our analyses revealed that epistasis tends to increase substitution rates compared with the rates under site-independent evolution. We then assessed the epistatic sensitivity of individual site and discovered a counterintuitive effect: Highly connected sites were less influenced by epistasis relative to exposed sites. Lastly, we show that, despite the unrealistic assumptions, traditional models perform comparably well in the presence and absence of epistasis and provide reasonable summaries of average selection intensities. We conclude that epistatic models are critical to understanding protein evolutionary dynamics, but epistasis might not be required for reasonable inference of selection pressure when averaging over time and sites.

scholarly journals Velocity and acceleration level inverse kinematic calculation alternatives for redundant manipulators

Meccanica ◽  
2021 ◽  
Author(s):  
Dóra Patkó ◽  
Ambrus Zelei
Keyword(s):  
Degrees Of Freedom ◽  
Direct Method ◽  
Tracking Error ◽  
Inverse Kinematic ◽  
Linear Feedback ◽  
Joint Position ◽  
Stability Properties ◽  
Acceleration Level ◽  
Error Elimination ◽  
The Stability

AbstractFor both non-redundant and redundant systems, the inverse kinematics (IK) calculation is a fundamental step in the control algorithm of fully actuated serial manipulators. The tool-center-point (TCP) position is given and the joint coordinates are determined by the IK. Depending on the task, robotic manipulators can be kinematically redundant. That is when the desired task possesses lower dimensions than the degrees-of-freedom of a redundant manipulator. The IK calculation can be implemented numerically in several alternative ways not only in case of the redundant but also in the non-redundant case. We study the stability properties and the feasibility of a tracking error feedback and a direct tracking error elimination approach of the numerical implementation of IK calculation both on velocity and acceleration levels. The feedback approach expresses the joint position increment stepwise based on the local velocity or acceleration of the desired TCP trajectory and linear feedback terms. In the direct error elimination concept, the increment of the joint position is directly given by the approximate error between the desired and the realized TCP position, by assuming constant TCP velocity or acceleration. We investigate the possibility of the implementation of the direct method on acceleration level. The investigated IK methods are unified in a framework that utilizes the idea of the auxiliary input. Our closed form results and numerical case study examples show the stability properties, benefits and disadvantages of the assessed IK implementations.

scholarly journals Evolutionary dynamics of the plastid inverted repeat: the effects of expansion, contraction, and loss on substitution rates

2015 ◽  
Vol 209 (4) ◽  
pp. 1747-1756 ◽  
Author(s):  
Andan Zhu ◽  
Wenhu Guo ◽  
Sakshi Gupta ◽  
Weishu Fan ◽  
Jeffrey P. Mower
Keyword(s):  
Inverted Repeat ◽  
Evolutionary Dynamics ◽  
Substitution Rates

scholarly journals A General Theorem on the Stability of a Class of Functional Equations Including Quartic-Cubic-Quadratic-Additive Equations

Mathematics ◽  
2018 ◽  
Vol 6 (12) ◽  
pp. 282
Author(s):  
Yang-Hi Lee ◽  
Soon-Mo Jung
Keyword(s):  
Functional Equations ◽  
Direct Method ◽  
General Theorem ◽  
Stability Problems ◽  
General Stability ◽  
Stability Theorems ◽  
Additive Type ◽  
The Stability

We prove general stability theorems for n-dimensional quartic-cubic-quadratic-additive type functional equations of the form by applying the direct method. These stability theorems can save us the trouble of proving the stability of relevant solutions repeatedly appearing in the stability problems for various functional equations.

scholarly journals Stability of Fractional Differential Equations with New Generalized Hattaf Fractional Derivative

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Khalid Hattaf
Keyword(s):  
Stability Analysis ◽  
Differential Equations ◽  
Fractional Derivative ◽  
Fractional Differential Equations ◽  
Fractional Derivatives ◽  
Direct Method ◽  
Lyapunov Direct Method ◽  
Science And Engineering ◽  
Fractional Differential ◽  
The Stability

This paper aims to study the stability of fractional differential equations involving the new generalized Hattaf fractional derivative which includes the most types of fractional derivatives with nonsingular kernels. The stability analysis is obtained by means of the Lyapunov direct method. First, some fundamental results and lemmas are established in order to achieve the goal of this study. Furthermore, the results related to exponential and Mittag–Leffler stability existing in recent studies are extended and generalized. Finally, illustrative examples are presented to show the applicability of our main results in some areas of science and engineering.

Evolutionary Stable Strategies for Supply Chains: Selfishness, Fairness, and Altruism

2018 ◽  
Vol 6 (6) ◽  
pp. 532-551 ◽  
Author(s):  
Caichun Chai ◽  
Hailong Zhu ◽  
Zhangwei Feng
Keyword(s):  
Supply Chains ◽  
Evolutionary Dynamics ◽  
Replicator Dynamics ◽  
Management Strategies ◽  
Individual Preference ◽  
Short Term ◽  
Evolutionary Stable Strategies ◽  
Pure Strategies ◽  
The Stability

Abstract The management strategies of a firm are inevitable affected by individual behavior preferences. The effect of individual preference on the evolutionary dynamics for supply chains is studied by employing replicator dynamics. Each firm has three behavior preferences: selfishness, fairness, and altruism. Firstly, the case that the strategy set of manufacturers and retailers including two pure strategies is considered and the effect of preference parameter on the equilibrium outcome in the short-term interaction is discussed. Secondly, the equilibrium state in the short-term is always disturbed because the change of the environment, firm’s structure, and so forth. Using the replicator dynamics, the evolutionary stable strategies of manufacturers and retailers in the long-term interaction are analyzed. Finally, the extend case that the strategy set of manufacturers and retailers include three pure strategies is investigated. These results are found that the strategy profile in which both manufacturer and retailer choose fairness or altruism, or one player chooses fair or altruistic strategy and the other player chooses selfish strategy may be evolutionary stable, the stability of these equilibria depends on the the preference parameters.

Stability Analysis of Multiple Time Delayed Systems Using the Direct Method

2003 ◽  
Author(s):  
Rifat Sipahi ◽  
Nejat Olgac
Keyword(s):  
Stability Analysis ◽  
Time Delays ◽  
Linear Time ◽  
Direct Method ◽  
Multiple Time ◽  
Delayed Systems ◽  
Practical Applications ◽  
Linear Time Invariant ◽  
Multiple Time Delays ◽  
The Stability

A novel treatment for the stability of a class of linear time invariant (LTI) systems with rationally independent multiple time delays using the Direct Method (DM) is studied. Since they appear in many practical applications in the systems and control community, this class of dynamics has attracted considerable interest. The stability analysis is very complex because of the infinite dimensional nature (even for single delay) of the dynamics and furthermore the multiplicity of these delays. The stability problem is much more challenging compared to the TDS with commensurate time delays (where time delays have rational relations). It is shown in an earlier publication of the authors that the DM brings a unique, exact and structured methodology for the stability analysis of commensurate time delayed cases. The transition from the commensurate time delays to multiple delay case motivates our study. It is shown that the DM reveals all possible stability regions in the space of multiple time delays. The systems that are considered do not have to possess stable behavior for zero delays. We present a numerical example on a system, which is considered “prohibitively difficult” in the literature, just to exhibit the strengths of the new procedure.

STABILITY ANALYSIS OF NONLINEAR INTERCONNECTED SYSTEMS VIA T–S FUZZY MODELS

2004 ◽  
Vol 04 (01) ◽  
pp. 41-55 ◽  
Author(s):  
WEI-LING CHIANG ◽  
CHENG-WU CHEN ◽  
FENG-HSIAG HSIAO
Keyword(s):  
Stability Analysis ◽  
Lyapunov Functions ◽  
Direct Method ◽  
Interconnected Systems ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Fuzzy Models ◽  
Fuzzy Techniques ◽  
The Stability ◽  
Takagi Sugeno

This paper is concerned with the stability problem of nonlinear interconnected systems. Each of them consists of a few interconnected subsystems which are approximated by Takagi–Sugeno (T–S) type fuzzy models. In terms of Lyapunov's direct method, a stability criterion is derived to guarantee the asymptotic stability of interconnected systems. It is shown that the stability analysis problems of nonlinear interconnected systems can be reduced to linear matrix inequality (LMI) problems via suitable Lyapunov functions and T–S fuzzy techniques. Finally, numerical examples with simulations are given to demonstrate the validity of the proposed approach.

Discontinuous equilibrium solutions and cavitation in nonlinear elasticity

1982 ◽  
Vol 306 (1496) ◽  
pp. 557-611 ◽  
Keyword(s):  
Singular Solution ◽  
Direct Method ◽  
Homogeneous Solution ◽  
Singular Solutions ◽  
Large Strains ◽  
Critical Surface ◽  
Surface Traction ◽  
Equilibrium Solutions ◽  
Growth Properties ◽  
The Stability

A study is made of a class of singular solutions to the equations of nonlinear elastostatics in which a spherical cavity forms at the centre of a ball of isotropic material placed in tension by means of given surface tractions or displacements. The existence of such solutions depends on the growth properties of the stored-energy function W for large strains and is consistent with strong ellipticity of W . Under appropriate hypotheses it is shown that a singular solution bifurcates from a trivial (homogeneous) solution at a critical value of the surface traction or displacement, at which the trivial solution becomes unstable. For incompressible materials both the singular solution and the critical surface traction are given explicitly, and the stability of all solutions with respect to radial motion is determined. For compressible materials the existence of singular solutions is proved for a class of strongly elliptic materials by means of the direct method of the calculus of variations, an important step in the analysis being to show that the only radial equilibrium solutions without cavities are homogeneous. Work of Gent & Lindley (1958) shows that the critical surface tractions obtained agree with those observed in the internal rupture of rubber.

scholarly journals Evolutionary Dynamics and Global Diversity of Influenza A Virus

2015 ◽  
Vol 89 (21) ◽  
pp. 10993-11001 ◽  
Author(s):  
Daniel Rejmanek ◽  
Parviez R. Hosseini ◽  
Jonna A. K. Mazet ◽  
Peter Daszak ◽  
Tracey Goldstein
Keyword(s):  
East Asia ◽  
Influenza A Virus ◽  
Influenza A ◽  
Evolutionary Dynamics ◽  
Nucleotide Substitution ◽  
Health Care Spending ◽  
Asian Countries ◽  
Substitution Rates ◽  
Country Level ◽  
Nucleotide Substitution Rates

ABSTRACTThe increasing number of zoonotic infections caused by influenza A virus (IAV) subtypes of avian origin (e.g., H5N1 and H7N9) in recent years underscores the need to better understand the factors driving IAV evolution and diversity. To evaluate the current feasibility of global analyses to contribute to this aim, we evaluated information in the public domain to explore IAV evolutionary dynamics, including nucleotide substitution rates and selection pressures, using 14 IAV subtypes in 32 different countries over a 12-year period (2000 to 2011). Using geospatial information from 39,785 IAV strains, we examined associations between subtype diversity and socioeconomic, biodiversity, and agricultural indices. Our analyses showed that nucleotide substitution rates for 11 of the 14 evaluated subtypes tended to be higher in Asian countries, particularly in East Asia, than in Canada and the United States. Similarly, at a regional level, subtypes H5N1, H5N2, and H6N2 exhibited significantly higher substitution rates in East Asia than in North America. In contrast, the selection pressures (measured as ratios of nonsynonymous to synonymous evolutionary changes [dN/dSratios]) acting on individual subtypes showed little geographic variation. We found that the strongest predictors for the detected subtype diversity at the country level were reporting effort (i.e., total number of strains reported) and health care spending (an indicator of economic development). Our analyses also identified major global gaps in IAV reporting (including a lack of sequences submitted from large portions of Africa and South America and a lack of geolocation information) and in broad subtype testing which, until addressed, will continue to hinder efforts to track the evolution and diversity of IAV around the world.IMPORTANCEIn recent years, an increasing number of influenza A virus (IAV) subtypes, including H5N1, H7N9, and H10N8, have been detected in humans. High fatality rates have led to an increased urgency to better understand where and how novel pathogenic influenza virus strains emerge. Our findings showed that mutational rates of 11 commonly encountered subtypes were higher in East Asian countries than in North America, suggesting that there may be a greater risk for the emergence of novel pathogenic strains in East Asia. In assessing the potential drivers of IAV subtype diversity, our analyses confirmed that reporting effort and health care spending were the best predictors of the observed subtype diversity at the country level. These findings underscore the need to increase sampling and reporting efforts for all subtypes in many undersampled countries throughout the world.

Stability of Cylindrical Shells Under Moving Loads by the Direct Method of Liapunov

1967 ◽  
Vol 34 (4) ◽  
pp. 991-998 ◽  
Author(s):  
G. A. Hegemier
Keyword(s):  
Constant Velocity ◽  
Local Stability ◽  
Shell Theory ◽  
Circular Cylindrical Shell ◽  
Direct Method ◽  
Sufficient Conditions ◽  
Functional Space ◽  
Moving Loads ◽  
The Stability ◽  
Shell Axis

The stability of a long, thin, elastic circular cylindrical shell subjected to axial compression and an axisymmetric load moving with constant velocity along the shell axis is studied. With the aid of the direct method of Liapunov, and employing a nonlinear Donnell-type shell theory, sufficient conditions for local stability of the axisymmetric response are established in a functional space whose metric is defined in an average sense. Numerical results, which are presented for the case of a moving decayed step load, reveal that the sufficient conditions for stability developed here and the sufficient conditions for instability obtained in a previous paper lead to the actual stability transition boundary.

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