Asymptotic Stability with a Discounted Criterion; Global and Local Analysis

1987 ◽  
pp. 97-123
Author(s):  
D. A. Carlson ◽  
A. Haurie
Keyword(s):  
Asymptotic Stability ◽  
Local Analysis ◽  
Global And Local ◽  
Discounted Criterion

Asymptotic Stability with a Discounted Criterion; Global and Local Analysis

1991 ◽  
pp. 125-148
Author(s):  
Dean A. Carlson ◽  
Alain B. Haurie ◽  
Arie Leizarowitz
Keyword(s):  
Asymptotic Stability ◽  
Local Analysis ◽  
Global And Local ◽  
Discounted Criterion

Adaptive Query Refinement Based on Global and Local Analysis

2005 ◽  
pp. 584-593 ◽  
Author(s):  
Chaoyuan Cui ◽  
Hanxiong Chen ◽  
Kazutaka Furuse ◽  
Nobuo Ohbo
Keyword(s):  
Local Analysis ◽  
Query Refinement ◽  
Global And Local

scholarly journals Energy Landscape of the SARS-CoV-2 Reveals Extensive Conformational Heterogeneity

2021 ◽  
Author(s):  
Ghoncheh Mashayekhi ◽  
John Vant ◽  
Abhishek Singharoy ◽  
Abbas Ourmazd
Keyword(s):  
Free Energy ◽  
Energy Landscape ◽  
Binding Pocket ◽  
Minimum Free Energy ◽  
Spike Protein ◽  
Local Analysis ◽  
Interaction Sites ◽  
Density Maps ◽  
The Stability ◽  
Global And Local

Cryo-electron microscopy (cryo-EM) has produced a number of structural models of the SARS-CoV-2 spike, already prompting biomedical outcomes. However, these reported models and their associated electrostatic potential maps represent an unknown admixture of conformations stemming from the underlying energy landscape of the spike protein. As for any protein, some of the spike's conformational motions are expected to be biophysically relevant, but cannot be interpreted only by static models. Using experimental cryo-EM images, we present the energy landscape of the spike protein conformations, and identify molecular rearrangements along the most-likely conformational path in the vicinity of the open (so called 1RBD-up) state. The resulting global and local atomic refinements reveal larger movements than those expected by comparing the reported 1RBD-up and 1RBD-down cryo-EM models. Here we report greater degrees of "openness" in global conformations of the 1RBD-up state, not revealed in the single-model interpretations of the density maps, together with conformations that overlap with the reported models. We discover how the glycan shield contributes to the stability of these conformations along the minimum free-energy pathway. A local analysis of seven key binding pockets reveals that six out them, including those for engaging ACE2, therapeutic mini-proteins, linoleic acid, two different kinds of antibodies, and protein-glycan interaction sites, switch conformations between their known apo- and holo-conformations, even when the global spike conformation is 1RBD-up. This is reminiscent of a conformational pre-equilibrium. We found only one binding pocket, namely antibody AB-C135 to remain closed along the entire minimum free energy path, suggesting an induced fit mechanism for this enzyme.

scholarly journals Local and global analysis of macromolecular atomic displacement parameters

2020 ◽  
Vol 76 (10) ◽  
pp. 926-937
Author(s):  
Rafiga C. Masmaliyeva ◽  
Kave H. Babai ◽  
Garib N. Murshudov
Keyword(s):  
Global Analysis ◽  
Expectation Maximization Algorithm ◽  
Atomic Displacement ◽  
Local Analysis ◽  
X Ray Crystallography ◽  
Inverse Gamma ◽  
Metal Atoms ◽  
Atomic Displacement Parameters ◽  
Global And Local ◽  
Validation Tool

This paper describes the global and local analysis of atomic displacement parameters (ADPs) of macromolecules in X-ray crystallography. The distribution of ADPs is shown to follow the shifted inverse-gamma distribution or a mixture of these distributions. The mixture parameters are estimated using the expectation–maximization algorithm. In addition, a method for the resolution- and individual ADP-dependent local analysis of neighbouring atoms has been designed. This method facilitates the detection of mismodelled atoms, heavy-metal atoms and disordered and/or incorrectly modelled ligands. Both global and local analyses can be used to detect errors in atomic models, thus helping in the (re)building, refinement and validation of macromolecular structures. This method can also serve as an additional validation tool during PDB deposition.

scholarly journals Global and Local Analysis for a Cournot Duopoly Game with Two Different Objective Functions

Mathematics ◽  
2021 ◽  
Vol 9 (23) ◽  
pp. 3119
Author(s):  
Sameh Askar ◽  
Abdulaziz Foul ◽  
Tarek Mahrous ◽  
Saleh Djemele ◽  
Emad Ibrahim
Keyword(s):  
Equilibrium Points ◽  
Logistic Map ◽  
Analytical Form ◽  
Local Analysis ◽  
Flip Bifurcation ◽  
Objective Functions ◽  
Critical Curves ◽  
Cournot Game ◽  
Bifurcation Phenomena ◽  
Global And Local

In this paper, a Cournot game with two competing firms is studied. The two competing firms seek the optimality of their quantities by maximizing two different objective functions. The first firm wants to maximize an average of social welfare and profit, while the second firm wants to maximize their relative profit only. We assume that both firms are rational, adopting a bounded rationality mechanism for updating their production outputs. A two-dimensional discrete time map is introduced to analyze the evolution of the game. The map has four equilibrium points and their stability conditions are investigated. We prove the Nash equilibrium point can be destabilized through flip bifurcation only. The obtained results show that the manifold of the game’s map can be analyzed through a one-dimensional map whose analytical form is similar to the well-known logistic map. The critical curves investigations show that the phase plane of game’s map is divided into three zones and, therefore, the map is not invertible. Finally, the contact bifurcation phenomena are discussed using simulation.

scholarly journals Determining Asymptotic Stability and Robustness of Networked Systems

Systems ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 39
Author(s):  
Elias August
Keyword(s):  
Asymptotic Stability ◽  
Equilibrium Points ◽  
Rational Functions ◽  
Computational Method ◽  
Multiple Equilibrium ◽  
Local Analysis ◽  
Stable Equilibrium Point ◽  
Continuous Stirred Tank Reactor ◽  
Novel Approach ◽  
Individual System

This paper is motivated by the notion that coupling systems allows for mitigating the failure of individual ones. We present a novel approach to determining asymptotic stability and robustness of a network consisting of coupled dynamical systems, where individual system dynamics are represented through polynomial or rational functions. The analysis relies on a local analysis; thus, making it computationally implementable. We present an efficient computational method that relies on semidefinite programming. Importantly, for cases where multiple equilibrium points exist, we show how to determine regions around an asymptotically stable equilibrium point that bounds solutions. These regions increase when systems are coupled as we observe when applying the presented analysis framework to a mathematical model of a continuous stirred tank reactor. Importantly, the presented work has implications to other fields as well.

A Computerised Method For The Rapid Global and Local Analysis of Ship Structures

1998 ◽  
Author(s):  
K F Stone ◽  
◽  
R Kumar ◽  
N Pegg ◽  
D Heath ◽  
...  
Keyword(s):  
Local Analysis ◽  
Ship Structures ◽  
Global And Local

Global versus Local Image Expansion in Estimating Time-to-Contact from Complex Optic Flow

Perception ◽  
10.1068/p5271 ◽  
2005 ◽  
Vol 34 (5) ◽  
pp. 577-585 ◽  
Author(s):  
Christos D Giachritsis ◽  
Mike G Harris
Keyword(s):  
Optic Flow ◽  
Local Analysis ◽  
Systematic Effect ◽  
Global Pattern ◽  
Time To Contact ◽  
Local Expansion ◽  
Rotation Rates ◽  
Global And Local ◽  
Local Image ◽  
Image Expansion

Previous work (Harris and Giachritsis 2000, Vision Research40 601–611) has shown that, when global and local image expansion are placed in conflict, estimates of time-to-contact (TTC) are based almost exclusively upon global expansion. Here we extend this finding by demonstrating that global image expansion continues to predominate even under conditions that seem more favourable to a local analysis. We added a global rotation to the stimulus so that the global pattern of expansion was distorted while leaving the local expansion unaffected. Even under relatively high rotation rates (30° s−1), local expansion continued to have little systematic effect upon estimates of TTC.

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