Distributed Mirror Descent with Integral Feedback: Convergence Analysis from a Dynamical System Perspective

2021 ◽  
Author(s):  
Youbang Sun ◽  
Shahin Shahrampour
Keyword(s):  
Dynamical System ◽  
Convergence Analysis ◽  
System Perspective ◽  
Mirror Descent ◽  
Integral Feedback

scholarly journals Potential Well in Poincaré Recurrence

Entropy ◽  
2021 ◽  
Vol 23 (3) ◽  
pp. 379
Author(s):  
Miguel Abadi ◽  
Vitor Amorim ◽  
Sandro Gallo
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Stochastic Processes ◽  
Recurrence Time ◽  
Potential Well ◽  
Exponential Approximation ◽  
Mixing Processes ◽  
System Perspective ◽  
Return Times ◽  
Error Terms

From a physical/dynamical system perspective, the potential well represents the proportional mass of points that escape the neighbourhood of a given point. In the last 20 years, several works have shown the importance of this quantity to obtain precise approximations for several recurrence time distributions in mixing stochastic processes and dynamical systems. Besides providing a review of the different scaling factors used in the literature in recurrence times, the present work contributes two new results: (1) For ϕ-mixing and ψ-mixing processes, we give a new exponential approximation for hitting and return times using the potential well as the scaling parameter. The error terms are explicit and sharp. (2) We analyse the uniform positivity of the potential well. Our results apply to processes on countable alphabets and do not assume a complete grammar.

Towards a More Holistic Approach to Quality Improvements in Aluminium Die Casting

2009 ◽  
Vol 618-619 ◽  
pp. 341-344
Author(s):  
Sandrine Zanna ◽  
Yakov Frayman ◽  
Bruce Gunn ◽  
Saeid Nahavandi
Keyword(s):  
Dynamical System ◽  
System Theory ◽  
Die Casting ◽  
Holistic Approach ◽  
Natural Process ◽  
Dynamical System Theory ◽  
Quality Improvements ◽  
System Perspective ◽  
Porosity Defects ◽  
Natural Equilibrium

This work evaluates the feasibility of using a holistic approach, based on dynamical system theory, to reduce porosity defects in high pressure aluminum die casting. Quality improvements, from a dynamical system perspective mean the ability to move the die casting process out of its natural equilibrium to a more beneficial state and the ability to maintain this new process state. This more beneficial state may be achieved in several ways. One way is to increase the amount of forcing to overcome natural process resistance. This forcing approach is represented by typical continuous intervention policy, with modifications in die/part design and/or process parameters. An alternative approach is to reduce the amount of natural process resistance, in particular the amount of process disturbance, allowing the process to move out of its natural equilibrium with much less forcing. This alternative uses the self-regulating ability of dynamical systems thus decreasing the amount of human intervention required. In this respect, the influence of vacuum on time on chattering at the first stage of the casting shot was identified as a good process candidate for testing using dynamical system theory. A significant reduction in porosity defects was achieved, which also set the process on a path of slow but consistent self-improvement.

scholarly journals Cosmological dynamics of brane gravity: A global dynamical system perspective

2018 ◽  
Vol 98 (8) ◽  
Author(s):  
Hmar Zonunmawia ◽  
Wompherdeiki Khyllep ◽  
Jibitesh Dutta ◽  
Laur Järv
Keyword(s):  
Dynamical System ◽  
System Perspective ◽  
Brane Gravity

scholarly journals A Switching Hybrid Dynamical System: Toward Understanding Complex Interpersonal Behavior

2018 ◽  
Vol 9 (1) ◽  
pp. 39
Author(s):  
Yuji Yamamoto ◽  
Akifumi Kijima ◽  
Motoki Okumura ◽  
Keiko Yokoyama ◽  
Kazutoshi Gohara
Keyword(s):  
Dynamical System ◽  
Phase Synchronization ◽  
Transition Probabilities ◽  
Discrete Dynamical System ◽  
Interpersonal Behavior ◽  
Switching Behavior ◽  
System Perspective ◽  
Hybrid Dynamics ◽  
Switching Dynamics ◽  
Coordination Patterns

Complex human behavior, including interlimb and interpersonal coordination, has been studied from a dynamical system perspective. We review the applications of a dynamical system approach to a sporting activity, which includes continuous, discrete, and switching dynamics. Continuous dynamics identified switching between in- and anti-phase synchronization, controlled by an interpersonal distance of 0.1 m during expert kendo matches, using a relative phase analysis. In the discrete dynamical system, return map analysis was applied to the time series of movements during kendo matches. Offensive and defensive maneuvers were classified as six coordination patterns, that is, attractors and repellers. Furthermore, these attractors and repellers exhibited two discrete states. Then, state transition probabilities were calculated based on the two states, which clarified the coordination patterns and switching behavior. We introduced switching dynamics with temporal inputs to clarify the simple rules underlying the complex behavior corresponding to switching inputs in a striking action as a non-autonomous system. As a result, we determined that the time evolution of the striking action was characterized as fractal-like movement patterns generated by a simple Cantor set rule with rotation. Finally, we propose a switching hybrid dynamics to understand both court-net sports, as strongly coupled interpersonal competition, and weakly coupled sports, such as martial arts.

Dynamical system perspective on turbo codes

1998 ◽  
Vol 34 (8) ◽  
pp. 754 ◽  
Author(s):  
S.A. Barbulescu
Keyword(s):  
Dynamical System ◽  
Turbo Codes ◽  
System Perspective

scholarly journals Flexible sensorimotor computations through rapid reconfiguration of cortical dynamics

2018 ◽  
Author(s):  
Evan D. Remington ◽  
Devika Narain ◽  
Eghbal A. Hosseini ◽  
Mehrdad Jazayeri
Keyword(s):  
Dynamical System ◽  
Initial Conditions ◽  
Control Strategies ◽  
Brain Activity ◽  
Specific Stimulus ◽  
System Perspective ◽  
Stimulus Response ◽  
Dorsomedial Frontal Cortex ◽  
Internal States ◽  
Context Specific

SummarySensorimotor computations can be flexibly adjusted according to internal states and contextual inputs. The mechanisms supporting this flexibility are not understood. Here, we tested the utility of a dynamical system perspective to approach this problem. In a dynamical system whose state is determined by interactions among neurons, computations can be rapidly and flexibly reconfigured by controlling the system‘s inputs and initial conditions. To investigate whether the brain employs such control strategies, we recorded from the dorsomedial frontal cortex (DMFC) of monkeys trained to measure time intervals and subsequently produce timed motor responses according to multiple context-specific stimulus-response rules. Analysis of the geometry of neural states revealed a control mechanism that relied on the system‘s inputs and initial conditions. A tonic input specified by the behavioral context adjusted firing rates throughout each trial, while the dynamics in the measurement epoch allowed the system to establish initial conditions for the ensuing production epoch. This initial condition in turn set the speed of neural dynamics in the production epoch allowing the animal to aim for the target interval. These results provide evidence that the language of dynamical systems can be used to parsimoniously link brain activity to sensorimotor computations.

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