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.

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.

Dynamical Constraints on Using Precise Spike Timing to Compute in Recurrent Cortical Networks

2008 ◽  
Vol 20 (4) ◽  
pp. 974-993 ◽  
Author(s):  
Arunava Banerjee ◽  
Peggy Seriès ◽  
Alexandre Pouget
Keyword(s):  
Dynamical System ◽  
Initial Conditions ◽  
Internal State ◽  
Spike Timing ◽  
Spiking Neurons ◽  
Spatiotemporal Patterns ◽  
Cortical Networks ◽  
Temporal Precision ◽  
Cortical Areas ◽  
Dynamical Constraints

Several recent models have proposed the use of precise timing of spikes for cortical computation. Such models rely on growing experimental evidence that neurons in the thalamus as well as many primary sensory cortical areas respond to stimuli with remarkable temporal precision. Models of computation based on spike timing, where the output of the network is a function not only of the input but also of an independently initializable internal state of the network, must, however, satisfy a critical constraint: the dynamics of the network should not be sensitive to initial conditions. We have previously developed an abstract dynamical system for networks of spiking neurons that has allowed us to identify the criterion for the stationary dynamics of a network to be sensitive to initial conditions. Guided by this criterion, we analyzed the dynamics of several recurrent cortical architectures, including one from the orientation selectivity literature. Based on the results, we conclude that under conditions of sustained, Poisson-like, weakly correlated, low to moderate levels of internal activity as found in the cortex, it is unlikely that recurrent cortical networks can robustly generate precise spike trajectories, that is, spatiotemporal patterns of spikes precise to the millisecond timescale.

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 Soil nutrient cycles as a nonlinear dynamical system

2004 ◽  
Vol 11 (5/6) ◽  
pp. 589-598 ◽  
Author(s):  
S. Manzoni ◽  
A. Porporato ◽  
P. D'Odorico ◽  
F. Laio ◽  
I. Rodriguez-Iturbe
Keyword(s):  
Dynamical System ◽  
Initial Conditions ◽  
Nonlinear Dynamical System ◽  
Soil Nutrient ◽  
Steady State Solution ◽  
Basins Of Attraction ◽  
Climatic Conditions ◽  
Stable Node ◽  
Nutrient Cycles ◽  
Stable Focus

Abstract. An analytical model for the soil carbon and nitrogen cycles is studied from the dynamical system point of view. Its main nonlinearities and feedbacks are analyzed by considering the steady state solution under deterministic hydro-climatic conditions. It is shown that, changing hydro-climatic conditions, the system undergoes dynamical bifurcations, shifting from a stable focus to a stable node and back to a stable focus when going from dry, to well-watered, and then to saturated conditions, respectively. An alternative degenerate solution is also found in cases when the system can not sustain decomposition under steady external conditions. Different basins of attraction for "normal" and "degenerate" solutions are investigated as a function of the system initial conditions. Although preliminary and limited to the specific form of the model, the present analysis points out the importance of nonlinear dynamics in the soil nutrient cycles and their possible complex response to hydro-climatic forcing.

Behaviorism and Developments in Instructional Design and Technology

2011 ◽  
pp. 153-172 ◽  
Author(s):  
Irene Chen
Keyword(s):  
Instructional Design ◽  
Mathematical Analysis ◽  
Black Box ◽  
Design And Technology ◽  
Thought Processes ◽  
Specific Stimulus ◽  
Learning To Read ◽  
Stimulus Response ◽  
Observable Change ◽  
The Mind

The theory of behaviorism concentrates on the study of overt behaviors that can be observed and measured (Good & Brophy, 1990). In general, the behavior theorists view the mind as a “black box” in the sense that response to stimulus can be observed quantitatively, ignoring the possibility of thought processes occurring in the mind. Behaviorists believe that learning takes place as the result of a response that follows on a specific stimulus. By repeating the S-R (stimulus-response) cycle, the organism (may it be an animal or human) is conditioned into repeating the response whenever the same stimulus is present. The behavioral emphasis on breaking down complex tasks, such as learning to read, into subskills that are taught separately, has a powerful influence on instructional design. Behaviors can be modified, and learning is measured by observable change in behavior. The behavior theorists emphasize the need of objectivity, which leads to great accentuation of statistical and mathematical analysis.

scholarly journals Bifurcation and global dynamical behavior of the f(T) theory

2014 ◽  
Vol 29 (07) ◽  
pp. 1450033 ◽  
Author(s):  
Chao-Jun Feng ◽  
Xin-Zhou Li ◽  
Li-Yan Liu
Keyword(s):  
Dynamical System ◽  
Critical Points ◽  
Initial Conditions ◽  
Dynamical Behavior ◽  
Nonlinear Effects ◽  
Local Analysis ◽  
Local Method ◽  
Initial Values ◽  
Bifurcation Phenomenon

Usually, in order to investigate the evolution of a theory, one may find the critical points of the system and then perform perturbations around these critical points to see whether they are stable or not. This local method is very useful when the initial values of the dynamical variables are not far away from the critical points. Essentially, the nonlinear effects are totally neglected in such kind of approach. Therefore, one cannot tell whether the dynamical system will evolute to the stable critical points or not when the initial values of the variables do not close enough to these critical points. Furthermore, when there are two or more stable critical points in the system, local analysis cannot provide the information on which the system will finally evolute to. In this paper, we have further developed the nullcline method to study the bifurcation phenomenon and global dynamical behavior of the f(T) theory. We overcome the shortcoming of local analysis. And, it is very clear to see the evolution of the system under any initial conditions.

Do tasks matter in task switching? Dissociating domain-general from context-specific brain activity

NeuroImage ◽  
2014 ◽  
Vol 99 ◽  
pp. 332-341 ◽  
Author(s):  
Paul S. Muhle-Karbe ◽  
Wouter De Baene ◽  
Marcel Brass
Keyword(s):  
Task Switching ◽  
Brain Activity ◽  
Context Specific

scholarly journals On the Solution of an Imprecisely Defined Nonlinear Time-Fractional Dynamical Model of Marriage

Mathematics ◽  
2019 ◽  
Vol 7 (8) ◽  
pp. 689 ◽  
Author(s):  
Rajarama Mohan Jena ◽  
Snehashish Chakraverty ◽  
Dumitru Baleanu
Keyword(s):  
Dynamical System ◽  
Fuzzy Numbers ◽  
Initial Conditions ◽  
Coupled System ◽  
Dynamical Model ◽  
Transform Method ◽  
System Parameters ◽  
Nonlinear Coupled System ◽  
Differential Transform ◽  
Fractional Dynamical System

The present paper investigates the numerical solution of an imprecisely defined nonlinear coupled time-fractional dynamical model of marriage (FDMM). Uncertainties are assumed to exist in the dynamical system parameters, as well as in the initial conditions that are formulated by triangular normalized fuzzy sets. The corresponding fractional dynamical system has first been converted to an interval-based fuzzy nonlinear coupled system with the help of a single-parametric gamma-cut form. Further, the double-parametric form (DPF) of fuzzy numbers has been used to handle the uncertainty. The fractional reduced differential transform method (FRDTM) has been applied to this transformed DPF system for obtaining the approximate solution of the FDMM. Validation of this method was ensured by comparing it with other methods taking the gamma-cut as being equal to one.

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