scholarly journals Dynamical system model predicts when social learners impair collective performance

2021 ◽  
Vol 118 (35) ◽  
pp. e2106292118
Author(s):  
Vicky Chuqiao Yang ◽  
Mirta Galesic ◽  
Harvey McGuinness ◽  
Ani Harutyunyan
Keyword(s):  
Dynamical System ◽  
Initial Conditions ◽  
Cognitive Strategies ◽  
Collective Decision ◽  
System Model ◽  
Critical Threshold ◽  
Mathematical Framework ◽  
Complex Interactions ◽  
Decision Outcomes ◽  
Collective Performance

A key question concerning collective decisions is whether a social system can settle on the best available option when some members learn from others instead of evaluating the options on their own. This question is challenging to study, and previous research has reached mixed conclusions, because collective decision outcomes depend on the insufficiently understood complex system of cognitive strategies, task properties, and social influence processes. This study integrates these complex interactions together in one general yet partially analytically tractable mathematical framework using a dynamical system model. In particular, it investigates how the interplay of the proportion of social learners, the relative merit of options, and the type of conformity response affect collective decision outcomes in a binary choice. The model predicts that, when the proportion of social learners exceeds a critical threshold, a bistable state appears in which the majority can end up favoring either the higher- or lower-merit option, depending on fluctuations and initial conditions. Below this threshold, the high-merit option is chosen by the majority. The critical threshold is determined by the conformity response function and the relative merits of the two options. The study helps reconcile disagreements about the effect of social learners on collective performance and proposes a mathematical framework that can be readily adapted to extensions investigating a wider variety of dynamics.

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.

scholarly journals An Organizing Principle for the Water-Energy-Food Nexus

2020 ◽  
Vol 12 (19) ◽  
pp. 8135
Author(s):  
Chad W. Higgins ◽  
Majdi Abou Najm
Keyword(s):  
Climate Change ◽  
Research Community ◽  
Future Generations ◽  
Mathematical Representation ◽  
Mathematical Framework ◽  
Natural Processes ◽  
Anthropogenic Inputs ◽  
Complex Interactions ◽  
Management Concept ◽  
Growth Habits

The nexus between water, energy, and food has recently evolved as a resource-management concept to deal with this intimately interwoven set of resources, their complex interactions, and the growing and continuously changing internal and external set of influencing factors, including climate change, population growth, habits and lifestyles alternations, and the dynamic prices of water, energy, and food. While an intriguing concept, the global research community is yet to identify a unifying conceptual and mathematical framework capable of adapting to integrate gathered knowledge and ensuring inclusivity by accounting for all significant interactions and feedbacks (including natural processes and anthropogenic inputs) within all nexus domains. We present an organizing roadmap for a conceptual and mathematical representation of the nexus. Our hope is that this representation will organize the nexus research and formalize a way for a generalizable framework that can be used to advance our understanding of those complex interactions, with hope that such an approach will lead to a more resilient future with sustained resources for the future generations.

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.

scholarly journals Rational time investment during collective decision making in Temnothorax ants

2019 ◽  
Vol 15 (10) ◽  
pp. 20190542 ◽  
Author(s):  
Takao Sasaki ◽  
Benjamin Stott ◽  
Stephen C. Pratt
Keyword(s):  
Decision Making ◽  
Collective Decision ◽  
Collective Decision Making ◽  
Ant Colonies ◽  
Temnothorax Albipennis ◽  
Time Investment ◽  
Decision Outcomes ◽  
Nest Site Choice ◽  
The Difference ◽  
Underlying Mechanisms

The study of rational choice in humans and other animals typically focuses on decision outcomes, but rationality also applies to decision latencies, especially when time is scarce and valuable. For example, the smaller the difference in quality between two options, the faster a rational actor should decide between them. This is because the consequences of choosing the inferior option are less severe if the options are similar. Experiments have shown, however, that humans irrationally spend more time choosing between similar options. In this study, we assessed the rationality of time investment during nest-site choice by the rock ant, Temnothorax albipennis . Previous studies have shown that collective decision-making allows ant colonies to avoid certain irrational errors. Here we show that the same is true for time investment. Individual ants, like humans, irrationally took more time to complete an emigration when choosing between two similar nests than when choosing between two less similar nests. Whole colonies, by contrast, rationally made faster decisions when the options were more similar. We discuss the underlying mechanisms of decision-making in individuals and colonies and how they lead to irrational and rational time investment, respectively.

scholarly journals DAMAGE SPREADING IN THE BAK–SNEPPEN MODEL: SENSITIVITY TO THE INITIAL CONDITIONS AND EQUILIBRATION DYNAMICS

2003 ◽  
Vol 14 (06) ◽  
pp. 805-814 ◽  
Author(s):  
UGUR TIRNAKLI ◽  
MARCELO L. LYRA
Keyword(s):  
Distance Measure ◽  
Hamming Distance ◽  
Initial Conditions ◽  
Biological Evolution ◽  
Finite Size ◽  
Continuous Phase ◽  
Mathematical Framework ◽  
Damage Spreading ◽  
Time Dynamics ◽  
Equilibrium Configurations

The short-time and long-time dynamics of the Bak–Sneppen model of biological evolution are investigated using the damage spreading technique. By defining a proper Hamming distance measure, we are able to make it exhibit an initial power-law growth which, for finite size systems, is followed by a decay towards equilibrium. In this sense, the dynamics of self-organized critical states is shown to be similar to the one observed at the usual critical point of continuous phase transitions and at the onset of chaos of nonlinear low-dimensional dynamical maps. The transient, pre-asymptotic and asymptotic exponential relaxation of the Hamming distance between two initially uncorrelated equilibrium configurations is also shown to be fit within a single mathematical framework.

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