Neural Population Dynamics Modeled by Mean-Field Graphs

2011 ◽  
Author(s):  
Robert Kozma ◽  
Marko Puljic ◽  
Theodore E. Simos ◽  
George Psihoyios ◽  
Ch. Tsitouras ◽  
...  
Keyword(s):  
Population Dynamics ◽  
Mean Field ◽  
Neural Population

scholarly journals Population dynamics with spatial structure and an Allee effect

2020 ◽  
Author(s):  
Anudeep Surendran ◽  
Michael Plank ◽  
Matthew Simpson
Keyword(s):  
Population Dynamics ◽  
Spatial Structure ◽  
Short Range ◽  
Allee Effect ◽  
Mean Field ◽  
Mean Field Approximation ◽  
Continuum Approximation ◽  
Spatial Moment ◽  
Mean Field Models ◽  
The Mean

AbstractAllee effects describe populations in which long-term survival is only possible if the population density is above some threshold level. A simple mathematical model of an Allee effect is one where initial densities below the threshold lead to population extinction, whereas initial densities above the threshold eventually asymptote to some positive carrying capacity density. Mean field models of population dynamics neglect spatial structure that can arise through short-range interactions, such as short-range competition and dispersal. The influence of such non mean-field effects has not been studied in the presence of an Allee effect. To address this we develop an individual-based model (IBM) that incorporates both short-range interactions and an Allee effect. To explore the role of spatial structure we derive a mathematically tractable continuum approximation of the IBM in terms of the dynamics of spatial moments. In the limit of long-range interactions where the mean-field approximation holds, our modelling framework accurately recovers the mean-field Allee threshold. We show that the Allee threshold is sensitive to spatial structure that mean-field models neglect. For example, we show that there are cases where the mean-field model predicts extinction but the population actually survives and vice versa. Through simulations we show that our new spatial moment dynamics model accurately captures the modified Allee threshold in the presence of spatial structure.

scholarly journals Learning stable, regularised latent models of neural population dynamics

2012 ◽  
Vol 23 (1-2) ◽  
pp. 24-47 ◽  
Author(s):  
Lars Buesing ◽  
Jakob H. Macke ◽  
Maneesh Sahani
Keyword(s):  
Population Dynamics ◽  
Neural Population ◽  
Latent Models

scholarly journals Low Dimensionality, High Robustness in Neural Population Dynamics

Neuron ◽  
2019 ◽  
Vol 103 (2) ◽  
pp. 177-179 ◽  
Author(s):  
Román Rossi-Pool ◽  
Ranulfo Romo
Keyword(s):  
Population Dynamics ◽  
Neural Population ◽  
Low Dimensionality

Transition Dynamics of Generalized Periodic Discharges Observed in EEG Waveforms

2019 ◽  
Vol 29 (13) ◽  
pp. 1930038
Author(s):  
Honghui Zhang ◽  
Zichen Deng ◽  
Shuang Liu
Keyword(s):  
Ampa Receptors ◽  
Gaba Receptors ◽  
Mean Field ◽  
Neural Population ◽  
Model Parameters ◽  
Synaptic Connections ◽  
Mean Field Model ◽  
Metabolic Encephalopathy ◽  
Periodic Discharges ◽  
Mode Transitions

Generalized periodic discharges (GPD) are generalized waveforms that recur with a relatively uniform morphology and duration observed in EEG recordings of many types of metabolic encephalopathy, which are often referred to as epileptiform. In this paper, we try to link these spatiotemporal electrocortical activities and significant attributes of cortex based on Liley’s mean field model, and seek possible generation mechanisms of GPD rhythms from several factors. To these ends, the dynamical properties of simulated EEG consistent with neurophysiological features of human cortex are investigated, among which GPD patterns are our focus. Firstly, with different value sets of model parameters, we reproduce some typical simulation waveforms which are analogous to mammalian normal or abnormal brain activities detected by EEG. Or in other words, we put more emphasis on brain waveforms of GPD states, normal states, and low firing rate states in our numerical simulations, and mode transitions among different firing states are our main interests. Secondly, through analysis of maximum Lyapunov exponents and frequency spectrum, we give several mode transitions by varying synaptic connections between excitatory and inhibitory populations, which support the conjecture that selective changes of synaptic connections can trigger GPD states, such as in excitatory (AMPA receptors) and inhibitory neurotransmitters (GABA receptors). Thirdly, we stress the importance of time delay on neural population connections and find that they are free to transfer among different firing modes with appropriate time delays. Furthermore, considering the effects of external inputs to cerebral cortex, we verify that stimulation can lead to good controls on GPD patterns, including facilitation and elimination. Finally, we show that more dynamical rhythms can be produced when taking into account the cortico-cortical connections. These modeling results are expected to shed light into the pathophysiological mechanisms of GPD modes from a theoretical viewpoint.

scholarly journals Thirst regulates motivated behavior through modulation of brainwide neural population dynamics

Science ◽  
2019 ◽  
Vol 364 (6437) ◽  
Author(s):  
William E. Allen ◽  
Michael Z. Chen ◽  
Nandini Pichamoorthy ◽  
Rebecca H. Tien ◽  
Marius Pachitariu ◽  
...  
Keyword(s):  
Population Dynamics ◽  
Neural Population ◽  
Motivated Behavior

scholarly journals Neural Population Dynamics Underlying Motor Learning Transfer

Neuron ◽  
2018 ◽  
Vol 97 (5) ◽  
pp. 1177-1186.e3 ◽  
Author(s):  
Saurabh Vyas ◽  
Nir Even-Chen ◽  
Sergey D. Stavisky ◽  
Stephen I. Ryu ◽  
Paul Nuyujukian ◽  
...  
Keyword(s):  
Population Dynamics ◽  
Motor Learning ◽  
Learning Transfer ◽  
Neural Population
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