Neural Sequences as an Optimal Dynamical Regime for the Readout of Time

2020 ◽  
Author(s):  
Shanglin Zhou ◽  
Sotiris Masmanidis ◽  
Dean Buonomano
Keyword(s):  
Dynamical Regime ◽  
Neural Sequences

scholarly journals Neural Sequences as an Optimal Dynamical Regime for the Readout of Time

Neuron ◽  
2020 ◽  
Vol 108 (4) ◽  
pp. 651-658.e5 ◽  
Author(s):  
Shanglin Zhou ◽  
Sotiris C. Masmanidis ◽  
Dean V. Buonomano
Keyword(s):  
Dynamical Regime ◽  
Neural Sequences

scholarly journals Reconstruction scheme for excitatory and inhibitory dynamics with quenched disorder: application to zebrafish imaging

2021 ◽  
Author(s):  
Lorenzo Chicchi ◽  
Gloria Cecchini ◽  
Ihusan Adam ◽  
Giuseppe de Vito ◽  
Roberto Livi ◽  
...  
Keyword(s):  
Structural Information ◽  
Activity Patterns ◽  
Synthetic Data ◽  
Light Sheet ◽  
Time Lapse ◽  
Inhibitory Neurons ◽  
Mean Field Approximation ◽  
Directed Network ◽  
Dynamical Regime ◽  
Power Law Distribution

AbstractAn inverse procedure is developed and tested to recover functional and structural information from global signals of brains activity. The method assumes a leaky-integrate and fire model with excitatory and inhibitory neurons, coupled via a directed network. Neurons are endowed with a heterogenous current value, which sets their associated dynamical regime. By making use of a heterogenous mean-field approximation, the method seeks to reconstructing from global activity patterns the distribution of in-coming degrees, for both excitatory and inhibitory neurons, as well as the distribution of the assigned currents. The proposed inverse scheme is first validated against synthetic data. Then, time-lapse acquisitions of a zebrafish larva recorded with a two-photon light sheet microscope are used as an input to the reconstruction algorithm. A power law distribution of the in-coming connectivity of the excitatory neurons is found. Local degree distributions are also computed by segmenting the whole brain in sub-regions traced from annotated atlas.

scholarly journals Flux expulsion with dynamics

2016 ◽  
Vol 791 ◽  
pp. 568-588 ◽  
Author(s):  
Andrew D. Gilbert ◽  
Joanne Mason ◽  
Steven M. Tobias
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Lorentz Force ◽  
Differential Rotation ◽  
Time Scale ◽  
Scaling Laws ◽  
Dynamical Regime ◽  
Kinematic Evolution ◽  
Flux Expulsion ◽  
The Magnetic Field

In the process of flux expulsion, a magnetic field is expelled from a region of closed streamlines on a $TR_{m}^{1/3}$ time scale, for magnetic Reynolds number $R_{m}\gg 1$ ($T$ being the turnover time of the flow). This classic result applies in the kinematic regime where the flow field is specified independently of the magnetic field. A weak magnetic ‘core’ is left at the centre of a closed region of streamlines, and this decays exponentially on the $TR_{m}^{1/2}$ time scale. The present paper extends these results to the dynamical regime, where there is competition between the process of flux expulsion and the Lorentz force, which suppresses the differential rotation. This competition is studied using a quasi-linear model in which the flow is constrained to be axisymmetric. The magnetic Prandtl number $R_{m}/R_{e}$ is taken to be small, with $R_{m}$ large, and a range of initial field strengths $b_{0}$ is considered. Two scaling laws are proposed and confirmed numerically. For initial magnetic fields below the threshold $b_{core}=O(UR_{m}^{-1/3})$, flux expulsion operates despite the Lorentz force, cutting through field lines to result in the formation of a central core of magnetic field. Here $U$ is a velocity scale of the flow and magnetic fields are measured in Alfvén units. For larger initial fields the Lorentz force is dominant and the flow creates Alfvén waves that propagate away. The second threshold is $b_{dynam}=O(UR_{m}^{-3/4})$, below which the field follows the kinematic evolution and decays rapidly. Between these two thresholds the magnetic field is strong enough to suppress differential rotation, leaving a magnetically controlled core spinning in solid body motion, which then decays slowly on a time scale of order $TR_{m}$.

scholarly journals What is the dynamical regime of cerebral cortex?

Neuron ◽  
2021 ◽  
Author(s):  
Yashar Ahmadian ◽  
Kenneth D. Miller
Keyword(s):  
Cerebral Cortex ◽  
Dynamical Regime

scholarly journals Method to characterize directional changes in Arctic sea ice drift and associated deformation due to synoptic atmospheric variations using Lagrangian dispersion statistics

2017 ◽  
Vol 11 (4) ◽  
pp. 1707-1731 ◽  
Author(s):  
Jennifer V. Lukovich ◽  
Cathleen A. Geiger ◽  
David G. Barber
Keyword(s):  
Sea Ice ◽  
Single Particle ◽  
Weather Forecasting ◽  
Particle Dispersion ◽  
Arctic Sea Ice ◽  
Maximum Pressure ◽  
Dynamical Regime ◽  
Scaling Exponent ◽  
Ice Drift ◽  
Sea Ice Drift

Abstract. A framework is developed to assess the directional changes in sea ice drift paths and associated deformation processes in response to atmospheric forcing. The framework is based on Lagrangian statistical analyses leveraging particle dispersion theory which tells us whether ice drift is in a subdiffusive, diffusive, ballistic, or superdiffusive dynamical regime using single-particle (absolute) dispersion statistics. In terms of sea ice deformation, the framework uses two- and three-particle dispersion to characterize along- and across-shear transport as well as differential kinematic parameters. The approach is tested with GPS beacons deployed in triplets on sea ice in the southern Beaufort Sea at varying distances from the coastline in fall of 2009 with eight individual events characterized. One transition in particular follows the sea level pressure (SLP) high on 8 October in 2009 while the sea ice drift was in a superdiffusive dynamic regime. In this case, the dispersion scaling exponent (which is a slope between single-particle absolute dispersion of sea ice drift and elapsed time) changed from superdiffusive (α ∼ 3) to ballistic (α ∼ 2) as the SLP was rounding its maximum pressure value. Following this shift between regimes, there was a loss in synchronicity between sea ice drift and atmospheric motion patterns. While this is only one case study, the outcomes suggest similar studies be conducted on more buoy arrays to test momentum transfer linkages between storms and sea ice responses as a function of dispersion regime states using scaling exponents. The tools and framework developed in this study provide a unique characterization technique to evaluate these states with respect to sea ice processes in general. Application of these techniques can aid ice hazard assessments and weather forecasting in support of marine transportation and indigenous use of near-shore Arctic areas.

scholarly journals Stimulus-Driven and Spontaneous Dynamics in Excitatory-Inhibitory Recurrent Neural Networks for Sequence Representation

2021 ◽  
pp. 1-43
Author(s):  
Alfred Rajakumar ◽  
John Rinzel ◽  
Zhe S. Chen
Keyword(s):  
Neural Networks ◽  
Recurrent Neural Networks ◽  
Connectivity Matrix ◽  
Motor Tasks ◽  
Neural Representations ◽  
Input Signals ◽  
Sequence Representation ◽  
The Stability ◽  
Dynamic Attractors ◽  
Neural Sequences

Abstract Recurrent neural networks (RNNs) have been widely used to model sequential neural dynamics (“neural sequences”) of cortical circuits in cognitive and motor tasks. Efforts to incorporate biological constraints and Dale's principle will help elucidate the neural representations and mechanisms of underlying circuits. We trained an excitatory-inhibitory RNN to learn neural sequences in a supervised manner and studied the representations and dynamic attractors of the trained network. The trained RNN was robust to trigger the sequence in response to various input signals and interpolated a time-warped input for sequence representation. Interestingly, a learned sequence can repeat periodically when the RNN evolved beyond the duration of a single sequence. The eigenspectrum of the learned recurrent connectivity matrix with growing or damping modes, together with the RNN's nonlinearity, were adequate to generate a limit cycle attractor. We further examined the stability of dynamic attractors while training the RNN to learn two sequences. Together, our results provide a general framework for understanding neural sequence representation in the excitatory-inhibitory RNN.

Non-Smooth Dynamics and Non-Classical Bifurcations in Impulse-Impact Oscillators

1999 ◽  
Author(s):  
Stefano Lenci ◽  
Giuseppe Rega
Keyword(s):  
Local Level ◽  
Basins Of Attraction ◽  
Dynamical Regime ◽  
Impact Oscillator ◽  
Stable And Unstable Manifolds ◽  
Impact Oscillators ◽  
Unstable Manifolds ◽  
Local And Global Bifurcations ◽  
Initial Description ◽  
Smooth Dynamics

Abstract Some aspects of the nonlinear dynamics of an impulse-impact oscillator are investigated. After an initial description of the prototype mechanical model used to illustrate the results, attention is paid to the classical local and global bifurcations which are at the base of the changes of dynamical regime. Some non-classical phenomena due to the particular nature of the investigated system are then considered. At a local level, it is shown that periodic solutions may appear (or disappear) through a non-classical bifurcation which involves synchronization of impulses and impacts. Similarities and differences with the classical bifurcations are discussed. At a global level, the effects of the non-continuity of the orbits in the phase space on the basins of attraction topology are investigated. It is shown how this property is at the base of a non-classical homoclinic bifurcation where the homoclinic points disappear after the first touch between the stable and unstable manifolds.

The observation of different aerosols types in the Mount Etna environment and their relative and mutual impacts on local radiative balance

2021 ◽  
Author(s):  
Pasquale Sellitto ◽  
Giuseppe Salerno ◽  
Simona Scollo ◽  
Alcide Giorgio di Sarra ◽  
Antonella Boselli ◽  
...  
Keyword(s):  
Spatial Scales ◽  
Source Parameters ◽  
Mount Etna ◽  
Volcanic Plume ◽  
Dynamical Regime ◽  
Radiative Balance ◽  
Volcanic Aerosols ◽  
Aerosol Types ◽  
Lidar Observations

<p>The EPL-RADIO (Etna Plume Lab - Radioactive Aerosols and other source parameters for better atmospheric Dispersion and Impact estimatiOns) and EPL-REFLECT (near-source estimations of Radiative EFfects of voLcanic aErosols for Climate and air quality sTudies) projects, funded by the EC Horizon2020 ENVRIplus and EUROVOLC Transnational Access to European Observatories programmes, aim to advance the understanding of Mount Etna as a persistent source of atmospheric aerosols and its impact on the  radiative budget at proximal to regional spatial scales. Research was tackled by carrying out three campaigns in the summers of 2016, 2017 and 2019 to observe the volcanic plume produced by passive degassing, proximally and distally from the summit craters, using a wide array of remote sensing and in situ instruments. Diverse data are collected to explore the link of inner degassing mechanisms to the characterisation of near-source aerosol physicochemical properties and subsequent impacts on the atmosphere, environment and regional climate system.</p><p>The results of the three campaigns have shown that the volcanic plume emitted by Mount Etna often mixes with aerosols of different origins generating a complex layered pattern. Frequent mineral dust transport events were observed by both LiDAR observations located at Serra La Nave (~7 km south-west from summit craters) and at a medium-term radiometric station, equipped with a Multi-Filter Rotating Shadowband Radiometer (MFRSR), and other instruments located at Milo (~10 km eastwards from the craters). LiDAR observations also allowed to study the coexistence of volcanic aerosols and biomass burning particles from local to more distal smoke plumes transports (like for the well-documented large fires from continental southern Italy in July 2017). In situ filter and optical particles counter measurements confirmed the presence of dust at Milo. The interaction/mixing among volcanic, wildfire, and dust aerosols occurs in an overall dynamical regime which appears to be dominated by sea breeze, which is strengthened by the presence of the dark volcanic lava flanks. Photolysis process also possibly play a role in determining the daily evolution of the aerosol plume.</p><p>The sources of these different aerosol types are studied in detail using Lagrangian trajectories and meteorological data. Off-line radiative transfer calculations, using EPL-RADIO/REFLECT observations as input data, are used to estimate the relative radiative impact of the different aerosol types with respect to the background passive-degassing aerosols coming from Mount Etna.</p>

The Road to Chaos by Time-Asymmetric Hebbian Learning in Recurrent Neural Networks

2007 ◽  
Vol 19 (1) ◽  
pp. 80-110 ◽  
Author(s):  
Colin Molter ◽  
Utku Salihoglu ◽  
Hugues Bersini
Keyword(s):  
Supervised Learning ◽  
Hebbian Learning ◽  
Learning Algorithm ◽  
Initial Conditions ◽  
A Priori ◽  
Computational Cost ◽  
Chaotic Regime ◽  
Dynamical Regime ◽  
New Form ◽  
The Impact

This letter aims at studying the impact of iterative Hebbian learning algorithms on the recurrent neural network's underlying dynamics. First, an iterative supervised learning algorithm is discussed. An essential improvement of this algorithm consists of indexing the attractor information items by means of external stimuli rather than by using only initial conditions, as Hopfield originally proposed. Modifying the stimuli mainly results in a change of the entire internal dynamics, leading to an enlargement of the set of attractors and potential memory bags. The impact of the learning on the network's dynamics is the following: the more information to be stored as limit cycle attractors of the neural network, the more chaos prevails as the background dynamical regime of the network. In fact, the background chaos spreads widely and adopts a very unstructured shape similar to white noise. Next, we introduce a new form of supervised learning that is more plausible from a biological point of view: the network has to learn to react to an external stimulus by cycling through a sequence that is no longer specified a priori. Based on its spontaneous dynamics, the network decides “on its own” the dynamical patterns to be associated with the stimuli. Compared with classical supervised learning, huge enhancements in storing capacity and computational cost have been observed. Moreover, this new form of supervised learning, by being more “respectful” of the network intrinsic dynamics, maintains much more structure in the obtained chaos. It is still possible to observe the traces of the learned attractors in the chaotic regime. This complex but still very informative regime is referred to as “frustrated chaos.”

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