scholarly journals A Biophysical Counting Mechanism for Keeping Time

2021 ◽  
Author(s):  
Klavdia Zemlianova ◽  
Amitabha Bose ◽  
JOHN RINZEL
Keyword(s):  
Musical Instrument ◽  
Neural Mechanisms ◽  
Biophysical Model ◽  
Time Interval ◽  
Time Estimate ◽  
Counting Problem ◽  
One Dimensional ◽  
Neural Architecture ◽  
Central Clock ◽  
Open Question

The ability to estimate and produce appropriately timed responses is central to many behaviors including speaking, dancing, and playing a musical instrument. A classical framework for estimating or producing a time interval is the pacemaker-accumulator model in which pulses of a pacemaker are counted and compared to a stored representation. However, the neural mechanisms for how these pulses are counted remains an open question. The presence of noise and stochasticity further complicate the picture. We present a biophysical model of how to keep count of a pacemaker in the presence of various forms of stochasticity using a system of bistable Wilson-Cowan units asymmetrically connected in a one-dimensional array; all units receive the same input pulses from a central clock but only one unit is active at any point in time. With each pulse from the clock, the position of the activated unit changes thereby encoding the total number of pulses emitted by the clock. This neural architecture maps the counting problem into the spatial domain, which in turn translates count to a time estimate. We further extend the model to a hierarchical structure to be able to robustly achieve higher counts.

scholarly journals On the Numerical Simulation of HPDEs Using θ-Weighted Scheme and the Galerkin Method

Mathematics ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 78
Author(s):  
Haifa Bin Jebreen ◽  
Fairouz Tchier
Keyword(s):  
Differential Equation ◽  
Galerkin Method ◽  
Linear Ordinary Differential Equation ◽  
Time Interval ◽  
Hyperbolic Partial Differential Equation ◽  
Time Step ◽  
Numerical Examples ◽  
One Dimensional ◽  
The Stability ◽  
The Galerkin Method

Herein, an efficient algorithm is proposed to solve a one-dimensional hyperbolic partial differential equation. To reach an approximate solution, we employ the θ-weighted scheme to discretize the time interval into a finite number of time steps. In each step, we have a linear ordinary differential equation. Applying the Galerkin method based on interpolating scaling functions, we can solve this ODE. Therefore, in each time step, the solution can be found as a continuous function. Stability, consistency, and convergence of the proposed method are investigated. Several numerical examples are devoted to show the accuracy and efficiency of the method and guarantee the validity of the stability, consistency, and convergence analysis.

The Cognitive Neuroscience of Source Monitoring

2015 ◽  
Author(s):  
Karen J. Mitchell
Keyword(s):  
Source Monitoring ◽  
Brain Activity ◽  
Historical Context ◽  
Neural Mechanisms ◽  
Multiple Features ◽  
Neural Architecture ◽  
Big Picture ◽  
Key Issues ◽  
Neuroimaging Techniques

Source monitoring is a metamemory function that includes processes for encoding and organizing the content of memories, and processes that selectively revive, cumulate, and evaluate that content in the service of making attributions about the origin of the information (e.g., perception vs imagination). Neuroimaging techniques, especially functional magnetic resonance imaging (fMRI), are encouraging rapid developments in understanding the neural mechanisms supporting source monitoring. This chapter reviews current findings, placing them in historical context. It highlights key issues of particular relevance, including: neural reinstatement—the match between brain activity at encoding and later remembering; the role of lateral parietal cortex in cumulating multiple features and attending to information during remembering; functional specificity of the prefrontal cortex with respect to cognitive control; and identifying functional networks that support source monitoring. Suggestions are made for clarifying the big picture and increasing the specificity of our understanding of source monitoring and its neural architecture.

Long-Time Solutions to Heat-Conduction Transients with Time-Dependent Inputs

1980 ◽  
Vol 102 (1) ◽  
pp. 115-120 ◽  
Author(s):  
H. T. Ceylan ◽  
G. E. Myers
Keyword(s):  
Heat Conduction ◽  
Lower Cost ◽  
Piecewise Linear ◽  
Three Dimensional ◽  
Linear Functions ◽  
Time Dependent ◽  
Time Interval ◽  
Piecewise Linear Functions ◽  
One Dimensional ◽  
Long Time

An economical method for obtaining long-time solutions to one, two, or three-dimensional heat-conduction transients with time-dependent forcing functions is presented. The conduction problem is spatially discretized by finite differences or by finite elements to obtain a system of first-order ordinary differential equations. The time-dependent input functions are each approximated by continuous, piecewise-linear functions each having the same uniform time interval. A set of response coefficients is generated by which a long-time solution can be carried out with a considerably lower cost than for conventional methods. A one-dimensional illustrative example is included.

scholarly journals LQG Homing in a Finite Time Interval

2011 ◽  
Vol 2011 ◽  
pp. 1-3 ◽  
Author(s):  
Mario Lefebvre
Keyword(s):  
Optimal Control ◽  
Diffusion Process ◽  
First Passage Time ◽  
Passage Time ◽  
Time Interval ◽  
Finite Time Interval ◽  
First Passage ◽  
One Dimensional ◽  
Dimensional Diffusion ◽  
Fixed Constant

LetX(t)be a controlled one-dimensional diffusion process having constant infinitesimal variance. We consider the problem of optimally controllingX(t)until timeT(x)=min{T1(x),t1}, whereT1(x)is the first-passage time of the process to a given boundary andt1is a fixed constant. The optimal control is obtained explicitly in the particular case whenX(t)is a controlled Wiener process.

scholarly journals Directional reversals enable Myxococcus xanthus cells to produce collective one-dimensional streams during fruiting-body formation

2015 ◽  
Vol 12 (109) ◽  
pp. 20150049 ◽  
Author(s):  
Shashi Thutupalli ◽  
Mingzhai Sun ◽  
Filiz Bunyak ◽  
Kannappan Palaniappan ◽  
Joshua W. Shaevitz
Keyword(s):  
Fruiting Body ◽  
Myxococcus Xanthus ◽  
Three Dimensional ◽  
Spatial Location ◽  
Fruiting Body Formation ◽  
Body Formation ◽  
One Dimensional ◽  
Motile Cells ◽  
Cell Groups ◽  
Open Question

The formation of a collectively moving group benefits individuals within a population in a variety of ways. The surface-dwelling bacterium Myxococcus xanthus forms dynamic collective groups both to feed on prey and to aggregate during times of starvation. The latter behaviour, termed fruiting-body formation, involves a complex, coordinated series of density changes that ultimately lead to three-dimensional aggregates comprising hundreds of thousands of cells and spores. How a loose, two-dimensional sheet of motile cells produces a fixed aggregate has remained a mystery as current models of aggregation are either inconsistent with experimental data or ultimately predict unstable structures that do not remain fixed in space. Here, we use high-resolution microscopy and computer vision software to spatio-temporally track the motion of thousands of individuals during the initial stages of fruiting-body formation. We find that cells undergo a phase transition from exploratory flocking, in which unstable cell groups move rapidly and coherently over long distances, to a reversal-mediated localization into one-dimensional growing streams that are inherently stable in space. These observations identify a new phase of active collective behaviour and answer a long-standing open question in Myxococcus development by describing how motile cell groups can remain statistically fixed in a spatial location.

scholarly journals Asymptotical approximation of one dimensional gas dynamics problem

2013 ◽  
Vol 54 ◽  
Author(s):  
Aleksandras Krylovas ◽  
Olga Lavcel-Budko
Keyword(s):  
Asymptotic Approximation ◽  
Gas Dynamics ◽  
Resonant Interaction ◽  
Ideal Gas ◽  
Time Interval ◽  
One Dimensional ◽  
Long Time

We analyze nonlinear one dimensional gas dynamics system. The constructed asymptotic approximation which describes periodic acoustics waves resonant interaction is uniformly valid in the long time interval. The results allow to determine the resonance conditions for the emergence and summarizes the previous analyzed polytropic ideal-gas case.

scholarly journals A Model for Time Interval Learning in The Purkinje Cell

2018 ◽  
Author(s):  
Daniel Majoral ◽  
Ajmal Zemmar ◽  
Raul Vicente
Keyword(s):  
Purkinje Cell ◽  
Purkinje Cells ◽  
Classical Theory ◽  
Biophysical Model ◽  
Calcium Signal ◽  
Time Interval ◽  
Time Intervals ◽  
Delay Conditioning ◽  
Cerebellar Function ◽  
Experimental Findings

AbstractRecent experimental findings indicate that Purkinje cells in the cerebellum represent time intervals by mechanisms other than conventional synaptic weights. This finding adds to the theoretical and experimental observations suggesting the presence of intra-cellular mechanisms for adaptation and processing. To account for these experimental results we developed a biophysical model for time interval learning in a Purkinje cell. The numerical model focuses on a classical delay conditioning task (e.g. eyeblink conditioning) and relies on a few computational steps. In particular, the model posits the activation by the parallel fiber input of a local intra-cellular calcium store which can be modulated by intra-cellular pathways. The reciprocal interaction of the calcium signal with several proteins forming negative and positive feedback loops ensures that the timing of inhibition in the Purkinje cell anticipates the interval between parallel and climbing fiber inputs during training. We show that the model is able to learn along the 150-1000 ms interval range. Finally, we discuss how this model would allow the cerebellum to detect and generate specific spatio-temporal patterns, a classical theory for cerebellar function.Author SummaryThe prevailing view in neurosciences considers synaptic weights between neurons the determinant factor for learning and processing information in the nervous system. Theoretical considerations [1, 2] and experiments [3, 4] examined some potential limitations of this classical paradigm, pointing out that adaptation and computation might also have to rely on other mechanisms besides the learning of synaptic weights. Recent experimental findings [5–7] indicate that Purkinje cells in the cerebellum represent time intervals by mechanisms other than conventional synaptic weights. We propose here a biologically plausible model which complements the modification of synaptic weights for learning one time interval in one synapse of one Purkinje cell. In the model a calcium signal in a small domain keeps track of time. Several molecules read and modify this calcium signal to learn a time interval. We discuss how this model would allow the cerebellum to detect and generate specific patterns in space and time, a classical theory for cerebellar function proposed by Braitenberg [8, 9].

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