18,934 research outputs found
H2/H∞ output information-based disturbance attenuation for differential linear repetitive processes
Repetitive processes propagate information in two independent directions where the duration of one is finite. They pose control problems that cannot be solved by application of results for other classes of 2D systems. This paper develops controller design algorithms for differential linear processes, where information in one direction is governed by a matrix differential equation and in the other by a matrix discrete equation, in an H2/H∞ setting. The objectives are stabilization and disturbance attenuation, and the controller used is actuated by the process output and hence the use of a state observer is avoided
The Utility of Phase Models in Studying Neural Synchronization
Synchronized neural spiking is associated with many cognitive functions and
thus, merits study for its own sake. The analysis of neural synchronization
naturally leads to the study of repetitive spiking and consequently to the
analysis of coupled neural oscillators. Coupled oscillator theory thus informs
the synchronization of spiking neuronal networks. A crucial aspect of coupled
oscillator theory is the phase response curve (PRC), which describes the impact
of a perturbation to the phase of an oscillator. In neural terms, the
perturbation represents an incoming synaptic potential which may either advance
or retard the timing of the next spike. The phase response curves and the form
of coupling between reciprocally coupled oscillators defines the phase
interaction function, which in turn predicts the synchronization outcome
(in-phase versus anti-phase) and the rate of convergence. We review the two
classes of PRC and demonstrate the utility of the phase model in predicting
synchronization in reciprocally coupled neural models. In addition, we compare
the rate of convergence for all combinations of reciprocally coupled Class I
and Class II oscillators. These findings predict the general synchronization
outcomes of broad classes of neurons under both inhibitory and excitatory
reciprocal coupling.Comment: 18 pages, 5 figure
Decoupling and iterative approaches to the control of discrete linear repetitive processes
This paper reports new results on the analysis and control of discrete linear repetitive processes which are a distinct class of 2D discrete linear systems of both systems theoretic and applications interest. In particular, we first propose an extension to the basic state-space model to include a coupling term previously neglected but which arises in some applications and then proceed to show how computationally efficient control laws can be designed for this new model
The space-clamped Hodgkin-Huxley system with random synaptic input: inhibition of spiking by weak noise and analysis with moment equations
We consider a classical space-clamped Hodgkin-Huxley model neuron stimulated
by synaptic excitation and inhibition with conductances represented by
Ornstein-Uhlenbeck processes. Using numerical solutions of the stochastic model
system obtained by an Euler method, it is found that with excitation only there
is a critical value of the steady state excitatory conductance for repetitive
spiking without noise and for values of the conductance near the critical value
small noise has a powerfully inhibitory effect. For a given level of inhibition
there is also a critical value of the steady state excitatory conductance for
repetitive firing and it is demonstrated that noise either in the excitatory or
inhibitory processes or both can powerfully inhibit spiking. Furthermore, near
the critical value, inverse stochastic resonance was observed when noise was
present only in the inhibitory input process.
The system of 27 coupled deterministic differential equations for the
approximate first and second order moments of the 6-dimensional model is
derived. The moment differential equations are solved using Runge-Kutta methods
and the solutions are compared with the results obtained by simulation for
various sets of parameters including some with conductances obtained by
experiment on pyramidal cells of rat prefrontal cortex. The mean and variance
obtained from simulation are in good agreement when there is spiking induced by
strong stimulation and relatively small noise or when the voltage is
fluctuating at subthreshold levels. In the occasional spike mode sometimes
exhibited by spinal motoneurons and cortical pyramidal cells the assunptions
underlying the moment equation approach are not satisfied
Panoramic-reconstruction temporal imaging for seamless measurements of slowly-evolved femtosecond pulse dynamics
Single-shot real-time characterization of optical waveforms with
sub-picosecond resolution is essential for investigating various ultrafast
optical dynamics. However, the finite temporal recording length of current
techniques hinders comprehensive understanding of many intriguing ultrafast
optical phenomena that evolve over a time scale much longer than their fine
temporal details. Inspired by the space-time duality and by stitching of
multiple microscopic images to achieve a larger field of view in the spatial
domain, here a panoramic-reconstruction temporal imaging (PARTI) system is
devised to scale up the temporal recording length without sacrificing the
resolution. As a proof-of-concept demonstration, the PARTI system is applied to
study the dynamic waveforms of slowly-evolved dissipative Kerr solitons in an
ultrahigh-Q microresonator. Two 1.5-ns-long comprehensive evolution portraits
are reconstructed with 740-fs resolution and dissipative Kerr soliton
transition dynamics, in which a multiplet soliton state evolves into stable
singlet soliton state, are depicted
Finite-region boundedness and stabilization for 2D continuous-discrete systems in Roesser model
This paper investigates the finite-region boundedness (FRB) and stabilization problems for two-dimensional continuous-discrete linear Roesser models subject to two kinds of disturbances. For two-dimensional continuous-discrete system, we first put forward the concepts of finite-region stability and FRB. Then, by establishing special recursive formulas, sufficient conditions of FRB for two-dimensional continuous-discrete systems with two kinds of disturbances are formulated. Furthermore, we analyze the finite-region stabilization issues for the corresponding two-dimensional continuous-discrete systems and give generic sufficient conditions and sufficient conditions that can be verified by linear matrix inequalities for designing the state feedback controllers which ensure the closed-loop systems FRB. Finally, viable experimental results are demonstrated by illustrative examples
Dynamical response of the Hodgkin-Huxley model in the high-input regime
The response of the Hodgkin-Huxley neuronal model subjected to stochastic
uncorrelated spike trains originating from a large number of inhibitory and
excitatory post-synaptic potentials is analyzed in detail. The model is
examined in its three fundamental dynamical regimes: silence, bistability and
repetitive firing. Its response is characterized in terms of statistical
indicators (interspike-interval distributions and their first moments) as well
as of dynamical indicators (autocorrelation functions and conditional
entropies). In the silent regime, the coexistence of two different coherence
resonances is revealed: one occurs at quite low noise and is related to the
stimulation of subthreshold oscillations around the rest state; the second one
(at intermediate noise variance) is associated with the regularization of the
sequence of spikes emitted by the neuron. Bistability in the low noise limit
can be interpreted in terms of jumping processes across barriers activated by
stochastic fluctuations. In the repetitive firing regime a maximization of
incoherence is observed at finite noise variance. Finally, the mechanisms
responsible for spike triggering in the various regimes are clearly identified.Comment: 14 pages, 24 figures in eps, submitted to Physical Review
Quantum sensing with arbitrary frequency resolution
Quantum sensing takes advantage of well controlled quantum systems for
performing measurements with high sensitivity and precision. We have
implemented a concept for quantum sensing with arbitrary frequency resolution,
independent of the qubit probe and limited only by the stability of an external
synchronization clock. Our concept makes use of quantum lock-in detection to
continuously probe a signal of interest. Using the electronic spin of a single
nitrogen vacancy center in diamond, we demonstrate detection of oscillating
magnetic fields with a frequency resolution of 70 uHz over a MHz bandwidth. The
continuous sampling further guarantees an excellent sensitivity, reaching a
signal-to-noise ratio in excess of 10,000:1 for a 170 nT test signal measured
during a one-hour interval. Our technique has applications in magnetic
resonance spectroscopy, quantum simulation, and sensitive signal detection.Comment: Manuscript resubmitted to Science. Includes Supplementary Material
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