Locking of correlated neural activity to ongoing oscillations

Population-wide oscillations are ubiquitously observed in mesoscopic signals of cortical activity. In these network states a global oscillatory cycle modulates the propensity of neurons to fire. Synchronous activation of neurons has been hypothesized to be a separate channel of signal processing information in the brain. A salient question is therefore if and how oscillations interact with spike synchrony and in how far these channels can be considered separate. Experiments indeed showed that correlated spiking co-modulates with the static firing rate and is also tightly locked to the phase of beta-oscillations. While the dependence of correlations on the mean rate is well understood in feed-forward networks, it remains unclear why and by which mechanisms correlations tightly lock to an oscillatory cycle. We here demonstrate that such correlated activation of pairs of neurons is qualitatively explained by periodically-driven random networks. We identify the mechanisms by which covariances depend on a driving periodic stimulus. Mean-field theory combined with linear response theory yields closed-form expressions for the cyclostationary mean activities and pairwise zero-time-lag covariances of binary recurrent random networks. Two distinct mechanisms cause time-dependent covariances: the modulation of the susceptibility of single neurons (via the external input and network feedback) and the time-varying variances of single unit activities. For some parameters, the effectively inhibitory recurrent feedback leads to resonant covariances even if mean activities show non-resonant behavior. Our analytical results open the question of time-modulated synchronous activity to a quantitative analysis.Comment: 57 pages, 12 figures, published versio

Deterministic and stochastic dynamics of multi-variable neuron models : resonance, filtered fluctuations and sodium-current inactivation

Neurons are the basic elements of the networks that constitute the computational units of the brain. They dynamically transform input information into sequences of electrical pulses. To conceive the complex function of the brain, it is crucial to understand this transformation and identify simple neuron models which accurately reproduce the known features of biological neurons. This thesis addresses three different features of neurons. We start by exploring the effect of subthreshold resonance on the response of a periodically forced neuron using a simple threshold model. The response is studied in terms of an implicit one-dimensional time map that corresponds to the Poincar´e map of the forced system. Qualitatively distinct responses are found, including mode locking and chaos. We analytically find the stability regions of mode-locking solutions, and identify the transition to chaos through period-adding bifurcations. We show that the response becomes chaotic when the forcing frequency is close to the resonant frequency. Then we will consider an experimentally verified model with realistic spikegenerating mechanism and study the effect of filtered synaptic fluctuations on the firing-rate response of the neuron. Using a population density method as well as an efficient numerical method, we find the steady-state firing rate in two limits of fast and slow synaptic inputs and present the linear response theory for the firing rate of the model in response to both time-dependent mean inputs and time-dependent noise intensity. Finally, a novel model is introduced that incorporates threshold variability of neurons. We determine the modulation of the input-output properties of the model due to oscillatory inputs and in the presence of filtered synaptic fluctuations.EThOS - Electronic Theses Online ServiceUniversity of WarwickOverseas Research Students Awards Scheme (ORSAS)GBUnited Kingdo

Emergence of Resonances in Neural Systems: The Interplay between Adaptive Threshold and Short-Term Synaptic Plasticity

In this work we study the detection of weak stimuli by spiking (integrate-and-fire) neurons in the presence of certain level of noisy background neural activity. Our study has focused in the realistic assumption that the synapses in the network present activity-dependent processes, such as short-term synaptic depression and facilitation. Employing mean-field techniques as well as numerical simulations, we found that there are two possible noise levels which optimize signal transmission. This new finding is in contrast with the classical theory of stochastic resonance which is able to predict only one optimal level of noise. We found that the complex interplay between adaptive neuron threshold and activity-dependent synaptic mechanisms is responsible for this new phenomenology. Our main results are confirmed by employing a more realistic FitzHugh-Nagumo neuron model, which displays threshold variability, as well as by considering more realistic stochastic synaptic models and realistic signals such as poissonian spike trains

Nonlinear Dynamics, Synchronisation and Chaos in Coupled FHN Cardiac and Neural Cells

Physiological systems are amongst the most challenging systems to investigate from a mathematically based approach. The eld of mathematical biology is a relatively recent one when compared to physics. In this thesis I present an introduction to the physiological aspects needed to gain access to both cardiac and neural systems for a researcher trained in a mathematically based discipline. By using techniques from nonlinear dynamical systems theory I show a number of results that have implications for both neural and cardiac cells. Examining a reduced model of an excitable biological oscillator I show how rich the dynamical behaviour of such systems can be when coupled together. Quantifying the dynamics of coupled cells in terms of synchronisation measures is treated at length. Most notably it is shown that for cells that themselves cannot admit chaotic solutions, communication between cells be it through electrical coupling or synaptic like coupling, can lead to the emergence of chaotic behaviour. I also show that in the presence of emergent chaos one nds great variability in intervals of activity between the constituent cells. This implies that chaos in both cardiac and neural systems can be a direct result of interactions between the constituent cells rather than intrinsic to the cells themselves. Furthermore the ubiquity of chaotic solutions in the coupled systems may be a means of information production and signaling in neural systems

Neuromorphic computation with a single magnetic domain wall

Machine learning techniques are commonly used to model complex relationships but implementations on digital hardware are relatively inefficient due to poor matching between conventional computer architectures and the structures of the algorithms they are required to simulate. Neuromorphic devices, and in particular reservoir computing architectures, utilize the inherent properties of physical systems to implement machine learning algorithms and so have the potential to be much more efficient. In this work, we demonstrate that the dynamics of individual domain walls in magnetic nanowires are suitable for implementing the reservoir computing paradigm in hardware. We modelled the dynamics of a domain wall placed between two anti-notches in a nickel nanowire using both a 1D collective coordinates model and micromagnetic simulations. When driven by an oscillating magnetic field, the domain exhibits non-linear dynamics within the potential well created by the anti-notches that are analogous to those of the Duffing oscillator. We exploit the domain wall dynamics for reservoir computing by modulating the amplitude of the applied magnetic field to inject time-multiplexed input signals into the reservoir, and show how this allows us to perform machine learning tasks including: the classification of (1) sine and square waves; (2) spoken digits; and (3) non-temporal 2D toy data and hand written digits. Our work lays the foundation for the creation of nanoscale neuromorphic devices in which individual magnetic domain walls are used to perform complex data analysis tasks

Oscillatory mechanisms for controlling information flow in neural circuits

Mammalian brains generate complex, dynamic structures of oscillatory activity, in which distributed regions transiently engage in coherent oscillation, often at specific stages in behavioural or cognitive tasks. Much is now known about the dynamics underlying local circuit synchronisation and the phenomenology of where and when such activity occurs. While oscillations have been implicated in many high level processes, for most such phenomena we cannot say with confidence precisely what they are doing at an algorithmic or implementational level. This thesis presents work towards understanding the dynamics and possible function of large scale oscillatory network activity. We first address the question of how coherent oscillatory activity emerges between local networks by measuring phase response curves of an oscillating network in vitro. The network phase response curves provide mechanistic insight into inter-region synchronisation of local network oscillators. Highly simplified firing models are shown to reproduce the experimental data with remarkable accuracy. We then focus on one hypothesised computational function of network oscillations; flexibly controlling the gain of signal flow between anatomically connected networks. We investigate coding strategies and algorithmic operations that support flexible control of signal flow by oscillations, and their implementation by network dynamics. We identify two readout algorithms which selectively recover population rate coded signal with specific oscillatory modulations while ignoring other distracting inputs. By designing a spiking network model that implements one of these mechanisms, we demonstrate oscillatory control of signal flow in convergent pathways. We then investigate constraints on the structures of oscillatory activity that can be used to accurately and selectively control signal flow. Our results suggest that for inputs to be accurately distinguished from one another their oscillatory modulations must be close to orthogonal. This has implications for interpreting in vivo oscillatory activity, and may be an organising principle for the spatio-temporal structure of brain oscillations

Exploiting nonlinearity and noise in optical tweezers and semiconductor lasers : from resonant damping to stochastic logic gates and extreme pulses

This thesis is focused on the study of stochastic and nonlinear dynamics in optical systems. First, we study experimentally the dynamics of a Brownian nanometer particle in an optical trap subjected to an external forcing. Specifically, we consider the effects of parametric noise added to a monostable or bistable optical trap and discovered a new effect which we named stochastic resonant damping (SRD). SRD concerns the minimization of the output variance position of a particle held in a harmonic trap, when an external parametric noise was added to the position trap. We compared the classical stochastic resonance (SR) with SRD and found that they are two phenomena which coexist in the same system but in different regimes. The experimentally studied monostable system showed a maximum in the signal to noise ratio, a clear signature of a resonance. We also developed a new technique to increase 10-fold the detection range of the quadrant photodiode that we used in this study, which exploits the channel crosstalk. Second, we study the stochastic dynamics of a type of semiconductor laser (SCL), known as vertical-cavity surface-emitting laser (VCSEL), that exhibits polarization bistability and hysteresis, either when the injection current or when the optically injected power are varied. We have shown how these properties can be exploited for logic operations due to the effect of the spontaneous emission noise. Two logical input signals have been encoded in three levels of optically injected power from a master laser, and the logical output response was decoded from the emitted polarization of the injected VCSEL. Correct and robust operation was obtained when the three levels of injected power were adjusted to favor one polarization at two levels and to favor the orthogonal polarization at the third level. We numerically demonstrated that the VCSEL-based logic operator allows to reproduce the truth table for the OR and NOR logic operators, while the extension to AND and NAND is straightforward. With this all-optical configuration we have been able to reduce the minimum bit time required for correct operation from 30 ns, obtained in a previous work with an optoelectronic configuration, to 5 ns. The third focus of this thesis is the study of the chaotic nonlinear dynamics of a SCL optically injected, in the regime where it can display sporadic huge intensities pulses, referred to as Rogue Waves (RWs). We found that, when adding optical noise, the region where RWs appear becomes wider. This behavior is observed for high enough noise; however, on the contrary, for very weak noise we found that noise diminishes the number of RW events in certain regions. In order to suppress or induce extreme pulses, we investigated the effects of an external periodic modulation of the laser current. We found that the modulation at specific frequencies modifies the dynamics from chaotic to periodic. Depending on the parameter region, current modulation can contribute to an increased threshold for RWs. Therefore, we concluded that the modulation can be effective for suppressing the RWs dynamics

Entrainment in forced Winfree systems

Rhythmic behavior is widely present in living organisms. The rhythms can be innate and usually they are externally stimulated by the environment. One such stimulus is the 24 h natural light-dark cycle which governs the activity-inactivity cycle of many plants, animals and humans. The cells in the suprachiasmatic nucleus that govern our circadian rhythms are ideally regarded as a group of biological oscillators. In the Winfree model, the biological oscillators are regarded as coupled oscillators. The Winfree model was used to describe the synchronization of a large system of globally coupled phase oscillators. Considering that external stimuli and environmental factors, such as the change of light and darkness, have great influence on the rhythmic behavior, a periodic forcing is added to Winfree system. The thesis focuses on a case where the mean natural frequency of the oscillators is the same with the frequency of the external forcing. A simple case is analyzed with the Poincare map for only one forced oscillator. Then through a careful study of synchronized states and stability on identical oscillators, we obtain the entrainment degree. For a more general case, we study the state diagrams of non-identical oscillators whose natural frequencies follow a uniform or a Lorentz distribution. The Ott-Antonsen is used to give a low-dimensional dynamical description of the system. Then we study the case of detuned systems. We investigate the difference between the detuned and non-detuned cases for identical oscillators and understand the entrainment patterns using stability theory