Past decades of auditory research have identified several acoustic features that influence perceptual organization of sound, in particular, the frequency of tones and the rate of presentation. One class of stimuli that have been intensively studied are sequences of tones that alternate in frequency. They are typically presented in patterns of repeating doublets ABAB… or repeating triplets ABA-ABA-... where the symbol “-” stands for a gap of silence between triplets repeats. The duration of each tone or silence is typically tens to hundreds of milliseconds, and listeners hearing the sequence perceive either one auditory object ("stream integration") or two separate auditory objects (“stream segregation”). Animal studies have characterized single- and multi- unit neural activity and event-related local field potentials while systematically varying frequency separation between tones (ΔF) or the presentation rate (PR). They found that the B tone responses in doublets were differentially suppressed with increasing PR and that the B tones responses in triplets decreased with larger ΔF. However, the neural mechanisms underlying these animal data have yet to be explained. In this study, we built an integrate-and-fire network model of the primary auditory cortex (AC) that accurately reproduced the experimental results. Then, we extended the model to account for basic spectro-temporal features of electrocorticography (ECoG) recordings from the posteriomedial part of the Heschl's gyrus (HGPM; cortical area equivalent to the AC of monkeys), obtained from humans listening to sequences of triplets ABA-. Finally, we constructed a firing rate reduced model of the proposed integrate-and-fire network and analyzed its dynamics as function of parameters. A large network of voltage-dependent leaky integrate-and-fire neurons (3600 excitatory, 900 inhibitory) was constructed to simulate neural activity from layers 3/4 of AC during streaming of tone triplets. Parameters describing synaptic and membrane properties were based on experimental data from early studies of AC. Network structure assumed spatially-dependent probability of connections and tonotopic organization. Subpopulations of neurons were tuned to different frequencies along the tonotopic map. In-silico recordings were performed during the presentation of long sequences of triplets and/or doublets. The network’s output was derived with two types of measurements in mind: spiking activity of individual neurons and/or local populations of neurons, and local field potentials. The network spiking neural activity reproduced reliably data reports, including dependence of responses to the B tone in triplets ABA- on stimulus parameter ΔF. Approximations of average evoked potentials (AEPs) from ECoG signals recorded at four depth contacts placed over human HGPM during auditory streaming of triplets were also obtained.

A stochastic leaky integrate-and-fire neuron model was implemented in this study to simulate the spiking activity of the electrosensory "P-unit" receptor neurons of the weakly electric fish Apteronotus leptorhynchus. In the context of sensory coding, these cells have been previously shown to respond in experiment to natural random narrowband signals with either a linear or nonlinear coding scheme, depending on the intrinsic firing rate of the cell in the absence of external stimulation. It was hypothesised in this study that this duality is due to the relation of the stimulus to the neuron's excitation threshold. This hypothesis was validated with the model by lowering the threshold of the neuron or increasing its intrinsic noise, or randomness, either of which made the relation between firing rate and input strength more linear. Furthermore, synchronous P-unit firing to a common input also plays a role in decoding the stimulus at deeper levels of the neural pathways. Synchronisation and desynchronisation between multiple model responses for different types of natural communication signals were shown to agree with experimental observations. A novel result of resonance-induced synchrony enhancement of P-units to certain communication frequencies was also found.

A stochastic leaky integrate-and-fire neuron model was implemented in this study to simulate the spiking activity of the electrosensory "P-unit" receptor neurons of the weakly electric fish Apteronotus leptorhynchus. In the context of sensory coding, these cells have been previously shown to respond in experiment to natural random narrowband signals with either a linear or nonlinear coding scheme, depending on the intrinsic firing rate of the cell in the absence of external stimulation. It was hypothesised in this study that this duality is due to the relation of the stimulus to the neuron's excitation threshold. This hypothesis was validated with the model by lowering the threshold of the neuron or increasing its intrinsic noise, or randomness, either of which made the relation between firing rate and input strength more linear. Furthermore, synchronous P-unit firing to a common input also plays a role in decoding the stimulus at deeper levels of the neural pathways. Synchronisation and desynchronisation between multiple model responses for different types of natural communication signals were shown to agree with experimental observations. A novel result of resonance-induced synchrony enhancement of P-units to certain communication frequencies was also found.

A stochastic leaky integrate-and-fire neuron model was implemented in this study to simulate the spiking activity of the electrosensory "P-unit" receptor neurons of the weakly electric fish Apteronotus leptorhynchus. In the context of sensory coding, these cells have been previously shown to respond in experiment to natural random narrowband signals with either a linear or nonlinear coding scheme, depending on the intrinsic firing rate of the cell in the absence of external stimulation. It was hypothesised in this study that this duality is due to the relation of the stimulus to the neuron's excitation threshold. This hypothesis was validated with the model by lowering the threshold of the neuron or increasing its intrinsic noise, or randomness, either of which made the relation between firing rate and input strength more linear. Furthermore, synchronous P-unit firing to a common input also plays a role in decoding the stimulus at deeper levels of the neural pathways. Synchronisation and desynchronisation between multiple model responses for different types of natural communication signals were shown to agree with experimental observations. A novel result of resonance-induced synchrony enhancement of P-units to certain communication frequencies was also found.

A stochastic leaky integrate-and-fire neuron model was implemented in this study to simulate the spiking activity of the electrosensory "P-unit" receptor neurons of the weakly electric fish Apteronotus leptorhynchus. In the context of sensory coding, these cells have been previously shown to respond in experiment to natural random narrowband signals with either a linear or nonlinear coding scheme, depending on the intrinsic firing rate of the cell in the absence of external stimulation. It was hypothesised in this study that this duality is due to the relation of the stimulus to the neuron's excitation threshold. This hypothesis was validated with the model by lowering the threshold of the neuron or increasing its intrinsic noise, or randomness, either of which made the relation between firing rate and input strength more linear. Furthermore, synchronous P-unit firing to a common input also plays a role in decoding the stimulus at deeper levels of the neural pathways. Synchronisation and desynchronisation between multiple model responses for different types of natural communication signals were shown to agree with experimental observations. A novel result of resonance-induced synchrony enhancement of P-units to certain communication frequencies was also found.

Neurons communicate by action potentials. This process can be described by very detailed biochemical models of neuronal membrane and its channels, or by simpler phenomenological models of membrane potential (integrate-and- fire models) or even by very abstract models when only time of spikes are considered. We took one particular description - stochastic leaky integrate-and-fire model - and compared it with recorded in-vivo intracellular activity of the neuron. We estimated parameters of this model, compared how the model simulation corresponds with a real neuron. It can be concluded that the data are generally consistent with the model. At a more abstract level of description, the spike trains are analyzed without considering exact membrane voltage and one asks how the external stimulus is encoded in the spike train emitted by neurons. There are many neuronal codes described in literature and we focused on the open problem of neural code responsible for spatial hearing in mammals. Several theories explaining the experimental findings have been proposed and we suggest a specific variant of so called slope-encoding model. Neuronal circuit mimick- ing auditory pathway up to the first binaural neuron was constructed and experimental results were reproduced. Finally, we estimated the minimal number of such...

Neurons communicate by action potentials. This process can be described by very detailed biochemical models of neuronal membrane and its channels, or by simpler phenomenological models of membrane potential (integrate-and- fire models) or even by very abstract models when only time of spikes are considered. We took one particular description - stochastic leaky integrate-and-fire model - and compared it with recorded in-vivo intracellular activity of the neuron. We estimated parameters of this model, compared how the model simulation corresponds with a real neuron. It can be concluded that the data are generally consistent with the model. At a more abstract level of description, the spike trains are analyzed without considering exact membrane voltage and one asks how the external stimulus is encoded in the spike train emitted by neurons. There are many neuronal codes described in literature and we focused on the open problem of neural code responsible for spatial hearing in mammals. Several theories explaining the experimental findings have been proposed and we suggest a specific variant of so called slope-encoding model. Neuronal circuit mimick- ing auditory pathway up to the first binaural neuron was constructed and experimental results were reproduced. Finally, we estimated the minimal number of such...

Este trabalho trata sobre a transferência de frequência em neurônios de disparo, especificamente neurônios integra-e-dispara com escoamento e neurônios de Izhikevich. Através de análises matemáticas analíticas e sistemáticas simulações numéricas é obtida a função de ganho, a transferência de frequência estacionária e dinâmica dos neurônios utilizados, para diversos valores dos parâmetros do modelo. Desse modo, são realizados múltiplos ajustes às curvas obtidas, e os coeficientes estimados são apresentados. Com base em todos esses dados, são obtidas diversas características dessas relações de transferência de frequência, e como suas propriedades variam com relação aos principais parâmetros do modelo de neurônio e sinapse utilizados. Diversos resultados interessantes foram apresentados, incluindo evidências de que a função ganho do neurônio integra-e-dispara pode se comportar de modo bastante semelhante à função de ganho e transferência estacionária do neurônio de Izhikevich, dependendo dos parâmetros adotados; a divisão do plano de parâmetros do modelo integra-e-dispara de acordo com a linearidade da transferência de frequência dinâmica; o limiar da intensidade de corrente contínua e de frequência de spikes pré-sinápticos de um neurônio de Izhikevich é determinado apenas pelo parâmetro b, no intervalo de parâmetros usual; modelos de sinapses distintos tendem a não alterar a forma da transferência de frequência estacionária de um neurônio de Izhikevich. / This work is about the frequency transfer of spiking neurons, specifically integrate-and-fire neurons and Izhikevich neurons. Through analytical and systematic numerical simulations the gain function, the stationary and dynamic frequency transfer of the adopted neuron models, are obtained for several values of the model parameters. Thus, multiple fits are made to the curves obtained, and the estimated coefficients are presented. Based on all these data, several characteristics of the frequency transfer relations are obtained, and information is obtained about how their properties vary with respect the parameters of the adopted neuron and synapse model. Several interesting results have been presented, including evidences that the integrate-and-fire neuron\'s gain function can behave quite similarly to the Izhikevich neuron\'s stationary transfer and gain function, depending of the adopted parameters. We also obtained the division of the parameters plane of integrate-and-fire model according to the linearity of the dynamic frequency transfer. It was also verified that the thresholds of the presynaptic spikes\' current intensity and frequency of an Izhikevich neuron are determined only by the parameter b, in the usual parameter range. In addition, it was observed that the considered distinct synapses models tend not to depart from the stationary frequency transfer of an Izhikevich neuron.

Um die komplexe Dynamik von Neuronen und deren Informationsverarbeitung mittels Pulssequenzen zu verstehen, ist es wichtig, die stationäre Puls-Aktivität zu charakterisieren. Die statistischen Eigenschaften von Pulssequenzen können durch vereinfachte stochastische Neuronenmodelle verstanden werden. Eine gut ausgearbeitete Theorie existiert für die Klasse der Erneuerungsmodelle, welche die statistische Unabhängigkeit der Interspike-Intervalle (ISI) annimmt. Experimente haben jedoch gezeigt, dass viele Neuronen Korrelationen zwischen ISIs aufweisen und daher nicht gut durch einen Erneuerungsprozess beschrieben werden. Solche Korrelationen können durch Nichterneuerungs-Modelle erfasst werden, welche jedoch theoretisch schlecht verstanden sind. Diese Arbeit ist eine analytische Studie von Nichterneuerungs-Modellen, die zwei bedeutende Korrelationsmechanismen untersucht: farbiges Rauschen, welches zeitlich-korrelierten Input darstellt, und negative Puls-Rückkopplung, welche Feuerraten-Adaption realisiert. Für das "Perfect-Integrate-and-Fire" (PIF) Modell, welchen durch ein allgemeines Gauss''sches farbiges Rauschen getrieben ist, werden die Statistiken höherer Ordnung der Output-Pulssequenz hergeleitet, insbesondere der Koeffizient der Variation, der serielle Korrelationskoeffizient (SCC), die ISI-Dichte und der Fano-Faktor. Weiterhin wird die Dynamik des PIF Modells mit Puls-getriggertem Adaptionsstrom und weissem Stromrauschen im Detail analysiert. Die Theorie liefert einen Ausdruck für den SCC, der für schwaches Rauschen aber beliebige Adaptions-Stärke und Zeitskale gültig ist, sowie die lineare Antwortfunktion und das Leistungsspektrum der Pulssequenz. Ausserdem wird gezeigt, dass ein stochastischer Adaptionsstrom wie ein langsames farbiges Rauschen wirkt, was ermöglicht, die dominierende Quellen des Rauschen in einer auditorischen Rezeptorzelle zu bestimmen. Schliesslich wird der SCC für das fluktuations-getriebene Feuerregime berechnet. / To understand the complex dynamics of neurons and its ability to process information using a sequence of spikes, it is vital to characterize its stationary spontaneous spiking activity. The statistical properties of spike trains can be explained by reduced stochastic neuron models that account for various sources of noise. A well-developed theory exists for the class of renewal models, in which the interspike intervals (ISIs) are statistically independent. However, experimental studies show that many neurons are not well described by a renewal process because of correlations between ISIs. Such correlations can be captured by generalized, non-renewal models, which are, however, poorly understood theoretically. This thesis represents an analytical study of non-renewal models, focusing on two prominent correlation mechanisms: colored-noise driving representing temporally correlated inputs, and negative feedback currents realizing spike-frequency adaptation. For the perfect integrate-and-fire (PIF) model driven by a general Gaussian colored noise input, the higher-order statistics of the output spike train is derived using a weak-noise analysis of the Fokker-Planck equation. This includes formulas for the coefficient of variation, the serial correlation coefficient (SCC), the ISI density and the Fano factor. Then, the dynamics of a PIF model with a spike-triggered adaptation and a white-noise current is analyzed in detail. The theory yields an expression for the SCC valid for weak noise but arbitrary adaptation strengths and time scale, and also provides the linear response to time-dependent stimuli and the spike train power spectrum. Furthermore, it is shown that a stochastic adaptation current acts like a slow colored noise, which permits to determine the source of spiking variability observed in an auditory receptor neuron. Finally, the SCC is calculated for the fluctuation-driven spiking regime by assuming discrete states of colored noise or adaptation current.

One of the most powerful and important applications that the brain accomplishes is solving the sensory "cocktail party problem:" to adaptively suppress extraneous signals in an environment. Theoretical studies suggest that the solution to the problem involves an adaptive filter, which learns to remove the redundant noise. However, neural learning is also in its infancy and there are still many questions about the stability and application of synaptic learning rules for neural computation. In this thesis, the implementation of an adaptive filter in the brain of a weakly electric fish, A. Leptorhynchus, was studied. It was found to require a cerebellar architecture that could supply independent frequency channels of delayed feedback and multiple burst learning rules that could shape this feedback. This unifies two ideas about the function of the cerebellum that were previously separate: the cerebellum as an adaptive filter and as a generator of precise temporal inputs.