How does the brain encode the spatial structure of the external world? A partial answer comes through place cells, hippocampal neurons which become associated to approximately convex regions of the world known as their place fields. When an organism is in the place field of some place cell, that cell will fire at an increased rate. A neural code describes the set of firing patterns observed in a set of neurons in terms of which subsets fire together and which do not. If the neurons the code describes are place cells, then the neural code gives some information about the relationships between the place fields–for instance, two place fields intersect if and only if their associated place cells fire together. Since place fields are convex, we are interested in determining which neural codes can be realized with convex sets and in finding convex sets which generate a given neural code when taken as place fields. To this end, we study algebraic invariants associated to neural codes, such as neural ideals and toric ideals. We work with a special class of convex codes, known as inductively pierced codes, and seek to identify these codes through the Gröbner bases of their toric ideals.

Neural responses in the primate ventral visual system become more complex in the later stages of the pathway. For example, not only do neurons in IT cortex respond to complete objects, they also learn to respond invariantly with respect to the viewing angle of an object and also with respect to the location of an object. These types of neural responses have helped guide past research with VisNet, a computational model of the primate ventral visual pathway that self-organises during learning. In particular, previous research has focussed on presenting to the model one object at a time during training, and has placed emphasis on the transform invariant response properties of the output neurons of the model that consequently develop. This doctoral thesis extends previous VisNet research and investigates the performance of the model with a range of more challenging and ecologically valid training paradigms. For example, when multiple objects are presented to the network during training, or when objects partially occlude one another during training. The different mechanisms that help output neurons to develop object selective, transform invariant responses during learning are proposed and explored. Such mechanisms include the statistical decoupling of objects through multiple object pairings, and the separation of object representations by independent motion. Consideration is also given to the heterogeneous response properties of neurons that develop during learning. For example, although IT neurons demonstrate a number of differing invariances, they also convey spatial information and view specific information about the objects presented on the retina. A updated, scaled-up version of the VisNet model, with a significantly larger retina, is introduced in order to explore these heterogeneous neural response properties.

The Vestibulo-Ocular Reflex (VOR) produces compensatory eye movements in response to head and body rotations movements, over a wide range of frequencies and in a variety of dimensions. The individual components of the VOR are separated into parallel pathways, each dealing with rotations or movements in individual planes or axes. The Horizontal VOR (hVOR) compensates for eye movements in the Horizontal plane, and comprises a linear and non-linear pathway. The linear pathway of the hVOR provides fast and accurate compensation for rotations, the response being produced through 3-neuron arc, producing a direct translation of detected head velocity to compensatory eye velocity. However, single neurons involved in the middle stage of this 3-neuron arc cannot account for the wide frequency over which the reflex compensates, and the response is produced through the population response of the Medial Vestibular Nucleus (MVN) neurons involved. Population Heterogeneity likely plays a role in the production of high fidelity population response, especially for high frequency rotations. Here we present evidence that, in populations of bio-physical compartmental models of the MVN neurons involved, Heterogeneity across the population, in the form of diverse spontaneous firing rates, improves the response fidelity of the population over Homogeneous populations. Further, we show that the specific intrinsic membrane properties that give rise to this Heterogeneity may be the diversity of certain slow voltage activated Potassium conductances of the neurons. We show that Heterogeneous populations perform significantly better than Homogeneous populations, for a wide range of input amplitudes and frequencies, producing a much higher fidelity response. We propose that variance of Potassium conductances provides a plausible biological means by which Heterogeneity arises, and that the Heterogeneity plays an important functional role in MVN neuron population responses. We discuss our findings in relation to the specific mechanism of Desynchronisation through which the benfits of Heterogeneity may arise, and place those findings in the context of previous work on Heterogeneity both in general neural processing, and the VOR in particular. Interesting findings regarding the emergence of phase leads are also discussed, as well as suggestions for future work, looking further at Heterogeneity of MVN neuron populations.

We present a multi-layer multi-column computational model of neocortex that is built based on the activity and connections of known neuronal cell types and includes activity-dependent short term plasticity. This model, a network of spiking neurons, is validated by showing that it exhibits activity close to biology in terms of several characteristics: (1) proper laminar flow of activity; (2) columnar organization with focality of inputs; (3) low-threshold-spiking (LTS) and fast-spiking (FS) neurons function as observed in normal cortical circuits; and (4) different stages of epileptiform activity can be obtained with either increasing the level of inhibitory blockade, or simulation of NMDA receptor enhancement. The aim of this research is to provide insight into the fundamental properties of vertical and horizontal inhibition in neocortex and their influence on epileptiform activity. The developed model was used to test novel ideas about modulation of inhibitory neuronal types in a developmentally malformed cortex. The novelty of the proposed research includes: (1) design and implementation of a multi-layer multi-column model of the cortex with multiple neuronal types and short-time plasticity, (2) modification of the Izhikevich neuron model in order to model biological maximum firing rate property, (3) generating local field potential (LFP) and EEG signals without modeling multiple neuronal compartments, (4) modeling several known conditions to validate that the cortex model matches the biology in several aspects,(5) modeling different abnormalities in malformed cortex to test existing and to generate novel hypotheses.

Head direction cells signal the orientation of the head in the horizontal plane. This thesis shows how some of the known head direction cell response properties might develop through learning. The research methodology employed is the computer simulation of neural network models of head direction cells that self-organize through learning. The preferred firing directions of head direction cells will change in response to the manipulation of distal visual cues, but not in response to the manipulation of proximal visual cues. Simulation results are presented of neural network models that learn to form separate representations of distal and proximal visual cues that are presented simultaneously as visual input to the network. These results demonstrate the computation required for a subpopulation of head direction cells to learn to preferentially respond to distal visual cues. Within a population of head direction cells, the angular distance between the preferred firing directions of any two cells is maintained across different environments. It is shown how a neural network model can learn to maintain the angular distance between the learned preferred firing directions of head direction cells across two different visual training environments. A population of head direction cells can update the population representation of the current head direction, in the absence of visual input, using internal idiothetic (self-generated) motion signals alone. This is called the path integration of head direction. It is important that the head direction cell system updates its internal representation of head direction at the same speed as the animal is rotating its head. Neural network models are simulated that learn to perform the path integration of head direction, using solely idiothetic signals, at the same speed as the head is rotating.

I investigated how two types of rhythmic complexity, syncopation and tempo fluctuation, affect the neural and behavioral responses of listeners. The aim of Experiment 1 was to explore the role of attention in pulse and meter perception using complex rhythms. A selective attention paradigm was used in which participants attended either to a complex auditory rhythm or a visually presented list of words. Performance on a reproduction task was used to gauge whether participants were attending to the appropriate stimulus. Selective attention to rhythms led to increased BOLD (Blood Oxygen Level-Dependent) responses in basal ganglia, and basal ganglia activity was observed only after the rhythms had cycled enough times for a stable pulse percept to develop. These observations show that attention is needed to recruit motor activations associated with the perception of pulse in complex rhythms. Moreover, attention to the auditory stimulus enhanced activity in an attentional sensory network including primary auditory, insula, anterior cingulate, and prefrontal cortex, and suppressed activity in sensory areas associated with attending to the visual stimulus. In Experiment 2, the effect of tempo fluctuation in expressive music on emotional responding in musically experienced and inexperienced listeners was investigated. Participants listened to a skilled music performance, including natural fluctuations in timing and sound intensity that musicians use to evoke emotional responses, and a mechanical performance of the same piece, that served as a control. Participants reported emotional responses on a 2-dimensional rating scale (arousal and valence), before and after fMRI scanning. During fMRI scanning, participants listened without reporting emotional responses. Tempo fluctuations predicted emotional arousal ratings for all listeners. / Expressive performance was associated with BOLD increases in limbic areas for all listeners and in limbic and reward related areas forthose with musical experience. Activity in the dorsal anterior cingulate, which may reflect temporal expectancy, was also dependent on the musical experience of the listener. Changes in tempo correlated with activity in a mirror neuron network in all listeners, and mirror neuron activity was associated with emotional arousal in experienced listeners. These results suggest that emotional responding to music occurs through an empathic motor resonance. / by Heather L. Chapin. / Thesis (Ph.D.)--Florida Atlantic University, 2009. / Includes bibliography. / Electronic reproduction. Boca Raton, Fla., 2009. Mode of access: World Wide Web.

This dissertation investigated the nature of pulse in the tempo fluctuation of music performance and how people entrain with these performed musical rhythms. In Experiment 1, one skilled pianist performed four compositions with natural tempo fluctuation. The changes in tempo showed long-range correlation and fractal (1/f) scaling for all four performances. To determine whether the finding of 1/f structure would generalize to other pianists, musical styles, and performance practices, fractal analyses were conducted on a large database of piano performances in Experiment 3. Analyses revealed signicant long-range serial correlations in 96% of the performances. Analysis showed that the degree of fractal structure depended on piece, suggesting that there is something in the composition's musical structure which causes pianists' tempo fluctuations to have a similar degree of fractal structure. Thus, musical tempo fluctuations exhibit long-range correlations and fractal scaling. To examine how people entrain to these temporal fluctuations, a series of behavioral experiments were conducted where subjects were asked to tap the pulse (beat) to temporally fluctuating stimuli. The stimuli for Experiment 2 were musical performances from Experiment 1, with mechanical versions serving as controls. Subjects entrained to all stimuli at two metrical levels, and predicted the tempo fluctuations observed in Experiment 1. Fractal analyses showed that the fractal structure of the stimuli was reected in the inter-tap intervals, suggesting a possible relationship between fractal tempo scaling, pulse perception, and entrainment. Experiments 4-7 investigated the extent to which people use long-range correlation and fractal scaling to predict tempo fluctuations in fluctuating rhythmic sequences. / Both natural and synthetic long-range correlations enabled prediction, as well as shuffled versions which contained no long-term fluctuations. Fractal structure of the stimuli was again in the inter-tap intervals, with persistence for the fractal stimuli, and antipersistence for the shuffled stimuli. 1/f temporal structure is suficient though not necessary for prediction of fluctuations in a stimulus with large temporal fluctuations. / by Summer K. Rankin. / Vita. / Thesis (Ph.D.)--Florida Atlantic University, 2010. / Includes bibliography. / Electronic reproduction. Boca Raton, Fla., 2010. Mode of access: World Wide Web.

A precisão de uma ação motora depende de vários fatores, como: 1) grau de variabilidade da força gerada por cada músculo envolvido, 2) velocidade de geração da força, 3) coordenação das ativações dos músculos. A geração e o controle da força muscular possuem mecanismos que ainda precisam ser mais bem estabelecidos, tanto para o aprimoramento das teorias de controle motor, quanto para o desenvolvimento de técnicas que permitam a prevenção ou a compensação de certas deficiências. A perda de desempenho motor pode ser decorrente de doenças que afetam o sistema neuromuscular ou de alterações associadas ao envelhecimento. Sabe-se, por exemplo, que idosos podem possuir maior variabilidade e menor velocidade de desenvolvimento da força, quando comparados com jovens. Uma das formas de se entender os mecanismos responsáveis pelos fenômenos observados em experimentos neurofisiológicos, em indivíduos saudáveis, em pacientes ou em idosos, é por meio de uma representação adequada de tais mecanismos em modelos matemáticos. Tais modelos podem, pela escolha de um conjunto de parâmetros e de sinais de entrada, ser simulados, explorando-se toda gama de cenários plausíveis para a geração de um determinado fenômeno, tendo como referência os dados obtidos experimentalmente. Resumidamente, o presente trabalho trata do estudo do sistema neuromuscular por modelagem matemática e simulação computacional, com particular interesse nos músculos do tríceps sural e no primeiro interósseo dorsal (um músculo intrínseco da mão), sendo estes músculos amplamente utilizados em estudos experimentais e de modelagem. Maior enfoque é dado em contrações isométricas (i.e., ângulo articular mantido fixo), avaliando-se a organização do núcleo motor, em termos anatômicos e fisiológicos, recebendo como entrada a atividade sináptica das vias pré-motoneuronais, e estudando como diferentes arranjos das propriedades neurais podem resultar em características encontradas experimentalmente para a força muscular. Inicialmente foi feita uma ampla expansão de um simulador existente (ReMoto), tanto em aspectos de modelagem quanto de interface. Em seguida, este modelo expandido foi empregado para um estudo da influência do grau de rigidez muscular nas respostas reflexas do tornozelo. Posteriormente, um novo modelo de pool de motoneurônios, com ampla representação de características biofísicas, foi desenvolvido e, por fim, este modelo foi utilizado, em conjunto com modelos de tratos descendentes e da geração de força muscular, para representar a geração de forças isométricas em jovens e idosos. / The precision of a motor action depends on several factors such as: 1) the level of force variability of each involved muscle, 2) the rate of force development, 3) the coordination of the activations of the muscles involved. Several mechanisms underlying the force generation in a muscle and its control by the nervous system remain to be fully comprehended. An appropriate description of these mechanisms would allow an improvement in motor control theories and could contribute to the development of techniques for the prevention or compensation of some disabilities. Losses in motor performance may be caused by diseases affecting the neuromuscular system or due to aging processes. For instance, old adults may exhibit higher force variability and lower velocity of force development than young adults. Proper representations of such mechanisms in mathematical models constitute a promising way to test hypotheses raised by neurophysiological experiments to explain an observed phenomenon. These models can be used to investigate aspects of health/disease or young/old subjects and, by varying their parameter sets, it is possible to explore a broad range of plausible scenarios under which the experimentally observed phenomena are replicated. This project deals with the study of the neuromuscular system by mathematical modeling and computer simulations, applied to the triceps surae and the first dorsal interosseus (two of the most experimentally and theoretically studied muscles). The principal focus is on isometric contractions (i.e., fixed joint angle) and the study of the organization of the motor nucleus (anatomical and physiological aspects) receiving inputs from premotoneuronal pathways. The study analyzes how different patterns of organization result in experimentally observed aspects of muscle force. Initially, an existing simulator of the neuromuscular system (ReMoto) was broadly extended to include new models and a friendly interface. The extended model was used to investigate the influence of muscle stiffness on the reflex responses in the ankle joint. Next, a new motoneuron pool mathematical model was developed based on known biophysics. Finally, this model was integrated with models of pre-motoneuronal neurons estabilishing synapses with motoneurons and of muscle force generation in order to represent isometric force generation in young and old adults.

Desde que surgiu, o computador vem sendo utilizado na modelagem de fenômenos em todas as áreas do conhecimento. Em neurociências, a modelagem computacional é utilizada para descrever, reproduzir e fazer previsões sobre o comportamento dos diferentes componentes do sistema nervoso. Assim como em outras áreas das ciências, este procedimento tem-se mostrado eficiente no estudo e aprimoramento das teorias a respeito da função cerebral. Com o crescente aumento do poder computacional, maiores e mais detalhados modelos podem ser construídos com um grau de realismo biológico cada vez maior. Neste trabalho, apresentamos modelos computacionais biologicamente plausíveis de neurônios corticais do sistema somestésico primário. Os modelos foram construídos com base no formalismo de Hodgkin-Huxley para a implementação de canais iônicos e na técnica de compartimentalização de Rall para modelar sua extensão espacial. Os parâmetros foram ajustados a partir de resultados experimentais 'in vivo' e 'in vitro' com neurônios, retirados da literatura. Os resultados das simulações mostraram que os modelos são biologicamente aceitáveis e de qualidade superior a de outros modelos construídos anteriormente, possibilitando a construção de modelos de redes neuronais em larga escala mais precisos. / Since its appearance, the computer has been used to model phenomena in all areas of knowledge. In neuroscience, computer modeling is used to describe, reproduce and predict behaviors of different components of the nervous system. As well as in other areas of sciences, this procedure has been shown to be efficient in the study and improvement of theories on brain function. With the increasing power of computers, larger and more detailed models can be constructed with an increasing degree of biological realism. In this work, we present biologically plausible computer models of cortical neurons from the primary somatosensory system. The models have been implemented based on the Hodgkin-Huxley formalism for ionic channels and the Rall´s compartmental technique for spatial extent. The parametrs have been adjusted based on in vivo and in vitro experimental results taken from the literature. Simulation results have shown that the models are biologically acceptable and of superior quality in comparison with previous models, allowing the construction of more precise large-scale neuronal network models.

Este trabalho descreve uma simulação computacional biologicamente plausível do sistema olfativo de vertebrados. O modelo construído foi capaz de reproduzir satisfatoriamente características importantes observadas no sistema olfativo de vertebrados, incluindo a recepção de diferentes concentrações e tipos de odores no epitélio olfativo e a propagação dessa informação para o bulbo. Ele também tornou possível a observação de diferentes padrões de resposta odorífera, tanto no epitélio como no bulbo, associados a diferentes odores usados nas simulações. / This work describes a biologically plausible simulation of the olfactory system of vertebrates. The constructed model was capable of reproducing satisfactorily important characterisitics observed in the vertebrate olfactory system, including the reception of different concentrations and odor types at the epithelium and the propagation of this information to the olfactory bulb. Also, it made possible the observation of the different response patterns, both in the epithelium as in the olfactory bulb, associated with different odors used in the simulations.