We investigate field theories defined on spaces with non-commutative coordinates corresponding to deformations of flat spaces as e.g. the Euclidean plane or Minkowski space. When E-expressed in terms of ordinary complex fields, the interactions are non-local. Despite this fact, these field theories exhibit the same kind of divergencies as the non-deformed models, due to special graph-topological properties of cocylcles connected with the non-commutative coordinates.

Microelectrode recording of electrical activity provides a means to measure the discharge patterns of nerve cells with high spatial and temporal resolution and with minimal damage to nervous tissue. For these reasons it has long been the principal method for analyzing the behavior and function of neurons and neural networks. An additional and extremely useful application of microelectrode technology is the ability to inject tracers directly into neurons through an intracellular microelectrode in order to label the cells and identify their location, morphology, and synaptic contacts with other neurons and effectors. The first investigations of single neuron activity were carried out with microelectrodes for extracellular recording, which led to the identification of previously uncharacterized cell types and synaptic circuits (e.g., Lorente de Nó, 1938; Renshaw, 1946; see Eccles (1964) and McLennan (1970) for additional examples). Shortly thereafter, micropipettes for intracellular recording were developed (Ling and Gerard 1949). These were used to measure membrane potentials and to uncover voltage-and time-dependent properties that determine neuron excitability. Intracellular recording also revealed the nature and functional significance of excitatory and inhibitory postsynaptic potentials and helped to identify the underlying membrane conductance mechanisms (Combs, Eccles and Fatt 1955a-c). Subsequent adaptation of voltage-clamp technology for use with microelectrodes (Brennecke and Lindemann 1974a,b; Wilson and Goldner 1975; Adams and Gage 1979; Finkel and Redman 1984) permitted measurement of membrane currents and estimates of conductances in vitro (Adams et al. 1982a,b; Johnston et al. 1980) and in vivo (Dunn and Wilson 1977; Finkel and Redman 1983a; Richter et al. 1996). Further advances in neurophysiological investigation came with the development of techniques which enabled investigators to record the electrical activity of neurons and then label them by intracellular injections of fluorescent dyes (Thomas and Wilson 1966; Stretton and Kravitz 1968). Microelectrode recording of electrophysiological properties and labeling of neurons continue to be important tools for analyzing the behavior and function of single nerve

Saccades are known to influence subsequent arm movements. There is less information to suggest that the characteristics of saccades depend on the reaching movements they accompany. To explore this issue, we studied the systematic errors of saccades generated by two adult female Rhesus monkeys (Macaca Mulata), which were trained to perform center-out saccades and reaching arm movements to the memorized location of targets. The mean error of saccades executed in isolation differed significantly from that of saccades that were executed towards the same target location and accompanied a reaching movement. This difference was observed in both animals whether they used their right or left arm, whether the size of the movement was equal to 10 or 15 degrees and whether there was no delay or a 3 s delay between the extinction of a visual target and the cue to move. Moreover, the endpoints of saccades and those of the arm-reaching movements in the reaching task were significantly correlated. These data suggest that signals specifying the metrics of limb movements influence those specifying the metrics of preceding saccades at a programming stage.

Epidural electrical stimulation (EES) of the spinal cord restores locomotion in animal models of spinal cord injury (SCI) but is less effective in humans. Here, we hypothesized that this interspecies discrepancy is due to interference between EES and proprioceptive information in humans. Computational simulations, preclinical and clinical experiments reveal that EES blocks a significant amount of proprioceptive input in humans, but not in rats. This transient deafferentation prevents the modulation of reciprocal inhibitory networks involved in locomotion and reduces or abolishes the conscious perception of leg position. Consequently, continuous EES can only facilitate locomotion within a narrow range of stimulation parameters and is unable to provide meaningful locomotor improvements in humans without rehabilitation. Simulations showed that burst stimulation and spatiotemporal stimulation profiles mitigate the cancellation of proprioceptive information, enabling robust control over motoneuron activity. This demonstrates Users may view, print, copy, and download text and data-mine the content in such documents, for the purposes of academic research, subject always to the full Conditions of use:

Medial frontal cortex enables performance monitoring, indexed by the error-related negativity (ERN) and manifest by performance adaptations. In monkeys performing a saccade countermanding (stop signal) task, we recorded EEG over and neural spiking across all layers of the supplementary eye field (SEF), an agranular cortical area. Neurons signaling error production, feedback predicting reward gain or loss, and delivery of fluid reward had different spike widths and were concentrated differently across layers. Neurons signaling error or loss of reward were more common in layers 2 and 3 (L2/3), while neurons signaling gain of reward were more common in layers 5 and 6 (L5/6). Variation of error-and reinforcement-related spike rates in L2/3 but not L5/6 predicted response time adaptation. Variation in error-related spike rate in L2/3 but not L5/6 predicted ERN magnitude. These findings reveal novel features of cortical microcircuitry supporting performance monitoring and confirm one cortical source of the ERN. Effective behavior requires evaluating the outcomes of actions and adapting performance to optimize consequences. The countermanding (stop signal) task affords investigation of performance monitoring and executive control 1 , because humans and macaque monkeys performing saccade countermanding strategically adapt saccade latency according to performance outcomes 2. Medial frontal cortex contributes to performance monitoring and executive control, but specific mechanisms remain uncertain 3,4. Hypotheses have been tested using the noninvasive measure of the error-related negativity (ERN) in humans 5 , which is also observed in macaque monkeys 6. However, mechanistic hypotheses require information about neural spiking patterns across cortical layers 7. It is well-known that neural spiking in anterior Users may view, print, copy, and download text and data-mine the content in such documents, for the purposes of academic research, subject always to the full Conditions of use:

During coordinated eye-hand movements, saccade reaction times (SRTs) and reach reaction times (RRTs) are correlated in humans and monkeys. Reaction times (RTs) measure the degree of movement preparation and can correlate with movement speed and accuracy. However, RTs can also reflect effector nonspecific influences, such as motivation and arousal. We use a combination of behavioral psychophysics and computational modeling to identify plausible mechanisms for correlations in SRTs and RRTs. To disambiguate nonspecific mechanisms from mechanisms specific to movement coordination, we introduce a dual-task paradigm in which a reach and a saccade are cued with a stimulus onset asynchrony (SOA). We then develop several variants of integrate-to-threshold models of RT, which postulate that responses are initiated when the neural activity encoding effector-specific movement preparation reaches a threshold. The integrator models formalize hypotheses about RT correlations and make predictions for how each RT should vary with SOA. To test these hypotheses, we trained three monkeys to perform the eye-hand SOA task and analyzed their SRTs and RRTs. In all three subjects, RT correlations decreased with increasing SOA duration. Additionally, mean SRT decreased with decreasing SOA, revealing facilitation of saccades with simultaneous reaches, as predicted by the model. These results are not consistent with the predictions of the models with common modulation or common input but are compatible with the predictions of a model with mutual excitation between two effector-specific integrators. We propose that RT correlations are not simply attributable to motivation and arousal and are a signature of coordination.