A Computational Theory for the Learning of Equivalence Relations

Equivalence relations (ERs) are logical entities that emerge concurrently with the development of language capabilities. In this work we propose a computational model that learns to build ERs by learning simple conditional rules. The model includes visual areas, dopaminergic, and noradrenergic structures as well as prefrontal and motor areas, each of them modeled as a group of continuous valued units that simulate clusters of real neurons. In the model, lateral interaction between neurons of visual structures and top-down modulation of prefrontal/premotor structures over the activity of neurons in visual structures are necessary conditions for learning the paradigm. In terms of the number of neurons and their interaction, we show that a minimal structural complexity is required for learning ERs among conditioned stimuli. Paradoxically, the emergence of the ER drives a reduction in the number of neurons needed to maintain those previously specific stimulus–response learned rules, allowing an efficient use of neuronal resources

Bang-Bang Control of Feeding: Role of Hypothalamic and Satiety Signals

Rats, people, and many other omnivores eat in meals rather than continuously. We show by experimental test that eating in meals is regulated by a simple bang-bang control system, an idea foreshadowed by Le Magnen and many others, shown by us to account for a wide range of behavioral data, but never explicitly tested or tied to neurophysiological facts. The hypothesis is simply that the tendency to eat rises with time at a rate determined by satiety signals. When these signals fall below a set point, eating begins, in on–off fashion. The delayed sequelae of eating increment the satiety signals, which eventually turn eating off. Thus, under free conditions, the organism eats in bouts separated by noneating activities. We report an experiment with rats to test novel predictions about meal patterns that are not explained by existing homeostatic approaches. Access to food was systematically but unpredictably interrupted just as the animal tried to start a new meal. A simple bang-bang model fits the resulting meal-pattern data well, and its elements can be identified with neurophysiological processes. Hypothalamic inputs can provide the set point for longer-term regulation carried out by a comparator in the hindbrain. Delayed gustatory and gastrointestinal aftereffects of eating act via the nucleus of the solitary tract and other hindbrain regions as neural feedback governing short-term regulation. In this way, the model forges real links between a functioning feedback mechanism, neuro–hormonal data, and both short-term (meals) and long-term (eating-rate regulation) behavioral data

Blood pressure long term regulation: A neural network model of the set point development

<p>Abstract</p> <p>Background</p> <p>The notion of the nucleus tractus solitarius (NTS) as a comparator evaluating the error signal between its rostral neural structures (RNS) and the cardiovascular receptor afferents into it has been recently presented. From this perspective, stress can cause hypertension via set point changes, so offering an answer to an old question. Even though the local blood flow to tissues is influenced by circulating vasoactive hormones and also by local factors, there is yet significant sympathetic control. It is well established that the state of maturation of sympathetic innervation of blood vessels at birth varies across animal species and it takes place mostly during the postnatal period. During ontogeny, chemoreceptors are functional; they discharge when the partial pressures of oxygen and carbon dioxide in the arterial blood are not normal.</p> <p>Methods</p> <p>The model is a simple biological plausible adaptative neural network to simulate the development of the sympathetic nervous control. It is hypothesized that during ontogeny, from the RNS afferents to the NTS, the optimal level of each sympathetic efferent discharge is learned through the chemoreceptors' feedback. Its mean discharge leads to normal oxygen and carbon dioxide levels in each tissue. Thus, the sympathetic efferent discharge sets at the optimal level if, despite maximal drift, the local blood flow is compensated for by autoregulation. Such optimal level produces minimum chemoreceptor output, which must be maintained by the nervous system. Since blood flow is controlled by arterial blood pressure, the long-term mean level is stabilized to regulate oxygen and carbon dioxide levels. After development, the cardiopulmonary reflexes play an important role in controlling efferent sympathetic nerve activity to the kidneys and modulating sodium and water excretion.</p> <p>Results</p> <p>Starting from fixed RNS afferents to the NTS and random synaptic weight values, the sympathetic efferents converged to the optimal values. When learning was completed, the output from the chemoreceptors became zero because the sympathetic efferents led to normal partial pressures of oxygen and carbon dioxide.</p> <p>Conclusions</p> <p>We introduce here a simple simulating computational theory to study, from a neurophysiologic point of view, the sympathetic development of cardiovascular regulation due to feedback signals sent off by cardiovascular receptors. The model simulates, too, how the NTS, as emergent property, acts as a comparator and how its rostral afferents behave as set point.</p

Neural set point for the control of arterial pressure: role of the nucleus tractus solitarius

<p>Abstract</p> <p>Background</p> <p>Physiological experiments have shown that the mean arterial blood pressure (MAP) can not be regulated after chemo and cardiopulmonary receptor denervation. Neuro-physiological information suggests that the nucleus tractus solitarius (NTS) is the only structure that receives information from its rostral neural nuclei and from the cardiovascular receptors and projects to nuclei that regulate the circulatory variables.</p> <p>Methods</p> <p>From a control theory perspective, to answer if the cardiovascular regulation has a set point, we should find out whether in the cardiovascular control there is something equivalent to a comparator evaluating the error signal (between the rostral projections to the NTS and the feedback inputs). The NTS would function as a comparator if: a) its lesion suppresses cardiovascular regulation; b) the negative feedback loop still responds normally to perturbations (such as mechanical or electrical) after cutting the rostral afferent fibers to the NTS; c) perturbation of rostral neural structures (RNS) to the NTS modifies the set point without changing the dynamics of the elicited response; and d) cardiovascular responses to perturbations on neural structures within the negative feedback loop compensate for much faster than perturbations on the NTS rostral structures.</p> <p>Results</p> <p>From the control theory framework, experimental evidence found currently in the literature plus experimental results from our group was put together showing that the above-mentioned conditions (to show that the NTS functions as a comparator) are satisfied.</p> <p>Conclusions</p> <p>Physiological experiments suggest that long-term blood pressure is regulated by the nervous system. The NTS functions as a comparator (evaluating the error signal) between its RNS and the cardiovascular receptor afferents and projects to nuclei that regulate the circulatory variables. The mean arterial pressure (MAP) is regulated by the feedback of chemo and cardiopulmonary receptors and the baroreflex would stabilize the short term pressure value to the prevailing carotid MAP. The discharge rates of rostral neural projections to the NTS would function as the set point of the closed and open loops of cardiovascular control. No doubt, then, the RNS play a functional role not only under steady-state conditions, but also in different behaviors and pathologies.</p

Synaptic weights between neurons of modules <i>Y</i> and <i>K</i>.

<p><b>(a)</b> Synaptic weights configuration that allows the model to solve the SRT, consistent with the transition probabilities shown in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0186959#pone.0186959.g002" target="_blank">Fig 2</a>. It can be seen that a specific arrangement of synaptic weights are required. <b>(b)</b> Synaptic weights configuration that allows the model to solve a DT. In contrast with the SRT, all high synaptic weights correspond to pre-post synaptic neurons that are systematically active when reward is obtained. Neurons <i>L</i>₁ and <i>L</i>₂ codify the stimuli that signal which rule is current in a given trial of the DT.</p

Specificity of responses in module <i>K</i> given the firing of presynaptic neurons.

<p>The matrices show the probabilities of postsynaptic <i>K</i> neurons being active at time <i>t</i> given the state of the presynaptic neurons in module <i>Y</i> and module <i>K</i> at time <i>t</i> − 1. Probability magnitudes are consistent with the Markov chain of <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0186959#pone.0186959.g002" target="_blank">Fig 2</a>. This representation gives a hint about how the synaptic weights ought to be. High transition probabilities can be achieved by setting high synaptic weights between a given presynaptic pair and the target postsynaptic neuron, and low synaptic weights for all other postsynaptic neurons.</p

Effect of trials per block on model performance.

<p>Networks were trained in the SRT during 10000 trials, and average SI <b>(a)</b> and performance <b>(b)</b> were computed in 2000 trials without plasticity. Each point in the plot belongs to one network trained with the number of trials per block specified in the x axis. Average SI values were computed from the SI values between pairs of contingencies with shared <i>s</i>(<i>T</i>) or <i>s</i>(<i>T</i> − 1), which are the contingencies with the highest SI, as shown in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0186959#pone.0186959.g009" target="_blank">Fig 9</a>.</p

Serial Reversal protocol and complex network connectivity.

<p><b>(a)</b> Diagram representing the general connectivity of the complex network. Each cue and reward stimulus is coded by the <i>Y</i> neuron population, like in the simple network. Besides, the executed motor response gives sensory feedback, such that each response is also coded by module <i>Y</i>. Module <i>Y</i> connects to all neurons in the integration module <i>K</i>, which in turn connect with each other and with each neuron in the decision module <i>D</i>. Each neuron <i>D</i> is hardwired to one neuron <i>R</i>, so that the response executed is entirely defined by the <i>D</i> module. Synapses between module <i>Y</i> and module <i>K</i>, and within module <i>K</i> are plastic, subject to plasticity rule defined in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0186959#pone.0186959.e063" target="_blank">Eq (23)</a>, which is applied at all times and is not dependent on reward. Synapses between module <i>K</i> and module <i>D</i> are plastic, subject to plasticity rule defined in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0186959#pone.0186959.e064" target="_blank">Eq (24)</a>, which depends on reward. <b>(b)</b> Serial reversal protocol for training the network depicted in (a). Stimuli are presented for 25 ms, and the motor response to be executed is chosen at <i>t</i>_{<i>decision</i>} = 15 ms from cue onset. Plasticity between <i>K</i> and <i>D</i> neurons is applied only if there was reward and within a window spanning from <i>t</i>_{<i>decision</i>} to the end of cue presentation.</p