A neurocomputational model for the processing of conflicting information in context-dependent decision tasks

Context-dependent computation is a relevant characteristic of neural systems, endowing them with the capacity of adaptively modifying behavioral responses and flexibly discriminating between relevant and irrelevant information in a stimulus. This ability is particularly highlighted in solving conflicting tasks. A long-standing problem in computational neuroscience, flexible routing of information, is also closely linked with the ability to perform context-dependent associations. Here we present an extension of a context-dependent associative memory model to achieve context-dependent decision-making in the presence of conflicting and noisy multi-attribute stimuli. In these models, the input vectors are multiplied by context vectors via the Kronecker tensor product. To outfit the model with a noisy dynamic, we embedded the context-dependent associative memory in a leaky competing accumulator model, and, finally, we proved the power of the model in the reproduction of a behavioral experiment with monkeys in a context-dependent conflicting decision-making task. At the end, we discuss the neural feasibility of the tensor product and made the suggestive observation that the capacities of tensor context models are surprisingly in alignment with the more recent experimental findings about functional flexibility at different levels of brain organization.

     

Assessing evolutionary epistemology

There are two interrelated but distinct programs which go by the name evolutionary epistemology. One attempts to account for the characteristics of cognitive mechanisms in animals and humans by a straightforward extension of the biological theory of evolution to those aspects or traits of animals which are the biological substrates of cognitive activity, e.g., their brains, sensory systems, motor systems, etc. (EEM program). The other program attempts to account for the evaluation of ideas, scientific theories and culture in general by using models and metaphors drawn from evolutionary biology (EET program). The paper begins by distinguishing the two programs and discussing the relationship between them. The next section addresses the metaphorical and analogical relationship between evolutionary epistemology and evolutionary biology. Section IV treats the question of the locus of the epistemological problem in the light of an evolutionary analysis. The key questions here involve the relationship between evolutionary epistemology and traditional epistemology and the legitimacy of evolutionary epistemology as epistemology. Section V examines the underlying ontological presuppositions and implications of evolutionary epistemology. Finally, section VI, which is merely the sketch of a problem, addresses the parallel between evolutionary epistemology and evolutionary ethics.This research was supported, in part, by a grant from the National Science Foundation # SES—8308720. I want to thank Richard Lewontin and the Museum of Comparative Zoology, Harvard University for their hospitality and support during Spring 1984. I also want to thank David Hull, Charles Dyke and Michael Ruse for helpful comments on an earlier draft, and Andy Altman for pointing out to me the passage from Inherit the Wind.     

A computational mechanism for unified gain and timing control in the cerebellum

Precise gain and timing control is the goal of cerebellar motor learning. Because the basic neural circuitry of the cerebellum is homogeneous throughout the cerebellar cortex, a single computational mechanism may be used for simultaneous gain and timing control. Although many computational models of the cerebellum have been proposed for either gain or timing control, few models have aimed to unify them. In this paper, we hypothesize that gain and timing control can be unified by learning of the complete waveform of the desired movement profile instructed by climbing fiber signals. To justify our hypothesis, we adopted a large-scale spiking network model of the cerebellum, which was originally developed for cerebellar timing mechanisms to explain the experimental data of Pavlovian delay eyeblink conditioning, to the gain adaptation of optokinetic response (OKR) eye movements. By conducting large-scale computer simulations, we could reproduce some features of OKR adaptation, such as the learning-related change of simple spike firing of model Purkinje cells and vestibular nuclear neurons, simulated gain increase, and frequency-dependent gain increase. These results suggest that the cerebellum may use a single computational mechanism to control gain and timing simultaneously.     

Set theory formulation of the model-free problem and the diffusion seeded model-free paradigm

Model-free analysis of NMR relaxation data, which describes the motion of individual atoms, is a problem intricately linked to the Brownian rotational diffusion of the macromolecule. The diffusion tensor parameters strongly influence the optimisation of the various model-free models and the subsequent model selection between them. Finding the optimal model of the dynamics of the system among the numerous diffusion and model-free models is hence quite complex. Using set theory, the entirety of this global problem has been encapsulated by the universal set Ll, and its resolution mathematically formulated as the universal solution Ll. Ever since the original Lipari and Szabo papers the model-free dynamics of a molecule has most often been solved by initially estimating the diffusion tensor. The model-free models which depend on the diffusion parameter values are then optimised and the best model is chosen to represent the dynamics of the residue. Finally, the global model of all diffusion and model-free parameters is optimised. These steps are repeated until convergence. For simplicity this approach to Ll will be labelled the diffusion seeded model-free paradigm. Although this technique suffers from a number of problems many have been solved. All aspects of the diffusion seeded paradigm and its consequences, together with a few alternatives to the paradigm, will be reviewed through the use of set notation.     

Stability and stabilization for models of chemostats with multiple limiting substrates

We study chemostat models in which multiple species compete for two or more limiting nutrients. First, we consider the case where the nutrient flow and species removal rates and input nutrient concentrations are all given as positive constants. In that case, we use Brouwer degree theory to give conditions guaranteeing that the models admit globally asymptotically stable componentwise positive equilibrium points, from all componentwise positive initial states. Then we use the results to develop stabilization theory for a class of controlled chemostats with two or more limiting nutrients. For cases where the dilution rate and input nutrient concentrations can be selected as controls, we prove that many different componentwise positive equilibria can be made globally asymptotically stable. This extends the existing control results for chemostats with one limiting nutrient. We demonstrate our methods in simulations.     

Stability and stabilization for models of chemostats with multiple limiting substrates

We study chemostat models in which multiple species compete for two or more limiting nutrients. First, we consider the case where the nutrient flow and species removal rates and input nutrient concentrations are all given as positive constants. In that case, we use Brouwer degree theory to give conditions guaranteeing that the models admit globally asymptotically stable componentwise positive equilibrium points, from all componentwise positive initial states. Then we use the results to develop stabilization theory for a class of controlled chemostats with two or more limiting nutrients. For cases where the dilution rate and input nutrient concentrations can be selected as controls, we prove that many different componentwise positive equilibria can be made globally asymptotically stable. This extends the existing control results for chemostats with one limiting nutrient. We demonstrate our methods in simulations.     

The capabilities and limitations of conductance-based compartmental neuron models with reduced branched or unbranched morphologies and active dendrites

Conductance-based neuron models are frequently employed to study the dynamics of biological neural networks. For speed and ease of use, these models are often reduced in morphological complexity. Simplified dendritic branching structures may process inputs differently than full branching structures, however, and could thereby fail to reproduce important aspects of biological neural processing. It is not yet well understood which processing capabilities require detailed branching structures. Therefore, we analyzed the processing capabilities of full or partially branched reduced models. These models were created by collapsing the dendritic tree of a full morphological model of a globus pallidus (GP) neuron while preserving its total surface area and electrotonic length, as well as its passive and active parameters. Dendritic trees were either collapsed into single cables (unbranched models) or the full complement of branch points was preserved (branched models). Both reduction strategies allowed us to compare dynamics between all models using the same channel density settings. Full model responses to somatic inputs were generally preserved by both types of reduced model while dendritic input responses could be more closely preserved by branched than unbranched reduced models. However, features strongly influenced by local dendritic input resistance, such as active dendritic sodium spike generation and propagation, could not be accurately reproduced by any reduced model. Based on our analyses, we suggest that there are intrinsic differences in processing capabilities between unbranched and branched models. We also indicate suitable applications for different levels of reduction, including fast searches of full model parameter space.     

Multi/infinite dimensional neural networks, multi/infinite dimensional logic theory

A mathematical model of an arbitrary multi-dimensional neural network is developed and a convergence theorem for an arbitrary multi-dimensional neural network represented by a fully symmetric tensor is stated and proved. The input and output signal states of a multi-dimensional neural network/logic gate are related through an energy function, defined over the fully symmetric tensor (representing the connection structure of a multi-dimensional neural network). The inputs and outputs are related such that the minimum/maximum energy states correspond to the output states of the logic gate/neural network realizing a logic function. Similarly, a logic circuit consisting of the interconnection of logic gates, represented by a block symmetric tensor, is associated with a quadratic/higher degree energy function. Infinite dimensional logic theory is discussed through the utilization of infinite dimension/order tensors.     

Stability of delayed memristive neural networks with time-varying impulses

This paper addresses the stability problem on the memristive neural networks with time-varying impulses. Based on the memristor theory and neural network theory, the model of the memristor-based neural network is established. Different from the most publications on memristive networks with fixed-time impulse effects, we consider the case of time-varying impulses. Both the destabilizing and stabilizing impulses exist in the model simultaneously. Through controlling the time intervals of the stabilizing and destabilizing impulses, we ensure the effect of the impulses is stabilizing. Several sufficient conditions for the globally exponentially stability of memristive neural networks with time-varying impulses are proposed. The simulation results demonstrate the effectiveness of the theoretical results.     

Knowledge management of the neuroscientific literature: the data model and underlying strategy of the NeuroScholar system.

This paper describes the underlying strategy and system's design of a knowledge management system for the neuroscientific literature called 'NeuroScholar'. The problem that the system is designed to address is to delineate fully the neural circuitry involved in a specific behaviour. The use of this system provides experimental neuroscientists with a new method of building computational models ('knowledge models') of the contents of the published literature. These models may provide input for analysis (conceptual or computational), or be used as constraint sets for conventional neural modelling work. The underlying problems inherent in this approach, the general framework for the proposed solution, the practical issues concerning usage of the system and a detailed, technical account of the system are described. The author uses a widely used software specification language (the Universal Modelling Language) to describe the design of the system and present examples from published work concerned with classical eyeblink conditioning in the rabbit.     

Development and evolution of cerebellar neural circuits

The cerebellum controls smooth and skillful movements and it is also involved in higher cognitive and emotional functions. The cerebellum is derived from the dorsal part of the anterior hindbrain and contains two groups of cerebellar neurons: glutamatergic and gamma-aminobutyric acid (GABA)ergic neurons. Purkinje cells are GABAergic and granule cells are glutamatergic. Granule and Purkinje cells receive input from outside of the cerebellum from mossy and climbing fibers. Genetic analysis of mice and zebrafish has revealed genetic cascades that control the development of the cerebellum and cerebellar neural circuits. During early neurogenesis, rostrocaudal patterning by intrinsic and extrinsic factors, such as Otx2, Gbx2 and Fgf8, plays an important role in the positioning and formation of the cerebellar primordium. The cerebellar glutamatergic neurons are derived from progenitors in the cerebellar rhombic lip, which express the proneural gene Atoh1. The GABAergic neurons are derived from progenitors in the ventricular zone, which express the proneural gene Ptf1a. The mossy and climbing fiber neurons originate from progenitors in the hindbrain rhombic lip that express Atoh1 or Ptf1a. Purkinje cells exhibit mediolateral compartmentalization determined on the birthdate of Purkinje cells, and linked to the precise neural circuitry formation. Recent studies have shown that anatomy and development of the cerebellum is conserved between mammals and bony fish (teleost species). In this review, we describe the development of cerebellar neurons and neural circuitry, and discuss their evolution by comparing developmental processes of mammalian and teleost cerebellum.     

Use of Neural Networks to Correlate Spine and Rib Deformity in Scoliosis

Artificial neural networks (ANN's) recognize patterns relating input and output data in a manner analogous to the function of biological neurons. Here, we show that ANN's can predict rib deformity in scoliosis more accurately than regression analysis. ANN's and linear regression models were developed to predict rib rotation from several combinations of input spinal indices including Cobb angle, vertebral rotation, apex location and orientation of the plane of maximal curvature. ANN's averaged 60% correct predictions compared to 34% for regression analysis. This study provides evidence for the utility of artificial neural networks in scoliosis research. These data lend credence to the use of ANN's in future work on the prediction of scoliotic spinal deformity from torso surface data, which would permit assessment of scoliosis severity with minimal use of harmful X-rays.     

Evaluation of cross-sectional geometry and mass density distributions of humans and laboratory animals using computerized tomography

The purpose of this study was to determine the cross-sectional geometry and mass density distribution of a young porcine subject using the X-ray computerized tomographic (CT) method and to perform a comparative study of anatomical features of this subject and a 3 yr old female child specimen. The cross-sectional CT scans of the porcine subject were obtained at 1 cm intervals. The outlines of each cross section and of selected anatomical components within each section were obtained by standard picture processing techniques. The mass and inertia tensor for each cross section and for each anatomical structure in a section were computed based on the CT numbers. The porcine subject was then sacrificed, frozen, sectioned and photographed. These sectional photographs were then compared with those obtained from the CT method. Tabulated cross-sectional mass and inertia tensor obtained from CT scans of the porcine subject were also used to compare with similar results derived from previously completed CT scans of the 3 yr old female child specimen. In particular, the comparisons were made on the location of the center of gravity and the inertia tensor in the head, neck, head and neck and cervical spine regions. Some immediate applications of this data are inputs to finite element models, lumped parameter biodynamic models, computer simulation of vehicle crash victims, and dummy design.     

End-to-end neural system identification with neural information flow

Neural information flow (NIF) provides a novel approach for system identification in neuroscience. It models the neural computations in multiple brain regions and can be trained end-to-end via stochastic gradient descent from noninvasive data. NIF models represent neural information processing via a network of coupled tensors, each encoding the representation of the sensory input contained in a brain region. The elements of these tensors can be interpreted as cortical columns whose activity encodes the presence of a specific feature in a spatiotemporal location. Each tensor is coupled to the measured data specific to a brain region via low-rank observation models that can be decomposed into the spatial, temporal and feature receptive fields of a localized neuronal population. Both these observation models and the convolutional weights defining the information processing within regions are learned end-to-end by predicting the neural signal during sensory stimulation. We trained a NIF model on the activity of early visual areas using a large-scale fMRI dataset recorded in a single participant. We show that we can recover plausible visual representations and population receptive fields that are consistent with empirical findings.     

Embedding Responses in Spontaneous Neural Activity Shaped through Sequential Learning

Recent experimental measurements have demonstrated that spontaneous neural activity in the absence of explicit external stimuli has remarkable spatiotemporal structure. This spontaneous activity has also been shown to play a key role in the response to external stimuli. To better understand this role, we proposed a viewpoint, “memories-as-bifurcations,” that differs from the traditional “memories-as-attractors” viewpoint. Memory recall from the memories-as-bifurcations viewpoint occurs when the spontaneous neural activity is changed to an appropriate output activity upon application of an input, known as a bifurcation in dynamical systems theory, wherein the input modifies the flow structure of the neural dynamics. Learning, then, is a process that helps create neural dynamical systems such that a target output pattern is generated as an attractor upon a given input. Based on this novel viewpoint, we introduce in this paper an associative memory model with a sequential learning process. Using a simple Hebbian-type learning, the model is able to memorize a large number of input/output mappings. The neural dynamics shaped through the learning exhibit different bifurcations to make the requested targets stable upon an increase in the input, and the neural activity in the absence of input shows chaotic dynamics with occasional approaches to the memorized target patterns. These results suggest that these dynamics facilitate the bifurcations to each target attractor upon application of the corresponding input, which thus increases the capacity for learning. This theoretical finding about the behavior of the spontaneous neural activity is consistent with recent experimental observations in which the neural activity without stimuli wanders among patterns evoked by previously applied signals. In addition, the neural networks shaped by learning properly reflect the correlations of input and target-output patterns in a similar manner to those designed in our previous study.     

Recurrent cerebellar architecture solves the motor-error problem

Current views of cerebellar function have been heavily influenced by the models of Marr and Albus, who suggested that the climbing fibre input to the cerebellum acts as a teaching signal for motor learning. It is commonly assumed that this teaching signal must be motor error (the difference between actual and correct motor command), but this approach requires complex neural structures to estimate unobservable motor error from its observed sensory consequences. We have proposed elsewhere a recurrent decorrelation control architecture in which Marr-Albus models learn without requiring motor error. Here, we prove convergence for this architecture and demonstrate important advantages for the modular control of systems with multiple degrees of freedom. These results are illustrated by modelling adaptive plant compensation for the three-dimensional vestibular ocular reflex. This provides a functional role for recurrent cerebellar connectivity, which may be a generic anatomical feature of projections between regions of cerebral and cerebellar cortex.     

Equilibrium points for nonlinear compartmental models.

Equilibrium points for nonlinear autonomous compartmental models with constant input are discussed. Upper and lower bounds for the steady states are derived. Theorems guaranteeing existence and uniqueness of equilibrium points for a large collection of system are proved. New information relating to mean residence times is developed. Asymptotic results and a section on stability are included. A recursive process is discussed that generates iterates that converge to steady states for certain types of models. An interesting range of models are included as examples. An attempt is made to provide general qualitative theory for such nonlinear compartmental systems.     

Use of Neural Networks to Correlate Spine and Rib Deformity in Scoliosis

Abstract

Artificial neural networks (ANN's) recognize patterns relating input and output data in a manner analogous to the function of biological neurons. Here, we show that ANN's can predict rib deformity in scoliosis more accurately than regression analysis. ANN's and linear regression models were developed to predict rib rotation from several combinations of input spinal indices including Cobb angle, vertebral rotation, apex location and orientation of the plane of maximal curvature. ANN's averaged 60% correct predictions compared to 34% for regression analysis. This study provides evidence for the utility of artificial neural networks in scoliosis research. These data lend credence to the use of ANN's in future work on the prediction of scoliotic spinal deformity from torso surface data, which would permit assessment of scoliosis severity with minimal use of harmful X-rays.     

Determinants of synaptic integration and heterogeneity in rebound firing explored with data-driven models of deep cerebellar nucleus cells

Significant inroads have been made to understand cerebellar cortical processing but neural coding at the output stage of the cerebellum in the deep cerebellar nuclei (DCN) remains poorly understood. The DCN are unlikely to just present a relay nucleus because Purkinje cell inhibition has to be turned into an excitatory output signal, and DCN neurons exhibit complex intrinsic properties. In particular, DCN neurons exhibit a range of rebound spiking properties following hyperpolarizing current injection, raising the question how this could contribute to signal processing in behaving animals. Computer modeling presents an ideal tool to investigate how intrinsic voltage-gated conductances in DCN neurons could generate the heterogeneous firing behavior observed, and what input conditions could result in rebound responses. To enable such an investigation we built a compartmental DCN neuron model with a full dendritic morphology and appropriate active conductances. We generated a good match of our simulations with DCN current clamp data we recorded in acute slices, including the heterogeneity in the rebound responses. We then examined how inhibitory and excitatory synaptic input interacted with these intrinsic conductances to control DCN firing. We found that the output spiking of the model reflected the ongoing balance of excitatory and inhibitory input rates and that changing the level of inhibition performed an additive operation. Rebound firing following strong Purkinje cell input bursts was also possible, but only if the chloride reversal potential was more negative than −70 mV to allow de-inactivation of rebound currents. Fast rebound bursts due to T-type calcium current and slow rebounds due to persistent sodium current could be differentially regulated by synaptic input, and the pattern of these rebounds was further influenced by HCN current. Our findings suggest that active properties of DCN neurons could play a crucial role for signal processing in the cerebellum.