Thomas P. Trappenberg

A Model of Saccade Initiation Based on the Competitive Integration of Exogenous and Endogenous Signals in the Superior Colliculus

Significant advances in cognitive neuroscience can be achieved by combining techniques used to measure behavior and brain activity with neural modeling. Here we apply this approach to the initiation of rapid eye movements (saccades), which are used to redirect the visual axis to targets of interest. It is well known that the superior colliculus (SC) in the midbrain plays a major role in generating saccadic eye movements, and physiological studies have provided important knowledge of the activity pattern of neurons in this structure. Based on the observation that the SC receives localized sensory (exogenous) and voluntary (endogenous) inputs, our model assumes that this information is integrated by dynamic competition across local collicular interactions. The model accounts well for the effects upon saccadic reaction time (SRT) due to removal of fixation, the presence of distractors, execution of pro-versus antisaccades, and variation in target probability, and suggests a possible mechanism for the generation of express saccades. In each of these cases, the activity patterns of neurons within the model closely resemble actual cell behavior in the intermediate layer of the SC. The interaction structure we employ is instrumental for producing a physiologically faithful model and results in new insights and hypotheses regarding the neural mechanisms underlying saccade initiation.

A unified model of spatial and episodic memory.

Medial temporal lobe structures including the hippocampus are implicated by separate investigations in both episodic memory and spatial function. We show that a single recurrent attractor network can store both the discrete memories that characterize episodic memory and the continuous representations that characterize physical space. Combining both types of representation in a single network is actually necessary if objects and where they are located in space must be stored. We thus show that episodic memory and spatial theories of medial temporal lobe function can be combined in a unified model.

Self-organizing continuous attractor networks and path integration: two-dimensional models of place cells.

Single-neuron recording studies have demonstrated the existence of neurons in the hippocampus which appear to encode information about the place where a rat is located, and about the place at which a macaque is looking. We describe ‘continuous attractor’ neural network models of place cells with Gaussian spatial fields in which the recurrent collateral synaptic connections between the neurons reflect the distance between two places. The networks maintain a localized packet of neuronal activity that represents the place where the animal is located. We show for two related models how the representation of the two-dimensional space in the continuous attractor network of place cells could self-organize by modifying the synaptic connections between the neurons, and also how the place being represented can be updated by idiothetic (self-motion) signals in a neural implementation of path integration.

Selecting inputs for modeling using normalized higher order statistics and independent component analysis

The problem of input variable selection is well known in the task of modeling real-world data. In this paper, we propose a novel model-free algorithm for input variable selection using independent component analysis and higher order cross statistics. Experimental results are given which indicate that the method is capable of giving reliable performance and that it outperforms other approaches when the inputs are dependent.

Overlap versus imbalance

In this paper we give a systematic analysis of the relationship between imbalance and overlap as factors influencing classifier performance We demonstrate that these two factors have interdependent effects and that we cannot form a full understanding of their effects by considering them only in isolation Although the imbalance problem can be considered a symptom of the small disjuncts problem which is solved by using larger training sets, the overlap problem is of a fundamentally different character and the performance of learned classifiers can actually be made worse by using more training data when overlap is present We also examine the effects of overlap and imbalance on the complexity of the learned model and demonstrate that overlap is a far more serious factor than imbalance in this respect.

Spatial interactions in the superior colliculus predict saccade behavior in a neural field model

During natural vision, eye movements are dynamically controlled by the combinations of goal-related top–down (TD) and stimulus-related bottom–up (BU) neural signals that map onto objects or locations of interest in the visual world. In primates, both BU and TD signals converge in many areas of the brain, including the intermediate layers of the superior colliculus (SCi), a midbrain structure that contains a retinotopically coded map for saccades. How TD and BU signals combine or interact within the SCi map to influence saccades remains poorly understood and actively debated. It has been proposed that winner-take-all competition between these signals occurs dynamically within this map to determine the next location for gaze. Here, we examine how TD and BU signals interact spatially within an artificial two-dimensional dynamic winner-take-all neural field model of the SCi to influence saccadic RT (SRT). We measured point images (spatially organized population activity on the SC map) physiologically to inform the TD and BU model parameters. In this model, TD and BU signals interacted nonlinearly within the SCi map to influence SRT via changes to the (1) spatial size or extent of individual signals, (2) peak magnitude of individual signals, (3) total number of competing signals, and (4) the total spatial separation between signals in the visual field. This model reproduced previous behavioral studies of TD and BU influences on SRT and accounted for multiple inconsistencies between them. This is achieved by demonstrating how, under different experimental conditions, the spatial interactions of TD and BU signals can lead to either increases or decreases in SRT. Our results suggest that dynamic winner-take-all modeling with local excitation and distal inhibition in two dimensions accurately reflects both the physiological activity within the SCi map and the behavioral changes in SRT that result from BU and TD manipulations.

Modeling inhibition of return as short-term depression of early sensory input to the superior colliculus.

Inhibition of return (IOR) is an orienting phenomenon characterized by slower behavioral responses to spatially cued, relative to uncued targets, when the cue-target onset asynchronies (CTOAs) are long enough that cue-elicited attentional capture has dispersed. Here, we implement a short-term depression (STD) account of IOR within a neuroscientifically based dynamic neural field model (DNF) of the superior colliculus (SC). In addition to the prototypical findings in the cue-target paradigm (i.e., the biphasic pattern of behavioral enhancement at short CTOAs and behavioral costs at long CTOAs), a variety of findings in the literature are generated with this model, including IOR in averaging saccades and the co-existence of IOR and endogenous orienting at the same location. Many findings that cannot be accommodated by this model could be accounted for by incorporating cortical contributions.

Broken phase of the 4-dimensional Ising model in a finite volume☆

Abstract The volume dependence of physical quantities, like renormalized mass and coupling, is numerically investigated in the broken phase of the 4-dimensional Ising model. It is shown that finite volume effects in small and intermediate volumes are dominated by vacuum tunneling. The tunneling phenomenon is investigated in detail. The splitting of the ground states due to tunneling turns out to be given to a good approximation by an instanton-like calculation. The large volume limit of the physical quantities is compared to the prediction of the perturbative renormalization group which connects the scaling behaviour on both sides of the phase transition. A good agreement with the 3-loop β-function is observed.

A Heuristic for Free Parameter Optimization with Support Vector Machines

A heuristic is proposed to address free parameter selection for Support Vector Machines, with the goals of improving generalization performance and providing greater insensitivity to training set selection. The many local extrema in these optimization problems make gradient descent algorithms impractical. The main point of the proposed heuristic is the inclusion of a model complexity measure to improve generalization performance. We also use simulated annealing to improve parameter search efficiency compared to an exhaustive grid search, and include an intensity-weighted centre of mass of the most optimum points to reduce volatility. We examine two standard classification problems for comparison, and apply the heuristic to bioinformatics and retinal electrophysiology classification.

Vacuum tunneling in the four-dimensional Ising model

Abstract In the broken phase of the four-dimensional Ising model tunneling between the two degenerate minima of the effective potential takes place in a finite volume. We study this phenomenon numerically. The energies of the lowest zero momentum states are determined on both sides of the phase transition and their different correspondence to particle states in the infinite-volume limit is discussed. A Z2-invariant definition of the field expectation value and susceptibility is exploited for calculation of the quantities in finite volumes.