Bifurcation study of a neural field competition model with an application to perceptual switching in motion integration

A dynamical model of visual motion processing for arbitrary stimuli including type II plaids

To explore the operating principle of visual motion processing in the brain underlying perception and eye movements, we model the information processing of velocity estimate of the visual stimulus at the algorithmic level using the dynamical system approach. In this study, we formulate the model as an optimization process of an appropriately defined objective function. The model is applicable to arbitrary visual stimuli. We find that our theoretical predictions qualitatively agree with time evolution of eye movement reported by previous works across various types of stimulus. Our results suggest that the brain implements the present framework as the internal model of motion vision. We anticipate our model to be a promising building block for more profound understanding of visual motion processing as well as for the development of robotics.

The uncoupling limit of identical Hopf bifurcations with an application to perceptual bistability

We study the dynamics arising when two identical oscillators are coupled near a Hopf bifurcation where we assume a parameter ϵ uncouples the system at [Formula: see text]. Using a normal form for [Formula: see text] identical systems undergoing Hopf bifurcation, we explore the dynamical properties. Matching the normal form coefficients to a coupled Wilson-Cowan oscillator network gives an understanding of different types of behaviour that arise in a model of perceptual bistability. Notably, we find bistability between in-phase and anti-phase solutions that demonstrates the feasibility for synchronisation to act as the mechanism by which periodic inputs can be segregated (rather than via strong inhibitory coupling, as in the existing models). Using numerical continuation we confirm our theoretical analysis for small coupling strength and explore the bifurcation diagrams for large coupling strength, where the normal form approximation breaks down.

'Two vs one' rivalry by the Loxley-Robinson model

We apply the competitive model of Loxley and Robinson (Phys Rev Lett 102:258701, 2009. doi: 10.1103/PhysRevLett.102.258701 ) to the study of a special case of visual rivalry. Three-peaked inputs with maxima at symmetrical locations are introduced, and the role of three-bump configurations is then considered. The model yields conditions for what can be interpreted as a bistable percept analogous to the one-dimensional version of a competition between the central and flanking parts of an image.

Recurrent network dynamics reconciles visual motion segmentation and integration

In sensory systems, a range of computational rules are presumed to be implemented by neuronal subpopulations with different tuning functions. For instance, in primate cortical area MT, different classes of direction-selective cells have been identified and related either to motion integration, segmentation or transparency. Still, how such different tuning properties are constructed is unclear. The dominant theoretical viewpoint based on a linear-nonlinear feed-forward cascade does not account for their complex temporal dynamics and their versatility when facing different input statistics. Here, we demonstrate that a recurrent network model of visual motion processing can reconcile these different properties. Using a ring network, we show how excitatory and inhibitory interactions can implement different computational rules such as vector averaging, winner-take-all or superposition. The model also captures ordered temporal transitions between these behaviors. In particular, depending on the inhibition regime the network can switch from motion integration to segmentation, thus being able to compute either a single pattern motion or to superpose multiple inputs as in motion transparency. We thus demonstrate that recurrent architectures can adaptively give rise to different cortical computational regimes depending upon the input statistics, from sensory flow integration to segmentation.

Bump competition and lattice solutions in two-dimensional neural fields

Some forms of competition among activity bumps in a two-dimensional neural field are studied. First, threshold dynamics is included and rivalry evolutions are considered. The relations between parameters and dominance durations can match experimental observations about ageing. Next, the threshold dynamics is omitted from the model and we focus on the properties of the steady-state. From noisy inputs, hexagonal grids are formed by a symmetry-breaking process. Particular issues about solution existence and stability conditions are considered. We speculate that they affect the possibility of producing basis grids which may be combined to form feature maps.

Neural Field Models with Threshold Noise

The original neural field model of Wilson and Cowan is often interpreted as the averaged behaviour of a network of switch like neural elements with a distribution of switch thresholds, giving rise to the classic sigmoidal population firing-rate function so prevalent in large scale neuronal modelling. In this paper we explore the effects of such threshold noise without recourse to averaging and show that spatial correlations can have a strong effect on the behaviour of waves and patterns in continuum models. Moreover, for a prescribed spatial covariance function we explore the differences in behaviour that can emerge when the underlying stationary distribution is changed from Gaussian to non-Gaussian. For travelling front solutions, in a system with exponentially decaying spatial interactions, we make use of an interface approach to calculate the instantaneous wave speed analytically as a series expansion in the noise strength. From this we find that, for weak noise, the spatially averaged speed depends only on the choice of covariance function and not on the shape of the stationary distribution. For a system with a Mexican-hat spatial connectivity we further find that noise can induce localised bump solutions, and using an interface stability argument show that there can be multiple stable solution branches.

Neuromechanistic Model of Auditory Bistability

Sequences of higher frequency A and lower frequency B tones repeating in an ABA- triplet pattern are widely used to study auditory streaming. One may experience either an integrated percept, a single ABA-ABA- stream, or a segregated percept, separate but simultaneous streams A-A-A-A- and -B---B--. During minutes-long presentations, subjects may report irregular alternations between these interpretations. We combine neuromechanistic modeling and psychoacoustic experiments to study these persistent alternations and to characterize the effects of manipulating stimulus parameters. Unlike many phenomenological models with abstract, percept-specific competition and fixed inputs, our network model comprises neuronal units with sensory feature dependent inputs that mimic the pulsatile-like A1 responses to tones in the ABA- triplets. It embodies a neuronal computation for percept competition thought to occur beyond primary auditory cortex (A1). Mutual inhibition, adaptation and noise are implemented. We include slow NDMA recurrent excitation for local temporal memory that enables linkage across sound gaps from one triplet to the next. Percepts in our model are identified in the firing patterns of the neuronal units. We predict with the model that manipulations of the frequency difference between tones A and B should affect the dominance durations of the stronger percept, the one dominant a larger fraction of time, more than those of the weaker percept—a property that has been previously established and generalized across several visual bistable paradigms. We confirm the qualitative prediction with our psychoacoustic experiments and use the behavioral data to further constrain and improve the model, achieving quantitative agreement between experimental and modeling results. Our work and model provide a platform that can be extended to consider other stimulus conditions, including the effects of context and volition.

Humans have an astonishing ability to separate out different sound sources in a busy room: think of how we can hear individual voices in a bustling coffee shop. Rather than voices, we use sound stimuli in the lab: repeating patterns of high and low tones. The tone sequences are ambiguous and can be interpreted in different ways—either grouped into a single stream, or separated out into different streams. When listening for a long time, one’s perception switches every few seconds, a phenomenon called auditory bistability. Based on knowledge of the organization of brain areas involved in separating out different sound sources and how neurons in these areas respond to the ambiguous sequences, we developed a computational model of auditory bistabilty. Our model is less abstract than existing models and shows how groups of neurons may compete in order to dictate what you perceive. We predict how the difference between the two tone sequences affects what you hear over time and we performed an experiment with human listeners to confirm our prediction. The model provides groundwork to further explore the way the brain deals with the busy and often ambiguous world of sound.

Rich spectrum of neural field dynamics in the presence of short-term synaptic depression

In continuous attractor neural networks (CANNs), spatially continuous information such as orientation, head direction, and spatial location is represented by Gaussian-like tuning curves that can be displaced continuously in the space of the preferred stimuli of the neurons. We investigate how short-term synaptic depression (STD) can reshape the intrinsic dynamics of the CANN model and its responses to a single static input. In particular, CANNs with STD can support various complex firing patterns and chaotic behaviors. These chaotic behaviors have the potential to encode various stimuli in the neuronal system.

Construction and evaluation of an integrated dynamical model of visual motion perception

Although numerous models describe the individual neural mechanisms that may be involved in the perception of visual motion, few of them have been constructed to take arbitrary stimuli and map them to a motion percept. Here, we propose an integrated dynamical motion model (IDM), which is sufficiently general to handle diverse moving stimuli, yet sufficiently precise to account for a wide-ranging set of empirical observations made on a family of random dot kinematograms. In particular, we constructed models of the cortical areas involved in motion detection, motion integration and perceptual decision. We analyzed their parameters through dynamical simulations and numerical continuation to constrain their proper ranges. Then, empirical data from a family of random dot kinematograms experiments with systematically varying direction distribution, presentation duration and stimulus size, were used to evaluate our model and estimate corresponding model parameters. The resulting model provides an excellent account of a demanding set of parametrically varied behavioral effects on motion perception, providing both quantitative and qualitative elements of evaluation.

Dynamic resolution of ambiguity during tri-stable motion perception

Multi-stable perception occurs when an image falling onto the retina has multiple incompatible interpretations. We probed this phenomenon in psychophysical experiments using a moving barber-pole visual stimulus configured as a square to generate three competing perceived directions, horizontal, diagonal and vertical. We characterised patterns in reported switching type and percept duration, classifying switches into three groups related to the direction cues driving such transitions i.e. away from diagonal, towards diagonal and between cardinals. The proportions of each class reported by participants depended on contrast. The two including diagonals dominated at low contrast and those between cardinals increased in proportion as contrast was increased. At low contrasts, the less frequent cardinals persisted for shorter than the dominant diagonals and this was reversed at higher contrasts. This observed asymmetry between the dominance of transition classes appears to be driven by different underlying dynamics between cardinal and the oblique cues and their related transitions. At trial onset we found that transitions away from diagonal dominate, a tendency which later in the trial reverses to dominance by transitions excluding the diagonal, most prominently at higher contrasts. Thus ambiguity is resolved over a contrast dependent temporal integration similar to, but lasting longer than that observed when resolving the aperture problem to estimate direction. When the diagonal direction dominates perception, evidence is found for a noisier competition seen in broader duration distributions than during dominance of cardinal perception. There remain aspects of these identified differences in cardinal and oblique dynamics to be investigated in future.