Supervised spike-timing-dependent plasticity: a spatiotemporal neuronal learning rule for function approximation and decisions.

How can an animal learn from experience? How can it train sensors, such as the auditory or tactile system, based on other sensory input such as the visual system? Supervised spike-timing-dependent plasticity (supervised STDP) is a possible answer. Supervised STDP trains one modality using input from another one as "supervisor." Quite complex time-dependent relationships between the senses can be learned. Here we prove that under very general conditions, supervised STDP converges to a stable configuration of synaptic weights leading to a reconstruction of primary sensory input.

A two-dimensional cochlear fluid model based on conformal mapping.

Using conformal mapping, fluid motion inside the cochlear duct is derived from fluid motion in an infinite half plane. The cochlear duct is represented by a two-dimensional half-open box. Motion of the cochlear fluid creates a force acting on the cochlear partition, modeled by damped oscillators. The resulting equation is one-dimensional, more realistic, and can be handled more easily than existing ones derived by the method of images, making it useful for fast computations of physically plausible cochlear responses. Solving the equation of motion numerically, its ability to reproduce the essential features of cochlear partition motion is demonstrated. Because fluid coupling can be changed independently of any other physical parameter in this model, it allows the significance of hydrodynamic coupling of the cochlear partition to itself to be quantitatively studied. For the model parameters chosen, as hydrodynamic coupling is increased, the simple resonant frequency response becomes increasingly asymmetric. The stronger the hydrodynamic coupling is, the slower the velocity of the resulting traveling wave at the low frequency side is. The model's simplicity and straightforward mathematics make it useful for evaluating more complicated models and for education in hydrodynamics and biophysics of hearing.

Wake tracking and the detection of vortex rings by the canal lateral line of fish.

Research on the lateral line of fish has mainly focused on the detection of oscillating objects. Yet many fish are able to track vortex wakes that arise from other fish. It is not yet known what the sensory input from a wake looks like and how fish can extract relevant information from it. We present a mathematical model to determine how vortices stimulate the canal lateral line and verify it by neuronal recordings. We also show how the information about the orientation of a vortex ring is captured by the lateral-line sensors so as to enable fish to follow a vortex street.

Object localization through the lateral line system of fish: theory and experiment.

Fish acquire information about their aquatic environment by means of their mechanosensory lateral-line system. This system consists of superficial and canal neuromasts that sense perturbations in the water surrounding them. Based on a hydrodynamic model presented here, we propose a mechanism through which fish can localize the source of these perturbations. In doing so we include the curvature of the fish body, a realistic lateral line canal inter-pore distance for the lateral-line canals, and the surface boundary layer. Using our model to explore receptor behavior based on experimental data of responses to dipole stimuli we suggest that superficial and canal neuromasts employ the same mechanism, hence provide the same type of input to the central nervous system. The analytical predictions agree well with spiking responses recorded experimentally from primary lateral-line nerve fibers. From this, and taking into account the central organization of the lateral-line system, we present a simple biophysical model for determining the distance to a source.

Estimating position and velocity of a submerged moving object by the clawed frog Xenopus and by fish--a cybernetic approach.

The lateral-line system is a unique facility of aquatic animals to locate predator, prey, or conspecifics. We present a detailed model of how the clawed frog Xenopus, or fish, can localize submerged moving objects in three dimensions by using their lateral-line system. In so doing we develop two models of a slightly different nature. First, we exploit the characteristic properties of the velocity field, such as zeros and maxima or minima, that a moving object generates at the lateral-line organs and that are directly accessible neuronally, in the context of a simplified geometry. In addition, we show that the associated neuronal model is robust with respect to noise. Though we focus on the superficial neuromasts of Xenopus the same arguments apply mutatis mutandis to the canal lateral-line system of fish. Second, we present a full-blown three-dimensional reconstruction of the source on the basis of a maximum likelihood argument.

How a frog can learn what is where in the dark.

During the night 180 lateral-line organs allow the clawed frog Xenopus to localize prey by detecting water waves emanating from insects floundering on the water surface. Not only can the frog localize prey but it can also determine its character. This suggests waveform reconstruction, and a key question is how the frog can establish the appropriate neuronal hardware. Detecting time differences arising from the input on the skin is a key to neuronal information processing, and spike-timing-dependent synaptic plasticity (STDP) therefore seems to be the natural tool. We show how supervised STDP allows a frog to learn what is where in the dark. Learning can also be derived from a minimization principle.

Minimal model of prey localization through the lateral-line system.

The clawed frog Xenopus is an aquatic predator catching prey at night by detecting water movements caused by its prey. We present a general method, a "minimal model" based on a minimum-variance estimator, to explain prey detection through the frog's many lateral-line organs, even in case several of them are defunct. We show how waveform reconstruction allows Xenopus' neuronal system to determine both the direction and the character of the prey and even to distinguish two simultaneous wave sources. The results can be applied to many aquatic amphibians, fish, or reptiles such as crocodiles.

Zwicker tone illusion and noise reduction in the auditory system.

The Zwicker tone is an auditory aftereffect. For instance, after switching off a broadband noise with a spectral gap, one perceives it as a lingering pure tone with the pitch in the gap. It is a unique illusion in that it cannot be explained by known properties of the auditory periphery alone. Here we introduce a neuronal model explaining the Zwicker tone. We show that a neuronal noise-reduction mechanism in conjunction with dominantly unilateral inhibition explains the effect. A pure tone's "hole burning" in noisy surroundings is given as an illustration.