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The model of the SC due to Cuppini et al. reproduces development of

1. multi-sensory neurons
2. multi-sensory enhancement
3. intra-modality depression
5. inverse effectiveness

The model due to Anastasio and Patton reproduces multi-sensory enhancement.

Deactivating modulatory, cortical input also deactivates multi-sensory enhancement.

Enhancement, depression, multisensory interaction on the neural level are mathematically defined by Wallace and Stein as

$$100\times\frac{r_{mm}-\max(r_a,r_v)}{\max(r_a,r_v)},$$ where $r_a$, and $r_v$ are the mean responses to only an auditory or a visual stimulus and $r_{mm}$ is the response to the combination of the two.

The responses of some visuo-vestibular cells were enhanced, that of others was depressed by combined visuo-vestibular cues.

Neurons in the deep SC which show an enhancement in response to multisensory stimuli peak earlier.

The response profiles have superadditive, additive, and subadditive phases: Even for cross-sensory stimuli whose unisensory components are strong enough to elicit only an additive enhancement of the cumulated response, the response is superadditive over parts of the time course.

In the experiment by Xu et al., SC neurons in cats that were raised with congruent audio-visual stimuli distinguished between disparate combined stimuli, even if these stimuli were both in the neurons' receptive fields. Xu et al. state that this is different in naturally reared cats.

In the the experiment by Xu et al., SC neurons in cats that were raised with congruent audio-visual stimuli had a preferred time difference between onset of visual and auditory stimuli of 0s whereas this is around 50-100ms in normal cats.

In the the experiment by Xu et al., SC neurons in cats reacted best to auditory and visual stimuli that resembled those they were raised with (small flashing spots, broadband noise bursts), however, they generalized and reacted similarly to other stimuli.

Sub-threshold multisensory neurons respond directly only to one modality, however, the strength of the response is strongly influenced by input from another modality.

My theory on sub-threshold multisensory neurons: they receive only inhibitory input from the modality to which they do not directly respond in case that input is outside their receptive field; they receive no excitatory input from that modality if the stimulus is inside their RF.

In Anastasio et al. use their model to explain enhancement and the principle of inverse effectiveness.

Stanford et al. studied single-neuron responses to cross-modal stimuli in their receptive fields. In contrast to previous studies, they systematically tried out different combinations of levels of intensity levels in different modalities.

Input in Martin et al.'s model of multisensory integration in the SC replicates enhancement and, through the non-linear transfer function, superadditivity.

If enhancement in SC neurons due to exogenous, visual, spatial attention is due to residual cue-related activity which is combined (non-linearly) with target-related activity, then that casts an interesting light on (the lack of) intra-modal enhancement:

The only difference between an intra-modal cue-stimulus combination and an intra-modal stimulus-stimulus combination lies in the temporal order of the two. Therefore, if two visual stimuli presented in the receptive field of an SC at the same time) neuron do not enhance the response to each other, then the reason can only be a matter of timing.

The model due to Rowland and Stein manages to reproduce the nonlinear time course of neural responses to, and enhancement in magnitude and inverse effectiveness in multisensory integration in the SC.

Since the model does not include spatial properties, it does not reproduce the spatial principle (ie. no depression).

In the study due to Xu et al., multi-sensory enhancement in specially-raised cats decreased gradually with distance between uni-sensory stimuli instead of occurring if and only if stimuli were present in their RFs. This is different from cats that are raised normally in which enhancement occurs regardless of stimulus distance if both uni-sensory components both are within their RF.

Neural responses in the sc to spatially and temporally coincident cross-sensory stimuli can be much stronger than responses to uni-sensory stimuli.

In fact, they can be much greater than the sum of the responses to either stimulus alone.

Responses in multi-sensory neurons in the SC follow the so-called spatial principle.

Stanford et al. state that superadditivity seems quite common in cases of multi-sensory enhancement.

Enhancement in the SC happens only between stimuli from different modalities.

Depression in the SC happens between stimuli from the same modality.

Is there really no enhancement between different cues from the same modalities, like eg. contrast and color?

Patton and Anastasio present a model of "enhancement and modality-specific suppression in multi-sensory neurons" that requires no multiplicative interaction. It is a follow-up of their earlier functional model of these neurons which requires complex computation.

Anastasio et al. present a model of the response properties of multi-sensory SC neurons which explains enhancement, depression, and super-addititvity using Bayes' rule: If one assumes that a neuron integrates its input to infer the posterior probability of a stimulus source being present in its receptive field, then these effects arise naturally.

Anastasio et al.'s model of SC neurons assumes that these neurons receive multiple inputs with Poisson noise and apply Bayes' rule to calculate the posterior probability of a stimulus being in their receptive fields.

Without an intact association cortex (or LIP), SC neurons cannot develop or maintain cross-modal integration.

(Neither multi-sensory enhancement nor depression.)

On the behavioral side, cross-modal enhancement and depression have been identified as increasing and decreasing the relevance of a stimulus in one modality based on the influence of stimuli in another modality.

Multisensory enhancement and depression are an increased and decreased response of a multisensory neuron to congruent and incongruent stimuli, respectively.

Multisensory enhancement and depression are very different across neurons.

Enhancement is greatest for weak stimuli and least for strong stimuli. This is called inverse effectiveness.

The ANN model of multi-sensory integration in the SC due to Ohshiro et al. manages to replicate a number of physiological finding about the SC:

• inverse effectiveness,
• long-range inhibition and
• short-range activation,
• multisensory integration,
• different tuning to modalities between neurons,
• weighting of stimuli from different modalities.

It does not learn and it has no probabilistic motivation.

Deactivation of AES and rLS leads to a complete lack of cross-modal enhancement while leaving intact the ability of multi-sensory SC neurons to respond to uni-sensory input and even to add input from different sensory modalities.

Rowland et al. derive a model of cortico-collicular multi-sensory integration from findings concerning the influence of deactivation or ablesion of cortical regions anterior ectosylvian cortex (AES) and rostral lateral suprasylvian cortex.

Rowland et al. derive a model of cortico-collicular multi-sensory integration from findings concerning the influence of deactivation or ablesion of cortical regions anterior ectosylvian cortex (AES) and rostral lateral suprasylvian cortex.

It is a single-neuron model.

Cuppini et al. expand on their earlier work in modeling cortico-tectal multi-sensory integration.

They present a model which shows how receptive fields and multi-sensory integration can arise through experience.

Bauer and Wermter use the algorithm they proposed to model multi-sensory integration in the SC. They show that it can learn to near-optimally integrate noisy multi-sensory information and reproduces spatial register of sensory maps, the spatial principle, the principle of inverse effectiveness, and near-optimal audio-visual integration in object localization.