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``System S provides a core simulation of an object or process B just in case S is a concrete computational device that produces, via a temporal process, solutions to a computational model [...] that correctly represents B, either dynamically or statically. If in addition the computational model used by S correctly represents the structure of the real system R, then S provides a core simulation of system R with respect to B.''

A full simulation in Humphreys' sense is the combination of a core simulation with an output representation.

According to Humphreys, simulation is a set of techniques rather than a single tool. It includes

  • numerical solution of equations,
  • visualization,
  • error correction on the computational methods,
  • data analysis,
  • model explorations

A simple, somewhat lacking definition of computational science is, according to Humphreys:

``computational science consists in the development, exploration, and implementation of computational models of nonmathematical systems using concrete computational devices.''

According to Hartmann,

``A model is called dynamic, if it... includes assumptions about the time-evolution of the system. ... Simulations are closely related to dynamic models. More concretely, a simulation results when the equations of the underlying dynamic model are solved. This model is designed to imitate the time evolution of a real system. To put it another way, a simulation imitates one process by another process. In this definition, the term `process’ refers solely to some object or system whose state changes in time. If the simulation is run on a computer, it is called a computer simulation.''

According to Humphreys, Hartmann's definition of a simulation needs revision, but is basically correct.

In Humphreys' view, simulations need not include evolution over time.

Computational Neuroscience is computational science in neuroscience.

According to Humphreys, the difference between a simulation and a representation or computational model is that it the formulae are evaluated; The formula for an elliptic curve together with parameters (and initial conditions) is a representation of a planetary orbit and a specialized subset of Newtonian physics plus data is a computational model of it. But only the model plus solutions to the formulae for a finite number of time steps is a simulation. (My examples.)

A computational model has six components, according to Humphreys:

  1. A computational template', together with types of boundary and initial conditions—thebasic computational form';
  2. Construction assumptions;
  3. Correction set;
  4. An interpretation;
  5. Initial Justification of the template;
  6. An output representation.

A computational template in Humphreys diction, is a mathematical system (set of equations, logical formulae etc.) which is in itself out of context but can be applied to at least one area of discourse.

`Construction assumptions' in Humphreys' definition of computational models describe the correspondence between entities in the computational template and entities in the world together with the mismatch. They are a quintuple:

  1. Ontology
    which maps entities between computational template and world
  2. Idealizations
  3. Abstractions
  4. Constraints
  5. Approximations

The `correction set' seems to me to be a description of the knobs to turn to fit a computational model to empirical data.

A computational model according to Humphreys seems to me to be a computational theory (in the logician's sense) and a manual for applying it to the world.

A model is a substitution of variables in a theory by objects (individuals) which satisfies all the theory's sentences.

There are quite a number of different definitions of multi-sensory integration.

According to Palmer and Ramsey,

"Multisensory integration refers to the process by which information from different sensory modalities (e.g., vision, audition, touch) is combined to yield a rich, coherent representation of an object or event in the environment."

Hinoshita et al. define self-organization as the phenomenon of a global, coherent structure arising in a system through local interaction between its elements as opposed to through some sort of central control.

According to Hinoshita et al., recurrent neural networks are capable of self-organization.

According to Sun, a computational cognitive model is a theory of cognition which describes mechanisms and processes of cognition computationally and thus is `runnable'.

Simon calls theories in psychology which make predictions by quantitatively describing structural characteristics of the brain models.

Machamer et al. define mechanisms as:

[...] entities and activities organized such that they are productive of regular changes from start or set-up to finish or termination conditions.

Scientists do not always flesh out their theories in full. They often only describe those parts they are interested in (and leave the rest in an abstract form). Machamer et al. call descriptions of mechanisms which leave detailed specification of some of their activities and entities mechanism schemata.

Mechanism schemata and mechanism sketches seem to me to be what is often referred to as a model in computational neuroscience.

Machamer et al. call a mechanism schema with explicitly missing parts a mechanism sketch.

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.

Middlebrooks and Knudsen define a spatial receptive field of a neuron as that angular range from which a stimulus elicits any response above baseline.

The best area, on the other hand, is that range from which it a stimulus elicits at least 75% of the maximum response.

Middlebrooks and Knudsen note that other studies use different definitions.

The neural response of an SC neuron to one stimulus can be made weaker in some neurons by another stimulus at a different position in space. This stimulus can be in the same or in a different modality (in multi-sensory neurons). This effect is called depression.

Kadunce et al. did not find within-modality visual suppression as often as within-modality auditory suppression.

VIsual attention is the facilitation of visual processing of some stimuli over others.

Biomimetics is the approach of making use of the technological and theoretical insights of the biological sciences for engineering.

Often, the quest to understand a biological system leads to the recognition of new paradigms for engineering.

Often biology has a solution to a problem in the engineering disciplines.

Muscle synergies are coordinated activations of groups of muscles.

There is the hypothesis that complex motions are comprised of combinations of simple muscle synergies, which would reduce the dimensionality of the control signal.

A low-dimensional representation of motion patterns in a high-dimensional space restricts the actual dimensionality of those motions.

I'm not so sure that a low-dimensional representation of motion patterns in a high-dimensional space necessarily restricts the actual dimensionality of those motions:

$\mathbb{Q}^3$ is bijective to $\mathbb{Q}$ (right?).

It is probably the case for natural behavior, though.

Different branches of science have different, sometimes incompatible definitions of what a model is and what its relationship to a theory is.

Fetsch et al. define cue combination as the `combination of multiple sensory cues' arising from the same event or object.

The tectum includes both sc (optic tectum) and ic

Stein offers an operational definition of multisensory integration as

``...the process by which stimuli from different senses combine ... to produce a response that differs from those produced by the component stimuli individually.''

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.

"The intention and the result of a scientific inquiry is to obtain an understanding and control of some part of the universe."

Testing biological hypotheses using robots is called `biorobotics'.

Neurorobotics is a sub-field of biorobotics where it is concerned with testing biological hypotheses.

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.

There are different, unconnected notions of multimodality.

  • A PDF can be multi-modal, if it has more than one local maximum.
  • Anything can be called multi-modal that is related to more than one sensory modality.

Stein defines multi-sensory integration on the single-neuron level as

``a statistically significant difference between the number of impulses evoked by a cross-modal combination of stimuli and the number evoked by the most effective of these stimuli individually.''

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

A representation is a formal system for making explicit certain entities or types of information, together with a specification of how the system does this.

And I shall call the result of using a representation to describe a given entity a description of the entity in that representation.

Schroeder names two general definitions of multisensory integration: One includes any kind of interaction between stimuli from different senses, the other only integration of information about the same object of the real world from different sensory modalities.

These definitions both are definitions on the functional level as opposed to the biological level with which Stein's definition is concerned.