This is a specific example of the kinds of logical problems we face – this might get briefly a bit technical, bear with! The generalism above is so abstract it actually forms the basis of neural nets – possibly the most abstract generalisation of a system that does ‘stuff’. ...
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for medium-sized and large , where are natural numbers and is the divisor function (actually our methods can also treat a generalisation in which is non-integer, but for simplicity let us stick with the integer case for this discussion). Our methods also allow for one of the divisor functio...
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By talking of “M-modality”, I aim to cover the main different senses in which the ambiguous notions of absolute and metaphysical modality have been meant, so as to be able to engage in metaphilosophical generalisations over philosophical practices taking for granted those notions. In particular...
An interesting example of such a limiting Gelfand-Tsetlin pattern occurs when , which corresponds to being , where is an orthogonal projection to a random -dimensional subspace of . Here we have and so (9) in this case becomes A tedious calculation then gives the solution For , there ...
target article deals primarily with the issue or representa-tion, but as is pointed out in section 1.3, this should be considered with regard to the problem of pattern recognition and categoriza-tion. It is when we consid...
The advantage of this slight generalisation is that we can now we can consider the joint likelihoodconstrained on the parameter, giving This is in factBarndorff-Nielsen’splausibilityfunction. It can be considered as a measure ofself-consistency for a single parameter value (single model instance ...
If we accept this, and the generalisation of this example, then the remainder of our thought experiment becomes admissable — and, we hope, useful as an illustration of analysis using our model. 5.1. Straightforward rocks So what is it like to trust a rock? For a start, the answer is ...
There is a generalisation of this formula to (finite) posets, due to Hall, in which one sums over chains in the poset: Proposition 2 (Poset Möbius inversion) Let be a finite poset, and let be functions from that poset to an additive group . Then the following two claims are equival...