2,845 research outputs found

### Comparison between the two definitions of AI

Two different definitions of the Artificial Intelligence concept have been
proposed in papers [1] and [2]. The first definition is informal. It says that
any program that is cleverer than a human being, is acknowledged as Artificial
Intelligence. The second definition is formal because it avoids reference to
the concept of human being. The readers of papers [1] and [2] might be left
with the impression that both definitions are equivalent and the definition in
[2] is simply a formal version of that in [1]. This paper will compare both
definitions of Artificial Intelligence and, hopefully, will bring a better
understanding of the concept.Comment: added four new section

### Invariant Differential Operators for Non-Compact Lie Groups: the Sp(n,R) Case

In the present paper we continue the project of systematic construction of
invariant differential operators on the example of the non-compact algebras
sp(n,R), in detail for n=6. Our choice of these algebras is motivated by the
fact that they belong to a narrow class of algebras, which we call 'conformal
Lie algebras', which have very similar properties to the conformal algebras of
Minkowski space-time. We give the main multiplets and the main reduced
multiplets of indecomposable elementary representations for n=6, including the
necessary data for all relevant invariant differential operators. In fact, this
gives by reduction also the cases for n<6, since the main multiplet for fixed n
coincides with one reduced case for n+1.Comment: Latex2e, 27 pages, 8 figures. arXiv admin note: substantial text
overlap with arXiv:0812.2690, arXiv:0812.265

### Intertwining Operator Realization of the AdS/CFT Correspondence

We give a group-theoretic interpretation of the AdS/CFT correspondence as
relation of representation equivalence between representations of the conformal
group describing the bulk AdS fields $\phi$ and the coupled boundary fields
$\phi_0$ and ${\cal O}$. We use two kinds of equivalences. The first kind is
equivalence between bulk fields and boundary fields and is established here.
The second kind is the equivalence between coupled boundary fields. Operators
realizing the first kind of equivalence for special cases were given by Witten
and others - here they are constructed in a more general setting from the
requirement that they are intertwining operators. The intertwining operators
realizing the second kind of equivalence are provided by the standard conformal
two-point functions. Using both equivalences we find that the bulk field has in
fact two boundary fields, namely, the coupled boundary fields. Thus, from the
viewpoint of the bulk-boundary correspondence the coupled fields are on an
equal footing. Our setting is more general since our bulk fields are described
by representations of the Euclidean conformal group $G=SO(d+1,1)$, induced from
representations $\tau$ of the maximal compact subgroup $SO(d+1)$ of $G$. From
these large reducible representations we can single out representations which
are equivalent to conformal boundary representations labelled by the conformal
weight and by arbitrary representations $\mu$ of the Euclidean Lorentz group
$M=SO(d)$, such that $\mu$ is contained in the restriction of $\tau$ to $M$.
Thus, our boundary-to-bulk operators can be compared with those in the
literature only when for a fixed $\mu$ we consider a 'minimal' representation
$\tau=\tau(\mu)$ containing $\mu$.Comment: 25 pages, TEX file using harvmac.tex; v2: misprints corrected; to
appear in Nuclear Physics

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