1,299,363 research outputs found
Locating Overlap Information in Quantum Systems
When discussing the black hole information problem the term ``information
flow'' is frequently used in a rather loose fashion. In this article I attempt
to make this notion more concrete. I consider a Hilbert space which is
constructed as a tensor product of two subspaces (representing for example
inside and outside the black hole). I discuss how the system has the capacity
to contain information which is in NEITHER of the subspaces. I attempt to
quantify the amount of information located in each of the two subspaces, and
elsewhere, and analyze the extent to which unitary evolution can correspond to
``information flow''. I define the notion of ``overlap information'' which
appears to be well suited to the problem.Comment: 25 pages plain LaTeX, no figures. Imperial/TP/93-94/2
Is Consciousness Intrinsic?: A Problem for the Integrated Information Theory
The Integrated Information Theory of consciousness (IIT) claims that consciousness is identical to maximal integrated information, or maximal Φ. One objection to IIT is based on what may be called the intrinsicality problem: consciousness is an intrinsic property, but maximal Φ is an extrinsic property; therefore, they cannot be identical. In this paper, I show that this problem is not unique to IIT, but rather derives from a trilemma that confronts almost any theory of consciousness. Given most theories of consciousness, the following three claims are inconsistent. INTRINSICALITY: Consciousness is intrinsic. NON-OVERLAP: Conscious systems do not overlap with other conscious systems (a la Unger’s problem of the many). REDUCTIONISM: Consciousness is constituted by more fundamental properties (as per standard versions of physicalism and Russellian monism). In view of this, I will consider whether rejecting INTRINSICALITY is necessarily less plausible than rejecting NON-OVERLAP or REDUCTIONISM. I will also consider whether IIT is necessarily committed to rejecting INTRINSICALITY or whether it could also accept solutions that reject NON-OVERLAP or REDUCTIONISM instead. I will suggest that the best option for IIT may be a solution that rejects REDUCTIONISM rather than INTRINSICALITY or NON-OVERLAP
On the origin of ultrametricity
In this paper we show that in systems where the probability distribution of
the the overlap is non trivial in the infinity volume limit, the property of
ultrametricity can be proved in general starting from two very simple and
natural assumptions: each replica is equivalent to the others (replica
equivalence or stochastic stability) and all the mutual information about a
pair of equilibrium configurations is encoded in their mutual distance or
overlap (separability or overlap equivalence).Comment: 13 pages, 1 figur
Chaos in temperature in the Sherrington-Kirkpatrick model
We prove the existence of chaos in temperature in the
Sherringhton-Kirkpatrick model. The effect is exceedingly small, namely of the
ninth order in perturbation theory. The equations describing two systems at
different temperatures constrained to have a fixed overlap are studied
analytically and numerically, yielding information about the behaviour of the
overlap distribution function in finite-size systems.Comment: REVTEX, 6 pages, 2 figure
Milnor Fibre Homology via Deformation
In case of one-dimensional singular locus, we use deformations in order to
get refined information about the Betti numbers of the Milnor fibre.Comment: 14 pages. arXiv admin note: text overlap with arXiv:1411.264
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