108 research outputs found
Generalized Connectives for Multiplicative Linear Logic
In this paper we investigate the notion of generalized connective for multiplicative linear logic. We introduce a notion of orthogonality for partitions of a finite set and we study the family of connectives which can be described by two orthogonal sets of partitions.
We prove that there is a special class of connectives that can never be decomposed by means of the multiplicative conjunction ? and disjunction ?, providing an infinite family of non-decomposable connectives, called Girard connectives. We show that each Girard connective can be naturally described by a type (a set of partitions equal to its double-orthogonal) and its orthogonal type. In addition, one of these two types is the union of the types associated to a family of MLL-formulas in disjunctive normal form, and these formulas only differ for the cyclic permutations of their atoms
Decoherence properties of arbitrarily long histories
Within the decoherent histories formulation of quantum mechanics, we consider
arbitrarily long histories constructed from a fixed projective partition of a
finite-dimensional Hilbert space. We review some of the decoherence properties
of such histories including simple necessary decoherence conditions and the
dependence of decoherence on the initial state. Here we make a first step
towards generalization of our earlier results [Scherer and Soklakov, e-print:
quant-ph/0405080, (2004) and Scherer et al., Phys. Lett. A, vol. 326, 307,
(2004)] to the case of approximate decoherence.Comment: 8 pages, no figure
Initial states and decoherence of histories
We study decoherence properties of arbitrarily long histories constructed
from a fixed projective partition of a finite dimensional Hilbert space. We
show that decoherence of such histories for all initial states that are
naturally induced by the projective partition implies decoherence for arbitrary
initial states. In addition we generalize the simple necessary decoherence
condition [Scherer et al., Phys. Lett. A (2004)] for such histories to the case
of arbitrary coarse-graining.Comment: 10 page
Chaotic wave functions and exponential convergence of low-lying energy eigenvalues
We suggest that low-lying eigenvalues of realistic quantum many-body
hamiltonians, given, as in the nuclear shell model, by large matrices, can be
calculated, instead of the full diagonalization, by the diagonalization of
small truncated matrices with the exponential extrapolation of the results. We
show numerical data confirming this conjecture. We argue that the exponential
convergence in an appropriate basis may be a generic feature of complicated
("chaotic") systems where the wave functions are localized in this basis.Comment: 4 figure
Identification of complex biological network classes using extended correlation analysis
Modeling and analysis of complex biological networks necessitates suitable handling of data on a parallel scale. Using the IkB-NF-kB pathway model and a basis of sensitivity analysis, analytic methods are presented, extending correlation from the network kinetic reaction rates to that of the rate reactions. Alignment of correlated processed components, vastly outperforming correlation of the data source, advanced sets of biological classes possessing similar network activities. Additional construction generated a naturally structured, cardinally based system for component-specific investigation. The computationally driven procedures are described, with results demonstrating viability as mechanisms useful for fundamental oscillatory network activity investigation
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