1,583 research outputs found
Rerepresenting and Restructuring Domain Theories: A Constructive Induction Approach
Theory revision integrates inductive learning and background knowledge by
combining training examples with a coarse domain theory to produce a more
accurate theory. There are two challenges that theory revision and other
theory-guided systems face. First, a representation language appropriate for
the initial theory may be inappropriate for an improved theory. While the
original representation may concisely express the initial theory, a more
accurate theory forced to use that same representation may be bulky,
cumbersome, and difficult to reach. Second, a theory structure suitable for a
coarse domain theory may be insufficient for a fine-tuned theory. Systems that
produce only small, local changes to a theory have limited value for
accomplishing complex structural alterations that may be required.
Consequently, advanced theory-guided learning systems require flexible
representation and flexible structure. An analysis of various theory revision
systems and theory-guided learning systems reveals specific strengths and
weaknesses in terms of these two desired properties. Designed to capture the
underlying qualities of each system, a new system uses theory-guided
constructive induction. Experiments in three domains show improvement over
previous theory-guided systems. This leads to a study of the behavior,
limitations, and potential of theory-guided constructive induction.Comment: See http://www.jair.org/ for an online appendix and other files
accompanying this articl
Kraus representation of quantum evolution and fidelity as manifestations of Markovian and non-Markovian avataras
It is shown that the fidelity of the dynamically evolved system with its
earlier time density matrix provides a signature of non-Markovian dynamics.
Also, the fidelity associated with the initial state and the dynamically
evolved state is shown to be larger in the non-Markovian evolution compared to
that in the corresponding Markovian case. Starting from the Kraus
representation of quantum evolution, the Markovian and non-Markovian features
are discerned in its short time structure. These two features are in
concordance with each other and they are illustrated with the help of four
models of interaction of the system with its environment.Comment: 7 pages, 5 eps figures; Discussion on recent characterizations of
non-Markovianity included in this versio
Interplay of quantum stochastic and dynamical maps to discern Markovian and non-Markovian transitions
It is known that the dynamical evolution of a system, from an initial tensor
product state of system and environment, to any two later times, t1,t2 (t2>t1),
are both completely positive (CP) but in the intermediate times between t1 and
t2 it need not be CP. This reveals the key to the Markov (if CP) and nonMarkov
(if it is not CP) avataras of the intermediate dynamics. This is brought out
here in terms of the quantum stochastic map A and the associated dynamical map
B -- without resorting to master equation approaches. We investigate these
features with four examples which have entirely different physical origins (i)
a two qubit Werner state map with time dependent noise parameter (ii)
Phenomenological model of a recent optical experiment (Nature Physics, 7, 931
(2011)) on the open system evolution of photon polarization. (iii) Hamiltonian
dynamics of a qubit coupled to a bath of qubits and (iv) two qubit unitary
dynamics of Jordan et. al. (Phys. Rev. A 70, 052110 (2004)) with initial
product states of qubits. In all these models, it is shown that the
positivity/negativity of the eigenvalues of intermediate time dynamical B map
determines the Markov/non-Markov nature of the dynamics.Comment: 6 pages, 5 figures, considerably extended version of arXiv:1104.456
Classical Statistics Inherent in a Quantum Density Matrix
A density matrix formulation of classical bipartite correlations is
constructed. This leads to an understanding of the appearance of classical
statistical correlations intertwined with the quantum correlations as well as a
physical underpinning of these correlations. As a byproduct of this analysis, a
physical basis of the classical statistical correlations leading to additive
entropy in a bipartite system discussed recently by Tsallis et al emerges as
inherent classical spin fluctuations. It is found that in this example, the
quantum correlations shrink the region of additivity in phase space.Comment: 10 pages, 3 figure
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