29,818 research outputs found
Bootstrap methods for the empirical study of decision-making and information flows in social systems
Abstract: We characterize the statistical bootstrap for the estimation of information theoretic quantities from data, with particular reference to its use in the study of large-scale social phenomena. Our methods allow one to preserve, approximately, the underlying axiomatic relationships of information theoryâin particular, consistency under arbitrary coarse-grainingâthat motivate use of these quantities in the first place, while providing reliability comparable to the state of the art for Bayesian estimators. We show how information-theoretic quantities allow for rigorous empirical study of the decision-making capacities of rational agents, and the time-asymmetric flows of information in distributed systems. We provide illustrative examples by reference to ongoing collaborative work on the semantic structure of the British Criminal Court system and the conflict dynamics of the contemporary Afghanistan insurgency
Entropy and information in neural spike trains: Progress on the sampling problem
The major problem in information theoretic analysis of neural responses and
other biological data is the reliable estimation of entropy--like quantities
from small samples. We apply a recently introduced Bayesian entropy estimator
to synthetic data inspired by experiments, and to real experimental spike
trains. The estimator performs admirably even very deep in the undersampled
regime, where other techniques fail. This opens new possibilities for the
information theoretic analysis of experiments, and may be of general interest
as an example of learning from limited data.Comment: 7 pages, 4 figures; referee suggested changes, accepted versio
Quantum information and physics: Some future directions
I consider some promising future directions for quantum information theory that could influence the development of 21st century physics. Advances in the theory of the distinguishability of superoperators may lead to new strategies for improving the precision of quantum-limited measurements. A better grasp of the properties of multi-partite quantum entanglement may lead to deeper understanding of strongly-coupled dynamics in quantum many-body systems, quantum field theory, and quantum gravity
Four-point renormalized coupling constant and Callan-Symanzik beta-function in O(N) models
We investigate some issues concerning the zero-momentum four-point
renormalized coupling constant g in the symmetric phase of O(N) models, and the
corresponding Callan-Symanzik beta-function. In the framework of the 1/N
expansion we show that the Callan- Symanzik beta-function is non-analytic at
its zero, i.e. at the fixed-point value g^* of g. This fact calls for a check
of the actual accuracy of the determination of g^* from the resummation of the
d=3 perturbative g-expansion, which is usually performed assuming analyticity
of the beta-function. Two alternative approaches are exploited. We extend the
\epsilon-expansion of g^* to O(\epsilon^4). Quite accurate estimates of g^* are
then obtained by an analysis exploiting the analytic behavior of g^* as
function of d and the known values of g^* for lower-dimensional O(N) models,
i.e. for d=2,1,0. Accurate estimates of g^* are also obtained by a reanalysis
of the strong-coupling expansion of lattice N-vector models allowing for the
leading confluent singularity. The agreement among the g-, \epsilon-, and
strong-coupling expansion results is good for all N. However, at N=0,1,
\epsilon- and strong-coupling expansion favor values of g^* which are sligthly
lower than those obtained by the resummation of the g-expansion assuming
analyticity in the Callan-Symanzik beta-function.Comment: 35 pages (3 figs), added Ref. for GRT, some estimates are revised,
other minor change
Information-theoretic approach to quantum error correction and reversible measurement
Quantum operations provide a general description of the state changes allowed
by quantum mechanics. The reversal of quantum operations is important for
quantum error-correcting codes, teleportation, and reversing quantum
measurements. We derive information-theoretic conditions and equivalent
algebraic conditions that are necessary and sufficient for a general quantum
operation to be reversible. We analyze the thermodynamic cost of error
correction and show that error correction can be regarded as a kind of
``Maxwell demon,'' for which there is an entropy cost associated with
information obtained from measurements performed during error correction. A
prescription for thermodynamically efficient error correction is given.Comment: 31 pages, REVTEX, one figure in LaTeX, submitted to Proceedings of
the ITP Conference on Quantum Coherence and Decoherenc
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