76,014 research outputs found
Condition measures and properties of the central trajectory of a linear program
Includes bibliographical references (p. 37-39).M.A. Nunez and R.M. Freund
Condition measures and properties of the central trajectory of a linear program
Includes bibliographical references (p. 37-39).M.A. Nunez and R.M. Freund
Data Assimilation: A Mathematical Introduction
These notes provide a systematic mathematical treatment of the subject of
data assimilation
Finite Size Scaling and ``perfect'' actions: the three dimensional Ising model
Using Finite-Size Scaling techniques, we numerically show that the first
irrelevant operator of the lattice theory in three dimensions
is (within errors) completely decoupled at . This interesting
result also holds in the Thermodynamical Limit, where the renormalized coupling
constant shows an extraordinary reduction of the scaling-corrections when
compared with the Ising model. It is argued that Finite-Size Scaling analysis
can be a competitive method for finding improved actions.Comment: 13 pages, 3 figure
Predictability: a way to characterize Complexity
Different aspects of the predictability problem in dynamical systems are
reviewed. The deep relation among Lyapunov exponents, Kolmogorov-Sinai entropy,
Shannon entropy and algorithmic complexity is discussed. In particular, we
emphasize how a characterization of the unpredictability of a system gives a
measure of its complexity. Adopting this point of view, we review some
developments in the characterization of the predictability of systems showing
different kind of complexity: from low-dimensional systems to high-dimensional
ones with spatio-temporal chaos and to fully developed turbulence. A special
attention is devoted to finite-time and finite-resolution effects on
predictability, which can be accounted with suitable generalization of the
standard indicators. The problems involved in systems with intrinsic randomness
is discussed, with emphasis on the important problems of distinguishing chaos
from noise and of modeling the system. The characterization of irregular
behavior in systems with discrete phase space is also considered.Comment: 142 Latex pgs. 41 included eps figures, submitted to Physics Reports.
Related information at this http://axtnt2.phys.uniroma1.i
Theory of higher spin tensor currents and central charges
We study higher spin tensor currents in quantum field theory. Scalar, spinor
and vector fields admit unique "improved" currents of arbitrary spin, traceless
and conserved. Off-criticality as well as at interacting fixed points
conservation is violated and the dimension of the current is anomalous. In
particular, currents J^(s,I) with spin s between 0 and 5 (and a second label I)
appear in the operator product expansion of the stress tensor. The TT OPE is
worked out in detail for free fields; projectors and invariants encoding the
space-time structure are classified. The result is used to write and discuss
the most general OPE for interacting conformal field theories and
off-criticality. Higher spin central charges c_(s,I) with arbitrary s are
defined by higher spin channels of the many-point T-correlators and central
functions interpolating between the UV and IR limits are constructed. We
compute the one-loop values of all c_(s,I) and investigate the RG trajectories
of quantum field theories in the conformal window following our approach. In
particular, we discuss certain phenomena (perturbative and nonperturbative)
that appear to be of interest, like the dynamical removal of the I-degeneracy.
Finally, we address the problem of formulating an action principle for the RG
trajectory connecting pairs of CFT's as a way to go beyond perturbation theory.Comment: Latex, 46 pages, 4 figures. Final version, to appear in NPB. (v2:
added two terms in vector OPE
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