781 research outputs found
A Combined Preconditioning Strategy for Nonsymmetric Systems
We present and analyze a class of nonsymmetric preconditioners within a
normal (weighted least-squares) matrix form for use in GMRES to solve
nonsymmetric matrix problems that typically arise in finite element
discretizations. An example of the additive Schwarz method applied to
nonsymmetric but definite matrices is presented for which the abstract
assumptions are verified. A variable preconditioner, combining the original
nonsymmetric one and a weighted least-squares version of it, is shown to be
convergent and provides a viable strategy for using nonsymmetric
preconditioners in practice. Numerical results are included to assess the
theory and the performance of the proposed preconditioners.Comment: 26 pages, 3 figure
Open Quantum Dynamics: Complete Positivity and Entanglement
We review the standard treatment of open quantum systems in relation to
quantum entanglement, analyzing, in particular, the behaviour of bipartite
systems immersed in a same environment. We first focus upon the notion of
complete positivity, a physically motivated algebraic constraint on the quantum
dynamics, in relation to quantum entanglement, i.e. the existence of
statistical correlations which can not be accounted for by classical
probability. We then study the entanglement power of heat baths versus their
decohering properties, a topic of increasing importance in the framework of the
fast developing fields of quantum information, communication and computation.
The presentation is self contained and, through several examples, it offers a
detailed survey of the physics and of the most relevant and used techniques
relative to both quantum open system dynamics and quantum entanglement.Comment: LaTex, 77 page
Two-dimensional models as testing ground for principles and concepts of local quantum physics
In the past two-dimensional models of QFT have served as theoretical
laboratories for testing new concepts under mathematically controllable
condition. In more recent times low-dimensional models (e.g. chiral models,
factorizing models) often have been treated by special recipes in a way which
sometimes led to a loss of unity of QFT. In the present work I try to
counteract this apartheid tendency by reviewing past results within the setting
of the general principles of QFT. To this I add two new ideas: (1) a modular
interpretation of the chiral model Diff(S)-covariance with a close connection
to the recently formulated local covariance principle for QFT in curved
spacetime and (2) a derivation of the chiral model temperature duality from a
suitable operator formulation of the angular Wick rotation (in analogy to the
Nelson-Symanzik duality in the Ostertwalder-Schrader setting) for rational
chiral theories. The SL(2,Z) modular Verlinde relation is a special case of
this thermal duality and (within the family of rational models) the matrix S
appearing in the thermal duality relation becomes identified with the
statistics character matrix S. The relevant angular Euclideanization'' is done
in the setting of the Tomita-Takesaki modular formalism of operator algebras.
I find it appropriate to dedicate this work to the memory of J. A. Swieca
with whom I shared the interest in two-dimensional models as a testing ground
for QFT for more than one decade.
This is a significantly extended version of an ``Encyclopedia of Mathematical
Physics'' contribution hep-th/0502125.Comment: 55 pages, removal of some typos in section
Experimentally Analyzing the Impact of Leader Positivity on Follower Positivity and Performance
This field experimental study examined the role that positive leadership plays in producing effective leader and follower outcomes. Specifically, a sample of engineers (N = 106) from a very large aerospace firm were randomly assigned to four experimental conditions. Two conditions involved assigning these engineers to a low and high problem complexity condition. The other two conditions represented high versus low conveyed leader positivity. The results indicated a positive relationship between the leaders’ positivity and the followers’ positivity and performance, as well as a negative relationship between problem complexity and follower positivity. The study limitations, needed future research, and practical implications of these findings conclude the article
Premia in forward foreign exchange as unobserved components
Foreign Exchange;Models
Improved Sum-of-Squares Lower Bounds for Hidden Clique and Hidden Submatrix Problems
Given a large data matrix , we consider the
problem of determining whether its entries are i.i.d. with some known marginal
distribution , or instead contains a principal submatrix
whose entries have marginal distribution . As a special case, the hidden (or planted) clique problem
requires to find a planted clique in an otherwise uniformly random graph.
Assuming unbounded computational resources, this hypothesis testing problem
is statistically solvable provided for a suitable
constant . However, despite substantial effort, no polynomial time algorithm
is known that succeeds with high probability when .
Recently Meka and Wigderson \cite{meka2013association}, proposed a method to
establish lower bounds within the Sum of Squares (SOS) semidefinite hierarchy.
Here we consider the degree- SOS relaxation, and study the construction of
\cite{meka2013association} to prove that SOS fails unless . An argument presented by Barak implies that this lower bound
cannot be substantially improved unless the witness construction is changed in
the proof. Our proof uses the moments method to bound the spectrum of a certain
random association scheme, i.e. a symmetric random matrix whose rows and
columns are indexed by the edges of an Erd\"os-Renyi random graph.Comment: 40 pages, 1 table, conferenc
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