1,189 research outputs found
Tailoring Three-Point Functions and Integrability
We use Integrability techniques to compute structure constants in N=4 SYM to
leading order. Three closed spin chains, which represent the single trace
gauge-invariant operators in N=4 SYM, are cut into six open chains which are
then sewed back together into some nice pants, the three-point function. The
algebraic and coordinate Bethe ansatz tools necessary for this task are
reviewed. Finally, we discuss the classical limit of our results, anticipating
some predictions for quasi-classical string correlators in terms of algebraic
curves.Comment: 52 pages, 6 figures. v2: Typos corrected, references added and
update
Controlling the level of sparsity in MPC
In optimization routines used for on-line Model Predictive Control (MPC),
linear systems of equations are usually solved in each iteration. This is true
both for Active Set (AS) methods as well as for Interior Point (IP) methods,
and for linear MPC as well as for nonlinear MPC and hybrid MPC. The main
computational effort is spent while solving these linear systems of equations,
and hence, it is of greatest interest to solve them efficiently. Classically,
the optimization problem has been formulated in either of two different ways.
One of them leading to a sparse linear system of equations involving relatively
many variables to solve in each iteration and the other one leading to a dense
linear system of equations involving relatively few variables. In this work, it
is shown that it is possible not only to consider these two distinct choices of
formulations. Instead it is shown that it is possible to create an entire
family of formulations with different levels of sparsity and number of
variables, and that this extra degree of freedom can be exploited to get even
better performance with the software and hardware at hand. This result also
provides a better answer to an often discussed question in MPC; should the
sparse or dense formulation be used. In this work, it is shown that the answer
to this question is that often none of these classical choices is the best
choice, and that a better choice with a different level of sparsity actually
can be found
A General Transfer-Function Approach to Noise Filtering in Open-Loop Quantum Control
We present a general transfer-function approach to noise filtering in
open-loop Hamiltonian engineering protocols for open quantum systems. We show
how to identify a computationally tractable set of fundamental filter
functions, out of which arbitrary transfer filter functions may be assembled up
to arbitrary high order in principle. Besides avoiding the infinite recursive
hierarchy of filter functions that arises in general control scenarios, this
fundamental filter-functions set suffices to characterize the error suppression
capabilities of the control protocol in both the time and frequency domain. We
prove that the resulting notion of filtering order reveals conceptually
distinct, albeit complementary, features of the controlled dynamics as compared
to the order of error cancellation, traditionally defined in the Magnus sense.
Examples and implications are discussed.Comment: Paper plus supplementary material. 10 pages, 1 figure. Unnumbered
equation between 2 and 3 corrected. Results are unchange
Intensional properties of polygraphs
We present polygraphic programs, a subclass of Albert Burroni's polygraphs,
as a computational model, showing how these objects can be seen as first-order
functional programs. We prove that the model is Turing complete. We use
polygraphic interpretations, a termination proof method introduced by the
second author, to characterize polygraphic programs that compute in polynomial
time. We conclude with a characterization of polynomial time functions and
non-deterministic polynomial time functions.Comment: Proceedings of TERMGRAPH 2007, Electronic Notes in Computer Science
(to appear), 12 pages, minor changes from previous versio
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