69,423 research outputs found
Multiple-spin coherence transfer in linear Ising spin chains and beyond: numerically-optimized pulses and experiments
We study multiple-spin coherence transfers in linear Ising spin chains with
nearest neighbor couplings. These constitute a model for efficient information
transfers in future quantum computing devices and for many multi-dimensional
experiments for the assignment of complex spectra in nuclear magnetic resonance
spectroscopy. We complement prior analytic techniques for multiple-spin
coherence transfers with a systematic numerical study where we obtain strong
evidence that a certain analytically-motivated family of restricted controls is
sufficient for time-optimality. In the case of a linear three-spin system,
additional evidence suggests that prior analytic pulse sequences using this
family of restricted controls are time-optimal even for arbitrary local
controls. In addition, we compare the pulse sequences for linear Ising spin
chains to pulse sequences for more realistic spin systems with additional
long-range couplings between non-adjacent spins. We experimentally implement
the derived pulse sequences in three and four spin systems and demonstrate that
they are applicable in realistic settings under relaxation and experimental
imperfections-in particular-by deriving broadband pulse sequences which are
robust with respect to frequency offsets.Comment: 11 page
A method for computing Lucas sequences
AbstractMost of public-key cryptosystems rely on one-way functions, which can be used to encrypt and sign messages. Their encryption and signature operations are based on the computation of exponentiation. Recently, some public-key cryptosystems are proposed and based on Lucas functions, and the Lucas sequences are performed as S = V(d)modN. In this paper, we will transform the concept of addition chains for computing the exponentiation evaluations to the Lucas chains for computing the Lucas sequences. Theoretically, the shorter Lucas chain for d is generated, the less computation time for evaluating the value V(d) is required. Therefore, we proposed a heuristic algorithm for evaluating a shorter Lucas chain and then use it to compute the Lucas sequence with less modular multiplications
An Algorithm for Computing the Limit Points of the Quasi-component of a Regular Chain
For a regular chain , we propose an algorithm which computes the
(non-trivial) limit points of the quasi-component of , that is, the set
. Our procedure relies on Puiseux series expansions
and does not require to compute a system of generators of the saturated ideal
of . We focus on the case where this saturated ideal has dimension one and
we discuss extensions of this work in higher dimensions. We provide
experimental results illustrating the benefits of our algorithms
Equi-energy sampler with applications in statistical inference and statistical mechanics
We introduce a new sampling algorithm, the equi-energy sampler, for efficient
statistical sampling and estimation. Complementary to the widely used
temperature-domain methods, the equi-energy sampler, utilizing the
temperature--energy duality, targets the energy directly. The focus on the
energy function not only facilitates efficient sampling, but also provides a
powerful means for statistical estimation, for example, the calculation of the
density of states and microcanonical averages in statistical mechanics. The
equi-energy sampler is applied to a variety of problems, including exponential
regression in statistics, motif sampling in computational biology and protein
folding in biophysics.Comment: This paper discussed in: [math.ST/0611217], [math.ST/0611219],
[math.ST/0611221], [math.ST/0611222]. Rejoinder in [math.ST/0611224].
Published at http://dx.doi.org/10.1214/009053606000000515 in the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
The complex AGM, periods of elliptic curves over C and complex elliptic logarithms
We give an account of the complex Arithmetic-Geometric Mean (AGM), as first
studied by Gauss, together with details of its relationship with the theory of
elliptic curves over \C, their period lattices and complex parametrisation.
As an application, we present efficient methods for computing bases for the
period lattices and elliptic logarithms of points, for arbitrary elliptic
curves defined over \C. Earlier authors have only treated the case of
elliptic curves defined over the real numbers; here, the multi-valued nature of
the complex AGM plays an important role. Our method, which we have implemented
in both \Magma\ and \Sage, is illustrated with several examples using elliptic
curves defined over number fields with real and complex embeddings.Comment: The addional file elog_ex.sage contains a Sage script for the
examples in the last section of the paper, and the file elog_ex.out contains
the result of running that script with Sage version 5.
Information-Based Physics: An Observer-Centric Foundation
It is generally believed that physical laws, reflecting an inherent order in
the universe, are ordained by nature. However, in modern physics the observer
plays a central role raising questions about how an observer-centric physics
can result in laws apparently worthy of a universal nature-centric physics.
Over the last decade, we have found that the consistent apt quantification of
algebraic and order-theoretic structures results in calculi that possess
constraint equations taking the form of what are often considered to be
physical laws. I review recent derivations of the formal relations among
relevant variables central to special relativity, probability theory and
quantum mechanics in this context by considering a problem where two observers
form consistent descriptions of and make optimal inferences about a free
particle that simply influences them. I show that this approach to describing
such a particle based only on available information leads to the mathematics of
relativistic quantum mechanics as well as a description of a free particle that
reproduces many of the basic properties of a fermion. The result is an approach
to foundational physics where laws derive from both consistent descriptions and
optimal information-based inferences made by embedded observers.Comment: To be published in Contemporary Physics. The manuscript consists of
43 pages and 9 Figure
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