7,363 research outputs found
Tree-irreducible automorphisms of free groups
We introduce a new class of automorphisms of the non-abelian free
group of finite rank which contains all iwips (= fully
irreducible automorphisms), but also any automorphism induced by a
pseudo-Anosov homeomorphism of a surface with arbitrary many boundary
components. More generally, there may be subgroups of of rank on
which restricts to the identity.
We prove some basic facts about such {\em tree-irreducible} automorphisms,
and show that, together with Dehn twist automorphisms, they are the natural
basic building blocks from which any automorphism of \FN can be constructed
in a train track set-up. We then show:
{\bf Theorem:} {\it Every tree-irreducible automorphism of has induced
North-South dynamics on the Thurston compactification of Outer
space.}
Finally, we define a "blow-up" construction on the vertices of a train track
map, which, starting from iwips, produces tree-irreducible automorphisms which
in general are not iwip
Environmental modeling and recognition for an autonomous land vehicle
An architecture for object modeling and recognition for an autonomous land vehicle is presented. Examples of objects of interest include terrain features, fields, roads, horizon features, trees, etc. The architecture is organized around a set of data bases for generic object models and perceptual structures, temporary memory for the instantiation of object and relational hypotheses, and a long term memory for storing stable hypotheses that are affixed to the terrain representation. Multiple inference processes operate over these databases. Researchers describe these particular components: the perceptual structure database, the grouping processes that operate over this, schemas, and the long term terrain database. A processing example that matches predictions from the long term terrain model to imagery, extracts significant perceptual structures for consideration as potential landmarks, and extracts a relational structure to update the long term terrain database is given
Evolution of Quantum Discord and its Stability in Two-Qubit NMR Systems
We investigate evolution of quantum correlations in ensembles of two-qubit
nuclear spin systems via nuclear magnetic resonance techniques. We use discord
as a measure of quantum correlations and the Werner state as an explicit
example. We first introduce different ways of measuring discord and geometric
discord in two-qubit systems and then describe the following experimental
studies: (a) We quantitatively measure discord for Werner-like states prepared
using an entangling pulse sequence. An initial thermal state with zero discord
is gradually and periodically transformed into a mixed state with maximum
discord. The experimental and simulated behavior of rise and fall of discord
agree fairly well. (b) We examine the efficiency of dynamical decoupling
sequences in preserving quantum correlations. In our experimental setup, the
dynamical decoupling sequences preserved the traceless parts of the density
matrices at high fidelity. But they could not maintain the purity of the
quantum states and so were unable to keep the discord from decaying. (c) We
observe the evolution of discord for a singlet-triplet mixed state during a
radio-frequency spin-lock. A simple relaxation model describes the evolution of
discord, and the accompanying evolution of fidelity of the long-lived singlet
state, reasonably well.Comment: 9 pages, 7 figures, Phys. Rev. A (in press
Quantum information processing using strongly-dipolar coupled nuclear spins
Dipolar coupled homonuclear spins present challenging, yet useful systems for
quantum information processing. In such systems, eigenbasis of the system
Hamiltonian is the appropriate computational basis and coherent control can be
achieved by specially designed strongly modulating pulses. In this letter we
describe the first experimental implementation of the quantum algorithm for
numerical gradient estimation on the eigenbasis of a four spin system.Comment: 5 pages, 5 figures, Accepted in PR
Study of fault-tolerant software technology
Presented is an overview of the current state of the art of fault-tolerant software and an analysis of quantitative techniques and models developed to assess its impact. It examines research efforts as well as experience gained from commercial application of these techniques. The paper also addresses the computer architecture and design implications on hardware, operating systems and programming languages (including Ada) of using fault-tolerant software in real-time aerospace applications. It concludes that fault-tolerant software has progressed beyond the pure research state. The paper also finds that, although not perfectly matched, newer architectural and language capabilities provide many of the notations and functions needed to effectively and efficiently implement software fault-tolerance
Phase transition in the globalization of trade
Globalization processes interweave economic structures at a worldwide scale,
trade playing a central role as one of the elemental channels of interaction
among countries. Despite the significance of such phenomena, measuring economic
globalization still remains an open problem. More quantitative treatments could
improve the understanding of globalization at the same time that help a formal
basis for comparative economic history. In this letter, we investigate the time
evolution of the statistical properties of bilateral trade imbalances between
countries in the trade system. We measure their cumulative probability
distribution at different moments in time to discover a sudden transition circa
1960 from a regime where the distribution was always represented by a steady
characteristic function to a new state where the distribution dilates as time
goes on. This suggests that the rule that was governing the statistical
behavior of bilateral trade imbalances until the 60's abruptly changed to a new
form persistent in the last decades. In the new regime, the figures for the
different years collapse into a universal master curve when rescaled by the
corresponding global gross domestic product value. This coupling points to an
increased interdependence of world economies and its onset corresponds in time
with the starting of the last globalization wave.Comment: Final versio
Geometric Aspects of Composite Pulses
Unitary operations acting on a quantum system must be robust against
systematic errors in control parameters for reliable quantum computing.
Composite pulse technique in nuclear magnetic resonance (NMR) realises such a
robust operation by employing a sequence of possibly poor quality pulses. In
this article, we demonstrate that two kinds of composite pulses, one
compensates for a pulse length error in a one-qubit system and the other
compensates for a J-coupling error in a twoqubit system, have vanishing
dynamical phase and thereby can be seen as geometric quantum gates, which
implement unitary gates by the holonomy associated with dynamics of cyclic
vectors defined in the text.Comment: 20 pages, 4 figures. Accepted for publication in Philosophical
Transactions of the Royal Society
Twisted Conjugacy Classes in Abelian Extensions of Certain Linear Groups
Given an automorphism , one has an action of
on itself by -twisted conjugacy, namely, . The orbits
of this action are called -twisted conjugacy classes. One says that
has the -property if there are infinitely many
-twisted conjugacy classes for every automorphism of . In
this paper we show that SL and its congruence subgroups have
the -property. Further we show that any (countable) abelian extension
of has the -property where is a torsion free
non-elementary hyperbolic group, or SL, Sp or
a principal congruence subgroup of SL or the fundamental group
of a complete Riemannian manifold of constant negative curvature
Transplants of Limbic and Neocortex Reveal Mechanisms of Generating Phenotypic Diversity in the Cerebral Cortex
Storing entanglement of nuclear spins via Uhrig Dynamical Decoupling
Stroboscopic spin flips have already been shown to prolong the coherence
times of quantum systems under noisy environments. Uhrig's dynamical decoupling
scheme provides an optimal sequence for a quantum system interacting with a
dephasing bath. Several experimental demonstrations have already verified the
efficiency of such dynamical decoupling schemes in preserving single qubit
coherences. In this work we describe the experimental study of Uhrig's
dynamical decoupling in preserving two-qubit entangled states using an ensemble
of spin-1/2 nuclear pairs in solution state. We find that the performance of
odd-order Uhrig sequences in preserving entanglement is superior to both
even-order Uhrig sequences and periodic spin-flip sequences. We also find that
there exists an optimal length of the Uhrig sequence at which the decoherence
time gets boosted from a few seconds to about 30 seconds.Comment: 6 pages, 7 figure
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