3,930 research outputs found
Commutators as Powers in Free Products of Groups
The ways in which a nontrivial commutator can be a proper power in a free
product of groups are identified.Comment: AMS-LaTex, 6 pages, no figure
The Chemical Evolution of the Universe I: High Column Density Absorbers
We construct a simple, robust model of the chemical evolution of galaxies
from high to low redshift, and apply it to published observations of damped
Lyman-alpha quasar absorption line systems (DLAs). The elementary model assumes
quiescent star formation and isolated galaxies (no interactions, mergers or gas
flows). We consider the influence of dust and chemical gradients in the
galaxies, and hence explore the selection effects in quasar surveys. We fit
individual DLA systems to predict some observable properties of the absorbing
galaxies, and also indicate the expected redshift behaviour of chemical element
ratios involving nucleosynthetic time delays.
Despite its simplicity, our `monolithic collapse' model gives a good account
of the distribution and evolution of the metallicity and column density of
DLAs, and of the evolution of the global star formation rate and gas density
below redshifts z 3. However, from the comparison of DLA observations with our
model, it is clear that star formation rates at higher redshifts (z>3) are
enhanced. Galaxy interactions and mergers, and gas flows very probably play a
major role.Comment: 36 pages, 11 figures; accepted by MNRA
Experimental quantum verification in the presence of temporally correlated noise
Growth in the complexity and capabilities of quantum information hardware
mandates access to practical techniques for performance verification that
function under realistic laboratory conditions. Here we experimentally
characterise the impact of common temporally correlated noise processes on both
randomised benchmarking (RB) and gate-set tomography (GST). We study these
using an analytic toolkit based on a formalism mapping noise to errors for
arbitrary sequences of unitary operations. This analysis highlights the role of
sequence structure in enhancing or suppressing the sensitivity of quantum
verification protocols to either slowly or rapidly varying noise, which we
treat in the limiting cases of quasi-DC miscalibration and white noise power
spectra. We perform experiments with a single trapped Yb ion as a
qubit and inject engineered noise () to probe protocol
performance. Experiments on RB validate predictions that the distribution of
measured fidelities over sequences is described by a gamma distribution varying
between approximately Gaussian for rapidly varying noise, and a broad, highly
skewed distribution for the slowly varying case. Similarly we find a strong
gate set dependence of GST in the presence of correlated errors, leading to
significant deviations between estimated and calculated diamond distances in
the presence of correlated errors. Numerical simulations demonstrate
that expansion of the gate set to include negative rotations can suppress these
discrepancies and increase reported diamond distances by orders of magnitude
for the same error processes. Similar effects do not occur for correlated
or errors or rapidly varying noise processes,
highlighting the critical interplay of selected gate set and the gauge
optimisation process on the meaning of the reported diamond norm in correlated
noise environments.Comment: Expanded and updated analysis of GST, including detailed examination
of the role of gauge optimization in GST. Full GST data sets and
supplementary information available on request from the authors. Related
results available from
http://www.physics.usyd.edu.au/~mbiercuk/Publications.htm
Accumulation is late and brief in preferential choice
Preferential choices are often explained using models within the evidence accumulation framework: value drives the drift rate at which evidence is accumulated until a threshold is reached and an option is chosen. Although rarely stated explicitly, almost all such models assume that decision makers have knowledge at the onset of the choice of all available attributes and options. In reality however, choice information is viewed piece-by-piece, and is often not completely acquired until late in the choice, if at all. Across four eye-tracking experiments, we show that whether the information was acquired early or late is irrelevant in predicting choice: all that matters is whether or not it was acquired at all. Models with potential alternative assumptions were posited and tested, such as 1) accumulation of instantaneously available information or 2) running estimates as information is acquired. These provided poor fits to the data. We are forced to conclude that participants either are clairvoyant, accumulating using information before they have looked at it, or delay accumulating evidence until very late in the choice, so late that the majority of choice time is not time in which evidence is accumulated. Thus, although the evidence accumulation framework may still be useful in measurement models, it cannot account for the details of the processes involved in decision making
- …