2,428 research outputs found
Novel statistical methodology reveals that hip shape is associated with incident radiographic hip osteoarthritis among African American women
Hip shape is a risk factor for the development of hip osteoarthritis (OA), and current methods to assess hip shape from radiographs are limited; therefore this study explored current and novel methods to assess hip shape
Sampling Can Be Faster Than Optimization
Optimization algorithms and Monte Carlo sampling algorithms have provided the
computational foundations for the rapid growth in applications of statistical
machine learning in recent years. There is, however, limited theoretical
understanding of the relationships between these two kinds of methodology, and
limited understanding of relative strengths and weaknesses. Moreover, existing
results have been obtained primarily in the setting of convex functions (for
optimization) and log-concave functions (for sampling). In this setting, where
local properties determine global properties, optimization algorithms are
unsurprisingly more efficient computationally than sampling algorithms. We
instead examine a class of nonconvex objective functions that arise in mixture
modeling and multi-stable systems. In this nonconvex setting, we find that the
computational complexity of sampling algorithms scales linearly with the model
dimension while that of optimization algorithms scales exponentially
Conditional statistics of electron transport in interacting nanoscale conductors
Interactions between nanoscale semiconductor structures form the basis for
charge detectors in the solid state. Recent experimental advances have
demonstrated the on-chip detection of single electron transport through a
quantum dot (QD). The discreteness of charge in units of e leads to intrinsic
fluctuations in the electrical current, known as shot noise. To measure these
single-electron fluctuations a nearby coherent conductor, called a quantum
point contact (QPC), interacts with the QD and acts as a detector. An important
property of the QPC charge detector is noninvasiveness: the system physically
affects the detector, not visa-versa. Here we predict that even for ideal
noninvasive detectors such as the QPC, when a particular detector result is
observed, the system suffers an informational backaction, radically altering
the statistics of transport through the QD as compared to the unconditional
shot noise. We develop a theoretical model to make predictions about the joint
current probability distributions and conditional transport statistics. The
experimental findings reported here demonstrate the reality of informational
backaction in nanoscale systems as well as a variety of new effects, such as
conditional noise enhancement, which are in essentially perfect agreement with
our model calculations. This type of switching telegraph process occurs
abundantly in nature, indicating that these results are applicable to a wide
variety of systems.Comment: 16 pages, 3 figures, to appear in Nature Physic
Mapping the optimal route between two quantum states
A central feature of quantum mechanics is that a measurement is intrinsically
probabilistic. As a result, continuously monitoring a quantum system will
randomly perturb its natural unitary evolution. The ability to control a
quantum system in the presence of these fluctuations is of increasing
importance in quantum information processing and finds application in fields
ranging from nuclear magnetic resonance to chemical synthesis. A detailed
understanding of this stochastic evolution is essential for the development of
optimized control methods. Here we reconstruct the individual quantum
trajectories of a superconducting circuit that evolves in competition between
continuous weak measurement and driven unitary evolution. By tracking
individual trajectories that evolve between an arbitrary choice of initial and
final states we can deduce the most probable path through quantum state space.
These pre- and post-selected quantum trajectories also reveal the optimal
detector signal in the form of a smooth time-continuous function that connects
the desired boundary conditions. Our investigation reveals the rich interplay
between measurement dynamics, typically associated with wave function collapse,
and unitary evolution of the quantum state as described by the Schrodinger
equation. These results and the underlying theory, based on a principle of
least action, reveal the optimal route from initial to final states, and may
enable new quantum control methods for state steering and information
processing.Comment: 12 pages, 9 figure
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