183,118 research outputs found
Identification of a reversible quantum gate: assessing the resources
We assess the resources needed to identify a reversible quantum gate among a
finite set of alternatives, including in our analysis both deterministic and
probabilistic strategies. Among the probabilistic strategies we consider
unambiguous gate discrimination, where errors are not tolerated but
inconclusive outcomes are allowed, and we prove that parallel strategies are
sufficient to unambiguously identify the unknown gate with minimum number of
queries. This result is used to provide upper and lower bounds on the query
complexity and on the minimum ancilla dimension. In addition, we introduce the
notion of generalized t-designs, which includes unitary t-designs and group
representations as special cases. For gates forming a generalized t-design we
give an explicit expression for the maximum probability of correct gate
identification and we prove that there is no gap between the performances of
deterministic strategies an those of probabilistic strategies. Hence,
evaluating of the query complexity of perfect deterministic discrimination is
reduced to the easier problem of evaluating the query complexity of unambiguous
discrimination. Finally, we consider discrimination strategies where the use of
ancillas is forbidden, providing upper bounds on the number of additional
queries needed to make up for the lack of entanglement with the ancillas.Comment: 24 + 8 pages, published versio
Randomized Robust Subspace Recovery for High Dimensional Data Matrices
This paper explores and analyzes two randomized designs for robust Principal
Component Analysis (PCA) employing low-dimensional data sketching. In one
design, a data sketch is constructed using random column sampling followed by
low dimensional embedding, while in the other, sketching is based on random
column and row sampling. Both designs are shown to bring about substantial
savings in complexity and memory requirements for robust subspace learning over
conventional approaches that use the full scale data. A characterization of the
sample and computational complexity of both designs is derived in the context
of two distinct outlier models, namely, sparse and independent outlier models.
The proposed randomized approach can provably recover the correct subspace with
computational and sample complexity that are almost independent of the size of
the data. The results of the mathematical analysis are confirmed through
numerical simulations using both synthetic and real data
The 'Sphere': A Dedicated Bifurcation Aneurysm Flow-Diverter Device.
We present flow-based results from the early stage design cycle, based on computational modeling, of a prototype flow-diverter device, known as the 'Sphere', intended to treat bifurcation aneurysms of the cerebral vasculature. The device is available in a range of diameters and geometries and is constructed from a single loop of NITINOL(®) wire. The 'Sphere' reduces aneurysm inflow by means of a high-density, patterned, elliptical surface that partially occludes the aneurysm neck. The device is secured in the healthy parent vessel by two armatures in the shape of open loops, resulting in negligible disruption of parent or daughter vessel flow. The device is virtually deployed in six anatomically accurate bifurcation aneurysms: three located at the Basilar tip and three located at the terminus bifurcation of the Internal Carotid artery (at the meeting of the middle cerebral and anterior cerebral arteries). Both steady state and transient flow simulations reveal that the device presents with a range of aneurysm inflow reductions, with mean flow reductions falling in the range of 30.6-71.8% across the different geometries. A significant difference is noted between steady state and transient simulations in one geometry, where a zone of flow recirculation is not captured in the steady state simulation. Across all six aneurysms, the device reduces the WSS magnitude within the aneurysm sac, resulting in a hemodynamic environment closer to that of a healthy vessel. We conclude from extensive CFD analysis that the 'Sphere' device offers very significant levels of flow reduction in a number of anatomically accurate aneurysm sizes and locations, with many advantages compared to current clinical cylindrical flow-diverter designs. Analysis of the device's mechanical properties and deployability will follow in future publications
Aerodynamic shape optimization of a low drag fairing for small livestock trailers
Small livestock trailers are commonly used to transport animals from farms to market
within the United Kingdom. Due to the bluff nature of these vehicles there is great potential
for reducing drag with a simple add-on fairing. This paper explores the feasibility of
combining high-fidelity aerodynamic analysis, accurate metamodeling, and efficient
optimization techniques to find an optimum fairing geometry which reduces drag, without
significantly impairing internal ventilation. Airflow simulations were carried out using
Computational Fluid Dynamics (CFD) to assess the performance of each fairing based on
three design variables. A Moving Least Squares (MLS) metamodel was built on a fifty-point
Optimal Latin Hypercube (OLH) Design of Experiments (DoE), where each point
represented a different geometry configuration. Traditional optimization techniques were
employed on the metamodel until an optimum geometrical configuration was found. This
optimum design was tested using CFD and it matched closely to the metamodel prediction.
Further, the drag reduction was measured at 14.4% on the trailer and 6.6% for the
combined truck and trailer
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