7,905 research outputs found
Algorithm Developments for Discrete Adjoint Methods
This paper presents a number of algorithm developments for adjoint methods using the 'discrete' approach in which the discretisation of the non-linear equations is linearised and the resulting matrix is then transposed. With a new iterative procedure for solving the adjoint equations, exact numerical equivalence is maintained between the linear and adjoint discretisations. The incorporation of strong boundary conditions within the discrete approach is discussed, as well as a new application of adjoint methods to linear unsteady flow in turbomachinery
A formal soundness proof of region-based memory management for object-oriented paradigm.
Region-based memory management has been proposed as a viable alternative to garbage collection for real-time applications and embedded software. In our previous work we have developed a region type inference algorithm that provides an automatic compile-time region-based memory management for object-oriented paradigm. In this work we present a formal soundness proof of the region type system that is the target of our region inference. More precisely, we prove that the object-oriented programs accepted by our region type system achieve region-based memory management in a safe way. That means, the regions follow a stack-of-regions discipline and regions deallocation never create dangling references in the store and on the program stack. Our contribution is to provide a simple syntactic proof that is based on induction and follows the standard steps of a type safety proof. In contrast the previous safety proofs provided for other region type systems employ quite elaborate techniques
Readout of solid-state charge qubits using a single-electron pump
A major difficulty in realizing a solid-state quantum computer is the
reliable measurement of the states of the quantum registers. In this paper, we
propose an efficient readout scheme making use of the resonant tunneling of a
ballistic electron produced by a single electron pump. We treat the measurement
interaction in detail by modeling the full spatial configuration, and show that
for pumped electrons with suitably chosen energy the transmission coefficient
is very sensitive to the qubit state. We further show that by using a short
sequence of pumping events, coupled with a simple feedback control procedure,
the qubit can be measured with high accuracy.Comment: 5 pages, revtex4, 4 eps figures. v2: published versio
Jones matrix analysis for a polarization-sensitive optical coherence tomography system using fiber-optic components
A Sound and Complete Abstraction for Reasoning about Parallel Prefix Sums
Prefix sums are key building blocks in the implementation of many concurrent software applications, and recently much work has gone into efficiently implementing prefix sums to run on massively par-allel graphics processing units (GPUs). Because they lie at the heart of many GPU-accelerated applications, the correctness of prefix sum implementations is of prime importance. We introduce a novel abstraction, the interval of summations, that allows scalable reasoning about implementations of prefix sums. We present this abstraction as a monoid, and prove a sound-ness and completeness result showing that a generic sequential pre-fix sum implementation is correct for an array of length n if and only if it computes the correct result for a specific test case when instantiated with the interval of summations monoid. This allows correctness to be established by running a single test where the in
Set-Theoretic Types for Polymorphic Variants
Polymorphic variants are a useful feature of the OCaml language whose current
definition and implementation rely on kinding constraints to simulate a
subtyping relation via unification. This yields an awkward formalization and
results in a type system whose behaviour is in some cases unintuitive and/or
unduly restrictive. In this work, we present an alternative formalization of
poly-morphic variants, based on set-theoretic types and subtyping, that yields
a cleaner and more streamlined system. Our formalization is more expressive
than the current one (it types more programs while preserving type safety), it
can internalize some meta-theoretic properties, and it removes some
pathological cases of the current implementation resulting in a more intuitive
and, thus, predictable type system. More generally, this work shows how to add
full-fledged union types to functional languages of the ML family that usually
rely on the Hindley-Milner type system. As an aside, our system also improves
the theory of semantic subtyping, notably by proving completeness for the type
reconstruction algorithm.Comment: ACM SIGPLAN International Conference on Functional Programming, Sep
2016, Nara, Japan. ICFP 16, 21st ACM SIGPLAN International Conference on
Functional Programming, 201
Quantum Films Adsorbed on Graphite: Third and Fourth Helium Layers
Using a path-integral Monte Carlo method for simulating superfluid quantum
films, we investigate helium layers adsorbed on a substrate consisting of
graphite plus two solid helium layers. Our results for the promotion densities
and the dependence of the superfluid density on coverage are in agreement with
experiment. We can also explain certain features of the measured heat capacity
as a function of temperature and coverage.Comment: 13 pages in the Phys. Rev. two-column format, 16 Figure
A weighted reduced basis method for parabolic PDEs with random data
This work considers a weighted POD-greedy method to estimate statistical
outputs parabolic PDE problems with parametrized random data. The key idea of
weighted reduced basis methods is to weight the parameter-dependent error
estimate according to a probability measure in the set-up of the reduced space.
The error of stochastic finite element solutions is usually measured in a root
mean square sense regarding their dependence on the stochastic input
parameters. An orthogonal projection of a snapshot set onto a corresponding POD
basis defines an optimum reduced approximation in terms of a Monte Carlo
discretization of the root mean square error. The errors of a weighted
POD-greedy Galerkin solution are compared against an orthogonal projection of
the underlying snapshots onto a POD basis for a numerical example involving
thermal conduction. In particular, it is assessed whether a weighted POD-greedy
solutions is able to come significantly closer to the optimum than a
non-weighted equivalent. Additionally, the performance of a weighted POD-greedy
Galerkin solution is considered with respect to the mean absolute error of an
adjoint-corrected functional of the reduced solution.Comment: 15 pages, 4 figure
Quantifying the extent of plant functional specialization using Grime's CSR strategies
Specialization refers to a species adaptation to a restricted range of environmental conditions. While generalist species are able to exploit a wide variety of resources in a broad range of habitats, specialist species tend to have narrower niche breadths. From an evolutionary perspective, specialization is the result of a functional syndrome in which a suite of traits covary to allow the effective exploitation of specific resources. Accordingly, the measurement of specialization should be based on a multi-trait approach. In plant ecology, a well-known classification of the adaptive strategies of plants is Grime's competitor, stress tolerator, ruderal (CSR) theory in which the three principal strategies represent relatively easily measurable trait combinations from the global spectrum of plant form and function arising under conditions of competition, abiotic restriction to growth or periodic disturbance, respectively. In this paper, we thus introduce a method to summarize the functional specialization of plant species and communities by applying inequality measures to Grime's CSR strategies. The general idea is that a plant species that can be exclusively assigned to one CSR strategy can be considered a specialist (as it adopts only one adaptive strategy to access resources), while species that share functional characteristics of multiple CSR strategies can be considered more generalist. The behavior of the proposed measures is shown with one case study on the functional changes of six Alpine vegetation types ordered along a gradient, from pioneer to more stable communities
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