98 research outputs found
Formalizing a hierarchical file system
An abstract file system is defined here as a partial function from (absolute) paths to data. Such a file system determines the set of valid paths. It allows the file system to be read and written at a valid path, and it allows the system to be modified by the Unix operations for creation, removal, and moving of files and directories. We present abstract definitions (axioms) for these operations. This specification is refined towards a pointer implementation. The challenge is to have a natural abstraction function from the implementation to the specification, to define operations on the concrete store that behave exactly in the same way as the corresponding functions on the abstract store, and to prove these facts. To mitigate the problems attached to partial functions, we do this in two steps: first a refinement towards a pointer implementation with total functions, followed by one that allows partial functions. These two refinements are proved correct by means of a number of invariants. Indeed, the insights gained consist, on the one hand, of the invariants of the pointer implementation that are needed for the refinement functions, and on the other hand of the precise enabling conditions of the operations on the different levels of abstraction. Each of the three specification levels is enriched with a permission system for reading, writing, or executing, and the refinement relations between these permission systems are explored. Files and directories are distinguished from the outset, but this rarely affects our part of the specifications. All results have been verified with the proof assistant PVS, in particular, that the invariants are preserved by the operations, and that, where the invariants hold, the operations commute with the refinement functions
Stratifying quotient stacks and moduli stacks
Recent results in geometric invariant theory (GIT) for non-reductive linear
algebraic group actions allow us to stratify quotient stacks of the form [X/H],
where X is a projective scheme and H is a linear algebraic group with
internally graded unipotent radical acting linearly on X, in such a way that
each stratum [S/H] has a geometric quotient S/H. This leads to stratifications
of moduli stacks (for example, sheaves over a projective scheme) such that each
stratum has a coarse moduli space.Comment: 25 pages, submitted to the Proceedings of the Abel Symposium 201
A solid state light-matter interface at the single photon level
Coherent and reversible mapping of quantum information between light and
matter is an important experimental challenge in quantum information science.
In particular, it is a decisive milestone for the implementation of quantum
networks and quantum repeaters. So far, quantum interfaces between light and
atoms have been demonstrated with atomic gases, and with single trapped atoms
in cavities. Here we demonstrate the coherent and reversible mapping of a light
field with less than one photon per pulse onto an ensemble of 10 millions atoms
naturally trapped in a solid. This is achieved by coherently absorbing the
light field in a suitably prepared solid state atomic medium. The state of the
light is mapped onto collective atomic excitations on an optical transition and
stored for a pre-programmed time up of to 1 mu s before being released in a
well defined spatio-temporal mode as a result of a collective interference. The
coherence of the process is verified by performing an interference experiment
with two stored weak pulses with a variable phase relation. Visibilities of
more than 95% are obtained, which demonstrates the high coherence of the
mapping process at the single photon level. In addition, we show experimentally
that our interface allows one to store and retrieve light fields in multiple
temporal modes. Our results represent the first observation of collective
enhancement at the single photon level in a solid and open the way to multimode
solid state quantum memories as a promising alternative to atomic gases.Comment: 5 pages, 5 figures, version submitted on June 27 200
Non-polynomial Worst-Case Analysis of Recursive Programs
We study the problem of developing efficient approaches for proving
worst-case bounds of non-deterministic recursive programs. Ranking functions
are sound and complete for proving termination and worst-case bounds of
nonrecursive programs. First, we apply ranking functions to recursion,
resulting in measure functions. We show that measure functions provide a sound
and complete approach to prove worst-case bounds of non-deterministic recursive
programs. Our second contribution is the synthesis of measure functions in
nonpolynomial forms. We show that non-polynomial measure functions with
logarithm and exponentiation can be synthesized through abstraction of
logarithmic or exponentiation terms, Farkas' Lemma, and Handelman's Theorem
using linear programming. While previous methods obtain worst-case polynomial
bounds, our approach can synthesize bounds of the form
as well as where is not an integer. We present
experimental results to demonstrate that our approach can obtain efficiently
worst-case bounds of classical recursive algorithms such as (i) Merge-Sort, the
divide-and-conquer algorithm for the Closest-Pair problem, where we obtain
worst-case bound, and (ii) Karatsuba's algorithm for
polynomial multiplication and Strassen's algorithm for matrix multiplication,
where we obtain bound such that is not an integer and
close to the best-known bounds for the respective algorithms.Comment: 54 Pages, Full Version to CAV 201
Double hadron leptoproduction in the nuclear medium
First measurement of double-hadron production in deep-inelastic scattering
has been measured with the HERMES spectrometer at HERA using a 27.6 GeV
positron beam with deuterium, nitrogen, krypton and xenon targets. The
influence of the nuclear medium on the ratio of double-hadron to single-hadron
yields has been investigated. Nuclear effects are clearly observed but with
substantially smaller magnitude and reduced -dependence compared to
previously measured single-hadron multiplicity ratios. The data are in fair
agreement with models based on partonic or pre-hadronic energy loss, while they
seem to rule out a pure absorptive treatment of the final state interactions.
Thus, the double-hadron ratio provides an additional tool for studying
modifications of hadronization in nuclear matter
Spectral hole burning: examples from photosynthesis
The optical spectra of photosynthetic pigment–protein complexes usually show broad absorption bands, often consisting of a number of overlapping, ‘hidden’ bands belonging to different species. Spectral hole burning is an ideal technique to unravel the optical and dynamic properties of such hidden species. Here, the principles of spectral hole burning (HB) and the experimental set-up used in its continuous wave (CW) and time-resolved versions are described. Examples from photosynthesis studied with hole burning, obtained in our laboratory, are then presented. These examples have been classified into three groups according to the parameters that were measured: (1) hole widths as a function of temperature, (2) hole widths as a function of delay time and (3) hole depths as a function of wavelength. Two examples from light-harvesting (LH) 2 complexes of purple bacteria are given within the first group: (a) the determination of energy-transfer times from the chromophores in the B800 ring to the B850 ring, and (b) optical dephasing in the B850 absorption band. One example from photosystem II (PSII) sub-core complexes of higher plants is given within the second group: it shows that the size of the complex determines the amount of spectral diffusion measured. Within the third group, two examples from (green) plants and purple bacteria have been chosen for: (a) the identification of ‘traps’ for energy transfer in PSII sub-core complexes of green plants, and (b) the uncovering of the lowest k = 0 exciton-state distribution within the B850 band of LH2 complexes of purple bacteria. The results prove the potential of spectral hole burning measurements for getting quantitative insight into dynamic processes in photosynthetic systems at low temperature, in particular, when individual bands are hidden within broad absorption bands. Because of its high-resolution wavelength selectivity, HB is a technique that is complementary to ultrafast pump–probe methods. In this review, we have provided an extensive bibliography for the benefit of scientists who plan to make use of this valuable technique in their future research
Orbit Closures and Invariants
The first author would like to thank Sebastian Herpel for the conversations we had which led to the first iteration of some of the ideas in this paper, and also Stephen Donkin for some very helpful nudges towards the right literature. All three authors acknowledge the funding of EPSRC grant EP/L005328/1. We would like to thank the anonymous referee for their very insightful comments and for pointing out a subtle gap in the proof of Theorem 1.1.Peer reviewedPublisher PD
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