The Kato square root problem on vector bundles with generalised bounded geometry

We consider smooth, complete Riemannian manifolds which are exponentially locally doubling. Under a uniform Ricci curvature bound and a uniform lower bound on injectivity radius, we prove a Kato square root estimate for certain coercive operators over the bundle of finite rank tensors. These results are obtained as a special case of similar estimates on smooth vector bundles satisfying a criterion which we call generalised bounded geometry. We prove this by establishing quadratic estimates for perturbations of Dirac type operators on such bundles under an appropriate set of assumptions.Comment: Slight technical modification of the notion of "GBG constant section" on page 7, and a few technical modifications to Proposition 8.4, 8.6, 8.

Extremely narrow spectrum of GRB110920A: further evidence for localised, subphotospheric dissipation

Much evidence points towards that the photosphere in the relativistic outflow in GRBs plays an important role in shaping the observed MeV spectrum. However, it is unclear whether the spectrum is fully produced by the photosphere or whether a substantial part of the spectrum is added by processes far above the photosphere. Here we make a detailed study of the $\gamma-$ray emission from single pulse GRB110920A which has a spectrum that becomes extremely narrow towards the end of the burst. We show that the emission can be interpreted as Comptonisation of thermal photons by cold electrons in an unmagnetised outflow at an optical depth of $\tau \sim 20$. The electrons receive their energy by a local dissipation occurring close to the saturation radius. The main spectral component of GRB110920A and its evolution is thus, in this interpretation, fully explained by the emission from the photosphere including localised dissipation at high optical depths.Comment: 14 pages, 11 figures, accepted to MNRA

Visibilia ex invisibilibus: seeing at the nanoscale for improved preservation of parchment

This paper describes the application of atomic force microscopy (AFM) for the imaging of collagen denaturation as observed in parchment. Parchment is prepared from processed animal skin and collagen is the main component. Large collections in national archives, libraries and religious institutions contain numerous documents written on parchment. Their preservation presents an unsolved problem for conservators. The main challenge is to assess the state of collagen and to detect what conservators refer to as the pre-gelatinised state, which can cause surface cracking resulting in a loss of text and can increase the vulnerability of parchment to aqueous cleaning agents. Atomic force microscopy (AFM) was first used within the Improved Damage Assessment of Parchment (IDAP) project, enabling the characterisation of the collagen structure within parchment at the nanoscale. Damage categories were also established based on the extent of the ordered collagen structure that was observed in the AFM images. This paper describes the work following the IDAP project, where morphological changes in the fibres due to both artificial and natural ageing were observed and linked to observations made by AFM. It also explores the merits and drawbacks of different approaches used for sample preparation and the possibility of using a portable AFM for imaging directly on the surface of documents. A case study on a manuscript from the 18th century is presented

Separation of Test-Free Propositional Dynamic Logics over Context-Free Languages

For a class L of languages let PDL[L] be an extension of Propositional Dynamic Logic which allows programs to be in a language of L rather than just to be regular. If L contains a non-regular language, PDL[L] can express non-regular properties, in contrast to pure PDL. For regular, visibly pushdown and deterministic context-free languages, the separation of the respective PDLs can be proven by automata-theoretic techniques. However, these techniques introduce non-determinism on the automata side. As non-determinism is also the difference between DCFL and CFL, these techniques seem to be inappropriate to separate PDL[DCFL] from PDL[CFL]. Nevertheless, this separation is shown but for programs without test operators.Comment: In Proceedings GandALF 2011, arXiv:1106.081

Testing a word is not a test of word learning

Although vocabulary acquisition requires children learn names for multiple things, many investigations of word learning mechanisms teach children the name for only one of the objects presented. This is problematic because it is unclear whether children's performance reflects recall of the correct name-object association or simply selection of the only object that was singled out by being the only object named. Children introduced to one novel name may perform at ceiling as they are not required to discriminate on the basis of the name per se, and appear to rapidly learn words following minimal exposure to a single word. We introduced children to four novel objects. For half the children, only one of the objects was named and for the other children, all four objects were named. Only children introduced to one word reliably selected the target object at test. This demonstration highlights the over-simplicity of one-word learning paradigms and the need for a shift in word learning paradigms where more than one word is taught to ensure children disambiguate objects on the basis of their names rather than their degree of salience

Finite Automata for the Sub- and Superword Closure of CFLs: Descriptional and Computational Complexity

We answer two open questions by (Gruber, Holzer, Kutrib, 2009) on the state-complexity of representing sub- or superword closures of context-free grammars (CFGs): (1) We prove a (tight) upper bound of $2^{\mathcal{O}(n)}$ on the size of nondeterministic finite automata (NFAs) representing the subword closure of a CFG of size $n$. (2) We present a family of CFGs for which the minimal deterministic finite automata representing their subword closure matches the upper-bound of $2^{2^{\mathcal{O}(n)}}$ following from (1). Furthermore, we prove that the inequivalence problem for NFAs representing sub- or superword-closed languages is only NP-complete as opposed to PSPACE-complete for general NFAs. Finally, we extend our results into an approximation method to attack inequivalence problems for CFGs

Learning what to remember: vocabulary knowledge and children’s memory for object names and features

Although young children can map a novel name to a novel object, it remains unclear what they actually remember about objects when they initially make such a name-object association. In the current study we investigated 1) what children remembered after they were initially introduced to name-object associations and 2) how their vocabulary size and vocabulary structure influenced what they remembered. As a group, children had difficulty remembering each of the features of the original novel objects. Further analyses revealed that differences in vocabulary structure predicted children’s ability to remember object features. Specifically, children who produced many names for categories organized by similarity in shape (e.g., ball, cup) had the best memory for newly-learned objects’ features—especially their shapes. In addition, the more features children remembered, the more likely they were to retain the newly-learned name-object associations. Vocabulary size, however, was not predictive of children’s feature memory or retention. Taken together, these findings demonstrate that children’s existing vocabulary structure, rather than simply vocabulary size, influences what they attend to when encountering a new object and subsequently their ability to remember new name-object associations

Probing the temporal variability of Cygnus X-1 into the soft state

Building on results from previous studies of Cygnus~X-1, we analyze Rossi X-ray Timing Explorer (RXTE) data taken when the source was in the soft and transitional spectral states. We look at the power spectrum in the 0.01 -- 50 Hz range, using a model consisting of a cut-off power-law and two Lorentzian components. We are able to constrain the relation between the characteristic frequencies of the Lorentzian components, and show that it is consistent with a power-law relation having the same index (1.2) as previously reported for the hard state, but shifted by a factor ~2. Furthermore, it is shown that the change in the frequency relation seen during the transitions can be explained by invoking a shift of one Lorentzian component to a higher harmonic, and we explore the possible support for this interpretation in the other component parameters. With the improved soft state results we study the evolution of the fractional variance for each temporal component. This approach indicates that the two Lorentzian components are connected to each other, and unrelated to the power-law component in the power spectrum, pointing to at least two separate emission components.Comment: 11 pages, 10 figures, 1 electronic table. Accepted for publication in A&