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

Nonlinear resonance in a three-terminal carbon nanotube resonator

The RF-response of a three-terminal carbon nanotube resonator coupled to RF-transmission lines is studied by means of perturbation theory and direct numerical integration. We find three distinct oscillatory regimes, including one regime capable of exhibiting very large hysteresis loops in the frequency response. Considering a purely capacitive transduction, we derive a set of algebraic equations which can be used to find the output power (S-parameters) for a device connected to transmission lines with characteristic impedance $Z_0$.Comment: 16 pages, 8 figure

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

Dynamo effect in parity-invariant flow with large and moderate separation of scales

It is shown that non-helical (more precisely, parity-invariant) flows capable of sustaining a large-scale dynamo by the negative magnetic eddy diffusivity effect are quite common. This conclusion is based on numerical examination of a large number of randomly selected flows. Few outliers with strongly negative eddy diffusivities are also found, and they are interpreted in terms of the closeness of the control parameter to a critical value for generation of a small-scale magnetic field. Furthermore, it is shown that, for parity-invariant flows, a moderate separation of scales between the basic flow and the magnetic field often significantly reduces the critical magnetic Reynolds number for the onset of dynamo action.Comment: 44 pages,11 figures, significantly revised versio

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

Cold Physiology: Postprandial Blood Flow Dynamics and Metabolism in the Antarctic Fish Pagothenia borchgrevinki

Previous studies on metabolic responses to feeding (i.e. the specific dynamic action, SDA) in Antarctic fishes living at temperatures below zero have reported long-lasting increases and small peak responses. We therefore hypothesized that the postprandial hyperemia also would be limited in the Antarctic fish Pagothenia borchgrevinki. The proportion of cardiac output directed to the splanchnic circulation in unfed fish was 18%, which is similar to temperate fish species. Contrary to our prediction, however, gastrointestinal blood flow had increased by 88% at twenty four hours after feeding due to a significant increase in cardiac output and a significant decrease in gastrointestinal vascular resistance. While gastric evacuation time appeared to be longer than in comparable temperate species, digestion had clearly commenced twenty four hours after feeding as judged by a reduction in mass of the administered feed. Even so, oxygen consumption did not increase suggesting an unusually slowly developing SDA. Adrenaline and angiotensin II was injected into unfed fish to investigate neuro-humoral control mechanisms of gastrointestinal blood flow. Both agonists increased gastrointestinal vascular resistance and arterial blood pressure, while systemic vascular resistance was largely unaffected. The hypertension was mainly due to increased cardiac output revealing that the heart and the gastrointestinal vasculature, but not the somatic vasculature, are important targets for these agonists. It is suggested that the apparently reduced SDA in P. borchgrevinki is due to a depressant effect of the low temperature on protein assimilation processes occurring outside of the gastrointestinal tract, while the gastrointestinal blood flow responses to feeding and vasoactive substances resemble those previously observed in temperate species

Enhancing Network Intrusion Detection by Correlation of Modularly Hashed Sketches

The rapid development of network technologies entails an increase in traffic volume and attack count. The associated increase in computational complexity for methods of deep packet inspection has driven the development of behavioral detection methods. These methods distinguish attackers from valid users by measuring how closely their behavior resembles known anomalous behavior. In real-life deployment, an attacker is flagged only on very close resemblance to avoid false positives. However, many attacks can then go undetected. We believe that this problem can be solved by using more detection methods and then correlating their results. These methods can be set to higher sensitivity, and false positives are then reduced by accepting only attacks reported from more sources. To this end we propose a novel sketch-based method that can detect attackers using a correlation of particular anomaly detections. This is in contrast with the current use of sketch-based methods that focuses on the detection of heavy hitters and heavy changes. We illustrate the potential of our method by detecting attacks on RDP and SSH authentication by correlating four methods detecting the following anomalies: source network scan, destination network scan, abnormal connection count, and low traffic variance. We evaluate our method in terms of detection capabilities compared to other deployed detection methods, hardware requirements, and the attacker’s ability to evade detection