Singular Weyl-Titchmarsh-Kodaira theory for one-dimensional Dirac operators

We develop singular Weyl-Titchmarsh-Kodaira theory for one-dimensional Dirac operators. In particular, we establish existence of a spectral transformation as well as local Borg-Marchenko and Hochstadt-Liebermann type uniqueness results. Finally, we give some applications to the case of radial Dirac operators.Comment: 27 pages. arXiv admin note: substantial text overlap with arXiv:1110.2453, arXiv:1203.585

Chirped-pulse interferometry with finite frequency correlations

Chirped-pulse interferometry is a new interferometric technique encapsulating the advantages of the quantum Hong-Ou-Mandel interferometer without the drawbacks of using entangled photons. Both interferometers can exhibit even-order dispersion cancellation which allows high resolution optical delay measurements even in thick optical samples. In the present work, we show that finite frequency correlations in chirped-pulse interferometry and Hong-Ou-Mandel interferometry limit the degree of dispersion cancellation. Our results are important considerations in designing practical devices based on these technologies.Comment: 10 pages, 2 figure

Using lead market factors to assess the potential for a sustainability transition

AbstractThis paper considers how the lead market concept can contribute towards analysing system transformation as described by the multi-level perspective (MLP). Lead market arguments for the export potential of eco-innovations can provide an argument for policy support for environmental niches. International policy diffusion and learning across countries on the level of niche–regime interaction can improve the legitimacy of supporting policies. We propose how eco-innovation can be framed within an integrated MLP-lead market approach. Eco-innovations address two classes of regimes (infrastructure and eco-efficiency), which are likely to follow different transition pathways. The use of indicators for lead market factors for empirically analysing the opportunities for system transformation in the MLP framework is assessed. Indicators for the lead market factors can be attributed to the MLP. However, some of the indicators are more general in nature and do only indirectly point towards system transformation towards eco-innovations

Experimental bound entanglement in a four-photon state

Entanglement [1, 2] enables powerful new quantum technologies [3-8], but in real-world implementations, entangled states are often subject to decoherence and preparation errors. Entanglement distillation [9, 10] can often counteract these effects by converting imperfectly entangled states into a smaller number of maximally entangled states. States that are entangled but cannot be distilled are called bound entangled [11]. Bound entanglement is central to many exciting theoretical results in quantum information processing [12-14], but has thus far not been experimentally realized. A recent claim for experimental bound entanglement is not supported by their data [15]. Here, we consider a family of four-qubit Smolin states [16], focusing on a regime where the bound entanglement is experimentally robust. We encode the state into the polarization of four photons and show that our state exhibits both entanglement and undistillability, the two defining properties of bound entanglement. We then use our state to implement entanglement unlocking, a key feature of Smolin states [16].Comment: 10 pages, 6 figures. For a simultaneously submitted related work see arXiv:1005.196

New insights into the interstellar medium of the dwarf galaxy IC 10 : connection between magnetic fields, the radio--infrared correlation and star formation

This is a pre-copyedited, author-produced PDF of an article accepted for publication in Monthly Notices of the Royal Astronomical Society following peer review. Available at doi: https://doi.org/10.1093/mnras/stx1567.We present the highest sensitivity and angular resolution study at 0.32 GHz of the dwarf irregular galaxy IC\,10, observed using the Giant Metrewave Radio Telescope, probing $\sim45$ pc spatial scales. We find the galaxy-averaged radio continuum spectrum to be relatively flat, with a spectral index $\alpha = -0.34\pm0.01$ ($S_\nu \propto \nu^\alpha$), mainly due to a high contribution from free--free emission. At 0.32 GHz, some of the H{\sc ii} regions show evidence of free--free absorption as they become optically thick below $\sim0.41$ GHz with corresponding free electron densities of $\sim11-22~\rm cm^{-3}$. After removing the free--free emission, we studied the radio--infrared relations on 55, 110 and 165 pc spatial scales. We find that on all scales the non-thermal emission at 0.32 and 6.2 GHz correlates better with far-infrared (FIR) emission at $70\,\mu$m than mid-infrared emission at $24\,\mu$m. The dispersion of the radio--FIR relation arises due to variations in both magnetic field and dust temperature, and decreases systematically with increasing spatial scale. The effect of cosmic ray transport is negligible as cosmic ray electrons were only injected $\lesssim5$ Myr ago. The average magnetic field strength ($B$) of $12~\mu$G in the disc is comparable to that of large star-forming galaxies. The local magnetic field is strongly correlated with local star formation rate ($\mathrm{SFR}$) as $B \propto \mathrm{SFR}^{0.35\pm0.03}$, indicating a star-burst driven fluctuation dynamo to be efficient ($\sim10$ per cent) in amplifying the field in IC\,10. The high spatial resolution observations presented here suggest that the high efficiency of magnetic field amplification and strong coupling with SFR likely sets up the radio--FIR correlation in cosmologically young galaxies.Peer reviewedFinal Accepted Versio

Using Tracing To Enhance Data Cache Performance in CPUs: The creation of a Trace-Assisted Cache to increase cache hits and decrease runtime

The processor-memory gap is widening every year with no prospect of reprieve. More and more latency is being added to program runtimes as memory cannot satisfy the demands of CPUs quickly enough. In the past, this has been alleviated through caches of increasing complexity or techniques like prefetching, to give the illusion of faster memory. However, these techniques have drawbacks because they are reactive or rely on incomplete information. In general, this leads to large amounts of latency in programs due to processor stalls. It is our contention that through tracing a program's data accesses and feeding this information back to the cache, overall program runtime can be reduced. This is achieved through a new piece of hardware called a Trace-Assisted Cache (TAC). This uses traces to gain foreknowledge of the memory requests the processor is likely to make, allowing them to be actioned before the processor requests the data, overlapping memory and computation instructions. Comparing the TAC against a standard CPU without a cache, we see improvements in runtimes of up to 65%. However, we see degraded performance of around 8% on average when compared to Set-Associative and Direct-Mapped caches. This is because improvements are swamped by high overheads and synchronisation times between components. We also see that benchmarks that exhibit several qualities: a balance of computation and memory instructions and keeping data well spread out in memory fare better using TAC than other benchmarks on the same hardware. Overall this demonstrates that whilst there is potential to reduce runtime via increasing the agency of the cache through Trace Assistance, it requires a highly efficient implementation to be competitive otherwise any potential gains are negated by the increase in overheads