Just-In-Time Compilation of NumPy Vector Operations

In this paper, we introduce JIT compilation for thehigh-productivity framework Python/NumPy in order to boost theperformance significantly. The JIT compilation of Python/NumPyis completely transparent to the user – the runtime system willautomatically JIT compile and execute the NumPy instructionsencountered in a Python application. In other words, we introducea framework that provides the high-productivity from Pythonwhile maintaining the high-performance of a low-level, compiledlanguage.We transforms NumPy vector instruction into an AbstractSyntax Tree representation that creates the basis for furtheroptimizations. From the AST we auto-generate C code whichwe compile into computational kernels and execute. These incorporatetemporary array removal and loop-fusion which are mainbenefactors in the achieved speedups. In order to amortize theoverhead of creation, we also implement a cache for the compiledkernels.We evaluate the JIT compilation by executing several scientificcomputing benchmarks on an AMD. Compared to NumPy, weachieve speedups of a factor 4.72 for a N-Body application and7.51 for a Jacobi Stencil application executing on a single CPUcore

Photon number discrimination without a photon counter and its application to reconstructing non-Gaussian states

The non-linearity of a conditional photon-counting measurement can be used to `de-Gaussify' a Gaussian state of light. Here we present and experimentally demonstrate a technique for photon number resolution using only homodyne detection. We then apply this technique to inform a conditional measurement; unambiguously reconstructing the statistics of the non-Gaussian one and two photon subtracted squeezed vacuum states. Although our photon number measurement relies on ensemble averages and cannot be used to prepare non-Gaussian states of light, its high efficiency, photon number resolving capabilities, and compatibility with the telecommunications band make it suitable for quantum information tasks relying on the outcomes of mean values.Comment: 4 pages, 3 figures. Theory section expanded in response to referee comment

Signature of the Simplicial Supermetric

We investigate the signature of the Lund-Regge metric on spaces of simplicial three-geometries which are important in some formulations of quantum gravity. Tetrahedra can be joined together to make a three-dimensional piecewise linear manifold. A metric on this manifold is specified by assigning a flat metric to the interior of the tetrahedra and values to their squared edge-lengths. The subset of the space of squared edge-lengths obeying triangle and analogous inequalities is simplicial configuration space. We derive the Lund-Regge metric on simplicial configuration space and show how it provides the shortest distance between simplicial three-geometries among all choices of gauge inside the simplices for defining this metric (Regge gauge freedom). We show analytically that there is always at least one physical timelike direction in simplicial configuration space and provide a lower bound on the number of spacelike directions. We show that in the neighborhood of points in this space corresponding to flat metrics there are spacelike directions corresponding to gauge freedom in assigning the edge-lengths. We evaluate the signature numerically for the simplicial configuration spaces based on some simple triangulations of the three-sphere (S^3) and three-torus (T^3). For the surface of a four-simplex triangulation of S^3 we find one timelike direction and all the rest spacelike over all of the simplicial configuration space. For the triangulation of T^3 around flat space we find degeneracies in the simplicial supermetric as well as a few gauge modes corresponding to a positive eigenvalue. Moreover, we have determined that some of the negative eigenvalues are physical, i.e. the corresponding eigenvectors are not generators of diffeomorphisms. We compare our results with the known properties of continuum superspace.Comment: 24 pages, RevTeX, 4 eps Figures. Submitted to Classical Quantum Gravit

Selection of reliable reference genes for the normalisation of gene expression levels following time course LPS stimulation of murine bone marrow derived macrophages

© 2017 The Author(s). Background: Macrophages are key players in the initiation, perpetuation and regulation of both innate and adaptive immune responses. They largely perform these roles through modulation of the expression of genes, especially those encoding cytokines. Murine bone marrow derived macrophages (BMDMs) are commonly used as a model macrophage population for the study of immune responses to pro-inflammatory stimuli, notably lipopolysaccharide (LPS), which may be pertinent to the human situation. Evaluation of the temporal responses of LPS stimulated macrophages is widely conducted via the measurement of gene expression levels by RT-qPCR. While providing a robust and sensitive measure of gene expression levels, RT-qPCR relies on the normalisation of gene expression data to a stably expressed reference gene. Generally, a normalisation gene(s) is selected from a list of "traditional" reference genes without validation of expression stability under the specific experimental conditions of the study. In the absence of such validation, and given that many studies use only a single reference gene, the reliability of data is questionable. Results: The stability of expression levels of eight commonly used reference genes was assessed during the peak (6 h) and resolution (24 h) phases of the BMDM response to LPS. Further, this study identified two additional genes, which have not previously been described as reference genes, and the stability of their expression levels during the same phases of the inflammatory response were validated. Importantly, this study demonstrates that certain "traditional" reference genes are in fact regulated by LPS exposure, and, therefore, are not reliable candidates as their inclusion may compromise the accuracy of data interpretation. Testament to this, this study shows that the normalisation of gene expression data using an unstable reference gene greatly affects the experimental data obtained, and, therefore, the ultimate biological conclusions drawn. Conclusion: This study reaffirms the importance of validating reference gene stability for individual experimental conditions. Given that gene expression levels in LPS stimulated macrophages is routinely used to infer biological phenomena that are of relevance to human conditions, verification of reference gene expression stability is crucial