Flux-corrected transport techniques for transient calculations of strongly shocked flows

New flux-corrected transport algorithms are described for solving generalized continuity equations. These techniques were developed by requiring that the finite difference formulas used ensure positivity for an initially positive convected quantity. Thus FCT is particularly valuable for fluid-like problems with strong gradients or shocks. Repeated application of the same subroutine to mass, momentum, and energy conservation equations gives a simple solution of the coupled time-dependent equations of ideal compressible fluid dynamics without introducing an artificial viscosity. FCT algorithms span Eulerian, sliding-rezone, and Lagrangian finite difference grids in several coordinate systems. The latest FCT techniques are fully vectorized for parallel/pipeline processing

A problem around Mahler functions

Let $K$ be a field of characteristic zero and $k$ and $l$ be two multiplicatively independent positive integers. We prove the following result that was conjectured by Loxton and van der Poorten during the Eighties: a power series $F(z)\in K[[z]]$ satisfies both a $k$- and a $l$-Mahler type functional equation if and only if it is a rational function.Comment: 52 page

On the long-time behavior of spin echo and its relation to free induction decay

It is predicted that (i) spin echoes have two kinds of generic long-time decays: either simple exponential, or a superposition of a monotonic and an oscillatory exponential decays; and (ii) the long-time behavior of spin echo and the long-time behavior of the corresponding homogeneous free induction decay are characterized by the same time constants. This prediction extends to various echo problems both within and beyond nuclear magnetic resonance. Experimental confirmation of this prediction would also support the notion of the eigenvalues of time evolution operators in large quantum systems.Comment: 4 pages, 4 figure

Variance component score test for time-course gene set analysis of longitudinal RNA-seq data

As gene expression measurement technology is shifting from microarrays to sequencing, the statistical tools available for their analysis must be adapted since RNA-seq data are measured as counts. Recently, it has been proposed to tackle the count nature of these data by modeling log-count reads per million as continuous variables, using nonparametric regression to account for their inherent heteroscedasticity. Adopting such a framework, we propose tcgsaseq, a principled, model-free and efficient top-down method for detecting longitudinal changes in RNA-seq gene sets. Considering gene sets defined a priori, tcgsaseq identifies those whose expression vary over time, based on an original variance component score test accounting for both covariates and heteroscedasticity without assuming any specific parametric distribution for the transformed counts. We demonstrate that despite the presence of a nonparametric component, our test statistic has a simple form and limiting distribution, and both may be computed quickly. A permutation version of the test is additionally proposed for very small sample sizes. Applied to both simulated data and two real datasets, the proposed method is shown to exhibit very good statistical properties, with an increase in stability and power when compared to state of the art methods ROAST, edgeR and DESeq2, which can fail to control the type I error under certain realistic settings. We have made the method available for the community in the R package tcgsaseq.Comment: 23 pages, 6 figures, typo corrections & acceptance acknowledgemen

Contact Lie algebras of vector fields on the plane

The paper is devoted to the complete classification of all real Lie algebras of contact vector fields on the first jet space of one-dimensional submanifolds in the plane. This completes Sophus Lie's classification of all possible Lie algebras of contact symmetries for ordinary differential equations. As a main tool we use the abstract theory of filtered and graded Lie algebras. We also describe all differential and integral invariants of new Lie algebras found in the paper and discuss the infinite-dimensional case.Comment: 20 pages. Published copy, also available at http://www.maths.warwick.ac.uk/gt/GTVol3/paper1.abs.htm

Single-Spin Microscope with Sub-Nanoscale Resolution Based on Optically Detected Magnetic Resonance

We summarize our new scanning magnetic 3-D imaging system. This scanning system uses optically detected magnetic resonance in a single nitrogen vacancy center in a diamond nanocrystal. The theoretical analysis and the first experimental demonstrations have proved that this method has single spin sensitivity and a sub-nanoscale spatial resolution at room temperature.Comment: 4 pages, 2 figure

Recovery and Growth in the Manufacturing Sectors of CEE Transition Economies: Short and Long-Term Efficiency Improving Factors

The first aim of the paper was to explain a cross-sector differences in evolution of gross product of Slovenian manufacturing sectors in the period 1992-98 using different short and long-term factors. Results pointed out great importance of initial conditions (sector orientation to convertible or non-convertible markets, and distorted production structure), as well as structural reforms and macroeconomic and institutional environment. Added long-term factors revealed positive association with short term output growth during the transition period – it is obvious that these factors (FDI, exports, imports of inputs, cooperation) create channels for the transfer of technology, improving the efficiency of production. It turned out also that quality improving exports to the EU countries is significantly positively correlated with the sector output performance. The paper further studies the importance of both direct and indirect means of technology transfer for transition countries and its impact on productivity growth of local firms. Using firm-level data for eight transition countries for the period 1994 - 1998 and employing growth accounting approach, the paper explores the importance of FDI, intra-industry knowledge spillovers from FDI, firm's own R&D accumulation and of international R&D spillovers through trade for firm's TFP growth. Time-invariant firmspecific effects are taken into account using panel data techniques, and potential selection bias for foreign investment decisions is corrected by using a generalized Heckman two-step procedure. After controlling for common economic policy influences and industry effects, our results confirm for five advanced transition countries that technology is being transferred to domestic firms primarily through direct foreign linkages. Evidence on some international R&D spillovers through arm-length trade has been found for four transition countries. Our results also suggest that FDI do not generate positive intra-industry spillovers for domestic firms. Moreover, for three transition countries FDI were found to have significant crowding-out effects for local firms in the same industry.

Could Ren\'e Descartes have known this?

Below we discuss the partition of the space of real univariate polynomials according to the number of positive and negative roots and signs of the coefficients. We present several series of non-realizable combinations of signs together with the numbers of positive and negative roots. We provide a detailed information about possible non-realizable combinations as above up to degree 8 as well as a general conjecture about such combinations.Comment: 15 pages, no figure