A priori error analysis of a numerical stochastic homogenization method

This paper provides an a~priori error analysis of a localized orthogonal decomposition method (LOD) for the numerical stochastic homogenization of a model random diffusion problem. If the uniformly elliptic and bounded random coefficient field of the model problem is stationary and satisfies a quantitative decorrelation assumption in form of the spectral gap inequality, then the expected $L^2$ error of the method can be estimated, up to logarithmic factors, by $H+(\varepsilon/H)^{d/2}$; $\varepsilon$ being the small correlation length of the random coefficient and $H$ the width of the coarse finite element mesh that determines the spatial resolution. The proof bridges recent results of numerical homogenization and quantitative stochastic homogenization.Comment: to appear in SIAM J. Numer. Ana

Estimating mixed quantum states

We discuss single adaptive measurements for the estimation of mixed quantum states of qubits. The results are compared to the optimal estimation schemes using collective measurements. We also demonstrate that the advantage of collective measurements increases when the degree of mixing of the quantum states increases.Comment: RevTeX, 7 pages, 4 figure

Neurite Outgrowth of Mature Retinal Ganglion Cells and PC12 Cells Requires Activity of CK1δ and CK1ε

Mature retinal ganglion cells (RGCs) do not normally regenerate severed axons after optic nerve injury and show only little neurite outgrowth in culture. However, RGCs can be transformed into an active regenerative state after lens injury (LI) enabling these neurons to regrow axons in vitro and in vivo. In the current study we investigated the role of CK1δ and CK1ε activity in neurite outgrowth of LI stimulated RGCs and nerve growth factor (NGF) stimulated PC12 cells, respectively. In both cell types CK1δ and ε were localized in granular particles aligned at microtubules in neurites and growth cones. Although LI treatment did not measurably affect the expression of CK1δ and ε, it significantly elevated the specific kinase activity in the retina. Similarly, CK1δ/ε specific kinase activity was also elevated in NGF treated PC12 cells compared with untreated controls. Neurite extension in PC12 cells was associated with a change in the activity of CK1δ C-terminal targeting kinases, suggesting that activity of these kinases might be necessary for neurite outgrowth. Pharmacological inactivation of CK1δ and ε markedly compromised neurite outgrowth of both, PC12 cells and LI stimulated RGCs in a concentration dependent manner. These data provide evidence for a so far unknown, but essential role of CK1 isoforms in neurite growth

Towards Automatic Generation of Amplified Regression Test Oracles

Regression testing is crucial in ensuring that pure code refactoring does not adversely affect existing software functionality, but it can be expensive, accounting for half the cost of software maintenance. Automated test case generation reduces effort but may generate weak test suites. Test amplification is a promising solution that enhances tests by generating additional or improving existing ones, increasing test coverage, but it faces the test oracle problem. To address this, we propose a test oracle derivation approach that uses object state data produced during System Under Test (SUT) test execution to amplify regression test oracles. The approach monitors the object state during test execution and compares it to the previous version to detect any changes in relation to the SUT's intended behaviour. Our preliminary evaluation shows that the proposed approach can enhance the detection of behaviour changes substantially, providing initial evidence of its effectiveness.Comment: 8 pages, 1 figur

Group Composition of Guinea Baboons (Papio papio) at a Water Place Suggests a Fluid Social Organization

Baboon social systems are among the most studied in primates. Solid knowledge of the hamadryas and savannah baboon systems has accumulated, leading to a dichotomic view of baboon social systems. Hamadryas baboons live in multilayered troops based on 1-male units whereas savannah baboons live in multimale multifemale groups based on a network of related females. Less attention has been paid to their West African congenerics, the Guinea baboons, Papio papio. To fill this gap, in 2007 we initiated a long-term study of a baboon troop ranging in the Niokolo Koba National Park in southeastern Senegal. Earlier studies suggested a tendency for a multilayered social system in Guinea baboons, similar to the hamadryas baboon organization. Therefore, as a first approach to analyzing variability in party size and composition, we observed members of the troop crossing an open area from a fixed point for 3 mo during the dry and wet seasons. We counted individuals and recorded changes in composition of both arriving and departing parties. Party size and composition were highly variable on both a daily and a seasonal basis; 45.9% of the arriving parties changed in composition while crossing the open area, either splitting into smaller parties or fusing into larger ones, suggesting a fluid organization. Our data support the existence of neither a hamadryas baboon-like multilayered social organization nor a stable medium-sized multimale multifemale group as in savannah baboons. In light of our data we may need to revise the dichotomic view of baboon social systems and include space for greater variability of their social systems