An entry from the Cambridge Structural Database, the world’s repository for small molecule crystal structures. The entry contains experimental data from a crystal diffraction study. The deposited dataset for this entry is freely available from the CCDC and typically includes 3D coordinates, cell parameters, space group, experimental conditions and quality measures.
Debugging large-scale, data-intensive, distributed applications running in a datacenter (datacenter applications) is complex and time-consuming. The key obstacle is non-deterministic failures—hard-to-reproduce program misbehaviors that are immune to traditional cyclic debugging techniques. Datacenter applications are rife with such failures because they operate in highly non-deterministic environments: a typical setup employs thousands of nodes, spread across multiple datacenters, to process terabytes of data per day. In these environments, existing methods for debugging non-deterministic failures are of limited use. They either incur excessive production overheads or don't scale to multi-node, terabyte-scale processing. To help remedy the situation, we have built a new deterministic replay tool. Our tool, called DCR, enables the reproduction and debugging of non-deterministic failures in production datacenter runs. The key observation behind DCR is that debugging does not always require a precise replica of the original datacenter run. Instead, it often suffices to produce some run that exhibits the original behavior of the control-plane —the most error-prone component of datacenter applications. DCR leverages this observation to relax the determinism guarantees offered by the system, and consequently, to address key requirements of production datacenter applications: lightweight recording of long-running programs, causally consistent replay of large-scale clusters, and out-of-the box operation with existing, real-world applications running on commodity multiprocessors.
Multivariate resultants generalize the Sylvester resultant of two polynomials and characterize the solvability of a polynomial system. They also reduce the computation of all common roots to a problem in linear algebra. We propose a determinantal formula for the sparse resultant of an arbitrary system of n + 1 polynomials in n variables. This resultant generalizes the classical one and has significantly lower degree for polynomials that are sparse in the sense that their mixed volume is lower than their Bézout number. Our algorithm uses a mixed polyhedral subdivision of the Minkowski sum of the Newton polytopes in order to construct a Newton matrix. Its determinant is a nonzero multiple of the sparse resultant and the latter equals the GCD of at most n + 1 such determinants. This construction implies a restricted version of an effective sparse Nullstellensatz. For an arbitrary specialization of the coefficients, there are two methods that use one extra variable and yield the sparse resultant. This is the first algorithm to handle the general case with complexity polynomial in the resultant degree and simply exponential in n . We conjecture its extension to producing an exact rational expression for the sparse resultant.
Bulk amorphous alloys, such as the Zr41.2Ti13.8Cu12.5Ni10Be22.5 (at.%) alloy, have received much interest lately, particularly for their commercial application in golf club heads. This study seeks to investigate the fatigue behavior of this Zr-based amorphous metal in the presence of air and sodium chloride solution, with the specific goal of identifying mechanisms of environmentally assisted fatigue-crack growth in these environments. Results from experiments, including fatigue testing in air and sodium chloride, fatigue under potential control, and static load testing in sodium chloride, suggest that quite distinct mechanisms of fatigue-crack propagation are active in air and sodium chloride solution. Specifically, the fatigue-crack growth rates observed under static and cyclic loading in sodium chloride likely depend on an anodic process, which results in a brittle mode of failure. Conversely in air, fatigue-crack propagation is associated with alternating blunting and re-sharpening of the crack tip, as evidenced by the presence of classic fatigue striations.
