Large-scale inference with block structure

The detection of weak and rare effects in large amounts of data arises in a number of modern data analysis problems. Known results show that in this situation the potential of statistical inference is severely limited by the large-scale multiple testing that is inherent in these problems. Here we show that fundamentally more powerful statistical inference is possible when there is some structure in the signal that can be exploited, e.g. if the signal is clustered in many small blocks, as is the case in some relevant applications. We derive the detection boundary in such a situation where we allow both the number of blocks and the block length to grow polynomially with sample size. We derive these results both for the univariate and the multivariate settings as well as for the problem of detecting clusters in a network. These results recover as special cases the heterogeneous mixture detection problem [1] where there is no structure in the signal, as well as scan problem [2] where the signal comprises a single interval. We develop methodology that allows optimal adaptive detection in the general setting, thus exploiting the structure if it is present without incurring a relevant penalty in the case where there is no structure. The advantage of this methodology can be considerable, as in the case of no structure the means need to increase at the rate $\sqrt{\log n}$ to ensure detection, while the presence of structure allows detection even if the means \emph{decrease} at a polynomial rate

Accelerating Matrix/boundary Precipitations to Explore High-Strength and High-Ductile Co34cr32ni27al3.5ti3.5 Multicomponent Alloys through Hot Extrusion and Annealing

Annealing-regulated precipitation strengthening combined with cold-working is one of the most efficient strategies for resolving the conflict between strength and ductility in metals and alloys. However, precipitation control and grain refinement are mutually contradictory due to the excellent phase stability of multicomponent alloys. This work utilizes the high-temperature extrusion and annealing to optimize the microstructures and mechanical properties of the Co34Cr32Ni27Al3.5Ti3.5 multicomponent alloy. Hot extrusion effectively reduces grain sizes and simultaneously accelerates the precipitation of coherent L12 nanoparticles inside the face-centered cubic (FCC) matrix and grain boundary precipitations (i.e., submicron Cr-rich particles and L12-Ni3(Ti, Al) precipitates), resulting in strongly reciprocal interaction between dislocation slip and hierarchical-scale precipitates. Subsequent annealing regulates grain sizes, dislocations, twins, and precipitates, further allowing to tailor mechanical properties. The high yield strength is attributed to the coupled precipitation strengthening effects from nanoscale coherent L12 particles inside grains and submicron grain boundary precipitates under the support of pre-existing dislocations. The excellent ductility results from the synergistic activation of dislocations, stacking faults, and twins during plastic deformation. The present study provides a promising approach for regulating microstructures, especially defects, and enhancing the mechanical properties of multicomponent alloys