Complex anisotropy beneath the Peruvian flat slab from frequency-dependent, multiple-phase shear wave splitting analysis

Flat or shallow subduction is a relatively widespread global occurrence, but the dynamics remain poorly understood. In particular, the interaction between flat slabs and the surrounding mantle flow has yet to be studied in detail. Here we present measurements of seismic anisotropy to investigate mantle flow beneath the Peruvian flat-slab segment, the largest present-day region of flat subduction. We conduct a detailed shear wave splitting analysis at a long-running seismic station (NNA) located near Lima, Peru. We present measurements of apparent splitting parameters (fast direction ? and delay time ?t) for SKS, ScS, and local S phases from 80 events. We observe well-defined frequency dependence and backazimuthal variability, indicating the likely presence of complex anisotropy. Forward modeling the observations with two or three layers of anisotropy reveals a likely layer with a trench-normal fast direction underlying a layer with a more trench-oblique (to trench-subparallel) fast direction. In order to further constrain the anisotropic geometry, we analyzed the source-side splitting from events originating within the slab measured at distant stations. Beneath the flat-slab segment, we found trench-normal fast splitting directions in the subslab mantle, while within the dipping portion of the slab further to the east, likely trench-subparallel anisotropy within the slab itself. This subslab pattern contradicts observations from elsewhere in South America for “normal” (i.e., more steeply dipping) slab conditions. It is similar, however, to inferences from other shallowly dipping subduction zones around the world. While there is an apparent link between slab dip and the surrounding mantle flow, at least beneath Peru, the precise nature of the relationship remains to be clarified

Hipergráfok = Hypergraphs

A projekt célkitűzéseit sikerült megvalósítani. A négy év során több mint száz kiváló eredmény született, amiből eddig 84 dolgozat jelent meg a téma legkiválóbb folyóirataiban, mint Combinatorica, Journal of Combinatorial Theory, Journal of Graph Theory, Random Graphs and Structures, stb. Számos régóta fennálló sejtést bebizonyítottunk, egész régi nyitott problémát megoldottunk hipergráfokkal kapcsolatban illetve kapcsolódó területeken. A problémák némelyike sok éve, olykor több évtizede nyitott volt. Nem egy közvetlen kutatási eredmény, de szintén bizonyos értékmérő, hogy a résztvevők egyike a Norvég Királyi Akadémia tagja lett és elnyerte a Steele díjat. | We managed to reach the goals of the project. We achieved more than one hundred excellent results, 84 of them appeared already in the most prestigious journals of the subject, like Combinatorica, Journal of Combinatorial Theory, Journal of Graph Theory, Random Graphs and Structures, etc. We proved several long standing conjectures, solved quite old open problems in the area of hypergraphs and related subjects. Some of the problems were open for many years, sometimes for decades. It is not a direct research result but kind of an evaluation too that a member of the team became a member of the Norvegian Royal Academy and won Steele Prize

Sparse modeling of categorial explanatory variables

Shrinking methods in regression analysis are usually designed for metric predictors. In this article, however, shrinkage methods for categorial predictors are proposed. As an application we consider data from the Munich rent standard, where, for example, urban districts are treated as a categorial predictor. If independent variables are categorial, some modifications to usual shrinking procedures are necessary. Two $L_1$-penalty based methods for factor selection and clustering of categories are presented and investigated. The first approach is designed for nominal scale levels, the second one for ordinal predictors. Besides applying them to the Munich rent standard, methods are illustrated and compared in simulation studies.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS355 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org