Derived invariance of the cap product in Hochschild theory

We prove derived invariance of the cap product for associative algebras projective over a commutative ring.Comment: 4 page

Synchronization Strings: Explicit Constructions, Local Decoding, and Applications

This paper gives new results for synchronization strings, a powerful combinatorial object that allows to efficiently deal with insertions and deletions in various communication settings: $\bullet$ We give a deterministic, linear time synchronization string construction, improving over an $O(n^5)$ time randomized construction. Independently of this work, a deterministic $O(n\log^2\log n)$ time construction was just put on arXiv by Cheng, Li, and Wu. We also give a deterministic linear time construction of an infinite synchronization string, which was not known to be computable before. Both constructions are highly explicit, i.e., the $i^{th}$ symbol can be computed in $O(\log i)$ time. $\bullet$ This paper also introduces a generalized notion we call long-distance synchronization strings that allow for local and very fast decoding. In particular, only $O(\log^3 n)$ time and access to logarithmically many symbols is required to decode any index. We give several applications for these results: $\bullet$ For any $\delta0$ we provide an insdel correcting code with rate $1-\delta-\epsilon$ which can correct any $O(\delta)$ fraction of insdel errors in $O(n\log^3n)$ time. This near linear computational efficiency is surprising given that we do not even know how to compute the (edit) distance between the decoding input and output in sub-quadratic time. We show that such codes can not only efficiently recover from $\delta$ fraction of insdel errors but, similar to [Schulman, Zuckerman; TransInf'99], also from any $O(\delta/\log n)$ fraction of block transpositions and replications. $\bullet$ We show that highly explicitness and local decoding allow for infinite channel simulations with exponentially smaller memory and decoding time requirements. These simulations can be used to give the first near linear time interactive coding scheme for insdel errors

West African pholcid spiders: an overview, with descriptions of five new species (Araneae, Pholcidae)

This paper summarizes current knowledge about West African pholcids. West Africa is here defined as the area south of 17°N and west of 5°E, including mainly the Upper Guinean subregion of the Guineo-Congolian center of endemism. This includes all of Senegal, The Gambia, Guinea Bissau, Guinea, Sierra Leone, Liberia, Ivory Coast, Ghana, Togo and Benin. An annotated list of the 14 genera and 38 species recorded from this area is given, together with distribution maps and an identification key to genera. Five species are newly described: Anansus atewa sp. nov., Artema bunkpurugu sp. nov., Leptopholcus kintampo sp. nov., Spermophora akwamu sp. nov., and S. ziama sp. nov. The female of Quamtana kitahurira is newly described. Additional new records are given for 16 previously described species, including 33 new country records. Distribution patterns of West African pholcids are discussed, as well as possible explanations for relatively low West African pholcid species diversity as compared to Central and East Africa

Application of the electromotive force as a shock front indicator in the inner heliosphere

The electromotive force (EMF) describes how the evolution and generation of a large-scale magnetic field is influenced by small-scale turbulence. Recent studies of in-situ measurements have shown a significant peak in the EMF while a coronal mass ejection (CME) shock front passes by the spacecraft. The goal of this study is to use the EMF as an indicator for the arrival of CME shock fronts. With Helios spacecraft measurements we carry out a statistical study on the EMF during CMEs in the inner heliosphere. We develop an automated shock front detection algorithm using the EMF as the main detection criterion and compare the results to an existing CME database. The properties of the EMF during the recorded events are discussed as a function of the heliocentric distance. Our algorithm reproduces most of the the events from Kilpua et al. (2015) and finds many additional CME-like events which proves the EMF as a good shock front indicator. The largest peaks in the EMF are found from 0 to 50 minutes after the initial shock. We find a power law of -1.54 and -2.18 for two different formulations of the EMF with the heliocentric distance.Comment: 6 pages, 5 figures, publishe