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

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

This paper summarizes current knowledge about East African pholcids. East Africa is defined as the area from 12°S to 5°N and from 28° to 42°E, including all of Uganda, Kenya, Burundi, Rwanda, and Tanzania. An annotated list of the 15 genera and 87 species recorded from this area is given, together with distribution maps and an identification key to genera. Most East African species (90%) belong to one of only six genera: Buitinga Huber, 2003 (21 species); Smeringopus Simon, 1890 (18); Pholcus Walckenaer, 1805 (17); Spermophora Hentz, 1841 (12); Leptopholcus Simon, 1893 (5) and Quamtana Huber, 2003 (4). Eight species for which DNA sequence data have been published recently are newly described: Buitinga batwa sp. nov., B. wataita sp. nov., Spermophora mau sp. nov., S. maathaiae sp. nov., S. bukusu sp. nov., S. kirinyaga sp. nov., S. kyambura sp. nov. and Quamtana nyahururu sp. nov. Crossopriza johncloudsleyi Deeleman-Reinhold & van Harten, 2001, previously only known from Yemen, is redescribed based on specimens from Kenya. Additional new records are given for 21 previously described species

Mikroorganismen an Aesculus hippocastanum – olfaktorische Perspektive von Cameraria ohridella (Deschka & Dimic)

Since the 80s, the popular park- and city tree Aesculus hippocastanum has been infested with the leaf miner Cameraria ohridella (DESCHKA & DIMIC 1986). Additionally, the pathogenic fungi Guignardia aesculi causes leaf blotch disease and Erysiphe flexuosa causes powdery mildew on horse chestnuts. Often, all three diseases occur in parallel at the same leaves leading to a situation of competition. Moreover, recently some endophytic fungi were isolated from the leaf tissue of A. hippocastanum. In the present study, the volatile interaction between three trophic levels plant, insect, and fungi are discussed.Mikroorganismen an Aesculus hippocastanum – olfaktorische Perspektive von Cameraria ohridella (Deschka & Dimic) Seit den 80er Jahren wird die Gemeine Rosskastanie Aesculus hippocastanum durch den Minierer Cameraria ohridella (Lepidoptera, Gracillariidae) befallen. Außerdem wird die Rosskastanie durch den Blattbräunepilz Guignardia aesculi und den Mehltau Erysiphe flexuosa attackiert. Oft treten alle drei Organismen parallel am gleichen Blatt auf. Weiterhin konnten endophytische Pilze aus dem Blattgewebe isoliert werden. Im vorliegenden Beitrag wird die volatile Interaktion zwischen Pflanze, Mikroorganismen und Insekt diskutiert. Mit Hilfe der Gaschromatographie und gekoppelter Massenspektroskopie (GC-MS) wurden Duftproben gesunder und mit den pathogenen Pilzen G. aesculi und E. flexuosa gleichzeitig infizierter Blätter der Rosskastanie analysiert. Identifizierte Komponenten wurden elektrophysiologisch (EAG) an der Insektenantenne und in Verhaltensversuchen getestet. Mit den pathogenen Pilzen befallene Rosskastanienblätter geben 1-Octen-3-ol, 3-Octanon, ein Derivat von 2(5H)-Furanon, Nonanal und Decanal ab. C. ohridella war in der Lage, diese Substanzen zu detektieren. In Zweifachwahltests mit gesunden A. hippocastanum Zweigen reagierten Weibchen mit reduzierter Eiablage auf die Applikation von 1-Octen-3-ol, 3-Octanon, 2(5H)-Furanon und Decanal im Vergleich zur unbehandelten Kontrolle. Es ist bekannt, dass 1-Octen-3-ol und 3-Octanon von Pilzen selber emittiert werden. Nonanal und Decanal werden von Zellen, die nach Penetration durch Pilzhyphen unter oxidativem Stress stehen, produziert. Die Derivate von 2(5H)-Furanon wirken antimikrobiell und können auf einen Schutzmechanismus der Pflanze oder auf einen Konkurrenzmechanismus von Mikroorganismen um denselben Lebensraum hinweisen. Eine mögliche Erklärung wäre, dass diese Substanz von Endophyten zur Verteidigung des sie umgebenden Blattgewebes gegen die pathogenen Pilze produziert wird

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