For a continuous $\mathbb {N}^d$ or $\mathbb {Z}^d$ action on a compact space, we introduce the notion of Bohr chaoticity, which is an invariant of topological conjugacy and which is proved stronger than having positive entropy. We prove that all principal algebraic $\mathbb {Z}$ actions of positive entropy are Bohr chaotic. The same is proved for principal algebraic actions of $\mathbb {Z}^d$ with positive entropy under the condition of existence of summable homoclinic points.

We give an example of a principal algebraic action of the non-commutative free group ${\mathbb {F}}$ of rank two by automorphisms of a connected compact abelian group for which there is an explicit measurable isomorphism with the full Bernoulli 3-shift action of ${\mathbb {F}}$ . The isomorphism is defined using homoclinic points, a method that has been used to construct symbolic covers of algebraic actions. To our knowledge, this is the first example of a Bernoulli algebraic action of ${\mathbb {F}}$ without an obvious independent generator. Our methods can be generalized to a large class of acting groups.

The newly identified Paleolithic site Sima de Las Palomas de Teba hosts an almost seven-m-thick sediment profile investigated here to elucidate the rock shelter's chronostratigraphy and formation processes. At its base, the sediment sequence contains rich archeological deposits recording intensive occupation by Neanderthals. Luminescence provides a terminus ante quem of 39.4 ± 2.6 ka or 44.9 ± 4.1 ka (OSL) and 51.4 ± 8.4 ka (TL). This occupation ended with a rockfall event followed by accumulation of archeologically sterile sediments. These were covered by sediments containing few Middle Paleolithic artifacts, which either indicate ephemeral occupation by Neanderthals or reworking as suggested by micromorphological features. Above this unit, scattered lithic artifacts of undiagnostic character may represent undefined Paleolithic occupations. Sediment burial ages between about 23.0 ± 1.5 ka (OSL) and 40.5 ± 3.4 ka (pIRIR) provide an Upper Paleolithic chronology for sediments deposited above the rockfall. Finally, a dung-bearing Holocene layer in the uppermost part of the sequence contains a fragment of a human mandible dated to 4032 ± 39 14C yr BP. Overall, the sequence represents an important new site for studying the end of Neanderthal occupation in southern Spain.

Holocene environmental changes in the northern Fertile Crescent remain poorly understood because of the scarcity of local proxy records in the region. In this study we investigated pedogenic (soil-formed) carbonate coatings on stones at the Pre-Pottery Neolithic site Göbekli Tepe as an indicator of local early-mid Holocene environmental changes. The 14C ages and stable isotopic composition of carbon and oxygen in thin (0.2–0.3 mm thick) pedogenic carbonate lamina indicate two main periods of coating formation: the early-Holocene (ca. 10000–6000 cal yr BP) and the mid-Holocene (ca. 6000–4000 cal yr BP). During the first period, there was an inverse relationship between δ13C and δ18O curves: a decrease in δ13C values coincide with an increase in δ18O values. For this period a trend towards higher temperatures is suggested. In the mid-Holocene, the mean rate of coating growth was 2–3 times higher than in the early Holocene. Both δ13C and δ18O reached their maximum values during this time and the direction of changes of the δ13C and δ18O curves became similar. The combination of data suggests that this period was the most humid in the Holocene and on average warmer than the early Holocene. At ca. 4000 cal yr BP secondary accumulation of carbonate ceased, presumably reflecting a shift to a more arid climate.

We consider a construction of ${C}^{\ast } $-algebras from continuous piecewise monotone maps on the circle which generalizes the crossed product construction for homeomorphisms and more generally the construction of Renault, Deaconu and Anantharaman-Delaroche for local homeomorphisms. Assuming that the map is surjective and not locally injective we give necessary and sufficient conditions for the simplicity of the ${C}^{\ast } $-algebra and show that it is then a Kirchberg algebra. We provide tools for the calculation of the $K$-theory groups and turn them into an algorithmic method for Markov maps.

Göbekli Tepe is one of the most important archaeological discoveries of modern times, pushing back the origins of monumentality beyond the emergence of agriculture. We are pleased to present a summary of work in progress by the excavators of this remarkable site and their latest thoughts about its role and meaning. At the dawn of the Neolithic, hunter-gatherers congregating at Göbekli Tepe created social and ideological cohesion through the carving of decorated pillars, dancing, feasting—and, almost certainly, the drinking of beer made from fermented wild crops.

Cyclic algebraic ${\mathbb {Z}^{d}}$-actions are defined by ideals of Laurent polynomials in $d$ commuting variables. Such an action is expansive precisely when the complex variety of the ideal is disjoint from the multiplicative $d$-torus. For such expansive actions it is known that the limit of the growth rate of periodic points exists and is equal to the entropy of the action. In an earlier paper the authors extended this result to ideals whose variety intersects the $d$-torus in a finite set. Here we further extend it to the case where the dimension of intersection of the variety with the $d$-torus is at most $d-2$. The main tool is the construction of homoclinic points which decay rapidly enough to be summable.

A 12-year-old girl presented with a first prolonged syncope. She was successfully resuscitated by external defibrillation after recording torsade de pointes tachycardia. Repeated electrocardiograms and a 12-channel Holter monitoring showed an intermittent prolongation of the QT interval. Genetic analysis identified a heterozygous point mutation in the KCNH2 gene, which is thought to be associated with a rather mild clinical phenotype of the long QT syndrome.

We give three corrections to the paper [K. Schmidt and A. M. Vershik, Algebraic polymorphisms, Ergod. Th. & Dynam. Sys.28 (2008), 633–642].