The smallest known Devonian tetrapod shows unexpectedly derived features.

A new genus and species of Devonian tetrapod, Brittagnathus minutus gen. et sp. nov., is described from a single complete right lower jaw ramus recovered from the Acanthostega mass-death deposit in the upper part of the Britta Dal Formation (upper Famennian) of Stensiö Bjerg, Gauss Peninsula, East Greenland. Visualization by propagation phase contrast synchrotron microtomography allows a complete digital dissection of the specimen. With a total jaw ramus length of 44.8 mm, Brittagnathus is by far the smallest Devonian tetrapod described to date. It differs from all previously known Devonian tetrapods in having only a fang pair without a tooth row on the anterior coronoid and a large posterior process on the posterior coronoid. The presence of an incipient surangular crest and a concave prearticular margin to the adductor fossa together cause the fossa to face somewhat mesially, reminiscent of the condition in Carboniferous tetrapods. A phylogenetic analysis places Brittagnathus crownward to other Devonian tetrapods, adjacent to the Tournaisian genus Pederpes. Together with other recent discoveries, it suggests that diversification of 'Carboniferous-grade' tetrapods had already begun before the end of the Devonian and that the group was not greatly affected by the end-Devonian mass extinction

Uniform Diagonalization Theorem for Complexity Classes of Promise Problems including Randomized and Quantum Classes

Diagonalization in the spirit of Cantor's diagonal arguments is a widely used tool in theoretical computer sciences to obtain structural results about computational problems and complexity classes by indirect proofs. The Uniform Diagonalization Theorem allows the construction of problems outside complexity classes while still being reducible to a specific decision problem. This paper provides a generalization of the Uniform Diagonalization Theorem by extending it to promise problems and the complexity classes they form, e.g. randomized and quantum complexity classes. The theorem requires from the underlying computing model not only the decidability of its acceptance and rejection behaviour but also of its promise-contradicting indifferent behaviour - a property that we will introduce as "total decidability" of promise problems. Implications of the Uniform Diagonalization Theorem are mainly of two kinds: 1. Existence of intermediate problems (e.g. between BQP and QMA) - also known as Ladner's Theorem - and 2. Undecidability if a problem of a complexity class is contained in a subclass (e.g. membership of a QMA-problem in BQP). Like the original Uniform Diagonalization Theorem the extension applies besides BQP and QMA to a large variety of complexity class pairs, including combinations from deterministic, randomized and quantum classes.Comment: 15 page

Scaling limits of the treshold window - When does a monotone Boolean function fip its outcome? The tail of the crossing probability in near-critical percolation

Consider a monotone Boolean function f:{0,1}^n \to {0,1} and the canonical monotone coupling {eta_p:p in [0,1]} of an element in {0,1}^n chosen according to product measure with intensity p in [0,1]. The random point p in [0,1] where f(eta_p) flips from 0 to 1 is often concentrated near a particular point, thus exhibiting a threshold phenomenon. For a sequence of such Boolean functions, we peer closely into this threshold window and consider, for large n, the limiting distribution (properly normalized to be nondegenerate) of this random point where the Boolean function switches from being 0 to 1. We determine this distribution for a number of the Boolean functions which are typically studied and pay particular attention to the functions corresponding to iterated majorityand percolation crossings. It turns out that these limiting distributions have quite varying behavior. In fact, we show that any nondegenerate probability measure on R arises in this way for some sequence of Boolean functions

Cambrian stratigraphy of the Tomten-1 drill core, Västergötland, Sweden

The Tomten-1 drilling at Torbjörntorp in Västergötland, southern Sweden, penetrated 29.85 m of Cambrian Series 2, Cambrian Series 3, Furongian, and Lower–Middle Ordovician strata. Lithostratigraphically, the succession includes the File Haidar, Borgholm and Alum Shale formations, and the Latorp and Lanna limestones. The drill core succession is described herein for the first time, with special focus on the biostratigraphy of the Cambrian Alum Shale Formation. In the Cambrian Series 3, through Furongian Alum Shale Formation, agnostoids and trilobites have been identified to species level and the succession is subdivided into nine biozones (in ascending order): the Ptychagnostus gibbus, Ptychagnostus atavus, Lejopyge laevigata, Agnostus pisiformis, Olenus gibbosus, Parabolina spinulosa, Ctenopyge tumida, Ctenopyge bisulcata and Ctenopyge linnarssoni zones. The succession is interrupted by numerous stratigraphic gaps of variable magnitudes, as is evident from the biostratigraphy and conspicuous unconformities

Tides: A key environmental driver of osteichthyan evolution and the fish-tetrapod transition?

Tides are a major component of the interaction between the marine and terrestrial environments, and thus play an important part in shaping the environmental context for the evolution of shallow marine and coastal organisms. Here, we use a dedicated tidal model and palaeogeographic reconstructions from the Late Silurian to early Late Devonian (420 Ma, 400 Ma and 380 Ma, Ma = millions of years ago) to explore the potential significance of tides for the evolution of osteichthyans (bony fish) and tetrapods (land vertebrates). The earliest members of the osteichthyan crown-group date to the Late Silurian, approximately 425 Ma, while the earliest evidence for tetrapods is provided by trackways from the Middle Devonian, dated to approximately 393 Ma, and the oldest tetrapod body fossils are Late Devonian, approximately 373 Ma. Large tidal ranges could have fostered both the evolution of air-breathing organs in osteichthyans to facilitate breathing in oxygen-depleted tidal pools, and the development of weight-bearing tetrapod limbs to aid navigation within the intertidal zones. We find that tidal ranges over 4 m were present around areas of evolutionary significance for the origin of osteichthyans and the fish-tetrapod transition, highlighting the possible importance of tidal dynamics as a driver for these evolutionary processes