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

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

Electrodeposited cu thin layers as low cost and effective underlayers for Cu2O photocathodes in photoelectrochemical water electrolysis

Cu2O is one of the most studied semiconductors for photocathodes in photoelectrochemical water splitting (PEC-WS). Its low stability is counterbalanced by good activity, provided that a suitable underlayer/support is used. While Cu2O is mostly studied on Au underlayers, this paper proposes Cu(0) as a low-cost, easy to prepare and highly efficient alternative. Cu and Cu2O can be electrodeposited from the same bath, thus allowing in principle to tune the final material\u2019s physico-chemical properties with high precision with a scalable method. Electrodes and photoelectrodes are studied by means of electrochemical methods (cyclic voltammetry, Pb underpotential deposition) and by ex-situ X-ray absorption spectroscopy (XAS). While the potential applied for the deposition of Cu has no influence on the bulk structure and on the photocurrent displayed by the semiconductor, it plays a role on the dark currents, making this strategy promising for improving the material\u2019s stability. Au/Cu2O and Cu/Cu2O show similar performances, the latter having clear advantages in view of future use in practical applications. The influence of Cu underlayer thickness was also evaluated in terms of obtained photocurrent

Morphology of the earliest reconstructable tetrapod Parmastega aelidae.

The known diversity of tetrapods of the Devonian period has increased markedly in recent decades, but their fossil record consists mostly of tantalizing fragments1-15. The framework for interpreting the morphology and palaeobiology of Devonian tetrapods is dominated by the near complete fossils of Ichthyostega and Acanthostega; the less complete, but partly reconstructable, Ventastega and Tulerpeton have supporting roles2,4,16-34. All four of these genera date to the late Famennian age (about 365-359 million years ago)-they are 10 million years younger than the earliest known tetrapod fragments5,10, and nearly 30 million years younger than the oldest known tetrapod footprints35. Here we describe Parmastega aelidae gen. et sp. nov., a tetrapod from Russia dated to the earliest Famennian age (about 372 million years ago), represented by three-dimensional material that enables the reconstruction of the skull and shoulder girdle. The raised orbits, lateral line canals and weakly ossified postcranial skeleton of P. aelidae suggest a largely aquatic, surface-cruising animal. In Bayesian and parsimony-based phylogenetic analyses, the majority of trees place Parmastega as a sister group to all other tetrapods

Autonomous UAS-Based Agriculture Applications: General Overview and Relevant European Case Studies

Emerging precision agriculture techniques rely on the frequent collection of high-quality data which can be acquired efficiently by unmanned aerial systems (UAS). The main obstacle for wider adoption of this technology is related to UAS operational costs. The path forward requires a high degree of autonomy and integration of the UAS and other cyber physical systems on the farm into a common Farm Management System (FMS) to facilitate the use of big data and artificial intelligence (AI) techniques for decision support. Such a solution has been implemented in the EU project AFarCloud (Aggregated Farming in the Cloud). The regulation of UAS operations is another important factor that impacts the adoption rate of agricultural UAS. An analysis of the new European UAS regulations relevant for autonomous operation is included. Autonomous UAS operation through the AFarCloud FMS solution has been demonstrated at several test farms in multiple European countries. Novel applications have been developed, such as the retrieval of data from remote field sensors using UAS and in situ measurements using dedicated UAS payloads designed for physical contact with the environment. The main findings include that (1) autonomous UAS operation in the agricultural sector is feasible once the regulations allow this; (2) the UAS should be integrated with the FMS and include autonomous data processing and charging functionality to offer a practical solution; and (3) several applications beyond just asset monitoring are relevant for the UAS and will help to justify the cost of this equipment.publishedVersio

Low-temperature specific heat and thermal conductivity of glycerol

We have measured the thermal conductivity of glassy glycerol between 1.5 K and 100 K, as well as the specific heat of both glassy and crystalline phases of glycerol between 0.5 K and 25 K. We discuss both low-temperature properties of this typical molecular glass in terms of the soft-potential model. Our finding of an excellent agreement between its predictions and experimental data for these two independent measurements constitutes a robust proof of the capabilities of the soft-potential model to account for the low-temperature properties of glasses in a wide temperature range.Comment: 4 pages, 3 figures. To be published in Phys. Rev. B (2002