On Logical Depth and the Running Time of Shortest Programs

The logical depth with significance $b$ of a finite binary string $x$ is the shortest running time of a binary program for $x$ that can be compressed by at most $b$ bits. There is another definition of logical depth. We give two theorems about the quantitative relation between these versions: the first theorem concerns a variation of a known fact with a new proof, the second theorem and its proof are new. We select the above version of logical depth and show the following. There is an infinite sequence of strings of increasing length such that for each $j$ there is a $b$ such that the logical depth of the $j$th string as a function of $j$ is incomputable (it rises faster than any computable function) but with $b$ replaced by $b+1$ the resuling function is computable. Hence the maximal gap between the logical depths resulting from incrementing appropriate $b$'s by 1 rises faster than any computable function. All functions mentioned are upper bounded by the Busy Beaver function. Since for every string its logical depth is nonincreasing in $b$, the minimal computation time of the shortest programs for the sequence of strings as a function of $j$ rises faster than any computable function but not so fast as the Busy Beaver function.Comment: 12 pages LaTex (this supercedes arXiv:1301.4451

The last Anthracothere Brachyodus onoideus (Mammalia, Artiodactyla) from westernmost Europe and its extinction

This paper deals with B. onoideus specimens from Portugal. This species occurs in the Lisbon area (in the upper part of the lower Miocene, ca.18 to 17.6 Ma) in a very accurate stratigraphic framing (age, lithostratigraphic, climatic and palaeoecologic control being most complete). Some mandibular dental size variation, sex characters, functional interpretation, ecology and predation, chemical corrosion, and extinction are discussed

The Deinotherium (Proboscidea, Mammalia): an abnormal tusk from Lisbon, the Miocene record in Portugal and the first appearance datum. Evidence from Lisbon, Portugal

An exceptionally favourable stratigraphic and chronologic context concerning the Miocene series in Lisbon allows us to stress that there are two successive data as far as the Proboscideans' immigration into western Europe is concerned: firstly, that of Gomphotheres, and later that of Deinotheres. The study of a Langhian (in age) tusk has shown that Deinotherinm havaricum was still present then. The time span of this species could be accurately recognized. A discussion on the genus Deinotherium is presented, as well as its occurrence in Portugal and on its ecologic meaning

Assessment of the traffic noise on thin layers

Traffic noise is an important branch of the environment pollution which deeply affects the population and for that reason it has been included in the set of pavement performance indicators. Nevertheless, the knowledge on the environmental impact of the existing surface pavement layers is very limited, particularly for what respects to tyre/road noise of thin layers. These layers are at the present time widely used in a great extent with rubberized asphalt both in urban and rural roads especially in the north of Portugal due to environmental concerns. In this paper the comparison of the tyre/road noise (Lmax) generated in roads with thin surface layers is made. The noise levels generated by light and heavy vehicles are set according to the Statistical Pass-By Method (SPB) of which test methods is described in the standard ISO 11819-1:1997. At management level the information provided by tyre/road noise tests is essential to support environmentally sustainable construction and maintenance alternatives. Furthermore, at project level, the results give some insight about the relation surface layers/traffic composition

Rupicapra rupicapra (Mammalia) in the Late Pleistocene of Portugal

The presence of the genus Rupicapra in Portugal is shown for the first time, on some dental and skeletal remains from the upper Pleistocene (Solutrean) of Salemas cave. The fossil material may be ascribed to R. rupicapra pyrenaica

Aerosol and precipitation chemistry in a remote site in Central Amazonia: the role of biogenic contribution

International audienceA long-term (2?3 years) measurement of aerosol and precipitation chemistry was carried out in a remote site in Central Amazonia, Balbina, (1°55' S, 59°29' W, 174 m above sea level), about 200 km north of Manaus city. Aerosols were sampled using stacked filter units (SFU), which separate fine (d<2.5 ?m) and coarse mode (2.5 ?