On Seiffert-like means

We investigate the representation of homogeneous, symmetric means in the form M(x,y)=\frac{x-y}{2f((x-y)/(x+y))}. This allows for a new approach to comparing means. As an example, we provide optimal estimate of the form (1-\mu)min(x,y)+ \mu max(x,y)<= M(x,y)<= (1-\nu)min(x,y)+ \nu max(x,y) and M((x+y)/2-\mu(x-y)/2,(x+y)/2+\mu(x-y)/2)<= N(x,y)<= M((x+y)/2-\nu(x-y)/2,(x+y)/2+\nu(x-y)/2) for some known means

Geochemical analysis of Cenozoic fossil conifers at high latitudes: Implications for molecular preservation and environmental change

Fossil materials record ancient life and their adapted environment. Arctic plant fossils are critical for our understanding of the Earth’s paleoenvironment when high latitudes were under ice-free conditions. All Arctic plant fossils in this research are conifers, plants conducive for morphological and molecular study because of their incredible genetic stability. Miocene (15 million year old) and Pliocene (5 million year old) conifer leaves were collected from Banks Island, Canada (Williams et al., 2008). Samples were analyzed and compared with Paleocene (60 million year old) and Eocene (45 million year old) samples from Axel Heiberg Island, Canada and with modern equivalent species from Washington D.C., USA (William et al., 2008). This paper has three main sample analyses. First, Pyrolysis-Mass Spectrometry-Gas Chromatography technology was used to detect organic volatile compounds. The amounts and types of organic volatile compounds provide further insights into the molecular preservation of the Miocene and Pliocene fossilized samples. Molecular preservation from this research was compared to previous research that used Scanning Electron Microscope observations of Paleocene and Eocene transverse sections to indicate extraordinary morphological preservation (Yang et al., 2005; Yang et al., 2007). Second, Miocene and Pliocene bulk peat were cross-referenced with known species in the region to reconstruct Arctic environmental changes between 5 million and 15 million years ago. Third, the ratios of three stable compounds were analyzed as biomarkers, essentially benchmarks for plant fossil preservation. However, biomarkers were inconclusive because of complications including age, species type, and environmental conditions. Overall, our analyses provide the first assessments of molecular preservation for these rare Arctic fossils which offer unique material for further paleoclimate analysis

Schemes for Learning and Behaviour: A New Expectancy Model

PhD Thesi

Two-variable Logic with Counting and a Linear Order

We study the finite satisfiability problem for the two-variable fragment of first-order logic extended with counting quantifiers (C2) and interpreted over linearly ordered structures. We show that the problem is undecidable in the case of two linear orders (in the presence of two other binary symbols). In the case of one linear order it is NEXPTIME-complete, even in the presence of the successor relation. Surprisingly, the complexity of the problem explodes when we add one binary symbol more: C2 with one linear order and in the presence of other binary predicate symbols is equivalent, under elementary reductions, to the emptiness problem for multicounter automata