Combinatorics of n-point functions via Hopf algebra in quantum field theory

We use a coproduct on the time-ordered algebra of field operators to derive simple relations between complete, connected and 1-particle irreducible n-point functions. Compared to traditional functional methods our approach is much more intrinsic and leads to efficient algorithms suitable for concrete computations. It may also be used to efficiently perform tree level computations.Comment: 26 pages, LaTeX + AMS + eepic; minor corrections and modification

Combinatorics of 1-particle irreducible n-point functions via coalgebra in quantum field theory

We give a coalgebra structure on 1-vertex irreducible graphs which is that of a cocommutative coassociative graded connected coalgebra. We generalize the coproduct to the algebraic representation of graphs so as to express a bare 1-particle irreducible n-point function in terms of its loop order contributions. The algebraic representation is so that graphs can be evaluated as Feynman graphs

Generating loop graphs via Hopf algebra in quantum field theory

We use the Hopf algebra structure of the time-ordered algebra of field operators to generate all connected weighted Feynman graphs in a recursive and efficient manner. The algebraic representation of the graphs is such that they can be evaluated directly as contributions to the connected n-point functions. The recursion proceeds by loop order and vertex number.Comment: 22 pages, LaTeX + AMS + eepic; new section with alternative recursion formula added, further minor changes and correction

Correlation of estuarine sedimentary cores based on color analysis: an example from the Algarve region (Portugal)

Coastal zones play a significant role in the regional development and have been an important area for human occupation through time. The study of estuarine sediments applied to sea level changes had always been of extreme importance, as it reflects the coastal line evolution, either by local, regional or global changes

Regional sea level change study based on estuarine sediment color and biogeochemistry - preliminary results

Coastal zones play a significant role in the regional development and have been an important area for human occupation through time. The study of estuarine sediments applied to sea level changes had always been of extreme importance, as it reflects the coastal line evolution, either by local, regional or global changes

An attempt to use color as a tool for high resolution correlations between estuarine sedimentary cores from Algarve (Portugal)

Nowadays, paleoenvironmental and climatological researches focus on studying shortterm climatic changes and one of the more sensitive environments for recording those short-term climatic variations are the high sedimentation rate of coastal regions. Accordingly, 4 estuaries from the Algarve region, south of Portugal, have been cored in order to study sedimentary and climatic variations during recent times (c.a. 5000 yrs). For this purpose, we applied sampling and analytical techniques from deep-sea studies, allowing the acquirement of almost continuous data profiles, as the color data obtained with the spectrophotometer Colortron

Is it possible to use "twin cores" as a unique sedimentary record? An experimental design based on sediment color

Sedimentary cores are widely used for studying Quaternary records. However, the amount of sediment that is available is proportional to the diameter of the core, which is rarely bigger than 15 cm. One way to obtain more sediment is to use two cores retrieved from almost the same location and use them as if they represent a unique sedimentary record. In the present work, an experimental design has been applied to verify if “twin cores” from an estuary can be considered as representing the same sedimentary record with twice the amount of sediment to study. Because sediment can be characterized based on its color, the variables used as replicates in the experimental design are the three Lab CIE colors acquired with a X-Rite Colortron spectrophotometer. Sediment cores were retrieved from the upper saltmarsh of Gilão River’s estuary, southern Portugal. Twin cores, with in between distances of 50 cm, 100 cm and 200 cm, from two different sites were analysed. Results from a nested ANOVA show that even for the closest twin cores (50 cm apart) there is at least one color variable that shows significant variations between the profiles of both cores. These results clearly show that “twin cores” cannot be used as a unique sedimentary record without any previous testing, at least in such transitional regions

Elliptic curves of large rank and small conductor

For r=6,7,...,11 we find an elliptic curve E/Q of rank at least r and the smallest conductor known, improving on the previous records by factors ranging from 1.0136 (for r=6) to over 100 (for r=10 and r=11). We describe our search methods, and tabulate, for each r=5,6,...,11, the five curves of lowest conductor, and (except for r=11) also the five of lowest absolute discriminant, that we found.Comment: 16 pages, including tables and one .eps figure; to appear in the Proceedings of ANTS-6 (June 2004, Burlington, VT). Revised somewhat after comments by J.Silverman on the previous draft, and again to get the correct page break