Restricted walks in regular trees

Let T be the Cayley graph of a finitely generated free group F. Given two vertices in T consider all the walks of a given length between these vertices that at a certain time must follow a number of predetermined steps. We give formulas for the number of such walks by expressing the problem in terms of equations in F and solving the corresponding equations.

Generating trees for permutations avoiding generalized patterns

We construct generating trees with with one, two, and three labels for some classes of permutations avoiding generalized patterns of length 3 and 4. These trees are built by adding at each level an entry to the right end of the permutation, which allows us to incorporate the adjacency condition about some entries in an occurrence of a generalized pattern. We use these trees to find functional equations for the generating functions enumerating these classes of permutations with respect to different parameters. In several cases we solve them using the kernel method and some ideas of Bousquet-Mélou [2]. We obtain refinements of known enumerative results and find new ones.

The equation xpyq=zr and groups that act freely on Λ-trees

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Polynomial functors and trees

We explore the relationship between polynomial functors and trees. In the first part we characterise trees as certain polynomial functors and obtain a completely formal but at the same time conceptual and explicit construction of two categories of rooted trees, whose main properties we describe in terms of some factorisation systems. The second category is the category Ω of Moerdijk and Weiss. Although the constructions are motivated and explained in terms of polynomial functors, they all amount to elementary manipulations with finite sets. Included in Part 1 is also an explicit construction of the free monad on a polynomial endofunctor, given in terms of trees. In the second part we describe polynomial endofunctors and monads as structures built from trees, characterising the images of several nerve functors from polynomial endofunctors and monads into presheaves on categories of trees. Polynomial endofunctors and monads over a base are characterised by a sheaf condition on categories of decorated trees. In the absolute case, one further condition is needed, a projectivity condition, which serves also to characterise polynomial endofunctors and monads among (coloured) collections and operads.

Level-wise node size distribution of randomly generated regular trees

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Biophysical requirements of power-supply systems: nuclear energy and fossil energy

The report presents a grammar capable of analyzing the process of production of electricity in modular elements for different power-supply systems, defined using semantic and formal categories. In this way it becomes possible to individuate similarities and differences in the process of production of electricity, and then measure and compare “apples” with “apples” and “oranges” with “oranges”. For instance, when comparing the various unit operations of the process of production of electricity with nuclear energy to the analogous unit operations of the process of production of fossil energy, we see that the various phases of the process are the same. The only difference is related to characteristics of the process associated with the generation of heat which are completely different in the two systems. As a matter of facts, the performance of the production of electricity from nuclear energy can be studied, by comparing the biophysical costs associated with the different unit operations taking place in nuclear and fossil power plants when generating process heat or net electricity. By adopting this approach, it becomes possible to compare the performance of the two power-supply systems by comparing their relative biophysical requirements for the phases that both nuclear energy power plants and fossil energy power plants have in common: (i) mining; (ii) refining/enriching; (iii) generating heat/electricity; (iv) handling the pollution/radioactive wastes. This report presents the evaluation of the biophysical requirements for the two powersupply systems: nuclear energy and fossil energy. In particular, the report focuses on the following requirements: (i) electricity; (ii) fossil-fuels, (iii) labor; and (iv) materials.

Fossil resource depletion and climate change emissions: the role of physical constrictions

[spa] En lo que concierne al cambio climático, los pronósticos de cercanos picos de combustible fósiles parecen buenas noticias pues la mayoría de las emisiones proceden de la quema de combustibles fósiles. Sin embargo, esto podría resultar engañoso de confirmarse las enormes estimaciones de reservas de carbón pues puede divisarse un intercambio de combustible fósiles con baja concentración de carbono (petróleo y gas) por otros de mayor (carbón). Ciñéndonos a esta hipótesis desarrollamos escenarios donde tan pronto el petróleo y el gas natural alcanzan su cénit la extracción de carbón crece lo necesario para compensar el descenso de los primeros. Estimamos las emisiones que se deriva de tales supuestos y las comparamos con el peor escenario del IPCC. Si bien dicho escenario parece improbable concluimos que los picos de petróleo y gas no son suficientes para evitar peligrosas sendas de gases de efecto invernadero. Las concentraciones de CO2 halladas superan con creces las 450 ppm sin signos de remisión.

What trees tell us: dendrochronological and statistical analysis of the data

Trees are a great bank of data, named sometimes for this reason as the "silentwitnesses" of the past. Due to annual formation of rings, which is normally influenced directly by of climate parameters (generally changes in temperature and moisture or precipitation) and other environmental factors; these changes, occurred in the past, are"written" in the tree "archives" and can be "decoded" in order to interpret what hadhappened before, mainly applied for the past climate reconstruction.Using dendrochronological methods for obtaining samples of Pinus nigra fromthe Catalonian PrePirineous region, the cores of 15 trees with total time spine of about 100 - 250 years were analyzed for the tree ring width (TRW) patterns and had quite high correlation between them (0.71 ¿ 0.84), corresponding to a common behaviour for the environmental changes in their annual growth.After different trials with raw TRW data for standardization in order to take outthe negative exponential growth curve dependency, the best method of doubledetrending (power transformation and smoothing line of 32 years) were selected for obtaining the indexes for further analysis.Analyzing the cross-correlations between obtained tree ring width indexes andclimate data, significant correlations (p<0.05) were observed in some lags, as forexample, annual precipitation in lag -1 (previous year) had negative correlation with TRW growth in the Pallars region. Significant correlation coefficients are between 0.27- 0.51 (with positive or negative signs) for many cases; as for recent (but very short period) climate data of Seu d¿Urgell meteorological station, some significant correlation coefficients were observed, of the order of 0.9.These results confirm the hypothesis of using dendrochronological data as aclimate signal for further analysis, such as reconstruction of climate in the past orprediction in the future for the same locality.

The fossil record and evolution of freshwater plants: A review

Palaeobotany applied to freshwater plants is an emerging field of palaeontology. Hydrophytic plants reveal evolutionary trends of their own, clearly distinct from those of the terrestrial and marine flora. During the Precambrian, two groups stand out in the fossil record of freshwater plants: the Cyanobacteria (stromatolites) in benthic environments and the prasinophytes (leiosphaeridian acritarchs) in transitional planktonic environments. During the Palaeozoic, green algae (Chlorococcales, Zygnematales, charophytes and some extinct groups) radiated and developed the widest range of morphostructural patterns known for these groups. Between the Permian and Early Cretaceous, charophytes dominated macrophytic associations, with the consequence that over tens of millions of years, freshwater flora bypassed the dominance of vascular plants on land. During the Early Cretaceous, global extension of the freshwater environments is associated with diversification of the flora, including new charophyte families and the appearance of aquatic angiosperms and ferns for the first time. Mesozoic planktonic assemblages retained their ancestral composition that was dominated by coenobial Chlorococcales, until the appearance of freshwater dinoflagellates in the Early Cretaceous. In the Late Cretaceous, freshwater angiosperms dominated almost all macrophytic communities worldwide. The Tertiary was characterised by the diversification of additional angiosperm and aquatic fern lineages, which resulted in the first differentiation of aquatic plant biogeoprovinces. Phytoplankton also diversified during the Eocene with the development of freshwater diatoms and chrysophytes. Diatoms, which were exclusively marine during tens of millions of years, were dominant over the Chlorococcales during Neogene and in later assemblages. During the Quaternary, aquatic plant communities suffered from the effects of eutrophication, paludification and acidification, which were the result of the combined impact of glaciation and anthropogenic disturbance.

Fossil resource depletion and climate change emissions: the role of physical constrictions

[spa] En lo que concierne al cambio climático, los pronósticos de cercanos picos de combustible fósiles parecen buenas noticias pues la mayoría de las emisiones proceden de la quema de combustibles fósiles. Sin embargo, esto podría resultar engañoso de confirmarse las enormes estimaciones de reservas de carbón pues puede divisarse un intercambio de combustible fósiles con baja concentración de carbono (petróleo y gas) por otros de mayor (carbón). Ciñéndonos a esta hipótesis desarrollamos escenarios donde tan pronto el petróleo y el gas natural alcanzan su cénit la extracción de carbón crece lo necesario para compensar el descenso de los primeros. Estimamos las emisiones que se deriva de tales supuestos y las comparamos con el peor escenario del IPCC. Si bien dicho escenario parece improbable concluimos que los picos de petróleo y gas no son suficientes para evitar peligrosas sendas de gases de efecto invernadero. Las concentraciones de CO2 halladas superan con creces las 450 ppm sin signos de remisión.

On the preservation of combinatorial types for maps on trees

We study the preservation of the periodic orbits of an A-monotone tree map f:T→T in the class of all tree maps g:S→S having a cycle with the same pattern as A. We prove that there is a period-preserving injective map from the set of (almost all) periodic orbits of ƒ into the set of periodic orbits of each map in the class. Moreover, the relative positions of the corresponding orbits in the trees T and S (which need not be homeomorphic) are essentially preserved

Stratification of the severity of critically ill patients with classification trees

Background: Development of three classification trees (CT) based on the CART (Classification and Regression Trees), CHAID (Chi-Square Automatic Interaction Detection) and C4.5 methodologies for the calculation of probability of hospital mortality; the comparison of the results with the APACHE II, SAPS II and MPM II-24 scores, and with a model based on multiple logistic regression (LR). Methods: Retrospective study of 2864 patients. Random partition (70:30) into a Development Set (DS) n = 1808 and Validation Set (VS) n = 808. Their properties of discrimination are compared with the ROC curve (AUC CI 95%), Percent of correct classification (PCC CI 95%); and the calibration with the Calibration Curve and the Standardized Mortality Ratio (SMR CI 95%). Results: CTs are produced with a different selection of variables and decision rules: CART (5 variables and 8 decision rules), CHAID (7 variables and 15 rules) and C4.5 (6 variables and 10 rules). The common variables were: inotropic therapy, Glasgow, age, (A-a)O2 gradient and antecedent of chronic illness. In VS: all the models achieved acceptable discrimination with AUC above 0.7. CT: CART (0.75(0.71-0.81)), CHAID (0.76(0.72-0.79)) and C4.5 (0.76(0.73-0.80)). PCC: CART (72(69- 75)), CHAID (72(69-75)) and C4.5 (76(73-79)). Calibration (SMR) better in the CT: CART (1.04(0.95-1.31)), CHAID (1.06(0.97-1.15) and C4.5 (1.08(0.98-1.16)). Conclusion: With different methodologies of CTs, trees are generated with different selection of variables and decision rules. The CTs are easy to interpret, and they stratify the risk of hospital mortality. The CTs should be taken into account for the classification of the prognosis of critically ill patients.

Spatiotemporal variability in radial growth of trees in the Central Pyrenees: climatic and site influences.

To understand how tree growth has responded to recent climate warming, an understanding of the tree-climate-site complex is necessary. To achieve this, radial growth variability among 204 trees established before 1850 was studied in relation to both climatic and site factors. Seventeen forest stands were sampled in the Spanish Central Pyrenees. Three species were studied: Pinus uncinata, Abies alba, and Pinus sylvestris. For each tree, a ring-width residual chronology was built. All trees cross-dated well, indicating a common influence of the regional climate. For the 1952-1993 period, the radial growth of all species, especially P. uncinata, was positively correlated with warm Novembers during the year before ring formation and warm Mays of the year the annual ring formed. Differences in species-stand elevation modulated the growth-climate associations. Radial growth in P. uncinata at high elevation sites was reduced when May temperatures were colder and May precipitation more abundant. In the 20th century, two contrasting periods in radial growth were observed: one (1900-1949) with low frequency of narrow and wide rings, low mean annual sensitivity, and low common growth variation; and another (1950-1994) with the reverse characteristics. The increased variability in radial growth since the 1950s was observed for all species and sites, which suggests a climatic cause. The low shared variance among tree chronologies during the first half of the 20th century may result from a"relaxation" of the elevation gradient, allowing local site conditions to dominate macroclimatic influence. These temporal trends may be related to the recently reported increase of climatic variability and warmer conditions. This study emphasizes the need to carefully assess the relationships between radial growth and site conditions along ecological gradients to improve dendroclimatic reconstructions.

The fossil crown wasp Electrostephanus petiolatus Brues in Baltic Amber (Hymenoptera, Stephanidae): designation of a neotype, revised classification,and a key to amber Stephanidae.

The fossil crown wasp Electrostephanus petiolatus Brues comb. rev.(Stephanidae, Electrostephaninae) is re-described from a single male preserved in middle Eocene Baltic Amber. The holotype was lost or destroyed around the time of World War II and subsequent interpretations of its identity have been based solely on the brief descriptive comments provided by Brues in his original account. The new specimen matches the original description and illustration provided by Brues in every detail and we hereby consider them to be conspecific, selecting the specimen as a neotype for the purpose of stabilizing the nomenclature for this fossil species. This neotype exhibits a free first metasomal tergum and sternum, contrary to the assertion of previous workers who indicated these to be fused. Accordingly, this species does indeed belong to the genus Electrostephanus Brues rather than to Denaeostephanus Engel & Grimaldi (Stephaninae). Electrostephanus petiolatus is transferred to a new subgenus, Electrostephanodes n. subgen. , based on its elongate pseudo- petiole and slender gaster, but may eventually warrant generic status as the phylogenetic placement of these fossil lineages continues to be clarifi ed. A revised key to the Baltic amber crown wasps is provided.