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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Diversity of Vibrionaceae bacteria isolated from the haemolymph of the spider crab Maja brachydactyla

Aims: The aim of this study was to characterise and identify vibrios isolated from the haemolymph of apparently healthy adult spider crabs (Maja brachydactyla) wild-caught in the Spanish localities of Galician coast and in the Canary Islands and also from captive animals held at IRTA’s facilities in the Ebro Delta of Catalonia, north-west Spanish Mediterranean coast. Methods and Results: A total of 277 bacterial isolates were obtained, and of these, 171 were characterised with rep-PCR, resulting electrophoretic bands were analysed and clusters formed. Identification of representative strains of each cluster was made by sequencing the 16S rRNA. Samples from animals caught in Galicia and captive at IRTA (around 15–18 C) rendered mostly species belonging to the Splendidus clade (72Æ2 and 76Æ6% respectively), commonly found in cold waters (below 20 C). Higher species diversity was found in the haemolymph of the captive animals. In the warmer Canary Islands waters (around 21 C), the diversity of vibrios is dominated by three clades, Harveyi (Vibrio core group, 39Æ3%), Orientalis (23Æ2%) and Splendidus (21Æ4%) with a species diversity that equals that of the colder captive animals. Conclusions: Differences in the vibrios populations were found in the haemolymph extracted from animals collected from the three localities. Potential new species were found, and their description is under way. Significance and Impact of Study: As with other invertebrates, spider crabs also contain a diverse population of vibrios. These findings should help researchers to diagnose when a crab is infected.

Precursor uptake assays and metabolic analyses in isolated tomato fruit chromoplasts

Background Carotenoids are the most widespread group of pigments found in nature. In addition to their role in the physiology of the plant, carotenoids also have nutritional relevance as their incorporation in the human diet provides health benefits. In non-photosynthetic tissues, carotenoids are synthesized and stored in specialized plastids called chromoplasts. At present very little is known about the origin of the metabolic precursors and cofactors required to sustain the high rate of carotenoid biosynthesis in these plastids. Recent proteomic data have revealed a number of biochemical and metabolic processes potentially operating in fruit chromoplasts. However, considering that chloroplast to chromoplast differentiation is a very rapid process during fruit ripening, there is the possibility that some of the proteins identified in the proteomic analysis could represent remnants no longer having a functional role in chromoplasts. Therefore, experimental validation is necessary to prove whether these predicted processes are actually operative in chromoplasts. Results A method has been established for high-yield purification of tomato fruit chromoplasts suitable for metabolic studies. Radiolabeled precursors were efficiently incorporated and further metabolized in isolated chromoplast. Analysis of labeled lipophilic compounds has revealed that lipid biosynthesis is a very efficient process in chromoplasts, while the relatively low incorporation levels found in carotenoids suggest that lipid production may represent a competing pathway for carotenoid biosynthesis. Malate and pyruvate are efficiently converted into acetyl-CoA, in agreement with the active operation of the malic enzyme and the pyruvate dehydrogenase complex in the chromoplast. Our results have also shown that isolated chromoplasts can actively sustain anabolic processes without the exogenous supply of ATP, thus suggesting that these organelles may generate this energetic cofactor in an autonomous way. Conclusions We have set up a method for high yield purification of intact tomato fruit chromoplasts suitable for precursor uptake assays and metabolic analyses. Using targeted radiolabeled precursors we have been able to unravel novel biochemical and metabolic aspects related with carotenoid and lipid biosynthesis in tomato fruit chromoplasts. The reported chromoplast system could represent a valuable platform to address the validation and characterization of functional processes predicted from recent transcriptomic and proteomic data.

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.

Model of single-electron decay from a strongly isolated quantum dot

Recent measurements of electron escape from a nonequilibrium charged quantum dot are interpreted within a two-dimensional (2D) separable model. The confining potential is derived from 3D self-consistent Poisson-Thomas-Fermi calculations. It is found that the sequence of decay lifetimes provides a sensitive test of the confining potential and its dependence on electron occupation

Statistical mechanical theory of an oscillating isolated system: The relaxation to equilibrium

In this Contribution we show that a suitably defined nonequilibrium entropy of an N-body isolated system is not a constant of the motion, in general, and its variation is bounded, the bounds determined by the thermodynamic entropy, i.e., the equilibrium entropy. We define the nonequilibrium entropy as a convex functional of the set of n-particle reduced distribution functions (n ? N) generalizing the Gibbs fine-grained entropy formula. Additionally, as a consequence of our microscopic analysis we find that this nonequilibrium entropy behaves as a free entropic oscillator. In the approach to the equilibrium regime, we find relaxation equations of the Fokker-Planck type, particularly for the one-particle distribution function.

Inhibition of glutathione efflux in the perfused rat liver and isolated hepatocytes by organic anions and bilirubin. Kinetics, sidedness, and molecular forms.

Using isolated, in situ, single-pass perfused rat livers, incubations of freshly isolated hepatocytes, and sinusoidal membrane-enriched vesicles, we and others have shown the saturability of transport (efflux) of hepatic glutathione (GSH). These observations have implicated a carrier mechanism. Our present studies were designed to provide further evidence in support of a carrier mechanism for hepatic GSH efflux by demonstrating competition by liver-specific ligands which are taken up by hepatocytes. Perfusing livers with different substances, we found that: (a) sulfobromophthalein-GSH (BSP-GSH) had a dose-dependent and fully reversible inhibitory effect on GSH efflux, while GSH alone did not have any effect; (b) taurocholate had no inhibitory effect; (c) all of the organic anions studied, i.e., BSP, rose bengal, indocyanine green, and unconjugated bilirubin (UCB), manifested potent, dose-dependent inhibitory effects, with absence of toxic effects and complete reversibility of inhibition in the case of UCB. The inhibitory effects of UCB could be overcome partially by raising (CoCl2-induced) hepatic GSH concentration. Because of the physiological importance of UCB, we conducted a detailed study of its inhibitory kinetics in the isolated hepatocyte model in the range of circulating concentrations of UCB. Studies with Cl- -free media, to inhibit the uptake of UCB by hepatocytes, showed that the inhibition of GSH efflux by UCB is apparently from inside the cell. This point was confirmed by showing that the inhibition is overcome only when bilirubin-loaded cells are cleared of bilirubin (incubation with 5% bovine serum albumin). Using Gunn rat hepatocytes and purified bilirubin mono- and diglucuronides, we found that both UCB and glucuronide forms of bilirubin inhibit GSH efflux in a dose-dependent manner. We conclude that the organic anions, although taken up by a mechanism independent of GSH, may competitively inhibit the carrier for GSH efflux from inside the hepatocyte.

Magnetism of isolated Mn12 single-molecule magnets detected by magnetic circular dichroism: Observation of spin tunneling with a magneto-optical technique

We report magnetic and magneto-optical measurements of two Mn12 single-molecule magnet derivatives isolated in organic glasses. Field-dependent magnetic circular dichroism (MCD) intensity curves (hysteresis cycles) are found to be essentially identical to superconducting quantum interference device magnetization results and provide experimental evidence for the potential of the optical technique for magnetic characterization. Optical observation of magnetic tunneling has been achieved by studying the decay of the MCD signal at weak applied magnetic field

Magnetism of isolated Mn12 single-molecule magnets detected by magnetic circular dichroism: Observation of spin tunneling with a magneto-optical technique

We report magnetic and magneto-optical measurements of two Mn12 single-molecule magnet derivatives isolated in organic glasses. Field-dependent magnetic circular dichroism (MCD) intensity curves (hysteresis cycles) are found to be essentially identical to superconducting quantum interference device magnetization results and provide experimental evidence for the potential of the optical technique for magnetic characterization. Optical observation of magnetic tunneling has been achieved by studying the decay of the MCD signal at weak applied magnetic field

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