Lagrangian and Hamiltonian BRST structures of the antysimmetric tensor gauge theory

We study the Becchi-Rouet-Stora-Tyutin (BRST) structure of a self-interacting antisymmetric tensor gauge field, which has an on-shell null-vector gauge transformation. The Batalin-Vilkovisky covariant general formalism is briefly reviewed, and the issue of on-shell nilpotency of the BRST transformation is elucidated. We establish the connection between the covariant and the canonical BRST formalisms for our particular theory. Finally, we point out the similarities and differences with Wittens string field theory.

Equivalence of reduced, Polyakov, Faddeev-Popov, and Faddeev path-integral quantization of gauge theories

A geometrical treatment of the path integral for gauge theories with first-class constraints linear in the momenta is performed. The equivalence of reduced, Polyakov, Faddeev-Popov, and Faddeev path-integral quantization of gauge theories is established. In the process of carrying this out we find a modified version of the original Faddeev-Popov formula which is derived under much more general conditions than the usual one. Throughout this paper we emphasize the fact that we only make use of the information contained in the action for the system, and of the natural geometrical structures derived from it.

Generalized Schmidt decomposition and classification of three-quantum-bit states

We prove for any pure three-quantum-bit state the existence of local bases which allow one to build a set of five orthogonal product states in terms of which the state can be written in a unique form. This leads to a canonical form which generalizes the two-quantum-bit Schmidt decomposition. It is uniquely characterized by the five entanglement parameters. It leads to a complete classification of the three-quantum-bit states. It shows that the right outcome of an adequate local measurement always erases all entanglement between the other two parties.

Diffusion on a solid surface: anomalous is normal

We present a numerical study of classical particles diffusing on a solid surface. The particles motion is modeled by an underdamped Langevin equation with ordinary thermal noise. The particle-surface interaction is described by a periodic or a random two-dimensional potential. The model leads to a rich variety of different transport regimes, some of which correspond to anomalous diffusion such as has recently been observed in experiments and Monte Carlo simulations. We show that this anomalous behavior is controlled by the friction coefficient and stress that it emerges naturally in a system described by ordinary canonical Maxwell-Boltzmann statistics.

From subdiffusion to superdiffusion of particles on solid surfaces

We present a numerical and partially analytical study of classical particles obeying a Langevin equation that describes diffusion on a surface modeled by a two-dimensional potential. The potential may be either periodic or random. Depending on the potential and the damping, we observe superdiffusion, large-step diffusion, diffusion, and subdiffusion. Superdiffusive behavior is associated with low damping and is in most cases transient, albeit often long. Subdiffusive behavior is associated with highly damped particles in random potentials. In some cases subdiffusive behavior persists over our entire simulation and may be characterized as metastable. In any case, we stress that this rich variety of behaviors emerges naturally from an ordinary Langevin equation for a system described by ordinary canonical Maxwell-Boltzmann statistics.

Neurogenic subventricular zone stem/progenitor cells are notch1-dependent in their active but not quiescent state.

The adult mammalian forebrain contains neural stem/progenitor cells (NSCs) that generate neurons throughout life. As in other somatic stem cell systems, NSCs are proposed to be predominantly quiescent and proliferate only sporadically to produce more committed progeny. However, quiescence has recently been shown not to be an essential criterion for stem cells. It is not known whether NSCs show differences in molecular dependence based on their proliferation state. The subventricular zone (SVZ) of the adult mouse brain has a remarkable capacity for repair by activation of NSCs. The molecular interplay controlling adult NSCs during neurogenesis or regeneration is not clear but resolving these interactions is critical in order to understand brain homeostasis and repair. Using conditional genetics and fate mapping, we show that Notch signaling is essential for neurogenesis in the SVZ. By mosaic analysis, we uncovered a surprising difference in Notch dependence between active neurogenic and regenerative NSCs. While both active and regenerative NSCs depend upon canonical Notch signaling, Notch1-deletion results in a selective loss of active NSCs (aNSCs). In sharp contrast, quiescent NSCs (qNSCs) remain after Notch1 ablation until induced during regeneration or aging, whereupon they become Notch1-dependent and fail to fully reinstate neurogenesis. Our results suggest that Notch1 is a key component of the adult SVZ niche, promoting maintenance of aNSCs, and that this function is compensated in qNSCs. Therefore, we confirm the importance of Notch signaling for maintaining NSCs and neurogenesis in the adult SVZ and reveal that NSCs display a selective reliance on Notch1 that may be dictated by mitotic state.

Statistical mechanics in the extended Gaussian ensemble

The extended Gaussian ensemble (EGE) is introduced as a generalization of the canonical ensemble. This ensemble is a further extension of the Gaussian ensemble introduced by Hetherington [J. Low Temp. Phys. 66, 145 (1987)]. The statistical mechanical formalism is derived both from the analysis of the system attached to a finite reservoir and from the maximum statistical entropy principle. The probability of each microstate depends on two parameters ß and ¿ which allow one to fix, independently, the mean energy of the system and the energy fluctuations, respectively. We establish the Legendre transform structure for the generalized thermodynamic potential and propose a stability criterion. We also compare the EGE probability distribution with the q-exponential distribution. As an example, an application to a system with few independent spins is presented.

On the many-time formulation of classical particle dynamics

Starting from the standard one-time dynamics of n nonrelativistic particles, the n-time equations of motion are inferred, and a variational principle is formulated. A suitable generalization of the classical LieKnig theorem is demonstrated, which allows the determination of all the associated presymplectic structures. The conditions under which the action of an invariance group is canonical are studied, and a corresponding Noether theorem is deduced. A formulation of the theory in terms of n first-class constraints is recovered by means of coisotropic imbeddings. The proposed approach also provides for a better understanding of the relativistic particle dynamics, since it shows that the different roles of the physical positions and the canonical variables is not peculiar to special relativity, but rather to any n-time approach: indeed a nonrelativistic no-interaction theorem is deduced.

Dirac and reduced quantization: A Lagrangian approach and Application to Coset Spaces

A Lagrangian treatment of the quantization of first class Hamiltonian systems with constraints and Hamiltonian linear and quadratic in the momenta, respectively, is performed. The first reduce and then quantize and the first quantize and then reduce (Diracs) methods are compared. A source of ambiguities in this latter approach is pointed out and its relevance on issues concerning self-consistency and equivalence with the first reduce method is emphasized. One of the main results is the relation between the propagator obtained la Dirac and the propagator in the full space. As an application of the formalism developed, quantization on coset spaces of compact Lie groups is presented. In this case it is shown that a natural selection of a Dirac quantization allows for full self-consistency and equivalence. Finally, the specific case of the propagator on a two-dimensional sphere S2 viewed as the coset space SU(2)/U(1) is worked out. 1995 American Institute of Physics.

Soil and phytosociological characterization of an area with predominance of arnica (Lychnophora pohlii sch. bip.)

Lychnophora pohlii Sch. Bip. (Asteraceae), known as "Arnica mineira", is widely used in folk medicine and very abundant in the altitude vegetation of rocky grassland. The aim of this work was to study the density of this species and its relationship with soil parameters in rocky grassland in Diamantina, in the Upper Jequitinhonha region, Minas Gerais. Ten contiguous 20 x 50 m plots were marked (total sampled area 10,000 m²) on the campus Juscelino Kubitschek of the Federal University of Jequitinhonha and Mucuri Valleys (UFVJM). The plants in these plots were evaluated for frequency, dominance and density. The relationship between the density of this species with nine soil physical and chemical properties was analyzed by means of canonical correspondence analysis (CCA). The highest plant abundance (I) of the species Lychnophora pohlii Sch. Bip. was found in the vegetation sampling areas: plot 6 with 255 plants, plot 7 with 173, plot 8 with 189, plot 9 with 159, and plot 1 with 151 plants. In these areas, the floristic soil characteristics were similar, resulting in spatial proximity in the ACC diagrams. The density of Lychnophora pohlii was higher in plots with higher pH, P-rem and base saturation, the variables most strongly correlated with the first axis of canonical correspondence analysis.

Relationships between microbial activity and soil physical and chemical properties in native and reforested Araucaria angustifolia forests in the state of São Paulo, Brazil

Araucaria angustifolia (Bert.) O. Kuntze is the main component of the Mixed Ombrophilous forest and, in the State of São Paulo, it is associated with a high diversity of soil organisms, essential for the maintenance of soil quality, making the conservation of this ecosystem a major and pressing challenge. The objective of this study was to identify the physical and chemical properties that are most closely correlated with dehydrogenase enzyme activity, basal respiration and microbial biomass under native (NF) and replanted (RF) Araucaria angustifolia forests in three regions of the state of São Paulo, in winter and summer. The main differentiating factors between the areas were also determined. Each forest was represented by three true replications; at each site, from around the araucaria trees, 15 soil samples (0-20 cm) were collected to evaluate the soil physical, chemical and microbiological properties. At the same points, forest litter was sampled to assess mass and chemical properties. The following microbiological properties were evaluated: microbial biomass carbon (MBC), basal respiration (CO2-C), metabolic quotient (Q: CO2), dehydrogenase enzyme activity (DHA) as well as the physical properties (moisture, bulk density, macroporosity and total porosity), soil chemical properties [pH, organic carbon (org-C), P, Ca, K, Mg, Al, H+Al], litter dry mass, and C, N and S contents. The data were subjected to analysis of variance (TWO-WAY: ANOVA). A Canonical Discriminant Analysis (CDA) and a Canonical Correlation Analysis (CCA) were also performed. In the soil under NF, the values of K, P, soil macroporosity, and litter dry mass were higher and Q: CO2 and DHA lower, regardless of the sampling period, and DHA was lower in winter. In the RF areas, the levels of moisture, porosity and Q: CO2 were higher in both sampling periods, and DHA was higher in winter. The MBC was only higher under NF in the summer, while the litter contents of C, N and S were greater in winter. In winter, CCA showed a high correlation of DHA with CO2-C, pH and H+Al, while in the summer org-C, moisture, Mg, pH and litter C were more associated with DHA and CO2-C. The CDA indicated H+Al, available P, total porosity, litter S content, and soil moisture as the most discriminating variables between NF and RF, but moisture was the most relevant, in both seasons and CO2-C only in winter. The combined analysis of CCA and CDA showed that the contribution of the microbiological variables to a differentiation of the areas was small at both samplings, which may indicate that the period after reforestation was long enough to allow an almost complete recovery of the microbial activity.

TCRep 3D: an automated in silico approach to study the structural properties of TCR repertoires.

TCRep 3D is an automated systematic approach for TCR-peptide-MHC class I structure prediction, based on homology and ab initio modeling. It has been considerably generalized from former studies to be applicable to large repertoires of TCR. First, the location of the complementary determining regions of the target sequences are automatically identified by a sequence alignment strategy against a database of TCR Vα and Vβ chains. A structure-based alignment ensures automated identification of CDR3 loops. The CDR are then modeled in the environment of the complex, in an ab initio approach based on a simulated annealing protocol. During this step, dihedral restraints are applied to drive the CDR1 and CDR2 loops towards their canonical conformations, described by Al-Lazikani et. al. We developed a new automated algorithm that determines additional restraints to iteratively converge towards TCR conformations making frequent hydrogen bonds with the pMHC. We demonstrated that our approach outperforms popular scoring methods (Anolea, Dope and Modeller) in predicting relevant CDR conformations. Finally, this modeling approach has been successfully applied to experimentally determined sequences of TCR that recognize the NY-ESO-1 cancer testis antigen. This analysis revealed a mechanism of selection of TCR through the presence of a single conserved amino acid in all CDR3β sequences. The important structural modifications predicted in silico and the associated dramatic loss of experimental binding affinity upon mutation of this amino acid show the good correspondence between the predicted structures and their biological activities. To our knowledge, this is the first systematic approach that was developed for large TCR repertoire structural modeling.

The role of AUF1 in AU-rich interleukin-6 mRNA regulation

Abstract: The AU-rich elements (AREs) consisting of repeated AUUUA motifs confer rapid degradation to many cellular mRNAs when present in the 3' untranslated region (3'UTR). We have studied the instability of interleukin-6 mRNA by grafting its 3' untranslated region to a stable green fluorescent protein mRNA. Subsequent scanning mutagenesis identified two conserved elements, which taken together account for most of the instability. The first corresponds to a short non-canonical AU-rich element. The other comprises a sequence predicted to form astern-loop structure. Both elements need to be present in order to confer full instability (Paschoud et al. 2006). Destabilization of ARE-containing mRNAs is thought to involve ARE-binding proteins such as AUF1. We tested whether AUF1 binding to interleukin-6 mRNA correlates with decreased mRNA stability. Overexpression of myc-tagged p37AUFl and p42AUF1 as well as suppression of all four AUF1 isoforms by RNA interference stabilized the interleukin-6 mRNA. Furthermore, the interleukin-6 mRNA co-immunoprecipitated specifically with myc-tagged p37AUF1 and p42AUF1 in cell extracts. Both the stabilization and AUF1-binding required the non-canonical AU-rich sequence. These results indicate that AUF1 binds to the AU-rich element in vivo and promotes interleukin6 mRNA degradation. The combination of mRNA co-immunoprecipitation with microarray technology revealed that at least 500 cellular mRNAs associate with AUF1. Résumé: "La présence d'éléments riches en A et U (ARE), en particulier les motifs répétés d'AUUUA dans la région 3' non traduite, confère une dégradation rapide à beaucoup d'ARN cellulaires. Nous avons étudié l'instabilité de l'ARN codant pour l'interleukine 6 en greffant sa région 3' non traduite à un ARN stable codant pour la protéine fluorescente verte. La mutagenèse systématique des séquences non traduites a permis l'identification de deux éléments conservés qui confèrent l'instabilité à l'ARN. Le premier correspond à un élément AU-riche non canonique court. Le second comporte une structure en 'épingle à cheveux'. Tous les deux éléments doivent être présents afin de conférer une instabilité complète (Paschoud et al. 2006). On pense que des protéines telles que AUF1, pouvant se lier aux éléments ARE, sont impliquées dans la dégradation des ARN messagers. Nous avons examiné si la liaison de AUFl sur l'ARN de l'interleukine 6 corrèle avec une stabilité diminuée. La surexpression des protéines p37AUF1 et de p42AUF1 myc-étiquetées ainsi que la suppression de chacun des quatre isoformes de AUF1 par interférence d'ARN a stabilisé l'ARN messager d'interleukine 6. En outre, cet ARN co-immunoprécipite spécifiquement avec p37AUF1 et p42AUF1 dans des extraits cellulaires. La présence de l'élément AUriche non canonique est nécessaire pour la stabilisation de l'ARN et sa liaison avec AUFI. Ces résultats indiquent qu'AUF1 se lie à l'élément AU-riche in vivo et favorise la dégradation de l'ARN messager d'interleukine 6. La combinaison des techniques de coimmunoprécipitation des ARN messagers et des analyses par `microarray' indique qu'au moins 500 ARN cellulaires s'associent à AUF1.

Multivariate analysis applied to the study of the relationship between soil and plant properties in a peach orchard

In the State of Rio Grande do Sul, the municipality of Pelotas is responsible for 90 % of peach production due to its suitable climate and soil conditions. However, there is the need for new studies that aim at improved fruit quality and increased yield. The aim of this study was to evaluate the relationship that exists between soil physical properties and properties in the peach plant in the years 2010 and 2011 by the technique of multivariate canonical correlation. The experiment was conducted in a peach orchard located in the municipality of Morro Redondo, RS, Brazil, where an experimental grid of 101 plants was established. In a trench dug beside each one of the 101 plants, soil samples were collected to determine silt, clay, and sand contents, soil density, total porosity, macroporosity, microporosity, and volumetric water content in the 0.00-0.10 and 0.10-0.20 m layers, as well as the depth of the A horizon. In each plant and in each year, the following properties were assessed: trunk diameter, fruit size and number of fruits per plant, average weight of the fruit per plant, fruit pulp firmness, Brix content, and yield from the orchard. Exploratory analysis of the data was undertaken by descriptive statistics, and the relationships between the physical properties of the soil and of the plant were assessed by canonical correlation analysis. The results showed that the clay and microporosity variables were those that exhibited the highest coefficients of canonical cross-loading with the plant properties in the soil layers assessed, and that the variable of mean weight of the fruit per plant was that which had the highest coefficients of canonical loading within the plant group for the two years assessed.

World-line condition and the noninteraction theorem

A 6N-dimensional alternative formulation is proposed for constrained Hamiltonian systems. In this context the noninteraction theorem is derived from the world-line conditions. A model of two interacting particles is exhibited where physical coordinates are canonical.