A reduction of order two for infinite-order Lagrangians

Given a Lagrangian system depending on the position derivatives of any order, and assuming that certain conditions are satisfied, a second-order differential system is obtained such that its solutions also satisfy the Euler equations derived from the original Lagrangian. A generalization of the singular Lagrangian formalism permits a reduction of order keeping the canonical formalism in sight. Finally, the general results obtained in the first part of the paper are applied to Wheeler-Feynman electrodynamics for two charged point particles up to order 1/c4.

Perturbation theory for classical thermodynamic Green's functions

A systematic time-dependent perturbation scheme for classical canonical systems is developed based on a Wick's theorem for thermal averages of time-ordered products. The occurrence of the derivatives with respect to the canonical variables noted by Martin, Siggia, and Rose implies that two types of Green's functions have to be considered, the propagator and the response function. The diagrams resulting from Wick's theorem are "double graphs" analogous to those introduced by Dyson and also by Kawasaki, in which the response-function lines form a "tree structure" completed by propagator lines. The implication of a fluctuation-dissipation theorem on the self-energies is analyzed and compared with recent results by Deker and Haake.

Supersymmetric black rings and three-charge supertubes

We present supergravity solutions for 1/8-supersymmetric black supertubes with three charges and three dipoles. Their reduction to five dimensions yields supersymmetric black rings with regular horizons and two independent angular momenta. The general solution contains seven independent parameters and provides the first example of nonuniqueness of supersymmetric black holes. In ten dimensions, the solutions can be realized as D1-D5-P black supertubes. We also present a worldvolume construction of a supertube that exhibits three dipoles explicitly. This description allows an arbitrary cross section but captures only one of the angular momenta.

Motion of a classical charged particle

The Lorentz-Dirac equation is not an unavoidable consequence of solely linear and angular momenta conservation for a point charge. It also requires an additional assumption concerning the elementary character of the charge. We here use a less restrictive elementarity assumption for a spinless charge and derive a system of conservation equations that are not properly the equation of motion because, as it contains an extra scalar variable, the future evolution of the charge is not determined. We show that a supplementary constitutive relation can be added so that the motion is determined and free from the troubles that are customary in the Lorentz-Dirac equation, i.e., preacceleration and runaways.

A Supersymmetric black ring

A new supersymmetric black hole solution of five-dimensional supergravity is presented. It has an event horizon of topology S1 X S2. This is the first example of a supersymmetric, asymptotically flat black hole of nonspherical topology. The solution is uniquely specified by its electric charge and two independent angular momenta. These conserved charges can be arbitrarily close, but not exactly equal, to those of a supersymmetric black hole of spherical topology.

Relationship Between Edaphic Factors and Vegetation in Savannas of the Brazilian Midwest Region

The Brazilian savanna is a mosaic of phytophysiognomies influenced by edaphic and topographic factors that range from the occurrence of fires to anthropic disturbance. The goal of this study was a comparative analysis between two cerrado areas in southeastern Goiás, relating the floristic composition and structure of the vegetation to soil properties to better understand the physiognomic characteristics of the region. Twenty-five 20 × 20 m plots were used. All plants with circumference at breast height of more than 15 cm were measured. Soil samples collected at a depth of 0-20 cm were subjected to physical and chemical analyses. Canonical correspondence analysis (CCA) was used to detect possible correlations between the soil properties and species abundance and distribution. The density and total basal area were 1,647 ind/ha and 15.57 m2/ha, respectively, in Ouroana. At this site, 107 species were sampled. In Montes Claros de Goiás, the density and total basal area were 781 ind/ha and 17.62 m2/ha, and 120 species were sampled. The soil texture of Ouroana was sandy and significantly different from the medium to clayey texture of Montes Claros. The soils of both areas are dystrophic, however, more fertile in Montes Claros and aluminum-toxic in Ouroana. The species of vegetation were distributed according to soil fertility levels. The CCAs grouped species according to soil properties that defined location and abundance as well as the phytophysiognomies of the studied areas.

Front form and point form formulation in P.R.M. noninteractions theorems

The front form and the point form of dynamics are studied in the framework of predictive relativistic mechanics. The non-interaction theorem is proved when a Poincar-invariant Hamiltonian formulation with canonical position coordinates is required.

Classical predictive electrodynamics of two charges with radiation: Energy and 3. momentum balance and scattering crossections-II

We deal with a classical predictive mechanical system of two spinless charges where radiation is considered and there are no external fields. The terms (2,2)Paa of the expansion in the charges of the HamiltonJacobi momenta are calculated. Using these, together with known previous results, we can obtain the paa up to the fourth order. Then we have calculated the radiated energy and the 3-momentum in a scattering process as functions of the impact parameter and the incident energy for the former and 3-momentum for the latter. Scattering cross-sections are also calculated. Good agreement with well known results, including those of quantum electrodynamics, has been found.

The problem of physical coordinates in predictive Hamiltonian systems

In the Hamiltonian formulation of predictive relativistic systems, the canonical coordinates cannot be the physical positions. The relation between them is given by the individuality differential equations. However, due to the arbitrariness in the choice of Cauchy data, there is a wide family of solutions for these equations. In general, those solutions do not satisfy the condition of constancy of velocities moduli, and therefore we have to reparametrize the world lines into the proper time. We derive here a condition on the Cauchy data for the individuality equations which ensures the constancy of the velocities moduli and makes the reparametrization unnecessary.

A family of inhomogeneous cosmological Einstein - Rosen metrics

Some generalized soliton solutions of the cosmological EinsteinRosen type defined in the space-time region t2=z2 in terms of canonical coordinates are considered. Vacuum solutions are studied and interpreted as cosmological models. Fluid solutions are also considered and are seen to represent inhomogeneous cosmological models that become homogeneous at t?8. A subset of them evolve toward isotropic FriedmannRobertsonWalker metrics.

Cooperative kinking at distant sites in mechanically stressed DNA.

In cells, DNA is routinely subjected to significant levels of bending and twisting. In some cases, such as under physiological levels of supercoiling, DNA can be so highly strained, that it transitions into non-canonical structural conformations that are capable of relieving mechanical stress within the template. DNA minicircles offer a robust model system to study stress-induced DNA structures. Using DNA minicircles on the order of 100 bp in size, we have been able to control the bending and torsional stresses within a looped DNA construct. Through a combination of cryo-EM image reconstructions, Bal31 sensitivity assays and Brownian dynamics simulations, we have been able to analyze the effects of biologically relevant underwinding-induced kinks in DNA on the overall shape of DNA minicircles. Our results indicate that strongly underwound DNA minicircles, which mimic the physical behavior of small regulatory DNA loops, minimize their free energy by undergoing sequential, cooperative kinking at two sites that are located about 180° apart along the periphery of the minicircle. This novel form of structural cooperativity in DNA demonstrates that bending strain can localize hyperflexible kinks within the DNA template, which in turn reduces the energetic cost to tightly loop DNA.

The assignment game: core bounds for mixed-pair coalitions

In the assignment game framework, we try to identify those assignment matrices in which no entry can be increased without changing the coreof the game. These games will be called buyer¿seller exact games and satisfy the condition that each mixed¿pair coalition attains the corresponding matrix entry in the core of the game. For a given assignment game, a unique buyerseller exact assignment game with the same core is proved to exist. In order to identify this matrix and to provide a characterization of those assignment games which are buyer¿seller exact in terms of the assignment matrix, attainable upper and lower core bounds for the mixed¿pair coalitions are found. As a consequence, an open question posed in Quint (1991) regarding a canonical representation of a ¿45o¿lattice¿ by means of the core of an assignment game can now be answered

Role of β-catenin and γ-catenin in haematopoiesis : Generation of floxed Delta like 4 gene targeted mice

Résumé La voie de signalisation de Wnt est extrêmement conservée au cours de l'évolution. Les protéines Wnt sont des molécules sécrétées qui se lient à la famille de récepteurs Frizzled. Cette interaction mène à la stabilisation de la protéine β-caténine, qui va s'accumuler dans le cytoplasme puis migrer dans le noyau où elle peut s'hétérodimériser avec les facteurs de transcription de la famille TCF/LEF. Il a été démontré que cette voie de signalisation joue un rôle important durant la lymphopoïèse et de récents résultats suggèrent un rôle clé de cette voie dans le renouvellement des Cellules Souches Hématopoïétique (CSH). Des études se basant sur un système de surexpression de protéines montrent clairement que la voie Wnt peut influencer l'hématopoïèse. Cependant, le rôle de la protéine β-caténine dans le système hématopoïétique n'a jamais été testé directement. Ce projet de thèse se propose d'étudier la fonction de la protéine β-caténine par sa délétion inductible via le système Cre-loxP. De façon surprenante, nous avons pu démontrer que les progéniteurs de la moelle osseuse, déficients en β-caténine, ne montrent aucune altération dans leur capacité à s'auto-renouveler et/ou à reconstituer toutes les lignées hématopoïétiques (myéloïde, érythroïde et lymphoïde) dans les souris-chimères. De plus, le développement, la survie des thymocytes ainsi que la prolifération des cellules T périphériques induite par un antigène, sont indépendants de β-caténine. Ces résultats suggèrent soit que la protéine β-caténine ne joue pas un rôle primordial dans le système hématopoiétique, soit que son absence pourrait être compensée par une autre protéine. Un candidat privilégié susceptible de se substituer à β-caténine, serait plakoglobine, aussi connu sous le nom de γ-caténine. En effet, ces deux protéines partagent de multiples caractéristiques structurelles. Afin de démontrer que la protéine γ-caténine peut compenser l'absence de β-caténine, nous avons généré des souris dans lesquelles, le système hématopoïétique est déficient pour ces deux protéines. Cette déficience combinée de β- caténine et γ-caténine ne perturbe pas la capacité des Cellules Souche Hématopoïétique-Long Terme (CSH-LT) de se renouveler, par contre elle agit sur un progéniteur précoce déjà différencié de la moelle osseuse. Ces résultats mettent en évidence que la protéine γ-caténine est capable de compenser l'absence de protéine β-caténine dans le système hématopoïétique. Par conséquent, ce travail contribue à une meilleure connaissance de la cascade Wnt dans l'hématopoïèse. Summary The canonical Wnt signal transduction pathway is a developmentally highly conserved. Wnts are secreted molecules which bind to the family of Frizzled receptors in a complex with the low density lipoprotein receptor related protein (LRP-5/6). This initial activation step leads to the stabilization and accumulation of β-catenin, first in the cytoplasm and subsequently in the nucleus where it forms heterodimers with TCF/LEF transcription factor family members. Wnt signalling has been shown to be important during early lymphopoiesis and has more recently, been suggested to be a key player in self-renewal of haematopoietic stem cells (HSCs). Although mostly gain of function studies indicate that components of the Wnt signalling pathway can influence the haematopoietic system, the role of β-catenin has never been directly investigated. The aim of this thesis project is to investigate the putatively critical role of β-catenin in vivo using the Cre-loxP mediated conditional loss of function approach. Surprisingly, β-catenin deficient bone marrow (BM) progenitors arc not impaired in their ability to self-renew and/or to reconstitute all haematopoietic lineages (myeloid, erythroid and lymphoid) in both mixed and straight bone marrow chimeras. In addition, both thymocyte development and survival, and antigen-induced proliferation of peripheral T cells are β- catenin independent. Our results do not necessarily exclude the possibility of an important function for β-catenin mediated Wnt signalling in the haematopoietic system, it rather raises the question that β-catenin is compensated for by another protein. A prime candidate that may take over the function of β-catenin in its absence, is the close relative plakoglobin, also know as γ-catenin. This protein shares multiple structural features with β-catenin. In order to investigate whether γ-catenin can compensate for the loss of β-catenin we have generated mice in which the haematopoietic compartment is deficient for both proteins. Combined deficiency of β-catenin and γ-catenin does not perturb Long Term-Haematopoietic Stem Cells (LT-HSC) self renewal, but affects an already lineage committed progenitor population within the BM. Our results demonstrate that y-catenin can indeed compensate for the loss of β-catenin within the haematopoietie system.

Enhanced pulse propagation in non-linear arrays of oscillators

The propagation of a pulse in a nonlinear array of oscillators is influenced by the nature of the array and by its coupling to a thermal environment. For example, in some arrays a pulse can be speeded up while in others a pulse can be slowed down by raising the temperature. We begin by showing that an energy pulse (one dimension) or energy front (two dimensions) travels more rapidly and remains more localized over greater distances in an isolated array (microcanonical) of hard springs than in a harmonic array or in a soft-springed array. Increasing the pulse amplitude causes it to speed up in a hard chain, leaves the pulse speed unchanged in a harmonic system, and slows down the pulse in a soft chain. Connection of each site to a thermal environment (canonical) affects these results very differently in each type of array. In a hard chain the dissipative forces slow down the pulse while raising the temperature speeds it up. In a soft chain the opposite occurs: the dissipative forces actually speed up the pulse, while raising the temperature slows it down. In a harmonic chain neither dissipation nor temperature changes affect the pulse speed. These and other results are explained on the basis of the frequency vs energy relations in the various arrays

Stabilised beta-catenin in postnatal ventricular myocardium leads to dilated cardiomyopathy and premature death.

Beta-catenin is a component of the intercalated disc in cardiomyocytes, but can also be involved in signalling and activation of gene transcription. We wanted to determine how long-term changes in beta-catenin expression levels would affect mature cardiomyocytes. Conditional transgenic mice that either lacked beta-catenin or that expressed a non-degradable form of beta-catenin in the adult ventricle were created. While mice lacking beta-catenin in the ventricle do not have an overt phenotype, mice expressing a non-degradable form develop dilated cardiomyopathy and do not survive beyond 5 months. A detailed analysis could reveal that this phenotype is correlated with a distinct localisation of beta-catenin in adult cardiomyocytes, which cannot be detected in the nucleus, no matter how much protein is present. Our report is the first study that addresses long-term effects of either the absence of beta-catenin or its stabilisation on ventricular cardiomyocytes and it suggests that beta-catenin's role in the nucleus may be of little significance in the healthy adult heart.