Clustering in a model with repulsive long-range interactions

A striking clustering phenomenon in the antiferromagnetic Hamiltonian Mean-Field model has been previously reported. The numerically observed bicluster formation and stabilization is here fully explained by a non linear analysis of the Vlasov equation.Comment: 8 pages, 5 Fig

A Hamiltonian functional for the linearized Einstein vacuum field equations

By considering the Einstein vacuum field equations linearized about the Minkowski metric, the evolution equations for the gauge-invariant quantities characterizing the gravitational field are written in a Hamiltonian form by using a conserved functional as Hamiltonian; this Hamiltonian is not the analog of the energy of the field. A Poisson bracket between functionals of the field, compatible with the constraints satisfied by the field variables, is obtained. The generator of spatial translations associated with such bracket is also obtained.Comment: 5 pages, accepted in J. Phys.: Conf. Serie

Constants of motion associated with alternative Hamiltonians

It is shown that if a non-autonomous system of $2n$ first-order ordinary differential equations is expressed in the form of the Hamilton equations in terms of two different sets of coordinates, $(q_{i}, p_{i})$ and $(Q_{i}, P_{i})$, then the determinant and the trace of any power of a certain matrix formed by the Poisson brackets of the $Q_{i}, P_{i}$ with respect to $q_{i}, p_{i}$, are constants of motion

Metagenomics for Bacteriology

The study of bacteria, or bacteriology, has gone through transformative waves since its inception in the 1600s. It all started by the visualization of bacteria using light microscopy by Antonie van Leeuwenhoek, when he first described “animalcules.” Direct cellular observation then evolved into utilizing different wavelengths on novel platforms such as electron, fluorescence, and even near-infrared microscopy. Understanding the link between microbes and disease (pathogenicity) began with the ability to isolate and cultivate organisms through aseptic methodologies starting in the 1700s. These techniques became more prevalent in the following centuries with the work of famous scientists such as Louis Pasteur and Robert Koch, and many others since then. The relationship between bacteria and the host’s immune system was first inferred in the 1800s, and to date is continuing to unveil its mysteries. During the last century, researchers initiated the era of molecular genetics. The discovery of the first-generation sequencing technology, the Sanger method, and, later, the polymerase chain reaction technology propelled the molecular genetics field by exponentially expanding the knowledge of relationship between gene structure and function. The rise of commercially available next-generation sequencing methodologies, in the beginning of this century, is drastically allowing larger amount of information to be acquired, in a manner open to the democratization of the approach

Hamilton-Jacobi theory for Hamiltonian systems with non-canonical symplectic structures

A proposal for the Hamilton-Jacobi theory in the context of the covariant formulation of Hamiltonian systems is done. The current approach consists in applying Dirac's method to the corresponding action which implies the inclusion of second-class constraints in the formalism which are handled using the procedure of Rothe and Scholtz recently reported. The current method is applied to the nonrelativistic two-dimensional isotropic harmonic oscillator employing the various symplectic structures for this dynamical system recently reported.Comment: 17 pages, no figure

Local continuity laws on the phase space of Einstein equations with sources

Local continuity equations involving background fields and variantions of the fields, are obtained for a restricted class of solutions of the Einstein-Maxwell and Einstein-Weyl theories using a new approach based on the concept of the adjoint of a differential operator. Such covariant conservation laws are generated by means of decoupled equations and their adjoints in such a way that the corresponding covariantly conserved currents possess some gauge-invariant properties and are expressed in terms of Debye potentials. These continuity laws lead to both a covariant description of bilinear forms on the phase space and the existence of conserved quantities. Differences and similarities with other approaches and extensions of our results are discussed.Comment: LaTeX, 13 page