Extended Hamiltonian systems in multisymplectic field theories

We consider Hamiltonian systems in first-order multisymplectic field theories. We review the properties of Hamiltonian systems in the so-called restricted multimomentum bundle, including the variational principle which leads to the Hamiltonian field equations. In an analogous way to how these systems are defined in the so-called extended (symplectic) formulation of non-autonomous mechanics, we introduce Hamiltonian systems in the extended multimomentum bundle. The geometric properties of these systems are studied, the Hamiltonian equations are analyzed using integrable multivector fields, the corresponding variational principle is also stated, and the relation between the extended and the restricted Hamiltonian systems is established. All these properties are also adapted to certain kinds of submanifolds of the multimomentum bundles in order to cover the case of almost-regular field theories.Comment: 36 pp. The introduction and the abstract have been rewritten. New references are added and some little mistakes are corrected. The title has been slightly modifie

Geometric Hamilton-Jacobi Theory

The Hamilton-Jacobi problem is revisited bearing in mind the consequences arising from a possible bi-Hamiltonian structure. The problem is formulated on the tangent bundle for Lagrangian systems in order to avoid the bias of the existence of a natural symplectic structure on the cotangent bundle. First it is developed for systems described by regular Lagrangians and then extended to systems described by singular Lagrangians with no secondary constraints. We also consider the example of the free relativistic particle, the rigid body and the electron-monopole system.Comment: 40 page

Geometric Hamilton-Jacobi Theory for Nonholonomic Dynamical Systems

The geometric formulation of Hamilton--Jacobi theory for systems with nonholonomic constraints is developed, following the ideas of the authors in previous papers. The relation between the solutions of the Hamilton--Jacobi problem with the symplectic structure defined from the Lagrangian function and the constraints is studied. The concept of complete solutions and their relationship with constants of motion, are also studied in detail. Local expressions using quasivelocities are provided. As an example, the nonholonomic free particle is considered.Comment: 22 p

`Similar' coordinate systems and the Roche geometry. Application

A new equivalence relation, named relation of 'similarity' is defined and applied in the restricted three-body problem. Using this relation, a new class of trajectories (named 'similar' trajectories) are obtained; they have the theoretical role to give us new details in the restricted three-body problem. The 'similar' coordinate systems allow us in addition to obtain a unitary and an elegant demonstration of some analytical relations in the Roche geometry. As an example, some analytical relations published in Astrophysical Journal by Seidov in 2004 are demonstrated.Comment: 9 pages (preprint format), 9 figures, published in Astrophysics and Space Scienc

Cellular heterogeneity mediates inherent sensitivity–specificity tradeoff in cancer targeting by synthetic circuits

Synthetic gene circuits are emerging as a versatile means to target cancer with enhanced specificity by combinatorial integration of multiple expression markers. Such circuits must also be tuned to be highly sensitive because escape of even a few cells might be detrimental. However, the error rates of decision-making circuits in light of cellular variability in gene expression have so far remained unexplored. Here, we measure the single-cell response function of a tunable logic AND gate acting on two promoters in heterogeneous cell populations. Our analysis reveals an inherent tradeoff between specificity and sensitivity that is controlled by the AND gate amplification gain and activation threshold. We implement a tumor-mimicking cellculture model of cancer cells emerging in a background of normal ones, and show that molecular parameters of the synthetic circuits control specificity and sensitivity in a killing assay. This suggests that, beyond the inherent tradeoff, synthetic circuits operating in a heterogeneous environment could be optimized to efficiently target malignant state with minimal loss of specificity. Keywords: synthetic gene circuits; cellular heterogeneity; cancer gene therapy; cell-state targeting; mammalian synthetic biolog

Unravelling the gut bacteriome of Ips (Coleoptera: Curculionidae: Scolytinae): identifying core bacterial assemblage and their ecological relevance

Bark beetles often serve as forest damaging agents, causing landscape-level mortality. Understanding the biology and ecology of beetles are important for both, gathering knowledge about important forest insects and forest protection. Knowledge about the bark beetle gut-associated bacteria is one of the crucial yet surprisingly neglected areas of research with European tree-killing bark beetles. Hence, in this study, we survey the gut bacteriome from five Ips and one non-Ips bark beetles from Scolytinae. Results reveal 69 core bacterial genera among five Ips beetles that may perform conserved functions within the bark beetle holobiont. The most abundant bacterial genera from different bark beetle gut include Erwinia, Sodalis, Serratia, Tyzzerella, Raoultella, Rahnella, Wolbachia, Spiroplasma, Vibrio, and Pseudoxanthomonas. Notable differences in gut-associated bacterial community richness and diversity among the beetle species are observed. Furthermore, the impact of sampling location on the overall bark beetle gut bacterial community assemblage is also documented, which warrants further investigations. Nevertheless, our data expanded the current knowledge about core gut bacterial communities in Ips bark beetles and their putative function such as cellulose degradation, nitrogen fixation, detoxification of defensive plant compounds, and inhibition of pathogens, which could serve as a basis for further metatranscriptomics and metaproteomics investigations

Depth-resolved measurement of mucosal microvascular blood content using low-coherence enhanced backscattering spectroscopy

Low-coherence enhanced backscattering (LEBS) spectroscopy is a light scattering technique which uses partial spatial coherence broadband illumination to interrogate the optical properties at sub-diffusion length scales. In this work, we present a post-processing technique which isolates the hemoglobin concentration at different depths within a sample using a single spectroscopic LEBS measurement with a fixed spatial coherence of illumination. We verify the method with scattering (spectralon reflectance standard and polystyrene microspheres) and absorbing (hemoglobin) phantoms. We then demonstrate the relevance of this method for quantifying hemoglobin content as a function of depth within biological tissue using the azoxymethane treated animal model of colorectal cancer

Fabrication and Test of an Optical Magnetic Mirror

Traditional mirrors at optical wavelengths use thin metalized or dielectric layers of uniform thickness to approximate a perfect electric field boundary condition. The electron gas in such a mirror configuration oscillates in response to the incident photons and subsequently re-emits fields where the propagation and electric field vectors have been inverted and the phase of the incident magnetic field is preserved. We proposed fabrication of sub-wavelength-scale conductive structures that could be used to interact with light at a nano-scale and enable synthesis of the desired perfect magnetic-field boundary condition. In a magnetic mirror, the interaction of light with the nanowires, dielectric layer and ground plate, inverts the magnetic field vector resulting in a zero degree phase shift upon reflection. Geometries such as split ring resonators and sinusoidal conductive strips were shown to demonstrate magnetic mirror behavior in the microwave and then in the visible. Work to design, fabricate and test a magnetic mirror began in 2007 at the NASA Goddard Space Flight Center (GSFC) under an Internal Research and Development (IRAD) award Our initial nanowire geometry was sinusoidal but orthogonally asymmetric in spatial frequency, which allowed clear indications of its behavior by polarization. We report on the fabrication steps and testing of magnetic mirrors using a phase shifting interferometer and the first far-field imaging of an optical magnetic mirror