Control of integrable Hamiltonian systems and degenerate bifurcations

In this dissertation, we study the control of near-integrable systems. A near-integrable system is one whose phase space has a similar structure to an integrable system during short time periods and for some parameter regime. We begin by studying the control of integrable Hamiltonian systems. The controller targets an exact solution to the integrable system using dissipative and conservative terms. We find that a Takens-Bogdanov bifurcation occurs in the limit of no dissipative control. The presence of a Takens-Bogdanov bifurcation implies that the control is highly susceptible to noise. We illustrate our results using a two- and four-dimensional integrable systems generated by low order truncations of solutions to the nonlinear Schrodinger equation (NLS). We then extend our results to a near-integrable system related to the NLS; the Ginzburg-Landau equation. We attempt to control the Ginzburg-Landau equation to a plane wave solution of the NLS. We show that for a certain parameter regime; a Takens-Bogdanov bifurcation occurs in the limit of no dissipative control. Through this example, we show that solutions of integrable systems can be viable control targets for related near-integrable systems

Composition and Analysis of Music Using Mathematica

In this paper we demonstrate how to create and analyze musical compositions using Mathematica. In §1, we begin by demonstrating how to create a musical composition for an orchestra based on the butterfly curve using traditional means. In §2, we then show how a computer generated piece based on any curve can be composed using Mathematica. Finally, in §3, we show how Mathematica can be used to analyze musical compositions using the methods from nonlinear time series analysis

Enhancing Humoral Responses Against HIV Envelope Trimers via Nanoparticle Delivery with Stabilized Synthetic Liposomes

An HIV vaccine capable of eliciting durable neutralizing antibody responses continues to be an important unmet need. Multivalent nanoparticles displaying a high density of envelope trimers may be promising immunogen forms to elicit strong and durable humoral responses to HIV, but critical particle design criteria remain to be fully defined. To this end, we developed strategies to covalently anchor a stabilized gp140 trimer, BG505 MD39, on the surfaces of synthetic liposomes to study the effects of trimer density and vesicle stability on vaccine-elicited humoral responses in mice. CryoEM imaging revealed homogeneously distributed and oriented MD39 on the surface of liposomes irrespective of particle size, lipid composition, and conjugation strategy. Immunization with covalent MD39-coupled liposomes led to increased germinal center and antigen-specific T follicular helper cell responses and significantly higher avidity serum MD39-specific IgG responses compared to immunization with soluble MD39 trimers. A priming immunization with liposomal-MD39 was important for elicitation of high avidity antibody responses, regardless of whether booster immunizations were administered with either soluble or particulate trimers. The stability of trimer anchoring to liposomes was critical for these effects, as germinal center and output antibody responses were further increased by liposome compositions incorporating sphingomyelin that exhibited high in vitro stability in the presence of serum. Together these data highlight key liposome design features for optimizing humoral immunity to lipid nanoparticle immunogens.National Institute of Allergy and Infectious Diseases (U.S.) (Award UM1AI100663)National Institutes of Health (U.S.) (Award P01-AI104715)National Institutes of Health (U.S.) (Award P01-AI048240)National Cancer Institute (U.S.) (Grant P30-CA14051

The James Webb Space Telescope Mission: Optical Telescope Element Design, Development, and Performance

The James Webb Space Telescope (JWST) is a large, infrared space telescope that has recently started its science program which will enable breakthroughs in astrophysics and planetary science. Notably, JWST will provide the very first observations of the earliest luminous objects in the Universe and start a new era of exoplanet atmospheric characterization. This transformative science is enabled by a 6.6 m telescope that is passively cooled with a 5-layer sunshield. The primary mirror is comprised of 18 controllable, low areal density hexagonal segments, that were aligned and phased relative to each other in orbit using innovative image-based wavefront sensing and control algorithms. This revolutionary telescope took more than two decades to develop with a widely distributed team across engineering disciplines. We present an overview of the telescope requirements, architecture, development, superb on-orbit performance, and lessons learned. JWST successfully demonstrates a segmented aperture space telescope and establishes a path to building even larger space telescopes.Comment: accepted by PASP for JWST Overview Special Issue; 34 pages, 25 figure

The James Webb Space Telescope Mission

Twenty-six years ago a small committee report, building on earlier studies, expounded a compelling and poetic vision for the future of astronomy, calling for an infrared-optimized space telescope with an aperture of at least $4m$. With the support of their governments in the US, Europe, and Canada, 20,000 people realized that vision as the $6.5m$ James Webb Space Telescope. A generation of astronomers will celebrate their accomplishments for the life of the mission, potentially as long as 20 years, and beyond. This report and the scientific discoveries that follow are extended thank-you notes to the 20,000 team members. The telescope is working perfectly, with much better image quality than expected. In this and accompanying papers, we give a brief history, describe the observatory, outline its objectives and current observing program, and discuss the inventions and people who made it possible. We cite detailed reports on the design and the measured performance on orbit.Comment: Accepted by PASP for the special issue on The James Webb Space Telescope Overview, 29 pages, 4 figure

Detecting nonlinearity in short and noisy time series using the permutation entropy

Permutation entropy contains the information about the temporal structure associated with the underlying dynamics of a time series. Its estimation is simple, and because it is based on the comparison of neighboring values, it becomes significantly robust to noise. It is also computationally efficient and invariant with respect to nonlinear monotonous transformations. For all these reasons, the permutation entropy seems to be particularly suitable as a discriminative measure for unveiling nonlinear dynamics in arbitrary real-world data. In this paper, we study the efficacy of a conventional surrogate method with a linear stochastic process as the null hypothesis but implementing the permutation entropy as a nonlinearity measure. Its discriminative power is tested by implementing several analyses on numerical signals whose dynamical properties are known a priori (linear discrete and continuous models, chaotic regimes of discrete and continuous systems). The performance of the proposed approach in real-world applications (chaotic laser data, monthly smoothed sunspot index and neuro-physiological recordings) is also demonstrated. The results obtained allow us to conclude that this symbolic tool is very useful for discriminating nonlinear characteristics in very short and noisy data.Fil: Zunino, Luciano José. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Centro de Investigaciones Ópticas. Provincia de Buenos Aires. Gobernación. Comisión de Investigaciones Científicas. Centro de Investigaciones Ópticas. Universidad Nacional de La Plata. Centro de Investigaciones Ópticas; Argentina. Universidad Nacional de La Plata. Facultad de Ingeniería; ArgentinaFil: Kulp, Christopher W.. Lycoming College; Estados Unido

Using missing ordinal patterns to detect nonlinearity in time series data

The number of missing ordinal patterns (NMP) is the number of ordinal patterns that do not appear in a series after it has been symbolized using the Bandt and Pompe methodology. In this paper, the NMP is demonstrated as a test for nonlinearity using a surrogate framework in order to see if the NMP for a series is statistically different from the NMP of iterative amplitude adjusted Fourier transform (IAAFT) surrogates. It is found that the NMP works well as a test statistic for nonlinearity, even in the cases of very short time series. Both model and experimental time series are used to demonstrate the efficacy of the NMP as a test for nonlinearity.Fil: Kulp, Christopher W.. Lycoming College; Estados UnidosFil: Zunino, Luciano José. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Centro de Investigaciones Ópticas. Provincia de Buenos Aires. Gobernación. Comisión de Investigaciones Científicas. Centro de Investigaciones Ópticas. Universidad Nacional de La Plata. Centro de Investigaciones Ópticas; ArgentinaFil: Osborne, Thomas. Lycoming College; Estados UnidosFil: Zawadzki, Brianna. Lycoming College; Estados Unido

Glycan clustering stabilizes the mannose patch of HIV-1 and preserves vulnerability to broadly neutralizing antibodies

The envelope spike of HIV-1 employs a 'glycan shield' to protect itself from antibody-mediated neutralization. Paradoxically, however, potent broadly neutralizing antibodies (bnAbs) that target this shield have been isolated. The unusually high glycan density on the gp120 subunit limits processing during biosynthesis, leaving a region of under-processed oligomannose-type structures, which is a primary target of these bnAbs. Here we investigate the contribution of individual glycosylation sites in the formation of this so-called intrinsic mannose patch. Deletion of individual sites has a limited effect on the overall size of the intrinsic mannose patch but leads to changes in the processing of neighbouring glycans. These structural changes are largely tolerated by a panel of glycan-dependent bnAbs targeting these regions, indicating a degree of plasticity in their recognition. These results support the intrinsic mannose patch as a stable target for vaccine design.</p

Innate immune recognition of glycans targets HIV nanoparticle immunogens to germinal centers

In vaccine design, antigens are often arrayed in a multivalent nanoparticle form, but in vivo mechanisms underlying the enhanced immunity elicited by such vaccines remain poorly understood. We compared the fates of two different heavily glycosylated HIV antigens, a gp120-derived mini-protein and a large, stabilized envelope trimer, in protein nanoparticle or “free” forms after primary immunization. Unlike monomeric antigens, nanoparticles were rapidly shuttled to the follicular dendritic cell (FDC) network and then concentrated in germinal centers in a complement-, mannose-binding lectin (MBL)–, and immunogen glycan–dependent manner. Loss of FDC localization in MBL-deficient mice or via immunogen deglycosylation significantly affected antibody responses. These findings identify an innate immune–mediated recognition pathway promoting antibody responses to particulate antigens, with broad implications for humoral immunity and vaccine design