Rigidity and gluing for Morse and Novikov complexes

We obtain rigidity and gluing results for the Morse complex of a real-valued Morse function as well as for the Novikov complex of a circle-valued Morse function. A rigidity result is also proved for the Floer complex of a hamiltonian defined on a closed symplectic manifold $(M,\omega)$ with $c_{1}|_{\pi_{2}(M)}=[\omega]|_{\pi_{2}(M)}=0$. The rigidity results for these complexes show that the complex of a fixed generic function/hamiltonian is a retract of the Morse (respectively Novikov or Floer) complex of any other sufficiently $C^{0}$ close generic function/hamiltonian. The gluing result is a type of Mayer-Vietoris formula for the Morse complex. It is used to express algebraically the Novikov complex up to isomorphism in terms of the Morse complex of a fundamental domain. Morse cobordisms are used to compare various Morse-type complexes without the need of bifurcation theory.Comment: 46 pages, LATEX file with XYPIC diagrams, and one .EPS file. Final version, accepted for publication by the Journal of the European Mathematical Societ

Emerging Viruses Are a Global Health Concern Requiring Science-based Solutions and Local Action

On 11 March 2020, COVID-19 was officially characterized as a pandemic. By this time, the SARS-CoV-2 virus had already spread across continents, causing significant morbidity and mortality, and affecting social and economic systems. The complexities of the impact of COVID-19 call for multidisciplinary to trans-disciplinary research that goes beyond epidemiology research and practice. We aimed to (1) provide a narrative review of scientific knowledge of COVID-19, (2) place the developments by international organizations, governments, and individuals (including researchers at all levels) into a wider context, (3) provide practical suggestions for all actors to respond to the COVID-19 pandemic in the short term within the context of large uncertainties, and (4) describe the need for systemic transformations for sustainability using a trans-disciplinary systems approach. In summary, the literature revealed that improvements of surveillance, prevention, and control programs for the prevention of pandemics are needed to safeguard public health. Embracing a trans-disciplinary systems-based approach with experts from a wide variety of fields will be essential to prevent future outbreaks and other health risks, taking into account the complexities of natural and social systems

An sl_n stable homotopy type for matched diagrams

There exists a simplified Bar-Natan Khovanov complex for open 2-braids. The Khovanov cohomology of a knot diagram made by gluing tangles of this type is therefore often amenable to calculation. We lift this idea to the level of the Lipshitz-Sarkar stable homotopy type and use it to make new computations. Similarly, there exists a simplified Khovanov-Rozansky sl_n complex for open 2-braids with oppositely oriented strands and an even number of crossings. Diagrams made by gluing tangles of this type are called matched diagrams, and knots admitting matched diagrams are called bipartite knots. To a pair consisting of a matched diagram and a choice of integer n >= 2, we associate a stable homotopy type. In the case n = 2 this agrees with the Lipshitz-Sarkar stable homotopy type of the underlying knot. In the case n >= 3 the cohomology of the stable homotopy type agrees with the sl_n Khovanov-Rozansky cohomology of the underlying knot. We make some consistency checks of this sl_n stable homotopy type and show that it exhibits interesting behaviour. For example we find a CP^2 in the sl_3 type for some diagram, and show that the sl_4 type can be interesting for a diagram for which the Lipshitz-Sarkar type is a wedge of Moore spaces.Comment: 62 pages, color figure

Swashplate control system

A mechanical system to control the position of a rotating swashplate is developed. This system provides independent lateral cyclic, longitudinal cyclic and collective pitch control of a helicopter rotor attached to the swashplate, without use of a mixer box. The system also provide direct, linear readout of cyclic and collective swashplate positions

Spectral and scattering theory for symbolic potentials of order zero

The spectral and scattering theory is investigated for a generalization, to scattering metrics on two-dimensional compact manifolds with boundary, of the class of smooth potentials on the Euclidean plane which are homogeneous of degree zero near infinity. The most complete results require the additional assumption that the restriction of the potential to the circle(s) at infinity be Morse. Generalized eigenfunctions associated to the essential spectrum at non-critical energies are shown to originate both at minima and maxima, although the latter are not germane to the $L^2$ spectral theory. Asymptotic completeness is shown, both in the traditional $L^2$ sense and in the sense of tempered distributions. This leads to a definition of the scattering matrix, the structure of which will be described in a future publication.Comment: 69 page

Evaluation of the effectiveness of the Senior Year Plus Program in Iowa

Iowa’s public institutions graduate students with the sixth highest student loan debt in the nation (Project on Student Debt, 2008). As a result, Iowa Governor Chet Culver has proposed the Senior Year Plus Program, which is a state-funded dual-enrollment program. This program’s purpose is to help alleviate the debts students incur while attending college. However, there are no examinations to this point that focus on the financial, as well as the personal and professional developmental benefits of the program, particularly in comparison to the four-year institution. The current research utilized a qualitative research design. Ten (5 Dual-Enrollers/5 Non-Dual Enrollers) participants currently enrolled at a four-year institution in Iowa were interviewed. Significant themes and insights emerged that highlighted a need to reconsider the investment made in this program in terms of financial gain, which was related to length of enrollment, as well as the holistic developmental benefits available to students who enroll in the Senior Year Plus Program

Improving Searches for Gravitational Wave Bursts.

The first half of this dissertation discusses the details of calibrating a resonant mass gravitational wave antenna and determining its sensitivity. We dispense with the assumption of a perfectly tuned antenna and transducer and model the system using a coordinate rotation. We demonstrate that all of the important model parameters can be directly measured. We demonstrate that the signal response of the two detector modes should be equal despite any mistuning and that the mistuning parameter can be measured in two separate ways. These properties are useful for determining the degree to which a real detector\u27s behavior parallels that of an ideal two-mode system. We compare the predictions of the model to the output of the ALLEGRO system and determine that a resonance in the hardware used to apply calibration signals is the source of an observed 15% difference in signal response. We extend the model to include this additional resonance. The second half of this dissertation discusses the problem of comparing lists of candidate events acquired from different gravitational wave detectors in search of statistically meaningful coincidences. We demonstrate that a Bayesian approach is the most robust method of inferring if signals are present in the data. We use a combination of multinomial and Poisson distributions to form a likelihood function describing the results of any coincidence experiment. We establish a meaningful basis for choosing a prior probability for Bayesian analyses. We show that the results of a Bayesian analysis do not depend arbitrarily on how the data is subdivided. Finally, using the results of the 1991 and 1994 ALLEGRO and EXPLORER runs, we establish an upper limit on the mean rate of detectable gravity wave bursts that is no more than 9 events per year above a dimensionless strain threshold of 2.3 x 10-18