Towards a higher-dimensional construction of stable/unstable Lagrangian laminations

We generalize some properties of surface automorphisms of pseudo-Anosov type. First, we generalize the Penner construction of a pseudo-Anosov homeomorphism and show that a symplectic automorphism which is constructed by our generalized Penner construction has an invariant Lagrangian branched submanifold and an invariant Lagrangian lamination, which are higher-dimensional generalizations of a train track and a geodesic lamination in the surface case. Moreover, if a pair consisting of a symplectic automorphism $\psi$ and a Lagrangian branched surface $B_{\psi}$ satisfies some assumptions, we prove that there is an invariant Lagrangian lamination $\mathcal{L}$ which is a higher-dimensional generalization of a geodesic lamination.Comment: 43 pages, 10 figure

Biodegradation of Desorption -Resistant Organic Contaminants in Wetland Soils.

Contaminant bioavailability depends on physicochemical processes such as adsorption/desorption, diffusion, and dissolution. The rates of sorption and desorption of trichloroethylene (TCE) and 1,3-Dichlororbenzene (1,3-DCB) were studied. Desorption kinetics of 3-month and 5-month old contaminated soils showed that progressively less amount of contaminant was available for facile desorption compared to freshly contaminated soil in an empirical non-linear model. Microcosm batch studies were conducted to study the biodegradation of 1,3-DCB in the aqueous and soil phase containing a freshly contaminated soil and a soil containing only the desorption resistant fraction. The presence of the soil reduced the rates of biodegradation. It is clear that from the freshly contaminated soil, 1,3-DCB readily desorbed into the aqueous phase and was bioavailable from microbial consumption whereas for the soils containing the desorption-resistant 1,3-DCB, mass transfer into the aqueous phase limited the contaminant availability. Biodegradation of TCE by toluene-degrading bacteria was measured under aerobic conditions in aqueous and soil-slurry batch microcosms containing a freshly contaminated soil and a soil containing only the desorption resistant fraction of TCE. Presence of soil resulted in biodegradation rates substantially lower than those determined in the absence of soil. An appreciable increase in the rate and extent of determined in the absence of soil. An appreciable increase in the rate and extent of TCE biodegradation was observed in microcosms when toluene was added multiple times. The availability of CB-sorbed soils to CB degrading bacteria was assessed using a kinetic mineralization assay. It was demonstrated that soil-sorbed CB was available to CB-degrading bacteria, and that the extents of bioavailability of soil-sorbed CB decreased with prolonged aging. The rates of sorption and desorption of 1,4-DCB depend on aging, and soil types, and were investigated with the aid of Freundlich isotherm. According to a hysteresis index, hysteresis was not necessarily correlated with aging. Desorption isotherms demonstrated that desorption patterns in marsh soil were linear than in PPI soil even when the contaminant was aged. Bioavailability of 1,4-DCB was occurred both in freshly bounded into soil as well as in desorption resistant fraction in soils without a distinctive difference in two fractions. No significant differences in biodegradation were monitored in different wetland soil types containing various organic fractions

Information inference for cyber-physical systems with application to aviation safety and space situational awareness

Due to the rapid advancement of technologies on sensors and processors, engineering systems have become more complex and highly automated to meet ever stringent performance and safety requirements. These systems are usually composed of physical plants (e.g., aircraft, spacecraft, ground vehicles, etc.) and cyber components (e.g., sensing, communication, and computing units), and thus called as Cyber-Physical Systems (CPSs). For safe, efficient, and sustainable operation of a CPS, the states and physical characteristics of the system need to be effectively estimated or inferred from sensing data by proper information inference algorithms. However, due to the complex nature of the interacting multiple-heterogeneous elements of the CPS, the information inference of the CPS is a challenging task, where exiting methods designed for a single-element dynamic system (or for even dynamic systems with multiple-homogenous elements) could not be applicable. Moreover, the increasing number of sensor resources in CPSs makes the task even more challenging as meaningful information needs to be accurately and effectively inferred from huge amount of data, which is usually noise corrupted. Many aerospace systems such as air traffic control systems, pilot-automation integrated systems, networked unmanned aircraft systems, and space surveillance systems are good examples of CPSs and thus have the aforementioned challenging problems. The goals of this research are to 1) overcome the challenges in complex CPSs by developing new information inference methodologies based on control, estimation, hybrid systems and information theories, and 2) successfully apply them to various complex and safety-critical aerospace systems such as air transportation systems, space surveillance systems, and integrated human-machine systems, to promote their efficiency and safety

Pseudo-Anosov autoquivalances arising from Symplectic topology and their hyperbolic actions on stability conditions

Within $N$-Calabi-Yau categories associated with quivers whose base graphs form trees, we delve into the study of the asymptotic behaviors of autoequivalences of a specific type. These autoequivalences, which we call "Penner type," exhibit straightforward asymptotic characteristics, making them noteworthy exemplars of "pseudo-Anosov" autoequivalences in the sense of \cite{Fan-Filip-Haiden-Katzarkov-Liu21}, and also in a stronger sense that we define in the present paper. In addition, we provide a practical methodology for calculating the stretching factors of Penner type autoequivalences. We expect that this computational approach can have applications. As an example, we establish a positive lower bound on the translation length of the induced action these autoequivalences have on the space of stability conditions. Our anticipation is that this lower bound is, in fact, exact. Notably, we have observed instances of Penner type $\Phi$ where the induced actions align precisely with this lower bound. In other words, these examples induce hyperbolic actions on the space of stability conditions.Comment: 97 pages, 2 figures, Comments are welcom