Interpolation and model reduction of nonlinear systems in the Loewner framework

This thesis studies the problem of interpolation and model order reduction for dynamical systems, with the primary objective being the development of an enhancement of the Loewner framework for general families of nonlinear differential-algebraic systems. First, an interconnection-based interpretation of the Loewner framework for linear time-invariant systems is developed. This interpretation does not rely on frequency domain notions, yielding a natural approach for enhancement of the Loewner framework to more complex systems possessing nonlinear dynamics. Next, the interconnection-based interpretation is used to develop the framework, first for systems of nonlinear ordinary differential equations, then for systems of nonlinear differential-algebraic equations, and interpolants are constructed using the so-called tangential data mappings and Loewner functions. Following this, parameterized families of systems interpolating the tangential data mappings are given. The problem of constructing interpolants from tangential data mappings and Loewner functions is considered in the most general scenario, and a dynamic extension approach to interpolant construction is developed. As a result, all systems matching the tangential data mappings, and having dimension at least as large as that of the auxiliary interpolation systems, are parameterized under mild conditions. Hence, if an interpolant exists while possessing additional desired properties, then it is contained in the dynamically extended family of interpolants. Finally, the use of behaviourally equivalent representations of a system is investigated with the goal of selecting a representation having less stringent conditions guaranteeing the existence of solution to partial differential equations. This is accomplished for a class of semi-explicit nonlinear differential-algebraic systems by making use of the explicit algebraic constraints to simplify the model of the system.Open Acces

Periodic Nonlinear Adaptive Control of Rapidly Time-Varying Linear Systems

In adaptive control the goal is to deal with systems that have unknown and/or time-varying parameters. Most techniques are proven for the case in which any time-variation is slow, with results for systems with fast time-variations limited to those for which the time-variation is of a known form or for which the plant has stable zero dynamics. Here we propose a new adaptive controller design methodology for which the time-variation can be rapid. While the plant is allowed to have unstable-zero dynamics, it must satisfy several structural conditions which have been proven to be necessary in the literature; we also impose some mild regularity conditions. The proposed controller is nonlinear and periodic, and in each period the parameter values are estimated and an appropriate stabilizing control signal is applied. Under the technical assumptions that the plant is relative degree one and that the plant uncertainty is in terms of a single scalar variable, it is proven that the closed loop system is stable under fast parameter variations with persistent jumps

Balancing Intrapreneurial Innovation Vs. Entrepreneurial Spinoffs During Periods of Technological Ferment

The period immediately after a technological discontinuity allows an innovative startup to exploit a period of ferment and great uncertainty. Meanwhile, mature innovators must develop intrapreneurial capabilities to compete with these new entrants. Using multiple data sources, we examine the innovation capabilities of Linkabit, a firm that exploited the opportunities related to digital communications, and how those capabilities were transferred to informal spinoffs which formed at twice the rate of Fairchild Semiconductor. We discuss the contingent value of innovation capabilities for early stages in a technological regime, as well as the conflicting goals of intrapreneurial development vs. restraining entrepreneurial exodus

Breaking the Disk/Halo Degeneracy with Gravitational Lensing

The degeneracy between the disk and the dark matter contribution to galaxy rotation curves remains an important uncertainty in our understanding of disk galaxies. Here we discuss a new method for breaking this degeneracy using gravitational lensing by spiral galaxies, and apply this method to the spiral lens B1600+434 as an example. The combined image and lens photometry constraints allow models for B1600+434 with either a nearly singular dark matter halo, or a halo with a sizable core. A maximum disk model is ruled out with high confidence. Further information, such as the circular velocity of this galaxy, will help break the degeneracies. Future studies of spiral galaxy lenses will be able to determine the relative contribution of disk, bulge, and halo to the mass in the inner parts of galaxies.Comment: Replaced with minor revisions, a typo fixed, and reference added; 21 pages, 8 figures, ApJ accepte

Human let-7a mirna blocks protein production on actively translating polyribosomes

MicroRNAs (miRNAs) regulate gene expression at a post-transcriptional level through base-pairing to 3¢ untranslated regions (UTRs) of messenger RNAs. The mechanism by which human let-7a miRNA regulates mRNA translation was examined in HeLa cells expressing reporter mRNAs containing the Caenorhabditis elegans lin-41 3¢ UTR. let-7a miRNA strongly repressed translation, yet the majority of control and lin-41-bearing RNAs sedimented with polyribosomes in sucrose gradients; these polyribosomes, together with let-7a miRNA and the miRISC protein AGO, were released from those structures by puromycin. RNA containing the lin-41 3¢ UTR and an iron response element in the 5¢ UTR sedimented with polysomes when cells were incubated with iron, but showed ribosome run-off when the iron was chelated. These data indicate that let-7a miRNA inhibits actively translating polyribosomes. Nascent polypeptide coimmunoprecipitation experiments further suggest that let-7a miRNA interferes with the accumulation of growing polypeptides. miRNAs are evolutionarily conserved noncoding RNAs B21 nucleotides (nt) in length that regulate gene expression at the posttranscriptional level by base-pairing to partially complementary sequences in 3¢ UTRs of target mRNAs 1 . miRNAs control several biological processes in worms, flies, zebrafish and mammals, including developmental timing, cell differentiation, cell proliferation, apoptosis and patterning of the nervous system 2,3 . In addition, the mutation or misexpression of miRNAs correlates with various human cancers, indicating that they might act as tumor suppressors or oncogenes 4 . let-7a miRNA regulates developmental timing in the nematode C. elegans and controls the expression of several transcription factors, including the 'RING, B-box, coiled-coil' (RBCC) protein LIN-41, which functions as a translational repressor of the transcription factor LIN-29 during the larval-to-adult transition In C. elegans, the lin-4 miRNA target mRNAs lin-14 and lin-28 sediment with polyribosomes, although little LIN-14 or LIN-28 protein has been detected, indicating that mRNA expression is inhibited after translation initiation 10,11 . This post-initiation repression is also suggested by the observation that miRNAs sediment with polyribosomes in mammalian cells and in worms These experiments suggest that miRNAs might function at multiple levels, which prompted us to examine the mechanism by which the C. elegans lin-41 3¢ UTR, containing two phylogenetically conserved let-7a miRNA sites RESULTS Human let-7a miRNA represses translation in HeLa cells To investigate the mechanism by which miRNAs repress mRNA translation in human cells, we transfected HeLa cells with plasmid

Periodic Adaptive Stabilization of Rapidly Time-Varying Linear Systems

This is a post-peer-review, pre-copyedit version of an article published in Mathematics of Control, Signals, and Systems. The final authenticated version is available online at: http://dx.doi.org/https://doi.org/10.1007/s00498-019-0236-6Adaptive control deals with systems that have unknown and/or time-varying parameters. Most techniques are proven for the case in which any time variation is slow, with results for systems with fast time variations limited to those for which the time variation is of a known form or for which the plant has stable zero dynamics. In this paper, a new adaptive controller design methodology is proposed in which the time variation can be rapid and the plant may have unstable zero dynamics. Under the structural assumptions that the plant is relative degree one and that the plant uncertainty is a single scalar variable, as well as some mild regularity assumptions, it is proven that the closed-loop system is exponentially stable under fast parameter variations with persistent jumps. The proposed controller is nonlinear and periodic, and in each period the parameter is estimated and an appropriate stabilizing control signal is applied.C. Nielsen and D. E. Miller: Research supported by a grant from the Natural Sciences and Engineering Research Council of Canada

Characterization of Seven Ultra-Wide Trans-Neptunian Binaries

The low-inclination component of the Classical Kuiper Belt is host to a population of extremely widely-separated binaries. These systems are similar to other Trans-Neptunian binaries (TNBs) in that the primary and secondary components of each system are of roughly equal size. We have performed an astrometric monitoring campaign of a sample of seven wide-separation, long-period TNBs and present the first-ever well-characterized mutual orbits for each system. The sample contains the most eccentric (2006 CH69, e=0.9) and the most widely-separated, weakly bound (2001 QW322, a/Rh~0.22) binary minor planets known, and also contains the system with lowest-measured mass of any TNB (2000 CF105, M~1.85E17 kg). Four systems orbit in a prograde sense, and three in a retrograde sense. They have a different mutual inclination distribution compared to all other TNBs, preferring low mutual-inclination orbits. These systems have geometric r-band albedos in the range of 0.09-0.3, consistent with radiometric albedo estimates for larger solitary low-inclination Classical Kuiper Belt objects, and we limit the plausible distribution of albedos in this region of the Kuiper Belt. We find that gravitational collapse binary formation models produce a similar orbital distribution to that currently observed, which along with a confluence of other factors supports formation of the cold Classical Kuiper Belt in situ through relatively rapid gravitational collapse rather than slow hierarchical accretion. We show that these binary systems are sensitive to disruption via collisions, and their existence suggests that the size distribution of TNOs at small sizes remains relatively shallow.Comment: 22 pages, 14 Figures, in press in the Astrophysical Journal, updated to reflect bibliographic corrections and additional table added in proo

Metabarcoding: A Powerful Yet Still Underestimated Approach for the Comprehensive Study of Vector-Borne Pathogen Transmission Cycles and Their Dynamics

The implementation of sustainable control strategies aimed at disrupting the transmission of vector-borne pathogens requires a comprehensive knowledge of the vector ecology in the different eco-epidemiological contexts, as well as the local pathogen transmission cycles and their dynamics. However, even when focusing only on one specific vector-borne disease, achieving this knowledge is highly challenging, as the pathogen may exhibit a high genetic diversity and multiple vector species or subspecies and host species may be involved. In addition, the development of the pathogen and the vectorial capacity of the vectors may be affected by their midgut and/or salivary gland microbiome. The recent advent of Next-Generation Sequencing (NGS) technologies has brought powerful tools that can allow for the simultaneous identification of all these essential components, although their potential is only just starting to be realized. We present a metabarcoding approach that can facilitate the description of comprehensive host-pathogen networks, integrate important microbiome and coinfection data, identify at-risk situations, and disentangle the transmission cycles of vector-borne pathogens. This powerful approach should be generalized to unravel the transmission cycles of any pathogen and their dynamics, which in turn will help the design and implementation of sustainable, effective, and locally adapted control strategies

Representing the function and sensitivity of coastal interfaces in earth system models

© The Author(s), 2020. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Ward, N. D., Megonigal, J. P., Bond-Lamberty, B., Bailey, V. L., Butman, D., Canuel, E. A., Diefenderfer, H., Ganju, N. K., Goni, M. A., Graham, E. B., Hopkinson, C. S., Khangaonkar, T., Langley, J. A., McDowell, N. G., Myers-Pigg, A. N., Neumann, R. B., Osburn, C. L., Price, R. M., Rowland, J., Sengupta, A., Simard, M., Thornton, P. E., Tzortziou, M., Vargas, R., Weisenhorn, P. B., & Windham-Myers, L. Representing the function and sensitivity of coastal interfaces in earth system models. Nature Communications, 11(1), (2020): 2458, doi:10.1038/s41467-020-16236-2.Between the land and ocean, diverse coastal ecosystems transform, store, and transport material. Across these interfaces, the dynamic exchange of energy and matter is driven by hydrological and hydrodynamic processes such as river and groundwater discharge, tides, waves, and storms. These dynamics regulate ecosystem functions and Earth’s climate, yet global models lack representation of coastal processes and related feedbacks, impeding their predictions of coastal and global responses to change. Here, we assess existing coastal monitoring networks and regional models, existing challenges in these efforts, and recommend a path towards development of global models that more robustly reflect the coastal interface.Funding for this work was provided by Pacific Northwest National Laboratory (PNNL) Laboratory Directed Research & Development (LDRD) as part of the Predicting Ecosystem Resilience through Multiscale Integrative Science (PREMIS) Initiative. PNNL is operated by Battelle for the U.S. Department of Energy under Contract DE-AC05-76RL01830. Additional support to J.P.M. was provided by the NSF-LTREB program (DEB-0950080, DEB-1457100, DEB-1557009), DOE-TES Program (DE-SC0008339), and the Smithsonian Institution. This manuscript was motivated by discussions held by co-authors during a three-day workshop at PNNL in Richland, WA: The System for Terrestrial Aquatic Research (STAR) Workshop: Terrestrial-Aquatic Research in Coastal Systems. The authors thank PNNL artist Nathan Johnson for preparing the figures in this manuscript and Terry Clark, Dr. Charlette Geffen, and Dr. Nancy Hess for their aid in organizing the STAR workshop. The authors thank all workshop participants not listed as authors for their valuable insight: Lihini Aluwihare (contributed to biogeochemistry discussions and development of concept for Fig. 3), Gautam Bisht (contributed to modeling discussion), Emmett Duffy (contributed to observational network discussions), Yilin Fang (contributed to modeling discussion), Jeremy Jones (contributed to biogeochemistry discussions), Roser Matamala (contributed to biogeochemistry discussions), James Morris (contributed to biogeochemistry discussions), Robert Twilley (contributed to biogeochemistry discussions), and Jesse Vance (contributed to observational network discussions). A full report on the workshop discussions can be found at https://www.pnnl.gov/publications/star-workshop-terrestrial-aquatic-research-coastal-systems