Rigorous data-driven computation of spectral properties of Koopman operators for dynamical systems

Koopman operators are infinite-dimensional operators that globally linearize nonlinear dynamical systems, making their spectral information useful for understanding dynamics. However, Koopman operators can have continuous spectra and infinite-dimensional invariant subspaces, making computing their spectral information a considerable challenge. This paper describes data-driven algorithms with rigorous convergence guarantees for computing spectral information of Koopman operators from trajectory data. We introduce residual dynamic mode decomposition (ResDMD), which provides the first scheme for computing the spectra and pseudospectra of general Koopman operators from snapshot data without spectral pollution. Using the resolvent operator and ResDMD, we also compute smoothed approximations of spectral measures associated with measure-preserving dynamical systems. We prove explicit convergence theorems for our algorithms, which can achieve high-order convergence even for chaotic systems, when computing the density of the continuous spectrum and the discrete spectrum. We demonstrate our algorithms on the tent map, Gauss iterated map, nonlinear pendulum, double pendulum, Lorenz system, and an $11$-dimensional extended Lorenz system. Finally, we provide kernelized variants of our algorithms for dynamical systems with a high-dimensional state-space. This allows us to compute the spectral measure associated with the dynamics of a protein molecule that has a 20,046-dimensional state-space, and compute nonlinear Koopman modes with error bounds for turbulent flow past aerofoils with Reynolds number $>10^5$ that has a 295,122-dimensional state-space

Density Functional Theory in the Prediction of Mutagenicity: A Perspective

As a field, computational toxicology is concerned with using in silico models to predict and understand the origins of toxicity. It is fast, relatively inexpensive, and avoids the ethical conundrum of using animals in scientific experimentation. In this perspective, we discuss the importance of computational models in toxicology, with a specific focus on the different model types that can be used in predictive toxicological approaches toward mutagenicity (SARs and QSARs). We then focus on how quantum chemical methods, such as density functional theory (DFT), have previously been used in the prediction of mutagenicity. It is then discussed how DFT allows for the development of new chemical descriptors that focus on capturing the steric and energetic effects that influence toxicological reactions. We hope to demonstrate the role that DFT plays in understanding the fundamental, intrinsic chemistry of toxicological reactions in predictive toxicology

Density Functional Theory Transition-State Modeling for the Prediction of Ames Mutagenicity in 1,4 Michael Acceptors

Assessing the safety of new chemicals, without introducing the need for animal testing, is a task of great importance. The Ames test, a widely used bioassay to assess mutagenicity, can be an expensive, wasteful process with animal-derived reagents. Existing in silico methods for the prediction of Ames test results are traditionally based on chemical category formation and can lead to false positive predictions. Category formation also neglects the intrinsic chemistry associated with DNA reactivity. Activation energies and HOMO/LUMO energies for thirty 1,4 Michael acceptors were calculated using a model nucleobase and were further used to predict the Ames test result of these compounds. The proposed model builds upon existing work and examines the fundamental toxicant-target interactions using density functional theory transition-state modeling. The results show that Michael acceptors with activation energies &lt; 20.7 kcal/mol and LUMO energies &lt; -1.85 eV are likely to act as direct mutagens upon exposure to DNA.</p

Density Functional Theory Transition-State Modeling for the Prediction of Ames Mutagenicity in 1,4 Michael Acceptors

Assessing the safety of new chemicals, without introducing the need for animal testing, is a task of great importance. The Ames test, a widely used bioassay to assess mutagenicity, can be an expensive, wasteful process with animal-derived reagents. Existing in silico methods for the prediction of Ames test results are traditionally based on chemical category formation and can lead to false positive predictions. Category formation also neglects the intrinsic chemistry associated with DNA reactivity. Activation energies and HOMO/LUMO energies for thirty 1,4 Michael acceptors were calculated using a model nucleobase and were further used to predict the Ames test result of these compounds. The proposed model builds upon existing work and examines the fundamental toxicant-target interactions using density functional theory transition-state modeling. The results show that Michael acceptors with activation energies <20.7 kcal/mol and LUMO energies < -1.85 eV are likely to act as direct mutagens upon exposure to DNA

Phylogeography of Rift Valley Fever Virus in Africa and the Arabian Peninsula

Rift Valley Fever is an acute zoonotic viral disease caused by Rift Valley Fever virus (RVFV) that affects ruminants and humans in Sub-Saharan Africa and the Arabian Peninsula. We used phylogenetic analyses to understand the demographic history of RVFV populations, using sequence data from the three minigenomic segments of the virus. We used phylogeographic approaches to infer RVFV historical movement patterns across its geographic range, and to reconstruct transitions among host species. Results revealed broad circulation of the virus in East Africa, with many lineages originating in Kenya. Arrival of RVFV in Madagascar resulted from three major waves of virus introduction: the first from Zimbabwe, and the second and third from Kenya. The two major outbreaks in Egypt since 1977 possibly resulted from a long-distance introduction from Zimbabwe during the 1970s, and a single introduction took RVFV from Kenya to Saudi Arabia. Movement of the virus between Kenya and Sudan, and CAR and Zimbabwe, was in both directions. Viral populations in West Africa appear to have resulted from a single introduction from Central African Republic. The overall picture of RVFV history is thus one of considerable mobility, and dynamic evolution and biogeography, emphasizing its invasive potential, potentially more broadly than its current distributional limits

Functional Lymphatic Changes and the Immune Response During Lymphedema Development

The lymphatic system serves important roles in fluid balance and immune system regulation within the body. Through both passive and active transport of fluid, the lymphatic network transports interstitial fluid back into the circulatory system. When the lymphatic system fails, that excess fluid can no longer be properly transported back into the circulation. This leads to a disease called lymphedema, which manifests as swelling of distal limbs and normally occurs following injury to the lymphatic network. The mechanisms of lymphedema development are not completely understood, but the immune response is known to play an important role in lymphedema pathogenesis. The main goal of this thesis is to investigate both the functional response of the intact lymphatic vasculature and changes in leukocyte populations within draining lymph nodes (dLNs) during lymphedema progression. In the first aim, we used near-infrared (NIR) imaging techniques to quantify changes in lymphatic function in vivo following induction of lymphedema in mice using a novel lymphedema model. We specifically investigated the effect of two potential therapeutic mechanisms, antagonism of leukotriene B4 (LTB4) production and deletion of epsin, on lymphatic function following lymphedema surgery. Further in vivo and ex vivo analysis was performed to elucidate potential mechanisms regulating the effect of LTB4 on lymphatic contractile function. In the second aim, we used flow cytometry to investigate changes in leukocyte populations within dLNs during acute lymphedema progression. Our novel lymphedema model leaves a pair of intact collecting lymphatic vessels on one side of the mouse tail while other tail lymphatics are ligated, allowing for analysis of the immune response within dLNs experiencing differences in drainage. Further analysis using a nanoparticle delivery system was used to quantify differences in particle uptake between dLNs as lymphedema progressed. The effect of LTB4 antagonism on the immune response was also elucidated. Overall, this work furthers understanding of the mechanisms driving lymphedema pathogenesis, by combining comprehensive analysis of changes in lymphatic contractile function in vivo and ex vivo with investigation of changes in the immune response within dLNs.Ph.D

Comparing the Performances of Force Fields in Conformational Searching of Hydrogen-Bond-Donating Catalysts

Here, we compare the relative performances of different force fields for conformational searching of hydrogen-bond-donating catalyst-like molecules. We assess the force fields by their predictions of conformer energies, geometries, low-energy, nonredundant conformers, and the maximum numbers of possible conformers. Overall, MM3, MMFFs, and OPLS3e had consistently strong performances and are recommended for conformationally searching molecules structurally similar to those in this study

Machine learning activation energies of chemical reactions

Application of machine learning (ML) to the prediction of reaction activation barriers is a new and exciting field for these algorithms. The works covered here are specifically those in which ML is trained to predict the activation energies of homogeneous chemical reactions, where the activation energy is given by the energy difference between the reactants and transition state of a reaction. Particular attention is paid to works that have applied ML to directly predict reaction activation energies, the limitations that may be found in these studies, and where comparisons of different types of chemical features for ML models have been made. Also explored are models that have been able to obtain high predictive accuracies, but with reduced datasets, using the Gaussian process regression ML model. In these studies, the chemical reactions for which activation barriers are modeled include those involving small organic molecules, aromatic rings, and organometallic catalysts. Also provided are brief explanations of some of the most popular types of ML models used in chemistry, as a beginner's guide for those unfamiliar