Recognizing Graphs Close to Bipartite Graphs with an Application to Colouring Reconfiguration

We continue research into a well-studied family of problems that ask whether the vertices of a graph can be partitioned into sets $A$ and~$B$, where $A$ is an independent set and $B$ induces a graph from some specified graph class ${\cal G}$. We let ${\cal G}$ be the class of $k$-degenerate graphs. This problem is known to be polynomial-time solvable if $k=0$ (bipartite graphs) and NP-complete if $k=1$ (near-bipartite graphs) even for graphs of maximum degree $4$. Yang and Yuan [DM, 2006] showed that the $k=1$ case is polynomial-time solvable for graphs of maximum degree $3$. This also follows from a result of Catlin and Lai [DM, 1995]. We consider graphs of maximum degree $k+2$ on $n$ vertices. We show how to find $A$ and $B$ in $O(n)$ time for $k=1$, and in $O(n^2)$ time for $k\geq 2$. Together, these results provide an algorithmic version of a result of Catlin [JCTB, 1979] and also provide an algorithmic version of a generalization of Brook's Theorem, which was proven in a more general way by Borodin, Kostochka and Toft [DM, 2000] and Matamala [JGT, 2007]. Moreover, the two results enable us to complete the complexity classification of an open problem of Feghali et al. [JGT, 2016]: finding a path in the vertex colouring reconfiguration graph between two given $\ell$-colourings of a graph of maximum degree $k$

Implications of Silurian granite genesis to the tectonic history of the Nashoba terrane, Eastern Massachusetts

Thesis advisor: J. Christopher HepburnThe Nashoba terrane is a highly metamorphosed and sheared Paleozoic tectonic block in eastern Massachusetts. The metamorphic rocks that compose the terrane are intruded by a series of diorites, tonalites, and granites. The Andover Granite is a complex multiphase granitic suite found in the northern part of the Nashoba terrane and is composed of both foliated and unfoliated granites as well as a granodiorite phase. The Sgr Group of granites is a series of unfoliated granites exposed along the Nashoba-Avalon terrane boundary. New crystallization ages for the foliated Andover Granite and the Sudbury Granite, southernmost body of the Sgr Group of granites, are presented. CA-TIMS U-Pb geochronology on zircons collected from these granites yielded 419.43 ± 0.52 Ma and 419.65 ± 0.51 Ma crystallization ages for the foliated Andover Granite and a 420.49 ± 0.52 Ma crystallization age for the Sudbury Granite. Geochemical and petrographic analysis of these granites indicate that the foliated Andover Granite is a high-K calc-alkaline, peralmuminous, S-type, biotite + muscovite granite and the Sudbury granite is high-K calc-alkaline, metaluminous to slightly peraluminous, I-type, biotite granite. These two granites are interpreted to have formed from the anatexis of either Nashoba terrane metasedimentary rocks and/or its underlying basement just prior to the Acadian orogeny. It is proposed that when Silurian diorite/tonalite magmas intruded into the Nashoba terrane, the influx of magmatic heat was sufficient to trigger crustal melting and promote granite genesis. This petrogenetic scenario fits well with regional tectonic models showing the Silurio-Devonian convergence of Avalonia towards Ganderia (which formed the eastern side of composite Laurentia at the time) in the northern Appalachians. Prior to the collision of Avalonia to composite Laurentia, mafic and intermediate composition arc magmas intruded the eastern Ganderian margin. The large amount of heat that accompanied these intrusions is believed to have contributed to Acadian metamorphism and influenced the formation of granitic plutons along the margin. It is therefore proposed that the plutonic record of the Nashoba terrane shows that by the Late Silurian - Early Devonian, Avalonia was still outboard of Laurentia in the vicinity of southern New England.Thesis (MS) — Boston College, 2014.Submitted to: Boston College. Graduate School of Arts and Sciences.Discipline: Earth and Environmental Sciences

Bayesian Physics Informed Neural Networks for Data Assimilation and Spatio-Temporal Modelling of Wildfires

We apply the Physics Informed Neural Network (PINN) to the problem of wildfire fire-front modelling. We use the PINN to solve the level-set equation, which is a partial differential equation that models a fire-front through the zero-level-set of a level-set function. The result is a PINN that simulates a fire-front as it propagates through the spatio-temporal domain. We show that popular optimisation cost functions used in the literature can result in PINNs that fail to maintain temporal continuity in modelled fire-fronts when there are extreme changes in exogenous forcing variables such as wind direction. We thus propose novel additions to the optimisation cost function that improves temporal continuity under these extreme changes. Furthermore, we develop an approach to perform data assimilation within the PINN such that the PINN predictions are drawn towards observations of the fire-front. Finally, we incorporate our novel approaches into a Bayesian PINN (B-PINN) to provide uncertainty quantification in the fire-front predictions. This is significant as the standard solver, the level-set method, does not naturally offer the capability for data assimilation and uncertainty quantification. Our results show that, with our novel approaches, the B-PINN can produce accurate predictions with high quality uncertainty quantification on real-world data.Comment: Accepted for publication in Spatial Statistic

Nuclear Magnetic Resonance and Magnetization Studies of the Ferromagnetic Ordering Temperature Suppression in Ru Deficient SrRuO3

The synthesis of SrRuO3 under high-pressure oxygen produces a nonstoichiometric form with randomly distributed vacancies on the Ru-sites, along with a significantly reduced ferromagnetic ordering temperature. In order to gain additional insight into the suppression of the ferromagnetism, local studies utilizing 99,101 Ru zero-field spin-echo NMR, and Ru K-edge XAFS, along with complimentary magnetization and x-ray diffraction measurements, have been carried out on samples of SrRuO3 annealed at both ("ambient") atmospheric pressure and "high-pressure" oxygen (600 atm). Consistent with previous work, the NMR spectrum for "ambient" SrRuO3 consists of two well-defined peaks at 64.4 MHz and 72.2 MHz corresponding to the 99Ru and 101Ru isotopes, respectively, and a hyperfine field of 329 kG. Although the magnetization measurements show a lower ferromagnetic ordering temperature for the "high-pressure" oxygen sample (90 K compared to 160 K for the "ambient" sample), the NMR spectrum shows no significant shift in the two peak frequencies. However, the two peaks exhibit considerable broadening, along with structure on both the low and high frequency sides which is believed to be quadrupolar in origin. Analysis of the Ru K-edge XAFS reveals more disorder in the Ru-O bond for the "high-pressure" oxygen sample compared to the "ambient" sample. Furthermore, XANES of Ru K-edge analysis indicates no difference in the valence of Ru between the two samples. The magnetic behavior indicates the existence of some vacancies on the Ru sites for the "high-pressure" oxygen sample.Comment: Proceedings of the 3rd Polish-US Workshop on Magnetism and Superconductivity of Advanced Materials, July 14-19, 2002, Ladek Zdroj (Poland), to appear in Physica

A survey of spectral models of gravity coupled to matter

This is a survey of the historical development of the Spectral Standard Model and beyond, starting with the ground breaking paper of Alain Connes in 1988 where he observed that there is a link between Higgs fields and finite noncommutative spaces. We present the important contributions that helped in the search and identification of the noncommutative space that characterizes the fine structure of space-time. The nature and properties of the noncommutative space are arrived at by independent routes and show the uniqueness of the Spectral Standard Model at low energies and the Pati-Salam unification model at high energies.Comment: An appendix is added to include scalar potential analysis for a Pati-Salam model. 58 Page

An intelligent interface for integrating climate, hydrology, agriculture, and socioeconomic models

Understanding the interactions between natural processes and human activities poses major challenges as it requires the integration of models and data across disparate disciplines. It typically takes many months and even years to create valid end-to-end simulations as different models need to be configured in consistent ways and generate data that is usable by other models. MINT is a novel framework for model integration that captures extensive knowledge about models and data and aims to automatically compose them together. MINT guides a user to pose a well-formed modeling question, select and configure appropriate models, find and prepare appropriate datasets, compose data and models into end-to-end workflows, run the simulations, and visualize the results. MINT currently includes hydrology, agriculture, and socioeconomic models.Office of the VP for Researc

Molecular excitation in the Interstellar Medium: recent advances in collisional, radiative and chemical processes

We review the different excitation processes in the interstellar mediumComment: Accepted in Chem. Re