A Hike Through the Forest: The Knapsack Problem in Graph Theory

Graph theory is a branch of mathematics which studies graphs a collection of a set of edges and vertices used to sometimes model structures. My interest in graph theory began last semester in a math/computer science course entitled “Discrete Structures. One aspect which makes graph theory an appealing area to research is the amount of understanding that comes from a relatively short amount of time spent learning the subject material. The visual appeal of being able to draw a graph along practical applications that surface daily make graph theory a prime candidate for further research. Through research of the history of graph theory, reading of research papers, and manipulation of theorems and definitions, the importance of communication within the realm of mathematics is discovered, resulting in an appreciation of what math research entails. By learning more about open graph theory research problems and seeing how many of the problems, if solved, provide a solution for many other research problems, the importance of math research, specifically graph theory research, is demonstrated. After deepening knowledge about definitions of terms, solving home- work problems and proving theorems, I selected a certain subset of graph theory, namely the Knapsack combinatorial optimization problem, to try to create new techniques for obtaining approximations of solutions. Through experimentation and trial and error, conclusions are drawn about the open research problem. As a result of performing independent undergraduate research in graph theory, graduate math research is experienced in preparation for graduate school, reiterating the importance of verbal and writ- ten communication of mathematical concepts and ideas while deepening my mathematical appreciation and understanding of graph theory

Directions of seismic anisotropy in laboratory models of mantle plumes

A recent expansion in global seismic anisotropy data provides important new insights about the style of mantle convection. Interpretations of these geophysical measurements rely on complex relationships between mineral physics, seismology, and mantle dyn

Patterns in seismic anisotropy driven by rollback subduction beneath the High Lava Plains

We present three-dimensional laboratory modeling of the evolution of finite strain and compare these to shear wave splitting observations in the Northwest U.S. under the High Lava Plains (HLP). We show that relationships between mantle flow and anisotropy are complicated in subduction zones and factors such as initial orientation of the olivine fast-axis, style of subduction, and time evolving flow are important. Due to increased horizontal shear, systems with a component of rollback subduction have simple trench-normal strain alignment within the central region of the backarc mantle wedge while those with more simple longitudinal sinking are often variable and complex. In the HLP, splitting observations are consistent with rollback-driven laboratory results. © 2011 by the American Geophysical Union

Strings, Bears, & Boards: Making Fractions Meaning-filled (pp. 54--60)

To successfully operate with fractions, decimals and percents, it is imperative to first provide pre-service teachers the opportunity for making sense of the meaning of fractions. The Common Core State Standards and associated Progressions document provide guidelines for building fraction understanding. In this article, the authors present a series of fraction meaning activities designed for pre-service teachers that have been implemented and improved through ten iterations of lesson study. The activities use physical models that link pre-service elementary teachers’ fraction reasoning to Common Core Standards. Using string, counting bears, and geoboards, these meaningful fraction activities show how a copies of 1/b of some whole, or a/b, can be seen in linear, discrete, and area contexts.

Bifurcation of the Yellowstone plume driven by subduction-induced mantle flow

The causes of volcanism in the northwestern United States over the past 20 million years are strongly contested. Three drivers have been proposed: melting associated with plate subduction; tectonic extension and magmatism resulting from rollback of a sub

Plume-slab interaction: The Samoa-Tonga system

Mantle plume behavior near subducting plates is still poorly understood and in fact varies significantly from the classical hotspot model. We investigate using 3D laboratory models how subduction-driven flow relates to the deformation and dispersal of a nearby plume. Results show slab-driven flow severely distorts plume-driven flow, entraining and passively advecting plume material despite its thermal buoyancy. Downdip sinking of the slab initially stalls vertical plume ascent while the combination of downdip and rollback sinking motions redistribute material throughout the system. As a consequence of the subduction-induced flow, surface expressions differ significantly from traditional plume expectations. Variations in slab sinking style and plume position lead to a range in head and conduit melting signatures, as well as migrating hotspots. For the Samoa-Tonga system, model predictions are consistent with proposed entrainment of plume material around the subducting plate

Directions of seismic anisotropy in laboratory models of mantle plumes

A recent expansion in global seismic anisotropy data provides important new insights about the style of mantle convection. Interpretations of these geophysical measurements rely on complex relationships between mineral physics, seismology, and mantle dynamics. We report on 3-D laboratory experiments using finite strain markers evolving in time-dependent, viscous flow fields to quantify the range in expected anisotropy patterns within buoyant plumes surfacing in a variety of tectonic settings. A surprising result is that laboratory proxies for the olivine fast axis overwhelmingly align tangential to radial outflow in plumes well before reaching the surface. These remarkably robust, and ancient, anisotropy patterns evolve differently in stagnant, translational, and divergent plate tectonic settings and are essentially orthogonal to patterns typically referenced when prospecting for plume signals in seismic data. Results suggest a fundamental change in the mineral physics-seismology-circulation relationship used in accepting or rejecting a plume model. © 2013. American Geophysical Union. All Rights Reserved

Bifurcation of the Yellowstone plume driven by subduction-induced mantle flow

The causes of volcanism in the northwestern United States over the past 20 million years are strongly contested. Three drivers have been proposed: melting associated with plate subduction; tectonic extension and magmatism resulting from rollback of a subducting slab; or the Yellowstone mantle plume. Observations of the opposing age progression of two neighbouring volcanic chains - the Snake River Plain and High Lava Plains - are often used to argue against a plume origin for the volcanism. Plumes are likely to occur near subduction zones, yet the influence of subduction on the surface expression of mantle plumes is poorly understood. Here we use experiments with a laboratory model to show that the patterns of volcanism in the northwestern United States can be explained by a plume upwelling through mantle that circulates in the wedge beneath a subduction zone. We find that the buoyant plume may be stalled, deformed and partially torn apart by mantle flow induced by the subducting plate. Using plausible model parameters, bifurcation of the plume can reproduce the primary volcanic features observed in the northwestern United States, in particular the opposite progression of two volcanic chains. Our results support the presence of the Yellowstone plume in the northwestern United States, and also highlight the power of plume-subduction interactions to modify surface geology at convergent plate margins

ACCESS datasets for CMIP6: methodology and idealised experiments

The Australian Community Climate and Earth System Simulator (ACCESS) has contributed to the World Climate Research Programme’s Coupled Model Intercomparison Project Phase 6 (CMIP6) using two fully coupled model versions (ACCESS-CM2 and ACCESS-ESM1.5) and two ocean–sea-ice model versions (1° and 0.25° resolution versions of ACCESS-OM2). The fully coupled models differ primarily in the configuration and version of their atmosphere components (including the aerosol scheme), with smaller differences in their sea-ice and land model versions. Additionally, ACCESS-ESM1.5 includes biogeochemistry in the land and ocean components and can be run with an interactive carbon cycle. CMIP6 comprises core experiments and associated thematic Model Intercomparison Projects (MIPs). This paper provides an overview of the CMIP6 submission, including the methods used for the preparation of input forcing datasets and the post-processing of model output, along with a comprehensive list of experiments performed, detailing their initialisation, duration, ensemble number and computational cost. A small selection of model output is presented, focusing on idealised experiments and their variants at global scale. Differences in the climate simulation of the two coupled models are highlighted. ACCESS-CM2 produces a larger equilibrium climate sensitivity (4.7°C) than ACCESS-ESM1.5 (3.9°C), likely a result of updated atmospheric parameterisation in recent versions of the atmospheric component of ACCESS-CM2. The idealised experiments run with ACCESS-ESM1.5 show that land and ocean carbon fluxes respond to both changing atmospheric CO2 and to changing temperature. ACCESS data submitted to CMIP6 are available from the Earth System Grid Federation (https://doi.org/10.22033/ESGF/CMIP6.2281 and https://doi.org/10.22033/ESGF/CMIP6.2288). The information provided in this paper should facilitate easier use of these significant datasets by the broader climate community

Plume Subduction Beneath the Neuquén Basin and the Last Mountain Building Stage of the Southern Central Andes

The occurrence of a Neogene shallow subduction stage, as well as, a Pliocene slab-tearing, and steepening of the Nazca plate in the southern Central Andes are well established. However, a satisfactory explanation for the origin and connection between these complex processes is still elusive. In this contribution, we revise the late Cenozoic tectonic and magmatic evolution of the southern Central Andes between 35° and 38° S and discuss different proposals for the Miocene slab shallowing and its Pliocene destabilization. Recent plate kinematic reconstructions show that Neogene arc-front expansion linked to slab shallowing, fold belt reactivation in the main cordillera and intraplate contraction in the San Rafael Block correlates with the subduction of the ancient Payenia plume, a deep mantle anomaly potentially rooted in the lower mantle. Also, the Nazca slab tear determined from tomographic analyses and subsequent slab steepening may also be a direct consequence of this plume subduction process. Considering the westward drift of South America and the presence of several neighbor hotspots over the Nazca plate, the Payenia plume overriding could be the first of future episodes of plume?trench interaction in the Andes.Fil: Gianni, Guido Martin. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Estudios Andinos "Don Pablo Groeber". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Estudios Andinos "Don Pablo Groeber"; Argentina. Universidad Nacional de San Juan. Facultad de Ciencias Exactas, Físicas y Naturales. Instituto Geofísico Sismológico Volponi; ArgentinaFil: Pesce, Agustina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Juan; Argentina. Universidad Nacional de San Juan. Facultad de Ciencias Exactas, Físicas y Naturales. Instituto Geofísico Sismológico Volponi; ArgentinaFil: García, Luciano Héctor. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Juan; Argentina. Universidad Nacional de San Juan. Facultad de Ciencias Exactas, Físicas y Naturales. Instituto Geofísico Sismológico Volponi; ArgentinaFil: Lupari, Marianela Nadia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Juan; Argentina. Universidad Nacional de San Juan. Facultad de Ciencias Exactas, Físicas y Naturales. Instituto Geofísico Sismológico Volponi; ArgentinaFil: Correa Otto, Sebastian Ariel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Juan; Argentina. Universidad Nacional de San Juan. Facultad de Ciencias Exactas, Físicas y Naturales. Instituto Geofísico Sismológico Volponi; ArgentinaFil: Nacif Suvire, Silvina Valeria. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Juan; Argentina. Universidad Nacional de San Juan. Facultad de Ciencias Exactas, Físicas y Naturales. Instituto Geofísico Sismológico Volponi; ArgentinaFil: Folguera Telichevsky, Andres. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Estudios Andinos "Don Pablo Groeber". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Estudios Andinos "Don Pablo Groeber"; Argentin