On the Design, Analysis, and Implementation of Algorithms for Selected Problems in Graphs and Networks

This thesis studies three problems in network optimization, viz., the minimum spanning tree verification (MSTV) problem, the undirected negative cost cycle detection (UNCCD) problem, and the negative cost girth (NCG) problem. These problems find applications in several domains including program verification, proof theory, real-time scheduling, social networking, and operations research.;The MSTV problem is defined as follows: Given an undirected graph G = (V,E) and a spanning tree T, is T a minimum spanning tree of G? We focus on the case where the number of distinct edge weights is bounded. Using a bucketed data structure to organize the edge weights, we present an efficient algorithm for the MSTV problem, which runs in O (| E| + |V| · K) time, where K is the number of distinct edge weights. When K is a fixed constant, this algorithm runs in linear time. We also profile our MSTV algorithm with the current fastest known MSTV implementation. Our results demonstrate the superiority of our algorithm when K ≤ 24.;The UNCCD problem is defined as follows: Given an undirected graph G = (V,E) with arbitrarily weighted edges, does G contain a negative cost cycle? We discuss two polynomial time algorithms for solving the UNCCD problem: the b-matching approach and the T-join approach. We obtain new results for the case where the edge costs are integers in the range {lcub}--K ·· K{rcub}, where K is a positive constant. We also provide the first extensive empirical study that profiles the discussed UNCCD algorithms for various graph types, sizes, and experiments.;The NCG problem is defined as follows: Given a directed graph G = (V,E) with arbitrarily weighted edges, find the length, or number of edges, of the negative cost cycle having the least number of edges. We discuss three strongly polynomial NCG algorithms. The first NCG algorithm is known as the matrix multiplication approach in the literature. We present two new NCG algorithms that are asymptotically and empirically superior to the matrix multiplication approach for sparse graphs. We also provide a parallel implementation of the matrix multiplication approach that runs in polylogarithmic parallel time using a polynomial number of processors. We include an implementation profile to demonstrate the efficiency of the parallel implementation as we increase the graph size and number of processors. We also present an NCG algorithm for planar graphs that is asymptotically faster than the fastest topology-oblivious algorithm when restricted to planar graphs

Combining active restoration and targeted grazing to establish native plants and reduce fuel loads in invaded ecosystems

Many drylands have been converted from perennial-dominated ecosystems to invaded, annual-dominated, fire-prone systems. Innovative approaches are needed to disrupt fire-invasion feedbacks. Targeted grazing can reduce invasive plant abundance and associated flammable fuels, and fuelbreaks can limit fire spread. Restored strips of native plants (native greenstrips) can function as fuelbreaks while also providing forage and habitat benefits. However, methods for establishing native greenstrips in invaded drylands are poorly developed. Moreover, if fuels reduction and greenstrip establishment are to proceed simultaneously, it is critical to understand how targeted grazing interacts with plant establishment. We determined how targeted grazing treatments interacted with seed rate, spatial planting arrangement (mixtures vs. monoculture strips), seed coating technology, and species identity (five native grasses) to affect standing biomass and seeded plant density in experimental greenstrips. We monitored for two growing seasons to document effects during the seedling establishment phase. Across planting treatments, ungrazed paddocks had the highest second-year seeded plant densities and the highest standing biomass. Paddocks grazed in fall of the second growing season had fewer seedlings than paddocks grazed in spring, five months later. High seed rates minimized negative effects of grazing on plant establishment. Among seeded species, Elymus trachycaulus and Poa secunda had the highest second-year densities, but achieved this via different pathways. Elymus trachycaulus produced the most first-year seedlings, but declined in response to grazing, whereas P. secunda had moderate first-year establishment but high survival across grazing treatments. We identified clear tradeoffs between reducing fuel loads and establishing native plants in invaded sagebrush steppesimilar tradeoffs may exist in other invaded drylands. In our system, tradeoffs were minimized by boosting seed rates, using grazing-tolerant species, and delaying grazing. In invaded ecosystems, combining targeted grazing with high-input restoration may create opportunities to limit wildfire risk while also shifting vegetation toward more desirable species

N-Doped Fe@CNT for Combined RWGS/FT CO ₂ Hydrogenation

The conversion of CO₂ into chemical fuels represents an attractive route for greenhouse gas emission reductions and renewable energy storage. Iron nanoparticles supported on graphitic carbon materials (e.g., carbon nanotubes (CNTs)) have proven themselves to be effective catalysts for this process. This is due to their stability and ability to support simultaneous reverse water-gas shift (RWGS) and Fischer–Tropsch (FT) catalysis. Typically, these catalytic iron particles are postdoped onto an existing carbon support via wet impregnation. Nitrogen doping of the catalyst support enhances particle–support interactions by providing electron-rich anchoring sites for nanoparticles during wet impregnation. This is typically credited for improving CO₂ conversion and product selectivity in subsequent catalysis. However, the mechanism for RWGS/FT catalysis remains underexplored. Current research places significant emphasis on the importance of enhanced particle–support interactions due to N doping, which may mask further mechanistic effects arising from the presence or absence of nitrogen during CO₂ hydrogenation. Here we report a clear relationship between the presence of nitrogen in the CNT support of an RWGS/FT iron catalyst and significant shifts in the activity and product distribution of the reaction. Particle–support interactions are maximized (and discrepancies between N-doped and pristine support materials are minimized) by incorporating iron and nitrogen directly into the support during synthesis. Reactivity is thus rationalized in terms of the influence of C–N dipoles in the support upon the adsorption properties of CO₂ and CO on the surface rather than improved particle–support interactions. These results show that the direct hydrogenation of CO₂ to hydrocarbons is a potentially viable route to reduce carbon emissions from human activities

The orbits of the quadruple star system 88 Tau A from PHASES differential astrometry and radial velocity

We have used high precision differential astrometry from the Palomar High-precision Astrometric Search for Exoplanet Systems (PHASES) project and radial velocity measurements covering a time-span of 20 years to determine the orbital parameters of the 88 Tau A system. 88 Tau is a complex hierarchical multiple system comprising a total of six stars; we have studied the brightest 4, consisting of two short-period pairs orbiting each other with an 18-year period. We present the first orbital solution for one of the short-period pairs, and determine the masses of the components and distance to the system to the level of a few percent. In addition, our astrometric measurements allow us to make the first determination of the mutual inclinations of the orbits. We find that the sub-systems are not coplanar.Comment: Corrected Author Ordering; 12 Pages, Accepted for publication in Ap

Modal Platonism and the problem of negativity.

The Platonic account of modality says, roughly, that truths about alien possibilities are grounded in uninstantiated universals. Recently, Ingram has raised a problem for this kind of view, which is that it apparently requires negative facts to play a truthmaking role. Ingram offers an alternative Platonic account which makes use of modal instantiation relations. In this paper, I highlight some of the costs of Ingram’s new account and argue that a more appealing version of Platonism—and modal theory in general—is one that is supplemented with an ontology of totality facts

Electronic Structure, Pore Size Distribution, and Sorption Characterization of an Unusual MOF, {[Ni(dpbz)][Ni(CN)\u3csub\u3e4\u3c/sub\u3e]}n, dpbz = 1,4-bis(4-pyridyl)benzene

The monoclinic (Ni(L)[Ni(CN)4] (L= 1,4-Bis(4-pyridyl) benzene) compound (defined as Ni-dpbz) is a flexible metal organic framework which assumes a pillared structure with layers defined by 2D Ni[Ni(CN)4]n nets and dpbz ligands as pillars. The structure features an entrapped dpbz ligand that links between the open ends of four-fold Ni sites from two neighboring chains. This arrangement results in an unusual 5-fold pseudo square-pyramid environment for Ni and a significantly long Ni-N distance of 2.369(4) Å. Using Density Functional Theory calculations, the different bonding characteristics between the 5-fold and 6-fold Ni\u27s were determined. We found that there is weak covalent bonding between the 5-fold Ni and N in the entrapped ligand, and the 6-fold Ni-N bonds provide effective electronic conduction. The disordered dimethyl sulfoxide (DMSO) solvent molecules are not bonded to the framework. The material has a single pore with a diameter of 4.1 Å. This pore includes approximately 55% of the total free volume (based on a zero-diameter probe). The accessible pore surface area and pore volume were calculated to be 507 m2/g and 6.99 cm3/kg, respectively. The maximum amount of CO2 that can be accommodated in the pores after DMSO is removed was found to be 204 mg/g, agreeing with the results of adsorption/desorption experiments of about 220 mg/g

Detecting the Companions and Ellipsoidal Variations of RS CVn Primaries: II. omicron Draconis, a Candidate for Recent Low-Mass Companion Ingestion

To measure the stellar and orbital properties of the metal-poor RS CVn binary o Draconis (o Dra), we directly detect the companion using interferometric observations obtained with the Michigan InfraRed Combiner at Georgia State University's Center for High Angular Resolution Astronomy (CHARA) Array. The H-band flux ratio between the primary and secondary stars is the highest confirmed flux ratio (370 +/- 40) observed with long-baseline optical interferometry. These detections are combined with radial velocity data of both the primary and secondary stars, including new data obtained with the Tillinghast Reflector Echelle Spectrograph on the Tillinghast Reflector at the Fred Lawrence Whipple Observatory and the 2-m Tennessee State University Automated Spectroscopic Telescope at Fairborn Observatory. We determine an orbit from which we find model-independent masses and ages of the components (M_A = 1.35 +\- 0.05 M_Sun, M_B = 0.99 +\- 0.02 M_Sun, system age = 3.0 -\+ 0.5 Gyr). An average of a 23-year light curve of o Dra from the Tennessee State University Automated Photometric Telescope folded over the orbital period newly reveals eclipses and the quasi-sinusoidal signature of ellipsoidal variations. The modeled light curve for our system's stellar and orbital parameters confirm these ellipsoidal variations due to the primary star partially filling its Roche lobe potential, suggesting most of the photometric variations are not due to stellar activity (starspots). Measuring gravity darkening from the average light curve gives a best-fit of beta = 0.07 +\- 0.03, a value consistent with conventional theory for convective envelope stars. The primary star also exhibits an anomalously short rotation period, which, when taken with other system parameters, suggests the star likely engulfed a low-mass companion that had recently spun-up the star.Comment: 14 pages, 13 figures, Accepted to Ap