Zero Forcing Parameters And Minimum Rank Problems, 2017 University of Tennessee, Chattanooga

#### Zero Forcing Parameters And Minimum Rank Problems, Francesco Barioli, Wayne Barrett, Shaun M. Fallat, H. Tracy Hall, Leslie Hogben, Bryan Shader, P. Van Den Driessche, Hein Van Der Holst

*Leslie Hogben*

The zero forcing number Z(G), which is the minimum number of vertices in a zero forcing set of a graph G, is used to study the maximum nullity/minimum rank of the family of symmetric matrices described by G. It is shown that for a connected graph of order at least two, no vertex is in every zero forcing set. The positive semidefinite zero forcing number Z+(G) is introduced, and shown to be equal to |G|-OS(G), where OS(G) is the recently defined ordered set number that is a lower bound for minimum positive semidefinite rank ...

Propagation Time For Zero Forcing On A Graph, 2017 Iowa State University

#### Propagation Time For Zero Forcing On A Graph, Leslie Hogben, My Huynh, Nicole Kingsley, Sarah Meyer, Shanise Walker, Michael Young

*Leslie Hogben*

Zero forcing (also called graph infection) on a simple, undirected graph G is based on the color-change rule: if each vertex of G is colored either white or black, and vertex v is a black vertex with only one white neighbor w, then change the color of w to black. A minimum zero forcing set is a set of black vertices of minimum cardinality that can color the entire graph black using the color change rule. The propagation time of a zero forcing set B of graph G is the minimum number of steps that it takes to force all ...

Techniques For Determining The Minimum Rank Of A Small Graph, 2017 Iowa State University

#### Techniques For Determining The Minimum Rank Of A Small Graph, Laura Deloss, Jason Grout, Leslie Hogben, Tracy Mckay, Jason Smith, Geoff Tims

*Leslie Hogben*

The minimum rank of a simple graph G is defined to be the smallest possible rank over all symmetric real matrices whose ijth entry (for i≠j) is nonzero whenever {i,j} is an edge in G and is zero otherwise. Minimum rank is a difficult parameter to compute. However, there are now a number of known reduction techniques and bounds that can be programmed on a computer; we have developed a program using the open-source mathematics software Sage to implement several techniques. We have also established several additional strategies for computation of minimum rank. These techniques have been used ...

Zero Forcing, Linear And Quantum Controllability For Systems Evolving On Networks, 2017 Aberystwyth University

#### Zero Forcing, Linear And Quantum Controllability For Systems Evolving On Networks, Daniel Burgarth, Domenico D'Alessandro, Leslie Hogben, Simone Severini, Michael Young

*Leslie Hogben*

We study the dynamics of systems on networks from a linear algebraic perspective. The control theoretic concept of controllability describes the set of states that can be reached for these systems. Our main result says that controllability in the quantum sense, expressed by the Lie algebra rank condition, and controllability in the sense of linear systems, expressed by the controllability matrix rank condition, are equivalent conditions. We also investigate how the graph theoretic concept of a zero forcing set impacts the controllability property; if a set of vertices is a zero forcing set, the associated dynamical system is controllable. These ...

Parameters Related To Tree-Width, Zero Forcing, And Maximum Nullity Of A Graph, 2017 University of Tennessee, Chattanooga

#### Parameters Related To Tree-Width, Zero Forcing, And Maximum Nullity Of A Graph, Francesco Barioli, Wayne Barrett, Shaun M. Fallat, Leslie Hogben, Bryan Shader, P. Van Den Driessche, Hein Van Der Holst

*Leslie Hogben*

Tree-width, and variants that restrict the allowable tree decompositions, play an important role in the study of graph algorithms and have application to computer science. The zero forcing number is used to study the maximum nullity/minimum rank of the family of symmetric matrices described by a graph. We establish relationships between these parameters, including several Colin de Verdière type parameters, and introduce numerous variations, including the minor monotone floors and ceilings of some of these parameters. This leads to new graph parameters and to new characterizations of existing graph parameters. In particular, tree-width, largeur d'arborescence, path-width, and proper ...

Expected Values Of Parameters Associated With The Minimum Rank Of A Graph, 2017 Brigham Young University

#### Expected Values Of Parameters Associated With The Minimum Rank Of A Graph, H. Tracy Hall, Leslie Hogben, Ryan R. Martin, Bryan Shader

*Leslie Hogben*

We investigate the expected value of various graph parameters associated with the minimum rank of a graph, including minimum rank/maximum nullity and related Colin de Verdière-type parameters. Let G(v,p) denote the usual Erdős-Rényi random graph on v vertices with edge probability p. We obtain bounds for the expected value of the random variables mr(G(v,p)), M(G(v,p)), ν(G(v,p)) and ξ(G(v,p)), which yield bounds on the average values of these parameters over all labeled graphs of order v.

Note On Nordhaus-Gaddum Problems For Colin De Verdière Type Parameters, 2017 Brigham Young University

#### Note On Nordhaus-Gaddum Problems For Colin De Verdière Type Parameters, Wayne Barrett, Shaun M. Fallat, H. Tracy Hall, Leslie Hogben

*Leslie Hogben*

We establish the bounds 4 3 6 b 6 b 6 p 2, where b and b are the Nordhaus-Gaddum sum upper bound multipliers, i.e., (G)+(G) 6 bjGj and (G)+(G) 6 bjGj for all graphs G, and and are Colin de Verdiere type graph parameters. The Nordhaus-Gaddum sum lower bound for and is conjectured to be jGj 2, and if these parameters are replaced by the maximum nullity M(G), this bound is called the Graph Complement Conjecture in the study of minimum rank/maximum nullity problems.

An Upper Bound For The Minimum Rank Of A Graph, 2017 Technion-Israel Institute of Technology

#### An Upper Bound For The Minimum Rank Of A Graph, Avi Berman, Shmuel Friedland, Leslie Hogben, Uriel G. Rothblum, Bryan Shader

*Leslie Hogben*

For a graph G of order n, the minimum rank of G is defined to be the smallest possible rank over all real symmetric n×n matrices A whose (i,j)th entry (for i≠j) is nonzero whenever {i,j} is an edge in G and is zero otherwise. We prove an upper bound for minimum rank in terms of minimum degree of a vertex is valid for many graphs, including all bipartite graphs, and conjecture this bound is true over for all graphs, and prove a related bound for all zero-nonzero patterns of (not necessarily symmetric) matrices. Most ...

A Linear Algebraic View Of Partition Regular Matrices, 2017 Iowa State University

#### A Linear Algebraic View Of Partition Regular Matrices, Leslie Hogben, Jillian Mcleod

*Leslie Hogben*

Rado showed that a rational matrix is partition regular over N if and only if it satisfies the columns condition. We investigate linear algebraic properties of the columns condition, especially for oriented (vertex-arc) incidence matrices of directed graphs and for sign pattern matrices. It is established that the oriented incidence matrix of a directed graph Γ has the columns condition if and only if Γ is strongly connected, and in this case an algorithm is presented to find a partition of the columns of the oriented incidence matrix with the maximum number of cells. It is shown that a sign ...

On The Graph Complement Conjecture For Minimum Rank, 2017 University of Tennessee, Chattanooga

#### On The Graph Complement Conjecture For Minimum Rank, Francesco Barioli, Wayne Barrett, Shaun M. Fallat, H. Tracy Hall, Leslie Hogben, Hein Van Der Holst

*Leslie Hogben*

The minimum rank of a graph has been an interesting and well studied parameter investigated by many researchers over the past decade or so. One of the many unresolved questions on this topic is the so-called graph complement conjecture, which grew out of a workshop in 2006. This conjecture asks for an upper bound on the sum of the minimum rank of a graph and the minimum rank of its complement, and may be classified as a Nordhaus–Gaddum type problem involving the graph parameter minimum rank. The conjectured bound is the order of the graph plus two. Other variants ...

Willingness To Pay For Clear Lake Cleanup, 2017 Iowa State University

#### Willingness To Pay For Clear Lake Cleanup, Christopher D. Azevedo, Joseph A. Herriges Sr., Catherine L. Kling

*Catherine Kling*

The water quality in Iowa’s lakes has been a hot topic lately. Concerns about the water quality in many of the state’s lakes have brought increased attention to the value of the lakes as a recreational resource. One lake that has experienced recent water quality problems, as well as the accompanying publicity, is Clear Lake, located in Cerro Gordo County.

Valuing Water Quality In Midwestern Lake Ecosystems, 2017 Iowa State University

#### Valuing Water Quality In Midwestern Lake Ecosystems, Kevin J. Egan, Joseph A. Herriges Sr., Catherine L. Kling, John A. Downing

*Catherine Kling*

As increased attention is focused on the issue of water quality in the state of Iowa, policymakers must grapple with the pressures of balancing federal water quality requirements, tight conservation budgets, and citizen concern for environmental preservation and restoration of Iowa’s water resources. Efforts to improve water quality typically entail significant costs, either in the form of state resources to fund cleanup efforts or private costs associated with altering land uses, farming practices, municipal treatment facility expansions, or other investments.

Research Needs And Challenges In The Few System: Coupling Economic Models With Agronomic, Hydrologic, And Bioenergy Models For Sustainable Food, Energy, And Water Systems, 2017 Iowa State University

#### Research Needs And Challenges In The Few System: Coupling Economic Models With Agronomic, Hydrologic, And Bioenergy Models For Sustainable Food, Energy, And Water Systems, Catherine L. Kling, Raymond W. Arritt, Gray Calhoun, David A. Keiser, John M. Antle, Jeffery G. Arnold, Miguel Carriquiry, Indrajeet Chaubey, Peter Christensen, Baskar Ganapathysubramanian, Philip Gassman, William Gutowski, Thomas W. Hertel, Gerritt Hoogenboom, Elena Irwin, Madhu Khanna, Pierre Mérel, Daniel J. Phaneuf, Andrew Plantinga, Stephen Polasky, Paul Preckel, Sergey Rabotyagov, Ivan Rudik, Silvia Secchi, Aaron Smith, Andrew Vanloocke, Calvin Wolter, Jinhua Zhao, Wendong Zhang

*Catherine Kling*

On October 12–13, a workshop funded by the National Science Foundation was held at Iowa State University in Ames, Iowa with a goal of identifying research needs related to coupled economic and biophysical models within the FEW system. Approximately 80 people attended the workshop with about half representing the social sciences (primarily economics) and the rest from the physical and natural sciences. The focus and attendees were chosen so that findings would be particularly relevant to SBE research needs while taking into account the critical connectivity needed between social sciences and other disciplines. We have identified several major gaps ...

The Optimality Of Using Marginal Land For Bioenergy Crops: Tradeoffs Between Food, Fuel, And Environmental Services, 2017 Iowa State University

#### The Optimality Of Using Marginal Land For Bioenergy Crops: Tradeoffs Between Food, Fuel, And Environmental Services, Adriana M. Valcu-Lisman, Catherine L. Kling, Philip W. Gassman

*Catherine Kling*

We assess empirically how agricultural lands should be used to produce the highest valued outputs, which include food, energy, and environmental goods and services. We explore efficiency tradeoffs associated with allocating land between food and bioenergy and use a set of market prices and nonmarket environmental values to value the outputs produced by those crops. We also examine the degree to which using marginal land for energy crops is an approximately optimal rule. Our empirical results for an agricultural watershed in Iowa show that planting energy crops on marginal land is not likely to yield the highest valued output.

Valuing Preservation And Improvements Of Water Quality In Clear Lake, 2017 Iowa State University

#### Valuing Preservation And Improvements Of Water Quality In Clear Lake, Christopher D. Azevedo, Joseph A. Herriges Sr., Catherine Kling

*Catherine Kling*

This report presents summary statistics and other results of a survey of Clear Lake visitors and residents. Drawing on survey results, the authors present information on recreational usage of the lake, attitudes of recreators and local residents toward possible watershed management changes, and estimates of visitors' and residents' willingness to pay for water quality improvements at the lake. Support for the survey was provided by the Iowa Department of Natural Resources.

Testing The Consistency Of Nested Logit Models With Utility Maximization, 2017 Iowa State University

#### Testing The Consistency Of Nested Logit Models With Utility Maximization, Joseph A. Herriges, Catherine L. Kling

*Catherine Kling*

The Nested Multinomial Logit (NMNL) model is used extensively in modeling consumer choices among discrete alternatives when the number of alternatives is large. Unfortunately, applied researchers often find that estimated NMNL models fail to meet the Daly-ZacharyMcFadden (DZM) sufficient conditions for consistency with stochastic utility maximization. Borsch-Supan (1990) provides a relaxed set of conditions to test for consistency. While these conditions are increasingly cited, they are seldom tested. This paper corrects and extends BorschSupan's Theorem 2, providing simple necessary conditions on first, second, and third derivatives of choice probabilities and a graph oft he bounds they place on dissimilarity ...

Least-Cost Control Of Agricultural Nutrient Contributions To The Gulf Of Mexico Hypoxic Zone, 2017 University of Washington

#### Least-Cost Control Of Agricultural Nutrient Contributions To The Gulf Of Mexico Hypoxic Zone, Sergey S. Rabotyagov, Todd Campbell, Manoj K. Jha, Hongli Feng, Philip W. Gassman, Lyubov A. Kurkalova, Sylvia Secchi, Catherine L. Kling

*Catherine Kling*

No abstract provided.

Impacts Of Climate Change On Hydrology, Water Quality And Crop Productivity In The Ohio-Tennessee River Basin, 2017 Iowa State University

#### Impacts Of Climate Change On Hydrology, Water Quality And Crop Productivity In The Ohio-Tennessee River Basin, Yiannis Panagopoulos, Philip W. Gassman, Raymond W. Arritt, Daryl E. Herzmann, Todd D. Campbell, Adriana Valcu, Manoj K. Jha, Catherine L. Kling, Raghavan Srinivasan, Michael White, Jeffrey G. Arnold

*Catherine Kling*

Nonpoint source pollution from agriculture is the main source of nitrogen and phosphorus in the stream systems of the Corn Belt region in the Midwestern US. The eastern part of this region is comprised of the Ohio-Tennessee River Basin (OTRB), which is considered a key contributing area for water pollution and the Northern Gulf of Mexico hypoxic zone. A point of crucial importance in this basin is therefore how intensive corn-based cropping systems for food and fuel production can be sustainable and coexist with a healthy water environment, not only under existing climate but also under climate change conditions in ...

Incentives To Boost Conservation Tillage Adoption, 2017 Iowa State University

#### Incentives To Boost Conservation Tillage Adoption, Lyubov A. Kurkalova, Catherine L. Kling

*Catherine Kling*

With increasing public demand for clear air and clean water, many inside and outside Washington, D.C., have suggested that federal farm income support should be tied to enhanced conservation practices.

Iowa’S Wetlands: Who Will Pay For Preservation?, 2017 Iowa State University

#### Iowa’S Wetlands: Who Will Pay For Preservation?, Joseph A. Herriges Sr., Catherine L. Kling

*Catherine Kling*

It is estimated that before the 1750s, Iowa had around 2.3 million acres of wetlands. Today, Iowa has about 35,000 acres, with over 98 percent of the original wetlands converted to other uses—primarily agricultural production.