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Let G be a simple graph on n vertices, and let S(G) be the class of all real-valued symmetric nxn matrices whose nonzero off-diagonal entries occur in exactly the positions corresponding to the edges of G. The smallest rank achieved by a matrix in S(G) is called the minimum rank of G, denoted mr(G). The maximum nullity achieved by a matrix in S(G) is denoted M(G). For each graph G, there is an associated minimum rank class, MR(G) consisting of all matrices A in S(G) with rank A = mr(G). Although no restrictions are applied to the diagonal entries of matrices in S(G), sometimes diagonal entries corresponding to specific vertices of G must be zero for all matrices in MR(G). These vertices are known as nil vertices (see [6]). In this paper I discuss some basic results about nil vertices in general and nil vertices in cographs and prove that cographs with a nil vertex of a particular form contain two other nil vertices symmetric to the first. I discuss several open questions relating to these results and a counterexample. I prove that for all cographs G without an induced complete tripartite graph with independent sets all of size 3, the zero-forcing number Z(G), a graph theoretic parameter, is equal to M(G). In fact this result holds for a slightly larger class of cographs and in particular holds for all threshold graphs. Lastly, I prove that the maximum of the minimum ranks of all cographs on n vertices is the floor of 2n/3.

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This study aims to investigate the issues concerning the implementation of the “Suicide Zero” policy  adopted  by  Region  Värmland  in  2015.  The  findings  of  this  study  showcase  the problematic  gap  between  policy,  implementation  and  the  actual  preventative  measures  for those  in  need.  Through  an  in-depth  analysis  of  the  implementation  process,  this  study illustrates how the preventative measures were influences by the political decisions made and how the process itself, long and bureaucratic both in a national an regional level, complicates the  understanding  of  who  is  responsible  for  what  in  the  political  arena  in  which  decisions were made. Keywords: implementation, ”Suicide Zero” policy, Region Värmland, implementation process

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Since the regulatory framework Basel II was implemented in 2007, banks have been allowed to develop internal risk models for quantifying the capital requirement. By using data on retail non-performing loans from Hoist Finance, the thesis assesses the Advanced Internal Ratings-Based approach. In particular, it focuses on how banks active in the non-performing loan industry, can risk-classify their loans despite limited data availability of the debtors. Moreover, the thesis analyses the effect of the maximum-recovery period on the capital requirement. In short, a comparison of five different mathematical models based on prior research in the field, revealed that the loans may be modelled by a two-step tree model with binary logistic regression and zero-inflated beta-regression, resulting in a maximum-recovery period of eight years. Still it is necessary to recognize the difficulty in distinguishing between low- and high-risk customers by primarily assessing rudimentary data about the borrowers. Recommended future amendments to the analysis in further research would be to include macroeconomic variables to better capture the effect of economic downturns. / Sedan det regulatoriska ramverket Basel II implementerades 2007, har banker tillåtits utveckla interna riskmodeller för att beräkna kapitalkravet. Genom att använda data på fallerade konsumentlån från Hoist Finance, utvärderar uppsatsen den avancerade interna riskklassificeringsmodellen. I synnerhet fokuserar arbetet på hur banker aktiva inom sektorn för fallerade lån, kan riskklassificera sina lån trots begränsad datatillgång om låntagarna. Dessutom analyseras effekten av maximala inkassoperioden på kapitalkravet. I sammandrag visade en jämförelse av fem modeller, baserade på tidigare forskning inom området, att lånen kan modelleras genom en tvåstegs trädmodell med logistisk regression samt s.k. zero-inflated beta regression, resulterande i en maximal inkassoperiod om åtta år. Samtidigt är det värt att notera svårigheten i att skilja mellan låg- och högriskslåntagare genom att huvudsakligen analysera elementär data om låntagarna. Rekommenderade tillägg till analysen i fortsatt forskning är att inkludera makroekonomiska variabler för att bättre inkorporera effekten av ekonomiska nedgångar.

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For centuries chemists have sought to improve humankind’s quality of life and address many of society’s most pressing needs through the development of chemical processes and synthesis of new compounds, often with phenomenal results. Unfortunately, there also are many examples where these chemicals have had unintended, detrimental consequences that are not apparent until years or decades after their initial use. There are numerous halogenated molecules in this category that are globally dispersed, resistant to natural degradation processes, bioaccumulative, and toxic to living organisms. Chemicals such as these are classified as persistent organic pollutants (POPs), and due to their negative environmental and health effects, they require safe, effective, and inexpensive means of remediation. This research focuses on the development and optimization of a reaction matrix capable of reductively dehalogenating several POPs. Initial experiments determined that powdered magnesium and 1% V/V acetic acid in absolute ethanol was the most effective system for degrading polychlorinated biphenyl (PCB), an extraordinarily recalcitrant environmental contaminant. Further studies showed that this matrix also was capable of degrading polychlorinated dibenzo-p-dioxins (PCDDs), polybrominated diphenyl ethers (PBDEs), and four organochlorine pesticides (OCPs); dieldrin, heptachlor, heptachlor epoxide, and chlordane. During this phase of testing, field samples contaminated with chlordane were washed with ethanol and this ethanol/chlordane solution was degraded using the same reaction matrix, thereby demonstrating this technology’s potential for “real-world” remediation projects. Finally, a set of experiments designed to provide some insight into the mechanism of dechlorination seems to indicate that two distinct processes are necessary for degradation to occur. First, the passivated iv outer layer of the magnesium must be removed in order to expose the zero-valent magnesium core. Next, an electron is transferred from the magnesium to the target molecule, causing the cleavage of the halide bond and the subsequent abstraction of either a hydrogen or proton from a solvent molecule. It is anticipated that an understanding of these fundamental chemical processes will allow this system to be tailored to a wide range of complex environmental media

No Child Left Behind and Race to the Top are Federal educational policies that have evoked criticism from teachers and administrators. Both policies extended the federal government’s reach into local education by tying federal funds to a school’s student growth and teacher effectiveness. With an increasing emphasis on economic mechanisms such as choice and competition, teachers’ effectiveness is now determined by standardized and quantifiable measurements. These policies have created a data driven and high stakes accountability culture within each school. Teachers are finding themselves in a new balancing act of recording quantifiable yearly progress for all students while trying to work against environmental factors that are out of their control. The rising trend to utilize a “no zero” homework policy under these new pressures merits investigation into its role within teacher culture and these current tensions. The recent call for anthropology to re-enter the classroom as a cultural site allows the researcher to provide context to the fluid relationships that often lead to the reproduction of or resistance against dominant ideology. Using the case study method, this ethnography employs the critical theory framework to examine policy impact on teacher culture and gain an understanding for how and why trends such as the “no zero” homework become a part of school policy. By looking at a “school of choice” and a traditional “feeder middle school,” this thesis gives context to how the local trends illuminate larger cultural shifts