Extremal Values of the Interval Number of a Graph

The interval number $i( G )$ of a simple graph $G$ is the smallest number $t$ such that to each vertex in $G$ there can be assigned a collection of at most $t$ finite closed intervals on the real line so that there is an edge between vertices $v$ and $w$ in $G$ if and only if some interval for $v$ intersects some interval for $w$. The well known interval graphs are precisely those graphs $G$ with $i ( G )\leqq 1$. We prove here that for any graph $G$ with maximum degree $d, i ( G )\leqq \lceil \frac{1}{2} ( d + 1 ) \rceil$. This bound is attained by every regular graph of degree $d$ with no triangles, so is best possible. The degree bound is applied to show that $i ( G )\leqq \lceil \frac{1}{3}n \rceil$ for graphs on $n$ vertices and $i ( G )\leqq \lfloor \sqrt{e} \rfloor$ for graphs with $e$ edges

Pro Se Aspects of Hampden County Housing Court: Helping People Help Themselves

Great changes in American life have occurred over the last score of years. With these changes has come an increasing public interest in the law and how it affects individual rights. This growing interest may account for alterations in the administration of the law and in the legal profession itself. Today, attorneys find themselves hard-pressed to stay abreast of the ever-broadening law, as each decision weaves greater detail and specificity into the older law. While the public continues to demand judicial resolutions to societal problems, the need for professional legal expertise in many routine legal matters is being questioned. It is often thought that laymen should be allowed to perform some of these tasks themselves. The legal profession itself is beginning to realize that some matters cost far more to handle than lawyers can properly charge. Often clients are better off doing some things for themselves, or having paralegals rather than lawyers perform the more routine services. Public pressures to enable individuals to handle simple legal matters without attorneys have led to an increasing use of the courts by unrepresented parties. The extension of prose adjudication into the realm of landlord-tenant problems partially explains the creation of courts like the Hampden County Housing Court. The Hampden County Housing Court began operation two years after the establishment of the Boston Housing Court. Hampden County tenants responsible for the court\u27s creation cited the need for a specialized housing court since the district courts could not adequately deal with housing problems on a timely basis due to its crowded schedule and because the right to appeal to the higher superior court was nondiscretionary. Additionally, the tenants felt that the juxtaposition of housing-related cases with the usual district court docket of more serious crimes would make housing matters appear relatively less important to the presiding judges. With the advent of the Boston Housing Court in 1971 at a superior court level, a forum was created where urban housing cases could be heard by judges in a specialized atmosphere and with the assistance of a specially trained staff. In Springfield, the Commonwealth\u27s second largest city, support for a second housing court was not widespread until fire destroyed a condemned, but still occupied house, taking the lives of two small children. The result was the bill creating the Hampden County Housing Court, the first housing court in the nation with county-wide jurisdiction able to deal with urban, suburban and rural housing cases. The atmosphere of a people\u27s court surrounded the housing court from its early stages, when the governor agreed to allow an ad hoc public committee to participate in interviewing and recommending candidates for both the judge and clerk of the new court. A Citizens Advisory Committee to the court was created as a result. These actions helped to create the impression that the rules followed in other courts need not necessarily apply in the Hampden County Housing Court. In addition, the Massachusetts Supreme Court in Commonwealth v. Haddad affirmed the right of a private citizen to enter complaints for a violation of the law, thus confirming the status of a citizen complainant in a criminal proceeding seeking to enforce the state sanitary code. This decision allowed the courts to take complaints from citizens when municipal officials failed to act. Of course, the conception of the housing court as a free-form court operating with different rules is false. Hampden County Housing Court operates under the same rules of criminal procedure as the district courts of the Commonwealth, and under the same civil rules and appellate rules as the superior courts of the Commonwealth with a few exceptions. The most important special rules concern the right to transfer any case within the county to the housing court simply by filing a transfer form and the right to accept a written report from a housing, building or other governmental inspector into evidence without requiring that the inspector be in court to give testimony. By giving the court concurrent jurisdiction with both district and superior courts, the advantages of both courts are gained. Additionally, equity powers which district courts lack, and the right of appeal to the Commonwealth\u27s Appeals Court which negates appeals for the sake of delay are realized. These few rule changes do not amount to a people\u27s court. Rather, they create an aura of service and openness to the people who use the courts and pay the salaries. In addition, two positive steps have been taken to help citizens more easily use the court

Flux networks in metabolic graphs

A metabolic model can be represented as bipartite graph comprising linked reaction and metabolite nodes. Here it is shown how a network of conserved fluxes can be assigned to the edges of such a graph by combining the reaction fluxes with a conserved metabolite property such as molecular weight. A similar flux network can be constructed by combining the primal and dual solutions to the linear programming problem that typically arises in constraint-based modelling. Such constructions may help with the visualisation of flux distributions in complex metabolic networks. The analysis also explains the strong correlation observed between metabolite shadow prices (the dual linear programming variables) and conserved metabolite properties. The methods were applied to recent metabolic models for Escherichia coli, Saccharomyces cerevisiae, and Methanosarcina barkeri. Detailed results are reported for E. coli; similar results were found for the other organisms.Comment: 9 pages, 4 figures, RevTeX 4.0, supplementary data available (excel

Compendium of Chemical Carcinogens by Target Organ: Results of Chronic Bioassays in Rats, Mice, Hamsters, Dogs, and Monkeys

Acompendiumof carcinogenesi s bioassay results organized by target organ is presented for 738 chemicals that are carcinogenic in chronic-exposure , long-term bioassays in at least 1 species. This compendium is based primarily on experiments in rats or mice; results in hamsters, monkeys, and dogs are also reported. The compendium can be used to identify chemicals that induce tumors at particular sites and to determine whether target sites are the same for chemicals positive in more than 1 species. The source of information is the Carcinogeni c Potency Database (CPDB), which includes results of 6073 experiments on 1458 chemicals (positive or negative for carcinogenicity) that have been reported in Technical Reports of the National Cancer Institute/National Toxicology Program or in papers in the general published literature. The published CPDB includes detailed analyses of each test and citations. The CPDB is publicly available in several formats (http://potency.berkeley.edu). Chemical carcinogens are reported for 35 different target organs in rats or mice. Target organs in humans are also summarized for 82 agents that have been evaluated as human carcinogens at a particular target site by the International Agency for Research on Cancer (IARC). Comparisons are provided of target organs for mutagens versus nonmutagens and rats versus mice

Forage or Biofuel: Assessing Native Warm-season Grass Production among Seed Mixes and Harvest Frequencies within a Wildlife Conservation Framework

Native warm-season grasses (NWSG) are gaining merit as biofuel feedstocks for ethanol production with potential for concomitant production of cattle forage and wildlife habitat provision. However, uncertainty continues regarding optimal production approaches for biofuel yield and forage quality within landscapes of competing wildlife conservation objectives. We used a randomized complete block design of 4 treatments to compare vegetation structure, forage and biomass nutrients, and biomass yield between Panicum virgatum (Switchgrass) monocultures and NWSG polycultures harvested once or multiple times near West Point, MS, 2011–2013. Despite taller vegetation and greater biomass in Switchgrass monocultures, NWSG polycultures had greater vegetation structure heterogeneity and plant diversity that could benefit wildlife. However, nutritional content from harvest timings optimal for wildlife conservation (i.e., late dormant season-collected biomass and mid-summer hay samples) demonstrated greater support for biofuel production than quality cattle forage. Future research should consider testing various seed mixes for maximizing biofuel or forage production among multiple site conditions with parallel observations of wildlife use