Maximally Edge-Connected Realizations and Kundu's kk-factor Theorem

A simple graph $G$ with edge-connectivity $\lambda(G)$ and minimum degree $\delta(G)$ is maximally edge connected if $\lambda(G)=\delta(G)$. In 1964, given a non-increasing degree sequence $\pi=(d_{1},\ldots,d_{n})$, Jack Edmonds showed that there is a realization $G$ of $\pi$ that is $k$-edge-connected if and only if $d_{n}\geq k$ with $\sum_{i=1}^{n}d_{i}\geq 2(n-1)$ when $d_{n}=1$. We strengthen Edmonds's result by showing that given a realization $G_{0}$ of $\pi$ if $Z_{0}$ is a spanning subgraph of $G_{0}$ with $\delta(Z_{0})\geq 1$ such that $|E(Z_{0})|\geq n-1$ when $\delta(G_{0})=1$, then there is a maximally edge-connected realization of $\pi$ with $G_{0}-E(Z_{0})$ as a subgraph. Our theorem tells us that there is a maximally edge-connected realization of $\pi$ that differs from $G_{0}$ by at most $n-1$ edges. For $\delta(G_{0})\geq 2$, if $G_{0}$ has a spanning forest with $c$ components, then our theorem says there is a maximally edge-connected realization that differs from $G_{0}$ by at most $n-c$ edges. As an application we combine our work with Kundu's $k$-factor Theorem to find maximally edge-connected realizations with a $(k_{1},\dots,k_{n})$-factor for $k\leq k_{i}\leq k+1$ and present a partial result to a conjecture that strengthens the regular case of Kundu's $k$-factor theorem.Comment: 13 pages, 1 figur

User\u27s Manual for Tardigrade Risk Assessment

This user-guide provides instructions for operating Tardigrade 1.1.3, a cybersecurity software for Nollysoft, LLC. This guide instructs users step-by-step on how to set security controls, risk assessments, and administrative maintenance. Tardigrade 1.1.3 is a Risk Assessment Enterprise that evaluates the risk level of corporations and offers solutions to any security gaps within an organization. Tardigrade 1.1.3 is a role-based software that operates through three modules, Cybersecurity Assessment, Internal Control, and Security Requirement Traceability Matrix

Educating the Whole Child: Evidence of Health and Wellness Instruction in the Schools Serving Low-Income Students

Educators in the United States are expressing concern about student physical and mental well-being. Childhood obesity has more than doubled in the past three decades, and today, one in five children experiences symptoms of mental illness. Low-income children are especially subject to these conditions. The long-term consequences for the country as a whole are significant. Schools are particularly well placed to address these problems by supporting the well-being of the whole child. Efforts have begun in select schools and districts to incorporate health and wellness instruction into the school day. This study identifies existing health and wellness components that three participating Title I schools in one school district have incorporated into their health and wellness program. The study also examines how socioeconomically different students have responded both physically and psychologically to their school\u27s program. Findings from this mixed-methodological study indicate socioeconomically different students physically and psychologically respond to health and wellness in three important ways. First, low-income students at participating schools evidenced parents and children collectively engaging in regular physical activity. Higher-income students also identified parents as physically active, but parent physical activity regularly occurred separate from the child. Second, although all students expressed dissatisfaction with school lunches, the way students responded varied by student socioeconomic status and caused concern for district personnel. Psychologically, low-income students identified personal experiences with on-campus bullying or interpersonal conflict while more affluent students spoke to such situations as third party observers, or said bullying is not a problem at their school. School district stakeholders recognize that differences in leadership, staff, and resources exist at participating schools and have created three different health and wellness programmatic models. School A maximizes staff and volunteer enthusiasm to promote physical wellness, School B offers district health and wellness components provided to all schools, and School C takes strides to support mental wellness. This study delineates the programmatic constructs and student physical and psychological responses at the three schools to highlight the importance of school-based health and wellness reform. The study also discusses the relationship of the three programs to the Whole School, Whole Community, Whole Child model

Frequency-dependent selection by wild birds promotes polymorphism in model salamanders

<p>Abstract</p> <p>Background</p> <p>Co-occurrence of distinct colour forms is a classic paradox in evolutionary ecology because both selection and drift tend to remove variation from populations. Apostatic selection, the primary hypothesis for maintenance of colour polymorphism in cryptic animals, proposes that visual predators focus on common forms of prey, resulting in higher survival of rare forms. Empirical tests of this frequency-dependent foraging hypothesis are rare, and the link between predator behaviour and maintenance of variation in prey has been difficult to confirm. Here, we show that predatory birds can act as agents of frequency-dependent selection on terrestrial salamanders. Polymorphism for presence/absence of a dorsal stripe is widespread in many salamander species and its maintenance is a long-standing mystery.</p> <p>Results</p> <p>We used realistic food-bearing model salamanders to test whether selection by wild birds maintains a stripe/no-stripe polymorphism. In experimental manipulations, whichever form was most common was most likely to be attacked by ground-foraging birds, resulting in a survival advantage for the rare form.</p> <p>Conclusion</p> <p>This experiment demonstrates that frequency-dependent foraging by wild birds can maintain colour polymorphism in cryptic prey.</p

Frequency-dependent selection by wild birds promotes polymorphism in model salamanders

Background Co-occurrence of distinct colour forms is a classic paradox in evolutionary ecology because both selection and drift tend to remove variation from populations. Apostatic selection, the primary hypothesis for maintenance of colour polymorphism in cryptic animals, proposes that visual predators focus on common forms of prey, resulting in higher survival of rare forms. Empirical tests of this frequency-dependent foraging hypothesis are rare, and the link between predator behaviour and maintenance of variation in prey has been difficult to confirm. Here, we show that predatory birds can act as agents of frequency-dependent selection on terrestrial salamanders. Polymorphism for presence/absence of a dorsal stripe is widespread in many salamander species and its maintenance is a long-standing mystery. Results We used realistic food-bearing model salamanders to test whether selection by wild birds maintains a stripe/no-stripe polymorphism. In experimental manipulations, whichever form was most common was most likely to be attacked by ground-foraging birds, resulting in a survival advantage for the rare form. Conclusion This experiment demonstrates that frequency-dependent foraging by wild birds can maintain colour polymorphism in cryptic prey

Threshold Digraphs

A digraph whose degree sequence has a unique vertex labeled realization is called threshold. In this paper we present several characterizations of threshold digraphs and their degree sequences, and show these characterizations to be equivalent. Using this result, we obtain a new, short proof of the Fulkerson-Chen theorem on degree sequences of general digraphs

Field-scale simulation of matrix-fracture interactions

Simulation of flow in fractured media continues to be among the most challenging problems faced in geothermal reservoir engineering. Because of a lack of information regarding specific matrix-fracture characteristics (e.g., fracture distribution, spacing, and aperture, and interfacial area for exchange of fluid), explicit representation of the reservoir is generally not feasible. Instead, a multiple (but usually dual) continua model is used. In multiple continua models, specific details of the reservoir are replaced with averaged properties (average fracture spacing, for example). Such averaging facilitates the simulation of fractured reservoirs; however, field-scale simulation remains numerically intensive. For example, it has been stated that 5-10 nested shells are required in the Multiple Interacting Continua formulation in order to adequately resolve transient pressure and saturation gradients between the fracture and matrix domains. While this results in a large amount of additional work (compared with a single porosity system of the same dimension), it should be noted that the MINC method is capable of resolving such transients, whereas most dual porosity simulators cannot