Integer programming approach to static monopolies in graphs

A subset M of vertices of a graph is called a static monopoly, if any vertex v outside M has at least \(\lceil \tfrac{1 }{2}\deg (v)\rceil \) neighbors in M. The minimum static monopoly problem has been extensively studied in graph theoretical context. We study this problem from an integer programming point of view for the first time and give a linear formulation for it. We study the facial structure of the corresponding polytope, classify facet defining inequalities of the integer programming formulation and introduce some families of valid inequalities. We show that in the presence of a vertex cut or an edge cut in the graph, the problem can be solved more efficiently by adding some strong valid inequalities. An algorithm is given that solves the minimum monopoly problem in trees and cactus graphs in linear time. We test our methods by performing several experiments on randomly generated graphs. A software package is introduced that solves the minimum monopoly problem using open source integer linear programming solvers.     

Functional Form for the Zero-Inflated Generalized Poisson Regression Model

The generalized Poisson (GP) regression is an increasingly popular approach for modeling overdispersed as well as underdispersed count data. Several parameterizations have been performed for the GP regression, and the two well known models, the GP-1 and the GP-2, have been applied. The GP-P regression, which has been recently proposed, has the advantage of nesting the GP-1 and the GP-2 parametrically, besides allowing the statistical tests of the GP-1 and the GP-2 against a more general alternative. In several cases, count data often have excessive number of zero outcomes than are expected in the Poisson. This zero-inflation phenomenon is a specific cause of overdispersion, and the zero-inflated Poisson (ZIP) regression model has been proposed. However, if the data continue to suggest additional overdispersion, the zero-inflated negative binomial (ZINB-1 and ZINB-2) and the zero-inflated generalized Poisson (ZIGP-1 and ZIGP-2) regression models have been considered as alternatives. This article proposes a functional form of the ZIGP which mixes a distribution degenerate at zero with a GP-P distribution. The suggested model has the advantage of nesting the ZIP and the two well known ZIGP (ZIGP-1 and ZIGP-2) regression models, besides allowing the statistical tests of the ZIGP-1 and the ZIGP-2 against a more general alternative. The ZIP and the functional form of the ZIGP regression models are fitted, compared and tested on two sets of count data; the Malaysian insurance claim data and the German healthcare data.     

Selection of the best well control system by using fuzzy multiple-attribute decision-making methods

There are numerous difficulties involved in drilling operations of an oil well, one of the most important of them being well control. Well control systems are applied when we have irruption of liquids or unwanted intrusion of the reservoir's liquid (oil, gas or brine) into the well, during drilling when the pressure of well fluid column is less than formation pressure, and the permeability of the reservoir has a value that is able to pass the liquid through. For this purpose, a variety of methods including Driller, wait and weight, and the concurrent methods were used to control the well at different drilling sites. In this study, we investigate the optimum method for well control using a fussy method based on many parameters, including technical factors (mud weight, drilling rate, blockage of pipes, sensitivity to drilling network changes, etc.) and security factors (existence of effervescent mud, drilling circuit control, etc.), and cost of selection, which is one of the most important decisions that are made under critical conditions such as irruption. Till now, these methods were selected based on the experience of field personnel in drilling sites. The technical criteria and standards were influenced by experience, so the soft computerizing system (fuzzy method) was used. Thus, both these criteria and standards would be of greater importance and indicate whether the optimum numerical method is the same one that is expressed by human experience. The concurrent method was selected as the best for well control, using the fuzzy method at the end of the evaluation, while field personnel experience suggests the Driller method.     

‘So God Made a Farmer’: The US Agrarian Imaginary and the Lived Assemblages of Settlement and Empire

ABSTRACT

In support of the National FFA Organization (formerly, the Future Farmers of America), Ram Trucks declared 2013 the ‘Year of the Farmer.’ Their commemorative Super Bowl commercial featured radio broadcaster Paul Harvey’s iconic 1978 speech, ‘So God Made a Farmer.’ This essay interrogates Harvey’s speech and its aestheticization and reception during Super Bowl XLVII in order to trace how U.S. settler colonialism is embodied and recognized, particularly in relation to narratives of the ‘secularization’ of the United States and U.S. political life. It argues that the resolutely Christian visions of social life and selfhood, modes of ethics, and place-making within the nostalgic speech and commercial continue to order and naturalize the interface between heteropatriarchy, white supremacy, and U.S. settler colonialism. It also argues that although such religiose forms of relationality are reproduced and amplified in the spectatorship of the Super Bowl, they are imbued with ostensibly secular national and imperial meaning, and thus obfuscated as such. This essay ultimately argues that such religiose invocations of proper relationality – as a node of racialization and the production of power – can shuttle between religious and secular contexts while continuing to encode and reproduce formations of U.S. settler colonialism and imperialism.     

First-Fit colorings of graphs with no cycles of a prescribed even length

The First-Fit (or Grundy) chromatic number of a graph G denoted by \(\chi _{{_\mathsf{FF}}}(G)\), is the maximum number of colors used by the First-Fit (greedy) coloring algorithm when applied to G. In this paper we first show that any graph G contains a bipartite subgraph of Grundy number \(\lfloor \chi _{{_\mathsf{FF}}}(G) /2 \rfloor +1\). Using this result we prove that for every \(t\ge 2\) there exists a real number \(c>0\) such that in every graph G on n vertices and without cycles of length 2t, any First-Fit coloring of G uses at most \(cn^{1/t}\) colors. It is noted that for \(t=2\) this bound is the best possible. A compactness conjecture is also proposed concerning the First-Fit chromatic number involving the even girth of graphs.     

On a hybrid data cloning method and its application in generalized linear mixed models

The data cloning method is a new computational tool for computing maximum likelihood estimates in complex statistical models such as mixed models. This method is synthesized with integrated nested Laplace approximation to compute maximum likelihood estimates efficiently via a fast implementation in generalized linear mixed models. Asymptotic behavior of the hybrid data cloning method is discussed. The performance of the proposed method is illustrated through a simulation study and real examples. It is shown that the proposed method performs well and rightly justifies the theory. Supplemental materials for this article are available online.