Upward-Closed Hereditary Families In The Dominance Order

The majorization relation orders the degree sequences of simple graphs into posets called dominance orders. As shown by Ruch and Gutman (1979) and Merris (2002), the degree sequences of threshold and split graphs form upward-closed sets within the dominance orders they belong to, i.e., any degree sequence majorizing a split or threshold sequence must itself be split or threshold, respectively. Motivated by the fact that threshold graphs and split graphs have characterizations in terms of forbidden induced subgraphs, we define a class F of graphs to be dominance monotone if whenever no realization of e contains an element F as an induced subgraph, and d majorizes e, then no realization of d induces an element of F. We present conditions necessary for a set of graphs to be dominance monotone, and we identify the dominance monotone sets of order at most 3

Upward-closed hereditary families in the dominance order

The majorization relation orders the degree sequences of simple graphs into posets called dominance orders. As shown by Ruch and Gutman (1979) and Merris (2002), the degree sequences of threshold and split graphs form upward-closed sets within the dominance orders they belong to, i.e., any degree sequence majorizing a split or threshold sequence must itself be split or threshold, respectively. Motivated by the fact that threshold graphs and split graphs have characterizations in terms of forbidden induced subgraphs, we define a class F of graphs to be dominance monotone if whenever no realization of e contains an element F as an induced subgraph, and d majorizes e, then no realization of d induces an element of F. We present conditions necessary for a set of graphs to be dominance monotone, and we identify the dominance monotone sets of order at most 3

Single Bidders and Tacit Collusion in Highway Procurement Auctions

Collusion in auctions can take different forms, one of which is refraining from bidding. Such behavior may be overt or tacit.Certain aspects of highway procurement auctions facilitate collusive outcomes. We collect data on asphalt paving auctions conducted by the Kentucky Transportation Cabinet from 2005 to 2007. We analyze both the bid participation decision and the pricing decision. We include variables that affect firm’s’ costs as well as variables that capture competitive and strategic effects. Most importantly, we determine the potential service area of each asphalt plant and use that information to determine the potential bidders for each paving project. We find that, in geographic markets with only a few feasible suppliers, county boundaries serve as a coordinating mechanism for softening competition, significantly influencing firms’ decisions whether and how much to bid

Graphs with few trivial characteristic ideals

We give a characterization of the graphs with at most three trivial characteristic ideals. This implies the complete characterization of the regular graphs whose critical groups have at most three invariant factors equal to 1 and the characterization of the graphs whose Smith groups have at most 3 invariant factors equal to 1. We also give an alternative and simpler way to obtain the characterization of the graphs whose Smith groups have at most 3 invariant factors equal to 1, and a list of minimal forbidden graphs for the family of graphs with Smith group having at most 4 invariant factors equal to 1

New approach to phase and modulation resolved spectra

Time domain fluorescence spectrometry offers a versatile and powerful approach to the analysis of heterogeneous emitting systems. In this paper we describe a new approach, based on software, to the acquisition of phase and modulation resolved spectra. Mixtures of fluorophores with different lifetimes can be analyzed in real time to give the individual excitation or emission spectra. Examples of two- and three-component mixtures are given and comparisons are made with the commercially available hardware approach. © 1985, American Chemical Society. All rights reserved

Neighborhood degree lists of graphs

The neighborhood degree list (NDL) is a graph invariant that refines information given by the degree sequence and joint degree matrix of a graph and is useful in distinguishing graphs having the same degree sequence. We show that the space of realizations of an NDL is connected via a switching operation. We then determine the NDLs that have a unique realization by a labeled graph; the characterization ties these NDLs and their realizations to the threshold graphs and difference graphs

Upward-closed hereditary families in the dominance order

The majorization relation orders the degree sequences of simple graphs into posets called dominance orders. As shown by Ruch and Gutman (1979) and Merris (2002), the degree sequences of threshold and split graphs form upward-closed sets within the dominance orders they belong to, i.e., any degree sequence majorizing a split or threshold sequence must itself be split or threshold, respectively. Motivated by the fact that threshold graphs and split graphs have characterizations in terms of forbidden induced subgraphs, we define a class $\mathcal{F}$ of graphs to be dominance monotone if whenever no realization of $e$ contains an element $\mathcal{F}$ as an induced subgraph, and $d$ majorizes $e$, then no realization of $d$ induces an element of $\mathcal{F}$. We present conditions necessary for a set of graphs to be dominance monotone, and we identify the dominance monotone sets of order at most 3

Assessment of an alanine EPR dosimetry technique with enhanced precision and accuracy.

Dose reconstruction in the course of a series of blind tests demonstrated that an accuracy of 10 mGy for low doses and 1% for high doses can be achieved using EPR spectroscopy. This was accomplished using a combination of methodologies including polynomial filtration of the EPR spectrum, dosimeter rotation during scanning, use of an EPR standard fixed into the resonator and subtraction of all nonradiogenic signals. Doses were reconstructed over the range of 0.01-1000 Gy using this compound spectral EPR analysis. This EPR technique, being equally applicable to fractionated doses (such as those delivered during multiple radiotherapy treatments), was verified to exhibit dose reciprocity. Irradiated alanine dosimeters which were stored exhibited compound spectral EPR signal fading of ca 3 % over 9 months. All error estimates given in this paper are given at the 1 standard deviation level and unless otherwise specified do not account for uncertainties in source calibration