Semigroups Arising From Asynchronous Automata

We introduce a new class of semigroups arising from a restricted class of asynchronous automata. We call these semigroups "expanding automaton semigroups." We show that the class of synchronous automaton semigroups is strictly contained in the class of expanding automaton semigroups, and that the class of expanding automaton semigroups is strictly contained in the class of asynchronous automaton semigroups. We investigate the dynamics of expanding automaton semigroups acting on regular rooted trees, and show that undecidability arises in these actions. We show that this class is not closed under taking normal ideal extensions, but the class of asynchronous automaton semigroups is closed under taking these extensions. We construct every free partially commutative monoid as a synchronous automaton semigroup.Comment: 31 pages, 4 figure

Reconstruction of Partially Conductive Cracks using Boundary Data

This paper develops an algorithm for finding one or more non-insulated, pair-wise disjoint, linear cracks in a two dimensional region using boundary measurements

Paradoxical Oddities in Two Multiwinner Elections from Scotland

Ranked-choice voting anomalies such as monotonicity paradoxes have been extensively studied through creating hypothetical examples and generating elections under various models of voter behavior. However, very few real-world examples of such voting paradoxes have been found and analyzed. We investigate two single-transferable vote elections from Scotland that demonstrate upward monotonicity, downward monotonicity, no-show, and committee size paradoxes. These paradoxes are rarely observed in real-world elections, and this article is the first case study of such paradoxes in multiwinner elections

A Mathematical Analysis of the 2022 Alaska Special Election for US House

The August 2022 Alaska Special Election for US House contained many interesting features from the perspective of social choice theory. This election used instant runoff voting (often referred to as ranked choice voting) to elect a winner, and many of the weaknesses of this voting method were on display in this election. For example, the Condorcet winner is different from the instant runoff winner, and the election demonstrated a monotonicity paradox. The election also demonstrated a no show paradox; as far as we are aware, this election represents the first document American ranked choice election to demonstrate this paradox

Monotonicity Anomalies in Scottish Local Government Elections

The single transferable vote (STV) voting method is used to elect multiple candidates in ranked-choice elections. One weakness of STV is that it fails multiple fairness criteria related to monotonicity and no-show paradoxes. We analyze 1,079 local government STV elections in Scotland to estimate the frequency of such monotonicity anomalies in real-world elections, and compare our results with prior empirical and theoretical research about the rates at which such anomalies occur. In 41 of the 1079 elections we found some kind of monotonicity anomaly. We generally find that the rates of anomalies are similar to prior empirical research and much lower than what most theoretical research has found. Most of the STV anomalies we find are the first of their kind to be documented in real-world elections.Comment: 30 page

An Empirical Analysis of the Effect of Ballot Truncation on Ranked-Choice Electoral Outcomes

In ranked-choice elections voters cast preference ballots which provide a voter's ranking of the candidates. The method of ranked-choice voting (RCV) chooses a winner by using voter preferences to simulate a series of runoff elections. Some jurisdictions which use RCV limit the number of candidates that voters can rank on the ballot, imposing what we term a truncation level, which is the number of candidates that voters are allowed to rank. Given fixed voter preferences, the winner of the election can change if we impose different truncation levels. We use a database of 1171 real-world ranked-choice elections to empirically analyze the potential effects of imposing different truncation levels in ranked-choice elections. Our general finding is that if the truncation level is at least three then restricting the number of candidates which can be ranked on the ballot rarely affects the election winner

Proportional Consistency of Apportionment Methods

We analyze a little-known property of apportionment methods that captures how allocations scale with the size of the house: specifically, if, for a fixed population distribution, the house size and allocation can be scaled down within the set of integers, then the apportionment should be correspondingly scaled down. Balinski and Young (2001) include this property among the minimal requirements for a "reasonable" apportionment method. We argue that this property is better understood as a consistency requirement since quota-based apportionments that are "less proportional" meet this requirement while others that are "more proportional" do not. We also show that the family of quotatone methods based on stationary divisors (including the quota method) do not satisfy this property

Population pharmacokinetics of cyclophosphamide and metabolites in children with neuroblastoma: a report from the children's oncology group.

Cyclophosphamide-based regimens are front-line treatment for numerous pediatric malignancies; however, current dosing methods result in considerable interpatient variability in tumor response and toxicity. In this pediatric population, the authors' objectives were (1) to quantify and explain the pharmacokinetic variability of cyclophosphamide and 2 of its metabolites, hydroxycyclophosphamide (HCY) and carboxyethylphosphoramide mustard (CEPM), and (2) to apply a population pharmacokinetic model to describe the disposition of cyclophosphamide and these metabolites. A total of 196 blood samples were obtained from 22 children with neuroblastoma receiving intravenous cyclophosphamide (400 mg/m2/d) and topotecan. Blood samples were quantitated for concentrations of cyclophosphamide, HCY, and CEPM using liquid chromatography-mass spectrometry and analyzed using nonlinear mixed-effects modeling with the NONMEM software system. After model building was complete, the area under the concentration-time curve (AUC) was computed using NONMEM. Cyclophosphamide elimination was described by noninducible and inducible routes, with the latter producing HCY. Glomerular filtration rate was a covariate for the fractional elimination of HCY and its conversion to CEPM. Considerable interpatient variability was observed in the AUC of cyclophosphamide, HCY, and CEPM. These results represent a critical first step in developing pharmacokinetic-linked pharmacodynamic studies in children receiving cyclophosphamide to determine the clinical relevance of the pharmacokinetic variability in cyclophosphamide and its metabolites

Marbles: The Application of Input-Output Concepts to Safety Management Systems

The goal of this research was to apply the economic concept titled Input-Output Analysis to an aviation safety concept titled Safety Management Systems (SMS). Input-Output (IO) is based upon the interrelationships of various components of an economic system and what happens to the system when one or more of those components changes. Since SMS is, by definition, a system with definable components, the research sought to determine if the interrelationships between those components could be determined and quantified. The term ‘‘marbles’’ was used to describe the activities that led to the IO-SMS matrix. Marbles was used as a metaphor for quantifying interrelationships. A team of SMS experts was assembled to collectively determine the interrelationships among the four components of SMS. Next the team determined the relative values of the elements and processes inside each component. (There are 24 discrete items—elements and processes—in SMS.) Once these values were determined and placed into a 24 6 24 matrix, IO matrix mathematics was applied to produce the IO-SMS Matrix. The SMS matrix that resulted from this experiment may be a powerful management tool that can determine the impact of any numerical input, such as an SMS survey, on the total system. It can also be used to perform ‘‘what if’’ analysis by changing the value of one element or process within the SMS. The weakness of the IO-SMS matrix is that it is highly sensitive to the original input data that define the interrelationships among the components