Village of Horseheads, NY and CSEA Local 1000, Unit #6359

In the matter of the fact-finding between the Village of Horseheads, NY, employer, and CSEA Local 1000, Unit#6359, union. PERB case no. 2011-146. Before: Timothy W. Gorman, fact finder

Asymptotically Optimal Bounds for (t,2) Broadcast Domination on Finite Grids

Let $G=(V,E)$ be a graph and $t,r$ be positive integers. The \emph{signal} that a tower vertex $T$ of signal strength $t$ supplies to a vertex $v$ is defined as $sig(T,v)=max(t-dist(T,v),0),$ where $dist(T,v)$ denotes the distance between the vertices $v$ and $T$. In 2015 Blessing, Insko, Johnson, and Mauretour defined a \emph{$(t,r)$ broadcast dominating set}, or simply a \emph{$(t,r)$ broadcast}, on $G$ as a set $\mathbb{T}\subseteq V$ such that the sum of all signals received at each vertex $v \in V$ from the set of towers $\mathbb{T}$ is at least $r$. The $(t,r)$ broadcast domination number of a finite graph $G$, denoted $\gamma_{t,r}(G)$, is the minimum cardinality over all $(t,r)$ broadcasts for $G$. Recent research has focused on bounding the $(t,r)$ broadcast domination number for the $m \times n$ grid graph $G_{m,n}$. In 2014, Grez and Farina bounded the $k$-distance domination number for grid graphs, equivalent to bounding $\gamma_{t,1}(G_{m,n})$. In 2015, Blessing et al. established bounds on $\gamma_{2,2}(G_{m,n})$, $\gamma_{3,2}(G_{m,n})$, and $\gamma_{3,3}(G_{m,n})$. In this paper, we take the next step and provide a tight upper bound on $\gamma_{t,2}(G_{m,n})$ for all $t>2$. We also prove the conjecture of Blessing et al. that their bound on $\gamma_{3,2}(G_{m,n})$ is tight for large values of $m$ and $n$.Comment: 8 pages, 4 figure

Enantioselective Synthesis of 5-epi-Citreoviral Using Ruthenium-Catalyzed Asymmetric Ring-Closing Metathesis

Chiral ruthenium olefin metathesis catalysts can perform asymmetric ring-closing reactions in ≥90% ee with low catalyst loadings. To illustrate the practicality of these reactions and the products they form, an enantioselective total synthesis of 5-epi-citreoviral was completed by using an asymmetric ring-closing olefin metathesis reaction as a key step early in the synthesis. All of the stereocenters in the final compound were set by using the chiral center generated by asymmetric olefin metathesis

Barker, Town of and International Brotherhood of Teamsters (IBT), AFL-CIO, Local 317

In the matter of the fact-finding between the Town of Barker, employer, and the International Brotherhood of Teamsters (IBT), AFL-CIO, Local 317, union. PERB case no. M2015-259. Before: Timothy W. Gorman, fact finder

Deposit Central School District and Deposit Teachers Association, NYSUT

In the matter of the fact-finding between the Deposit Central School District, employer, and the Deposit Teachers Association, NYSUT, union. PERB case no. M2010-300. Before: Timothy W. Gorman, fact finder

A 'Friend and Advisor': Management, Auditors, and Confidence in Germany's Credit Cooperatives, 1889-1914

Economic enterprises face two, related, managerial problems: effective management of the enterprise's activities, and communicating to outsiders that the enterprise is in fact well-run. These problems were especially difficult in the credit cooperative movement that grew up in Germany in the second half of the nineteenth century. These successful cooperatives thrived because they could harness the information and ties among local people to obviate many of the problems that faced other lenders. Doing so required managers who were themselves local people. Yet few if any locals had any banking experience, and most were not even familiar with basic accounting methods. These local managers created internal management problems and enhanced outside suspicion of the cooperatives as banking enterprises. The methods developed to overcome these problems relied on a combination of local initiative and regional assistance that was typical of the movement as a whole. The movement's ability to train its own talent suggests a broader impact not captured by statistics on membership or financial assets.credit cooperative, external audit

Commentary on "Optimal monetary policy under uncertainty: a Markov jump-linear-quadratic approach"

Monetary policy ; Econometric models

Reputational Externality and Self-Regulation

Professional associations and other producer groups often complain that their reputation is damaged by other groups providing a similar but lower-quality service and that the latter should be regulated. We examine the conditions under which a common regulatory regime can induce Pareto-improvements by creating a common reputation for quality among heterogeneous producers, when the regulator cannot commit to a given quality. A common reputation can be created only if the groups are not too different and if marginal cost is declining. High cost groups and small groups benefit most from forming a common regime