Nonvanishing cohomology and classes of Gorenstein rings

We give counterexamples to the following conjecture of Auslander: given a finitely generated module $M$ over an Artin algebra $\Lambda$, there exists a positive integer $n_M$ such that for all finitely generated $\Lambda$-modules $N$, if \Ext_{\Lambda}^i(M,N)=0 for all $i\gg 0$, then \Ext_{\Lambda}^i(M,N)=0 for all $i\geq n_M$. Some of our examples moreover yield homologically defined classes of commutative local rings strictly between the class of local complete intersections and the class of local Gorenstein rings.Comment: 16 page

Poincar\'e series of modules over compressed Gorenstein local rings

Given positive integers e and s we consider Gorenstein Artinian local rings R of embedding dimension e whose maximal ideal $\mathfrak{m}$ satisfies $\mathfrak{m}^s\ne 0=\mathfrak{m}^{s+1}$. We say that R is a compressed Gorenstein local ring when it has maximal length among such rings. It is known that generic Gorenstein Artinian algebras are compressed. If $s\ne 3$, we prove that the Poincare series of all finitely generated modules over a compressed Gorenstein local ring are rational, sharing a common denominator. A formula for the denominator is given. When s is even this formula depends only on the integers e and s. Note that for $s=3$ examples of compressed Gorenstein local rings with transcendental Poincare series exist, due to B{\o}gvad.Comment: revised version, to appear in Adv. Mat

How Labor-Management Partnerships Improve Patient Care, Cost Control, and Labor Relations: Case Studies of Fletcher Allen Health Care, Kaiser Permanente, and Montefiore Medical Center’s Care Management Corporation

[Excerpt] This paper explores the ways in which healthcare unions and their members are strategically engaging with management through partnership to control costs and improve the patient experience, clinical outcomes, workplace environment, and labor relations. These initiatives depend on making use of the knowledge of front-line healthcare workers, improving communication between all staff members, and increasing transparency. In turn, these initiatives can also lead to more robust and dynamic local unions. Through participating in joint work activities, many union members note feeling more respected in their workplace and more connected to their union. Unions can benefit from these activities by offering their members the ability to inform decisions about how work gets done