A 24-year-old woman presented with 2 months of episodic vertigo, vomiting, and headache triggered by abrupt head movements, lasting from a few minutes to 1 hour. She was asymptomatic between the attacks and had mild gait ataxia on examination. Brain MRI revealed obstructive hydrocephalus and a cystic lesion in the fourth ventricle (figures 1 and 2). Her symptoms subsided after cyst excision; a ...

We prove the case t = 2 of a conjecture Bruns-Conca-Varbaro, describing minimal relations between x minors generic matrix. Interpreting these as polynomial functors, and applying transpose duality in work Sam-Snowden, this problem is equivalent to understanding satisfied by generalized permanents. Our proof follows combining Koszul homology calculations on side, with study subspace varieties pe...

The group of calcium-binding proteins known as the calbindins (CaBPs) plays a cardinal role in calcium metabolism, acting either as an intracellular facilitator of calcium diffusion or as an intracellular buffer of calcium (Wasserman and Fullmer, 1983; Norman, 1990). The presence of CaBP-D28K in nerve terminals (Jande et al., 1981a,b; Baimbridge and Miller, 1982; Resibois et al., 1988a) suggest...

Progress on two main studies on fungal ectomycorrhizal communities in the Sierra National Forest is discussed. One study examined the short-term effects of ground fire on the ectomycorrhizal community and the other examined the ectomycorrhizal associates of snow plant (Sarcodes sanguinea). In the ground-fire study we found that a large initial reduction in ectomycorrhizal biomass is caused prim...

We prove regularity bounds for Koszul cycles holding for every ideal of dimension ≤ 1 in a polynomial ring; see Theorem 3.5. In Theorem 4.7 we generalize the “c + 1” lower bound for the Green–Lazarsfeld index of Veronese rings proved in (Bruns et al., arXiv:0902.2431) to the multihomogeneous setting. For the Koszul complex of the c-th power of the maximal ideal in a Koszul ring we prove that th...

Conjecture, and the big and small Cohen Macaulay Conjectures. Many of these are shown to imply others. This document contains notes for a course taught by Tom Marley during the 2009 spring semester at the University of Nebraska-Lincoln. The notes loosely follow the treatment given in Chapters 8 and 9 of Cohen-Macaulay Rings, by W. Bruns and J. Herzog, although many other sources, including arti...

We used the framework identified by the National Implementation Research Network’s (NIRN) analysis of 35 years of implementation outcomes literature from diverse fields of endeavor to review the current state of wraparound implementation research. Model definition, model fidelity and intervention outcomes were areas of relatively greater development, while target population, theory base and the...

For a graph of an n-cycle ∆ with Alexander dual ∆, we study the free resolution of a subideal G(n) of the Stanley-Reisner ideal I∆∗ . We prove that if G(n) is generated by 3 generic elements of I∆∗ , then the second syzygy module of G(n) is isomorphic to the second syzygy module of (x1, x2, . . . , xn). A result of Bruns shows that there is always a 3-generated ideal with this property. We show...