Topological geodesics and virtual rigidity

We introduce the notion of a topological geodesic in a 3-manifold. Under suitable hypotheses on the fundamental group, for instance word-hyperbolicity, topological geodesics are shown to have the useful properties of, and play the same role in several applications as, geodesics in negatively curved spaces. This permits us to obtain virtual rigidity results for 3-manifolds.Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol1/agt-1-18.abs.htm

Uniqueness of Ground States for Short-Range Spin Glasses in the Half-Plane

We consider the Edwards-Anderson Ising spin glass model on the half-plane $Z \times Z^+$ with zero external field and a wide range of choices, including mean zero Gaussian, for the common distribution of the collection J of i.i.d. nearest neighbor couplings. The infinite-volume joint distribution $K(J,\alpha)$ of couplings J and ground state pairs $\alpha$ with periodic (respectively, free) boundary conditions in the horizontal (respectively, vertical) coordinate is shown to exist without need for subsequence limits. Our main result is that for almost every J, the conditional distribution $K(\alpha|J)$ is supported on a single ground state pair.Comment: 20 pages, 3 figure

Fluctuation Bounds For Interface Free Energies in Spin Glasses

We consider the free energy difference restricted to a finite volume for certain pairs of incongruent thermodynamic states (if they exist) in the Edwards-Anderson Ising spin glass at nonzero temperature. We prove that the variance of this quantity with respect to the couplings grows proportionally to the volume in any dimension greater than or equal to two. As an illustration of potential applications, we use this result to restrict the possible structure of Gibbs states in two dimensions.Comment: 19 pages, 0 figure

Short-range spin glasses and Random Overlap Structures

Properties of Random Overlap Structures (ROSt)'s constructed from the Edwards-Anderson (EA) Spin Glass model on $\Z^d$ with periodic boundary conditions are studied. ROSt's are $\N\times\N$ random matrices whose entries are the overlaps of spin configurations sampled from the Gibbs measure. Since the ROSt construction is the same for mean-field models (like the Sherrington-Kirkpatrick model) as for short-range ones (like the EA model), the setup is a good common ground to study the effect of dimensionality on the properties of the Gibbs measure. In this spirit, it is shown, using translation invariance, that the ROSt of the EA model possesses a local stability that is stronger than stochastic stability, a property known to hold at almost all temperatures in many spin glass models with Gaussian couplings. This fact is used to prove stochastic stability for the EA spin glass at all temperatures and for a wide range of coupling distributions. On the way, a theorem of Newman and Stein about the pure state decomposition of the EA model is recovered and extended.Comment: 27 page

Delirium Education for Family Caregivers of Patients in the Intensive Care Unit: A Pilot Study

Objectives Delirium, an acute change in mental state, seen in hospitalized older adults is a growing public health concern with implications for both patients and caregivers; however, there is minimal research on educating caregivers about delirium. Utilizing family caregivers to assist with delirium management in acute care settings demonstrates improved health outcomes supporting the need for patient and family centered care. The primary aims of the study were to determine feasibility of implementing a delirium education video for caregivers of patients in an adult oncology intensive care unit and compare delirium knowledge to caregivers in a control group. Methods A quasi-experimental design comprised of 31 family caregivers of adult patients in an oncology intensive care unit to determine feasibility of implementing a delirium education video. Results The results demonstrate feasibility of implementing a caregiver education video in-person and virtually. While total delirium knowledge scores were not statistically significant, knowledge gained within the delirium presentation subgroup was significant (p = .05). Conclusion This study demonstrates feasibility of implementing a caregiver education video and findings support further research in this area. Innovation Collaborating with caregivers to develop virtual video education for delirium allows for a versatile approach to connect with caregivers to support their caregiving role

A simple derivation of the naked singularity in spherical dust collapse

We describe a simple method of determining whether the singularity that forms in the spherically symmetric collapse of inhomogeneous dust is naked or covered. This derivation considerably simplifies the analysis given in the earlier literature, while giving the same results as have been obtained before.Comment: Latex, 9 page

The use of methyl methacrylate cranioplasty in forehead reconstruction

The use of methyl methacrylate for forehead reconstruction in congenital anomalies, tumor infection, trauma and cosmetic defects is presented. Seventy-one cases are analyzed with long term follow-up. The complication rate is low and the operating time is short. This is recommended as a rapid and safe method of forehead reconstruction. It should be avoided in the growing child and if there is any suggestion of direct connection with sinuses.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46679/1/238_2004_Article_BF00298947.pd

A shadowing problem in the detection of overlapping communities: lifting the resolution limit through a cascading procedure

Community detection is the process of assigning nodes and links in significant communities (e.g. clusters, function modules) and its development has led to a better understanding of complex networks. When applied to sizable networks, we argue that most detection algorithms correctly identify prominent communities, but fail to do so across multiple scales. As a result, a significant fraction of the network is left uncharted. We show that this problem stems from larger or denser communities overshadowing smaller or sparser ones, and that this effect accounts for most of the undetected communities and unassigned links. We propose a generic cascading approach to community detection that circumvents the problem. Using real and artificial network datasets with three widely used community detection algorithms, we show how a simple cascading procedure allows for the detection of the missing communities. This work highlights a new detection limit of community structure, and we hope that our approach can inspire better community detection algorithms.Comment: 14 pages, 12 figures + supporting information (5 pages, 6 tables, 3 figures