Optimal Bounds for the kk-cut Problem

In the $k$-cut problem, we want to find the smallest set of edges whose deletion breaks a given (multi)graph into $k$ connected components. Algorithms of Karger & Stein and Thorup showed how to find such a minimum $k$-cut in time approximately $O(n^{2k})$. The best lower bounds come from conjectures about the solvability of the $k$-clique problem, and show that solving $k$-cut is likely to require time $\Omega(n^k)$. Recent results of Gupta, Lee & Li have given special-purpose algorithms that solve the problem in time $n^{1.98k + O(1)}$, and ones that have better performance for special classes of graphs (e.g., for small integer weights). In this work, we resolve the problem for general graphs, by showing that the Contraction Algorithm of Karger outputs any fixed $k$-cut of weight $\alpha \lambda_k$ with probability $\Omega_k(n^{-\alpha k})$, where $\lambda_k$ denotes the minimum $k$-cut size. This also gives an extremal bound of $O_k(n^k)$ on the number of minimum $k$-cuts and an algorithm to compute a minimum $k$-cut in similar runtime. Both are tight up to lower-order factors, with the algorithmic lower bound assuming hardness of max-weight $k$-clique. The first main ingredient in our result is a fine-grained analysis of how the graph shrinks -- and how the average degree evolves -- in the Karger process. The second ingredient is an extremal bound on the number of cuts of size less than $2 \lambda_k/k$, using the Sunflower lemma.Comment: Final version of arXiv:1911.09165 with new and more general proof

Place naming strategies in Lower Tanana Dene

National Foreign Language Resource Cente

Application of rapid manufacturing techniques in support of maxillofacial treatment: evidence of the requirements of clinical applications

The concept of applying rapid manufacturing technology to maxillofacial treatment has been described previously; however, these reports did not take into account the practicality of its actual incorporation into clinical practice. Patents in the field are based on imaging techniques combined with rapid manufacturing, which theoretically lead to reconstruction of faces. Some cases studies reported have dealt with the manufacture of prostheses on the laboratory scale. Here two case studies are reported that used imaging and rapid manufacturing techniques for making an ear prosthesis and a burns mask for two patients. Laser scanning was chosen for imaging and Thermojet printing and fused deposition modelling for rapid manufacturing. Outcomes of the study were threefold: improvement in the process, improvement in patient care, and clinical application of existing technology to healthcare. With further research this technology may aid maxillofacial prosthetists in busy facial clinics, reduce patient clinic time, and improve the final product

Is there a correlation between infection control performance and other hospital quality measures?

Quality measures are increasingly reported by hospitals to the Centers for Medicare and Medicaid Services (CMS), yet there may be tradeoffs in performance between infection control (IC) and other quality measures. Hospitals that performed best on IC measures did not perform well on most CMS non–IC quality measures

Analysis of breast milk fatty acid composition using dried milk samples.

BACKGROUND: The effect of breast milk fatty acid (FA) composition, particularly levels of docosahexaenoic acid (DHA), on infant health outcomes is unclear. Part of the reason for this is difficulties in collecting, storing and shipping milk samples to the laboratory. Here we report the validation of a dried milk spot (DMS) system to measure FA composition to help overcome these obstacles. Milk FA were measured by gas chromatography and reported as percent of total FA; the FA of primary interest in this study were DHA and industrially produced trans FA (iTFA). Experiments were carried out using pooled milk samples from US (n = 5) and Malawian women (n = 50). Experiments compared liquid vs. DMS samples (n = 55), assessed stability of FA composition under different storage conditions (n = 5), and compared the results from two different labs using the same methods (n = 5). RESULTS: Both % DHA and % iTFA levels in liquid and DMS samples were strongly correlated (R(2) = 0.99 and 0.99, respectively, P < 0.0001). The % DHA in DMS samples was stable for up to four weeks at room temperature and up to three years at -80 °C; only slight deviations from the acceptable range of variability (±15 %) occurred in the 4 °C and -20 °C conditions for % DHA. The % iTFA was stable under all conditions. All % DHA and % iTFA were within 15 % of the referent when analyzed in two laboratories. CONCLUSIONS: Valid FA composition values can be obtained from DMS samples using this robust collection and transport system which should facilitate studies of the role of milk FA composition in infant development

Determining anion-quadrupole interactions among protein, DNA, and ligand molecules

Background An extensive search through the Protein Databank (about 4500 nonredundant structures) was previously completed within our lab to analyze the energetic and geometric characteristics of an understudied molecular interaction known as an anion-quadrupole (AQ) interaction. Such an interaction occurs when the positively charged edge of an aromatic ring, resulting from a quadruple moment (i.e., a dual dipole moment), renders the aromatic molecule noncovalently bound to a nearby anionic molecule. The study considered a very limited scenario of molecules that can participate in AQ interactions, consisting of the phenyl group of a phenylalanine (phe) amino acid as the aromatic participant and the carboxylate group of an aspartate (asp) or glutamate (glu) amino acid as the anionic participant. The results revealed anion-quadrupole pairs to be prevalent within most of the protein structures. It was also observed that the interaction energy for AQ pairs was heavily dependent on the angle between the anion and plane of the aromatic ring, favoring a more planar interaction. In light of these critical observations being made from such a limited scenario, only phe-glu and phe-asp pairs and in a reduced sample set of the PDB, we are now continuing this work of identifying AQ interactions using a greatly expanded strategy. We are following these four aims: 1. Optimizing the AQ-search program to run in a semi-parallel fashion and on a large cluster of processors in order to handle larger analyses, 2. Adding to our search additional anionic participants which will include non-protein structures such as DNA and small ligands, 3. Studying a subset of the AQ pairs with molecular dynamics simulations in buried and solvent exposed environments to observe non-static behavioral traits as well as the reproducibility of AQ interactions by force field parameters. 4. Building an online database for public access to our data and search program. Acknowledgments We would like to acknowledge the NSF-IGERT traineeship, Scalable Computing and Leading Edge Innovative Technologies (SCALE-IT), for providing the resources for this project

Design of experiment for the pilot evaluation of an airborne runway incursion alerting system

Runway incursions pose a significant threat to the continued safety of commercial aviation. In response, the Runway Collision Avoidance Function (RCAF) was developed by the University of Malta and evaluated at Cranfield University as part of the European Programme FLYSAFE. This paper discusses the design of experiment developed in preparation of the said evaluations, addressing the objectives of the test programme and explains how these objectives were met.peer-reviewe

Skunk River Review, Fall 2013 and Spring 2014

https://openspace.dmacc.edu/skunkriver/1023/thumbnail.jp