On a linear program for minimum-weight triangulation

Minimum-weight triangulation (MWT) is NP-hard. It has a polynomial-time constant-factor approximation algorithm, and a variety of effective polynomial-time heuristics that, for many instances, can find the exact MWT. Linear programs (LPs) for MWT are well-studied, but previously no connection was known between any LP and any approximation algorithm or heuristic for MWT. Here we show the first such connections: For an LP formulation due to Dantzig, Hoffman, and Hu [Math. Programming, 31 (1985), pp. 1-14], (i) the integrality gap is constant, and (ii) given any instance, if the aforementioned heuristics find the MWT, then so does the LP. © 2014 Society for Industrial and Applied Mathematics

Multi-Bunch Instability Diagnostics via Digital Feedback Systems

Longitudinal feedback systems based on a common programmable DSP architecture have been commissioned at 4 laboratories. In addition to longitudinal feedback and beam diagnostics these exible systems have been programmed to provide diagnostics for tranverse motion. The diagnostic functions are based on transient domain techniques which record the response of every bunch while the feedback system manipulates the beam. Operational experience from 4 installations is illustrated via experimental results from PEP-II, DA NE, ALS and SPEAR. Modal growth and damping rates for transverse and longitudinal planes are measured via short (20 ms) transient excitations for unstable and stable coupled-bunch modes. Data from steady-state measurements are used to identify unstable modes, noise-driven beam motion, and noise sources. Techniques are illustrated which allow the prediction of instability thresholds from low-current measurements of stable beams. Tranverse bunch train grow-damp sequences which measure the time evolution of instabilities along the bunch train are presented and compared to signatures expected from ion and fast ion instabilities. Invited talk presented at the IEEE Particle Accelerator Conference (PAC99

Approximating k-Forest with Resource Augmentation: A Primal-Dual Approach

In this paper, we study the $k$-forest problem in the model of resource augmentation. In the $k$-forest problem, given an edge-weighted graph $G(V,E)$, a parameter $k$, and a set of $m$ demand pairs $\subseteq V \times V$, the objective is to construct a minimum-cost subgraph that connects at least $k$ demands. The problem is hard to approximate---the best-known approximation ratio is $O(\min\{\sqrt{n}, \sqrt{k}\})$. Furthermore, $k$-forest is as hard to approximate as the notoriously-hard densest $k$-subgraph problem. While the $k$-forest problem is hard to approximate in the worst-case, we show that with the use of resource augmentation, we can efficiently approximate it up to a constant factor. First, we restate the problem in terms of the number of demands that are {\em not} connected. In particular, the objective of the $k$-forest problem can be viewed as to remove at most $m-k$ demands and find a minimum-cost subgraph that connects the remaining demands. We use this perspective of the problem to explain the performance of our algorithm (in terms of the augmentation) in a more intuitive way. Specifically, we present a polynomial-time algorithm for the $k$-forest problem that, for every $\epsilon>0$, removes at most $m-k$ demands and has cost no more than $O(1/\epsilon^{2})$ times the cost of an optimal algorithm that removes at most $(1-\epsilon)(m-k)$ demands

Multi-Bunch Longitudinal Dynamics and Diagnostics via a Digital

A bunch-by-bunch longitudinal feedback system based on a programmable DSP architecture is used to study coupled-bunch motion and its sources. Experimental results are presented from PEP-II, DA NE, ALS and SPEAR to highlight the operational experience from 4 installations, plus show novel accelerator diagnostics possible with the digital processing system. Modal growth and damping rates are measured via short ( 20 ms) transient recordings for unstable and stable coupled-bunch modes. Data from steady-state measurements are used to identify unstable modes and noise-driven beam motion. Anovel impedance measurement technique is presented which reveals the longitudinal impedance as a function of frequency. This technique uses the measured synchronous phase and charge of every bucket to calculate the impedance seen by the beam at revolution harmonics

Cloning and sequence analysis of cDNAs encoding the cytosolic precursors of subunits GapA and GapB of chloroplast glyceraldehyde-3-phosphate dehydrogenase from pea and spinach

Chloroplast glyceraldehyde-3-phosphate dehydrogenase (GAPDH) is composed of two different subunits, GapA and GapB. cDNA clones containing the entire coding sequences of the cytosolic precursors for GapA from pea and for GapB from pea and spinach have been identified, sequenced and the derived amino acid sequences have been compared to the corresponding sequences from tobacco, maize and mustard. These comparisons show that GapB differs from GapA in about 20% of its amino acid residues and by the presence of a flexible and negatively charged C-terminal extension, possibly responsible for the observed association of the enzyme with chloroplast envelopes in vitro. This C-terminal extension (29 or 30 residues) may be susceptible to proteolytic cleavage thereby leading to a conversion of chloroplast GAPDH isoenzyme I into isoenzyme II. Evolutionary rate comparisons at the amino acid sequence level show that chloroplast GapA and GapB evolve roughly two-fold slower than their cytosolic counterpart GapC. GapA and GapB transit peptides evolve about 10 times faster than the corresponding mature subunits. They are relatively long (68 and 83 residues for pea GapA and spinach GapB respectively) and share a similar amino acid framework with other chloroplast transit peptides

Genome Diversity of Epstein-Barr Virus from Multiple Tumor Types and Normal Infection

Epstein-Barr virus (EBV) infects most of the world’s population and is causally associated with several human cancers, but little is known about how EBV genetic variation might influence infection or EBV-associated disease. There are currently no published wild-type EBV genome sequences from a healthy individual and very few genomes from EBV-associated diseases. We have sequenced 71 geographically distinct EBV strains from cell lines, multiple types of primary tumor, and blood samples and the first EBV genome from the saliva of a healthy carrier. We show that the established genome map of EBV accurately represents all strains sequenced, but novel deletions are present in a few isolates. We have increased the number of type 2 EBV genomes sequenced from one to 12 and establish that the type 1/type 2 classification is a major feature of EBV genome variation, defined almost exclusively by variation of EBNA2 and EBNA3 genes, but geographic variation is also present. Single nucleotide polymorphism (SNP) density varies substantially across all known open reading frames and is highest in latency-associated genes. Some T-cell epitope sequences in EBNA3 genes show extensive variation across strains, and we identify codons under positive selection, both important considerations for the development of vaccines and T-cell therapy. We also provide new evidence for recombination between strains, which provides a further mechanism for the generation of diversity. Our results provide the first global view of EBV sequence variation and demonstrate an effective method for sequencing large numbers of genomes to further understand the genetics of EBV infection